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

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 relativity, and providing a deeper *physical* model for time and all its arrows and assymetries acrosss all realms. MDT's simple postulate is that the fourth dimension is exapnding relative to the three spatial dimensions at the rate of c; and time. entropy, quantum mechanics' nonlocality and entanglement, and relativity can all be seen to emerge from this deeper postualte and its simple equation: dx4/dt=ic. All relativity is derived form this simple postualte in my paper. And too, MDT Accounts for the gravitational slowing of light and time, as shown in the attached paper, which also shows that MDT's postualte sets both c--the velcoity of light, and h--Planck's constant, while showing that there is no need to quantize gravity. All quantum behavior arises because of the wave nature of the fourth dimensions' expansion--an exapnsion which distributes locality, manifesting Huygens' principle, Feynman's many-paths, and the Heisenberg Uncertainty Principle.

You write, "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)."

Does not a blockworld approach freeze time? So how does one explain that time flows--that it time anything but frozen--if one adopts a blockworld view?

Rather than seeking an answer to the *physical* nature of time in mathematical formalisms and tautologies, MDT seeks the mergent nature of time in a new, deeper *physical* model and a new, hitherto unsung universal invariant--the fourth dimension is expanding relative to the three spatial dimensions at c.

Again, I enjoyed your Smolin references, and a great book that everyone should read is Lee Smolin's THE TROUBLE WITH PHYSICS: THE RISE OF STRING THEORY, THE FALL OF SCIENCE, AND WHAT COMES NEXT.

And everyone should pay attention to Lee's section on time, for he supposes, as MDT shows, that the *physical* nature of time holds the keys to deeper physical unification:

Here are some quotes from Lee's book, and some responses, showing how MDT holds the key to a deeper physical unification of quantum mechanics, relativity, entropy, and time and all its arrows and assymetries.

http://fqxi.org/community/forum/topic/238

Lee writes, "Thus all the theories that triumphed had consequences for experiment that were simple to work out and could be tested within a few years. This does not mean that the theories could solved exactly--most theories never are. But it does mean that physical insight lead immediately to a prediction of a new physical effect." -Lee Smolin, The trouble With Physics, The Rise of String Theory, The Fall of Science, and What Comes Next

MDT presents a new, deeper, hitherto unsung physical invariance from where all of relativity arises. It also explains physical phenomena such as entanglement and action-at-a-distance as never before, with the very sme postualte and euqation that account for relativity, and which from relativity can be derived. And thus it also unifies relativity and QM with a simple *physical* model, which also accounts for time and all its arrows and assymetries across all realms. MDT shows that quantum mechanical, relativistic, and entropic phenomena derive from the same underlying physical reality--a fourth dimension that is expanding relative to the three spatial dimensions at c, distributing locality and fathering time.

Lee writes in TTWP, "Whatever else one says about string theory, loop quantum gravity, and other approaches, they have not delivered on that front. The standard excuse has been that experiments on this scale are impossible to perform-but, as we've seen, this is not the case. So there must be another reason. I believe there is something basic we are all missing, some wrong assumption we are all making. If this is so, then we need to isolate the wrong assumption and replace it with a new idea." -Lee Smolin, The trouble With Physics, The Rise of String Theory, The Fall of Science, and What Comes Next

The wrong assumption originates from the confusion of time with the fourth dimension. Time is not the fourth dimension, but it is an emergent phenomenon that arises from a fourth dimension that is expanding relative to the three spatial dimensions. Time inherits certain properties of the fourth dimension, but the over-extending of the dimensionality of time has lead to troubling and ridiculous situations such as Godel's block universe, wherein time is frozen; and wherein the past, present, and future already and always, exist.

The fourth dimension expands at the rate of c in units of the Planck length. Thus macroscopic objects rarely ever enter into the fourth expanding dimension deeper than the Planck length. A photon is matter that surfs the expanding fourth dimension, jumping from crest to crest of all the tiny expansions of the fourth dimension which manifest themselves as expanding spheres of locality in the three spatial dimensions. Thus a photon appears as a nonlocal, spherically-symmetric expanding wavefront of probability in the three spatial dimensions. Furthermore, a photon does not age as it stays in the exact same place in the fourth expanding dimension, causing its nonlocal, expanding probability wave to translate with a velocity of c in the three spatial dimensions. The expansion of this nonlocal, spherically-symmetric probability distribution that describes the photon's motion is a most fundamental clue that practically screams at us that the fourth dimension is expanidng relative to the the three spatial dimensions, as a photon remains stationary in the fourth dimension, and thus a photon's spherically-symmetric expandidng wavefront defines a locality in the fourth dimension, no matter how large it gets. Ergo nonlocality and entanglement, as well a steh fact that a photon does not age. Please see attachment #2.

Lee Smolin continues in TTWP, "What could that wrong assumption be? My guess is that it involves two things: the foundations of quantum mechanics and the nature of time. We have already discussed the first; I find it hopeful that new ideas about quantum mechanics have been proposed recently, motivated by studies of quantum gravity. But I strongly suspect that the key is time. More and more, I have the feeling that quantum theory and general relativity are both deeply wrong about the nature of time. It is not enough to combine them. There is a deeper problem, perhaps going back to the origin of physics." -Lee Smolin, The trouble With Physics, The Rise of String Theory, The Fall of Science, and What Comes Next

MDT takes us back to the origin of relativity--back to Einstein's 1912 Manuscript where Einstein does not state that time is the fourth dimension, but rather x4=ict, and MDT presents us with a fundamental view of reality that conforms to all experimental evidence, while not only resolving the paradoxes of the non-locality of the EPR effect and Godel's block universe, but unifying the resolution within a simple physical postulate. Before Einstein's relativity, space and time (as well as matter and energy) were considered to be disparate entities. Einstein's relativity united them, and suddenly time was mistakenly seen as the fourth dimension, rather than as an emergent property of a fourth dimension expanding relative to three spatial dimensions. Then, when Einstein correctly saw that all moving objects are shortened when energy is added--when they are rotated out of the three spatial dimensions and into a fourth dimension--just as a far-away ruler appears shortened as it is rotated, Einstein had the genius to call upon a the four-dimensional formulation of space-time.

However, this lead to confusion; as Einstein did not see that macroscopic object's-rest masses-never enter the fourth dimension deeper than the Planck length. Hence the past and future do not yet exist, but only the present. Nor did Einstein realize that the fourth dimension is expanding relative to the three spatial dimensions-a simple postulate with far-reaching consequences. Legend has it that Einstein eventually came up with relativity because he so often contemplated what it would be like to catch up with light--a pursuit which began in his childhood. I often wonder, had Einstein known that light actually propagates as a spherically-symmetric probabilistic wavefront at the rate of c--had he actually known quantum mechanics--would he have seen that the fourth dimension is expanding relative to the three spatial dimensions, or dx4/dt=ic?

What's really funny to me is not that people try to refute MDT, but that they try to refute the timeless, ageless photon, free will, quantum entanglement, nonlocality, entropy, time and all its arrows and assymetries, simple math, elegance, relativity, and novel physical theories that come with a postulate and equation.

MDT: The fourth dimension is expanding relative to the three spatial dimensions: dx4/dt = ic

Both Einstein and Minkowski wrote x4 = ict, but they never saw that this naturally implied dx4/dt = ic.

And Einstein's Relativity may be derived from dx4/dt= ic, which represents a more fundamental invariance of this universe--the fourth dimension is expanding relative to the three spatial dimensions at c. Einstein introduced relativity as a principle--as a law of nature not deduced from anything else, and well, I guess I was dumb enough to ask, 'why relativity?' And I found the answer in a more fundamental invariance--the fourth dimension is expanding relative to the three spatial dimensions, or dx4/dt = ic.

And not only can all of relativity be derived from this, but suddenly we are liberated from the block universe and time and progress in theoretical physics are unfrozen. And change is seen in a most fundamental equation that weaves change into the very fabric of space-time, where it needs to be, as change pervades every realm of physics and all acts of *physical* measurement. And suddenly we have a *physical* model for entropy, time and its arrows and assymetries in all realms, free will, and quantum mechanics' nonlocality, entanglement, and wave-particle duality. The fourth expanding dimension distributes locality, fathering time. MDT accounts for the constant speed of light c--both its independence of the source and its independence of the velocity of the observer, while establishing c as the fastest, slowest, and only velocity for all entities and objects moving through space-time, as well as the maximum velocity that anything is measured to move. And suddenly we see a *physical* basis for the dualities--for space/time, wave/matter, and energy/mass or E=mc^2. Energy and mass are the same thing--it's just that energy is mass caught upon the fourth expanding dimension, and thus it surfs along at "c."

Dr. Lee Smolin continues in TTWP, "Around the beginning of the seventeenth century, Descartes and Galileo made a wonderful discovery: You could draw a graph, with one axis being space and the other being time. A motion through space then becomes a curve on the graph. In this way, time is represented as if it were another dimension of space. Motion is frozen, and a whole history of constant motion and change is presented to us as something static and unchanging. If I had to guess (and guessing is what I do for a living), this is the scene of the crime". -Lee Smolin, The trouble With Physics, The Rise of String Theory, The Fall of Science, and What Comes Next

MDT unfreezes time, liberating us all with free will--the free will to move beyond ST & LQG, which are not inextricably locked into the fixed future of the block universe as Brian Green et al might have you suppose. Neither the future nor the past exists. Motion is inherent in the underlying four-dimensional space-time geometry, as the fourth dimension is expanding relative to the three spatial dimensions.

Finally a postualte and equation step forth to weave change into the fundamental fabric of space-time!

Einstein noted that all objects are moving through space-time at the velocity c. This never changes. An object stationary in the three spatial dimensions is translating through the fourth dimension at the rate of c. An object stationary in the fourth dimension--a photon--is translating through the three spatial dimensions at the rate of c. Hence it is obvious that the fourth dimension is expanding relative to the three spatial dimensions.

Lee Smolin writes in TTWP, "We have to find a way to unfreeze time-to represent time without turning it into space. I have to idea how to do this. I can't conceive of a mathematics that doesn't represent a world as if it were frozen it eternity. It's terribly hard to represent time, and that's why there's a good chance this representation is the missing piece." -Lee Smolin, The trouble With Physics, The Rise of String Theory, The Fall of Science, and What Comes Next

MDT unfreezes time, as well as progress in theoretical physics, and liberates us from the block universe!

There actually is no problem with the representation of time in physical theories, but only within the interpretations and extrapolations of modern theorists. Time, as it is defined, works perfectly in quantum mechanics and relativity, as it does in Newtonian mechanics and classical electrodynamics. Hence our cars and computers work perfectly well each and every day.

However, when the notion of time is warped and extrapolated to suit the fantasies of prominent physicists who ignore logic, reason, and experiment, in order to create multiverses/40 dimensions/parallel universes/wormholes and time machines, it only goes to show that time is not the fourth dimension, but an emergent property of a universe wherein a fourth dimension is expanding relative to the three spatial dimensions.

Lee Smolin continues in TTWP, "One thing is clear: I can't get anywhere thinking about this problem within the confines of string theory. Since string theory is limited to the description of strings and branes moving in fixed background spacetime geometries, it offers nothing for someone who wants to break new ground thinking about the nature of time or of quantum theory. Background-independent approaches offer a better starting point, because they have already transcended the classical pictures of space and time. And they are simple to define and easy to play with." -Lee Smolin, The trouble With Physics, The Rise of String Theory, The Fall of Science, and What Comes Next

Indeed String Theory has banned asking the questions that MDT addresses, such as "What is the nature of the physical framework underlying the observed phenomena of relativity and quantum mechanics?" String theory has bred an entire generation of physicists who believe that politics, hype, and name-calling are to be preferred over logic, reason, and truth to advance physics. String Theory, though funded with hundreds of millions, yet lacks the simple truth and beauty of this postulate and equation--"the fourth dimension is expanding relative to the three spatial dimensions. dx4/dt =ic." It is almost as if simple postulates and equations representing simple physical truths have been banned from physics, along with physics.

Dr. Smolin continues in TTWP, "I won't say any more about this, because I want to move on to a different question. Suppose an intellectually ambitious young person with an original and impatient mind wants to think deeply about the five great questions. Given our failure to solve any of them, I can't imagine why such a person would want to be limited to working in any of the current research programs. Clearly, if string theory or loop quantum gravity by themselves were the answer, we would know it by now. They may be starting points, they may be parts of the answer, they may contain necessary lessons. But the right theory must contain new elements, which our ambitious young person is perhaps uniquely qualified to search for." -Lee Smolin, The trouble With Physics, The Rise of String Theory, The Fall of Science, and What Comes Next

Everyone should read George Orwell's Animal Farm.

Perhaps the excessive funding of theories never backed by experiment, nor logic, simplicity, elegance, and reason for that matter, has resulted in institutions that now oppose the advancement of physics. Remember how in Ray Bradbury's Fahrenheit 451 the firemen existed to light fires and burn books, and not to save them? Well, is it any wonder that Esinetin's 1912 Manuscript is never assigned by the current regime, nor any of the other foundational papers? Imagine a school that assigned the foundational papers in every class! Why not learn relativity from Einstein's 1912 Manuscript? Perhaps then we'll see that he never said that time is the fourth dimension, but rather that x4 = ict.

Smolin is to be commended for firing a warning shot across the bow of all young physicists--letting them know that they, if they are to be true physicists, are essentially on their own. For the advancement of science has ever been the domain of the individual, as has the creation of all lasting art, philosophy, literature, and culture. Make no mistake-the individual truth seeker is not alone in the context of the greats-they stand upon the shoulders of giants-but they are often alone in the context of their contemporaries. String Theory, by deconstructing great physicists and science, and then instituting regimes independent of humility before reality, has tried to invert this, placing politics over philosophy and money over meaning, and that is why they are destined to fail. For as Shakespeare said, "foul deeds will rise, though all the earth overwhelm them, to men's eyes."

Smolin continues in TTWP, "What has my generation has bequeathed to these young scientists? Ideas and techniques they may or may not want to use, together with a cautionary tale of partial success in several directions, resulting in a general failure to finish the job Einstein started a hundred years ago. The worst thing we could do would be to hold them back by insisting that they work on our ideas. So the question for the last part of the book is a question I ask myself every morning: Are we doing all we can to support and encourage young scientists--and, by the virtue of this, ourselves--to transcend what we have done these last thirty years and find the true theory that solves the five greatest problems in physics?" -Lee Smolin, The trouble With Physics, The Rise of String Theory, The Fall of Science, and What Comes Next

Well, I guess the jury is still out on all this. But Max Planck warns us about the centralization of funding and power, as well as the micromanaging of curiosity:

"New scientific ideas never spring from a communal body, however organized, but rather from the head of an individually inspired researcher who struggles with his problems in lonely thought and unites all his thought on one single point which is his whole world for the moment." --Max Planck

"A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it." --Max Planck

"Great spirits have often encountered violent opposition from weak minds." --Einstein (e.g. Boltzman, Bruno, Galileo, Socrates, Dante, Jesus)

"The important thing is not to stop questioning. Curiosity has its own reason for existing." --Einstein. And the big questions which have driven science have always been asked by an individual.

"Equations are more important to me, because politics is for the present, but an equation is something for eternity." --Einstein. It is interesting to point out that neither ST nor LQG really have equations, nor meaningful postulates, for that matter. Contrast this to MDT: dx4/dt=ic: the fourth dimension is expanding relative to the three spatial dimensions.

"The further the spiritual evolution of mankind advances, the more certain it seems to me that the path to genuine religiosity does not lie through the fear of life, and the fear of death, and blind faith, but through striving after rational knowledge." --Einstein. Yes--the truth does set us free, from the block universe and frozen time and progress in theoretical physics.

Thanks for the paper Mark! I enjoyed the Smolin references/views, and I hope MDT might help you take it further!

Best,

Dr. E (The Real McCoy)Attachment #1: 1_9_MOVING_DIMENSIONS_THEORY_EXAMINES_THE_GRAVITATIONAL_REDSHIFT_SLOWING_OF_CLOCKS.pdfAttachment #2: 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 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 only through space.

As you know, there is but one velocity for every object through our 4D spacetime--c, and a photon's motion occurs entirely through the three spatial dimensions, while it remians stationary in the fourth dimension. I quote Brian Greene commenting on this below.

I basically asked the question, "What if we approach the invariant interval from the photon's frame?" Surely the photon is not moving through the fourth dimension, while also propagating at c through the three spatial dimensions, as if it were also moving through the fouth dimension it would have to travel faster than c.

Now we all know that photons do not age. Ergo a photon does not move through time. All of a photon's motion is through space.

A timeless, ageless photon remains stationary in time. It remains stationary in the fourth dimension, while propagating at c through space.

All of a photon's motion is through the three spatial dimensions.

None of the photon's motion is through the fourth dimension.

A photon does not age.

Of course time passes for us in the lab frame, and we will agree that time has passed while a photon travels, as our watches tick.

But no time passes for the timeless, ageless photon. Ergo, in the photon's frame, the photon has not moved in time. And thus the photon has not moved in the fourth dimension.

As Brian Greene points out in the Appendix to Chapter 2 of The Elegant Universe, we note that from the space-time position 4-vector x=(ct,x1,x2,x3), we can create the velocity 4-vector u=dx/d(tau), where tau is the proper time defined by d(tau)^2=dt^2-c^-2(dx1^2+dx2^2+dx3^2). Then the "speed through space-time" is the magnitude of the 4-vector u, ((c^2dt^2-dx^2)/(dt^2-c^-2dx^2))^(1/2), which is identically the speed of light c. Now, we can rearrange the equation c^2(dt/d(tau))^2-(dx/d(tau))^2=c^2 to be c^2(d(tau)/dt))^2+(dx/d(tau))^2=c^2. This shows that an increase of an object's speed through space, (dx/d(tau))^2)^(1/2)= dx/d(tau) must be accompanied by a decrease in d(tau)/dt which is the object's speed through time, which also may be considered the rate at which time elapses on it's own clock d(tau) or the proper time, as compared with that on our stationary clock dt.

Ergo the faster an object moves through space, the slower it moves through time; but all objects always move at c through the four dimensions; and light has all of its movement through space, and thus is can have none of it through the fourth dimension.

In An Elegant Universe, Brian Greene almost characterizes Moving Dimensions Theory's deeper reality:

"Einstein found that precisely this idea--the sharing of motion between different dimensions--underlies all of the remarkable physics of special relativity, so long as we realize that not only can spatial dimensions share an object's motion, but the time dimension can share this motion as well. In fact, in the majority of circumstances, most of an object's motion is through time, not space. Let's see what this means." Space, Time, and the Eye of the Beholder, An Elegant Universe, Brian Greene, p. 49

Right here Brian almost grasps MDT. But time is not a dimension. Time is an emergent phenomenon that arises because the fourth dimension is expanding relative to the three spatial dimensions at the rate of c. Let's rewrite Brian's paragraph with MDT's insights:

"Einstein found that precisely this idea--the sharing of motion between different dimensions--underlies all of the remarkable physics of special relativity, so long as we realize that not only can the three spatial dimensions share an object's motion, but the fourth dimension, which is moving relative to the three spatial dimensions, can share this motion as well. In fact, in the majority of circumstances, most of an object's motion is through the fourth dimension, not the three spatial dimensions. Let's see what this means." Space, Time, and the Eye of the Beholder, An Elegant Universe, Brian Greene, p. 49

Most objects are traveling far less than c through the three spatial dimensions. Thus most objects are traveling close to the rate of c through the fourth dimension. To be stationary in the three spatial dimensions implies a velocity of c through the fourth dimension. Ergo the fourth dimension is expanding relative to the three spatial dimensions. To be stationary in the fourth expandning dimension, as is the timeless, ageless, nonlocal photon, implies a velocity of c through the three spatial dimensions. Ergo the fourth dimension is expanding relative to the three spatial dimensions.

dx(4)/dt = ic

Brian Greene continues:

"Motion through space is a concept we learn about early in life. Although we often don't think of things in such terms, we also learn that we, our friends, our belongings, and so forth all move through time, as well. When we look at a clock or a wristwatch, even while we idly sit and watch TV, the reading on the watch is constantly changing, constantly "moving forward in time." We and everything around us are aging, inevitably passing from one moment of time to the next. In fact, the mathematician Hermann Minkowski, and ultimately Einstein as well, advocated thinking about time as another dimension of the universe--the fourth dimension--in some ways quite similar to the three spatial dimensions in which we find ourselves immersed." Space, Time, and the Eye of the Beholder, An Elegant Universe, Brian Greene, p. 49

What Greene misses is that the time measured on your watch--the ticking seconds--is not the fourth dimension, but it is a phenomenon that emerges because the fourth dimension is expanding relative to the three spatial dimensions. The time measured on a clock or watch relies on the emission and propagation of photons, be it in the context of an unwinding clock spring or an oscillating quartz crystal, or even the beating of a heart. And photons are matter that surf the fourth expanding dimension. As time is so inextricably wed to the emission and propagation of photons, and as photons are matter caught in the fourth expanding dimension, our notion of "time" inherits properties of the fourth expanding dimension. But the fact is that time emerges from a deeper physical reality--a fourth dimension that is expanding relative to the three spatial dimensions.

Brian Green continues on, heading off in the wrong direction that just misses the central postulate of MDT:

"Although it sounds abstract, the notion of time as a dimension is actually concrete."

But it is not. Can you move to where your watch reads three seconds back in time? Or can you move to where your watch reads an hour back in time? We can walk left or right. We can climb up or down. We can move forwards or backwards. But we can't move through time like we can through the three spatial dimensions. This is because time, as measured on our watch, is not the fourth dimension, but it is a construct we have devised which is based on the fundamental fact that the fourth dimension is expanding relative to the three spatial dimensions, governing the emission and propagation of photons, by which time is known and measured on our watches.

Brian Green continues on,

"When we want to meet someone, we tell them where "in space" we will expect to see them--for instance, the 9th floor of the building on the corner of 53rd Street and 7th avenue. There are three pieces of information here (9th floor, 53rd Street, 7th avenue) reflecting a particular location in the three spatial dimensions of the universe. Equally important, however, is our expectation of when we expect to meet them--for instance, at 3 PM. This piece of information tells us where "in time" our meeting will take place. Events are therefore specified by four pieces of information: three in space and one in time. Such data, it is said, specifies the location of the event in space and in time, or in spacetime, for short. In this sense, time is another dimension."

But again, time is different from the three spatial dimensions. Time is inextricably wed to our sense of the past--the order stored in our memory, long with our ability to imagine and dream of future events. The present is where we put our dreams into action. However, the time defined by past, present, and future is not a dimension akin to the three spatial dimensions, but rather it is a phenomenon that emerges because the fourth dimension is expanding relative to the three spatial dimensions.

MDT agrees 100% with all of relativity. In fact, relativity is derived from MDT in my paper.

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 viewpoint, which you call the "God's Eye View". I'm not sure why you're unwilling to embrace this perspective -- you cite Smolin's arguments, but once you allow for any retrocausality at all, the surviving arguments are fairly weak. I think you should tackle his arguments head-on, and not duck the issue. By *not* adoping such a viewpoint, you're opening yourself up to criticism that you're just picking and choosing the aspects of the block universe that you agree with, trying to have it both ways by sacrificing consistency.

Your stance also opens up a whole slew of questions in my own mind.... 1) Is there a God's Eye View for a sub-system of the universe? What does it look like? 2) Does the lack of global God's Eye View mean it's impossible to do quantum cosmology? Can you even do regular cosmology? 3) Once you dispatch with the God's Eye View, is there any non-trivial meaning left in the phrase "block world"? You seem to be telling me to adopt a particular viewpoint, and then you tell me that the viewpoint is invalid, and I'm not sure what I'm left with.

B) You claim that the only difference between QFT and classical physics is one of *degree* (rarified vs. dense sources). I find this rather incredible, for a variety of reasons... are you saying that stimulated emission of an intense laser in a solid-density lasing medium is a classical process?

C) I don't understand your approach to boundary conditions. For any system, what is given and what is calculated? Take the page 3 example concerning the relationship between X,Y and Z. You're eschewing the viewpoint that X is given as an initial boundary condition, which then determines Y and Z. That's all well and good... but what are you replacing this with? This section reads like you're starting with the assumption that X, Y and Z *will* happen, and the only question concerns their relationship. (I think perhaps you meant to expand on this issue, as hinted in your footnote #5, but perhaps it got edited out of this essay?) The SCC is great, but is certainly not enough to tell me what parts of a system one can simply take as given, and which parts have probabilities that one can calculate. For that you need boundary conditions, I think.

On a related issue to boundary conditions, you claim "The big bang... is ultimately no more special than any other point in spacetime." So you don't consider the Big Bang to be a boundary condition on the universe? No underlying reason why entropy started out so low to explain the 2nd law of thermodynamics? (The very fact that the big bang's entropy was so low seems to point to it being "special" in at least some way.)

D) You claim that "no formal or conceptual tensions remain between GR and quantum physics as unified by RBW", which is quite a statement... I'd like to see some further justification of this claim, ideally by using RBW to "fix" the aspects of QM and QFT that are unable to treat time and space on the same footing. In other words, use RBW to answer questions such as: 1) Why is there no time operator analogous to the spatial position operator in QM? 2) Why aren't most of the axioms in axiomatic QFT extendable to curved space-time? 3) How does one distinguish particles from antiparticles in curved space-time? Etc., etc...

Finally, I wasn't clear if your solution to the "collapse" was the same general idea that I'm arguing for in my essay, or something completely different. I'm still trying to figure out exactly where our ideas overlap, and where they don't. If I can get past point A) above, I think there will be quite a lot of overlap, so I'm looking forward to discussing this with you further...

Cheers!

Ken

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?

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 only change to discrete QFT (as practiced via lattice gauge theory for example) is that we don't use a hyper-cubic lattice (a change Wise (2006) has been investigating) and we propose a mechanism for constructing the 'core' or invariant part of Z (somewhat related to but more rigorous than the current method, i.e., guess at the underlying symmetry group). So, technically speaking, we're pretty conservative (certainly our approach does not require a major rewrite of quantum physics as you suggest).

Essentially the 'core' is that part of the integrand of Z that doesn't contain the integration variable, Q (remember, Z is a "path integral" as in least action so its integrand is the Lagrangian density). So, we view Z as a mathematical machine that measures the symmetry of that part of the discrete "Lagrangian density" that remains once it has been stripped of the integration variable (this is only clear in the discrete approach). This view differs from the dynamical view wherein Z is the probability amplitude for the transition of one state to another. 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. Thus, just like your formalism, we are using "future boundary conditions" when we construct the actional in accord with a particular outcome.

The difference between your ontology and ours is that we don't invoke retrocausation, rather we stick to an "all at once" view of the experiment, i.e., BW. Cramer and Price for example are clear that talk of retrocausation in the BW is "pedagogical" or "perspectivial" only, just like forward-causation. We do not take the wave function realistically, our explanation is acausal and global, rather than retrocausal; the details are in the Foundations and Studies papers. Hopefully this answers your question about the "collapse" problem, obviously there is no collapse b/c there is no wave function.

Now let's keep using our take on QM to talk more about unification generally in RBW. If you understand the formalism supra, it's obvious, technically speaking, how we propose to recover QFT and classical physics, i.e., precisely as lattice gauge theory gives QFT (space and time become discrete) and then hbar -- > 0 to get to classical physics. We're adding a realm whereby we let discrete time become continuous but keep discrete space and we liken this realm to QM which finishes our unification format. We've got a simple 2-source case worked out in our Foundations paper for discrete space and continuous time (sources are spatial delta functions) whereby we show "interaction without mediation." In this view of QM, a detector click is not viewed as resulting from a wave or particle traveling through empty space from the source to the detector. There's nothing in the formalism that serves as a counterpart to any 'things' other than the source and detector event. We rather say that the detector event is part of the detector as it relates to the source (all things are given relationally in our view). And, mysteries associated with the twin-slit experiment and EPR-Bell phenomena, for example, are understood to result from attempting to tell a dynamical story about an underlying adynamical phenomenon.

Thus reality is, at bottom, adynamical. You recover classical dynamical reality in the limit of dense events (hbar -- > 0). In that realm, we propose you use classical dynamical theories (would you use quantum physics to compute the trajectory of a baseball?). Dynamical theories include GR, which we use to do cosmology and of course we will recover per figure 1 if we are right. But note that the existence of a big bang is not something that requires a dynamical explanation on our view -- not only does the big bang exist timelessly per the BW, but what's fundamental is the adynamical self-consistency criterion (SCC). So yes, we are rejecting quantum cosmology in two senses: 1) we reject wave-function realism and 2) we reject the idea that the big bang (and the universe at large) has a dynamical explanation fundamental to the SCC at all. But, you ask, what's the underlying explanation for the big bang, which is special because it in turn explains the entropic arrow?

Yes, the big bang is special in that sense, although there is a question about what you mean by "the entropy of the entire universe" in GR (What counts as the universe? How can you talk about the global value of entropy when you can't talk about the global value of energy in GR? Etc.). And of course cosmic time is important in general for the narratives of cosmology. We have not answered those questions but, again, keep in mind whatever answer is forthcoming (if any) won't be dynamical. Perhaps the explanation will turn out to be one of self-consistency as we suggested, that is, like a jig-saw puzzle or cross-word puzzle, the big bang had to exist given certain other features of the universe. However this is just speculation at this juncture. So, why a big bang as opposed to, say, a steady-state world? Perhaps many possibilities are consistent with the SCC so that a unique cosmology follows only after some piece of the puzzle is given (typical boundary value problem).

But, back to the present reality. Might RBW have ANYTHING to say about cosmology or astrophysics as such? Or, do we have to rely solely on dynamical theories like GR at that level? It turns out, we might have something to say. Suppose two elliptical galaxies are colliding and you want to know the possible orientations of the spiral galaxies that might result. Would you use quantum physics for that? No. But, we suspect RBW might have something to say about the kinematical data for the classical theory you WOULD use. Why? Because we infer galactic kinematics (inter and intra) from redshifted spectra and that IS the realm of quantum physics! So, for example, the problem we're working on right now is to find out if RBW has any possible corrections to make to the flat rotational velocity profile of M31. In other words, what kinematical assumptions might be replaced in conjunction with the measured redshifts so that what we mean by the 'dynamical stellar velocity' of a particular region in M31 conforms to Newtonian gravitational dynamics? [Thus, no dark matter.] This, not large energy densities, is the realm of "quantum gravity" in our approach. [BTW, I'm sure you noticed that our approach automatically accounts for Novikov's self-consistency conjecture - the problematic worldlines simply don't exist b/c the vacuum solutions of GR are an approximation accurate only IF one can construct a divergence-free stress-energy tensor on the curves of interest.]

Ok, lastly, why do we say there is no God's eye POV on the one hand and that BW is important in our approach on the other? Are we in training to run for political office? Notice that there is no logical contradiction here, we're not claiming that existence is frame dependent and internal but rather that change and becoming are. There is nothing obviously fishy about claiming that all events are equally real AND there is no frame of reference from *outside the universe* from which you can perceive, theorize about, explain, etc., the BW--one must take seriously that relations are fundamental. Quantum cosmology presupposes that the universe is fundamentally "made of" things obeying dynamical equations of motion (wave functions, m-branes, quantum loops, whatever) and therefore constitutes a dynamical system in its own right in need of dynamical explanation; thereby leaving a mystery about the origins of initial and boundary conditions such as the big bang. But as we pointed out in the essay, that leads to serious seemingly inexplicable problems and raises the specter of never ending WHY questions such why our laws instead of others, etc. And of course when the universe itself including the big bang is the system we want to explain, what counts as boundary conditions? For example, in the case of the universal wave function, what is the preferred basis as given by environmental decoherence when the universe is by definition everything? Reality in RBW is more like Indra's Net (there is nothing outside it to explain it, just the inter-relations that make it up) than a *thing* governed by a dynamical law. Notice that even cyclical models of cosmology don't put a halt to why questions about laws, universal initial conditions, etc., they just push them back one. Every theory in the end has got to have some brute facts so the winner is the one who can explain the most with the least (reductionism per Weinberg).

Methodologically, as we described above, you can see that we use BW just as you do, via future boundary conditions. In that sense, BW is important to our approach. Is the experimentalist's view a God's eye POV? Yes and no. Formally, yes, the existence of the experimentalist is not (typically) put into the calculation, i.e., her gravitational or EM influence is not accounted for in the calculation. In that sense, they become a detached God-like observer. But, of course, they DO have SOME influence, we're just ignoring it because it's assumed negligible. [Remember when the moon's gravitational effect was noticed in a particle physics experiment? We don't always make the right assumption in these cases, but usually we're OK.] So precisely speaking, no, the experimentalist IS part of the universe and IS part of the situation and therefore does NOT possess a God's eye POV - even in conventional realism. In relationalism, inseparability occurs with a vengeance. This is consistent with your retrocausality, we suspect.

Ok, we've got about 2000 words here, 20% of our essay proper, so we should probably stop and let you jump in again :-)

Michael and Mark

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.

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

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 this is just semantics.

My assertion that RBW is not viable, in nontrivial topologies, comes from the understanding that it contains LI as "fundamental", which I took to mean not just a local illusion.

In nontrivial topologies, LI is certainly not fundamental but is just a local illusion. I came to understand this by realizing the following (which is discussed in my essay, in more detail and with pictures):

Consider a cylindrical space-time, with time in the axial direction. Two twins travel with opposing constant velocities, from some starting point, and meet again at the other side of the cylinder. Which is older? With SR's reciprocal time dilations, it cannot describe the twin's ages, when they meet again. Therefore, SR obviously cannot be fundamental, in this space; it can only hold locally, as an illusion. The Ether theory commonly known as the "Lorentz-Poincaré Ether Theory" (LPET) is fundamental in this space. The rest frame breaks the symmetry between the twins; unless they both have the same speed, with respect to the rest frame, in which case, they would have symmetrical motion.

I can give you twelve references that support what I have just said; but if you doubt me, just see the following, it is the most insightful:

P.C. Peters, Am. J. Phys. 51 (9), 791-795 (1983), Periodic boundary conditions in special Relativity.

Similarly, LPET must be fundamental, in the flat subspaces of any spatially nontrivial topology, as well as in any trivial topology containing a wormhole (I can give you an example of such a space, if you like).

If RBW can live with LI as a local illusion, then, by the above, it can apply in nontrivial topologies, but if not, it can't. However, as I have said, I have put forth a practical experiment that will dispense with LI. Therefore, if I am right, RBW must live or die with a rest frame that is observable with today's technology.

You said that you, "...would be shocked to discovery a verifiable test for such a frame." Well, if you like the really big surprises, in your life, you have to take some chances with things that you think can't be true. If you wait for some expert to say it is true, the surprise won't be nearly so big.

As I have said, my work is most falsifiable. My theory is compatible with all observations to date, since it uses the GR formalism (in case you are wondering, I discuss the PPN formalism briefly, in an appendix); and I have put forth an experiment. So if my work has a problem, a competent analysis will establish it, beyond question. I am a little surprised that no one has undertaken to test my work, since it is the only essay I have seen here that is so testable (I have not read them all). If you can find a problem with my work, I would be most grateful; and if you can't, tell some friends.

Take care,

Ken.

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 depends on how you impose the boundary conditions when you calculate Z. If you could elaborate on how to impose the boundary conditions (see point C in my earlier post), I'd appreciate it.

>The difference between your ontology and ours is that we don't invoke retrocausation, rather we stick to an "all at once" view of the experiment

This seems to me like a meaningless semantic distinction. In a block-world picture, of course everything happens "all at once"; there's no other way for things to happen. The same events, when viewed in a non-block-world picture, necessarily look like ordinary causation or retrocausation. View it in the opposite order and the retrocausation looks ordinary, and vice-versa. It's just a matter of perspective.

> And, mysteries associated with the twin-slit experiment and EPR-Bell phenomena, for example, are understood to result from attempting to tell a dynamical story about an underlying adynamical phenomenon.

>Thus reality is, at bottom, adynamical.

But that's just it: what looks like dynamical laws in a non-block-universe perspective can look (must look!) adynamical in a block universe. Your "story" should be able to go back and forth between the two views, even if one is more "correct" than the other.

The issue isn't really dynamical vs. adynamical "stories" -- it's causal vs. acausal stories. And by not talking about boundary conditions, your papers seem to me to be more on the acausal side of things. (I'm firmly on the causal side; the causes are the boundary conditions.) Maybe that's why you think I am "invoking retrocausation" -- because I'm talking about causes and you aren't? My point is that a cause in a non-block view can be mapped onto a boundary condition in a block-view.

>You recover classical dynamical reality in the limit of dense events (hbar -- > 0).

Again, I find this hard to swallow -- but it might make more sense if I knew which parts of your calculations were externally imposed (boundaries), and which are determined by the system itself. (Do the boundaries fundamentally change in the limit where hbar-->0?)

> There is nothing obviously fishy about claiming that all events are equally real AND there is no frame of reference from *outside the universe* from which you can perceive, theorize about, explain, etc., the BW

But what about a subsystem of the universe -- is there a "God's eye view" of that?

>So precisely speaking, no, the experimentalist IS part of the universe and IS part of the situation and therefore does NOT possess a God's eye POV - even in conventional realism.

But for a subsystem (in, say, a 4-volume V), there's a nice division between experimenter and system. In this case the experimenter is not in V. And together with the experimental equipment, the interaction with V occurs on the hypersurface boundary of V. So here's a case where the experiment is part of the boundary of V, but not part of V itself. Shouldn't the "God's eye view" for V work in this case?

And this boundary, of course, is precisely where I think the boundary conditions on that system should be imposed. Again, I'd like to hear your take on that.

Best,

Ken

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 experiments requires a theory; any language is a kind of theory. And the concept of experiment is socially determined and keeps changing.

One might wonder how a theory that does not talk about experiments can ever claim to say anything about experiments. If one looks carefully, there is usually an appeal to a naive theory of perception. The implicit claim is that we see things "as they are" and without mediation; no need for the theory to mention that process, therefore. Then relativity becomes irrelevant or meaningless; if no frame is needed, why should a change in frame be important? So the great success of physics since Newton flows mainly from his philosophy, not Plato's.

My main question is about the whole blockworld perspective. If the whole world is the block, who is looking at it? "Blockworld" suggests that it is sub species aeternitas, from the point of view of eternity, the God's-eye view. This is great for mathematicians, who are the Gods of the worlds they create, and who therefore can look down their noses on mere coordinate representations. But they are outside their system. They can sneeze without disturbing the prime numbers. Physicists do not have that option. They have no perceptions without unpredictable reactions on the perceived. Only coordinate measurements are available, and they are not faithful, but at least they acknowledge the existence of the reference frame for the coordinates. In my own work I respect the frame as much as possible.

If "blockworld" just means treating histories instead of instants, I am a blockworlder. My concern is, how detailed is the history supposed to be, and of what is it the history?

Best regards,

David

________________

Dear David,

Note that ours is a relational BW (ultimately no God's eye POV) and as you have sometimes suggested, in RBW space, time and matter are co-dependent and co-fundamental.

Cheers,

Michael

________________

Michael,

I'm still confused. I'll number my sentences so you can tell me which ones are wrong by its number.

1. Your equation (1) represents an operator that acts on the statevector of a system.

2. The system under study is not the universe, but a part of it.

3. The universe doesn't have statevectors.

4. So blockworld really means blocksystem for every system in the world.

If I catch your drift correctly then we are in accord. But I would like to touch base before running further.

Best,

David

____________________

David,

You asked: Your equation (1) represents an operator that acts on the statevector of a system.

Answer: No. Z is the probability amplitude, not the propagator acting on a state vector. [In wave language of course, the propagator is the wavefunction when ?(t=0) is a spatial delta function.] We don't have statevectors in Hilbert spaces, but probability amplitudes for specific outcomes in specific experimental arrangements in spacetime. We can do this (work in spacetime rather than Hilbert space) because we input future boundary conditions, i.e., the outcome(s). This is the basis for our claim that we're working in a blockworld.

As for the formalism, we're simply borrowing that of discrete QFT without a hypercubical spacetime lattice. There are a few others looking into graphical QFT in this generalized fashion, e.g., Wise is referenced in the essay. We're using the formalism a bit differently because we want to do what we consider to be a more fundamental calculation - instead of the dynamical characteristics associated with entire trajectories in various external EM fields (e.g., spatially continuous detector regions around particle accelerators), we're simply trying to get the probability amplitudes for the spatiotemporal distribution of discrete collections of detector clicks. Of course, that's what particle physics is doing, but QFT functions at the level of entire trajectories instead of individual clicks - in this sense, QFT is an approximation to the discrete approach, not vice-versa. [Note: while radical conceptually, it is conservative computationally.]

In QM and QFT, empirically, we're trying to find the probability amplitudes associated with the distributions of clicks in detectors. That's our claim anyway. Accordingly, particle physics is not fundamental - it's a classification scheme for the shapes of curves (sets of clicks) found in detectors. That we observe sets of clicks which lend themselves to such "dynamical" characterization is the direct consequence of a truly fundamental principle underlying the process of trans-temporal identification ("connect the dots" in particle physics' data). We believe this fundamental principle is "boundary of a boundary is zero" (same as in E&M, QED and GR), so we're trying to embody it in our proposed self-consistency criterion (SCC). As we say in the essay, the SCC is fundamental to the discrete action so, if for no other reason, our approach is computationally fundamental to discrete QFT.

While our view is conceptually radical, our approach is computationally conservative; we don't expect to find anything 'wrong' with physics as it is already practiced (although, we expect to find some revisions, e.g., corrections to kinematical input for astronomical calculations). We do expect to change physicists' attitudes about what physics is modeling (e.g., particle physics not being fundamental). Most of our papers have emphasized the conceptually radical aspects of RBW rather than its conservative formalism. We've received extensive feedback on the epistemological and ontological implications of RBW, but virtually nothing about the proposed technical approach. As a physicist, I'm looking for a critique of my proposed approach; I would greatly appreciate your input. We didn't address questions 2-4 as such because we hope this answers them all in that our view is anathema to anything like a Wheeler-DeWitt approach, our SCC at bottom is not an equation of motion and concerns spacetimematter considered as nonseparable amalgam. We are happy to have your interest so please ask additional questions at will.

Thanks for your time, David.

Michael

----------------

Michael,

Thanks, your explanation helps. In my usage a statevector defines and is defined by probability amplitudes it assigns to a basis of statevectors; or the probabilities it assigns to the vectors in two suitably chosen bases. So the difference between talking about statevectors and talking about probabily amplitudes is like the difference between talking about functions and about their values: a matter of how one chooses to organize the discourse. The statevector theory and the probability amplitude theory do not seem to me to be significantly different theories. Perhaps this is exactly your point?

The advantage to discreteness is finiteness. Is that your motivation? That is half of my motivation for building with spins. The other half is that spins can have the observed symmetries. Do you renounce these symmetries when you start from the discrete? Do you expect the observed symmetries to result from smoothing, and expect them to go away under better measurements?

To make sure we are on the same channel: Would blocksystem describe your approach, or is blockworld an essential part of the idea? Canonical quantum theory doesn't talk much about the world. It says as much as it can about the system, and as little as it has to about the frame (experimenter, laboratory, etc.).

Best regards,

David Ritz Finkelstein

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

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 (interference patterns), clicks distributed through space to form 'trajectories' (particle physics), etc. Therefore, we don't want to conflate theoretical concepts (charge, mass, spin, etc.) with the clicks themselves since a click has no properties other than where it occurs (relationally) in spacetime. These other theoretical concepts are higher level abstractions used to characterize click distributions, i.e., sets of clicks. Our theory is an attempt at finding the amplitudes for the relative spacetime locations of individual clicks.

For example, if you have the amplitudes for click rates at two detectors, you normalize over those two detectors for your relative rates. Now suppose you add a third detector, which may or may not affect the click rates at the first two detectors, e.g., put into the arm of an interferometer or added along the screen of an interference pattern, respectively. Then, you simply recompute the amplitudes (where necessary) and renormalize. There are no concerns about "complete sets of variables" at this level. [See, for example, how we explain the interferometer in our Foundations paper listed in the main essay references.]

As to our motivation for a discrete approach, we were looking to build "relata from relations" (relations are fundamental in RBW) so we had to consider building trans-temporal/dynamical entities from something more fundamental. Again, the reason we're motivated to decompose clicks non-dynamically isn't QFT, where sets of clicks are easily explained by the existence of dynamical particles moving through the detector. Rather, we wanted to model various experimental QM set-ups such as quantum liar experiment, delayed-choice, EPR and others that we argue either begged for or demand a fundamentally non-dynamical and relational explanation, especially if one wants to preserve locality over separability, square with special relativity, etc (see the Studies paper listed in the main essay references for details). Graph theory is well-suited for this non-dynamical decomposition. It's nice that this approach has no problem with the infinities plaguing GR, for example, but that was not our primary motivating factor. While problems faced by QFT were not a motivating factor for us, recent work suggests our approach will clarify renormalization, i.e., provide an explanation for why renormalization works.

What does this mean for particle physics? Essentially, QFT is a higher-level approximation needed when you're dealing with thousands of clicks from which you can construct "trajectories." Are there particles moving through the detector to cause these 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. Yes, many of the same dynamical attributes we find at the level of particle physics are manifest at the level of classical physics (momentum, mass, energy, charge, etc.), so one can, in that simple sense, think of particle physics as fundamental to classical physics. However, when you explore the realm of ever more rarefied click distributions, e.g., EPR-Bell phenomena, you find evidence for the fact that clicks are not caused by particles. So, we're claiming that particles (no matter how "macroscopic") are the result of increasingly dense click distributions, rather than the conventional, converse claim that clicks are caused by particles. Our view is always tenable, whereas the conventional view fails in a wide variety of QM experiments, or so we have argued (again, see our pubs in the references).

While conceptually radical, our fundamental claim and proposed computational technique strike us as simple and straightforward. Whether RBW can be made to work remains to be seen, but at least we're not starting from a contradiction to established physics. Quite the opposite, it looks like QM, QFT and GR will continue much as Newtonian mechanics continued after the advent of SR.

For example, the vacuum solutions of GR would still be considered relevant in their predictions of the trajectories for "small" objects ("small" meaning they don't change the spacetime geometry). The caveat? Since there is no empty spacetime in RBW, the only vacuum trajectories of GR which can be realized are those on which it is possible to construct a divergence-free stress-energy tensor (ST tns). You don't have to actually construct this "small," additional ST tns to know what will happen, it just has to be possible to do so. When it's possible to do so, you know the object in question will follow the trajectory given by the vacuum solution. When it's not possible to do so, the problematic vacuum trajectory does not exist, contrary to its inclusion in the GR spacetime manifold.

Thanks again for your input, David. It is GREATLY and SINCERELY appreciated!

Mark and MichaelAttachment #1: Finkelstein_Reply_08b.pdf

Note: the attached PDF to our previous post contains the formalism behind our reply to DRF.

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 conditions (see point C in my earlier post), I'd appreciate it.

Again, I find this [recovering classical dynamics] hard to swallow -- but it might make more sense if I knew which parts of your calculations were externally imposed (boundaries), and which are determined by the system itself. (Do the boundaries fundamentally change in the limit where hbar-->0?)

Reply : From these questions it looks like we've failed to convey the nature of our proposed approach. Let us repeat a slightly revised version of what we wrote to David earlier. Our formalism is simply borrowed from discrete QFT without a hypercubical spacetime lattice. [There are a few others looking into graphical QFT in this generalized fashion, e.g., Wise is referenced in the essay.] We're using the formalism a bit differently because we want to do what we consider to be a more fundamental calculation - instead of the dynamical characteristics associated with *entire trajectories* in various external EM fields (e.g., spatially continuous detector regions around particle accelerators), we're simply trying to get the probability amplitudes Z for the spatiotemporal distribution of discrete collections of detector clicks. Of course, that's what particle physics is doing, but QFT functions at the level of *entire trajectories* instead of *individual clicks* - in this sense, QFT is an approximation to the discrete approach, not vice-versa.

Ours is a very empirical approach -- we're trying to find the probability amplitudes associated with the distributions of clicks in detectors. That's the bottom line. According to our view, particle physics is *not* fundamental because it's a classification scheme for the shapes of curves (*sets of clicks*) found in detectors. That we observe sets of clicks which lend themselves to such "dynamical" characterization is the direct consequence of a *truly* fundamental principle underlying the process of trans-temporal identification ("connect the dots" in particle physics' data). We believe this fundamental principle is "boundary of a boundary is zero" (same as in E&M, QED and GR), so we're trying to embody it in our proposed self-consistency criterion (SCC). As we say in the essay, the SCC is fundamental to the discrete action so, if for no other reason, our approach is computationally fundamental to discrete QFT.

Anyway, when we compute Z, we do so for a *specific outcome* in a *specific* experimental configuration. Hopefully this explains how we incorporate "boundary conditions." As for obtaining classical dynamics in the limit hbar -- > zero, that's the understanding (although certainly not PROVEN) for quantum physics in general, and since ours is just a discrete foundation for quantum physics we simply add the steps delta t -- > 0 (for QM) and delta t -- > 0, delta x -- > 0 (for QFT). That's the technical answer, but we much prefer the picture we painted for David, so let us repeat the bulk of that here.

Essentially, QFT is a higher-level approximation needed when you're dealing with thousands of clicks from which you can construct "trajectories." Are there particles moving through the detector to cause these 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. Yes, many of the same dynamical attributes we find at the level of particle physics are manifest at the level of classical physics (momentum, mass, energy, charge, etc.), so one can, in that simple sense, think of particle physics as fundamental to classical physics. However, when you explore the realm of ever more rarefied click distributions, e.g., EPR-Bell phenomena, you find evidence for the fact that clicks are not caused by particles (see Studies paper) treated as transtemporal objects objects obeying locality. So, we're claiming that particles (no matter how "macroscopic") are the result of increasingly dense click distributions, rather than the conventional, converse claim that clicks are caused by particles.

Ken says:

The issue isn't really dynamical vs. adynamical "stories" -- it's causal vs. acausal stories. And by not talking about boundary conditions, your papers seem to me to be more on the acausal side of things. (I'm firmly on the causal side; the causes are the boundary conditions.) Maybe that's why you think I am "invoking retrocausation" -- because I'm talking about causes and you aren't? My point is that a cause in a non-block view can be mapped onto a boundary condition in a block-view.

>The difference between your ontology and ours is that we don't invoke retrocausation, rather we stick to an "all at once" view of the experiment

This seems to me like a meaningless semantic distinction. In a block-world picture, of course everything happens "all at once"; there's no other way for things to happen. The same events, when viewed in a non-block-world picture, necessarily look like ordinary causation or retrocausation. View it in the opposite order and the retrocausation looks ordinary, and vice-versa. It's just a matter of perspective.

Reply: You seem to be asserting both that the differences between us are semantic AND that there are deep differences between us because we emphasize the adynamical as opposed to your retrocausal. Since you are too smart to assert a contradiction, we know we're missing something but here goes. First, agreements. Yes, it's a BW with just one outcome for each experiment and we can exploit that fact to do QM in spacetime instead of Hilbert space by imposing future boundary conditions. There are others in our camp such as Huw Price, Cramer, etc. However, things get dicey beyond this point because as we elaborated in the Studies paper, there is disagreement about how best to exploit BW in a non-triviial fashion. Any story that amounts to merely asserting: it's a BW, it's all just there, including the outcomes of QM experiments, is guilty of triviality. We argued in the Studies paper that the various retrocausal devices in the literature are guilty of such trivilaity and guilty of not truly embracing BW thinking. Hence we have provided a truly acausal and adynamical alternative to playing this game.

We then work backwards to an adynamical theory of GQ eluded to in the essay, a theory which does not have either dynamics or dynamical entities at bottom, rather it has the SCC elaborated in the essay and the amalgam spacetimematter, all of which suggests a very non-standard (no pun intended) picture of unification and a unique answer to the problems of time. By contrast, if we understand you, you have the Klein-Gordon equation at bottom, which is second order in time, does not admit a positive definite conserved probability and the particles propagate both forwards and backwards in time. Leaving aside the question of how possibly you are going to start with this and get GQ and unification, with this ontology, we'll assume that like Price and others, you wish to preserve locality for particles by keeping all the action in such cases as EPR-correlations time-like, i.e., retrocausal. As you'll see in the Studies paper and Foundations paper, we showed that there are QM set-ups such as quantum-liar-experiment (QLE) where the QM correlations CANNOT be explained in this retrocausal fashion. In the language of Price, giving up "mu-innocence" isn't sufficient to preserve locality. Put another way, in QLE you cannot consistently maintain the following set of claims: particle ontology, locality and retrocausation.

By contrast, RBW maintains locality in any QM set-up by having relations (see above and replies to Finkelstein) as fundamental to particles and by replacing retrocausal stories with adynamical and acausal explanations. Note: this does not prevent us from mapping our story onto dynamical ones or toggling back and forth between both perspectives or indeed, even recovering the dynamical picture from the more fundamental adynamical one--indeed that's our goal! So, we maintain that retrocausal accounts no matter how clever are just merely thinly disguised phenomenology. And, as we pointed out in the Studies paper, Price and Cramer admit as much, echoing your own "perspectivial" remark above.

Now, if you want to maintain that causal talk is somehow deeper than dynamical talk in a BW or that imposing boundary conditions amounts to a causal story of EPR-correlations, be our guest, but keep in mind the following: 1)talk of retrocausation in a BW of the sort we live in is merely perspectivial as you said yourself, however pragmatically useful it may be, 2) As we showed retrocausal strategies aren't sufficient to preserve locality in all cases, which is pretty damning since such stories take particle talk as fundamental and wish to preserve locality thereby eliminating tension between EPR-correlations and the relativity of simultaneity (the best independent reason to believe in BW in the first place), 3)while one can perhaps always cook up SOME account of causation to explain EPR-correlations, as the Studies paper points out, it has proven problematic to use counterfactual accounts of causation (this would subsume your imposing of boundary conditions account as far as we can see) and no other notion of causation seems an obvious fit here, 4)but even if you can tell a coherent causal story whereby imposing boundary conditions is the CAUSE of QM correlations in every case, given that it's a BW with all that implies from the absolute perspective, you already know that such retrocausal (or any other causal OR dynamical account forward or backward in time)stories are NOT FUNDAMENTAL and that the deepest story for explaining QM correlations or any other feature of the BW is going to be adynamical and acausal. So RBW is an invitation to you and other retrocausal folk to join us in drilling where the wood is a little thicker BW wise, rather than just saving appearances. We know that William is your biological father but RBW is your true, spiritual father. Stop fighting us Ken, the future is now.

Cheers,

M&M'

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."

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)

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 probability distribution on all initial/final boundary pairs |Z|^2=W(I,F), and 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)], summing over all possible final outcomes F_i for that specific experimental configuration, then we're exactly on the same page.

The follow-up questions are then: 1) Is there a probability distribution over the experimental configuration as well as the outcomes? and 2) How does one determine which outcomes are permitted in the first place? (Without such knowledge, it's impossible to know what values to sum over in the above expression.)

For example, in your picture, what is the answer to why I can't measure half a photon on one detector, and half of the same photon on a different detector?

>Yes, it's a BW with just one outcome for each experiment and we can exploit that fact to do QM in spacetime instead of Hilbert space by imposing future boundary conditions.

This point, combined with your distaste of particles, would seem to point to you using classical fields in spacetime. I understand that by "tapping into" QFT's math it gets you a lot of built-in results, but QFT also comes along with so much space vs. time baggage that I'm not sure this is the right choice if one ever wants to incorporate GR. Surely if it were possible to make your same BW picture work with *classical* field theory, that would be of interest to you?

>Any story that amounts to merely asserting: it's a BW, it's all just there, including the outcomes of QM experiments, is guilty of triviality.

Not necessarily; it depends on which part of the story one is telling. When one has boundary conditions on a subsystem A, one doesn't look to A to explain the boundary itself; one looks to the boundary to explain A. To explain the boundary, you must expand your system to A+B, where B includes the other side of the boundary. If A+B can only be explained by the boundaries on that *larger* system, then it will be the boundary on A+B that explains the boundary on A. This is not trivial, so long as there is an ultimate cause that explains everything -- and following the above logic the ultimate cause would be the boundary condition on the whole universe. (Not just an initial boundary, but necessarily including any final cosmological boundary as well.)

So that's my way out of the "triviality" argument -- but I still don't understand yours.

>By contrast, if we understand you, you have the Klein-Gordon equation at bottom, which is second order in time, does not admit a positive definite conserved probability and the particles propagate both forwards and backwards in time. Leaving aside the question of how possibly you are going to start with this and get GQ and unification...

A bunch of issues here...

On the probability issue, like you, I'm also finding an amplitude for a full solution in spacetime. Such an amplitude need not correspond to a probability current -- indeed, the conventional wisdom that demands such a current is guilty of treating probability as a physical substance. Furthermore, when the final boundary condition is imposed at some time T, demanding a probability continuity for measurements at times just before T is misguided, because such measurements would require a different final boundary condition (and would have a correspondingly different probability amplitude). There's no principle that says that such an amplitude-based probability should act like a conserved current.

Also, I have no particles. It's all classical fields, all the way down.

I'm surprised to hear you using language concerning propagation "both forwards and backwards in time". Neither concept has any objective meaning. As you're surely aware, in a block universe there are only static solutions that can be viewed in different temporal directions. In a particle picture, the same worldline that can be said to "go forward" from one perspective, can equally well be said to "go backward" from a reversed perspective. There's no objective difference.

Finally, unification. Mark, I know you have a GR background, so you're of course aware that there is no barrier to incorporating classical fields into GR; it's quantum fields that cause all the trouble. So I think I have a perfectly straightforward path; it's your use of QFT concepts that makes me concerned that such a path is not open for your approach.

>but even if you can tell a coherent causal story whereby imposing boundary conditions is the CAUSE of QM correlations in every case, given that it's a BW with all that implies from the absolute perspective, you already know that such retrocausal (or any other causal OR dynamical account forward or backward in time)stories are NOT FUNDAMENTAL and that the deepest story for explaining QM correlations or any other feature of the BW is going to be adynamical and acausal.

Again, I think this is our biggest disagreement in our general approach. An acausal story is no story at all. At the end of the day, you still have to assume both experimental preparation and experimental outcomes in order to calculate anything at all. Looking to those same calculations to explain the experiments in the first place is only going to wind up being a giant circular argument.

Take a look at the laser cavity analogy in my essay. If it's okay to say that the boundaries of a laser cavity are the cause of the interior modes, then why can't it be okay to say that the hypersurface boundary of some static 4D block structure in spacetime is the cause of the interior of that boundary? This is a *fundamental* story that isn't dynamical in any way whatsoever, but it's still perfectly causal.

Thanks for the conversation!

Ken

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 bc's, are *necessarily* included in the computation of Z as one constructs the discrete core of the action per the self-consistency criterion (SCC). That is, initial and final boundary conditions have a different ontological status for RBW than is typically understood.

"The follow-up questions are then: 1) Is there a probability distribution over the experimental configuration as well as the outcomes? and 2) How does one determine which outcomes are permitted in the first place? (Without such knowledge, it's impossible to know what values to sum over in the above expression.)"

1) The configuration is not independent of the outcomes, i.e., placement of detectors is part of the "experimental configuration," just like the placement of mirrors, beam splitters, Stern-Gerlach magnets, phase plates, etc.

2) If you're not familiar enough with the experiment to know where the detectors are placed, you're not qualified to compute outcomes!

"For example, in your picture, what is the answer to why I can't measure half a photon on one detector, and half of the same photon on a different detector?"

It's just about clicks in detectors, Ken. You'll have to phrase your question in terms of detector clicks. See our reply to Finkelstein, but if you want to know what's ultimately behind the clicks, it's not particles or fields, but it's relations all the way down as we express graph theoretically.

"This point, combined with your distaste of particles, would seem to point to you using classical fields in spacetime."

That's bassackwards fm our approach - we propose a discrete, background independent approach to the computation of probability amplitudes!

"I understand that by "tapping into" QFT's math it gets you a lot of built-in results, but QFT also comes along with so much space vs. time baggage that I'm not sure this is the right choice if one ever wants to incorporate GR. Surely if it were possible to make your same BW picture work with *classical* field theory, that would be of interest to you?"

QFT represents an *approximation* to our proposed discrete approach, not the converse as is commonly assumed with lattice gauge theory (LGT). And, we don't have a fixed spacetime structure as in LGT, that would constitutes a "background." Determining the spacetime metric on the graph is part of the problem (per the SCC), just as in GR (where Einstein's eqns are the "self-consistency criterion").

Using graphs automatically avoids many pitfalls of field theory (classical or quantum), e.g., singularities associated with continuum variables. Also, it forces us to articulate the construct of trans-temporal objects, i.e., we were forced to construct the SCC fundamental to the action. We wanted to avoid a formalism with implicit trans-temporal identification, since we wanted that explicated. But perhaps this is a good place to bring up some puzzles we have about your approach: 1) What makes the Klein-Gordon equation "classical" or any more classical than the Dirac equation, isn't it a quantum scalar? 2) Why are you so fixated on the Klein-Gordon equation, given that it's not background independent and has little value computationally beyond the pedagogical and historical? 3) How does embracing fields (as opposed to particles or whatever) resolve any foundational questions in QM such as the measurement problem or the nature of EPR-correlations in a relativistic context, etc., and what is your answer to these foundational questions beyond the application of future boundary conditions? Obviously, the use of such future boundary conditions in no way requires or even obviously suggests Klein-Gordon.

4) Again, how can the Klein-Gordon equation possibly be the foundation for quantum gravity?

"When one has boundary conditions on a subsystem A, one doesn't look to A to explain the boundary itself; one looks to the boundary to explain A. To explain the boundary, you must expand your system to A+B, where B includes the other side of the boundary. If A+B can only be explained by the boundaries on that *larger* system, then it will be the boundary on A+B that explains the boundary on A. This is not trivial, so long as there is an ultimate cause that explains everything -- and following the above logic the ultimate cause would be the boundary condition on the whole universe. (Not just an initial boundary, but necessarily including any final cosmological boundary as well.)"

Isn't that problematic, since we don't even know whether the spacetime manifold *has* any boundaries? And, if what you say is true, aren't we screwed by the observational indeterminancy principle of cosmology, which tells us we can't even expect to know the *geometry* of our past light cone uniquely to some redshift z, a fortiori info concerning the spacetime boundaries (if they exist)? Furthermore, even if the universe has the appropriate boundary conditions, how are you going to explain the initial and final boundary conditions of the universe itself, are these just brute facts on your view? One thing is for sure, in a BW, the answer to that question can't be dynamical. This is part of Smolin's point and your view is stuck with treating boundary/initial conditions in the standard way.

"So that's my way out of the "triviality" argument -- but I still don't understand yours."

Our way out is the SCC, which is the rule by which one constructs the action (actually, the 'core' of the discrete action). BTW, this makes our approach fundamental to QFT, unlike LGT. The SCC gives us a non-dynamical explanation underneath BW itself, from which all the dynamical patterns in the block (both classical and non-classical emerge). Your view doesn't truly transcend dynamical/causal thinking, it just reverses it in time with retro-causation.

"On the probability issue, like you, I'm also finding an amplitude for a full solution in spacetime. Such an amplitude need not correspond to a probability current -- indeed, the conventional wisdom that demands such a current is guilty of treating probability as a physical substance. Furthermore, when the final boundary condition is imposed at some time T, demanding a probability continuity for measurements at times just before T is misguided, because such measurements would require a different final boundary condition (and would have a correspondingly different probability amplitude). There's no principle that says that such an amplitude-based probability should act like a conserved current."

This is very reasonable; spoken like a true blockworlder!

"Also, I have no particles. It's all classical fields, all the way down."

See our earlier questions about the efficacy of fields: invoking fields doesn't resolve any foundational questions by itself. Just curious, what is the ontological status of your fields? You use continuous fields to compute a distribution over the detectors, but only certain discrete outcomes will obtain (and therefore, it is only these 'clicks' which exist in the BW). Clearly, there is no *collapse* of your fields upon measurement, since nothing changes in a BW, so you have continuous fields through spacetime on the one hand, but only discrete outcomes actually exist in the BW on the other. In answering that question, we assume you will explain the mechanism responsible for converting the continuous waves in spacetime to discrete detector clicks in the absence of particles. And again, what makes you call Klein-Gordon "classical"? And if you were really only using classical fields, where would the non-commutative structure of QM come from?

"Finally, unification. Mark, I know you have a GR background, so you're of course aware that there is no barrier to incorporating classical fields into GR; it's quantum fields that cause all the trouble. So I think I have a perfectly straightforward path; it's your use of QFT concepts that makes me concerned that such a path is not open for your approach."

As stated supra, determining the spacetime metric on the graph is part of the problem one solves in satisfying the SCC for the construct of the core of the discrete action. Keep in mind, we're proposing a formalism *fundamental to QFT*, not *derived from it*. Our theory is background independent, we're already there and unlike you, we don't have to revamp QM.

"Again, I think this is our biggest disagreement in our general approach. An acausal story is no story at all. At the end of the day, you still have to assume both experimental preparation and experimental outcomes in order to calculate anything at all. Looking to those same calculations to explain the experiments in the first place is only going to wind up being a giant circular argument.

"Take a look at the laser cavity analogy in my essay. If it's okay to say that the boundaries of a laser cavity are the cause of the interior modes, then why can't it be okay to say that the hypersurface boundary of some static 4D block structure in spacetime is the cause of the interior of that boundary? This is a *fundamental* story that isn't dynamical in any way whatsoever, but it's still perfectly causal."

This is just semantics. For example, one could say any experimental outcome, per our approach, was "caused by" the existence of the SCC. Indeed, Albrecht showed that merely postulating the existence of "things" (called quasiseparability) is sufficient to break the symmetry of solution space and yield a reality amenable to dynamical law. We're arguably going farther when we postulate a prescription for the construct of "things" via the SCC. So, in that sense, one could say the SCC is the BW 'causal' counterpart to the big bang (or whatever boundary conditions you have) in a dynamical picture. The difference is, of course, the SCC is in no non-trivial sense causal, it's locally applicable and imminently available, neither of these attributes is true of boundary conditions for the entire spacetime manifold! And again, you seem to want to have it both ways here: "the acausal story is no story at all" AND "there is no objective difference between forwards and retro causation in a BW." As a matter of logic, to assert the latter claim is to deny the former. That is, we agree completely that forwards and retro-causation amount to the same thing--that's the adynamical/acausal perspective, because from the absolute perspective, nothing is happening, there is no PRODUCTION or BRINGING INTO BEING in the BW, of either a dynamical or causal nature. That said, from within the BW there are many patterns that count as dynamical or causal, if you want to count final boundary conditions as causes of a counterfactual sort, be our guest, but again, this claim is no less trivial than merely asserting it's a BW and the outcomes are just there. And again, when you get to the universe itself your game runs out because you have no way of addressing the initial and final boundary conditions of the universe itself. Think of the Tralfamadorian's and Dr. Manhattan's perspective Ken and give up this retro-retro-causation business; you have already done so in the future, you might as well get ahead of the game, come to blockhead.

"Thanks for the conversation!"

Yes, thanks very much!

M & M.