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**Cristi Stoica**: *on* 1/2/09 at 14:46pm UTC, wrote This is good news! Cristi

**Mark Stuckey**: *on* 12/31/08 at 20:09pm UTC, wrote Thanks, Cristi. In the wks following the contest deadline we have found the...

**Cristi Stoica**: *on* 12/30/08 at 13:40pm UTC, wrote Dear Professors Stuckey and Silberstein, My limited familiarity with the...

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**Dr. E (The Real McCoy)**: *on* 12/15/08 at 5:03am UTC, wrote Hello Mark, Here is another passage pertaining to the fact that photons...

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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 27, 2021

CATEGORY:
The Nature of Time Essay Contest (2008)
[back]

TOPIC: Time, Space and Matter in the Relational Blockworld: A New Approach to the Problems of Time by Mark Stuckey [refresh]

TOPIC: Time, Space and Matter in the Relational Blockworld: A New Approach to the Problems of Time by Mark Stuckey [refresh]

According to Smolin’s taxonomy, time is either emergent in some limit a la string-theory, it’s an illusion a la Barbour/Wheeler-Dewitt or it’s fundamental a la his new Heraclitean evolving laws approach. We offer a fourth possibility regarding the nature of time, i.e., time as part of a fundamental (pregeometric) regime wherein the notions of space, time and matter are co-defined and co-determining such that we ultimately speak of RaumZeitMaterie (to borrow from Weyl). This pregeometric formalism is motivated by, and inextricably linked to, our Relational Blockworld (RBW) interpretation of quantum mechanics and paints a picture of “spacetimematter” more integrated than that of general relativity (and, a fortiori, quantum physics). In order to generate a discrete action for the transition amplitude at the basis of physics, we propose a self-consistency criterion (SCC) in the context of discrete graph theory a la Wise; the SCC is our counterpart to “quasiseparability” per Albrecht and Iglesias. To do this, we use graph theory and identify the invariant core of the discrete action which we call the “actional.” We then construct the source-free portion of the actional consistent with its counterpart for coupled harmonic oscillators on the graph. Defining the discrete source relationally via links of the graph then suggests an SCC fundamental to the discrete action of the transition amplitude, or what we call the "symmetry amplitude." As predicted by Toffoli, our basis for the action (SCC -> actional) results from a mathematical tautology, viz., the topological maxim “the boundary of a boundary is zero,” which already guarantees the consistency of fields and divergence-free sources in general relativity, classical electromagnetism and quantum electrodynamics. We then explain how RBW holds out the promise of unification that treads a middle path between the timelessness of Barbour and the fundamentality of time in Smolin.

Mark Stuckey is a Professor of Physics at Elizabethtown College. He received his PhD in general relativistic cosmology in 1987 under Louis Witten at the University of Cincinnati. In 2004, he and Dr. Michael Silberstein, Associate Professor of Philosophy at Elizabethtown College and University of Maryland, College Park, developed the Relational Blockworld interpretation of quantum mechanics, which was introduced in 2005 at “New Directions in the Foundations of Physics” (organized by Jeffrey Bub) and “Time-Symmetry in Quantum Mechanics” (organized by Huw Price), and published in 2008 in Foundations of Physics and Studies in History and Philosophy of Modern Physics.

Hello Mark,

I enjoyed your paper and the Smolin references!

I'm not sure I agree with the need for the block universe, as Moving Dimensions Theory liberates us from the block universe and unfreezes time, while providing a deeper foundation for relativity and quantum mechanics; while weaving change into the fundamental fabric of spacetime for the first time in the history of...

view entire post

I enjoyed your paper and the Smolin references!

I'm not sure I agree with the need for the block universe, as Moving Dimensions Theory liberates us from the block universe and unfreezes time, while providing a deeper foundation for relativity and quantum mechanics; while weaving change into the fundamental fabric of spacetime for the first time in the history of...

view entire post

attachments: 1_9_MOVING_DIMENSIONS_THEORY_EXAMINES_THE_GRAVITATIONAL_REDSHIFT_SLOWING_OF_CLOCKS.pdf, 1_Photons_Remain_Stationary_in_the_Fourth_Expanding_Dimension1.pdf

Dr. E,

Thanks for the quotes, I've read TTWP in great detail and share many of Smolin's sentiments as evidenced in our essay.

As for MDT, it is not consistent with relativity as I explain on your site. We're trying to function in accord with GR (a fortiori, SR), QM and QFT so a theory such as MDT is of no use to us.

As to whether BW is a problem for physics, I agree with Hrvoje Nikolic that physics has nothing to say about subjective time. So, BW is fine for physics.

Good luck with MDT,

Mark

Thanks for the quotes, I've read TTWP in great detail and share many of Smolin's sentiments as evidenced in our essay.

As for MDT, it is not consistent with relativity as I explain on your site. We're trying to function in accord with GR (a fortiori, SR), QM and QFT so a theory such as MDT is of no use to us.

As to whether BW is a problem for physics, I agree with Hrvoje Nikolic that physics has nothing to say about subjective time. So, BW is fine for physics.

Good luck with MDT,

Mark

Thanks Mark,

MDT agrees 100% with all of relativity. In fact, relativity is derived from MDT in my paper. The postulate that the fourth dimension is expanding relative to the three spatial dimensions at c is a necessary and sufficient condition for the derivation of all of relativity.

You have to agree with the fact that a timeless, ageless photon does not move through time, but...

view entire post

MDT agrees 100% with all of relativity. In fact, relativity is derived from MDT in my paper. The postulate that the fourth dimension is expanding relative to the three spatial dimensions at c is a necessary and sufficient condition for the derivation of all of relativity.

You have to agree with the fact that a timeless, ageless photon does not move through time, but...

view entire post

Hi Mark and Michael,

Thanks for writing and posting this essay -- it's helping me understand your other papers, and I think there are some important ideas in here... But now that I understand it better, I'm coming up with some big-picture questions. So here goes...

A) The biggest surprise to me was that you're shying away from the primary consequence of the block-universe...

view entire post

Thanks for writing and posting this essay -- it's helping me understand your other papers, and I think there are some important ideas in here... But now that I understand it better, I'm coming up with some big-picture questions. So here goes...

A) The biggest surprise to me was that you're shying away from the primary consequence of the block-universe...

view entire post

Dear Ken,

i am not familiar with your mathematical/graphical theory jargon. The way i learned Physics was to first see the known observed facts, then develop some concepts that are logical and consistent with observed facts. Only when this job is done that one starts to use Mathematical techniques to explain the physical phenomenon. Your essay emphasis that one should start first with some Mathematical concepts and then develop the concepts needed in Physics accordingly. In the former picture, whenever, something not consistent with observed facts was noted, the same was ruled out even if the mathematics demanded it.

Like space, time is a concept to understand changes/motions that need to be described and understood in Physics. Thus,Einstein introduced in relativity, time as the fourth dimension of space, using x4 = ict. Now to discuss the nature of time, one understand it as one that takes care of motion between coordinates in spatial dimensions. The introduction of the constant 'c' with 't' signifies a tie with spacial dimension. However, the problem may arise if 'c' is not a constant. There has been recent cosmological measurements indicating that light coming from an object 12 billion years away, is seen to possess the value for 'c' a little higher than the value measured on earth thus far. In my essay, i have opened up a prospect that the early universe, first billion years, may well require the 'c' to have much higher value. Also, the other physical constants may show different scale of variations. The strengths of the four force/fields may also show variation from the currently accepted relative values, if we need to understand the initial conditions of existence of the Universe. It was more homogeneous, much much in turmoil with little conserving aspect (low entropy). Today, the universe is very very heterogeneous both micro and macroscopically, with lesser turmoil and greater conservation (high entropy). Thus, the Physics developed in last hundreds of years may well not be applicable to understand the Universe in its first billion years of life. Only such cosmological measurements may help clarify the picture existing then!

What have to say on such an aspect using your theory?

i am not familiar with your mathematical/graphical theory jargon. The way i learned Physics was to first see the known observed facts, then develop some concepts that are logical and consistent with observed facts. Only when this job is done that one starts to use Mathematical techniques to explain the physical phenomenon. Your essay emphasis that one should start first with some Mathematical concepts and then develop the concepts needed in Physics accordingly. In the former picture, whenever, something not consistent with observed facts was noted, the same was ruled out even if the mathematics demanded it.

Like space, time is a concept to understand changes/motions that need to be described and understood in Physics. Thus,Einstein introduced in relativity, time as the fourth dimension of space, using x4 = ict. Now to discuss the nature of time, one understand it as one that takes care of motion between coordinates in spatial dimensions. The introduction of the constant 'c' with 't' signifies a tie with spacial dimension. However, the problem may arise if 'c' is not a constant. There has been recent cosmological measurements indicating that light coming from an object 12 billion years away, is seen to possess the value for 'c' a little higher than the value measured on earth thus far. In my essay, i have opened up a prospect that the early universe, first billion years, may well require the 'c' to have much higher value. Also, the other physical constants may show different scale of variations. The strengths of the four force/fields may also show variation from the currently accepted relative values, if we need to understand the initial conditions of existence of the Universe. It was more homogeneous, much much in turmoil with little conserving aspect (low entropy). Today, the universe is very very heterogeneous both micro and macroscopically, with lesser turmoil and greater conservation (high entropy). Thus, the Physics developed in last hundreds of years may well not be applicable to understand the Universe in its first billion years of life. Only such cosmological measurements may help clarify the picture existing then!

What have to say on such an aspect using your theory?

Dear Ken,

Thanks VERY much for such a careful reading of our essay and such a thorough response! We believe we can answer many of your questions by clarifying our proposed formalism.

We are proposing a “quantum” not a “classical” realm at bottom. The fundamental calculation is that of a transition amplitude Z (in parlance of QFT) per a discrete path integral approach. Our...

view entire post

Thanks VERY much for such a careful reading of our essay and such a thorough response! We believe we can answer many of your questions by clarifying our proposed formalism.

We are proposing a “quantum” not a “classical” realm at bottom. The fundamental calculation is that of a transition amplitude Z (in parlance of QFT) per a discrete path integral approach. Our...

view entire post

Dear Mark and Michael:

Thanks for the very interesting (though I must say, for me, very challenging) essay.

Much of your essay is beyond me, because I am not familiar with much of the language (at least I hope it is this, and not something else in me, haha). However, I do believe that I can make at least one useful comment.

You state, “Fifth, if our approach is correct, Lorentz invariance (LI) must just be a limiting case of the RaumZeitMaterie invariance afforded by the SCC. In that case, contra Smolin, LI is effectively fundamental.” If this is so, then, by longstanding prior results (to my knowledge, starting with Brans and Stewart, in 1973), RBW can only apply in spatially trivial universes; since each spatially nontrivial topology has a state of rest, only with respect to which light travels with the same speed, in all directions (the dragging of inertial frames was not considered). In these prior results, the state of rest is only observable by a global observation, around a nontrivial subspace; but, even so, LI is certainly not fundamental, in nontrivial spaces, spherical universes being the most likely examples.

In addition, I have put forward, in my own essay, a practical experiment to observe rest; so our results are certainly at odds. I noticed, in Dr. Dreyer’s forum, that you, Michael, are aware that there is a Lorentz interpretation of the Special-Relativity formalism. This is nice to see, since so few physicists even realize the possibility of a rest frame. This being the case, I would be interested to know what you think of my results. Since I have put forward a practical experiment, my results are most falsifiable. Furthermore, since my experiment tests LI, your results would also be falsifiable, if my reasoning is correct. I would be very interested to see if I can withstand your scrutiny. Should you be interested, my essay is at:

http://fqxi.org/data/essay-contest-files/Sasaki._TDoT.pdf

One last thing: Your statement, above, implies that Smolin believes that LI is not fundamental. Do you know the initial reference for this? I have read his two most recent books; and I especially remember, in “The Trouble With Physics”, that he was quite devoted to LI. I believe he said that he would find the loss of LI “abhorrent”. In addition, he coauthored a version of Doubly Special Relativity, called DSR II, at least in large part to save LI, at the Planck scales. So I am intrigued to hear that he does not consider it fundamental.

Thanks for any efforts.

Take care,

Ken.

Thanks for the very interesting (though I must say, for me, very challenging) essay.

Much of your essay is beyond me, because I am not familiar with much of the language (at least I hope it is this, and not something else in me, haha). However, I do believe that I can make at least one useful comment.

You state, “Fifth, if our approach is correct, Lorentz invariance (LI) must just be a limiting case of the RaumZeitMaterie invariance afforded by the SCC. In that case, contra Smolin, LI is effectively fundamental.” If this is so, then, by longstanding prior results (to my knowledge, starting with Brans and Stewart, in 1973), RBW can only apply in spatially trivial universes; since each spatially nontrivial topology has a state of rest, only with respect to which light travels with the same speed, in all directions (the dragging of inertial frames was not considered). In these prior results, the state of rest is only observable by a global observation, around a nontrivial subspace; but, even so, LI is certainly not fundamental, in nontrivial spaces, spherical universes being the most likely examples.

In addition, I have put forward, in my own essay, a practical experiment to observe rest; so our results are certainly at odds. I noticed, in Dr. Dreyer’s forum, that you, Michael, are aware that there is a Lorentz interpretation of the Special-Relativity formalism. This is nice to see, since so few physicists even realize the possibility of a rest frame. This being the case, I would be interested to know what you think of my results. Since I have put forward a practical experiment, my results are most falsifiable. Furthermore, since my experiment tests LI, your results would also be falsifiable, if my reasoning is correct. I would be very interested to see if I can withstand your scrutiny. Should you be interested, my essay is at:

http://fqxi.org/data/essay-contest-files/Sasaki._TDoT.pdf

One last thing: Your statement, above, implies that Smolin believes that LI is not fundamental. Do you know the initial reference for this? I have read his two most recent books; and I especially remember, in “The Trouble With Physics”, that he was quite devoted to LI. I believe he said that he would find the loss of LI “abhorrent”. In addition, he coauthored a version of Doubly Special Relativity, called DSR II, at least in large part to save LI, at the Planck scales. So I am intrigued to hear that he does not consider it fundamental.

Thanks for any efforts.

Take care,

Ken.

Dear Ken S.,

I’m not sure why “RBW can only apply in spatially trivial universes” follows from the fact that the SCC contains LI. Are you classifying all GR cosmologies as “spatially trivial universes?” GR is locally LI so RBW’s embodiment of LI does not preclude GR cosmologies. Actually, we didn’t want to go into it, but RBW suggests a novel “non-local” spacetime geometry on cosmological scales whereby GR’s local, differentiable manifold structure obtaining only as an approximation. But, that fact aside, we expect RBW to make correspondence with GR and therefore, with GR cosmology.

Regarding the Lorentz interpretation of SR that Olaf, Fontini and others are espousing, it is not a defense of an ether frame. Rather, it's a dynamical interpretation wherein geometry is just a codification of the behavior of matter. And as I pointed out to those people, this Lorentz interpretation doesn't entail a preferred frame and thus the blockworld implication of SR holds. If on the other hand, you are really defending an ether theory, I have nothing new to add to that debate and of course would be shocked to discovery a verifiable test for such a frame. Also note that establishing an arrow of time and a preferred frame are not necessarily equivalent.

Smolin now defends the Heraclitean view we described in the essay and that's not compatible with LI being fundamental. Go to the PI site and watch his talk from the Time, Clock and the Quantum conference.

Cheers,

Michael

I’m not sure why “RBW can only apply in spatially trivial universes” follows from the fact that the SCC contains LI. Are you classifying all GR cosmologies as “spatially trivial universes?” GR is locally LI so RBW’s embodiment of LI does not preclude GR cosmologies. Actually, we didn’t want to go into it, but RBW suggests a novel “non-local” spacetime geometry on cosmological scales whereby GR’s local, differentiable manifold structure obtaining only as an approximation. But, that fact aside, we expect RBW to make correspondence with GR and therefore, with GR cosmology.

Regarding the Lorentz interpretation of SR that Olaf, Fontini and others are espousing, it is not a defense of an ether frame. Rather, it's a dynamical interpretation wherein geometry is just a codification of the behavior of matter. And as I pointed out to those people, this Lorentz interpretation doesn't entail a preferred frame and thus the blockworld implication of SR holds. If on the other hand, you are really defending an ether theory, I have nothing new to add to that debate and of course would be shocked to discovery a verifiable test for such a frame. Also note that establishing an arrow of time and a preferred frame are not necessarily equivalent.

Smolin now defends the Heraclitean view we described in the essay and that's not compatible with LI being fundamental. Go to the PI site and watch his talk from the Time, Clock and the Quantum conference.

Cheers,

Michael

Dear Michael:

We certainly have differing understandings of the “Lorentz interpretation” of the SR formalism. In all of the literature I have read, Lorentz’ (and Poincaré’s) interpretation of the SR formalism did recognize a state of rest, only with respect to which light travels with the same speed in all directions. This is what I call the “Lorentz interpretation”. But...

view entire post

We certainly have differing understandings of the “Lorentz interpretation” of the SR formalism. In all of the literature I have read, Lorentz’ (and Poincaré’s) interpretation of the SR formalism did recognize a state of rest, only with respect to which light travels with the same speed in all directions. This is what I call the “Lorentz interpretation”. But...

view entire post

Hi Mark and Michael,

Thanks for your detailed response... I'll try to focus in on one particular issue here.

>In our view, Z is the probability amplitude for a certain experimental outcome in a certain BW experimental configuration, as modeled by this “invariant core” or “actional” as we call it.

I think we might be on the same page here, but I'm not sure yet -- it...

view entire post

Thanks for your detailed response... I'll try to focus in on one particular issue here.

>In our view, Z is the probability amplitude for a certain experimental outcome in a certain BW experimental configuration, as modeled by this “invariant core” or “actional” as we call it.

I think we might be on the same page here, but I'm not sure yet -- it...

view entire post

Dear Authors,

I appreciate the emphasis on experiment and finiteness in this paper. There are qualified physicists who say that theories must NOT talk about experiments; should be frame-independent and coordinate-independent. I think Newton and Bacon taught that one should talk ONLY about experiments (not frame hypotheses). Neither of this is entirely possible. Even talking about...

view entire post

I appreciate the emphasis on experiment and finiteness in this paper. There are qualified physicists who say that theories must NOT talk about experiments; should be frame-independent and coordinate-independent. I think Newton and Bacon taught that one should talk ONLY about experiments (not frame hypotheses). Neither of this is entirely possible. Even talking about...

view entire post

Hi David,

Just a few framing statements about communication. As we say in the essay, our fundamental theory resulted from working backward from our take on QM, so I have attached the just published piece on that in a special issue of SHPMP edited by Huw Price. Second, we worry that with us coming from the discrete path integral (discrete lattice gauge theory, etc) side and you working the algebraic end, that there may be some misinterpretation---we will try and remedy this when we respond more fully on the essay site. Third, our METHOD requires only blocksystem, but that leads us to take blockworld (BW) seriously. However, as we say in the essay, our BW is RELATIONAL, meaning among other things, that there is no God's eye POV, i.e., we reject Smolin's claim that a TOE must be a theory of cosmology in that it treats the universe qua universe as the ultimate entity to be explained; we think this is the sort of wrong thinking that leads to problem of time (Wheeler-DeWitt), Our BW is also relational in that THINGS (dynamical entities with transtemporal identity) are not fundamental, but rather they emerge from spacetimematter and the SCC; so far we have expressed this formally with discrete path integrals and discrete graph theory. Someone with your appreciation of Buddhism will perhaps not be put off by the analogy with Indra's Net or interdependent origination. It's truly relations all the way down for us, that's our ontology, not just instrumentalism as perhaps with Mermin. So we worry that RQFT is further away from our bottom than yours (so to speak) and that might also make it harder for us to communicate. Shortly we will post a more formal reply, so stay tune.

Thanks so much for your interest!

Michael and Mark

I am happy to see we agree on some simple deep things, and will post in the morning. Attached, a longer formulation in process.

David

Just a few framing statements about communication. As we say in the essay, our fundamental theory resulted from working backward from our take on QM, so I have attached the just published piece on that in a special issue of SHPMP edited by Huw Price. Second, we worry that with us coming from the discrete path integral (discrete lattice gauge theory, etc) side and you working the algebraic end, that there may be some misinterpretation---we will try and remedy this when we respond more fully on the essay site. Third, our METHOD requires only blocksystem, but that leads us to take blockworld (BW) seriously. However, as we say in the essay, our BW is RELATIONAL, meaning among other things, that there is no God's eye POV, i.e., we reject Smolin's claim that a TOE must be a theory of cosmology in that it treats the universe qua universe as the ultimate entity to be explained; we think this is the sort of wrong thinking that leads to problem of time (Wheeler-DeWitt), Our BW is also relational in that THINGS (dynamical entities with transtemporal identity) are not fundamental, but rather they emerge from spacetimematter and the SCC; so far we have expressed this formally with discrete path integrals and discrete graph theory. Someone with your appreciation of Buddhism will perhaps not be put off by the analogy with Indra's Net or interdependent origination. It's truly relations all the way down for us, that's our ontology, not just instrumentalism as perhaps with Mermin. So we worry that RQFT is further away from our bottom than yours (so to speak) and that might also make it harder for us to communicate. Shortly we will post a more formal reply, so stay tune.

Thanks so much for your interest!

Michael and Mark

I am happy to see we agree on some simple deep things, and will post in the morning. Attached, a longer formulation in process.

David

Stuckey and Silberstein Replies to David R. Finkelstein questions:

Methodologically, in order to get our project off the ground, we begin with the assumption that quantum physics is about ‘explaining’ click distributions in detectors, e.g., clicks per unit time at one detector compared to another detector (relative click rates), spatial distributions of clicks over a long period of time...

view entire post

Methodologically, in order to get our project off the ground, we begin with the assumption that quantum physics is about ‘explaining’ click distributions in detectors, e.g., clicks per unit time at one detector compared to another detector (relative click rates), spatial distributions of clicks over a long period of time...

view entire post

attachments: Finkelstein_Reply_08b.pdf

Dear Ken W.,

We greatly appreciate you taking the time to offer comments and questions on our approach. Let us begin our reply by addressing your two technical questions:

You say: I think we might be on the same page here, but I'm not sure yet -- it depends on how you impose the boundary conditions when you calculate Z. If you could elaborate on how to impose the boundary...

view entire post

We greatly appreciate you taking the time to offer comments and questions on our approach. Let us begin our reply by addressing your two technical questions:

You say: I think we might be on the same page here, but I'm not sure yet -- it depends on how you impose the boundary conditions when you calculate Z. If you could elaborate on how to impose the boundary...

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In the M&M post to Ken W. immediately supra we have:

"Per QFT, yes, there are particles causing these click distributions and the game in QFT is to find the properties of these click-causing particles. Per RBW, no, fundamentally, there are no click-causing particles moving through the detector so the game in QFT is to find the ‘dynamical attributes’ which characterize the different types of trajectories."

That should read:

"Per particle physics, yes, there are particles causing these click distributions and the game in QFT is to find the properties of these click-causing particles. Per RBW, no, fundamentally, there are no click-causing particles moving through the detector so the game in QFT is to find the ‘dynamical attributes’ which characterize the different types of trajectories."

"Per QFT, yes, there are particles causing these click distributions and the game in QFT is to find the properties of these click-causing particles. Per RBW, no, fundamentally, there are no click-causing particles moving through the detector so the game in QFT is to find the ‘dynamical attributes’ which characterize the different types of trajectories."

That should read:

"Per particle physics, yes, there are particles causing these click distributions and the game in QFT is to find the properties of these click-causing particles. Per RBW, no, fundamentally, there are no click-causing particles moving through the detector so the game in QFT is to find the ‘dynamical attributes’ which characterize the different types of trajectories."

Hello Mark,

Here is another passage pertaining to the fact that photons remain stationary in the fourth dimension:

From page 148 of Dr. Brian Greene's THE FABRIC OF THE COSMOS:

"Special relativity declares a similar law for all motion: the combined speed of any object's motion trhough space and its motion through time is always precisely equal to the speed of light. . . . Morover, the maximum speed through space is reached when all light-speed motion through time is fully diverted into light-speed motion through space--one way of understanding why it is impossible to go through space at a greater than light speed. Light, which always travels at light speed through space, is special in that it always achieves such total diversion. And just as traveling due east leaves no motion for traveling north, moving at light speed through space leaves no motion for traveling through time! Time stops when traveling at the speed of light through space. A watch worn by a particle of light would not tick at all. Light realizes the dream of Ponce de Leon and the cosmetics industry: it doesn't age." --From page 148 of Dr. Brian Greene's THE FABRIC OF THE COSMOS

Ergo, a photon experiences no motion through the foruth dimension. Ergo, a photon remains in one place in the fourth dimension. And as quantum mechanics describes a photon as an expanding spherically-symmetric probabilistic wavefront, the fourth dimension must be expanding as a sphecially-symmetric wavefront! The expansion of the fourth dimension at c underlies photon's invariant velocity of c, as well as the photon's nonlocality! And too, MDT accounts for the fact that a photon remains stationary in the fourth expanding dimension, while also provding a physical framework for time and all its arrows, all of relativity, quantum nonlocality and entanglement, and entropy!

Best,

Dr. E (The Real McCoy)

Here is another passage pertaining to the fact that photons remain stationary in the fourth dimension:

From page 148 of Dr. Brian Greene's THE FABRIC OF THE COSMOS:

"Special relativity declares a similar law for all motion: the combined speed of any object's motion trhough space and its motion through time is always precisely equal to the speed of light. . . . Morover, the maximum speed through space is reached when all light-speed motion through time is fully diverted into light-speed motion through space--one way of understanding why it is impossible to go through space at a greater than light speed. Light, which always travels at light speed through space, is special in that it always achieves such total diversion. And just as traveling due east leaves no motion for traveling north, moving at light speed through space leaves no motion for traveling through time! Time stops when traveling at the speed of light through space. A watch worn by a particle of light would not tick at all. Light realizes the dream of Ponce de Leon and the cosmetics industry: it doesn't age." --From page 148 of Dr. Brian Greene's THE FABRIC OF THE COSMOS

Ergo, a photon experiences no motion through the foruth dimension. Ergo, a photon remains in one place in the fourth dimension. And as quantum mechanics describes a photon as an expanding spherically-symmetric probabilistic wavefront, the fourth dimension must be expanding as a sphecially-symmetric wavefront! The expansion of the fourth dimension at c underlies photon's invariant velocity of c, as well as the photon's nonlocality! And too, MDT accounts for the fact that a photon remains stationary in the fourth expanding dimension, while also provding a physical framework for time and all its arrows, all of relativity, quantum nonlocality and entanglement, and entropy!

Best,

Dr. E (The Real McCoy)

Hello again...

>Anyway, when we compute Z, we do so for a *specific outcome* in a *specific* experimental configuration.

Ok, good. That's a final boundary condition on the system, then, for a given calculation of Z; let's call that particular condition F_o. I assume you're using initial boundaries as well; let's call those conditions I_o. If you're then treating |Z|^2 as a joint...

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>Anyway, when we compute Z, we do so for a *specific outcome* in a *specific* experimental configuration.

Ok, good. That's a final boundary condition on the system, then, for a given calculation of Z; let's call that particular condition F_o. I assume you're using initial boundaries as well; let's call those conditions I_o. If you're then treating |Z|^2 as a joint...

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Dear Ken W.,

“Ok, good. That's a final boundary condition on the system, then, … calculate the conditional probability P(I_o|F_o) with traditional normalization W(I_o,F_o)/[ Sum_i W(I_o,F_i)], … we're exactly on the same page.”

Yes, this is our approach, although you have to realize that for us, the entire configuration to include what you’re calling initial and final...

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“Ok, good. That's a final boundary condition on the system, then, … calculate the conditional probability P(I_o|F_o) with traditional normalization W(I_o,F_o)/[ Sum_i W(I_o,F_i)], … we're exactly on the same page.”

Yes, this is our approach, although you have to realize that for us, the entire configuration to include what you’re calling initial and final...

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Dear Professors Stuckey and Silberstein,

My limited familiarity with the technical difficulties of quantum gravity made for me difficult to read your essay, but the effort was highly rewarded. Great work! Because of the relational, acausal and adynamical approach, combined with the self-consistency criterion, your work qualifies, in my humble opinion, as one of the main research programs in quantum gravity. Congratulations!

Best wishes,

Cristi Stoica

My limited familiarity with the technical difficulties of quantum gravity made for me difficult to read your essay, but the effort was highly rewarded. Great work! Because of the relational, acausal and adynamical approach, combined with the self-consistency criterion, your work qualifies, in my humble opinion, as one of the main research programs in quantum gravity. Congratulations!

Best wishes,

Cristi Stoica

Thanks, Cristi. In the wks following the contest deadline we have found the two-source transition amplitude over a graph with N nodes per our 'renormalization'. We then used this result to obtain a formula for redshift z via the twin-slit experiment. To see these most recent results (warning: they've not been vetted!) start with the paragraph after Eq. (13) in the attachment. Obviously if we've managed to produce z via this formalism, we've a link to many experiments, including those indicating anomalous galactic velocity profiles.

Thanks again for your interest,

Mark

attachments: RBW__Redshift.pdf

Thanks again for your interest,

Mark

attachments: RBW__Redshift.pdf

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