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FQXi BLOGS

July 15, 2020

Sachdev is now using string theory techniques to explain the behavior of superconductors, a move that could finally bring string theory into touch with experiments. Before getting overly excited, string-sceptic Peter Woit notes that this doesn’t count as a test of string theory. "Just because a model works in one context, doesn't mean you can unify physics and get a fundamental theory of reality," he says in the Nature piece.

Still, doubtless it would exciting if Sachdev succeeds in his aim and relates one of the most esoteric disciplines with some of the practical aspects of physics. If you want to know what all the fuss is about then check out Kate Becker’s article “The Black Hole and the Babel Fish” which outlines Sachdev’s research program for uniting string theory with condensed matter and also describes the difficulty of bringing together two disparate physics communities. As physicist Jan Zaanen says of the math underlying the work in Becker’s piece: “This seems to hint at yet deeper meanings…and it might well be that it will trigger a major shift in the understanding of the foundations."

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Dear Zeeya,

I studied Experimental Solid State Physics in grad school at the U. of Texas before finishing my Doctorate in Phenomenological High Energy Physics at Florida State. I agree that there are similarities between these fields. We just had several related conversations on Topic #462 last week.

Sincerely,

Ray Munroe

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I studied Experimental Solid State Physics in grad school at the U. of Texas before finishing my Doctorate in Phenomenological High Energy Physics at Florida State. I agree that there are similarities between these fields. We just had several related conversations on Topic #462 last week.

Sincerely,

Ray Munroe

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This assumes a certain universality to physics. Graphene exhibits some quantum phase transition physics, such as quantum Hell effects and the "electron breakdown" of Landau fluids. It is worth noting that the D2-branein a Chern-Simons setting of some gauge field is a quiver system in a hexagonal tessellation. The structure is remarkably similar to graphene. Each node, analogous to a carbon in graphene, is a quiver with a groups system of gauge connections A_\mu, and edgelinks between them are chiral fields in a 2-component Weyl-Dirac theory. In 11-dimensions the 10 dimensional supergravity manifold admits this 2-brane, which is dual to a D8-brane by Poincare duality. This admits N=8SUSY and the tesslelation of this brane is given by the E_8 {3^{5,2,1}}. So the discrete tiling of the D2-brane is dual to a C^4/Z^8, which is the gauge theory F. It is then entirely possible that quantum phase transitions in condensed matter systems are similar to a phase transition which brought about the universe from the vacuum.

Lawrence B. Crowell

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Lawrence B. Crowell

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A single layer of graphine or "anything" for that matter, is really not able to sustain itself as a specific and "natural" SOLID/LIQUID/GAS. The reduction of a 3-Dimensional two-layer atomic structure to a 3-dimensional single layer structure is not unlike an "out of phase" or critical process. But try and reduce a 10-Dimensional "anything" is only possible via mathemagican process, strucure in the Universe peaks at 3-Dimensions?

Accordingly so, in string theory, when water turns to steam or visa versa, there is a dimensional transition?..the water appears to fall into the air via a higher or lower dimensionm for instance cold water to steam = 3-D >> 2-D. One reason that string theory has exponential energies for dimensional transitional reducions, is that as one lowers the dimensionality, the energy increases, thus there appears to be a correlation for temperature reduction having an exponential equivilence.

When you have the coldest temperature, you have (total) all the available energy of the system, break the system and you have a dynamical phase transition, from absolute zero to absolute everything, you can transform "nothing" to "everything"..except a single theory that is!

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Accordingly so, in string theory, when water turns to steam or visa versa, there is a dimensional transition?..the water appears to fall into the air via a higher or lower dimensionm for instance cold water to steam = 3-D >> 2-D. One reason that string theory has exponential energies for dimensional transitional reducions, is that as one lowers the dimensionality, the energy increases, thus there appears to be a correlation for temperature reduction having an exponential equivilence.

When you have the coldest temperature, you have (total) all the available energy of the system, break the system and you have a dynamical phase transition, from absolute zero to absolute everything, you can transform "nothing" to "everything"..except a single theory that is!

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Lawrence, Ray,

A solid state description of the physical universe, where space-time is treated like a conduction band, turns out to be very useful. If Hadrons and Leptons turn out to be the open superstrings that stretch across the conduction band energy gap, then we should be able to guess what they are ultimately made out of (energy? material from the stacked spheres, themselves?) In ordinary crystals, such as semiconductors, electrons come from the outer conduction band of the atoms. Occasionally, they scatter off of phonons (which are really just vibrations in the planar lattice). While scattering is nice, I'm more interested in the possibility of bonding between electrons and phonons. Whether or not that has ever been observed would be helpful towards what I'm really looking for.

For hyperdrive physics to work, I need to get Hadrons/Leptons to bond with tachyons, which presumably only exist in hyperspace. I think we will someday (future generations) discover a set of tachyonic quarks. The hope is to get a tachyonic quark to bond with a standard model quark using gluons. Obviously, stability is still a big problem. The idea is to couple standard model forces with hyperspace forces.

Yes, this is pure conjecture bearly good enough for a fun website on UFO's. But if hyperdrive technology really did exist somewhere, somehow, I'm betting it would involve force coupling between what we can control in our physical universe, and what we are trying to control in hyperspace. I think that getting the particles to be stable is going to require the ability to alter one or more physics constants, locally.

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A solid state description of the physical universe, where space-time is treated like a conduction band, turns out to be very useful. If Hadrons and Leptons turn out to be the open superstrings that stretch across the conduction band energy gap, then we should be able to guess what they are ultimately made out of (energy? material from the stacked spheres, themselves?) In ordinary crystals, such as semiconductors, electrons come from the outer conduction band of the atoms. Occasionally, they scatter off of phonons (which are really just vibrations in the planar lattice). While scattering is nice, I'm more interested in the possibility of bonding between electrons and phonons. Whether or not that has ever been observed would be helpful towards what I'm really looking for.

For hyperdrive physics to work, I need to get Hadrons/Leptons to bond with tachyons, which presumably only exist in hyperspace. I think we will someday (future generations) discover a set of tachyonic quarks. The hope is to get a tachyonic quark to bond with a standard model quark using gluons. Obviously, stability is still a big problem. The idea is to couple standard model forces with hyperspace forces.

Yes, this is pure conjecture bearly good enough for a fun website on UFO's. But if hyperdrive technology really did exist somewhere, somehow, I'm betting it would involve force coupling between what we can control in our physical universe, and what we are trying to control in hyperspace. I think that getting the particles to be stable is going to require the ability to alter one or more physics constants, locally.

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Ray,

The imaginary/negative masses that you are playing with are, I believe, 'place-holders' for the hyperdimensional physics that is to come, eventually. Whatever particles exist in hyperspace or alternate space-times, if force coupling between these particles is acheivable, then the imaginary masses will be replaced by the description of that particle's mass in our space-time. I'm sure it will be some function of the ratio between our space-time Egap and the Egap of the other space-time/hyperspace.

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The imaginary/negative masses that you are playing with are, I believe, 'place-holders' for the hyperdimensional physics that is to come, eventually. Whatever particles exist in hyperspace or alternate space-times, if force coupling between these particles is acheivable, then the imaginary masses will be replaced by the description of that particle's mass in our space-time. I'm sure it will be some function of the ratio between our space-time Egap and the Egap of the other space-time/hyperspace.

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Alternatively, Hyperspace Higgs field/space-time Higgs field will be equal to a function of the hyperspace Egap/space-time Egap. Expect lots of parameters and a heavy usage of superstrings/particles that are stable in both hyperspace/space-time. Of course, we haven't observed them yet, and the standard model doesn't predict them.

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Dear Jason,

If I am correctly identifying these tachyons, then they will couple to Gravi-Weak. We aren't talking 26 dimensional physics and an "infinite" number of parameters here. We are talking 7 or 8 dimensions - somewhere between "sane" and "crazy". I am still trying to wrap (or warp) my brain around conduction-branes. There seem to be too many unconstrained parameters in String Theory. I am hoping that we can derive reasonable theoretical expectations for conduction-branes IF they even exist. Whether they exist or not, it doesn't hurt to think outside of the box every once in a while - just don't get stuck there.

Have Fun!

Ray Munroe

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If I am correctly identifying these tachyons, then they will couple to Gravi-Weak. We aren't talking 26 dimensional physics and an "infinite" number of parameters here. We are talking 7 or 8 dimensions - somewhere between "sane" and "crazy". I am still trying to wrap (or warp) my brain around conduction-branes. There seem to be too many unconstrained parameters in String Theory. I am hoping that we can derive reasonable theoretical expectations for conduction-branes IF they even exist. Whether they exist or not, it doesn't hurt to think outside of the box every once in a while - just don't get stuck there.

Have Fun!

Ray Munroe

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Ray,

I wasn't given a box; they said I didn't need one. In any event, my job is stressful; it's the Survival show version of MPEG electronics. I need something that borders on crazy to keep me sane; lets just call it 'play' physics. We just don't have the exotic materials to test these theories, anyway. The advantage of playing with these ideas is that it might give us ideas on what...

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I wasn't given a box; they said I didn't need one. In any event, my job is stressful; it's the Survival show version of MPEG electronics. I need something that borders on crazy to keep me sane; lets just call it 'play' physics. We just don't have the exotic materials to test these theories, anyway. The advantage of playing with these ideas is that it might give us ideas on what...

view entire post

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Dear Jason,

As I said before. I once studied Solid State Physics. My reason was that half of all Physics employment was in that sector. Some good friends of mine went into that field and had lucrative careers. I got bored with it after a while because I was really interested in the "crazy" theoretical ideas. Read my book and you will see that I am trying to find similarities with tetrahedral, octahedral and icosahedral crystalline symmetries versus Boson GUT's. Of course, Garrett Lisi used the E8 Gosset lattice for his TOE model. These are all crystals and imply the possibility that hyperspace is crystallized. We know that this is not true for the bulk behavior of Spacetime, so inflation allowed Spacetime to separate from the possibly crystallized Hyperspace. If each branes has its own properties (this is likely because I suspect that the Weak-brane reflects some weird Weak properties, the Gravity-brane reflects some wierd Gravity properties, etc.), and is crystallized, then each brane may have different "conduction-brane" properties. But I really don't know...

Have Fun!

Ray Munroe

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As I said before. I once studied Solid State Physics. My reason was that half of all Physics employment was in that sector. Some good friends of mine went into that field and had lucrative careers. I got bored with it after a while because I was really interested in the "crazy" theoretical ideas. Read my book and you will see that I am trying to find similarities with tetrahedral, octahedral and icosahedral crystalline symmetries versus Boson GUT's. Of course, Garrett Lisi used the E8 Gosset lattice for his TOE model. These are all crystals and imply the possibility that hyperspace is crystallized. We know that this is not true for the bulk behavior of Spacetime, so inflation allowed Spacetime to separate from the possibly crystallized Hyperspace. If each branes has its own properties (this is likely because I suspect that the Weak-brane reflects some weird Weak properties, the Gravity-brane reflects some wierd Gravity properties, etc.), and is crystallized, then each brane may have different "conduction-brane" properties. But I really don't know...

Have Fun!

Ray Munroe

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Hi Ray,

Do I understand you correctly when you say that the bulk of space-time cannot be crystalized (solid state with conduction bands)? Is it because of the Big Bang model?

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Do I understand you correctly when you say that the bulk of space-time cannot be crystalized (solid state with conduction bands)? Is it because of the Big Bang model?

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Paul,

The phase transitions with graphene and related systems are not the standard second order phase transitions, but are transitions in the behavior of a Landau quantum fluid of electrons and quantum Hall effects. There is also anyonic physics on the 2-dim surface as well.

The analogue of a string in graphene is the occurrence of an effective magnetic monopole with the quantum Hall effect. The quantized currents on a graphene sheet with the quantum Hall effect can result in an effective magnetic monopole. The quantum flux of B-field due to currents around the sheet has an effect of setting one of the magnetic poles ---> infinity like the Dirac solonoid monopole. This sets up a duality between the electric and magnetic charges, e and b respectively, so that eb = nħ. This is the T-duality which a Type IIA string has with respect to D2, D4, D6, D8 and D10 branes.

Lawrence B. Crowell

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The phase transitions with graphene and related systems are not the standard second order phase transitions, but are transitions in the behavior of a Landau quantum fluid of electrons and quantum Hall effects. There is also anyonic physics on the 2-dim surface as well.

The analogue of a string in graphene is the occurrence of an effective magnetic monopole with the quantum Hall effect. The quantized currents on a graphene sheet with the quantum Hall effect can result in an effective magnetic monopole. The quantum flux of B-field due to currents around the sheet has an effect of setting one of the magnetic poles ---> infinity like the Dirac solonoid monopole. This sets up a duality between the electric and magnetic charges, e and b respectively, so that eb = nħ. This is the T-duality which a Type IIA string has with respect to D2, D4, D6, D8 and D10 branes.

Lawrence B. Crowell

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Ray,

I do remember you mentioning that you took Solid State at University of Texas, right; I just love explaining solid state because it's really cool.

I actually like the idea of a hyperdimensional lattice of crystals. Unfortunately, it doesn't fit very well with an expanding universe.

I had another idea, but I think it's kind of dumb. Light is the essence of geometry. In fact, so much so, that the expanding universe is actually one giant photon of light. That means that its expanding as a wavefront whose surface is our space-time. There is no absolute reference frame on it. The speed of light, on a giant photon of light, is the speed of light. Electromagnetism is just a vibration along the wavefront of this giant photon. It's not a very mechanistically satisfying idea. I hope its wrong.

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I do remember you mentioning that you took Solid State at University of Texas, right; I just love explaining solid state because it's really cool.

I actually like the idea of a hyperdimensional lattice of crystals. Unfortunately, it doesn't fit very well with an expanding universe.

I had another idea, but I think it's kind of dumb. Light is the essence of geometry. In fact, so much so, that the expanding universe is actually one giant photon of light. That means that its expanding as a wavefront whose surface is our space-time. There is no absolute reference frame on it. The speed of light, on a giant photon of light, is the speed of light. Electromagnetism is just a vibration along the wavefront of this giant photon. It's not a very mechanistically satisfying idea. I hope its wrong.

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It's funny; I think I heard a similar version of the gigantic photon idea before. I think someone who is popular on this website wrote something about space-time being a wavefront on a 4D+1 (5D) space-time. I didn't mean to call it a dumb idea, I just don't like the idea because it suggests that there is only one universe. If space-time is a wavefront on a 5D explosion, then the speed of light cannot be changed; there isn't any hyperspace. The speed of light c, and the planck constant, are embedded into the properties of the photon/wavefront. Cosmological and gravitional constants might depend upon geometry. I have no idea how this might explain dark matter/dark energy.

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Dear Jason,

In my model, I consider "E12" to be a "sub-TOE" (meaning it is a "TOE" in fewer than 26 dimensions). "E12" is not a simple crystal. It has a natural tendency to break into smaller "crystals" such as E8xH4. Immedialtely following the Big Bang was a period of extreme Inflation. I think the H4 inflated into Spacetime and thus separated from Hyperpace, whereas the E8 remained a Hyperspace Gosset-based crystal. Crystallization is still possible in certain types of materials in our Spacetime world, but it is not the rule as it would be in this proposed Hyperspace.

A single photon Universe? Huh? It must be a really smart photon to illuminate our changing world for us and to carry all of those radio, TV, microwave, etc, signals... I hope there's not just one of any fundamental particle. What if there is only one Higgs? The LHC would never find it...

Have Fun!

Ray Munroe

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In my model, I consider "E12" to be a "sub-TOE" (meaning it is a "TOE" in fewer than 26 dimensions). "E12" is not a simple crystal. It has a natural tendency to break into smaller "crystals" such as E8xH4. Immedialtely following the Big Bang was a period of extreme Inflation. I think the H4 inflated into Spacetime and thus separated from Hyperpace, whereas the E8 remained a Hyperspace Gosset-based crystal. Crystallization is still possible in certain types of materials in our Spacetime world, but it is not the rule as it would be in this proposed Hyperspace.

A single photon Universe? Huh? It must be a really smart photon to illuminate our changing world for us and to carry all of those radio, TV, microwave, etc, signals... I hope there's not just one of any fundamental particle. What if there is only one Higgs? The LHC would never find it...

Have Fun!

Ray Munroe

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The article about the bablel fish and the black hole is interesting. I wrote the following in response to that article on how graphene is a model system for 2D-branes.

The graphene system is fascinating for quantum field on the sheet are not restricted into being strictly fermionic or bosonic. Under an exchange of particles with state vectors |Ψ_1> and |Ψ_2> there is |Ψ_1Ψ_2> = e^{iθ}|Ψ_2Ψ_1>, which in dimensions > 2 has θ = {0, π} so the exchange is 1 for bosons and -1 for fermions. The spin statistic is defined by π_1(SO(n,1)) which for n > 2 is π_1(SO(n,1)) = Z_2, but for n = 2 is π_1(SO(2,1)) = Z. The first homotopy group indicates that orientation of the spin, which is infinitely cyclic in n = 2. Further this means the standard sequence

1 --> Z_2 --->spin(n) ---> SO(n) ---> 1

does not apply, so spin(2,1) is not a universal covering group. The projective system over SO(2,1) is the braid group B_2, which describes the anyon.

The analogue of a string in graphene is the occurrence of an effective magnetic monopole with the quantum Hall effect. The quantized currents on a graphene sheet with the quantum Hall effect can result in an effective magnetic monopole. The quantum flux of B-field due to currents around the sheet has an effect of setting one of the magnetic poles ---> infinity like the Dirac solonoid monopole. This sets up a duality between the electric and magnetic charges, e and b respectively, so that eb = nħ. This is the T-duality which a Type IIA string has with respect to D2, D4, D6, D8 and D10 branes. In 10 dimensions the T-duality obtains on a D8-brane, and the 11-dimensional duality obtains on a D9-brane, which gives a correspondence between Type IIB and Type IIA strings.

This physics is generalized into Chern-Simons theory. The 2+1 C-S theory is given by a Lagrangian

L = A Λ dA + (2/3)A Λ A Λ A,

Where this Lagrangian defines a cyclicity S = ∫d^3x L, with S --> S + 2πN, for N a winding number. By Poincare duality this is carried over to the 8 dimensional surface as the boundary of the 9 dimensional surface, here the surfaces in fact being D-branes and the two surface a D2-brane bounding a 3-dimensional region. The duality carries this information over to a supersymmetric WZW Lagrangian. The D2-branes exist in a foliation that is in the bulk transverse to C^4/Z^8, for Z^8 a set of discrete points (Z^8 a lattice of charges or roots of the E_8). The transversality condition preserves the anionic structure on the D2 as supersymmetry (N=8 SUSY) on the C^4/Z^8.

Lawrence B. Crowell

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The graphene system is fascinating for quantum field on the sheet are not restricted into being strictly fermionic or bosonic. Under an exchange of particles with state vectors |Ψ_1> and |Ψ_2> there is |Ψ_1Ψ_2> = e^{iθ}|Ψ_2Ψ_1>, which in dimensions > 2 has θ = {0, π} so the exchange is 1 for bosons and -1 for fermions. The spin statistic is defined by π_1(SO(n,1)) which for n > 2 is π_1(SO(n,1)) = Z_2, but for n = 2 is π_1(SO(2,1)) = Z. The first homotopy group indicates that orientation of the spin, which is infinitely cyclic in n = 2. Further this means the standard sequence

1 --> Z_2 --->spin(n) ---> SO(n) ---> 1

does not apply, so spin(2,1) is not a universal covering group. The projective system over SO(2,1) is the braid group B_2, which describes the anyon.

The analogue of a string in graphene is the occurrence of an effective magnetic monopole with the quantum Hall effect. The quantized currents on a graphene sheet with the quantum Hall effect can result in an effective magnetic monopole. The quantum flux of B-field due to currents around the sheet has an effect of setting one of the magnetic poles ---> infinity like the Dirac solonoid monopole. This sets up a duality between the electric and magnetic charges, e and b respectively, so that eb = nħ. This is the T-duality which a Type IIA string has with respect to D2, D4, D6, D8 and D10 branes. In 10 dimensions the T-duality obtains on a D8-brane, and the 11-dimensional duality obtains on a D9-brane, which gives a correspondence between Type IIB and Type IIA strings.

This physics is generalized into Chern-Simons theory. The 2+1 C-S theory is given by a Lagrangian

L = A Λ dA + (2/3)A Λ A Λ A,

Where this Lagrangian defines a cyclicity S = ∫d^3x L, with S --> S + 2πN, for N a winding number. By Poincare duality this is carried over to the 8 dimensional surface as the boundary of the 9 dimensional surface, here the surfaces in fact being D-branes and the two surface a D2-brane bounding a 3-dimensional region. The duality carries this information over to a supersymmetric WZW Lagrangian. The D2-branes exist in a foliation that is in the bulk transverse to C^4/Z^8, for Z^8 a set of discrete points (Z^8 a lattice of charges or roots of the E_8). The transversality condition preserves the anionic structure on the D2 as supersymmetry (N=8 SUSY) on the C^4/Z^8.

Lawrence B. Crowell

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This sort of theory is not sub-TOS as currently concieved of. The E_8xE_8 under bosnoization produces the 26-dim bosonic string. The E_8xH_4, or similarly the E_{12}, and their dual *(E_8xH_4) or *E_{12} should be a description of the heterotic string on an AdS spacetime. It might be sub-TOE if I am right and further up the energy ladder things are Λ_{24}. The Leech lattice Λ_{24} has connections to the 26-dim string. For that matter this might be sub-TOE, since the automorphism group is the Fischer-Griess group (the monster), which also has connections to the 26-dim bosonic string.

As for "one photon," it might be there is only one particle. This is pretty speculative, but it is possible the universe consists of one particle, but where the multiplicity of particles we observe are due to how this particle zig-zags between the initial and final state of the universe. This sig-zagged particle appears under different E_8 (or E_8xE_8) representations in a decoherent manner on a large scale.

I read an article by Don Page about "The Born Rule Dies," which makes a pretty compelling case that the Born rule can't be applied to the universe as a whole. However, I think QM is fairly exact to the quantum gravity level. With these lattice systems unitarity is probably replaced by modularity, which might then have the universe consisting of one particle (including gravitons and gravitational instantons that make up black holes) that zig-zags between the initial and final state of the universe under the grand path integral. We observe this particle from the "frog's eye" perspective in a decoherent (coarse grained) manner under different group representations.

Lawrence B. Crowell

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As for "one photon," it might be there is only one particle. This is pretty speculative, but it is possible the universe consists of one particle, but where the multiplicity of particles we observe are due to how this particle zig-zags between the initial and final state of the universe. This sig-zagged particle appears under different E_8 (or E_8xE_8) representations in a decoherent manner on a large scale.

I read an article by Don Page about "The Born Rule Dies," which makes a pretty compelling case that the Born rule can't be applied to the universe as a whole. However, I think QM is fairly exact to the quantum gravity level. With these lattice systems unitarity is probably replaced by modularity, which might then have the universe consisting of one particle (including gravitons and gravitational instantons that make up black holes) that zig-zags between the initial and final state of the universe under the grand path integral. We observe this particle from the "frog's eye" perspective in a decoherent (coarse grained) manner under different group representations.

Lawrence B. Crowell

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I came up with the "one photon universe" by playing around with dualities; bradyon/tachyon; disseminate parts/wholeness; localized/nonlocalized.

Tachyons and bradyons have to be symmetric across a speed of light, c, limit. As for tachyons, one way to be faster than light is to be everywhere simultaneously, like the Higgs particle. I started thinking about interactions between tachyons and bradyons. Space/space-time itself is not a particle, but is more like the dual of a particle. So I thought, maybe space is a tachyon. The fact that gravity acts over huge distances lends itself to "space-time warping" ideas. Yet, quantum mechanics bites at our ankles (ok, tugs at our pants) with it's quantum tiny-ness as if to say "don't forget about the little stuff". I can think of two ways to get the cosmic scale space-time stuff and the quantum stuff to interact naturally. Maybe those two ways unify, who knows.

1. Giant photon takes advantage of a possible disseminate/wholeness symmetry. One very complex object or many tiny objects equvialent to one large object. Particle-wave photon duality is restored; speed of light is assured at the 4D surface wavefront. The wave front itself has Energy Kin+Potential as a function of position/momentum/spin/etc... And the universe is expanding anyway like a balloon.

2. Tachyon/Bradyon interaction. Space itself behaves tachyonic, since its particles can be almost everywhere without us noticing. Wave functions are tachyonic in their ability to be everywhere (governed by kin+Pot energy). There are conserved chemistry-like interactions between tachyonic (space-time manifesting) particles (Higgs/gravitons) and Standard Model quantum particles. These reactions are conserved. These chemistry-like interactions between tachyons/bradyons produce the effect of particles moving in space-time.

I hope the idea(s) make sense. I gotta get back in my box and go to work.

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Tachyons and bradyons have to be symmetric across a speed of light, c, limit. As for tachyons, one way to be faster than light is to be everywhere simultaneously, like the Higgs particle. I started thinking about interactions between tachyons and bradyons. Space/space-time itself is not a particle, but is more like the dual of a particle. So I thought, maybe space is a tachyon. The fact that gravity acts over huge distances lends itself to "space-time warping" ideas. Yet, quantum mechanics bites at our ankles (ok, tugs at our pants) with it's quantum tiny-ness as if to say "don't forget about the little stuff". I can think of two ways to get the cosmic scale space-time stuff and the quantum stuff to interact naturally. Maybe those two ways unify, who knows.

1. Giant photon takes advantage of a possible disseminate/wholeness symmetry. One very complex object or many tiny objects equvialent to one large object. Particle-wave photon duality is restored; speed of light is assured at the 4D surface wavefront. The wave front itself has Energy Kin+Potential as a function of position/momentum/spin/etc... And the universe is expanding anyway like a balloon.

2. Tachyon/Bradyon interaction. Space itself behaves tachyonic, since its particles can be almost everywhere without us noticing. Wave functions are tachyonic in their ability to be everywhere (governed by kin+Pot energy). There are conserved chemistry-like interactions between tachyonic (space-time manifesting) particles (Higgs/gravitons) and Standard Model quantum particles. These reactions are conserved. These chemistry-like interactions between tachyons/bradyons produce the effect of particles moving in space-time.

I hope the idea(s) make sense. I gotta get back in my box and go to work.

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I guess I am not sure what a bradyon is. Spacetime is related to spacetime in a way. The Tachyon state is a_{-1}|0>, while a_{-1}(~a)_{-1}|0> defines a graviton by the right and left modes on a closed string. The ~ means "tilde." Yet it would not be correct to say that space or spacetime is a tachyon.

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When I wrote "Spacetime is related to spacetime in a way," I meant Spacetime is related to tachyons in a way.

A tachyon is a particle that is not at rest in any timelike frame. A particle with a mass travels at the speed of light along the x^4 direction in its frame. Another observer who watches the particle move along a spatial direction x_i with some velocity v sees a transformation which reduces the rate it moves along x^4. This is the time dilation effect. A tachyon in contrast moves along a spacelike direction, which means there is a timelike frame where the velocity of this particle is "infinite," or it travels between any spatial points x and y instantly.

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A tachyon is a particle that is not at rest in any timelike frame. A particle with a mass travels at the speed of light along the x^4 direction in its frame. Another observer who watches the particle move along a spatial direction x_i with some velocity v sees a transformation which reduces the rate it moves along x^4. This is the time dilation effect. A tachyon in contrast moves along a spacelike direction, which means there is a timelike frame where the velocity of this particle is "infinite," or it travels between any spatial points x and y instantly.

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Dear Jason and Lawrence,

Bradyon is not a commonly used physics expression. I always called it a tardon (similar to tardyon) to indicate particles of real mass that must always travel slower than the speed of light.

Regarding dual lattices, I think the dual lattices connect fermions ("matter") to bosons ("interactions"). Does this also connect "matter" to the "frame"? I'm pretty sure that tachyons and tardons/bradyons are not dual lattices to each other, but tardons can couple to a matter/anti-matter pair of tachyons via Gravi-Weak interactions (similar to Supersymmetry where Super-particles must be made in pairs to conserve "R" parity). Although they seem very different in nature, tachyons and tardons are just another broken symmetry.

Have Fun!

Ray Munroe

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Bradyon is not a commonly used physics expression. I always called it a tardon (similar to tardyon) to indicate particles of real mass that must always travel slower than the speed of light.

Regarding dual lattices, I think the dual lattices connect fermions ("matter") to bosons ("interactions"). Does this also connect "matter" to the "frame"? I'm pretty sure that tachyons and tardons/bradyons are not dual lattices to each other, but tardons can couple to a matter/anti-matter pair of tachyons via Gravi-Weak interactions (similar to Supersymmetry where Super-particles must be made in pairs to conserve "R" parity). Although they seem very different in nature, tachyons and tardons are just another broken symmetry.

Have Fun!

Ray Munroe

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Lawrence,

A bradyon is a particle that moves slower than c, pretty much everything we've measured. I was under the impression that a tachyon was any particle that could move faster than the speed of light; whether that is infinite m/s or 2c (twice speed of light).

I would have preferred the conduction band/solid state model; but it doesn't explain the Big Bang or how the universe can continue to expand. I just don't buy the idea that we can ignore space and not concern ourselves with why the laws of physics operate the way they do, nor ask why the physics constants are what they are. If it wasn't for the hyperinflation during the early part of the Big Bang, where the laws of physics behaved strangely (so I've heard), then a conduction band model in a hyperspace crystal would make more sense.

But trying to explain the expanding balloon of "space-time" with cosmic range General Relativity (space-curvature) and quantum behavior requires the use of a (1) a long range attribute to describe space/space-time that won't be hindered by c and (2) a QM attribute that handles the dynamics of quantum particles. They need to interact somehow.

By describing space as something ubiquitous (can be everywhere in space - like Higg's field) but with the ability to interact with quantum particles (obey conservation laws), then large accumulations of mass (like black holes) can distort the behavior of these "be everywhere" tachyon particles that I've suggested. I do understand that the difference between a particle and a field is its relationship the the Uncertainty Principle.

I believe that, in the absence of what we call space-time, their would be an infinite potential energy barrier that prevents particles from moving in it. Space-time, in effect, creates a 'conduction band' by allowing particles to move in it (up to the speed of light). Whatever space-time is, it has to obey QM in order to allow GR to occur. Whether space-time (our universe) in one really bizarre photon, tachyon particle/fields interacting with standard model particles, a Higgs field or something else, space itself has to be "something" that imposes the laws of physics.

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A bradyon is a particle that moves slower than c, pretty much everything we've measured. I was under the impression that a tachyon was any particle that could move faster than the speed of light; whether that is infinite m/s or 2c (twice speed of light).

I would have preferred the conduction band/solid state model; but it doesn't explain the Big Bang or how the universe can continue to expand. I just don't buy the idea that we can ignore space and not concern ourselves with why the laws of physics operate the way they do, nor ask why the physics constants are what they are. If it wasn't for the hyperinflation during the early part of the Big Bang, where the laws of physics behaved strangely (so I've heard), then a conduction band model in a hyperspace crystal would make more sense.

But trying to explain the expanding balloon of "space-time" with cosmic range General Relativity (space-curvature) and quantum behavior requires the use of a (1) a long range attribute to describe space/space-time that won't be hindered by c and (2) a QM attribute that handles the dynamics of quantum particles. They need to interact somehow.

By describing space as something ubiquitous (can be everywhere in space - like Higg's field) but with the ability to interact with quantum particles (obey conservation laws), then large accumulations of mass (like black holes) can distort the behavior of these "be everywhere" tachyon particles that I've suggested. I do understand that the difference between a particle and a field is its relationship the the Uncertainty Principle.

I believe that, in the absence of what we call space-time, their would be an infinite potential energy barrier that prevents particles from moving in it. Space-time, in effect, creates a 'conduction band' by allowing particles to move in it (up to the speed of light). Whatever space-time is, it has to obey QM in order to allow GR to occur. Whether space-time (our universe) in one really bizarre photon, tachyon particle/fields interacting with standard model particles, a Higgs field or something else, space itself has to be "something" that imposes the laws of physics.

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Hi Jason,

If Hyperspace (E8 in my model) is still crystallized, it may establish the foundation for QM and differences in interactions. Conduction bands or branes may still exist in the crystallized Hyperspace.

If Spacetime (H4 in my model) is vaporized (not crystallized) and expanding rapidly, it may cause GR and Dirac's Large Number. Conduction bands or branes cannot exist in a vaporized Spacetime.

Thus, the radical differences between QM and GR arise - Hyperspace and Spacetime are in two different "states of matter".

The Big Bang caused the forces to separate into distinct entities and allowed interaction strengths to vary (from near unity to 10^{-40} for Gravity - see my book - have I e-mailed you a copy?). The Big Bang also allowed the dimensions to splinter into branes. One 3-brane/string combo exploded to form Spacetime.

Spacetime's phase transition from crytallized to vaporized was caused by the Big Bang/ Inflation process.

It would be cool if we could use tachyons for a hyperdrive. But it would also be cool if we could use tachyons to better understand Hyperspace.

Obviously, there is a significant amount of conjecture here that I probably would not include in a research paper.

Have Fun!

Ray Munroe

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If Hyperspace (E8 in my model) is still crystallized, it may establish the foundation for QM and differences in interactions. Conduction bands or branes may still exist in the crystallized Hyperspace.

If Spacetime (H4 in my model) is vaporized (not crystallized) and expanding rapidly, it may cause GR and Dirac's Large Number. Conduction bands or branes cannot exist in a vaporized Spacetime.

Thus, the radical differences between QM and GR arise - Hyperspace and Spacetime are in two different "states of matter".

The Big Bang caused the forces to separate into distinct entities and allowed interaction strengths to vary (from near unity to 10^{-40} for Gravity - see my book - have I e-mailed you a copy?). The Big Bang also allowed the dimensions to splinter into branes. One 3-brane/string combo exploded to form Spacetime.

Spacetime's phase transition from crytallized to vaporized was caused by the Big Bang/ Inflation process.

It would be cool if we could use tachyons for a hyperdrive. But it would also be cool if we could use tachyons to better understand Hyperspace.

Obviously, there is a significant amount of conjecture here that I probably would not include in a research paper.

Have Fun!

Ray Munroe

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Tachyon states are cases where α’M^2 = {-1, -4} for open or closed strings. These states are built up from the vacuum according to α^i_{-1}|0>, for α^i_{-1} the string mode operator. If we call this field Ψ^i_t, then an interaction between tachyons V^{ij} ~ Ψ^j_t^† V Ψ^j_t, is the coupling between strings which form an M2-brane. This M2-brane has...

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Dear Lawrence,

Thanks for the explaination and the inspiration. I need to finish version 3.1 of my paper so that I may share it with you.

Dear Jason,

You have the old version 2.1 of my paper (I think Steve has version 1.3 - both of those versions have some defects so please don't take them too literally). In my book and in that paper, I spoke of "Hyperflavor". Hyperflavor is an extension of Pati-Salam Weak, but it exists on a "Gravi-Weak" 2-brane. From Lawrence's explaination, this must be the M2-brane.

Have Fun!

Ray Munroe

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Thanks for the explaination and the inspiration. I need to finish version 3.1 of my paper so that I may share it with you.

Dear Jason,

You have the old version 2.1 of my paper (I think Steve has version 1.3 - both of those versions have some defects so please don't take them too literally). In my book and in that paper, I spoke of "Hyperflavor". Hyperflavor is an extension of Pati-Salam Weak, but it exists on a "Gravi-Weak" 2-brane. From Lawrence's explaination, this must be the M2-brane.

Have Fun!

Ray Munroe

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Hi Ray and Lawrence,

You are both a wealth of knowledge. There are so many ideas to absorb and think about; and so little time to do it in.

Question: I need to get a good sound UFO physics theory. Including the Big Bang theory, can the ultimate hyper-verse/universe/multiverse be described with some kind of crystalline structure (admittedly hyperdimensional)? Our physical universe appears to be expanding like a balloon (not very crystal-like); can I still rely upon solid state physics to account for an expanding universe? You mentioned the stretched horizon idea...

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You are both a wealth of knowledge. There are so many ideas to absorb and think about; and so little time to do it in.

Question: I need to get a good sound UFO physics theory. Including the Big Bang theory, can the ultimate hyper-verse/universe/multiverse be described with some kind of crystalline structure (admittedly hyperdimensional)? Our physical universe appears to be expanding like a balloon (not very crystal-like); can I still rely upon solid state physics to account for an expanding universe? You mentioned the stretched horizon idea...

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Hi Yes ,

I agree ,They are strongs ,a big facility to play with theories and tools ,

The youngs admit ....lol

I speak a lot dear Ray and Lawrence ,but I respect both of you ,be sure .

You know yesterday I spoke with a friend about my arrogance and the critic of others theories ,It's silly because I must accept some realities ,it exists some business ,books ,works....and you see what I say .I recognize it's not necessary .

In all case ,I am going to write more quiet .

I d like ask you(Lawrence,Ray,Jason) ,all ,what do you think about a contraction of our Universe ?The fact to have an increase of mass can explain many things No?

I d like have your point of vue if you want .

regards

Steve

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I agree ,They are strongs ,a big facility to play with theories and tools ,

The youngs admit ....lol

I speak a lot dear Ray and Lawrence ,but I respect both of you ,be sure .

You know yesterday I spoke with a friend about my arrogance and the critic of others theories ,It's silly because I must accept some realities ,it exists some business ,books ,works....and you see what I say .I recognize it's not necessary .

In all case ,I am going to write more quiet .

I d like ask you(Lawrence,Ray,Jason) ,all ,what do you think about a contraction of our Universe ?The fact to have an increase of mass can explain many things No?

I d like have your point of vue if you want .

regards

Steve

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Dear Steve,

There is a Cosmological Model where the Universe expands out to its furthest expanse (perhaps like a large "sphere"), then reverses and contracts back to a single point, and another "Big Crunch/ Big Bang". Interesting theories have arisen as to how a contraction might affect the Second Law of Thermodynamics. Often, this model recycles the Universe, and we can imagine Big Bang leading to Big Crunch/ Big Bang leading to Big Crunch/ Big Bang, etc. I suspect that our measurement of "Dark Energy" (or the Cosmological Constant) is large enough that a Big Crunch is unlikely.

Regarding all of our many theories, it is possible that we are all correct, or all partially correct, or all wrong. You know that I have criticized Garrett Lisi's E8 TOE model both publicly and privately. However, I am now proposing that Hyperspace is an E8 Gosset lattice, so I do not ignore good ideas - I might just reapply them. Consider that String Theory began as a theory of the Strong Nuclear force and has since been reapplied as a theory of Quantum Gravity. I prefer to keep an open mind...

Dear Jason,

As I explained earlier today, I think the solid state ideas related to Hyperspace, and Spacetime has been vaporized.

Have Fun! And Thanks to both of you for the compliments!

Ray Munroe

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There is a Cosmological Model where the Universe expands out to its furthest expanse (perhaps like a large "sphere"), then reverses and contracts back to a single point, and another "Big Crunch/ Big Bang". Interesting theories have arisen as to how a contraction might affect the Second Law of Thermodynamics. Often, this model recycles the Universe, and we can imagine Big Bang leading to Big Crunch/ Big Bang leading to Big Crunch/ Big Bang, etc. I suspect that our measurement of "Dark Energy" (or the Cosmological Constant) is large enough that a Big Crunch is unlikely.

Regarding all of our many theories, it is possible that we are all correct, or all partially correct, or all wrong. You know that I have criticized Garrett Lisi's E8 TOE model both publicly and privately. However, I am now proposing that Hyperspace is an E8 Gosset lattice, so I do not ignore good ideas - I might just reapply them. Consider that String Theory began as a theory of the Strong Nuclear force and has since been reapplied as a theory of Quantum Gravity. I prefer to keep an open mind...

Dear Jason,

As I explained earlier today, I think the solid state ideas related to Hyperspace, and Spacetime has been vaporized.

Have Fun! And Thanks to both of you for the compliments!

Ray Munroe

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The crystaline picture can only be taken so far. The Planck unit of length or scale where the Schwarzschild radium of a black hole r = 2GM/c^2 is equal to its four dimensional deBroglie wavelength λp = ħ/2π in a rest frame p = Mc. Setting λ = 1/L_p and eliminating M gives L_p = sqrt{Għ/c^3} which is 1.6x10^{-33}cm. This is a pretty small region. This is the smallest...

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It's interesting all that .

Ray ,a big crunch is different than a concrete coded contraction .

What I find interesting in this idea is the link with dark matter.

The space has any activity ,I think it's spheres without rotations thus any mass .

The contraction is logic ,the expansion for ever has no sense for the optimization of interactions between mass systems...

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Ray ,a big crunch is different than a concrete coded contraction .

What I find interesting in this idea is the link with dark matter.

The space has any activity ,I think it's spheres without rotations thus any mass .

The contraction is logic ,the expansion for ever has no sense for the optimization of interactions between mass systems...

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I like the complexity and the simplicity in the same time ,like all things in fact .What I see with this kind of theory ,it's the lack of whole .

The strings ,even the M th and superstrings ,are a not necessary complexity .

What I try to tell you ,it's what the polytops exist since Mr Gosset ,what I try to tell you ,it's what frankly it's a little too simple .Fortunally Mr Gosset isn't here .he understood what I say .

What I find arrogant ,it's the pub name ,a theory of everything ,No but I dream or what .What I find arrogant it's that ,use sciences for the business .

These kinds of theories shall be loved by one part ,it's like that ,some books shall be publied ,and that and that ,like the strings .

I beleive what the rule of sciences is to take some roads in a whole point of vue .

The lie algebra and the polytops are mathematical extrapolations ,interestings but let's be serious .

I am very sorry to say that ,but The strings and E8 or E12.....or others don't explain nothing .The fact is not what That is not interesting ,the fact is what it's not foundamental.

It's the same with tachyons ,K Theory,L and the quadratic forms ...These mathematical tools are interesting in some azpllications but it's maths .

You know it's easier to play with all that....and indeed we see to appear the extrapolations holography,fourth dimension,D branes and that and that .

It's beautiful all that but since that exists ,I see some imaginary extrapolations but ....the complex and imaginaries still .

What I beleive important is the cosmological constant and the limits ,if we insert some different limits by imaginaries and math tools ,it's impossible ,really .

I am going to fnish this post ,sorry I must go .

until soon

Steve

I do

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The strings ,even the M th and superstrings ,are a not necessary complexity .

What I try to tell you ,it's what the polytops exist since Mr Gosset ,what I try to tell you ,it's what frankly it's a little too simple .Fortunally Mr Gosset isn't here .he understood what I say .

What I find arrogant ,it's the pub name ,a theory of everything ,No but I dream or what .What I find arrogant it's that ,use sciences for the business .

These kinds of theories shall be loved by one part ,it's like that ,some books shall be publied ,and that and that ,like the strings .

I beleive what the rule of sciences is to take some roads in a whole point of vue .

The lie algebra and the polytops are mathematical extrapolations ,interestings but let's be serious .

I am very sorry to say that ,but The strings and E8 or E12.....or others don't explain nothing .The fact is not what That is not interesting ,the fact is what it's not foundamental.

It's the same with tachyons ,K Theory,L and the quadratic forms ...These mathematical tools are interesting in some azpllications but it's maths .

You know it's easier to play with all that....and indeed we see to appear the extrapolations holography,fourth dimension,D branes and that and that .

It's beautiful all that but since that exists ,I see some imaginary extrapolations but ....the complex and imaginaries still .

What I beleive important is the cosmological constant and the limits ,if we insert some different limits by imaginaries and math tools ,it's impossible ,really .

I am going to fnish this post ,sorry I must go .

until soon

Steve

I do

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Dear Sphere-keeper Steve,

I agree with you that the name "Theory of Everything" sounds very pretentious. This is why I entitled my book "New Approaches Towards a Grand Unified Theory". "Theory of Everything" sounds like it should include God, Religion, All of the Natural Sciences, the Social Sciences, the Arts, etc. and it clearly does not. When I first read Lisi's "An Exceptionally Simple Theory of Everything" it disturbed me. I read it three times the first week to make sure I did not misunderstand his ideas. It did not include some fundamental ideas from my book that I consider obvious "truths of nature", so how could it be THE Theory of Everything? The title of my next paper is "A Case Study of the Geometrical Nature of Theories of Everything", and I do present E12 as my preferred candidate, but I offer other reasonable ideas as well. I am being consistent - calling a boson unification a GUT, calling a fermion unification a GUT, and calling a boson/fermion unification a TOE. I did not invent the term "TOE"...

I did not look for tachyons - those "crazy" things popped out of nowhere. It is an awkward characteristic of this theory, but perhaps it will enable a futuristic experiment to separate these ideas from others.

I like the Gosset lattice, but I think I have pushed the envelope a little further.

I want to describe Nature while balancing ideas of "Simplicity" and "Necessity". Lisi's ideas are simple, but I do not think they include all of the necessary features and details. Someone will surely argue that my ideas are not simple enough, but I am trying to be thorough. All I can ask is that people keep an open mind and wait (however many decades) for experimental data to decide the case.

Your Friend,

Dr. Cosmic Ray

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I agree with you that the name "Theory of Everything" sounds very pretentious. This is why I entitled my book "New Approaches Towards a Grand Unified Theory". "Theory of Everything" sounds like it should include God, Religion, All of the Natural Sciences, the Social Sciences, the Arts, etc. and it clearly does not. When I first read Lisi's "An Exceptionally Simple Theory of Everything" it disturbed me. I read it three times the first week to make sure I did not misunderstand his ideas. It did not include some fundamental ideas from my book that I consider obvious "truths of nature", so how could it be THE Theory of Everything? The title of my next paper is "A Case Study of the Geometrical Nature of Theories of Everything", and I do present E12 as my preferred candidate, but I offer other reasonable ideas as well. I am being consistent - calling a boson unification a GUT, calling a fermion unification a GUT, and calling a boson/fermion unification a TOE. I did not invent the term "TOE"...

I did not look for tachyons - those "crazy" things popped out of nowhere. It is an awkward characteristic of this theory, but perhaps it will enable a futuristic experiment to separate these ideas from others.

I like the Gosset lattice, but I think I have pushed the envelope a little further.

I want to describe Nature while balancing ideas of "Simplicity" and "Necessity". Lisi's ideas are simple, but I do not think they include all of the necessary features and details. Someone will surely argue that my ideas are not simple enough, but I am trying to be thorough. All I can ask is that people keep an open mind and wait (however many decades) for experimental data to decide the case.

Your Friend,

Dr. Cosmic Ray

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Hi Ray and Lawrence,

I've been thinking about universes and hyperspaces. Yes, yes...I will refrain from the eccentric terminology when I am describing physics ideas.

While conduction bands inside of crystals is a nice idea, I don't know of any inflatable crystals. I'm not too keen on the idea of a vaporized universe. But I do like the idea of an inflatable universe that expands...

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I've been thinking about universes and hyperspaces. Yes, yes...I will refrain from the eccentric terminology when I am describing physics ideas.

While conduction bands inside of crystals is a nice idea, I don't know of any inflatable crystals. I'm not too keen on the idea of a vaporized universe. But I do like the idea of an inflatable universe that expands...

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It's evident that the gravity is important .In some of my analyzes and with my theory ,the gravity changes ,increases all time,.....it's logic if we consider the activation of elementary particles (the rotating spheres)but of course these increases are very very weak 9.81.... m/s² for our Earth exemple.

What is interesting is the maximum gravity thus the finished Universal sphere and all...

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What is interesting is the maximum gravity thus the finished Universal sphere and all...

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Dear Steve,

I understand your concern that E12 is simply a framework, and many details (such as particle masses) are lacking.

You are very concerned about some of the fundamental constants. Remember, that I addressed much of this detail in my book under the title of "Quantum Statistical Grand Unified Theory (QSGUT)". I addressed the variability of "constants" such as the "Fine Structure Constant" and the "Gravitational Constant", which have been misinterpreted as "Dark Energy". The numbers that I gave in my book are fully based on experimental data. Is QSGUT an ad-hoc thing to be added onto E12, or vice versa? Or are both theories complementary theories (just as Classical Mechanics and Statistical Mechanics are complementary)?

These details that worry you may be ad-hoc parameters. For instance, in the essay contest Tony Smith is using the math of Hua Luogeng to introduce important parameters into the E8 framework. El Naschie and his followers have reproduced particle mass spectra using the Golden Ratio.

We are early on in this game - we do not know how it will play out.

Have Fun!

Ray Munroe

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I understand your concern that E12 is simply a framework, and many details (such as particle masses) are lacking.

You are very concerned about some of the fundamental constants. Remember, that I addressed much of this detail in my book under the title of "Quantum Statistical Grand Unified Theory (QSGUT)". I addressed the variability of "constants" such as the "Fine Structure Constant" and the "Gravitational Constant", which have been misinterpreted as "Dark Energy". The numbers that I gave in my book are fully based on experimental data. Is QSGUT an ad-hoc thing to be added onto E12, or vice versa? Or are both theories complementary theories (just as Classical Mechanics and Statistical Mechanics are complementary)?

These details that worry you may be ad-hoc parameters. For instance, in the essay contest Tony Smith is using the math of Hua Luogeng to introduce important parameters into the E8 framework. El Naschie and his followers have reproduced particle mass spectra using the Golden Ratio.

We are early on in this game - we do not know how it will play out.

Have Fun!

Ray Munroe

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The golden ratio is as aspect of the 120-cell and occurs in E_8. Tony Smith's writings I find suggestively interesting and at the same time frustrating. There is often little physical input, and he tends to write condensed versions of things that read like numerology. To be honest what Tony writes tends to be a bit autistic-like. There is little physical content, which in a way is where the hard work really is.

The cosmological constant may be due to the geometry of of H_4, which in ~H_4 tessellates AdS. The Enistein field equation ignoring matter-dust is R_{ab} = kΛg_{ab} which is an Einstein space. It is often written that the cosmological constant Λ is due to mass-energy contributions, which is the dark energy. Yet the above little equation really tells us that the cosmological constant is due to nonflatness of the Ricc tensor due to an intrinsic curvature in geometry, and frankly topology. So what we call dark energy may not be a source that curves the geometry of cosmological spacetime, but a manifestation of the quantum topology (topological charges, indices and quantum numbers) that manifest themselves as what we call dark energy.

Lawrence B. Crowell

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The cosmological constant may be due to the geometry of of H_4, which in ~H_4 tessellates AdS. The Enistein field equation ignoring matter-dust is R_{ab} = kΛg_{ab} which is an Einstein space. It is often written that the cosmological constant Λ is due to mass-energy contributions, which is the dark energy. Yet the above little equation really tells us that the cosmological constant is due to nonflatness of the Ricc tensor due to an intrinsic curvature in geometry, and frankly topology. So what we call dark energy may not be a source that curves the geometry of cosmological spacetime, but a manifestation of the quantum topology (topological charges, indices and quantum numbers) that manifest themselves as what we call dark energy.

Lawrence B. Crowell

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Hi all ,

The golden ratio is everywhere in the nature like some others infinities .

It's logic to have this ratio everywhere .You know ,ratios I can give you several kinds .

I understand the confusion dear Lawrence about the topology ,it's evident what after a time the parameters are too numerous to find the truth .But it's interesting ,the intelligence I think will be where...

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The golden ratio is everywhere in the nature like some others infinities .

It's logic to have this ratio everywhere .You know ,ratios I can give you several kinds .

I understand the confusion dear Lawrence about the topology ,it's evident what after a time the parameters are too numerous to find the truth .But it's interesting ,the intelligence I think will be where...

view entire post

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The 120-cell, or H_4, is a system of quaternions. They span a four dimensional space. One set of them have components 1/2(1+sqrt{5}), and 1/2(1+sqrt{5}) from whence comes the golden mean.

Lawrence B. Crowell

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Lawrence B. Crowell

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Dear Lawrence,

Certainly, the E8 has a symmetry of 240=8x2x3x5, and the H4 has a symmetry of 120=4x2x3x5, so the roots of both algebras have "triality" (x3), "pentality" (x5) and "hexality" (x2x3=x6) symmetries (expanding Garrett Lisi's triality concept). The pentality symmetry may be represented by a pentagon. Transcibe a five-pointed star within a pentagon and you will find multiple examples of the Golden Mean. It may be a fundamental aspect of our underlying symmetries, and thus El Naschie's ideas may be justified - besides the fact that the eye is comfortable with that ratio and is is a cool idea with

Dear Jason,

I like the soap bubble idea. The contents of the bubble are "vaporized", but it still maintains structure and a "horizon". After all, my geometries are more based on simplices than a true lattice. Simplices and branes may combine to yield CDT-like "net-branes" that outline your bubbles. Still Hyperspace would have smaller bubbles/ lattice-spacing than Spacetime because it did not experience as much inflation as Spacetime.

Dear Steve,

You mentioned the Neutralino of Supersymmetry. These weird tachyons may have a similar event signature as Supersymmetry - lots of missing mass and lots of missing momentum. One problem with "E12" is that a large number of new particles are predicted. If these particles fall too near the same mass regions, it may be difficult to untangle any data.

Have Fun!

Ray Munroe

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Certainly, the E8 has a symmetry of 240=8x2x3x5, and the H4 has a symmetry of 120=4x2x3x5, so the roots of both algebras have "triality" (x3), "pentality" (x5) and "hexality" (x2x3=x6) symmetries (expanding Garrett Lisi's triality concept). The pentality symmetry may be represented by a pentagon. Transcibe a five-pointed star within a pentagon and you will find multiple examples of the Golden Mean. It may be a fundamental aspect of our underlying symmetries, and thus El Naschie's ideas may be justified - besides the fact that the eye is comfortable with that ratio and is is a cool idea with

Dear Jason,

I like the soap bubble idea. The contents of the bubble are "vaporized", but it still maintains structure and a "horizon". After all, my geometries are more based on simplices than a true lattice. Simplices and branes may combine to yield CDT-like "net-branes" that outline your bubbles. Still Hyperspace would have smaller bubbles/ lattice-spacing than Spacetime because it did not experience as much inflation as Spacetime.

Dear Steve,

You mentioned the Neutralino of Supersymmetry. These weird tachyons may have a similar event signature as Supersymmetry - lots of missing mass and lots of missing momentum. One problem with "E12" is that a large number of new particles are predicted. If these particles fall too near the same mass regions, it may be difficult to untangle any data.

Have Fun!

Ray Munroe

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Dear Lawrence,

An addendum to my last posting... I gave a geometrical example of a five pointed star inscribed within a pentagon without fully explaining the mathematical motivation. These 10 legs (five legs of a pentagon plus five legs of a star) might represent an SO(5) Lie algebra (of order 10) that could "connect" the five components of our pentality symmetry to each other.

Have Fun!

Ray Munroe

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An addendum to my last posting... I gave a geometrical example of a five pointed star inscribed within a pentagon without fully explaining the mathematical motivation. These 10 legs (five legs of a pentagon plus five legs of a star) might represent an SO(5) Lie algebra (of order 10) that could "connect" the five components of our pentality symmetry to each other.

Have Fun!

Ray Munroe

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Hi ,

Dear Dr Cosmic Ray ,

If I resume the Gosset and Lie groups we begin with the abelian 1 .....E6(-78) compact and there 78 after the E6 complex and 156 ...E7(-133)compact 133 and we continue with E7 complex 266 ..E8(-248)rank 0 248...E88 rank 8 .....E8(-24) rank 4 and the max compact subgr....E8 complex 496 after F4(-32) 52 ..F4 complex 104 and ...28....

I see a kind of serie ,a harmonic ,like a sinus .

I can Understand ,what do you think about the 696 729 600 ,this order .

What represent this number .

Do you see a link with the number 45 and 9 .

Why quaternions and octonions are too insert in these imaginaries extrapolations .

Why the superstrings could imply graviton ?

About the golden ratio ,it's indeed obvious ,since a long times.Pythagore knew that ..de vinci ,fibonacci ...and many others .This divin proportion shows us still the evolution and its constants .There are so many ways to find this ratio.In the nature ,if you begin to analyze in details you see the ratios everywhere in the micro and macro fauna and flora .

I am going to continue to find the ratios in the spheres and their volumes .Oh my god ,there too they exist .

It's logic what we see this ratio everywhere ,because like the spheres ,it's foundamental .Thus the ratio will be always the same in all dynamic of evolution .

This ratio has permitted to build beautiful big house and others things ,it will permit many things still in all centers of interest .Like pi ,it's foundamenatl .

A small question ,in our solar system ....we have a sun ,8 planets and x moons ,if you calculate their volumes and their mass and with others parameters ...you find too the golden ratio ,the question is what is the method to find it ,I offer still a beautiful apple from belgium for the first who found .

I d like post some questions too for all ?

Where are the relevances about the quantum architecture and lie groups .

What are the relevances if we insert superstrings or M Theory .

Dear Ray ,

The neutralino is an hypothesis .

Attention I am going to create lol

lol Personaly ,I have invented a spheriton for main central sphere,and activaton for the dark matter ,thus the activaton becomes a spheriton ,the space becomes mass .hihihi lol

The graviton and the spheriton ,the spheriton is the ultim fractal of the graviton .

Laugh is good for health .

Steve

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Dear Dr Cosmic Ray ,

If I resume the Gosset and Lie groups we begin with the abelian 1 .....E6(-78) compact and there 78 after the E6 complex and 156 ...E7(-133)compact 133 and we continue with E7 complex 266 ..E8(-248)rank 0 248...E88 rank 8 .....E8(-24) rank 4 and the max compact subgr....E8 complex 496 after F4(-32) 52 ..F4 complex 104 and ...28....

I see a kind of serie ,a harmonic ,like a sinus .

I can Understand ,what do you think about the 696 729 600 ,this order .

What represent this number .

Do you see a link with the number 45 and 9 .

Why quaternions and octonions are too insert in these imaginaries extrapolations .

Why the superstrings could imply graviton ?

About the golden ratio ,it's indeed obvious ,since a long times.Pythagore knew that ..de vinci ,fibonacci ...and many others .This divin proportion shows us still the evolution and its constants .There are so many ways to find this ratio.In the nature ,if you begin to analyze in details you see the ratios everywhere in the micro and macro fauna and flora .

I am going to continue to find the ratios in the spheres and their volumes .Oh my god ,there too they exist .

It's logic what we see this ratio everywhere ,because like the spheres ,it's foundamental .Thus the ratio will be always the same in all dynamic of evolution .

This ratio has permitted to build beautiful big house and others things ,it will permit many things still in all centers of interest .Like pi ,it's foundamenatl .

A small question ,in our solar system ....we have a sun ,8 planets and x moons ,if you calculate their volumes and their mass and with others parameters ...you find too the golden ratio ,the question is what is the method to find it ,I offer still a beautiful apple from belgium for the first who found .

I d like post some questions too for all ?

Where are the relevances about the quantum architecture and lie groups .

What are the relevances if we insert superstrings or M Theory .

Dear Ray ,

The neutralino is an hypothesis .

Attention I am going to create lol

lol Personaly ,I have invented a spheriton for main central sphere,and activaton for the dark matter ,thus the activaton becomes a spheriton ,the space becomes mass .hihihi lol

The graviton and the spheriton ,the spheriton is the ultim fractal of the graviton .

Laugh is good for health .

Steve

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Dear Sphere-keeper Steve,

Patterns inside ... patterns inside ... patterns... I pray that you do not dream this crazy stuff like I do on occasion. The math part of my brain does not operate as efficiently when I am asleep as when I am awake. Read my book. You will see that “E10”, “E12”, and “E14” are extrapolations of a pattern somewhat similar to the pattern you are identifying.

I like your “spheriton”. We need Higgs or Goldstones or Yukawas or SOMETHING like a Spheriton to break the original symmetry. I am still waiting for one of us to connect the “Mother Sphere” to E-Infinity Theory…

Have Fun! Laughter is good for the soul.

Ray Munroe

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Patterns inside ... patterns inside ... patterns... I pray that you do not dream this crazy stuff like I do on occasion. The math part of my brain does not operate as efficiently when I am asleep as when I am awake. Read my book. You will see that “E10”, “E12”, and “E14” are extrapolations of a pattern somewhat similar to the pattern you are identifying.

I like your “spheriton”. We need Higgs or Goldstones or Yukawas or SOMETHING like a Spheriton to break the original symmetry. I am still waiting for one of us to connect the “Mother Sphere” to E-Infinity Theory…

Have Fun! Laughter is good for the soul.

Ray Munroe

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In the past ,I classed numbers .

the number nine was for me an obsession ,I had my tables .I added all lol.

But when you have this kind of obsession ,you find many interesting ratios ,constants ,harmonics,sinus,periodics ....

Here is for me an interesting add of series when I calculate like a crazzy .

1 3 7 15 31 63 127 255 511 1023.....1/3/7/6/4/9/1/3/7/6/4/9.....1 2 4 8 16...

14/16/17/22/25/26/31/35/38/47/56 ...7/8/4/7/8/4..2/4/7/8....7/10/13/19/22/25/28/31/34/40...1/

4/7...1/4/7....1/2/6/6/3/9/9/9/9/9/36/27/27/45/45/63/63/54/4

5/54.....3/9/9/9/9/18/18/18/27/27/27/18/27/45/36/27/27/45/36

...you can make some graphics .....this number are the result of a sum

The serie 1/2/6/6/3/9/.....comes by 1/2/6/24/120/720/5040/40320/362880/......./2 432 902 008 176 640 000 for the last one.

an other interesting is the link with 3/9/27/81/243/729/...../3 486 784 401/

It was a obsession ,but with that I see still the constant ,the harmonic series,the periodicity ,....

Where is the ratio thus where is the 1+rac 5/2...still a beautifull apple from belgium .Lol

Regards

Steve

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the number nine was for me an obsession ,I had my tables .I added all lol.

But when you have this kind of obsession ,you find many interesting ratios ,constants ,harmonics,sinus,periodics ....

Here is for me an interesting add of series when I calculate like a crazzy .

1 3 7 15 31 63 127 255 511 1023.....1/3/7/6/4/9/1/3/7/6/4/9.....1 2 4 8 16...

14/16/17/22/25/26/31/35/38/47/56 ...7/8/4/7/8/4..2/4/7/8....7/10/13/19/22/25/28/31/34/40...1/

4/7...1/4/7....1/2/6/6/3/9/9/9/9/9/36/27/27/45/45/63/63/54/4

5/54.....3/9/9/9/9/18/18/18/27/27/27/18/27/45/36/27/27/45/36

...you can make some graphics .....this number are the result of a sum

The serie 1/2/6/6/3/9/.....comes by 1/2/6/24/120/720/5040/40320/362880/......./2 432 902 008 176 640 000 for the last one.

an other interesting is the link with 3/9/27/81/243/729/...../3 486 784 401/

It was a obsession ,but with that I see still the constant ,the harmonic series,the periodicity ,....

Where is the ratio thus where is the 1+rac 5/2...still a beautifull apple from belgium .Lol

Regards

Steve

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Thanks ,

You know,for the quantum architecture ,I am persuaded what this architecture is the same in the geometry than the universal future sphere and its spheres in rotations .

Our quantum architecture is like a code of becoming for physical spheres .

Thus we can make a design .

Thus we must find two centers ,the main central quantum sphere and the universal central sphere .

Find the numbers of galaxies ,it's find the number of correlated quantum spheres .and the same with planets ,stars ,moons ,lifes .

When I classed some galaxies and others ,I find an interesting probability for our solar system .Our system is in plan ,this plan is relevant ,the plan permits I think the best interactions of evolution .In my theory of spherization by spheres ,the mass increases ,I think that the plan facilitates these interactions of spherization.Ideed ;imagine the plans like our galaxies ,our planets .It's easier for the gravity .Well thought by the big mathematician .

The quantum architecture is probably in the same optic .But several possibilities are possible about the quantum architecture and the evolution in time space ,the quantum architecture is correlated .But what is the representation ,the actual or the final sphere .All is there .Thus the plans are possible but perhaps no if the quantum architecture is the same than our future universal sphere ,finished thus harmonized in spheres .

If in the future our planets turn around the sun differently ,thus can we interpret the plans in the quantum architecture .

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You know,for the quantum architecture ,I am persuaded what this architecture is the same in the geometry than the universal future sphere and its spheres in rotations .

Our quantum architecture is like a code of becoming for physical spheres .

Thus we can make a design .

Thus we must find two centers ,the main central quantum sphere and the universal central sphere .

Find the numbers of galaxies ,it's find the number of correlated quantum spheres .and the same with planets ,stars ,moons ,lifes .

When I classed some galaxies and others ,I find an interesting probability for our solar system .Our system is in plan ,this plan is relevant ,the plan permits I think the best interactions of evolution .In my theory of spherization by spheres ,the mass increases ,I think that the plan facilitates these interactions of spherization.Ideed ;imagine the plans like our galaxies ,our planets .It's easier for the gravity .Well thought by the big mathematician .

The quantum architecture is probably in the same optic .But several possibilities are possible about the quantum architecture and the evolution in time space ,the quantum architecture is correlated .But what is the representation ,the actual or the final sphere .All is there .Thus the plans are possible but perhaps no if the quantum architecture is the same than our future universal sphere ,finished thus harmonized in spheres .

If in the future our planets turn around the sun differently ,thus can we interpret the plans in the quantum architecture .

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Sorry ,error of posting,

Thus can we insert the plans? ,personaly I think what the quantum architecture is without plan,like the harmonic future sphere ,thus with all balanced and that perfectly.

It's a big question for me ,the problem is not the numbers but the evolution in time space thus what shall be the variables and the foundamentals of the quantum architecture and its spheres in rotations implying mass .

About the E infinity ,it's impssible for me ,the only infinity is behind walls .The infinite fractals aren't foundamentals in the physical dynamics ,the numbers of galaxies is a specific numbers ,stars ,planets too .Thus the numbers of quantum spheres too is specifics and their volumes and rotations too .

The only infinity for me will be at the end of the physical universe ,the pure harmony ,thus the walls shall disappear too ,and the two worlds of entropy shall be in fusion ,like a pure mass and light fusion ,there is an ultim aim .The etrnity will be but the physical universe is limited and that in the quantum towards the cosmological dimension .

The Sphere and its spheres with its smaller spheres and the smallest spheres lol

Ray ,the spheriton ,is probably the biggest volume like the central universal sphere .

Do you know if some researchs focus on the search of this center ,the universal central sphere .We turn around this center ,where is it ?

Steve

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Thus can we insert the plans? ,personaly I think what the quantum architecture is without plan,like the harmonic future sphere ,thus with all balanced and that perfectly.

It's a big question for me ,the problem is not the numbers but the evolution in time space thus what shall be the variables and the foundamentals of the quantum architecture and its spheres in rotations implying mass .

About the E infinity ,it's impssible for me ,the only infinity is behind walls .The infinite fractals aren't foundamentals in the physical dynamics ,the numbers of galaxies is a specific numbers ,stars ,planets too .Thus the numbers of quantum spheres too is specifics and their volumes and rotations too .

The only infinity for me will be at the end of the physical universe ,the pure harmony ,thus the walls shall disappear too ,and the two worlds of entropy shall be in fusion ,like a pure mass and light fusion ,there is an ultim aim .The etrnity will be but the physical universe is limited and that in the quantum towards the cosmological dimension .

The Sphere and its spheres with its smaller spheres and the smallest spheres lol

Ray ,the spheriton ,is probably the biggest volume like the central universal sphere .

Do you know if some researchs focus on the search of this center ,the universal central sphere .We turn around this center ,where is it ?

Steve

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Dear Ray,

The E_8 is a symphony of 2,3,5 and 8. The 120-cell is in a sense half the E_8, and defines an icosian system of quaternions. The system isocian is an extension of SU(4) with the I_2(5). The Dynkin diagram for SU(4) is

o--o--o

and for H_4 there is

o---o--o--o

where the longer --- is the "5" roots of H_4. The 15 dimension of the SU(4) are extended by the "5" with an additional "3" due to a triality condition. An alternate way of seeing this is that since G_2 is automorphism on E_8 there is with S^8 ---> G_2 the addition of 8 dimensions on the elements of SU(4).

The SU(4) ~ SO(4,2) is the group for the AdS. The 8 on 5 folding of the SU(4) is an underlying homotopy with the 5-fold associator.

I have more on this on the section "Out of Plato's Cave?" on this.

Cheers,

LC

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The E_8 is a symphony of 2,3,5 and 8. The 120-cell is in a sense half the E_8, and defines an icosian system of quaternions. The system isocian is an extension of SU(4) with the I_2(5). The Dynkin diagram for SU(4) is

o--o--o

and for H_4 there is

o---o--o--o

where the longer --- is the "5" roots of H_4. The 15 dimension of the SU(4) are extended by the "5" with an additional "3" due to a triality condition. An alternate way of seeing this is that since G_2 is automorphism on E_8 there is with S^8 ---> G_2 the addition of 8 dimensions on the elements of SU(4).

The SU(4) ~ SO(4,2) is the group for the AdS. The 8 on 5 folding of the SU(4) is an underlying homotopy with the 5-fold associator.

I have more on this on the section "Out of Plato's Cave?" on this.

Cheers,

LC

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Dear Lawrence,

Yes, I have been following your conversation with Florin. We all have specialties that do not exactly overlap. I am truly more of a phenomenologist than a theorist, but I am attracted to theory.

OK. I think I have an SO(4,2) related to an M2 of Weak-brane. I think it is an SO(4,2) because the component symmetries break down into a 6+6+3=15, and then the 6's each break into a 4+2. Is this related to an SO(2,4)? I confess that I have gotten beyond my basic understanding of SO(N), SU(N), and E(N) Lie Algebras. I need to finish this rewrite so that you can read the whole thing at one time. I believe our ideas will build on each other.

Have Fun!

Ray

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Yes, I have been following your conversation with Florin. We all have specialties that do not exactly overlap. I am truly more of a phenomenologist than a theorist, but I am attracted to theory.

OK. I think I have an SO(4,2) related to an M2 of Weak-brane. I think it is an SO(4,2) because the component symmetries break down into a 6+6+3=15, and then the 6's each break into a 4+2. Is this related to an SO(2,4)? I confess that I have gotten beyond my basic understanding of SO(N), SU(N), and E(N) Lie Algebras. I need to finish this rewrite so that you can read the whole thing at one time. I believe our ideas will build on each other.

Have Fun!

Ray

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The M2-brane, which is a tachyon condensate in a black hole, has fields which are dual to fields observed by an observer on an event horizon. In this case what I have been working out is with a black hole. When it comes to SO(4,2) this is the Anti-de Sitter group, and I think that the duality holdds with the horizon there, or conformal boundary. To work this out will require placing a BTZ black hole in the *H_4, which contains SU(2,2) ~ SO(4,2) and extending the duality between the conformal boundary of this extended AdS to the horizon of the BTZ black hole. The conformal boundary of the AdS spacetime is a sort of repeller, where clock speeds are observed to increase the closer one observes to it. So the AdS acts as a sort of perfect box that hold the black hole.

E_8 and further the Leech lattice are symponies in 2,3,5,8 and for the Leech lattice also 24. The AdS with SU(2,2) (Euclideanized SU(4)) is 15 dimensional (dimSU(n) = n^2 - 1) , while the "5" and triality "3" impose an "8 times" on this for the 120-cell. Think of this as cooridnates for S^8 at each point. The I_2(5) is an associator which imposes an internal quantum homotopy and the "3" is a set of three elements (spinors) a,b,c for b = a^2, c = a^3 = 1. The SU(4) ~ SO(6), since dimSO(n) = n(n-1)/2.

Lawrence B. Crowell

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E_8 and further the Leech lattice are symponies in 2,3,5,8 and for the Leech lattice also 24. The AdS with SU(2,2) (Euclideanized SU(4)) is 15 dimensional (dimSU(n) = n^2 - 1) , while the "5" and triality "3" impose an "8 times" on this for the 120-cell. Think of this as cooridnates for S^8 at each point. The I_2(5) is an associator which imposes an internal quantum homotopy and the "3" is a set of three elements (spinors) a,b,c for b = a^2, c = a^3 = 1. The SU(4) ~ SO(6), since dimSO(n) = n(n-1)/2.

Lawrence B. Crowell

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Lawrence,

When you mentioned M2 tachyon condensate at the black hole event horizon, can that M2 be adjusted to describe the boundary between our space-time and a worm hole with a much higher speed of light? It would be nice if the model didnn't rely upon extreme gravitational waves. You mentioned M2 a number of times. I am looking for a space-time to hyperspace boundary for purely hypothetical purposes.

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When you mentioned M2 tachyon condensate at the black hole event horizon, can that M2 be adjusted to describe the boundary between our space-time and a worm hole with a much higher speed of light? It would be nice if the model didnn't rely upon extreme gravitational waves. You mentioned M2 a number of times. I am looking for a space-time to hyperspace boundary for purely hypothetical purposes.

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I guess I either wrote badly or am misunderstood. The M2-brane is the singularity of the BH at or near r --> 0. This is however related to the event horizon, for string field theoretic content there has some type of duality with strings on the horizon. Lenny Susskind demonstrated how the string as observed by a distant observer becomes stretched out over the horizon. He illustrates this by looking at a region very near the horizon. The g_{tt} metric component is written as

g_{tt} = (r-2M/r} ~ (r - 2M/2M).

The g_{rr} = 1/g_{tt} is used to compute the proper distance for equal time to the horizon by integrating the square root of this from 2M to r somewhat larger than 2M

R = ∫dr sqrt{2M/(r – 2M)} = sqrt{8M}sqrt{r – 2M},

which serves as a change in coordinates. Now one finds expresses the metric according to R and this gives a local metric similar to the Rindler metric for the accelerated observer. This is easier to work with. An observer who remains outside the horizon will observe the string passing the horizon to redshift and correspondingly it must elongate to make those modes observable. As the observer is removed from the horizon with smaller rapidity, or hyperbolic angle the string exists in a cool vacuum state, but for an observer close to the horizon the situation is hot, with lots of Unruh radiation, and so the string becomes indistinguishable from the vacuum state (or vacuum plus thermal bath). The dual perspective is where the observer (the foolish observer) sees the string on its infalling frame. This perspective has a duality to the Susskind perspective as seen by the wise observer who remains outside the BH.

The M2-brane is then a dual of the physics observed outside the BH, and it is dual to a D5-brane (the NS5-brane) as well. This is then a duality on the “black brane” and the field theoretic construction is reduced to some physics on a 2-dim brane with anyonic statistics. This might have some bearing on Penrose’s objection to the large number of dimensions in M/string theory, as pointed out in his “Road to Reality,” pg 883. While there are lots of variables and modes, this might provide some constraints on the space of solutions.

Cheers,

LC

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g_{tt} = (r-2M/r} ~ (r - 2M/2M).

The g_{rr} = 1/g_{tt} is used to compute the proper distance for equal time to the horizon by integrating the square root of this from 2M to r somewhat larger than 2M

R = ∫dr sqrt{2M/(r – 2M)} = sqrt{8M}sqrt{r – 2M},

which serves as a change in coordinates. Now one finds expresses the metric according to R and this gives a local metric similar to the Rindler metric for the accelerated observer. This is easier to work with. An observer who remains outside the horizon will observe the string passing the horizon to redshift and correspondingly it must elongate to make those modes observable. As the observer is removed from the horizon with smaller rapidity, or hyperbolic angle the string exists in a cool vacuum state, but for an observer close to the horizon the situation is hot, with lots of Unruh radiation, and so the string becomes indistinguishable from the vacuum state (or vacuum plus thermal bath). The dual perspective is where the observer (the foolish observer) sees the string on its infalling frame. This perspective has a duality to the Susskind perspective as seen by the wise observer who remains outside the BH.

The M2-brane is then a dual of the physics observed outside the BH, and it is dual to a D5-brane (the NS5-brane) as well. This is then a duality on the “black brane” and the field theoretic construction is reduced to some physics on a 2-dim brane with anyonic statistics. This might have some bearing on Penrose’s objection to the large number of dimensions in M/string theory, as pointed out in his “Road to Reality,” pg 883. While there are lots of variables and modes, this might provide some constraints on the space of solutions.

Cheers,

LC

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Lawrence,

Thank you for elaborating on these ideas. I'm afraid I do not have a PhD in string theory so it's a bit of a challenge to keep up.

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Thank you for elaborating on these ideas. I'm afraid I do not have a PhD in string theory so it's a bit of a challenge to keep up.

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I didn't do string theory as a thesis, I studied straight general relativity. String theory is something I have learned on the side or since then.

LC

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LC

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Whats the difference between "observer_dependant" and "co-ordinate_dependant" ?..is this akin to the Holographic Principle?..being an observer is at a co-ordinate (locaztion)..and thus his/her observations are dependant, or can vary? The input_ouput of certain Blackholes can and will have varying consequences, based on where and more importantly WHEN one exists?

For instance an infalling photon energy may be "tagged" as an "outfalling" or ejected Electron from blackhole horizons that are time dependant?

It's not that blackholes condense's matter, matter actually condense's a Black-Hole ;)

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For instance an infalling photon energy may be "tagged" as an "outfalling" or ejected Electron from blackhole horizons that are time dependant?

It's not that blackholes condense's matter, matter actually condense's a Black-Hole ;)

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Lawrence,

As an expert in General Relativity, you must have a very good understanding of time dialation effects. I remember reading that physicists proved that an airplane, with a higher potential energy in a gravitational field, had a slower running atomic clock then the stationary one on the ground. I think the airplane clock ran slightly slower because it had, overall, more kinetic energy (1/2mv2) and more potential energy (mgd). In your opinion, would that be a correct interpretation?

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As an expert in General Relativity, you must have a very good understanding of time dialation effects. I remember reading that physicists proved that an airplane, with a higher potential energy in a gravitational field, had a slower running atomic clock then the stationary one on the ground. I think the airplane clock ran slightly slower because it had, overall, more kinetic energy (1/2mv2) and more potential energy (mgd). In your opinion, would that be a correct interpretation?

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The observer dependency is of course with the frame. If this is in reference to string and black holes, there are two basic frames. The first frame is one where the observer stays outside the black hole, what I call the wise observer, who observes a string from afar. The other frame is for an observer who falls into the BH, the foolish observer, on a frame coincident with the string. Physics should be independent of the frame on is on. There might be some changes due to Doppler shifting and other covariant effects, but these differences should be transformable into each other so that the underlying physical principles are the same in all choices of frames. Physics should be independent of any coordinate system or frame on imposes on the problem. That is the gist of what I think occurs here with BHs.

Jason: This is indeed the case and was a topic I worked on with respect to GPS systems. Given an array of satellites with atomic clocks one wants to have them synchronized. A drift in the relative time measure of such atomic clocks will translate into a drift in a measured position on Earth. Distances are measured by radar delay times or laser ranging. So it is important to get clocks synchronized properly.

cheers,

Lawrence B. Crowell

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Jason: This is indeed the case and was a topic I worked on with respect to GPS systems. Given an array of satellites with atomic clocks one wants to have them synchronized. A drift in the relative time measure of such atomic clocks will translate into a drift in a measured position on Earth. Distances are measured by radar delay times or laser ranging. So it is important to get clocks synchronized properly.

cheers,

Lawrence B. Crowell

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Lawrence,

Satellites move pretty fast so relative velocity contributes to relativistic time dialation effects. But does their altitude within the earth's gravitational field, with respect to satellite dishes on the earth, add any relativistic contribution? Would a satellite that was in geosynchronous orbit above my satellite dish, thus zero relative velocity, still experience relativistic time dialation effects because the satellite is at a higher altitude within the earths gravity field?

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Satellites move pretty fast so relative velocity contributes to relativistic time dialation effects. But does their altitude within the earth's gravitational field, with respect to satellite dishes on the earth, add any relativistic contribution? Would a satellite that was in geosynchronous orbit above my satellite dish, thus zero relative velocity, still experience relativistic time dialation effects because the satellite is at a higher altitude within the earths gravity field?

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Jason,

Let me try to answer your questions. There are 2 basic effects here. First, an atomic clock in an airplane will register a different time than an identical clock at rest on the ground. The reason is that when the plane moves, this causes time dilations and length contractions. This happens regardless of the altitude of the plane and is dependent only on the plane speed.

However, there is a second effect. Think of a black hole. Light cannot escape from it. Why? As light moves out, it uses energy to climb against the gravitational potential. But energy is proportional with frequency, and as the light wave climbs up, its wavelength become larger and larger (or its frequency is smaller and smaller). (Now in a black hole the gravitational attraction is so big that the wavelength becomes infinite and its energy becomes zero before it can completely escape, but on Earth the effect is much less dramatic, almost zero.). What this has to do with clocks you may ask? I can use the light wave to act as a clock. Closer to the ground, you have high energy, high frequency, and time runs slow (Time =1/frequency). As you move up in the gravitational potential, light’s energy is smaller (it has to compensate the gravitational potential energy), frequency is lower, and the local time runs fast. Bottom line: stationary clocks run faster at higher altitudes than at lower ones.

Both effects are very small (nanoseconds), but significant enough for the GPS system to make adjustments for it.

Florin

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Let me try to answer your questions. There are 2 basic effects here. First, an atomic clock in an airplane will register a different time than an identical clock at rest on the ground. The reason is that when the plane moves, this causes time dilations and length contractions. This happens regardless of the altitude of the plane and is dependent only on the plane speed.

However, there is a second effect. Think of a black hole. Light cannot escape from it. Why? As light moves out, it uses energy to climb against the gravitational potential. But energy is proportional with frequency, and as the light wave climbs up, its wavelength become larger and larger (or its frequency is smaller and smaller). (Now in a black hole the gravitational attraction is so big that the wavelength becomes infinite and its energy becomes zero before it can completely escape, but on Earth the effect is much less dramatic, almost zero.). What this has to do with clocks you may ask? I can use the light wave to act as a clock. Closer to the ground, you have high energy, high frequency, and time runs slow (Time =1/frequency). As you move up in the gravitational potential, light’s energy is smaller (it has to compensate the gravitational potential energy), frequency is lower, and the local time runs fast. Bottom line: stationary clocks run faster at higher altitudes than at lower ones.

Both effects are very small (nanoseconds), but significant enough for the GPS system to make adjustments for it.

Florin

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Thanks florin for saving me from carpel tunel (sp). That is basically the case. The velocity of a body and its position in the gravity field contribut to a time dilation given by

t’ = t*sqrt(1 – (v/c)^2), t’ = t*sqrt(1 – 2GM/rc^2),

due to special relativity and gravity. These get mixed up and it is not hard to see this if you play with the Schwarschild metric, divide through by ds^2, get the 4-velocities U^a = dx^a/ds and do some algebra.

The magnitudes are small. A spacecraft in Earth orbit is about v = 7km/sec, and so v/c ~ 2e-5 and so a clock on a spacecraft moving at this velocity has a clock that ticks 0.999999999728 seconds for every second your clock ticks. That is not a big effect, one part in 5.4e-10. If I multiply that by the speed of light ~ 3e8m/s this amounts to an error in distance of 16 cm every second. It is not much with the time error, but the distance error is significant. Much the same holds for gravity. G/c^2 ~ 6.7e-11/9e16 = 7.4e-28 The earth has a mass ~ 5.7e24kg, and the radius of the earth is 6400km = 6.4e6m. So the gravity factor is 2GM/rc^2 ~ 1.3e-10. Now to be honest we have to consider the change in radial distance, so most GPS satellites are at half geosynchronous and for the sake of brevity we can ignore the gravity there since it is much smaller. So the time change is a 0.99999999868 difference. So the geosynch sat sees an earthbound clock tick that many second for every second it ticks off. That is a 1.32e-9 difference, which is larger. Others might want to check my numbers.

These clocks need to be adjusted accordingly. Otherwise it is clear that you will get meters worth of drift within a few seconds, kilometer drifts within less than an hour and so forth.

Cheers,

LC

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t’ = t*sqrt(1 – (v/c)^2), t’ = t*sqrt(1 – 2GM/rc^2),

due to special relativity and gravity. These get mixed up and it is not hard to see this if you play with the Schwarschild metric, divide through by ds^2, get the 4-velocities U^a = dx^a/ds and do some algebra.

The magnitudes are small. A spacecraft in Earth orbit is about v = 7km/sec, and so v/c ~ 2e-5 and so a clock on a spacecraft moving at this velocity has a clock that ticks 0.999999999728 seconds for every second your clock ticks. That is not a big effect, one part in 5.4e-10. If I multiply that by the speed of light ~ 3e8m/s this amounts to an error in distance of 16 cm every second. It is not much with the time error, but the distance error is significant. Much the same holds for gravity. G/c^2 ~ 6.7e-11/9e16 = 7.4e-28 The earth has a mass ~ 5.7e24kg, and the radius of the earth is 6400km = 6.4e6m. So the gravity factor is 2GM/rc^2 ~ 1.3e-10. Now to be honest we have to consider the change in radial distance, so most GPS satellites are at half geosynchronous and for the sake of brevity we can ignore the gravity there since it is much smaller. So the time change is a 0.99999999868 difference. So the geosynch sat sees an earthbound clock tick that many second for every second it ticks off. That is a 1.32e-9 difference, which is larger. Others might want to check my numbers.

These clocks need to be adjusted accordingly. Otherwise it is clear that you will get meters worth of drift within a few seconds, kilometer drifts within less than an hour and so forth.

Cheers,

LC

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Hi Ray,

Here is a quick answer to your earlier question. SO(2,4) is basically the same as SO(4,2). But let's not discuss SO(2,4) and consider SO(1,3) instead for simplicity reasons. SO(1,3) is the same as SO(3,1); it is a matter of convention: some books consider the Minkowski distance positive for space and negative for time, while others the other way around, but the physics is the same in both cases. To be fully pedantic though, there is a mathematical difference, but in general SO(p,q) is isomorphic with SO(q,p) for any p,q and for physics it makes no difference.

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Here is a quick answer to your earlier question. SO(2,4) is basically the same as SO(4,2). But let's not discuss SO(2,4) and consider SO(1,3) instead for simplicity reasons. SO(1,3) is the same as SO(3,1); it is a matter of convention: some books consider the Minkowski distance positive for space and negative for time, while others the other way around, but the physics is the same in both cases. To be fully pedantic though, there is a mathematical difference, but in general SO(p,q) is isomorphic with SO(q,p) for any p,q and for physics it makes no difference.

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Hey Lawrence,

As an expert in general relativity I was wondering what do you think about time travel?

Thanks,

Florin

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As an expert in general relativity I was wondering what do you think about time travel?

Thanks,

Florin

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Thanks Florin!

So it doesn't matter whether we call it SU(2,2) or SO(4,2) or SO(2,4), it represents a 3+6+6=15 symmetry, just like SU(4) and SO(6) both represent a 15-plet.

If I am working in four Spacetime dimensions plus two M2-brane Weak-brane dimensions, is it preferable to use the SO(4,2) terminology over the SU(2,2) terminology?

I'm probably making this harder than it is...

Ray

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So it doesn't matter whether we call it SU(2,2) or SO(4,2) or SO(2,4), it represents a 3+6+6=15 symmetry, just like SU(4) and SO(6) both represent a 15-plet.

If I am working in four Spacetime dimensions plus two M2-brane Weak-brane dimensions, is it preferable to use the SO(4,2) terminology over the SU(2,2) terminology?

I'm probably making this harder than it is...

Ray

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Florin,

In my mind, you are a genius! I've been wracking my brain for months trying to understand the deeper reality behind the mathematical physics. I had no idea that the frequency and wavelength of the photon, as it transmits energy between observers, could be the one thing that makes all of it makes sense. The photon, as a particle-wave, has duals of Energy/time, location/space, etc. In its inate nature of exp(kx-wt), it binds together space and time because it is bound by energy conservation.

I had almost given up on the hyperdrive. I have been wrestling with the nature of space/space-time (what is it made of, etc) and how is distance between objects enforced. What if virtual photons are being radiated and absorbed by everything? What if objects cannot even evolve in time unless they can exchange virtual photons with their environment?

What do you call an ocean of virtual photons that are always being emitted and absorbed (without us even noticing)? Because of their momentum/position duality, they conserve momentum. Because of their energy/time duality, they cause (1) objects to evolve in time, and (2) conserve energy. What do you call an ocean of virtual photons? One big photon? Space-time?

As for a hyperdrive, I need to find this non-existent aether.

Ray,

IMO, yes, you're making it too hard. :-)

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In my mind, you are a genius! I've been wracking my brain for months trying to understand the deeper reality behind the mathematical physics. I had no idea that the frequency and wavelength of the photon, as it transmits energy between observers, could be the one thing that makes all of it makes sense. The photon, as a particle-wave, has duals of Energy/time, location/space, etc. In its inate nature of exp(kx-wt), it binds together space and time because it is bound by energy conservation.

I had almost given up on the hyperdrive. I have been wrestling with the nature of space/space-time (what is it made of, etc) and how is distance between objects enforced. What if virtual photons are being radiated and absorbed by everything? What if objects cannot even evolve in time unless they can exchange virtual photons with their environment?

What do you call an ocean of virtual photons that are always being emitted and absorbed (without us even noticing)? Because of their momentum/position duality, they conserve momentum. Because of their energy/time duality, they cause (1) objects to evolve in time, and (2) conserve energy. What do you call an ocean of virtual photons? One big photon? Space-time?

As for a hyperdrive, I need to find this non-existent aether.

Ray,

IMO, yes, you're making it too hard. :-)

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Jason,

We spoke of photons and virtual photons as "disturbances" months ago. What was the sudden eureka moment or insight that has made the difference?

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We spoke of photons and virtual photons as "disturbances" months ago. What was the sudden eureka moment or insight that has made the difference?

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Ray,

Not always, it depends on your usage. Lie groups are describing continuous symmetries. In the neighborhood of the identity element of a Lie group, (which is also a manifold), the tangent plane creates a linear Lie algebra. Being a linear structure, it is more or less unique, and the same linear Lie algebra can correspond to different Lie groups. Those groups can have different global properties based on their topology. So while SU(2,2) is locally isomorphic with SO(2,4) or SO(4,2), it is not globally isomorphic with them. Think of the Earth and the Mercator map for example. Each point on the map corresponds to a point on Earth, but while map is a flat rectangle, and the Earth is a sphere. For all practical purposes SO(2,4) and SO(4,2) are the same, while SO(2,4) and SU(2,2) are not. In mathematical terms, SU(2,2)=Spin(4,2) is a double cover for SO(4,2) .

Florin

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Not always, it depends on your usage. Lie groups are describing continuous symmetries. In the neighborhood of the identity element of a Lie group, (which is also a manifold), the tangent plane creates a linear Lie algebra. Being a linear structure, it is more or less unique, and the same linear Lie algebra can correspond to different Lie groups. Those groups can have different global properties based on their topology. So while SU(2,2) is locally isomorphic with SO(2,4) or SO(4,2), it is not globally isomorphic with them. Think of the Earth and the Mercator map for example. Each point on the map corresponds to a point on Earth, but while map is a flat rectangle, and the Earth is a sphere. For all practical purposes SO(2,4) and SO(4,2) are the same, while SO(2,4) and SU(2,2) are not. In mathematical terms, SU(2,2)=Spin(4,2) is a double cover for SO(4,2) .

Florin

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Florin, agreed about the indices on group notation. It is really an arbitary signature. The SU(4) is a covering of SO(5), which extends to double indexed groups as well. SU(2,2) means that AdS conformal gravity is a curious mirror of QCD.

Time travel is unlikely, as are other exotic spacetime solutions. I don't have a lot of time right now, and today has been a bit tough with time. Yet the momentum-energy source in the Einstein field equation for these solutions violates the Hawking-Penrose energy conditions. This means that for the weak energy condition T^{00} < 0. This is a disaster for quantum field theory. It means there are no eigenstates bounded below. This means a quanta can transition down an infinite ladder and emit an infinite amount of radiation. This vast amount of energy couples back on the spacetme to generate enormous spacetime flutuations which ... well it is a mess.

Frankly understanding the universe and quantum gravity/cosmology will be a lot simplet if time travel is forbidden. It is tough enough as it is, but with closed timelike loops quantum gravity/cosmology would be horrendous. I think quantum gravity will rule out time travel, just as QED removed some spurious solutions of classical electrodynamics.

Lawrence B. Crowell

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Time travel is unlikely, as are other exotic spacetime solutions. I don't have a lot of time right now, and today has been a bit tough with time. Yet the momentum-energy source in the Einstein field equation for these solutions violates the Hawking-Penrose energy conditions. This means that for the weak energy condition T^{00} < 0. This is a disaster for quantum field theory. It means there are no eigenstates bounded below. This means a quanta can transition down an infinite ladder and emit an infinite amount of radiation. This vast amount of energy couples back on the spacetme to generate enormous spacetime flutuations which ... well it is a mess.

Frankly understanding the universe and quantum gravity/cosmology will be a lot simplet if time travel is forbidden. It is tough enough as it is, but with closed timelike loops quantum gravity/cosmology would be horrendous. I think quantum gravity will rule out time travel, just as QED removed some spurious solutions of classical electrodynamics.

Lawrence B. Crowell

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Jason,

You are kidding, right :) ? If I am that smart, how come I do not have the Nobel Prize yet? But hey, if you like my explanations, please read my Essay contest entry: http://www.fqxi.org/community/forum/topic/473 and comment on it.

F

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You are kidding, right :) ? If I am that smart, how come I do not have the Nobel Prize yet? But hey, if you like my explanations, please read my Essay contest entry: http://www.fqxi.org/community/forum/topic/473 and comment on it.

F

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Lawrence,

Of course there is no time travel, but why? I worked on this problem for some time and proven by a gedanken experiment that time travel is not possible in classical mechanics and by extension in physics in the range of the validity of the correspondence principle, and I am always looking to strengthen the result if possible.

Florin

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Of course there is no time travel, but why? I worked on this problem for some time and proven by a gedanken experiment that time travel is not possible in classical mechanics and by extension in physics in the range of the validity of the correspondence principle, and I am always looking to strengthen the result if possible.

Florin

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Georgina,

I'm trying to work out the bugs in my interpretation, but here is what I think.

Photons are the ABSOLUTE implementers of space and time (space-time); I haven't forgotten about gravitons and Higgs particles. Photons are THE reason why mathematical physics works. A photon emission radiates outward as a spherical wavefront of radius R=ct. Within the photon described by A exp [i(kx-wt)], space, time, momentum conservation, and energy conservation are all implemented.

My intuition tells me this (sorry, not a math proof): Every photon, regardless of its energy, will transmit to whatever detected it, the identical unit of energy-time; we know that unit of energy-time as h-bar = 6.6x10-34 J-s. In other words, every photon carries the same amount of energy-time. The Uncertainty Principle delta x delta p = delta E delta t >= h-bar has something to do with how momentum and energy conservation. The relative position and momentum between two objects can be implemented because virtual photons (spherical wave fronts of velocity c)are exchanging h-bar between the two objects. Causality is implemented as the delta t. I'll have to figure out how to understand/articulate this a little better.

I had to abandon the photon disturbance idea because Relativity kept reminding me that the speed of light is absolute for all observers. The interconnectivity between everything (every particle) is best implemented by virtual photons, spherical wavefronts whose oscillations are bound by kx-wt (momentum, location, frequency, causality). Particles interconnected by vibrating strings has problems because the connecting strings are not dynamic and don't re-emit frequently.

I think the density of space-time implementing virtual photons has something to do with the Cosmological constant (vacuum pressure).

Florin,

I want to read your paper; it's been incredibly busy. As it is, my girlfriend made me promise not to talk about physics tonight. Obviously, I will have to ask her for forgiveness. I think I'm a physics addict.

Oh, and I'm with Lawrence on time travel; it's restricted. You'll have to learn to ask for forgiveness and release the past. Also, please don't make me have to re-live my life's experiences because you want to time travel.

Lawrence,

Did you just say that there is no bottom for eigenstates? Doesn't that make the Alcubierre hyperdrive physically possible now?

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I'm trying to work out the bugs in my interpretation, but here is what I think.

Photons are the ABSOLUTE implementers of space and time (space-time); I haven't forgotten about gravitons and Higgs particles. Photons are THE reason why mathematical physics works. A photon emission radiates outward as a spherical wavefront of radius R=ct. Within the photon described by A exp [i(kx-wt)], space, time, momentum conservation, and energy conservation are all implemented.

My intuition tells me this (sorry, not a math proof): Every photon, regardless of its energy, will transmit to whatever detected it, the identical unit of energy-time; we know that unit of energy-time as h-bar = 6.6x10-34 J-s. In other words, every photon carries the same amount of energy-time. The Uncertainty Principle delta x delta p = delta E delta t >= h-bar has something to do with how momentum and energy conservation. The relative position and momentum between two objects can be implemented because virtual photons (spherical wave fronts of velocity c)are exchanging h-bar between the two objects. Causality is implemented as the delta t. I'll have to figure out how to understand/articulate this a little better.

I had to abandon the photon disturbance idea because Relativity kept reminding me that the speed of light is absolute for all observers. The interconnectivity between everything (every particle) is best implemented by virtual photons, spherical wavefronts whose oscillations are bound by kx-wt (momentum, location, frequency, causality). Particles interconnected by vibrating strings has problems because the connecting strings are not dynamic and don't re-emit frequently.

I think the density of space-time implementing virtual photons has something to do with the Cosmological constant (vacuum pressure).

Florin,

I want to read your paper; it's been incredibly busy. As it is, my girlfriend made me promise not to talk about physics tonight. Obviously, I will have to ask her for forgiveness. I think I'm a physics addict.

Oh, and I'm with Lawrence on time travel; it's restricted. You'll have to learn to ask for forgiveness and release the past. Also, please don't make me have to re-live my life's experiences because you want to time travel.

Lawrence,

Did you just say that there is no bottom for eigenstates? Doesn't that make the Alcubierre hyperdrive physically possible now?

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All of these strange solutions violate an energy condition. The standard one is the averaged weak energy condition T^{00} < 0. Wormholes, Albucierre warp drives, Krasnikov tubes and other strange spacetime configurations have some violation. The momentum energy tensor is built up from the Lagrangian of the source field of the spacetime curvature T^{ab} = ∂L/∂g_{ab} – g^{ab}L. The semi-classical source < |T^{ab}| > < 0 will produce an exotic spacetime, but the Hamiltonian for this has no lower bound.

Of course we might be confronted with this as a troublesome fact. If quantum physics can have no bounded eigenvalues then this suggests something is deeply wrong with out understanding of nature. As with classical mechanics, Kip Thorne argues that some classical systems exist which prevent closed timelike curves. Of course those are also a problem, for they involve a singular condition on a Cauchy horizon and possible infinite windings of loops. The problem with Kip’s argument IMO is that classical physics most often exhibits nonlinear chaos. So trajectories densely cover phase space, which means at a minimum there exist paths which come within an “epsilon” of being a closed curve.

Of course these tings are bread and butter for science fiction. Yet it appears that nature forbids these things. Florin’s essay on axiomatization is somewhat commensurate with this. We might not be able to understand physical principles completely from pure math, but we might at least be able to say what they are not. Physical and causal principles should at least not be logically contradictory. These solutions are connected with closed timelike loops, or time travel, and it is not hard to imagine how this leads to logical contradictions.

Cheers,

LC

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Of course we might be confronted with this as a troublesome fact. If quantum physics can have no bounded eigenvalues then this suggests something is deeply wrong with out understanding of nature. As with classical mechanics, Kip Thorne argues that some classical systems exist which prevent closed timelike curves. Of course those are also a problem, for they involve a singular condition on a Cauchy horizon and possible infinite windings of loops. The problem with Kip’s argument IMO is that classical physics most often exhibits nonlinear chaos. So trajectories densely cover phase space, which means at a minimum there exist paths which come within an “epsilon” of being a closed curve.

Of course these tings are bread and butter for science fiction. Yet it appears that nature forbids these things. Florin’s essay on axiomatization is somewhat commensurate with this. We might not be able to understand physical principles completely from pure math, but we might at least be able to say what they are not. Physical and causal principles should at least not be logically contradictory. These solutions are connected with closed timelike loops, or time travel, and it is not hard to imagine how this leads to logical contradictions.

Cheers,

LC

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Dear Lawrence and Florin,

Thank you for the information on SO(2,4) vs. SO(4,2) vs. SU(2,2).

Lawrence - I understand that you like the SU(2,2) terminology because it mirrors SU(3). I might be leaning towards the SO(2,4) terminology becuase an SO(2,4) (of Hyperflavor) on an M2-brane complements an SO(5,1) (of WIMP-Gravity) on the dual M5-brane. Furthermore, (2+4)+(5+1)=12 indicates how the 12 dimensions of E12 fragment, and shows the close compatibility with M-Theory's 4+2+5=11 (of Spacetime plus M2-brane plus M5-brane). I just have an extra 1-D string to explain...

Jason - I am also a physics addict, and my wife gets jealous of it at times as well...

Have Fun!

Ray Munroe

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Thank you for the information on SO(2,4) vs. SO(4,2) vs. SU(2,2).

Lawrence - I understand that you like the SU(2,2) terminology because it mirrors SU(3). I might be leaning towards the SO(2,4) terminology becuase an SO(2,4) (of Hyperflavor) on an M2-brane complements an SO(5,1) (of WIMP-Gravity) on the dual M5-brane. Furthermore, (2+4)+(5+1)=12 indicates how the 12 dimensions of E12 fragment, and shows the close compatibility with M-Theory's 4+2+5=11 (of Spacetime plus M2-brane plus M5-brane). I just have an extra 1-D string to explain...

Jason - I am also a physics addict, and my wife gets jealous of it at times as well...

Have Fun!

Ray Munroe

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Lawrence,

I agree with your arguments, but all this is known and the ultimate position the defenders of time travel are taking is that the final physical theory does not yet exist and as long as the impossibility is not proven in quantum gravity, there is still hope. We therefore need an ultimate proof.

I think the case against time travel is settled for classical mechanics, but not in quantum mechanics. Hawking came close using a back-reaction argument, but Matt Visser found a counter argument using the semi-classical approximation.

Also there is this paper some time ago by Greenberger and Svozil:

http://arxiv.org/abs/quant-ph/0506027 arguing (naively) for time travel. Non-interacting fields do not have unitarity violations even in a CTC region, but the moment you try to measure something you run into problems as pointed by Jacobson. Still, suppose you do not measure anything, can we prove explicitly that in general an interacting field cannot escape unitarity problems? (And do not use the correspondence principle in the argument?)

Florin

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I agree with your arguments, but all this is known and the ultimate position the defenders of time travel are taking is that the final physical theory does not yet exist and as long as the impossibility is not proven in quantum gravity, there is still hope. We therefore need an ultimate proof.

I think the case against time travel is settled for classical mechanics, but not in quantum mechanics. Hawking came close using a back-reaction argument, but Matt Visser found a counter argument using the semi-classical approximation.

Also there is this paper some time ago by Greenberger and Svozil:

http://arxiv.org/abs/quant-ph/0506027 arguing (naively) for time travel. Non-interacting fields do not have unitarity violations even in a CTC region, but the moment you try to measure something you run into problems as pointed by Jacobson. Still, suppose you do not measure anything, can we prove explicitly that in general an interacting field cannot escape unitarity problems? (And do not use the correspondence principle in the argument?)

Florin

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A quantum loop is possible. For a closed timelike loop that encloses a spacetime area ~ x^2, and in the conjugate momentum variable an area ~ p^2 then if

(px)^2 = (nħ)^2

I am not unhappy with that. This is not too dissimilar to some quantum optical results that show for small numbers of particles or modes there can be reversals of the 2 nd law of thermodynamics. This means there can in a Feynman path integral be particle paths that travel back in time. By x^2 we might think of this as a little parallelogram with one side spatial and the other time. The loop is then approximated by this little area. We might simplify further by making this a square with side x = ct, for t the vertical. We then make this distance x = nL_{Plank}, for n the number of Planck lengths. We then have xct = n^2L^2_{p} or

xct = n^2(Għ/c^3).

The momentum loop would then be on the order of

p^2 = (mħ)^2/(n^2(Għ/c^3)) = (m/n)^2(ħc^3/G) = (m/n)^2M^2_pc^2,

where the numbers m and n are likely the same, or at least not widely different from each other. M_p is the Planck mass, and the first equation can be seen as a Heisenberg uncertainty principle. So it is easy to suppose that closed timelike loops occur on a quantal level near the Planck scale.

Cheers,

LC

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(px)^2 = (nħ)^2

I am not unhappy with that. This is not too dissimilar to some quantum optical results that show for small numbers of particles or modes there can be reversals of the 2 nd law of thermodynamics. This means there can in a Feynman path integral be particle paths that travel back in time. By x^2 we might think of this as a little parallelogram with one side spatial and the other time. The loop is then approximated by this little area. We might simplify further by making this a square with side x = ct, for t the vertical. We then make this distance x = nL_{Plank}, for n the number of Planck lengths. We then have xct = n^2L^2_{p} or

xct = n^2(Għ/c^3).

The momentum loop would then be on the order of

p^2 = (mħ)^2/(n^2(Għ/c^3)) = (m/n)^2(ħc^3/G) = (m/n)^2M^2_pc^2,

where the numbers m and n are likely the same, or at least not widely different from each other. M_p is the Planck mass, and the first equation can be seen as a Heisenberg uncertainty principle. So it is easy to suppose that closed timelike loops occur on a quantal level near the Planck scale.

Cheers,

LC

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Florin,

I'm just curious. Would you settle for a "time travel" event that is very limited? Let's take an apple in a refrigerator for 6months. After 6months, it rots. If there were no causality events that pass into or out of this space; if nobody opened the refrigerator, and the temperature stayed the same; with no causality issues, maybe you could, hypothetically, run the clock backwards in time, at least until the last causality event that crossed the threshold.

Am I explaining it clearly?

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I'm just curious. Would you settle for a "time travel" event that is very limited? Let's take an apple in a refrigerator for 6months. After 6months, it rots. If there were no causality events that pass into or out of this space; if nobody opened the refrigerator, and the temperature stayed the same; with no causality issues, maybe you could, hypothetically, run the clock backwards in time, at least until the last causality event that crossed the threshold.

Am I explaining it clearly?

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Lawrence,

Sure, there is no problem at that scale. Even at higher scales it is possible as long as no one sees it. In a Feynman diagram those propagators can run forward and backward in time with no problem. Also we never observe bare particles and the self-interaction loops are renormalized in the end.

The correspondence principle which I use to prove my impossibility of the time travel result is mathematically very complex and I was just wondering if you had any other insight into the time travel problem that I did not consider before.

Speaking of the correspondence principle, I understand you too consider our universe to be unique. Here is then a puzzle by Guth: if there is no multiverse, then why is our universe happening only once? I speculate that the correspondence principle is indirectly related to this problem, but I want to hear your position first.

Jason,

I am sorry to disappoint, time travel exists only in science fiction. If not, either all sorts of paradoxes can happen or there is no free will and I was predestined to write this sentence from the time of the Big Bang.

Florin

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Sure, there is no problem at that scale. Even at higher scales it is possible as long as no one sees it. In a Feynman diagram those propagators can run forward and backward in time with no problem. Also we never observe bare particles and the self-interaction loops are renormalized in the end.

The correspondence principle which I use to prove my impossibility of the time travel result is mathematically very complex and I was just wondering if you had any other insight into the time travel problem that I did not consider before.

Speaking of the correspondence principle, I understand you too consider our universe to be unique. Here is then a puzzle by Guth: if there is no multiverse, then why is our universe happening only once? I speculate that the correspondence principle is indirectly related to this problem, but I want to hear your position first.

Jason,

I am sorry to disappoint, time travel exists only in science fiction. If not, either all sorts of paradoxes can happen or there is no free will and I was predestined to write this sentence from the time of the Big Bang.

Florin

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Florin,

In the science fiction version of time travel, the whole univers is rewinded back in time, but the traveler is unaffected. I don't like that idea. But if you do the reverse, a spherical region of radius R. Inside of this region, the clock is rewinded, but the rest of the universe is unaffected. Any causal event that crosses the surface, in either direction, will restrict time travel. Causality, I assume, occurs at the speed of light.

I just thought it was an interesting idea that might be useful to understand the physics better.

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In the science fiction version of time travel, the whole univers is rewinded back in time, but the traveler is unaffected. I don't like that idea. But if you do the reverse, a spherical region of radius R. Inside of this region, the clock is rewinded, but the rest of the universe is unaffected. Any causal event that crosses the surface, in either direction, will restrict time travel. Causality, I assume, occurs at the speed of light.

I just thought it was an interesting idea that might be useful to understand the physics better.

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I had another epiphany. The reversable time field inside of a spherical region of radius R is not a time machine; it's a 'rejuvenation machine'. You can look at sci-fi time travel as rejuvenation of the universe while leaving the 'time traveler' unchanged. But here is the cool part. If, as I speculated, virtual photons implement space-time, then we know how to avoid space-time. If I block incoming and outgoing virtual photons (the possible implementers of space-time) with some speculative surface that either reflects or absorbs ,at the boundary, all virual photons, would that be sufficient to remove everything inside this region from space-time itself? I think that might be helpful in getting into hyperspace.

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On another thread about "Why this universe?" the question is posed as to why the universe exists. The answer might just be that nothingness is unstable. The universe is a map from |Ψ>_i to |Ψ>_f. The intitial state is some Hilbert-like state vector over a super-group G with all dimensions, 27 or 26 for J^3(O) or the 26-dim string, or equivlanetly 10-11 dimensions for the number...

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Electromagnetic space (e.g., photons and the Sun) is both larger and smaller than typical or ordinary space (including the Earth). Any theory that unifies gravity and electromagnetism must describe a space that is BOTH larger and smaller at once. With scale unified, the force strengths become identical; and gravity and electromagnetism can be understood as repulsive and attractive.

Also note that perceptual distance and actual distance in relation to time are variable.

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Also note that perceptual distance and actual distance in relation to time are variable.

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There is nothing, actually absolutely NOTHING in existence that does not travel in time? Time travel is a part of our Universe physical process. What cannot happen is anything can travel away from the time domain, and thus everything in the now..today, and re-appear with

information about the journey. There is no light being emmited ia "yesterday"..the Sun has moved in "time" from yesterday to today..a now. You can only violate Relativity if your xistence is allready away, or specifically outside of "NOW".

Electrons can flit to and fro, so can neutrino's ossilate in and out of the "NOW" boundary of spacetime. To travel away from today bacwards, into yesterday, would need all the atomic structure that was part of "yesterday" to travel back with you, there are catagorically no atomic structure available in "yesterday" they are only available "today"..now, with a small percentage laying the foundations for tomorrow!

Forget any violation yester_daytips to any "yesterday", there is nothing there to intaract with, no light, think about this, there will be no visable light to bounce of atoms and enter your eye and reveal real_ative objects. Yesterday is dark, the day before is darker and last year darker still, first light is actually at the darkest location in the Universe!

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information about the journey. There is no light being emmited ia "yesterday"..the Sun has moved in "time" from yesterday to today..a now. You can only violate Relativity if your xistence is allready away, or specifically outside of "NOW".

Electrons can flit to and fro, so can neutrino's ossilate in and out of the "NOW" boundary of spacetime. To travel away from today bacwards, into yesterday, would need all the atomic structure that was part of "yesterday" to travel back with you, there are catagorically no atomic structure available in "yesterday" they are only available "today"..now, with a small percentage laying the foundations for tomorrow!

Forget any violation yester_daytips to any "yesterday", there is nothing there to intaract with, no light, think about this, there will be no visable light to bounce of atoms and enter your eye and reveal real_ative objects. Yesterday is dark, the day before is darker and last year darker still, first light is actually at the darkest location in the Universe!

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Paul,

I agree with you, there is only NOW. We are not frames on some movie projector; I agree, we have the freedeom to choose. I also strongly dislike the idea of an infinite number of identical worlds; that only works well in science fiction.

But the of this time travel business got me thinking about thermodynamics. It's impossible to push the whole universe backwards in time (except for the time traveler), like they do in time traveling movies. But when we consider rewinding time inside of a small region R (e.g. a lead box), we still have causality issues. In my opinion, there are virtual photons (Higgs/gravitions?) that continuously update the universe by transfering energy, momentum, time and space information to surrounding particles. I believe that is what keeps the universe and space-time consistent and conserved. Photons are quantum particles with wave function descriptions. That means they can be detected. Another way of describing 'detection' is that some other quantum particle can be the lucky recipient of all of the virutal photon's energy, momentum, and causality information. I expect there are plenty of virtual photons to go around.

To truly run the clock back, everything inside of the region R (the lead box) would have to get back all of those virtual (and real) photons, and also at the right phase for each. Obviously, that's not possible. But if it were, it would mean that whatever is inside of the region R (e.g. an apple) would have all of the photons come back to it, at just the right phase, to just the right proton, neutron, electron, in such a way as to precisely push it back the thermodynamic pathway that it came down. In other words, I suspect that the virtual photons, by virtue of their momentum, frequency, phase information, can choose just the right eigenstate for each quantum particle.

In a nutshell, eigenstates are chosen by these virtual photons (gravitons/Higgs) by presenting the right momentum, energy, phase.

I'm not stating these as facts; I'm just throwing the idea out there to see if either it sounds plausible or it violates Hiesenberg's Uncertainty Principle. I'm not taking a measurement, I am attempting to preprogram a planck unit (J-s) with a particular momentum/phase/frequency in order to select the desired eigenstate of a system.

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I agree with you, there is only NOW. We are not frames on some movie projector; I agree, we have the freedeom to choose. I also strongly dislike the idea of an infinite number of identical worlds; that only works well in science fiction.

But the of this time travel business got me thinking about thermodynamics. It's impossible to push the whole universe backwards in time (except for the time traveler), like they do in time traveling movies. But when we consider rewinding time inside of a small region R (e.g. a lead box), we still have causality issues. In my opinion, there are virtual photons (Higgs/gravitions?) that continuously update the universe by transfering energy, momentum, time and space information to surrounding particles. I believe that is what keeps the universe and space-time consistent and conserved. Photons are quantum particles with wave function descriptions. That means they can be detected. Another way of describing 'detection' is that some other quantum particle can be the lucky recipient of all of the virutal photon's energy, momentum, and causality information. I expect there are plenty of virtual photons to go around.

To truly run the clock back, everything inside of the region R (the lead box) would have to get back all of those virtual (and real) photons, and also at the right phase for each. Obviously, that's not possible. But if it were, it would mean that whatever is inside of the region R (e.g. an apple) would have all of the photons come back to it, at just the right phase, to just the right proton, neutron, electron, in such a way as to precisely push it back the thermodynamic pathway that it came down. In other words, I suspect that the virtual photons, by virtue of their momentum, frequency, phase information, can choose just the right eigenstate for each quantum particle.

In a nutshell, eigenstates are chosen by these virtual photons (gravitons/Higgs) by presenting the right momentum, energy, phase.

I'm not stating these as facts; I'm just throwing the idea out there to see if either it sounds plausible or it violates Hiesenberg's Uncertainty Principle. I'm not taking a measurement, I am attempting to preprogram a planck unit (J-s) with a particular momentum/phase/frequency in order to select the desired eigenstate of a system.

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Florin,

I'm still reading your paper during a very busy schedule. A heuristic approach is a great idea, but I doubt it can be boiled down to a mathematical system. I think by heuristic, you mean the process of reaching beyond a set of axioms.

I liked the idea of separating pure mathematics from mathematical physics that is based on experiments. With experimentally confirmed axioms, you can probably program a computer to shuffle/combine them in new ways. You might be able to get some mathematical GUT. In my personal opinion, even a GUT will not predict everything that could possibly be observed. There are emergent properties that the mathematics simply cannot describe.

It is fun to hypothesise from the mathematical physics. In some cases, the decision to spend a lot of money to build a tool or facility because the math says there is something useful there is a reasonable idea. But no mathematical theory will ever be conceived that will make experiments unnecesary; that, I will guarantee.

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I'm still reading your paper during a very busy schedule. A heuristic approach is a great idea, but I doubt it can be boiled down to a mathematical system. I think by heuristic, you mean the process of reaching beyond a set of axioms.

I liked the idea of separating pure mathematics from mathematical physics that is based on experiments. With experimentally confirmed axioms, you can probably program a computer to shuffle/combine them in new ways. You might be able to get some mathematical GUT. In my personal opinion, even a GUT will not predict everything that could possibly be observed. There are emergent properties that the mathematics simply cannot describe.

It is fun to hypothesise from the mathematical physics. In some cases, the decision to spend a lot of money to build a tool or facility because the math says there is something useful there is a reasonable idea. But no mathematical theory will ever be conceived that will make experiments unnecesary; that, I will guarantee.

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Lawrence,

It is amazing how we arrive at very similar conclusions from so different points of view. So again I agree with your position.

When you have a hammer, everything looks like a nail. So back to the corresponding principle I obsessed about: It turns out that there are only 3 possible solution representations of a quantal algebra. (a quantal algebra is a algebra based on 3 identities: Jacobi, Leibniz, and Petersen and is the unique mathematical structure arising from the correspondence principle) Those 3 solutions are QM, classical mechanics and a contextual QM based on split-complex numbers. My speculation is that the split-complex QM acts as the generator of universes, which are more or less identical. It would be interesting to try doing string theory and LQG with split-complex QM and see if it generates anything interesting. In that case SO(2,4) is replaced by SO(3,3).

Florin

PS: your argument for the space dimensionality based on Ricci and Weyl curvature is very interesting. I have a vague recollection I heard something similar, in Penrose’s before the big bang idea if I am not mistaken, I will need to look it up.

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It is amazing how we arrive at very similar conclusions from so different points of view. So again I agree with your position.

When you have a hammer, everything looks like a nail. So back to the corresponding principle I obsessed about: It turns out that there are only 3 possible solution representations of a quantal algebra. (a quantal algebra is a algebra based on 3 identities: Jacobi, Leibniz, and Petersen and is the unique mathematical structure arising from the correspondence principle) Those 3 solutions are QM, classical mechanics and a contextual QM based on split-complex numbers. My speculation is that the split-complex QM acts as the generator of universes, which are more or less identical. It would be interesting to try doing string theory and LQG with split-complex QM and see if it generates anything interesting. In that case SO(2,4) is replaced by SO(3,3).

Florin

PS: your argument for the space dimensionality based on Ricci and Weyl curvature is very interesting. I have a vague recollection I heard something similar, in Penrose’s before the big bang idea if I am not mistaken, I will need to look it up.

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Jason,

Than you for taking the time to read my essay. You state: “no mathematical theory will ever be conceived that will make experiments unnecesary;”. Here I disagree. There is no conceivable way to experimentally test the physics at the Plank scale. So what can we do in this case? How can we distinguish between competing theories like string theory, loop quantum gravity, non-commutative geometry, etc? If there is no way to settle the differences, then we will never be able to understand nature, and this is not true based on prior history. Mankind had always found a way to advance the understanding of nature. Maybe will not be done by us because our biases prohibit us to find the solution, but by our children and grandchildren.

Thanks again for reading my paper, and if you disagree with it, or with my answer above, please reply directly in the essay section so that other people can see and join the discussion.

Florin

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Than you for taking the time to read my essay. You state: “no mathematical theory will ever be conceived that will make experiments unnecesary;”. Here I disagree. There is no conceivable way to experimentally test the physics at the Plank scale. So what can we do in this case? How can we distinguish between competing theories like string theory, loop quantum gravity, non-commutative geometry, etc? If there is no way to settle the differences, then we will never be able to understand nature, and this is not true based on prior history. Mankind had always found a way to advance the understanding of nature. Maybe will not be done by us because our biases prohibit us to find the solution, but by our children and grandchildren.

Thanks again for reading my paper, and if you disagree with it, or with my answer above, please reply directly in the essay section so that other people can see and join the discussion.

Florin

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The final endpoint of this cosmological evolution indicates an evolution where the extra dimensions of the system are compactified and three spatial dimensions and one time dimension are large on the final state. This physics appears involved with the M2-brane with singularities and the anyonic physics involved. The three dimensions here are scalars, out of 27 for the Jordan system J^3(O) over...

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Nicely put Lawrence, I do favour certain phase evolutions, and there are a number of spanners that Ed Witten tried to resolve, which only resulted in moving the Proton decay Z goalposts"?

A quantum bang >>> cosmic crunch, a cosmic bang >> quantum crunch?

or sequence of cosmic string evolution, maybe?

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A quantum bang >>> cosmic crunch, a cosmic bang >> quantum crunch?

or sequence of cosmic string evolution, maybe?

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The word phase here is used to describe the structure of matter, such as a phase transition to superconductivity or the onset of Meissner effect at a critical temperature. I think this is possibly the missing ingredient in the landscape problem. The quantum amplitude for cosmology is selected for as the one which exhibits a quantum phase transition, similar to the breakdown of a Landau electron fluid and quasi-particle generation.

Lawrence B. Crowell

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Lawrence B. Crowell

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Florin,

I am happy that you have vigorously established your opposing viewpoint; I was concerned I had overstated your veiw as an extreme. My position is that there is no end to the universe's ability to surprise us. There will always be either emerging phenomena that can't be expressed by the mathematics, or perhaps even new phenomena caused by the way the mathematical universe is actually implemented. But I am happy to see you embrace your extreme view. I know that it will tempt the universe to prove you wrong. Perhaps a 14 billion year old universe finds humor in making fools of us all.

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I am happy that you have vigorously established your opposing viewpoint; I was concerned I had overstated your veiw as an extreme. My position is that there is no end to the universe's ability to surprise us. There will always be either emerging phenomena that can't be expressed by the mathematics, or perhaps even new phenomena caused by the way the mathematical universe is actually implemented. But I am happy to see you embrace your extreme view. I know that it will tempt the universe to prove you wrong. Perhaps a 14 billion year old universe finds humor in making fools of us all.

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Lawrence,

I see basically 2 problems for the end of the universe idea. First, the proton must decay. Second, the cosmological constant defines a temperature. How would a black hole evaporate when its temperature will fall below that temperature? The first problem is not a show stopper, because the charge of the electron exactly balances the one of the proton and this point towards a common origin, meaning a GUT. It is very likely any GUT will have at least a mechanism of cross talk, hence a decay channel. The second problem is more serious and I am not sure how to overcome it at this point.

Florin

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I see basically 2 problems for the end of the universe idea. First, the proton must decay. Second, the cosmological constant defines a temperature. How would a black hole evaporate when its temperature will fall below that temperature? The first problem is not a show stopper, because the charge of the electron exactly balances the one of the proton and this point towards a common origin, meaning a GUT. It is very likely any GUT will have at least a mechanism of cross talk, hence a decay channel. The second problem is more serious and I am not sure how to overcome it at this point.

Florin

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Jason,

Please see my reply in the essay section. I agree, my ideas are a paradigm changer (and therefore extreme) and I will gladly defend them with (hopefully) convincing arguments. Please do not be afraid to hold any punches. I am pretty confident my ideas will be able to withstand any criticism because I was thinking about this for a rather long time and what I present in the essay is not a quick speculation put together for the essay contest.

Florin

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Please see my reply in the essay section. I agree, my ideas are a paradigm changer (and therefore extreme) and I will gladly defend them with (hopefully) convincing arguments. Please do not be afraid to hold any punches. I am pretty confident my ideas will be able to withstand any criticism because I was thinking about this for a rather long time and what I present in the essay is not a quick speculation put together for the essay contest.

Florin

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The largest most massive black holes, 10billion solar masses or so, will decay in about 10^{100} years. So from 10^{50} to 10^{100} years a region bounded by the de Sitter cosmological horizon will have a black hole that slowly decays. The Hawking-Gibbon temperature of the cosmological horizon is far smaller than the temperature of even these thunderous boomer black holes. So after about 10^100 years the cosmological horizon should then just recede away to infinity as it emits the very weak form of radiation. The cosmological horizon will recede away, getting larget in fact, where significant changes will happen over incredibly long time frames of 10^{10^{10^100}}} years. It will take an infinite time for it to recede away to infinity.

Proton decay has a half life of about 10^{30} years. Around that time the galaxy clusters will be isolated in their cosmological "cacoon," and composed largely of stellar mass and larger black holes. As exponential expansion takes place these systems will become drawn apart, and those strongly enough bound together will form into large black holes.

It is a sort of dark, cold and bleak outlook for things. Yet I think that the universe will approach asymptotically a final state of being a Minkowski spacetime.

LC

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Proton decay has a half life of about 10^{30} years. Around that time the galaxy clusters will be isolated in their cosmological "cacoon," and composed largely of stellar mass and larger black holes. As exponential expansion takes place these systems will become drawn apart, and those strongly enough bound together will form into large black holes.

It is a sort of dark, cold and bleak outlook for things. Yet I think that the universe will approach asymptotically a final state of being a Minkowski spacetime.

LC

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Florin.there is no Proton decay in this Universe?..the proton decay at the dark far off future, is the "phase transition", or quantum tunneling process into the "next" cyclonic Universe process ! The "last" Photon in this Universe is transformed into the "first" Electron of the next Universe ]:

Via a short Quantum Tunnel of course.

Following observers, if they generate into similar type species, will have to develop a Theory Of Entropic States, or 10 dim T.O.E.S at least!

best p.v

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Via a short Quantum Tunnel of course.

Following observers, if they generate into similar type species, will have to develop a Theory Of Entropic States, or 10 dim T.O.E.S at least!

best p.v

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Proton decay is occurring right now, if the gauge field structure permits it. The universe will in around 10^{30} have decayed away about half of its current protons. The universe will generally be described from 10^{50}-10^{100} years as a de Sitter spacetime with a black hole in each Hubble region. Black holes will quantum decay away and the universe will then settle into a pure de Sitter vacuum state. Then Hawking-Gibbon radiation will decay the cosmological horizon which will over a fantastically vast time period removed the horizon to infinity. The universe will then end up as a pure Minkowski spacetime or void.

The distant future of the universe can only be inferred from working physics. We will not be around to observe this. There of course might be some phase change in the universe which adjusts the cosmological constant rapidly to some new value.

Cheers LC

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The distant future of the universe can only be inferred from working physics. We will not be around to observe this. There of course might be some phase change in the universe which adjusts the cosmological constant rapidly to some new value.

Cheers LC

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