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RECENT FORUM POSTS

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Grounded physicists are exploring the use of online and virtual-reality conferencing, and AI-controlled experiments, to maintain social distancing. Post-pandemic, these positive innovations could make science more accessible and environmentally-friendly.

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FQXi FORUM

January 19, 2021

CATEGORY:
Questioning the Foundations Essay Contest (2012)
[back]

TOPIC: Dark Energy or a Simple Mistake: Do We Understand How Non-Unique the Einstein Tensor Actually Is? by Jeff Baugher [refresh]

TOPIC: Dark Energy or a Simple Mistake: Do We Understand How Non-Unique the Einstein Tensor Actually Is? by Jeff Baugher [refresh]

The cosmological constant, within the Einstein field equation (EFE), is the leading method to account for the discovered accelerating expansion of the universe, whether or not an underlying cause is understood. The Einstein tensor within the EFE has proven to be the only tensor that meets a number of properties (divergence-free second rank tensor, etc.) as derived from the Riemann curvature tensor and the metric g. We point out however, simply from summation of tensors and the fundamental theorem of calculus, that this uniqueness of properties does not extend to a differential equation with a non-zero constant of integration. It is important to fully understand why these properties are required to maintain our current cosmological model of attractive gravity. If this were in error it would raise profound questions of how the accelerating expansion relates to not only a gravitationally repulsive cosmological constant, but to our entire understanding of physics.

The author is currently a PhD candidate in Dayton OH USA, after receiving his BSEE in 2008. Recently, during dissertation research, he became interested in elasticity tensors, the history of field theory and the paradox of the accelerating expansion.

In addition, for those interested in Lorentzian Ether Theory, I used the following forum to help me work through pedagogical difficulties, ways to simplify my argument to a few pages and to gain feedback on any logical inconsistencies. Cosmoquest ATM Thread for Resurrection of the Lorentzian Aether

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After conversations on here, it may be useful to have a simple graphical understanding of how positive curvature can produce either attractive or repulsive gravity. Simple sketch picture is attached. Only one of these naturally produces a dark energy effect.

attachments: Attractive_or_Repulsive.jpg

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attachments: Attractive_or_Repulsive.jpg

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I had some more questions being asked so made up this Powerpoint to help relay the idea. This was quickly done so let me know if you catch any mistakes.

attachments: Poisson_equation_and_metaphysics.pptx

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attachments: Poisson_equation_and_metaphysics.pptx

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Jeff,

You commented about my essay about the unification of gravity with the electromagnetic force and mentioned that my essay dovetailed with your essay. Actually, the book behind my essay covers a broader range of physics topics including the cosmological implications of using the starting assumption that the universe is only spacetime. With this assumption the expansion of the proper volume of the universe is explained as resulting from the transformation of the properties of spacetime. This transformation started with the Big Bang and continues today. This alternative model of cosmology entirely changes the perspective on dark energy and the cosmological constant. It is not possible to explain the implications for dark energy in this short post, but details are available here.

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You commented about my essay about the unification of gravity with the electromagnetic force and mentioned that my essay dovetailed with your essay. Actually, the book behind my essay covers a broader range of physics topics including the cosmological implications of using the starting assumption that the universe is only spacetime. With this assumption the expansion of the proper volume of the universe is explained as resulting from the transformation of the properties of spacetime. This transformation started with the Big Bang and continues today. This alternative model of cosmology entirely changes the perspective on dark energy and the cosmological constant. It is not possible to explain the implications for dark energy in this short post, but details are available here.

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John,

Found and downloaded your book. Look forward to getting into the details of your explanation as your descriptions seems to match some of the conclusions I have come to through another route.

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Found and downloaded your book. Look forward to getting into the details of your explanation as your descriptions seems to match some of the conclusions I have come to through another route.

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Dear Jeff Baugher,

Improbability of Gravitational collapse due to the acceleration of the expansion of existing universe is indicative of a Segmental universe in homeomorphism, in that the expansion of the observable segment of the existing universe is accelerating for the observer within that segment.

With best wishes,

Jayakar

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Improbability of Gravitational collapse due to the acceleration of the expansion of existing universe is indicative of a Segmental universe in homeomorphism, in that the expansion of the observable segment of the existing universe is accelerating for the observer within that segment.

With best wishes,

Jayakar

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Dear Jeff Baugher,

Let me refer you to an excellent essay (topic 1372), titled "Misinterpreting Reality: Confusing Mathematics for Physics" by Robert H McEachern in this contest. He says, "Equations contain very little information. This fact is what makes it possible to symbolically represent them, in a computer memory, by a very small number of bits. As a direct result of this fact, we can conclude, contrary to the fervent belief of most physicists, that equations cannot describe anything other than the most trivial physical phenomenon; those nearly devoid of all information. For complex phenomenon, it is the vast information content of the initial conditions (like the content of an observer's memory) rather than the tiny information content of equations, that really matters."

In general, I agree with your arguments. However, in my opinion, main strength of the mathematicl model of GR, (including EFE) is that it can be adjusted to simulate the Newtonian gravitation with the additional provision that a finite speed of propagation of gravitational influence is built in the model.

Regards

G S Sandhu

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Let me refer you to an excellent essay (topic 1372), titled "Misinterpreting Reality: Confusing Mathematics for Physics" by Robert H McEachern in this contest. He says, "Equations contain very little information. This fact is what makes it possible to symbolically represent them, in a computer memory, by a very small number of bits. As a direct result of this fact, we can conclude, contrary to the fervent belief of most physicists, that equations cannot describe anything other than the most trivial physical phenomenon; those nearly devoid of all information. For complex phenomenon, it is the vast information content of the initial conditions (like the content of an observer's memory) rather than the tiny information content of equations, that really matters."

In general, I agree with your arguments. However, in my opinion, main strength of the mathematicl model of GR, (including EFE) is that it can be adjusted to simulate the Newtonian gravitation with the additional provision that a finite speed of propagation of gravitational influence is built in the model.

Regards

G S Sandhu

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GS Sandhu,

I have obtained a copy of your paper that you linked to. I see where we have differing opinions on whether the manifold can be considered a physical 4 dimensional medium. We are both ending up at the same conclusion, but you are further along than I am so I look forward to learning the details of where the differences lie.

Regards,

Jeff Baugher

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I have obtained a copy of your paper that you linked to. I see where we have differing opinions on whether the manifold can be considered a physical 4 dimensional medium. We are both ending up at the same conclusion, but you are further along than I am so I look forward to learning the details of where the differences lie.

Regards,

Jeff Baugher

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GS Sandhu,

I am examining your paper published in Physics Essays more in depth. You state: "The GR is based on Riemannian 3D space in which the points of the space continuum are not considered invariant." Do you not mean a 4D space where the 3 spatial bases are not invariant? If not, can you explain more in depth?

Regards,

Jeff

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I am examining your paper published in Physics Essays more in depth. You state: "The GR is based on Riemannian 3D space in which the points of the space continuum are not considered invariant." Do you not mean a 4D space where the 3 spatial bases are not invariant? If not, can you explain more in depth?

Regards,

Jeff

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GS Sandhu,

In reference to equation (24) of your paper, just to make sure, the term with mass in it should >>1 and not

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In reference to equation (24) of your paper, just to make sure, the term with mass in it should >>1 and not

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Forum testing of Mimetex.

Does not seem to recognize addition symbol, there should be a plus sign between two 1s and oplus signs below

Seems to recognize rest of characters ~!@#$%^&*()_+`1234567890-=

?,./:";'

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Does not seem to recognize addition symbol, there should be a plus sign between two 1s and oplus signs below

Seems to recognize rest of characters ~!@#$%^&*()_+`1234567890-=

?,./:";'

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To help explain this essay better, and perhaps invite some more conversation, I present here what I consider to be a mathematical proof of our biggest physical misunderstanding, and a proof against General Relativity (and Einstein's actual biggest blunder).

(note that the addition sign is not working on my preview so I have substitued the oplus symbol)

The most general equation formed from the metric guv and the Riemann tensor is

In keeping with this essay contest, lets change the symbols for the cosmological constant and the Einstein tensor so that we do not confuse what these are thought to physically represent and thus leave only a mathematical meaning. Then we can have

Let the condition

apply. This then becomes:

so that

If we now also add the condition that

then this requires

This is a special case which results in the Einstein tensor since

and so

which is substituted back in after pulling a -1 from the coefficients of L_{uv} in the third equation back.

Therefore, while the regular Einstein field equation with the Einstein tensor and no cosmological constant is correct, no multiple of the metric can be summed with the Einstein tensor. If a multiple of the metric is required, then L_{uv} must be substituted for G_{uv} first. This provides a proof against attractive gravity and numerous other physical explanations of the geometric theory of gravity.

Thoughts?

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(note that the addition sign is not working on my preview so I have substitued the oplus symbol)

The most general equation formed from the metric guv and the Riemann tensor is

In keeping with this essay contest, lets change the symbols for the cosmological constant and the Einstein tensor so that we do not confuse what these are thought to physically represent and thus leave only a mathematical meaning. Then we can have

Let the condition

apply. This then becomes:

so that

If we now also add the condition that

then this requires

This is a special case which results in the Einstein tensor since

and so

which is substituted back in after pulling a -1 from the coefficients of L

Therefore, while the regular Einstein field equation with the Einstein tensor and no cosmological constant is correct, no multiple of the metric can be summed with the Einstein tensor. If a multiple of the metric is required, then L

Thoughts?

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Dear Jeff Baugher

Your essay was well written and I enjoyed reading it, I'll have to reread it again to understand some of your reasoning. This is why I like science we have so many different interpretations of what is real and what is an illusion. Some of the great scientist before us resolved some of these issues but by doing so they created more unresolved questions, that's where we come in.

In my opinion the paradox of the rapid expansion of the universe may be a simply process of universe rejuvenation, matter is broken down to its infinitesimally smallest parts, bosons, through the weak force interactions, black holes, supernova's etc where there diamagnetic-like mutual repulsion of each other is feeding the expansion of the universe. Dark energy and dark matter is said to make up as much as 95 percent of the universe and growing, yet we know very little about what it is made out of. The way I see it matter is radiating away at a much faster pace than we currently predict the universe will suddenly deflate (deflation) back into a singularity. The deflation won't be caused by gravitational influences, it will be caused by a universe wide collapsing condensate, Higgs field collapse.

As I said before Jeff I enjoyed reading your essay, good luck.

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Your essay was well written and I enjoyed reading it, I'll have to reread it again to understand some of your reasoning. This is why I like science we have so many different interpretations of what is real and what is an illusion. Some of the great scientist before us resolved some of these issues but by doing so they created more unresolved questions, that's where we come in.

In my opinion the paradox of the rapid expansion of the universe may be a simply process of universe rejuvenation, matter is broken down to its infinitesimally smallest parts, bosons, through the weak force interactions, black holes, supernova's etc where there diamagnetic-like mutual repulsion of each other is feeding the expansion of the universe. Dark energy and dark matter is said to make up as much as 95 percent of the universe and growing, yet we know very little about what it is made out of. The way I see it matter is radiating away at a much faster pace than we currently predict the universe will suddenly deflate (deflation) back into a singularity. The deflation won't be caused by gravitational influences, it will be caused by a universe wide collapsing condensate, Higgs field collapse.

As I said before Jeff I enjoyed reading your essay, good luck.

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Ron,

Thanks for taking the time to read my essay. The goal I am striving for is to be able to take someone who has an understanding of calculus, give them a mathematical argument, and then let them be able to compare that to published literature on General Relativity prior to the discovery of dark energy. Section 17.3 of Gravitation by Misner, Thorne and Wheeler is probably the leading text and a great section to compare my argument to. Someone who is capable of doing this should come to the same conclusion as I, that the argument corrects a well known (but currently accepted since it came to fit our physical understanding) error induced into GR that comes about from putting the cosmological constant in, but also means that the physical models within GR cannot possibly be correct.

I agree with your sentiments on being able to consider arguments and analogies put forth in the quest to understand our universe. I look forward to understanding the arguments that you present in your essay also.

Jeff

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Thanks for taking the time to read my essay. The goal I am striving for is to be able to take someone who has an understanding of calculus, give them a mathematical argument, and then let them be able to compare that to published literature on General Relativity prior to the discovery of dark energy. Section 17.3 of Gravitation by Misner, Thorne and Wheeler is probably the leading text and a great section to compare my argument to. Someone who is capable of doing this should come to the same conclusion as I, that the argument corrects a well known (but currently accepted since it came to fit our physical understanding) error induced into GR that comes about from putting the cosmological constant in, but also means that the physical models within GR cannot possibly be correct.

I agree with your sentiments on being able to consider arguments and analogies put forth in the quest to understand our universe. I look forward to understanding the arguments that you present in your essay also.

Jeff

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Dear Jeff,

I do not follow your ideas absolutely. What do you try to prove, or what you hope that your calculations will prove? I do not see meaning of your quantities Omega and L in equations (3) and (4). What they mean and what do you try to prove with them? Is vectorial r in eq. (5) and (6) unit vector? In opposite case r^3 should be in denominatror.

Otherwise, it seems to me, that you have good ideas with divergence free tensor G.

(BTW: Can you give, as expert, simple explanation for 8Pi factor in EFE?)

Did you read essay of Petkov? I recommend, maybe it is connected with your ideas.

What is your opinion of quantum gravity equation of Hadley

= 8 pi

http://www2.warwick.ac.uk/fac/sci/physics/staff/academic/mha

dley/papers/thesis/thesis.pdf

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I do not follow your ideas absolutely. What do you try to prove, or what you hope that your calculations will prove? I do not see meaning of your quantities Omega and L in equations (3) and (4). What they mean and what do you try to prove with them? Is vectorial r in eq. (5) and (6) unit vector? In opposite case r^3 should be in denominatror.

Otherwise, it seems to me, that you have good ideas with divergence free tensor G.

(BTW: Can you give, as expert, simple explanation for 8Pi factor in EFE?)

Did you read essay of Petkov? I recommend, maybe it is connected with your ideas.

What is your opinion of quantum gravity equation of Hadley

= 8 pi

http://www2.warwick.ac.uk/fac/sci/physics/staff/academic/mha

dley/papers/thesis/thesis.pdf

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Janko,

Thank you for the questions. First for your questions: Yes, the r with the vector symbol is a unit vector. See page 186 of General Relativity:An Introduction for Physicists for the normal equation with the cosmological constant (but as the authors note does not fit with our understanding of current physics) also shows that there is no r^{3} (since the nature of an Omega term does not allow the volume to be modeled as a point).

I have not found a definitive derivation of the 8pi, although I have looked.

I had not run across the Hadley thesis and I find it an excellent read. I would have to go more in depth but his thoughts are similar to mine. What I would add in with his equation is that the expected value of the quantum vacuum is a "potential" energy that might be designated as a multiple of the metric but that there is no known method to combine this with the expected value of G_{uv}.

I will look at the Petkov more in depth also.

Let me try another approach to explain this as compared to GR. In some ways, the whole problem also seems to stem from a notation problem.

Let us take the tensors for Omega and L, looking at this in an abstract manner without consideration of the meaning and derivation of T_{uv} yet, and let us assign some scalar values as a teaching tool. Looking at equation (3), assign the number 10^{100} to Omega, and let's refer to this as the curvature potential of spacetime. Then to G we will assign the curvature number due to matter viewed as a particle present at a point in spacetime, and to L we assign the curvature magnitude due to matter viewed as a wave at a point in spacetime. (apologies if a addition sign is missing) You can see that these would be of an opposite nature (can use either/or but not both at same time). From (4) we can see as G increases from zero, which is flat spacetime, the particle density must be increasing since the curvature is increasing. Likewise for the matter as waves, for flat spacetime L_{uv} is of an equal but opposite value of Omega g_{uv}. When the wave density increases, L_{uv} decreases in magnitude away from 10^{100} so that the curvature increases. You can view matter as a particle or a wave, but not both at the same time. This is what I mean by a notation mistake. The most general equation from the Riemann and metric is only written in the literature as but this is bad notational form, since strictly speaking the tensor "G_{uv}" in this equation does not technically have to equate to the Einstein tensor. It only is equivalent if the multiple of the metric in the equation is zero. Riemannian geometry should certainly have no preference for either way.

This explanation above might give someone who has studied deSitter space a fit. In deSitter space, there is no matter present so it is stated G_{uv} is zero, but as explained in GR there is a multiple of the metric remaining which of course means that there is curvature, which is now linked to the cosmological constant problem and dark energy, which doesn't seem to make sense mathematically and hasn't yet been explained physically. In addition, MTW explains why simply adding the cosmological constant creates mathematical difficulties. In my view this is akin to epicycles, where new empirical evidence causes one to simply attempt to justify adding new features. While that may have worked for Neptune, I think it may be time to instead go back to the original equation and take another look.

This leaves several reasons for why, if I have a choice, to prefer the L_{uv} with a multiple of the metric as waves.

1. The most general equation includes a constant of integration but there is no mathematical logic for preferring this to be zero, even with zero curvature. (Vacuum energy is a physical argument introduced by Zeldovich)

2. The L_{uv} version allows this multiple of the metric to exist, even with a very flat spacetime as measured by WMAP.

3. If one estimeates what the vector field for the Newtonian spherical mass gradient would appear like through L_{uv}, then it is of course an opposing gradient as the Newtonian one, but with the minus sign the gradients are mathematically equal. However, this should tend to make repulsive gravity seem like attraction at a distance.

4. The multiple Omega with the metric cannot be ignored in the Newtonian spherical mass gradient, but it would appear that this results in a point where the unit vector of the gravity switches to an opposite sign at a predictable point.

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Thank you for the questions. First for your questions: Yes, the r with the vector symbol is a unit vector. See page 186 of General Relativity:An Introduction for Physicists for the normal equation with the cosmological constant (but as the authors note does not fit with our understanding of current physics) also shows that there is no r

I have not found a definitive derivation of the 8pi, although I have looked.

I had not run across the Hadley thesis and I find it an excellent read. I would have to go more in depth but his thoughts are similar to mine. What I would add in with his equation is that the expected value of the quantum vacuum is a "potential" energy that might be designated as a multiple of the metric but that there is no known method to combine this with the expected value of G

I will look at the Petkov more in depth also.

Let me try another approach to explain this as compared to GR. In some ways, the whole problem also seems to stem from a notation problem.

Let us take the tensors for Omega and L, looking at this in an abstract manner without consideration of the meaning and derivation of T

This explanation above might give someone who has studied deSitter space a fit. In deSitter space, there is no matter present so it is stated G

This leaves several reasons for why, if I have a choice, to prefer the L

1. The most general equation includes a constant of integration but there is no mathematical logic for preferring this to be zero, even with zero curvature. (Vacuum energy is a physical argument introduced by Zeldovich)

2. The L

3. If one estimeates what the vector field for the Newtonian spherical mass gradient would appear like through L

4. The multiple Omega with the metric cannot be ignored in the Newtonian spherical mass gradient, but it would appear that this results in a point where the unit vector of the gravity switches to an opposite sign at a predictable point.

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To make it clearer, when L_{uv} is equal to Omega g_{uv}, there are no matter waves present and thus spacetime is flat.

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I could not write Hadley equation properly, so I repeat.

Its equation is 4.7 on the page 61.

It is < G > = 8 pi < T >

He ignored 8 pi.

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Its equation is 4.7 on the page 61.

It is < G > = 8 pi < T >

He ignored 8 pi.

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After reviewing the thesis some more, I would have to retract what I stated above. It does sound like I agree more with the paper they are criticizing. A specific reason why is if Omega g_{uv} is linked to the curvature potential/potential energy of all quantum harmonic oscillators for a point in spacetime, then L_{uv} would represent the remaining unoccupied states. Thus 8pi< T> represents those states that are occupied. Since I think that the Omega g_{uv}-L_{uv} is going to model gravity better, then I think that in a very real sense

"where the average is over an ensemble of possible outcomes, but it cannot reasonably give the exact value of the curvature due to a single particle as an average of all the things that might happen!"

is what may actually prove to be true.

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"where the average is over an ensemble of possible outcomes, but it cannot reasonably give the exact value of the curvature due to a single particle as an average of all the things that might happen!"

is what may actually prove to be true.

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Hi Jeff. A few useful remarks on your essay.

The way to unify gravity and electromagnetism requires balanced and equivalent attraction and repulsion and balanced and equivalent inertia and gravity.

The understanding of outer space is significantly limited, as it precludes and destroys thought entirely. You cannot get around this. A lesson to

FQXi.org as well. Telescopic observations make the unnatural/actually impossible experience of outer space even more incomprehensible. Telescopic observations do tell us something about how we see, however. We would never be able to survive long term/permanently in outer space, by the way.

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The way to unify gravity and electromagnetism requires balanced and equivalent attraction and repulsion and balanced and equivalent inertia and gravity.

The understanding of outer space is significantly limited, as it precludes and destroys thought entirely. You cannot get around this. A lesson to

FQXi.org as well. Telescopic observations make the unnatural/actually impossible experience of outer space even more incomprehensible. Telescopic observations do tell us something about how we see, however. We would never be able to survive long term/permanently in outer space, by the way.

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Hi Frank,

Not sure how to use your remarks. It sounds more philosophical than physically analogous, which I am not adept at utilizing. I don't see an essay posted to the contest under your name. I pretty much get lost without at least some equations that are tied to mainstream theory. I don't view math as more important than analogies, but without that toolbox I don't see how to actually build any structure. The strongest argument is the simplest mathematical one in my opinion.

"The understanding of outer space is significantly limited, as it precludes and destroys thought entirely. You cannot get around this." The understanding precludes and destroys thought or outer space does? I don't know what that means, except I keep visualizing how some people during the industrial revolution were worried that people would no longer be able to think at the high speeds that the locomotive was theorized to be able to reach. How is our lack of evolving with unnaturally high speeds any different than outer space?

Do you mean that the human species (or perhaps any) has any hope of ever understanding the inner workings of the cosmos? That sounds utterly defeatist if so, and even if it were true I still would not stop searching.

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Not sure how to use your remarks. It sounds more philosophical than physically analogous, which I am not adept at utilizing. I don't see an essay posted to the contest under your name. I pretty much get lost without at least some equations that are tied to mainstream theory. I don't view math as more important than analogies, but without that toolbox I don't see how to actually build any structure. The strongest argument is the simplest mathematical one in my opinion.

"The understanding of outer space is significantly limited, as it precludes and destroys thought entirely. You cannot get around this." The understanding precludes and destroys thought or outer space does? I don't know what that means, except I keep visualizing how some people during the industrial revolution were worried that people would no longer be able to think at the high speeds that the locomotive was theorized to be able to reach. How is our lack of evolving with unnaturally high speeds any different than outer space?

Do you mean that the human species (or perhaps any) has any hope of ever understanding the inner workings of the cosmos? That sounds utterly defeatist if so, and even if it were true I still would not stop searching.

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After reading through some of the essays in this contest, it may be helpful for any public readers to again consider the questions within the contest rules:

"What exactly are the basic physical and mathematical postulates in our "fundamental" physical theories or candidate theories?"

-- My answer to this would of course be that gravity is "attractive" and that there is no physical cosmological medium. The mathematical postulate is that flat spacetime cannot occur with a cosmological constant.

"Which of these could be replaced with a weaker or less restrictive postulate or even removed?"

-- I would state that the less restrictive postulate is to use the full modified Einstein field equation with a flat spacetime.

"What would be the potential benefits (or disadvantages) of these changes?"

-- It would account for the accelerating expansion, provide a basic model for understanding of quantum field theory and change cosmology into a coherent physical theory.

"What are the implicit assumptions we tend to forget we have postulated, or that have become so ingrained that they have become unquestioned dogma?"

-- It is ingrained in us to think of gravity as attractive between two massive bodies (action at a distance) while at the same time to now accept that the space in between has many properties. We implicitly assume that we are "particles" with energy density that are separate from the vacuum of nothingness, but have also come to accept at the very same time that this vacuum has an energy density.

"What are the most interesting current "anomalous" experiments, and what assumptions would we be forced to give up if we took them seriously?"

-- The most interesting anomalous experiment is of course the accelerating expansion. If we took this seriously, we might reconsider how the cosmological constant relates to attractive gravity.

"Which assumptions in physics and in cosmology are interdependent or required for self-consistency, and which could be modified?"

-- Energy density of the vacuum and how energy density relates to gravity.

"Where are there "paradoxes", or apparent contradictions stemming from the combination of seemingly reasonable assumptions? How do we reconcile these?"

-- How can vacuum have such a high energy density, be the cosmological constant, but yet have not only such a small effect on gravity, but a repulsive one at that?

"Are there “meta”-assumptions or criteria (e.g. "simplicity", or "beauty", or "utility") that can or should underlie some current “fundamental” assumptions?"

-- Symmetry of Riemannian geometry.

"(Note: Successful and interesting essays will not use this topic as an opportunity to trot out their pet theories simply because those theories reject assumptions of some other or established theory. Rather, the challenge here is to create new and insightful questions or analysis about basic, often tacit, assumptions that can be questioned but often are not.) "

-- If the Einstein field equation is a differential equation with a constant of integration, why have we never examined the consequences of any other combinations of the Einstein tensor and the cosmological constant?

"Foundational: This Contest is limited to works addressing, in one of its many facets, our understanding of the deep or "ultimate" nature of reality."

-- What exactly are we made of?

"Accessible to a diverse, well-educated but non-specialist audience, aiming in the range between the level of Scientific American and a review article in Science or Nature."

-- Hopefully I have kept this basic enough so that others can manipulate the equations and find flaws and strengths in my logic for themselves.

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"What exactly are the basic physical and mathematical postulates in our "fundamental" physical theories or candidate theories?"

-- My answer to this would of course be that gravity is "attractive" and that there is no physical cosmological medium. The mathematical postulate is that flat spacetime cannot occur with a cosmological constant.

"Which of these could be replaced with a weaker or less restrictive postulate or even removed?"

-- I would state that the less restrictive postulate is to use the full modified Einstein field equation with a flat spacetime.

"What would be the potential benefits (or disadvantages) of these changes?"

-- It would account for the accelerating expansion, provide a basic model for understanding of quantum field theory and change cosmology into a coherent physical theory.

"What are the implicit assumptions we tend to forget we have postulated, or that have become so ingrained that they have become unquestioned dogma?"

-- It is ingrained in us to think of gravity as attractive between two massive bodies (action at a distance) while at the same time to now accept that the space in between has many properties. We implicitly assume that we are "particles" with energy density that are separate from the vacuum of nothingness, but have also come to accept at the very same time that this vacuum has an energy density.

"What are the most interesting current "anomalous" experiments, and what assumptions would we be forced to give up if we took them seriously?"

-- The most interesting anomalous experiment is of course the accelerating expansion. If we took this seriously, we might reconsider how the cosmological constant relates to attractive gravity.

"Which assumptions in physics and in cosmology are interdependent or required for self-consistency, and which could be modified?"

-- Energy density of the vacuum and how energy density relates to gravity.

"Where are there "paradoxes", or apparent contradictions stemming from the combination of seemingly reasonable assumptions? How do we reconcile these?"

-- How can vacuum have such a high energy density, be the cosmological constant, but yet have not only such a small effect on gravity, but a repulsive one at that?

"Are there “meta”-assumptions or criteria (e.g. "simplicity", or "beauty", or "utility") that can or should underlie some current “fundamental” assumptions?"

-- Symmetry of Riemannian geometry.

"(Note: Successful and interesting essays will not use this topic as an opportunity to trot out their pet theories simply because those theories reject assumptions of some other or established theory. Rather, the challenge here is to create new and insightful questions or analysis about basic, often tacit, assumptions that can be questioned but often are not.) "

-- If the Einstein field equation is a differential equation with a constant of integration, why have we never examined the consequences of any other combinations of the Einstein tensor and the cosmological constant?

"Foundational: This Contest is limited to works addressing, in one of its many facets, our understanding of the deep or "ultimate" nature of reality."

-- What exactly are we made of?

"Accessible to a diverse, well-educated but non-specialist audience, aiming in the range between the level of Scientific American and a review article in Science or Nature."

-- Hopefully I have kept this basic enough so that others can manipulate the equations and find flaws and strengths in my logic for themselves.

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Another analogy with epicycles...

Like the interpretation of perfect circles to the concept of orbits, we assume that the Einstein tensor is the only interpretation of the full field equation. If we hold onto the perfect circles, then every modification must take those into account. If we hold onto G_{uv} describing particulate matter, every modification to GR must adhere to that concept.

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Like the interpretation of perfect circles to the concept of orbits, we assume that the Einstein tensor is the only interpretation of the full field equation. If we hold onto the perfect circles, then every modification must take those into account. If we hold onto G

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Hi Jeff:

I thoroughly enjoyed your concise and well-written essay.

Based on arguments and results presented in my paper - -“ From Absurd to Elegant Universe”, your following conclusion is fully vindicated:

“The cosmological constant, within the Einstein field equation (EFE), is the leading method to account for the discovered accelerating expansion of the universe, whether or not an underlying cause is understood. ……… If this were in error it would raise profound questions of how the accelerating expansion relates to not only a gravitationally repulsive cosmological constant, but to our entire understanding of physics.”

My paper provides a new fundamental understanding of the Cosmological Constant and relativistic universe expansion as an alternative to the widely accepted linear Hubble expansion. The current paradoxes and inconsistencies are shown to be artifacts of the missing (hidden) physics of the well-known phenomenon of spontaneous decay. A new Gravity Nullification Model for Universe Expansion (GNMUE) is proposed that integrates the missing physics of the spontaneous mass-energy conversion into a simplified form of general relativity. The model predicts the observed expansion of the universe and galaxies and other data. The model provides answers to key fundamental questions and resolves paradoxes among general relativity, quantum mechanics, and cosmology. It also bridges the gap between quantum mechanics and relativity theories via revealing relativistic understanding of the inner workings of quantum mechanics. The impact of the new understanding on widely-accepted fundamental assumptions is discussed and a new wholesome perspective on reality is provided.

I would greatly appreciate your comments on my paper.

Best Regards

Avtar Singh

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I thoroughly enjoyed your concise and well-written essay.

Based on arguments and results presented in my paper - -“ From Absurd to Elegant Universe”, your following conclusion is fully vindicated:

“The cosmological constant, within the Einstein field equation (EFE), is the leading method to account for the discovered accelerating expansion of the universe, whether or not an underlying cause is understood. ……… If this were in error it would raise profound questions of how the accelerating expansion relates to not only a gravitationally repulsive cosmological constant, but to our entire understanding of physics.”

My paper provides a new fundamental understanding of the Cosmological Constant and relativistic universe expansion as an alternative to the widely accepted linear Hubble expansion. The current paradoxes and inconsistencies are shown to be artifacts of the missing (hidden) physics of the well-known phenomenon of spontaneous decay. A new Gravity Nullification Model for Universe Expansion (GNMUE) is proposed that integrates the missing physics of the spontaneous mass-energy conversion into a simplified form of general relativity. The model predicts the observed expansion of the universe and galaxies and other data. The model provides answers to key fundamental questions and resolves paradoxes among general relativity, quantum mechanics, and cosmology. It also bridges the gap between quantum mechanics and relativity theories via revealing relativistic understanding of the inner workings of quantum mechanics. The impact of the new understanding on widely-accepted fundamental assumptions is discussed and a new wholesome perspective on reality is provided.

I would greatly appreciate your comments on my paper.

Best Regards

Avtar Singh

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Jeff:

I have responded to your questions/comments on my essay page.

Thanks,

Avtar

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I have responded to your questions/comments on my essay page.

Thanks,

Avtar

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I didn't specifically address it in my essay, but it could be asked if this isn't a violation of the Weak Energy Condition or just the unimodular approach. Taking a look at equation (1.33) of The Cosmological Constant Problem,an Inspiration for New Physics we have

The difference with what I am proposing is to replace the tensor T with a residual energy density. This would seem to be equivalent to just the energy momentum tensor of matter, but should solve some paradoxes. As for the WEC, this specifies that energy density cannot be negative. Since in this way I am defining energy density that we are familiar with as the difference between higher and lower positive tensors, it isn't a negative energy density.

Regards,

Jeff

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The difference with what I am proposing is to replace the tensor T with a residual energy density. This would seem to be equivalent to just the energy momentum tensor of matter, but should solve some paradoxes. As for the WEC, this specifies that energy density cannot be negative. Since in this way I am defining energy density that we are familiar with as the difference between higher and lower positive tensors, it isn't a negative energy density.

Regards,

Jeff

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Jeff. Life is fragile, and it is very precisely regulated and balanced -- this includes in relation to the direct experience of physical force/energy by the body. There is no surviving long term in outer space -- for an unlimited time with reproduction. That is a fact.

The direct experience of the force/energy of physics/physical experience by the body is fundamental/essential to the deepest, integrated, coherent, significant, extensive, and most fundamental ideas/theories/understanding(s) in physics.

My essay will be entered shortly.

The physical/full experience of outer space destroys us and precludes our thought and being entirely. Accordingly, our understanding of outer space is significantly limited. Thought cannot describe/approximate to what it is not, ultimately.

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The direct experience of the force/energy of physics/physical experience by the body is fundamental/essential to the deepest, integrated, coherent, significant, extensive, and most fundamental ideas/theories/understanding(s) in physics.

My essay will be entered shortly.

The physical/full experience of outer space destroys us and precludes our thought and being entirely. Accordingly, our understanding of outer space is significantly limited. Thought cannot describe/approximate to what it is not, ultimately.

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"There is no surviving long term in outer space -- for an unlimited time with reproduction. That is a fact."

Perhaps there are areas of research that I was not aware of but that sounds very much like an opinion, rather than an actual fact. Citation?

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Perhaps there are areas of research that I was not aware of but that sounds very much like an opinion, rather than an actual fact. Citation?

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I agree with the quote in your essay: "nothing short of a revolution in our understanding of fundamental physics will be required to achieve a full understanding of the cosmic acceleration." In addition, I do not believe that such a revolution can originate at any of the so-called top universities.

Now about your essay. I have two issues with it.

1) In §2 on page 2, you mention that when integrating over a specific interval [a, b] two different integrands (functions) can yield the same integral. Of course this is so, e.g. the function f(x) = 2x and the constant function g(x) = 1 yield the same integral over the interval [0,1]. But then you seem to go off on a tangent. You define f1 = C - f2 and then you show that both f1 and C - f2 yield the same integral over the interval [x1, x2]. But how is that an example of two different functions yielding the same integral? The functions "f1" and "C - f2" are, namely, identical by your own definition. And as a side note, the term "C" in this defintion of yours is a constant function, not a constant of integration (which is a number) as you seem to imply in figure 2. So why this example?

2) In General Relativity (GR), the index-free form of the Einstein field equation (EFE) is

I understand that you want to replace this EFE by this equation:

But why is that an improvement? With the EFE, one can calculate the metric tensor (or the metric tensor and the cosmological constant) given the stress-energy tensor T. But what is the physical interpretation of the tensor L in your equation? You might be able to calculate it, but what is it? You refer to figure 3 as an illustration, but what are the two scalar fields in the bottom picture physically? What is their physical source? What is the corresponding theory of gravitation (what is gravitation according to you)? It seems to me that your idea requires some further development.

All in all, the parallell between our essays is that we both question GR. But there are nuances. I believe that GR is correct in its area of application, but emergent instead of fundamental. You, on the other hand, seem to believe that GR isn't even correct in its area of application, as you suggest another field equation - I take it that you propose these as an improvement of the EFE even at macroscopic scale. Am I correct?

Good luck with the contest.

Best regards, Marcoen

@Steve: hail all hail to the revolution (Jon English).

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Now about your essay. I have two issues with it.

1) In §2 on page 2, you mention that when integrating over a specific interval [a, b] two different integrands (functions) can yield the same integral. Of course this is so, e.g. the function f(x) = 2x and the constant function g(x) = 1 yield the same integral over the interval [0,1]. But then you seem to go off on a tangent. You define f1 = C - f2 and then you show that both f1 and C - f2 yield the same integral over the interval [x1, x2]. But how is that an example of two different functions yielding the same integral? The functions "f1" and "C - f2" are, namely, identical by your own definition. And as a side note, the term "C" in this defintion of yours is a constant function, not a constant of integration (which is a number) as you seem to imply in figure 2. So why this example?

2) In General Relativity (GR), the index-free form of the Einstein field equation (EFE) is

I understand that you want to replace this EFE by this equation:

But why is that an improvement? With the EFE, one can calculate the metric tensor (or the metric tensor and the cosmological constant) given the stress-energy tensor T. But what is the physical interpretation of the tensor L in your equation? You might be able to calculate it, but what is it? You refer to figure 3 as an illustration, but what are the two scalar fields in the bottom picture physically? What is their physical source? What is the corresponding theory of gravitation (what is gravitation according to you)? It seems to me that your idea requires some further development.

All in all, the parallell between our essays is that we both question GR. But there are nuances. I believe that GR is correct in its area of application, but emergent instead of fundamental. You, on the other hand, seem to believe that GR isn't even correct in its area of application, as you suggest another field equation - I take it that you propose these as an improvement of the EFE even at macroscopic scale. Am I correct?

Good luck with the contest.

Best regards, Marcoen

@Steve: hail all hail to the revolution (Jon English).

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Hi Marcoen and thanks for the excellent questions:

(1) Perhaps I should state this as actually three different functions f_{1}, f_{2} and C. I do mean that C is a constant (i.e. a number) and not a function of x (i.e. C(x), a constant can still be integrated, so perhaps when I referred to it as a constant function this was misconstrued as meaning it to be a linear constant function of x, which it is not). A very elementary part of calculus, not something which stands out. The point is that from the answer alone, which would just be area, there is no way to tell whether I used an integration of f_{1} over x_{1} to x_{2} or the integration of C-f_{2}. If one finds the antiderivative of a function, there exists an arbitrary constant of integration which could have any value.

I use this specific example, in that if the cosmological constant is a constant of integration (sometimes called the unimodular approach), then it is a bit of a coincidence that one of the biggest paradoxes about it is that it should be extremely large (according to QFT) but that empirically it appears to be rather tiny. In my example, the constant C could be extremely large or it could be zero and there is no way from anti-differentiation to tell which.

(2) Why would my equation be an improvement over Einstein's tensor G? It could also be fairly asking whether I am making the equation more difficult. To answer this question fully, it might be helpful if we consider a model of a cosmological fluid (see the Dark Energy Task Force report on the use of these). With the modified EFE, there is no known way to put in the estimated value of the cosmological constant (10^{120} higher than observed) and also find a mechanism which makes it very small. However, by using the alternate equation I propose, a full theoretical value of the "vacuum" could be put in. Suppose then there is matter present at a point in this vacuum. If we model this particle as a reduction in the density of this cosmological fluid, the L_{uv} would be equated to the stress energy tensor of the remaining density kT^{res}_{uv}. Since this constant and remaining stress energy tensor together are mathematically equivalent to the Einstein tensor/stress energy tensor of matter, it should approximate Newtonian gravity, although calling that gravity "attractive" would be qualitatively incorrect. The main point of this though, is that it appears that it would not model it exactly, since at larger radii the Omega term would increase linearly to a point where the gravitational vector switches direction from an apparent attraction to a repulsion. Whether this matches what we empirically observe I do not yet know, but there are too many coincidences in the formation of field theory, action at a distance, GR and now a linear accelerating expansion that has been tied to the cosmological constant to not be suspicious. If this model gives us a more accurate picture of macro gravitational effects, I would also become very concerned about how abstract these cosmological fluid models actually are.

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(1) Perhaps I should state this as actually three different functions f

I use this specific example, in that if the cosmological constant is a constant of integration (sometimes called the unimodular approach), then it is a bit of a coincidence that one of the biggest paradoxes about it is that it should be extremely large (according to QFT) but that empirically it appears to be rather tiny. In my example, the constant C could be extremely large or it could be zero and there is no way from anti-differentiation to tell which.

(2) Why would my equation be an improvement over Einstein's tensor G? It could also be fairly asking whether I am making the equation more difficult. To answer this question fully, it might be helpful if we consider a model of a cosmological fluid (see the Dark Energy Task Force report on the use of these). With the modified EFE, there is no known way to put in the estimated value of the cosmological constant (10

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Forgot to answer: "You refer to figure 3 as an illustration, but what are the two scalar fields in the bottom picture physically? What is their physical source? What is the corresponding theory of gravitation (what is gravitation according to you)?"

The scalar fields are generic vector examples of Newtonian gravitational fields.

The first scalar field is a vector representation of the Omega (or equivalently the cosmological constant) term. It should actually be a scalar field with linearly increasing values radiating out in a circular fashion, but it complicates the explanation in that by definition gravitational force vector requires at least another mass. It is an isotropic pressure.

The second scalar field represents a vector formed from the gradient of stress energy tensor equated to L_{uv}. The field scalar values are of a much larger magnitude and the gradient is of an opposing direction, but of course the minus sign in front gives us an equivalent force vector to that of the regular Newtonian gradient. The illustration is to point out that the top vector field is what GR reduces down to in the weak limit, whereas the bottom two fields are closer to what is now empirically known.

Regards,

Jeff

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The scalar fields are generic vector examples of Newtonian gravitational fields.

The first scalar field is a vector representation of the Omega (or equivalently the cosmological constant) term. It should actually be a scalar field with linearly increasing values radiating out in a circular fashion, but it complicates the explanation in that by definition gravitational force vector requires at least another mass. It is an isotropic pressure.

The second scalar field represents a vector formed from the gradient of stress energy tensor equated to L

Regards,

Jeff

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Hello Jeff,

(1) If you write "f_{1} = C - f_{2}" then this is a relation between functions. That is, the term "f_{1}" on the left hand side is an element of a function space, and the term "C - f_{2}" on the right hand side is an element of a function space. That latter term "C - f_{2}" is the function obtained by adding the function "- f_{2}" to the constant function "C": in a function space, the binary operation addition takes two functions as an argument. If you want C to be a numerical constant (a number), then you can define the function "f_{1}" by defining its function value as in "f_{1}(x) = C - f_{2}(x)": this is a relation between numbers, so here C is a number (a constant of integration if you want). So subtleties in mathematical notation can make a big difference.

(2) I'm still having difficulties with the interpretation of your two scalar fields, illustrated by your figure 3. It seems to me that the first scalar field doesn't occur in the ontology of Newtonian mechanics. Isn't this something you want to add?

As a side note, in the framework of my own theory, the EPT, the observed space is a material substance which is transcended by matter waves (there are, thus, two different kinds of components). A metric may then be defined in terms of a difference between two scalars (close to what you suggest) but at this point it is not possible to conduct tensor algebra in this framework as the necessary mathematics have yet to be developed.

With best regards, Marcoen

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(1) If you write "f

(2) I'm still having difficulties with the interpretation of your two scalar fields, illustrated by your figure 3. It seems to me that the first scalar field doesn't occur in the ontology of Newtonian mechanics. Isn't this something you want to add?

As a side note, in the framework of my own theory, the EPT, the observed space is a material substance which is transcended by matter waves (there are, thus, two different kinds of components). A metric may then be defined in terms of a difference between two scalars (close to what you suggest) but at this point it is not possible to conduct tensor algebra in this framework as the necessary mathematics have yet to be developed.

With best regards, Marcoen

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Thinking about some of Marcoen's questions and I realize that my explanations aren't coming across clearly. Let's try this:

--In calculus, the indefinite integral of a given function (i.e., the set of all antiderivatives of the function) is only defined up to an additive constant, the constant of integration.

Suppose we take a measurement of gravitational force, lensing, etc. and we compare that to what our differential equations give us, and they agree for a given input. We are basically assuming that we are using the correct anti-derivative of our function.

Thinking about the hypothesized size of the cosmological constant, if , then from the definition of an indefinite integral, how do we KNOW whether this equation should be or If the second is not the correct choice, why?

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--In calculus, the indefinite integral of a given function (i.e., the set of all antiderivatives of the function) is only defined up to an additive constant, the constant of integration.

Suppose we take a measurement of gravitational force, lensing, etc. and we compare that to what our differential equations give us, and they agree for a given input. We are basically assuming that we are using the correct anti-derivative of our function.

Thinking about the hypothesized size of the cosmological constant, if , then from the definition of an indefinite integral, how do we KNOW whether this equation should be or If the second is not the correct choice, why?

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If we take (da)²/a)+c²k/a²=8pi/3Gro+the energy of the quantum hole/3 .

Now if we insert the hubble law and my equations, you can correlate with the expansion/contyraction correlated with the maximum volume of universal sphere. Considering that the density can imply a contraction at this critical point.So we can see where the points of equilibrium are.The SR and the GR are ok and if we consider a system closed, it becomes relevant considering the number of quantum entanglement having the serie of uniquness.

See that the parameters must be precise for a correct universal dynamic. The volumes , spherical are essential like the rotations spinal and orbital.The proportions appear with mass. If the mass polarises the light and so if the entropy, physical increases proportional with mass.We can see where is this maximum volume just before the contraction towards the perfect equilibrium between all physical spheres. The friedman lemaître equation can be optimized.

Good work :) with the integrations, substitutions, extrapolations, additions, multiplications, settings,.......

Regards

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Now if we insert the hubble law and my equations, you can correlate with the expansion/contyraction correlated with the maximum volume of universal sphere. Considering that the density can imply a contraction at this critical point.So we can see where the points of equilibrium are.The SR and the GR are ok and if we consider a system closed, it becomes relevant considering the number of quantum entanglement having the serie of uniquness.

See that the parameters must be precise for a correct universal dynamic. The volumes , spherical are essential like the rotations spinal and orbital.The proportions appear with mass. If the mass polarises the light and so if the entropy, physical increases proportional with mass.We can see where is this maximum volume just before the contraction towards the perfect equilibrium between all physical spheres. The friedman lemaître equation can be optimized.

Good work :) with the integrations, substitutions, extrapolations, additions, multiplications, settings,.......

Regards

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Hello Spherical Jedi (I like your nickname),

I haven't yet gotten into the Friedmann equations in depth, but I will be certain to re-examine your concepts once I do. Do you have a website where your material is listed?

Regards,

Jeff

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I haven't yet gotten into the Friedmann equations in depth, but I will be certain to re-examine your concepts once I do. Do you have a website where your material is listed?

Regards,

Jeff

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Hello Mr.Baugher,

thanks:) I am a Jedi and proud of being . We fight Darth Vador in fact.And Yoda is my master, my mentor.

I have not a website, I just share my theory on this platfrom mainly because I beleive it is a seious platform of sciences. I beleive that FQXi has a pure responsability for our sciences. They must be universal in fact.If not their system will not on the rational road. FqxI isd young and of course this kind of platform is going to attract several persons loving monney and opulences. They must sort the pseudos ! Because the sciences are so important for our earth. The sciences have the solutions, the business , it, is an under sciences ! Are we going to pay our air soon ?

Mr Tegmark and Mr Aguirre have a responsability for this earth.They must think about the sortings of members.Just for their credibility in fact.Fqxi is a wonderful platform.This platform must be helped for its good road on the entropical arrow of times.

Regards

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thanks:) I am a Jedi and proud of being . We fight Darth Vador in fact.And Yoda is my master, my mentor.

I have not a website, I just share my theory on this platfrom mainly because I beleive it is a seious platform of sciences. I beleive that FQXi has a pure responsability for our sciences. They must be universal in fact.If not their system will not on the rational road. FqxI isd young and of course this kind of platform is going to attract several persons loving monney and opulences. They must sort the pseudos ! Because the sciences are so important for our earth. The sciences have the solutions, the business , it, is an under sciences ! Are we going to pay our air soon ?

Mr Tegmark and Mr Aguirre have a responsability for this earth.They must think about the sortings of members.Just for their credibility in fact.Fqxi is a wonderful platform.This platform must be helped for its good road on the entropical arrow of times.

Regards

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"What could be causing this acceleration? Physicists call it dark energy, and it could make up more than 70 percent of the cosmos. But so much remains unknown about dark energy that some scientists are asking whether it exists at all.

What if, instead of a mysterious unseen energy, "there is something wrong with gravity?" asks Sean Carroll, a theoretical physicist at the California Institute of Technology.

Einstein's theory of general relativity represents gravity as the curvature of space and time. Perhaps this idea "is still right, but we're not solving the equations correctly," suggests Carroll. "

Who's Afraid of the Dark? Alternatives to Dark Energy

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What if, instead of a mysterious unseen energy, "there is something wrong with gravity?" asks Sean Carroll, a theoretical physicist at the California Institute of Technology.

Einstein's theory of general relativity represents gravity as the curvature of space and time. Perhaps this idea "is still right, but we're not solving the equations correctly," suggests Carroll. "

Who's Afraid of the Dark? Alternatives to Dark Energy

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Jeff

In the paper: Fedosin S.G. Cosmic Red Shift, Microwave Background, and New Particles. Galilean Electrodynamics, Spring 2012, Vol. 23, Special Issues No. 1, P. 3 - 13, I describe the possible reason for dark energy, red shift and microwave background. The explanation is based at the Theory of Infinite Hierarchical Nesting of Matter.

On the other hand, the cosmological constant was explained in the paper: Fedosin S.G. The Principle of Least Action in Covariant Theory of Gravitation. Hadronic Journal, February 2012, Vol. 35, No. 1, P. 35 - 70.

Other ideas about gravitation see my Essay.

I hope it will be useful for you.

Sergey Fedosin Essay

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In the paper: Fedosin S.G. Cosmic Red Shift, Microwave Background, and New Particles. Galilean Electrodynamics, Spring 2012, Vol. 23, Special Issues No. 1, P. 3 - 13, I describe the possible reason for dark energy, red shift and microwave background. The explanation is based at the Theory of Infinite Hierarchical Nesting of Matter.

On the other hand, the cosmological constant was explained in the paper: Fedosin S.G. The Principle of Least Action in Covariant Theory of Gravitation. Hadronic Journal, February 2012, Vol. 35, No. 1, P. 35 - 70.

Other ideas about gravitation see my Essay.

I hope it will be useful for you.

Sergey Fedosin Essay

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Jeff,

In accordance with the Theory of Infinite Hierarchical Nesting of Matter (my Essay), nuons are similar at the level of star to the white dwarfs, and nucleons to neutron stars and magnetar. Nuons are the result of evolution of cosmic substance under action of strong gravitation at the level of elementary particles. In Standard Model there is muons that almost the same as nuons. But the difference is their origin: muons are born in decays of pions and strong interactions of particles and unstable or have charge and magnetic moment. But the nuons are stable, they are result of natural evolution of matter and have no charge. In the absence of charge it is difficult to detect them. At LHC or similar collider we see muons. To check the idea of nuons: they are the supposed reason of dark matter, of redshift of remote galaxies, of microwave background, of attenuation of light spectra of supernova star and so on.

Sergey Fedosin Essay

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In accordance with the Theory of Infinite Hierarchical Nesting of Matter (my Essay), nuons are similar at the level of star to the white dwarfs, and nucleons to neutron stars and magnetar. Nuons are the result of evolution of cosmic substance under action of strong gravitation at the level of elementary particles. In Standard Model there is muons that almost the same as nuons. But the difference is their origin: muons are born in decays of pions and strong interactions of particles and unstable or have charge and magnetic moment. But the nuons are stable, they are result of natural evolution of matter and have no charge. In the absence of charge it is difficult to detect them. At LHC or similar collider we see muons. To check the idea of nuons: they are the supposed reason of dark matter, of redshift of remote galaxies, of microwave background, of attenuation of light spectra of supernova star and so on.

Sergey Fedosin Essay

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Jeff,

I really enjoyed your essay! Certainly if we find "dark energy" to be the dominant effect, it is more natural to "correct a repulsive force at small scales" than to "correct an attractive force at large scales," and the historical fact that we discovered "dark energy" relatively late should not deter us from this. However, I have a couple of questions.

1. Your 5th foundational question on page 2 involves the idea of curvature going to zero as matter content goes to zero, which is indeed a convincing point. However, I don't understand how repulsive gravity with a negative "cosmological constant" achieves this any more than attractive gravity with a positive "cosmological constant;" it seems that the difference is between positive curvature and negative curvature.

2. One argument for attractive gravity is based on the idea that gravity ought to be a "local effect." In other words, it is harder to think of objects at great distances "exerting greater and greater forces on each other" than to think of gravity as a local attractive "force" that simply dies out with distance and is overwhelmed by dark energy, whatever it is. What is your view on this?

3. Does dark matter factor into this in any obvious way?

If you want to know more about the motivation for these questions, you might look at my essay

On the Foundational Assumptions of Modern Physics

Basically, I am interested in the reasons for scale-dependence of the various interactions. Take care,

Ben Dribus

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I really enjoyed your essay! Certainly if we find "dark energy" to be the dominant effect, it is more natural to "correct a repulsive force at small scales" than to "correct an attractive force at large scales," and the historical fact that we discovered "dark energy" relatively late should not deter us from this. However, I have a couple of questions.

1. Your 5th foundational question on page 2 involves the idea of curvature going to zero as matter content goes to zero, which is indeed a convincing point. However, I don't understand how repulsive gravity with a negative "cosmological constant" achieves this any more than attractive gravity with a positive "cosmological constant;" it seems that the difference is between positive curvature and negative curvature.

2. One argument for attractive gravity is based on the idea that gravity ought to be a "local effect." In other words, it is harder to think of objects at great distances "exerting greater and greater forces on each other" than to think of gravity as a local attractive "force" that simply dies out with distance and is overwhelmed by dark energy, whatever it is. What is your view on this?

3. Does dark matter factor into this in any obvious way?

If you want to know more about the motivation for these questions, you might look at my essay

On the Foundational Assumptions of Modern Physics

Basically, I am interested in the reasons for scale-dependence of the various interactions. Take care,

Ben Dribus

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Hi Ben,

Thanks so much for the questions! I will attempt to return the favor in your thread but I am afraid that my questions may not be as pertinent as I am unfamiliar with some of the terminology in your essay. Will do my best though.

As for your questions here;

1. It may be that understanding positive curvature doesn't necessarily mean attractive gravity is a bit counter intuitive. Perhaps I should have prefaced this statement. My assumption is that, simply due to symmetry, the full equation should be able to work equally well with G_{uv} or Omega g_{uv}-L_{uv}, they both would give the same positive curvature. Curvature increases positively as G_{uv} increases from zero, or as L_{uv} decreases from the value of Omega g_{uv}.

The fascinating thing is though, the approximation to a Newtonian field gradient does not produce the exact same field equation. A symmetry breaking of classical gauge theory if you will. Without a quantitative analysis, it is plausible that this difference would only be detectable at larger radii. It also appears that to approximate this effect with only G_{uv} one would have to add in a very tiny multiple of the metric (dark energy).

So what the 5th point probably should state is that if G_{uv} and Omega g_{uv}-L_{uv} are both suitable for the EFE, but only G_{uv} requires an extra multiple of the metric that also breaks the condition of zero curvature with no matter, then Omega g_{uv}-L_{uv} should take precedence over G_{uv}-Lambda g_{uv}.

What this also means is that positive curvature can be equated to either attractive gravity or repulsive. G_{uv} and L_{uv} should result in very different field magnitudes of Phi. The Newtonian gravitational force, however, only depends on the spatial gradient of this field. The gradient vectors of Phi from G_{uv} and L_{uv} are of opposing directions of course, but vectors from G_{uv} and -L_{uv} are equivalent. What is even more interesting is how a constant multiple of the metric becomes a very tiny gradient vector opposing this.

Here is a small thought experiment and I apologize for the lack of mathematical rigor but it should show you what I mean. Take two vectors A and B, of equal large magnitude but they are placed tip to tip opposing each other. Their vector sum is a point, or a vector of zero magnitude. Now subtract from this sum a vector C pointing left that is smaller than either A or B. The total equivalence of all three vectors is a vector D that is of equal magnitude of C but pointing to the right. Occams Razor states that the simplest answer is only D, but the physical reality may be closer to A, B and C. Parsimony also requires that we choose the simplest anti-derivative to produce Newtonian gravity, and that we choose the simplest tensor for the Einstein field equation. Similarly, as vector D increases, you are increasing an attractive force, as vector C increases, you are decreasing a repulsion.

If I can parallel transport D on a curved surface, can I not also do the same for the sum of A, B and C? My guess is probably not and that we have missed something in manifold theory, although I am a long way from deriving this.

2. (Sorry 1 was so long!) My argument is that gravity is causal. The simplest way to understand what I mean is to state how I think gravity works. I think that matter at a point reduces the available field energy in a sphere surrounding it. The symmetry of the matter also depends on the symmetry of the reduced field energy. (this is not energy in the regular definition of matter-energy, more of a curvature potential) If another point within this sphere of reduced field energy also contains matter, it too reduces the available energy within a certain radius. The matter of these two points interfere with the symmetry of each, and both seeking symmetry (related to principle of least action) is manifested in a force where to tend to move together. The equations for the Newtonian approximation, however, seem to show that if clumps of matter were to spread far enough apart (past the constant within the EFE) then it would result in a purely linear repulsion. This would seem to fit a theory where the accelerating expansion only occurs after enough average distance between clumps of matter but it seems counter to our understanding of "expansion of space".

3. For Dark Matter, suppose that Omega g_{uv} can vary within a region not centered on baryonic matter. I suspect that this would add a stress energy tensor to the field equation. Since this tensor did not result from the exact point that matter is located, then the only way we would be able to detect it is through gravitational effects of matter passing through this region. I am a long way from deriving a set of christoffel symbols to account for this though.

Regards,

Jeff

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Thanks so much for the questions! I will attempt to return the favor in your thread but I am afraid that my questions may not be as pertinent as I am unfamiliar with some of the terminology in your essay. Will do my best though.

As for your questions here;

1. It may be that understanding positive curvature doesn't necessarily mean attractive gravity is a bit counter intuitive. Perhaps I should have prefaced this statement. My assumption is that, simply due to symmetry, the full equation should be able to work equally well with G

The fascinating thing is though, the approximation to a Newtonian field gradient does not produce the exact same field equation. A symmetry breaking of classical gauge theory if you will. Without a quantitative analysis, it is plausible that this difference would only be detectable at larger radii. It also appears that to approximate this effect with only G

So what the 5th point probably should state is that if G

What this also means is that positive curvature can be equated to either attractive gravity or repulsive. G

Here is a small thought experiment and I apologize for the lack of mathematical rigor but it should show you what I mean. Take two vectors A and B, of equal large magnitude but they are placed tip to tip opposing each other. Their vector sum is a point, or a vector of zero magnitude. Now subtract from this sum a vector C pointing left that is smaller than either A or B. The total equivalence of all three vectors is a vector D that is of equal magnitude of C but pointing to the right. Occams Razor states that the simplest answer is only D, but the physical reality may be closer to A, B and C. Parsimony also requires that we choose the simplest anti-derivative to produce Newtonian gravity, and that we choose the simplest tensor for the Einstein field equation. Similarly, as vector D increases, you are increasing an attractive force, as vector C increases, you are decreasing a repulsion.

If I can parallel transport D on a curved surface, can I not also do the same for the sum of A, B and C? My guess is probably not and that we have missed something in manifold theory, although I am a long way from deriving this.

2. (Sorry 1 was so long!) My argument is that gravity is causal. The simplest way to understand what I mean is to state how I think gravity works. I think that matter at a point reduces the available field energy in a sphere surrounding it. The symmetry of the matter also depends on the symmetry of the reduced field energy. (this is not energy in the regular definition of matter-energy, more of a curvature potential) If another point within this sphere of reduced field energy also contains matter, it too reduces the available energy within a certain radius. The matter of these two points interfere with the symmetry of each, and both seeking symmetry (related to principle of least action) is manifested in a force where to tend to move together. The equations for the Newtonian approximation, however, seem to show that if clumps of matter were to spread far enough apart (past the constant within the EFE) then it would result in a purely linear repulsion. This would seem to fit a theory where the accelerating expansion only occurs after enough average distance between clumps of matter but it seems counter to our understanding of "expansion of space".

3. For Dark Matter, suppose that Omega g

Regards,

Jeff

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Jeff

Excellent. We give very different proofs of very similar things.

(This is a reposed reply from my blog).

I turned from maths to ontological construction testing for the reason you give. Ken Wharton also exposes our foolhardy reliance on maths.

You might test this model; The axial anisotropic CMB flow is a scaled up version of a quasar jet. The CMB anisotropy itself has been resolved by computer into a helix, which precisely matches the quasar model, as the outflow jets from AGN's.

I have shown that AGN's are part of a galactic recycling process, re-ionizing all the dead stars and planetary matter to re-start the process with an open spiral on a perpendicuar axis. The common 'Kinetic decoupling' (perpedicular halo rotation) is thereby also finally explained along with other effects. Take a look at Centurus A (NASA HST) for a scale model of the universe.

Expansion is thus not accelerating but mainly reducing, except from the other end of the axis to the 'great attractor' (nonsense of course) in the direction of Leo. I've determined galaxies recycle every ~10-12Gyrs (a massive quasar peak is at z=1.7) so our 2nd iteration of the Milky Way is in middle age. A better analysis of the CMB anisotropy might constrain the same factor for our universe. (There may then be infinitely many numerically as well as temporally). If you're interested I'll link you to a past paper (new one in review).

Last technical point; I've found algerbaic vector apace cannot model motion as it's based on geometry where motion is an invalid concept, but I do know that to get a 'plus' sign hit; ampersand hash 43 semicolon. Like this; +

Peter

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Excellent. We give very different proofs of very similar things.

(This is a reposed reply from my blog).

I turned from maths to ontological construction testing for the reason you give. Ken Wharton also exposes our foolhardy reliance on maths.

You might test this model; The axial anisotropic CMB flow is a scaled up version of a quasar jet. The CMB anisotropy itself has been resolved by computer into a helix, which precisely matches the quasar model, as the outflow jets from AGN's.

I have shown that AGN's are part of a galactic recycling process, re-ionizing all the dead stars and planetary matter to re-start the process with an open spiral on a perpendicuar axis. The common 'Kinetic decoupling' (perpedicular halo rotation) is thereby also finally explained along with other effects. Take a look at Centurus A (NASA HST) for a scale model of the universe.

Expansion is thus not accelerating but mainly reducing, except from the other end of the axis to the 'great attractor' (nonsense of course) in the direction of Leo. I've determined galaxies recycle every ~10-12Gyrs (a massive quasar peak is at z=1.7) so our 2nd iteration of the Milky Way is in middle age. A better analysis of the CMB anisotropy might constrain the same factor for our universe. (There may then be infinitely many numerically as well as temporally). If you're interested I'll link you to a past paper (new one in review).

Last technical point; I've found algerbaic vector apace cannot model motion as it's based on geometry where motion is an invalid concept, but I do know that to get a 'plus' sign hit; ampersand hash 43 semicolon. Like this; +

Peter

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Jeff

You asked for the links I referred, initial ones below, (this posted on my blog but now so many entries I think we're as lost here as theoretical physics is!) Rob McEachern's brilliant analysis is also consistent with the basis of my analysis method, but I think you've read it.

You'll have to allow for the fact that the ontological construction termed the 'Discrete Field' model has continued to come on by leaps and bounds over the last year. The resolutions of anomalies are like a flood from a breached dyke. This means the papers are far from up to date. (The latest ones are currently either in review or accepted but not yet published).

The first short read may be last years essay. http://fqxi.org/community/forum/topic/803

Then the helical CMBR asymmetry one posted on vixra. http://vixra.org/abs/1102.0016

A 2010 one on aberration was http://vixra.org/abs/1007.0022

There are more but all older still.

Do point out any obvious updates needed!

Thanks

Peter

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You asked for the links I referred, initial ones below, (this posted on my blog but now so many entries I think we're as lost here as theoretical physics is!) Rob McEachern's brilliant analysis is also consistent with the basis of my analysis method, but I think you've read it.

You'll have to allow for the fact that the ontological construction termed the 'Discrete Field' model has continued to come on by leaps and bounds over the last year. The resolutions of anomalies are like a flood from a breached dyke. This means the papers are far from up to date. (The latest ones are currently either in review or accepted but not yet published).

The first short read may be last years essay. http://fqxi.org/community/forum/topic/803

Then the helical CMBR asymmetry one posted on vixra. http://vixra.org/abs/1102.0016

A 2010 one on aberration was http://vixra.org/abs/1007.0022

There are more but all older still.

Do point out any obvious updates needed!

Thanks

Peter

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Hi Jeff,

In your sketch you say that the repulsive Cosmological term makes no mathematical sense. It's kind of funny, I look at the Cosmological term differently. In my view, anything that doesn't make sense is treated as an intrinsic characteristic. Dark energy is said to be the explanation of why the universe is expanding at an accelerating rate.

"The only way I know to do this is to invert the equation so that instead of solid "particles" moving within a void, the stress energy tensor describes waves moving within a solid. "

A solid is something that I can whack with a hammer. I don't think a solid is the right characteristic for empty space.

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In your sketch you say that the repulsive Cosmological term makes no mathematical sense. It's kind of funny, I look at the Cosmological term differently. In my view, anything that doesn't make sense is treated as an intrinsic characteristic. Dark energy is said to be the explanation of why the universe is expanding at an accelerating rate.

"The only way I know to do this is to invert the equation so that instead of solid "particles" moving within a void, the stress energy tensor describes waves moving within a solid. "

A solid is something that I can whack with a hammer. I don't think a solid is the right characteristic for empty space.

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Technically it would be closer to a perfect fluid but that too has different connotations to different people. When people hear "fluid" they think of a water, but if I were to state that it was an elastic medium then they might think of rubber. A good qualitative description is difficult to give someone, so I just assume the best is to think of inverting the concept of what a particle is "made of" and what empty space is made of. What it would come down to is that if the hammer were to be made of waves, it apparently could normally only hit other waves.

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If I am talking about aether waves and you are talking about a fluid, then perhaps we can meet in the middle and talk about waves of a fluid medium. I approached the problem by defining a set of waves that obey,

The largest possible wavelength is the size of the universe, which yields the smallest possible frequency; the smallest size is the Planck length, which yields the largest possible frequency. These waves can be energized as a particle or just a photon or photons. Or these waves can be un-energized, have no energy, and just be the background of space(-time).

I treated gravity as an image of energy. Energy, and components of the stress energy tensor, are excitations of aether waves (or fluid medium waves?). Gravity is an image that is produced by mass and energy. Gravity manifests as acceleration fields; acceleration fields are frequency shifts at each frequency. This produces time dilation.

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The largest possible wavelength is the size of the universe, which yields the smallest possible frequency; the smallest size is the Planck length, which yields the largest possible frequency. These waves can be energized as a particle or just a photon or photons. Or these waves can be un-energized, have no energy, and just be the background of space(-time).

I treated gravity as an image of energy. Energy, and components of the stress energy tensor, are excitations of aether waves (or fluid medium waves?). Gravity is an image that is produced by mass and energy. Gravity manifests as acceleration fields; acceleration fields are frequency shifts at each frequency. This produces time dilation.

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Dear

Very interesting to see your essay.

Perhaps all of us are convinced that: the choice of yourself is right!That of course is reasonable.

So may be we should work together to let's the consider clearly defined for the basis foundations theoretical as the most challenging with intellectual of all of us.

Why we do not try to start with a real challenge is very close and are the focus of interest of the human science: it is a matter of mass and grain Higg boson of the standard model.

Knowledge and belief reasoning of you will to express an opinion on this matter:

You have think that: the Mass is the expression of the impact force to material - so no impact force, we do not feel the Higg boson - similar to the case of no weight outside the Earth's atmosphere.

Does there need to be a particle with mass for everything have volume? If so, then why the mass of everything change when moving from the Earth to the Moon? Higg boson is lighter by the Moon's gravity is weaker than of Earth?

The LHC particle accelerator used to "Smashed" until "Ejected" Higg boson, but why only when the "Smashed" can see it,and when off then not see it ?

Can be "locked" Higg particles? so when "released" if we do not force to it by any the Force, how to know that it is "out" or not?

You are should be boldly to give a definition of weight that you think is right for us to enjoy, or oppose my opinion.

Because in the process of research, the value of "failure" or "success" is the similar with science. The purpose of a correct theory be must is without any a wrong point ?

Glad to see from you comments soon,because still have too many of the same problems.

Regard !

Hải.Caohoàng of THE INCORRECT ASSUMPTIONS AND A CORRECT THEORY

August 23, 2012 - 11:51 GMT on this essay contest.

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Very interesting to see your essay.

Perhaps all of us are convinced that: the choice of yourself is right!That of course is reasonable.

So may be we should work together to let's the consider clearly defined for the basis foundations theoretical as the most challenging with intellectual of all of us.

Why we do not try to start with a real challenge is very close and are the focus of interest of the human science: it is a matter of mass and grain Higg boson of the standard model.

Knowledge and belief reasoning of you will to express an opinion on this matter:

You have think that: the Mass is the expression of the impact force to material - so no impact force, we do not feel the Higg boson - similar to the case of no weight outside the Earth's atmosphere.

Does there need to be a particle with mass for everything have volume? If so, then why the mass of everything change when moving from the Earth to the Moon? Higg boson is lighter by the Moon's gravity is weaker than of Earth?

The LHC particle accelerator used to "Smashed" until "Ejected" Higg boson, but why only when the "Smashed" can see it,and when off then not see it ?

Can be "locked" Higg particles? so when "released" if we do not force to it by any the Force, how to know that it is "out" or not?

You are should be boldly to give a definition of weight that you think is right for us to enjoy, or oppose my opinion.

Because in the process of research, the value of "failure" or "success" is the similar with science. The purpose of a correct theory be must is without any a wrong point ?

Glad to see from you comments soon,because still have too many of the same problems.

Regard !

Hải.Caohoàng of THE INCORRECT ASSUMPTIONS AND A CORRECT THEORY

August 23, 2012 - 11:51 GMT on this essay contest.

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Jeff,

You say,

"Although the possibility of this error raises more questions than can possibly be answered in an essay, we maintain that little progress can be made until it is understood that General Relativity does not trump its own foundations."

I'm not sure about your meaning when you say that GR does not trump its own foundations -- foundations referring to "space-time?"

My essay discusses gravity but with emphasis on empirical evidence.

Would be interested in hearing your thoughts on it.

Jim

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You say,

"Although the possibility of this error raises more questions than can possibly be answered in an essay, we maintain that little progress can be made until it is understood that General Relativity does not trump its own foundations."

I'm not sure about your meaning when you say that GR does not trump its own foundations -- foundations referring to "space-time?"

My essay discusses gravity but with emphasis on empirical evidence.

Would be interested in hearing your thoughts on it.

Jim

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Hi James,

My meaning concerning foundations involves understanding the Einstein field equations through unimodular gravity. This idea, originally proposed by Einstein, is thought to be equivalent to GR, but views the cosmological constant as a constant of integration. It would appear that despite this, the ramifications have never been considered if one does this before defining the Einstein tensor as the stress energy tensor of matter. The derivation of GR requires curvature to go to zero (R_{uv}=0)with no matter or energy present, but the presence of a cosmological constant means that we must ignore this requirement. Using a unimodular approach, and prior to defining the Einstein tensor, this requirement can still be enforced and end up with a constant of integration in the equations. It would seem that the value of this constant is large but would appear small to us due to the simultaneous change in our understanding of the Einstein tensor. This change should pass down through the weak field equations, but the main way we would notice is that gravity would appear to become repulsive after a certain radius.

Jeff

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My meaning concerning foundations involves understanding the Einstein field equations through unimodular gravity. This idea, originally proposed by Einstein, is thought to be equivalent to GR, but views the cosmological constant as a constant of integration. It would appear that despite this, the ramifications have never been considered if one does this before defining the Einstein tensor as the stress energy tensor of matter. The derivation of GR requires curvature to go to zero (R

Jeff

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Jeff,

For this contest, I decided to go through and comment on essays of interest and see what responses I got to my own essay. There are over 250 entries, so I narrowed down my evaluations. For only those who responded, I decided to reread and provide my evaluations before time expired, not making it a popularity contest but keeping in mind that I entered for an exchange of interesting ideas, whether I agree or not. Some concepts are superior and more persuasively supported.

Jim

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For this contest, I decided to go through and comment on essays of interest and see what responses I got to my own essay. There are over 250 entries, so I narrowed down my evaluations. For only those who responded, I decided to reread and provide my evaluations before time expired, not making it a popularity contest but keeping in mind that I entered for an exchange of interesting ideas, whether I agree or not. Some concepts are superior and more persuasively supported.

Jim

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Jeff,

This is in response to your post on my essay site regarding my new zero's relation to the stress energy tensor Guv. You said "Where I see this relating to your concept is that while a stress energy tensor for Guv may become zero or 'nothing', if the two tensors of the right half become equal, the sum may become zero but that certainly does not imply it is "empty". This would very much seem to fit the full void of 'sunya'."

I see it the same way. Space may be empty of matter, but that doesn't necessarily mean nothing is there. My new zero makes explicit the possibility of something potentially being there.

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This is in response to your post on my essay site regarding my new zero's relation to the stress energy tensor Guv. You said "Where I see this relating to your concept is that while a stress energy tensor for Guv may become zero or 'nothing', if the two tensors of the right half become equal, the sum may become zero but that certainly does not imply it is "empty". This would very much seem to fit the full void of 'sunya'."

I see it the same way. Space may be empty of matter, but that doesn't necessarily mean nothing is there. My new zero makes explicit the possibility of something potentially being there.

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After studying about 250 essays in this contest, I realize now, how can I assess the level of each submitted work. Accordingly, I rated some essays, including yours.

Cood luck.

Sergey Fedosin

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Cood luck.

Sergey Fedosin

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Dark energy/Dark matter 3:1 is mistake

Right answer Dark matter/dark energy 3:1

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Right answer Dark matter/dark energy 3:1

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If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is and was the quantity of people which gave you ratings. Then you have of points. After it anyone give you of points so you have of points and is the common quantity of the people which gave you ratings. At the same time you will have of points. From here, if you want to be R2 > R1 there must be: or or In other words if you want to increase rating of anyone you must give him more points then the participant`s rating was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process. I hope the FQXI community will change the rating process.

Sergey Fedosin

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Sergey Fedosin

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Mr. Baugher,

very interesting and insightful essay. I am especially intrigued by this explanation you posted a few days ago and its conclusion:

" The derivation of GR requires curvature to go to zero (Ruv=0)with no matter or energy present, but the presence of a cosmological constant means that we must ignore this requirement. Using a unimodular approach, and prior to defining the Einstein tensor, this requirement can still be enforced and end up with a constant of integration in the equations. It would seem that the value of this constant is large but would appear small to us due to the simultaneous change in our understanding of the Einstein tensor. This change should pass down through the weak field equations, but the main way we would notice is that gravity would appear to become repulsive after a certain radius. "

Is there a way to ruffly estimate this radius? I have a visual approach to physics and understand GR as if it describes the curvature of a 3D hypersurface of a hypersphere, similar to a 2D surface of water in the ocean, with the troughs of the waves corresponding to attractive gravity and the crests, repulsive. To paraphrase the saying, my geometrical approach (in 4D) states that "what curves in must eventually curve out", which implies that the repulsive aspect of gravity manifests itself in intergalactic voids, thus explaining why they are empty. In this regard, I would very much appreciate your feedback on my essay ( fqxi.org/community/forum/topic/1547 )

I wish I could follow the technical aspect of your essay, but intuitively I feel that yours is one the most important essays in this contest.

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very interesting and insightful essay. I am especially intrigued by this explanation you posted a few days ago and its conclusion:

" The derivation of GR requires curvature to go to zero (Ruv=0)with no matter or energy present, but the presence of a cosmological constant means that we must ignore this requirement. Using a unimodular approach, and prior to defining the Einstein tensor, this requirement can still be enforced and end up with a constant of integration in the equations. It would seem that the value of this constant is large but would appear small to us due to the simultaneous change in our understanding of the Einstein tensor. This change should pass down through the weak field equations, but the main way we would notice is that gravity would appear to become repulsive after a certain radius. "

Is there a way to ruffly estimate this radius? I have a visual approach to physics and understand GR as if it describes the curvature of a 3D hypersurface of a hypersphere, similar to a 2D surface of water in the ocean, with the troughs of the waves corresponding to attractive gravity and the crests, repulsive. To paraphrase the saying, my geometrical approach (in 4D) states that "what curves in must eventually curve out", which implies that the repulsive aspect of gravity manifests itself in intergalactic voids, thus explaining why they are empty. In this regard, I would very much appreciate your feedback on my essay ( fqxi.org/community/forum/topic/1547 )

I wish I could follow the technical aspect of your essay, but intuitively I feel that yours is one the most important essays in this contest.

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Ms. Vasilyeva,

Thank you for the kind words on my essay. I have put a powerpoint up top to help explain it also which includes the equation you are asking about.

I have read your very interesting essay and will comment on your page so that others can chime in also.

Thanks

Jeff

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Thank you for the kind words on my essay. I have put a powerpoint up top to help explain it also which includes the equation you are asking about.

I have read your very interesting essay and will comment on your page so that others can chime in also.

Thanks

Jeff

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The article is truly informative. However very recently there have been unexpected advances in understanding dark energy. In fact if the claim of the Egyptian Scientist M. S. El Naschie is correct, then there is no more a mystery regarding dark energy. El Naschie’s solution is disarmingly simple and was presented at two conferences which were almost entirely devoted to his work. The first was held in Bibliotheca Alexandrina early October 2012 and the second was in Shanghai a week or so ago. On both occasions El Naschie presented a revision of Einstein’s theory leading to an equation very similar to that of Einstein’s namely Energy equals mass x the square of the speed of the light. However unlike Einstein’s equation, the result is divided by 22. His explanation of 22 is as follows: As in the old string theory of strong interaction, space time of relativity should have been considered 26 dimensional. Taking 4 only is what Einstein did and that is how he got his famous result. Nevertheless Einstein ignored 22 dimensions. This is a scaling factor following Nottale’s theory as argued by El Naschie. Even in simpler terms, he reasons that Einstein knew only one elementary messenger particle namely the photon. He knew nothing about the other 11 messenger particles of the standard model which were not known in 1905. Adding 11 super partners it turned out that Einstein did not know about an additional 22 elementary particles. These are the particles needed to explain the missing dark energy. In this way El Naschie was able to show that 95.5% of the energy of the Universe is missing. Alternatively this energy was never there to start with because space time is a fractal and although it looks puffed up it boils down to very little similar to cotton candy. In addition the compactified 22 dimensions are the cause for the negative pressure which increases the acceleration of the Universe’s expansion. He claims to have tested his theory using 25 different methods including Witten’s M-Theory and reached the same result. Even more importantly this result agrees completely with observation. In other words mathematics and physics have been substantiated by measurement which led last year to the award of the Nobel Prize to the 3 team who obtained this incredible measurement and data. Click on this link to get more info re the above (under news) http://www.msel-naschie.com/ and also http://mohamed-elnaschie.blogspot.com/.

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Einstein's equation mc square is a relativistic equation. When you regard the entire energy of the cosmos you are dealing with an extreme case. The point with an extreme case is that partial theories fail. For instance when you want to know the origin of all forces then you are in the realm of unification and therefore in the realm of quantum gravity. When you ask about quantum gravity then you had better use a theory which combines relativity and quantum mechanics or else you will get the wrong answer or no answer at all. The situation is similar in the case of the missing energy of the cosmos, dubbed dark energy. To find quantitatively the right answer you cannot use E = mc square. You need a theory which combines E = mc square with relativity. We did it before within Schrodinger's equation when Dirac derived his equation combining Schrodinger with relativity. The same is true for quantum field theory. However E = mc square is something else. It needed the inclusion of quantum mechanics in a major way. The only person who was able to do that, whether we like it or not, is an Egyptian. Except for racial prejudice, we cannot judge a theory being right or wrong based on the nationality of the scientist otherwise we will end up back in the Middle Ages using Well's time machine. It is bad enough that Egypt as a whole seems to be moving towards the Middle Ages nowadays. Mohamed El Naschie, a professor of engineering, fused, to use his terminology, Hardy's quantum entanglement with Einstein's famous formula. To be able to do that Hardy's golden mean to the power of 5 had to be divided by 2 because it is originally due to the entanglement of two particles while Einstein's formula is there for one particle only. Intersection leads to the multiplication of Einstein's equation with half of Hardy's famous value. The result is exactly as Einstein predicted when we see it qualitatively. However to get the correct exact quantitative result you have to divide by 22.18033989 which is almost 22. If this is right, and I believe it is right, then the new quantum relativity equation of Mohamed El Naschie predicts only 4.5% of what Einstein's original equation predicted. In other words the 95.5% missing dark energy may well be a missing quantum gravity factor equal roughly to 1 divided by 22. This is amazing. It is amazing mainly because cosmological measurements say that this simple formula, almost as elegant as Einstein's original formula, must be correct. The measurement of dark energy goes back to the work of Perlmutter,Schmidt and Reiss and these three scientists may have without knowing, given us the definite experimental proof that Einstein's relativity and Heisenberg, Schrodinger, Dirac theories are true and when combined together, are absolutely true. The three scientists deserve the Nobel Prize threefold because they assured us of the entire rationality and solidness of our modern methods of investigation which is detached from any prejudice, including racial and religious prejudice. They confirmed the correct philosophy upon which the age of enlightenment, renaissance and separation of church and state is based. Moving in the other direction would be catastrophic.

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Farsy

You do not need all this complication. That equation is just the end conclusion. The fault lies at the outset. He conflated existence and observation of existence, so c, as in observational light, is non-existent. Having deemed light reality to be reality, he then used c as time, which is a constant, because he calibrated distance in x=vt with the duration elapsed if light travelled it. In simple terms: he shifted the actual time differential which is in the receipt of light to existence, and substituted observational light with time.

Paul

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You do not need all this complication. That equation is just the end conclusion. The fault lies at the outset. He conflated existence and observation of existence, so c, as in observational light, is non-existent. Having deemed light reality to be reality, he then used c as time, which is a constant, because he calibrated distance in x=vt with the duration elapsed if light travelled it. In simple terms: he shifted the actual time differential which is in the receipt of light to existence, and substituted observational light with time.

Paul

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