Hi, Tom. Ken's arXiv:0706.4075 was mentioned to me on Friday by David Miller in Sydney, so finding this FQXi essay hours later was a surprise to me, both in timing and, by comparison, in content. In response to your comment, I guess I don't yet see that Ken's research path is clear.

Hi, Ken. I'm sorry to say that I have all sorts of trouble with details of your essay. I've been doing...

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Hi, Tom. Ken's arXiv:0706.4075 was mentioned to me on Friday by David Miller in Sydney, so finding this FQXi essay hours later was a surprise to me, both in timing and, by comparison, in content. In response to your comment, I guess I don't yet see that Ken's research path is clear.

Hi, Ken. I'm sorry to say that I have all sorts of trouble with details of your essay. I've been doing mathematics of quantum fields and of random fields for some time, a small part of which is outlined in my FQXi essay. The mathematics is avowedly set against a block-world Minkowski space -- I s'pose anyone who works in QFT would be s'prised to be told they ain't working in terms of block world /models/.

I note that discussions about placing initial and final conditions on our models are academic, insofar as we only have empirical data about the world-tube in the universe that our world (or, more solipsistically but in a similar world-tube sense, my body) occupies in the block-world. And, at any moment of our effective psychological present, our data is limited to what we actually have gathered and recorded in the past.

I could take issue with almost every paragraph of your paper, but I will instead pick your last paragraph's comment that "physicists would be better off using the block universe to re-envision quantum theory from scratch". This is part of what I would say I have tried to do (you will judge to what extent I've succeeded), however I have no ontological commitment to the block world, it is merely a useful way to organize our empirical data (which is always only about the past, albeit the past is always increasing, and of limited detail), and our approximate predictions about the empirical data we will gather in the future.

Over-briefly, I will say of one detail that your strictures about particle configuration space in quantum mechanics do not apply once we model the world using quantum or random fields, at least on my essentially statistical field-theoretic interpretation. Additionally, however, as soon as we speak of statistics in Physics we have to identify an ensemble, for which we have to identify distinct regions of space-time as measured to be similar enough for them to be put together as an ensemble, but measured to be different enough for the statistics to be nontrivial (interesting and/or useful is good too). This is hard enough if we use a Minkowski space background, but much easier then than if we run experiments against a dynamical curved space background. The point for your view is, I think, that insofar as the experimental verification of a model requires ensembles and statistics, this requires more mathematical structure than a block world has traditionally provided.

To put what I think is a significant question as well as my position rudely, do you see your block world as an ontology or as an effective ordering principle for empirical data? You put your heart on your sleeve for a block world, but to me you don't give a strong enough sense of your philosophical intentions. Feel free to reply expansively; it's your comment thread.

Despite the above, I have commented here because of some common feeling with your essay.

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"Gradually the conviction gained recognition that all knowledge about things is exclusively a working-over of the raw material furnished by the senses. ... Galileo and Hume first upheld this principle with full clarity and decisiveness." --(Albert Einstein, Ideas and Opinions)

Hello Ken,

You write, "Our time-asymmetric intuitions make it difficult to be objective when considering the...

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"Gradually the conviction gained recognition that all knowledge about things is exclusively a working-over of the raw material furnished by the senses. ... Galileo and Hume first upheld this principle with full clarity and decisiveness." --(Albert Einstein, Ideas and Opinions)

Hello Ken,

You write, "Our time-asymmetric intuitions make it difficult to be objective when considering the nature of time. But these difficulties can be overcome by using the framework of the "block universe", where every event is mapped onto a static, four-dimensional structure. In this perspective, time is represented as a spatial dimension, so the block universe can never "change"; there is no additional time dimension for such a concept to even make sense."

Actually Godel had a huge problem with the block universe, as it implies time travel while denying the flow of time. Godel pointed out the paradoxical "timeless" implications of the block universe, as well as its inability to account for time as we experience it, and this problem has largely been swept under the rug, along with curiosities such as quantum entanglement, nonlocality and all the dualities--space/time, energy/mass, and wave/particle. Today we are told that that is "just the way things are" and not to worry about it. Perhaps this helps explains why physics has not really advanced in the past thirty years... for Einstein stated, "curiosity is more importnat than knowledge."

The block universe is an human-constructed artifact of certain interpretations of relativity, as physicists glossed over the fact that x4 or "ict" is very different from the three spatial dimensions, x1, x2, x3. But Einstein and Minkowski had it right there in Einstein's 1912 manuscript: x4 = ict. Ergo, if time moves, so must x4. My paper discusses the fourth expanding in far more detail.

Time as an Emergent Phenomenon: Traveling Back to the Heroic Age of Physics by Elliot McGucken

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

Yes--this
block time paradox/problem was swept under the rug on many levels, as well as the EPR paradox, and it is great that fqxi allows a forum to discuss such curious phenomena of our physical reality. MDT's simple principle, celebrating a hitherto unsung universal invariant--the fourth dimension is exapnding relative to the three spatial dimensions--provides a physical model liberating us from Godel's block universe while also accounting for the "spooky" action at a distance in the EPR Paradox.

You should read A World Without Time, by Palle Yourgrau

"For Godel, if there is time travel, there isn't time. The goal of the great logician was not to make room in physics for one's favorite episode of Star Trek, but rather to demonstrate that if one follows the logic of relativity further even than its father was willing to venture, the results will not just illuminate but eliminate the reality of time." -A World Without Time, Palle Yourgrau"

MDT posits that time travel into the past is not possible, as the past does not physically exist--an observation in line with all empirical observations. MDT chooses Godel, Einstein, and Minkowski over Star Trek.

You write, "This essay argues that the block universe is by far the best framework for physical theories, as general relativity is simply incompatible with any alternative."

General Relativity is completely compatible with MDT, as MDT's physical reality underlies all of relativity--indeed, relativity is derived from MDT in my paper. All of quantum mechanics is also completely compatibel with MDT.

You write, "The only part of physics that does not fit into such a "block" picture is quantum theory, as it was not originally developed in a block-universe framework. But far from implying that the block universe is incorrect, I argue that we can instead use lessons from the block universe to reconstruct quantum theory in a manner compatible with general relativity." Quantum gravity exists neither in reality, nor in any consistent theory.

You write, "Balderdash. Looking to quantum theory for answers about space-time is like looking to a roadmap for answers about geology: it's a tool designed for something else entirely."

Every physical measurement made of physical reality is governed by quantum mechanics. So please do not throw out all empirical evidence in contemplating the physical nature of time.

You say, "The solution to this dilemma is not to jettison the block universe; without the block universe we would never be able to make sense of relativity."

Actually, my essay liberates us from the block universe, while providing a *physical* foundation for relativity, while unfreezing time and providing a *physical* mechanism for entropy, nonlocality, quantum entanglement, all the dualities--wave/particle, space/time, mass/energy--and time and all its arrows and assymetries across all realms, as well as the pervasiveness of Huygens' Principle.

You write, "Instead, the solution is to reinvent every single piece of quantum theory in a block universe framework. It's a daunting task, but I'll outline how it might be done after I discuss why quantum theory can't just be "tweaked" into a block universe framework." Is this not what the quantum gravity regimes and string theorists have spent hundreds of millions of dollars trying to accomplish, with naught to show for it? As MDT shows that the block universe does not exist, there is no longer any need to send postdocs and graduate studnets dashing down dead-end roads. Indeed, we live in a strange era where physicits try to advance physics by paying other people to work out the details on their non-theories, raising funding by merely promising that they are on to something big, which oft neglects physical reality as a foundational premise.

You write, "So what happens to the "wasted" information in ø for those unperformed measurements? Well, in the Copenhagen interpretation, much of that information gets erased forever thanks to the "collapse" of the wavefunction. At this point one might ask: What is the point of using a high-dimensional configuration space to encode extraneous information that just gets erased anyway?"

By conducting physics in realms safe from measurement, as well as simple logic and reason and physical reality, one is generally guaranteed a lifetime of funding--a theorem proven time and again by string theory and other anti-theories.

You write, "Counterintuitive though this may be, our intuitions about time are notoriously unreliable. We need to free our intuition from time itself, taking all of our lessons from the static block universe."

Einstein would disagree--"The only real valuable thing is intuition."--Albert Einstein.

To reject *physical* intuition and replace it with the nonsensical block universe MDT does away with seems to go exactly against the spirit by which physics has ever advanced, according to Galileo, Einstein, and other noble physicists.

It seems a preposterous conclusion that quantum mechanics, which works so very well, must be thrown out and reformulated for something which MDT shows there is no need for--the block universe.

"In the long run my observations have convinced me that some men, reasoning preposterously, first establish some conclusion in their minds which, either because of its being their own or because of their having received it from some person who has their entire confidence, impresses them so deeply that one finds it impossible ever to get it out of their heads. Such arguments in support of their fixed idea ... gain their instant acceptance and applause. On the other hand whatever is brought forward against it, however ingenious and conclusive, they receive with disdain or with hot rage - if indeed it does not make them ill. Beside themselves with passion, some of them would not be backward even about scheming to suppress and silence their adversaries. I have had some experience of this myself. ... No good can come of dealing with such people, especially to the extent that their company may be not only unpleasant but dangerous."--(Galileo Galilei)

"my dear Kepler, what do you think of the foremost philosophers of this University? In spite of my oft-repeated efforts and invitations, they have refused, with the obstinacy of a glutted adder, to look at the planets or Moon or my telescope." --Galileo Galilei

We must forver keep physical reality in the front and center, along with logic and reason and *physical* intuition--otherwise progress in physics will grind to a halt, as it has for the past thirty years.

"But before mankind could be ripe for a science which takes in the whole of reality, a second fundamental truth was needed, which only became common property among philosophers with the advent of Kepler and Galileo. Pure logical thinking cannot yield us any knowledge of the empirical world; all knowledge of reality starts form experience and ends in it. Propositions arrived at by purely logical means are completely empty as regards reality. Because Galileo saw this, and particularly because he drummed it into the scientific world, he is the father of modern physics -- indeed, of modern science altogether." --Albert Einstein, Ideas and Opinions

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Peter,

Thanks for your interest -- and no, I certainly don't consider it rude to ask me about my ontology! (More on this in a sec.) By the way, I had already read your recent arXiv paper, and I had been planning to introduce myself once I read up on random fields. This week I'll head over to your own essay and see what I can find out...

>I s'pose anyone who works in QFT would be...

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Peter,

Thanks for your interest -- and no, I certainly don't consider it rude to ask me about my ontology! (More on this in a sec.) By the way, I had already read your recent arXiv paper, and I had been planning to introduce myself once I read up on random fields. This week I'll head over to your own essay and see what I can find out...

>I s'pose anyone who works in QFT would be s'prised to be told they ain't working in terms of block world /models/.

In that case, what's the difference between classical fields, random fields, and quantum fields? As I see it, the moment one takes the classical meaning of the x-coordinate and turns it into an *operator*, one has left the block universe behind. Furthermore, any QFT theorist would admit that many interpretational questions are shunted down to non-relativistic quantum mechanics. (If it were otherwise, QFT theorists could answer all the outstanding quantum mysteries just by taking the non-relativistic limit of QFT.)

>I note that discussions about placing initial and final conditions on our models are academic, insofar as we only have empirical data about the... past.

What about a double-slit experiment that happened back in 2003? Why shouldn't we be able to go back and apply the empirical data as boundary conditions on both the state-preparation stage and the data-acquisition stage of the experiment? That would be a final boundary condition on the intermediate system, but it's all still in the past. (And if that's okay, then we could certainly imagine doing the same thing for possible future outcomes of future experiments as a computational tool for making predictions.)

>insofar as the experimental verification of a model requires ensembles and statistics, this requires more mathematical structure than a block world has traditionally provided.

I wasn't trying to imply that we can get *all* of our answers from the block universe, any more than Einstein was able to derive GR from just the equivalence principle. But I think we can certainly include ensembles and statistics in a block universe; see my next post for more detail.

>do you see your block world as an ontology or as an effective ordering principle for empirical data?

I see the block universe as a framework that is a logical necessity for any physics model that includes space and time. So in that sense it's an ordering principle, but I'm applying it to more than just empirical data. After all, I want to be able to say what happens between quantum measurements, at all points in space-time. The ontology I'm proposing is simply that of classical fields, where all the "quantum weirdness" comes about from the closed-hypersurface boundary conditions on those fields (and a probability that is applied to the whole hypersurface, not just the outcome).

>I worry that a block world structure is not a sufficiently strong guiding principle by itself for constructing a new mathematics, and I don't see clearly what other mathematical or physical principles Ken advocates.

Your worry is well-founded; the block universe is certainly not enough by itself. But in addition to this framework, along with insights concerning space-time from general relativity, the principle that has guided me this far is simply this:

Fundamental physics proposes an underlying ontology to explain empirical data. Einstein taught us the importance of making sure the ontology is consistent when the same empirical data are viewed from different reference frames. I simply want to extend this consistency requirement to time-reversed reference frames.

Every single standard interpretation of quantum mechanics fails on this count; they all give *fundamentally different explanations* for the same empirical data, if simply viewed in the opposite temporal order. Fixing this problem is a very demanding principle, that leads almost inevitably to the type of conclusions that I am drawing. However, I realize that few people feel this type of symmetry is important, so the essay and the arXiv paper each explore different motivations that reach the same conclusions.

Best,

Ken

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Thanks Ken!

You write, "From your post, and from other very similar posts you've written on other threads, I take it that we are coming at this issue from diametrically opposite philosophical perspectives: you're railing against the block universe, while the block universe is central to my thinking. Apparently the detailed arguments for such a view in my paper have not swayed you, and your...

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Thanks Ken!

You write, "From your post, and from other very similar posts you've written on other threads, I take it that we are coming at this issue from diametrically opposite philosophical perspectives: you're railing against the block universe, while the block universe is central to my thinking. Apparently the detailed arguments for such a view in my paper have not swayed you, and your post has not swayed me. Perhaps we'll just have to agree to disagree."

There are vast problems with the block universe, including the fact that implies time travel, while offering no mechanism for the arrows of times, nor the assymetries of time. Also, the block universe freezes time, while robbing us of our free will.

These problems are not my mere "opinion," but rather they are realities noted by great minds including Kurt Godel and R. P. Feynman.

MDT resolves these problems, not by ignoring them and glossing over them, but by presenting a hitherto unsung universal invariant--the fourth dimension is expanding relative to the three spatial dimensions at c, distributing locality and fathering time: dx4/dt=ic.

Indeed, MDT finally provides, in Feyman's words, "the thing that makes the whole phenomena of the world seem to go one way."

While begin your essay with, "Our time-asymmetric intuitions make it difficult to be objective when considering the nature of time," Feynman instead embraces physical reality, and sees the ubiquitous presence of time's arrows and assymtries--and MDT agrees with Feynman, that we ought not ignore nature's *physical* reality, and that we need to find "the thing that makes the whole phenomena of the world seem to go one way."

"All knowledge of reality starts form experience and ends in it." --Einstein

And that "thing" is the invariant expansion of the fourth dimension--dx4/dt=ic.

Feynman stated, "Now if the world of nature is made of atoms, and we too are made of atoms and obey physical laws, the most obvious interpretation of this evident distinction between past and future, and this irreversibility of all phenomena, would be that some laws, some of the motion laws of the atoms, are going one way – that the atom laws are not such that they can go either way. There should be somewhere in the works some kind of principle that uxles only make wuxles, and never vice versa, and so the world is turning away from uxley character to wuxley character all the time – and this one-way business of the interactions of things should be the thing that makes the whole phenomena of the world seem to go one way. But we have not found this yet. That is, in all the laws of physics that we have found so far there does not seem to be any distinction between the past and the future. The moving picture should work the same going both ways, and the physicist who looks at it should not laugh."--(The Distinction of Past and Future, from The Character of Physical Law, Richard Feynman, 1965)

MDT also resolves the problems Godel had with a 4D block universe, which allowed time travel, while disallowing the flow of time. Time travel is impossible, because time, as measured on our watches, is an emergent phenomena that arises becase the fourth dimension is expanding relative to the three spatial dimensions at c, or dx4/dt=ic. In his 1912 Manuscript on Relativity, Einstein never stated that time is the fourth dimension, but rather he wrote x4 = ict. The fourth dimension is not time, but ict. Despite this, prominent physicists have oft equated time and the fourth dimension, leading to un-resolvable paradoxes and confusion regarding time’s physical nature, as physicists mistakenly projected properties of the three spatial dimensions onto a time dimension, resulting in curious concepts including frozen time and block universes in which the past and future are omni-present, thusly denying free will, while implying the possibility of time travel into the past, which visitors from the future have yet to verify. Beginning with the postulate that time is an emergent phenomenon resulting from a fourth dimension expanding relative to the three spatial dimensions at the rate of c, diverse phenomena from relativity, quantum mechanics, and statistical mechanics are accounted for. Time dilation, the equivalence of mass and energy, nonlocality, wave-particle duality, and entropy are shown to arise from a common, deeper physical reality expressed with dx4/dt=ic. This postulate and equation, from which Einstein’s relativity is derived, presents a fundamental model accounting for the emergence of time, the constant velocity of light, the fact that the maximum velocity is c, and the fact that c is independent of the velocity of the source, as photons are but matter surfing a fourth expanding dimension. In general relativity, Einstein showed that the dimensions themselves could bend, curve, and move. The present theory extends this principle, postulating that the fourth dimension is moving independently of the three spatial dimensions, distributing locality and fathering time. This physical model underlies and accounts for time in quantum mechanics, relativity, and statistical mechanics, as well as entropy, the universe’s expansion, and time’s arrows and assymetries.

Godel had a huge problem with the block universe, as it implies time travel while denying the flow of time. Godel pointed out the paradoxical "timeless" implications of the block universe, as well as its inability to account for time as we experience it, and this problem has largely been swept under the rug, along with curiosities such as quantum entanglement, nonlocality and all the dualities--space/time, energy/mass, and wave/particle. Today we are told that that is "just the way things are" and not to worry about it, nor ask foundational questions. Perhaps this helps explain why physics has not really advanced in the past thirty years... for Einstein stated, "curiosity is more important than knowledge."

"For Godel, if there is time travel, there isn't time. The goal of the great logician was not to make room in physics for one's favorite episode of Star Trek, but rather to demonstrate that if one follows the logic of relativity further even than its father was willing to venture, the results will not just illuminate but eliminate the reality of time." -A World Without Time, Palle Yourgrau"

Too many modern physicists resolve glaring problems these days by completely ignoring them. I think FQXI is sensitive to this--the fact that foundational questions are largely ignored by the modern academy; while those who ponder them are too often snarked.

"Forget time," we are told, while at the same *time* funding is sought for throwing out quantum mechanics and reality, so as to reformulate physics based on the unreal--the human construct of a block universe, while ignoring the real--the ever-flowing movement of time, which emerges because the fourth dimension is expanding relative to the three spatial dimensions at c.

Best,

Dr. E (The Real McCoy)

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Hi Mark,

I *am* suggesting that everything is really classical fields, but this is no stranger than a QFT theorist suggesting that everything is really quantum fields -- it's just a question of when you're allowed to approximate those fields as classical objects. (And no fair giving me a far-out scenario, and then appealing to common sense to prevent me from using fields! :-) After all,...

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Hi Mark,

I *am* suggesting that everything is really classical fields, but this is no stranger than a QFT theorist suggesting that everything is really quantum fields -- it's just a question of when you're allowed to approximate those fields as classical objects. (And no fair giving me a far-out scenario, and then appealing to common sense to prevent me from using fields! :-) After all, if one *ever* expects some weird field-like aspect of a macroscopic object to rear its head, it'll be in some sort of outlandish situation like this one...).

I found the Feynman reference -- it was a very similar example addressed in Wheeler/Feynman's 1949 paper (not the 1945 one). Check it out -- they conclude that all these paradoxes rely on an "all-or-nothing" sort of interaction, but once you allow continuous interactions (say, a glancing blow due to a slightly-misaligned trajectory through a CTC) there's always a resolution.

>Regarding your second point, are you claiming that a classical object won’t follow the self-inconsistent CTC simply because that path is highly improbable? If so, what makes it more improbable than any other?

Yes, that's almost what I'm claiming. Technically, I'm claiming that the precise initial conditions that would send it on such a trajectory, combined with the precise later conditions on space-time that the CTC exists, have a joint probability distribution that is related to the number of global solutions that satisfy all those conditions. If you postulate that there are no such solutions (as you do), then the probability is exactly zero.

>So, are you saying GR needs to be augmented with a self-consistency principle? How is it realized physically?

Now this question I'm surprised to hear coming from a "Block World Kindred Spirit"... To me, one of the biggest advantages of the block universe framework is that it *is* a consistency principle, in and of itself! Paradoxes can't happen in a block universe, by definition. In a non-block-universe framework, like standard QM, each of these possible paradoxes has to be ruled out, one at a time (although see arXiv: quant-ph/0506141 for David Pegg's excellent take on how QM can do this).

So GR doesn't need any new consistency principle as long as you don't impose so many boundary conditions that there's no solution, and QM wouldn't need one either if we re-build it along the lines I suggest in my essay. I would hope that adding a generic constraint on the allowed boundary conditions would naturally prevent overconstrained problems in classical GR (such as this one).

>Would I feel a mysterious force pushing the ball out of my hands as I’m about to start it on the self-inconsistent path? Would I suddenly change my mind, asking myself later, “Gee, why didn’t I release the ball?”

Well, everything's mysterious until you understand it... :-) They’ve done interference experiments with buckyballs, which are pretty darn big. Is the "force" that keeps those C60 molecules from hitting the dark fringes "mysterious" or not?

Regardless, you wouldn't ever *feel* such a quantum effect; you would just see the end result. That's because if you are measuring one set of parameters (like a force), then Heisenberg says you're losing information about some other parameters, and in my approach it's always in the unknown parameters where the "mysterious" quantum effects would come into play. (After all, the parameters that you measure are imposed as a boundary condition on the system.)

For that last part of your question, it sounds like you're trying to back me into a corner where I have to choose between free will and the block universe. I doubt that such a corner exists, but if it did, I'd come down on the side of the block universe every time. As a well-thought out explanation of why I might feel this way, check out Greg Egan's short story, "The Hundred Light Year Diary" in his collection "Axiomatic".

Cheers,

Ken

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Hi Ken. I think we use mathematical models that have effective ways to treat asymmetry, rather than that we can insist that there is no asymmetry.

For me, there are three layers of modeling, (1) lists of finite data of finite accuracy from experience, raw data such as Gregor Weihs can still send you as about 1.5GB from his Bell-EPR violating experiments running up to 1998, (2) statistics of...

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Hi Ken. I think we use mathematical models that have effective ways to treat asymmetry, rather than that we can insist that there is no asymmetry.

For me, there are three layers of modeling, (1) lists of finite data of finite accuracy from experience, raw data such as Gregor Weihs can still send you as about 1.5GB from his Bell-EPR violating experiments running up to 1998, (2) statistics of that data, and (3) idealized models, which in one way or another generate probabilities, expected values, and correlations, etc.

For the Weihs raw data, there is no doubt that it is presented as points in space-time. The time is listed for every data point, and the place is implied by which list a given time is found in. There is a detailed discussion of how to compare the times that are assigned at the two places. We know the experiment was done in Innsbruck, running up to 1998. We have no such raw data for experiments done in 2037.

To construct statistics, we have to identify an ensemble of data points, which requires that we decide on a way to identify regions of space-time as similar enough (but not identical, otherwise the statistics are trivial). There may be multiple ways to do this that are interesting, not all based only on identification of space-time regions.

Note that I'm not advocating a frequency interpretation of probability, only that we expect to be able to construct statistics that usefully correspond to expected values that are generated by a measure-theoretic mathematics, and that ultimately we **must** be able to construct an engineering method (which rules out ad-hoc models). There is of course a significant industry of estimation of parameters in probability models from statistics, significance testing, etc.

If I were Max Tegmark, I might claim unabashedly that there is a mathematical model that is identical to the raw data that I could gather, timelessly, if I were God, Maxwell's Demon, or a Physicist Supernatura. However, for my lifetime I suppose there will only be time-asymmetric lists of past data, while probability models will gaily predict what statistics there will be in the future. I'm not saying that there cannot be a block world mathematical model of the sort I take you to suggest --- perhaps our world is a classical finite automaton at the Planck scale, or a classical continuous field that has absolutely no fluctuations in the ultraviolet limit, even though the field fluctuates FAPP Lorentz-invariantly above the Planck scale (I note that it is only because of my analysis in "Bell inequalities for random fields" that I can legitimately daydream anything of the sort) --- but our present inability to handle the complexity of the initial conditions of such models means that we have to deal with statistics and probabilities. I consider that to do Physics is to stay away from the metaphysics of considering ontological structure, that Physics is to leave questions of what lies beyond the immense gaps in our knowledge to Philosophy and Religion. Of course on Philosophy days and on Sundays it's only proper for us to go there.

To do Physics should also be to show some humility about our models, to accept that future Physicists are likely to think of better ways to organize our experience, even if they aren't as smart as Physicists today, if they have enough time.

PS. Probability as substance doesn't fit with my epistemological stance.

PPS. So far, I can't see enough usefulness from using initial and final conditions to go there. I think the constraints of raw data on our models come from anywhere/when we happen to collect it. We certainly can't collect all the raw data on a space-like hyperplane. Sometimes we engineer the raw data (actually, we engineer the ensembles, we can't make events happen precisely when we like), sometimes it just happens to us.

I hope this is interesting enough to read it (all). I walk in a fine tradition in these comment streams of too much already.

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Hi Ken,

“I found the Feynman reference -- it was a very similar example addressed in Wheeler/Feynman's 1949 paper (not the 1945 one). Check it out -- they conclude that all these paradoxes rely on an "all-or-nothing" sort of interaction, but once you allow continuous interactions (say, a glancing blow due to a slightly-misaligned trajectory through a CTC) there's always a...

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Hi Ken,

“I found the Feynman reference -- it was a very similar example addressed in Wheeler/Feynman's 1949 paper (not the 1945 one). Check it out -- they conclude that all these paradoxes rely on an "all-or-nothing" sort of interaction, but once you allow continuous interactions (say, a glancing blow due to a slightly-misaligned trajectory through a CTC) there's always a resolution.”

The Novikov Conjecture would not be necessary if Polchinski's paradox was not a reality, i.e., if there were no self-inconsistent CTCs in GR solns. But, there are such CTCs in GR and the only resolution of cases like Polchinski’s paradox, besides pointing to their highly improbable nature, is that *something* will happen to prevent violations of the principle of non-contradiction. The Novikov Conjecture is an addendum to GR. Essentially, I’m trying to find out if your approach suggests an underlying physical mechanism that would prove Novikov’s conjecture.

“Now this question I'm surprised to hear coming from a "Block World Kindred Spirit"... To me, one of the biggest advantages of the block universe framework is that it *is* a consistency principle, in and of itself! Paradoxes can't happen in a block universe, by definition.”

That reality is a BW doesn’t rule out the existence of self inconsistencies, it would just be a BW with self inconsistencies. How would we describe such a reality? We don’t know because our brains are wired in accord with the principle of non-contradiction. As physicists we tacitly assume that reality doesn’t contain such violations, otherwise physics fails. So, I’m with you in that belief and I’m trying to find out how GR needs to be modified.

“So GR doesn't need any new consistency principle as long as you don't impose so many boundary conditions that there's no solution, and QM wouldn't need one either if we re-build it along the lines I suggest in my essay. I would hope that adding a generic constraint on the allowed boundary conditions would naturally prevent overconstrained problems in classical GR (such as this one).”

I don’t understand how self-inconsistent CTCs result from “overconstrained problems.” A CTC is simply a curve on the spacetime manifold whose metric is given by some soln to Einstein’s equations. If there were a problem with EEs being overly constrained in these cases, why is only one curve on the spacetime manifold affected?

“Well, everything's mysterious until you understand it... :-) They’ve done interference experiments with buckyballs, which are pretty darn big. Is the "force" that keeps those C60 molecules from hitting the dark fringes "mysterious" or not?”

Are you claiming that the “Bohm force,” responsible for interference in the twin-slit experiment, provides the physical mechanism underwriting Novikov’s Conjecture? In that case you’ve blurred an important distinction between screened-off particles and non-screened-off particles, e.g., macroscopic objects.

“Regardless, you wouldn't ever *feel* such a quantum effect; you would just see the end result. That's because if you are measuring one set of parameters (like a force), then Heisenberg says you're losing information about some other parameters, and in my approach it's always in the unknown parameters where the "mysterious" quantum effects would come into play. (After all, the parameters that you measure are imposed as a boundary condition on the system.)”

I still don’t see how the uncertainty associated with boundary conditions for any particular trajectory would serve to *absolutely prevent* the instantiation of that trajectory. Again, that argument could be applied to ANY trajectory, so why does ANYTHING have a trajectory?

According to statistical mechanics, there is an exceedingly small probability that all the air molecules in my office might suddenly move to the other side of the room. I’m not worried about this occurrence because the probability is low, but that’s not why there is no “problem.” There is no “problem” because I can compute the consequences to me, the room and its other contents should that happen. The problem with self-inconsistent CTCs is that we can’t compute their consequences. So, either the universe contains phenomena we can’t analyze or it doesn’t, in which case GR is to be corrected/amended. I’m just trying to figure out how you, via your approach, propose to amend it.

“For that last part of your question, it sounds like you're trying to back me into a corner where I have to choose between free will and the block universe. I doubt that such a corner exists, but if it did, I'd come down on the side of the block universe every time.”

No, I’m not addressing the issue of free will. Again, I’m trying to find out if your approach suggests an underlying physical mechanism that would ultimately prove Novikov’s conjecture.

Thanks very much for your response, Ken. I think we’re almost done!

Mark

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Dear Ken,

Thanks for your reply. I want to press one point b/c I don't know that you appreciate the "problem" I’m trying to convey.

"Mark: I don't see Novikov's self-consistency principle as being an "addition" to GR; it's just a tautology: if you apply so many constraints to a system of physical equations such that there is no solution, then there's no solution. And if the...

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Dear Ken,

Thanks for your reply. I want to press one point b/c I don't know that you appreciate the "problem" I’m trying to convey.

"Mark: I don't see Novikov's self-consistency principle as being an "addition" to GR; it's just a tautology: if you apply so many constraints to a system of physical equations such that there is no solution, then there's no solution. And if the solutions correspond to "reality", then it must be impossible to impose those inconsistent constraints in the first place. This must be true for *any* physical theory; not just GR."

I just gave a lecture to our engineering students on the different rates at which Earth-based clocks and orbiting clocks run according to the Schwarzschild soln (the GR corrections are now relevant to GPS satellite technology). We can use the vacuum solutions of GR to find the trajectories of small objects where "small" means their stress-energy tns (ST tns) doesn't appreciably affect the vacuum soln, of course. When we put an object into motion along one of these vacuum trajectories, the object follows the trajectory as one would expect since the object doesn’t change the spacetime curvature alg the trajectory.

Now, suppose I solve Einstein’s eqns and find a self-inconsistent CTC in some vacuum soln (these solns exist). Do I have a soln of GR that REALLY possesses a self-inconsistent trajectory? Yes. Do I have a soln of GR that possesses SELF-INCONSISTENCY? No, because while it’s true that a small object won’t change the CTC in question, technically speaking, the RHS of Einstein’s eqns (ST tns) must be divergence-free b/c the LHS is divergence-free (Einstein tns). So, technically speaking, no matter how small the object’s ST tns, it MUST be divergence-free in order to claim that you have a soln of GR. But, of course, I can’t construct the ST tns for a self-inconsistent situation (duh). So, GR does NOT possess self-inconsistency, even though it DOES possess self-inconsistent CTCs.

Hopefully you’ve jumped ahead of me and anticipate the question, “What if I have a soln with self-inconsistent CTCs, instantiate it physically and then place a small object on the self-inconsistent CTC?” This may or may not be a soln of GR. [Keep in mind that the object is small so it does not affect the existence or structure of the trajectory proper.] If the object is dry ice or something that evaporates before getting to the self-inconsistent region, we have a GR soln (like putting GPS satellites on free fall geodesics about Earth) and we know what will happen. If the object is a bowling ball, we don’t have a GR soln and we don’t know what will happen. So, what happens in that case? Do you see that the answer to that question lies outside of GR, even though GR clearly prompted it by saying this trajectory exists and gives me no reason why I can’t at least START an object thereupon. [This nicely captures the clash of relativity’s BW with dynamical experience.]

I’m just wondering if your approach suggests how GR might be corrected/augmented to answer this question. In the quote above I infer that you believe, as do I, that it must be impossible to realize this situation so SOMETHING must preclude it, i.e., make it impossible, not merely improbable. Per our discrete approach there is no empty spacetime, so the problematic trajectory really DOES NOT EXIST – the GR approximation is not accurate in saying that empty trajectories “exist” (although, trajectories in vacuum solns can be realized (made real, made to exist) via a small, divergence-free ST tns – but, no ST tns means no trajectory). What do you say?

Mark

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