Dear Dr Wharton
First quote from your essay: "The LSU blends time and space together just
like GR, while the NSU has to grapple with a dynamic evolution that seems to single out time as\special".
In my essay I write about this issue ,but contrary.
See my letter to Dr Stephen Weinberg.
http://fqxi.org/community/forum/topic/1413
Hi Peter,
I'm afraid that I still can't find the commonality between our ideas, but thanks for your nice words, and best of luck in the contest.
Dear Ben,
Thank you very much for the thoughtful questions. You're asking a lot of the same questions that I am, as I pursue this research program. Here are some attempts at answers, based on my current thinking. (Numbers match to your questions.)
1) The key question is why the path integral works in the first place. If you have to sum first, and then square, then you're correct: one needs all the paths to be "real". But there's another way to "double" the paths so that you never need to square the sum (Sinha and Sorkin, 1991), in which case one can imagine that the universe is just choosing one of these possibilities (weighted appropriately), and the unchosen paths aren't "real". The problem with this, as noted in that paper, is that if one is taking the particle perspective, then some of those probability weights have to be negative, in order to get interference. BUT -- I currently think that a field-configuration-path view can solve this problem, especially if a similar "doubling" is used. (To see my arguments for fields vs. particles, you can try my previous essay in this series, "quantum theory without quantization".) This is actually my main research focus right now.
2) Feynman's approach does indeed take the Lagrangian that classically yields a real, second-order Euler-Lagrange equation, and (via the path integral) makes equivalent predictions to a complex, first-order Schrodinger equation. (Dropping one order is offset by the real->complex transition.) But I'm not interested in generating NSU-style equations... The question is how to quantize a classical Lagrangian (such as GR's) without ever making such a step in the first place. No, it's not known how to do this yet, and I don't know of anyone else who is really working on it. (I'm looking forward to reading your paper, and hope to get to it soon.)
3) The latter. I mean, look at how beautiful GR is, with a few brilliant principles guiding the whole thing. Then look at the conceptual mess of QM and QFT. Which is more likely to be on the right track, especially when it comes to spacetime? Sure, maybe GR is also incorrect at some level, but it seems to be to be closer to the ultimate truth than QM (again, especially when it comes to spacetime).
4) Well, in any unified theory along the lines that I envision, the metric would also be solved "all at once", along with any matter fields. So an external hypersurface boundary condition on a manifold would generate the structure of the spacetime within that boundary as an effect. Is this giving up traditional causality? Sure. But traditional causality is just another aspect of the NSU. (Also, see the recent piece on my work with Huw Price.)
Maybe one way to think about it is to make an analogy with a high-Q laser cavity that contains a standing-wave EM field. Flipping time and space, the analogy to the NSU view would be that the left mirror causes the field, and the nodes of the field then determine where the right mirror is allowed to be. (Sort of a left-to-right causal order.) The LSU view is that both mirrors determine the allowed modes of the field that can be inside the cavity. Extending the field to include the spacetime metric, this solution would also determine how far apart the mirrors were in the first place. The global solution might then still look like a "left-to-right causal" relationship, but it would be an illusion.
5) Yes, I like the continuum -- and here I'll again point you to my last essay, 'quantum theory without quantization'. If it's not still on the fqxi site, a copy is here. Is this anthropocentric? I don't see how, but maybe it's a blind spot of mine. (Furthermore, I don't like Planck scale arguments for discreteness, because those scales aren't Lorentz invariant. Doubly special relativity doesn't solve the problem, I don't think, without introducing bigger problems at macroscopic scales.)
As far as why we live in 4D, sure, I'd like to know that, but would be content with an ultimate theory that took that as a given. My guess is that once we found an ultimate theory, we could experiment with other dimensionalities and at least narrow down the coherent possibilities. But it seems tough to do that without a working ultimate theory.
Thanks again for some great questions!
Ken
Hi Edwin,
Thanks for the kind words! I'll be looking forward to your comments.
Ah, in that case there might be more overlap than I thought. I'll do some reading and let you know if I find any connections.
Thanks, Peter -- good luck to you as well.
Frank, I'm afraid I don't really follow much of your comment, but good luck developing your ideas. Friedemann is an adjunct faculty member in our department, but he doesn't teach here, and is mostly at SETI. He's working on some very interesting things these days...
Hi Armin,
Yes, the LSU assumes a block universe, but so does the NSU and all of modern physics, as I see it. (With the exception of the measurement problem as applied to the standard quantum state; for more on this telling mismatch you'll have to dig up my entry to the very first FQXi contest.)
Denying a block universe is basically saying that we're parameterizing physics all wrong, and we shouldn't have functions that look like the classical Electric field E(x,y,z,t), but instead things like E(x,y,z,t_clock,t_obs), where t_clock is usual time and t_obs is the time at which one is discussing E. Maybe someone will develop such a physical theory, but until they do, physics assumes a block universe.
As for your second question, it depends on what you mean by "violations in causality". See the recent piece on my work with Huw Price.
Also, I'm not trying to "rationalize" away entanglement -- I'm trying to come up with a spacetime-based LSU model that quantitatively yields all of the same correlations as the standard configuration space version. I don't have it yet, but there are no conceptual show-stoppers. As for whether I'm 'giving up too soon'... I'm actually just exploring an alternate path towards the same goal. I don't think the century-old NSU-approach to quantum phenomena would suffer if a few researchers headed off in a new, promising direction. :-)
If your entry concerns the path integral, I'll put it near the top of my to-read-list... Thanks for the pointer!
Hi Yuri,
I think I disagree with Weinberg's response to your interesting question -- I don't think that you can discretize space while not discretizing time, at least not in any GR-friendly way.
That said, I'm not a particular fan of discretization at all -- at least not the conventional justifications for it. (That was the last essay contest, which I linked to above.)
My essay devoted at first to splitting space from time.
GR-is not completed theory,as SR.Why i must be friendly to her?
Some of the fundamental stuff:
(1.) Zaanen:
Quantum Critical Electron Systems: The Uncharted Sign Worlds
Mottness collapse and statistical quantum criticality
(From "Mottness collapse" above:) "For 'everything else' this connection with classical statistical physics is severed as the quantum partition sum contains both positive and negative 'probabilities': the fermion (or 'quantum') signs. On the one hand, these represent the greatest technical embarrassment of theoretical physics because there is not even a hint of mathematics that works in the presence of signs [30]."
Pacifying the Fermi-liquid: battling the devious fermion signs
Fermions, fermions, fermions! (PowerPoint converted to PDF)
(2.) Troyer and Wiese:
Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations (Main paper ... cited in all Zaanen above)
Quantum Monte Carlo and the negative sign problem (PowerPoint converted to PDF)
Hi Michael,
Yes, lots of points of agreement. But let's take the disagreements one point at a time.
First, you bring up the block universe. This is a red-herring that has little to do with NSU, LSU, or anything directly related. In my mind, the arguments against the block universe (arguments for presentism, or the growing block) are simply are not consistent with SR, GR, or how we parameterize physical events (see my post to Armin above). I know that lots of philosophers (and some physicists) seem to think that presentism or the growing-block is potentially viable, but the burden of proof is on them, not me. Smolin is trying to change physics to add a "now", which is fine, but physics does not currently have a "now". And most of the anti-block arguments sneak in multiple time dimensions in practically every sentence. Even the way you phrased it --" But from this it doesn't follow that the future is equally real or 'already there' ", is using the word "already" that treats time as a subject while using the word "future" that treats time as an object. Those are two different times (the time at which the future is discussed, and the time of the future in question), ergo one needs a model with two time dimensions to even have a physics-based discussion about presentism.
I'm confused about your sentence that reads: " As far as we can see, someone could (and they do) still believe in NSU/reject block universe and adopt all your other suggestions." This baffles me, and leads me to think I didn't write a very good essay, given that my primary suggestion is to reject NSU. And while I maintain that ordinary NSU physics implies a block universe, LSU *certainly* implies a block universe. What do future boundary conditions mean to someone who doesn't think the future is "real"? Who is "someone"?
For your next big point, I grant that I have no detailed model, just some of the pieces. You guys are way ahead of me on that front. (Actually, I have a beautifully simple model (hinted at the end of my essay), but I'm having a devilish time working out the math, so I don't yet know if it generates the right probabilities.) I also would like to see how my (future) model deals with all these things, but it's always nice to map out potential show-stoppers before one gets that far. In my experience, all of the proposed show-stoppers come from people implicitly assuming NSU without realizing it. Therefore I wrote this essay to help lay out the fact that NSU is a pervasive assumption, not a necessary logical position.
You write: " you still assume there would always be a 3+1 type explanation of a NM sort between the measurements, you just have to work backwards to get it.", but that's not quite right. In an LSU model, once you work backward to fill in the 4D spacetime, you can translate that 4D description to a 3+1D *description* of what is going on between measurements. But I do not think it will be "Newtonian", in that it will not always be a solution to some master differential equation , and I do not think it will be an "explanation", just a movie-like description of what actually happened. For an *explanation*, one will have to consider the whole 4D-LSU picture. Hopefully this makes it clearer how much difference there is between the NSU and the sort of LSU that I envision.
You end that part with "Also notice that the use of future boundary conditions doesn't require that QM systems have definite worldlines and the only reason to assume they must is some sort of NSU prejudice." First of all, you know I'm looking for field descriptions, not particle descriptions, so "worldlines" is a bit misleading. But I'm not sure what you're getting at, exactly... asking the universe to have some particular reality between measurements doesn't seem NSU or LSU, just *realist*. Again, that intermediate solution need not, in general, solve a differential equation.
Finally, you seem to imply that your RBW gives up "more of the NSU-type" picture than I want to myself, but I think you're conflating much of the realism of standard classical physics with the Newtonian Schema, as defined in my essay. Classical physics works on a continuum; does this make the continuum in any way part of the Newtonian Schema? No -- see the definition of NSU in section I. (After all, my main example of the NS is a computer, which are typically digital!) I grant that RBW gives up more of standard physics than I want to, but let's not throw out perfectly valid concepts unless we need to. What quantum phenomena force a spacetime-realist to give up is the NSU, not spacetime itself. Maybe spacetime will have to go as well, but I'm never going to make that leap without first undertaking a much better exploration of the spacetime-realist-LSU landscape.
Best, Ken
You certainly don't have to be friendly to GR or SR -- many quantum theorists take the same view.
For me, I guess I just have too much respect for Einstein's hard-won insights, and too little respect for our human intuitions about time.
My favorite quote from Einstein is:
"What I am really interested in is knowing whether God could have created the world in a different way; in other words, whether the requirement of logical simplicity admits a margin of freedom."
Dear Professor Wharton,
Thank you for your eloquent essay. As I am one of those lay persons for whom the Lagrangian approach is "non-intuitive", I can't pretend to follow all of your arguments in its favor. Yet, your criticisms of the Newtonian approach seem clear enough to me. My corresponding thought is that the laws of physics are algorithms summarizing, after the fact, empirical data. One tends to forget that, in favor of a notion that they have some independent causal power to "determine" the future. This is so only to the extent they can be extrapolated to new situations. Otherwise, 'determine' can mean only the human sense in which one does one's best to determine what is, or will be, the case, or will be observed. In other words, dynamical equations do not have causal power and do not describe determinism in nature, only the logical determinism that belongs to mathematical systems, which are products of definition. Whether the sample of data used to fit the equation to reality consists of an 'initial condition' (NSU) or of 'boundary condition' (LSU) seems to me irrelevant to this point, though there may be, as you say, advantages to the latter approach.
In any case, it seems common sense that the universe can "compute itself" only in the trivial sense that it is an analogue of itself--an "analogue computer". Even if the universe is ultimately discretized, in no way can we assume that it is a digital computer that "processes information" in the way that our computers do, obeying the laws of physics as a computer obeys its program. Such beliefs are but the worst sort of anthropomorphism, embracing current technology as the metaphor for reality. But that is nothing new in physics, which early embraced clockworks and machines as models, and now the computer as universal machine.
Dan
Dear Ken
First of all it's great to know that we are neighbors living in San Jose. I also have been a part-time lecturer at San Jose State in the past and have several faculty friends there. I would like to get in touch with you and meet you if you would like to share the mutually beneficial results of our work.
Your conclusion -"The universe is not a computer" is fully vindicated by the results presented in my paper - -" From Absurd to Elegant Universe". It is shown that the observed universe behavior can be predicted via proper inclusion of the missing physics of the well-known spontaneous decay of particles. This new physical understanding that is missing from QM and GR provides a better alternative than merely using an alternative mathematical scheme to solve the QM mysteries, inconsistencies, and understanding the universe. Inclusion of this missing physics provides the degree of freedom in the universe that a computer does not have. The QM uncertainty is shown to be an artifact of this degree of freedom so far ignored in physics/cosmology theories. There is no need to "....assuming the NSU must be correct, and using suspiciously anthropocentric reasoning to recast the universe in an image of our quantum calculations" as you have rightly said in your paper.
My paper provides a new fundamental understanding of the Cosmological Constant and relativistic universe expansion based on spontaneous motion. The current QM and GR paradoxes and inconsistencies are shown to be artifacts of the missing (hidden) physics of the well-known phenomenon of spontaneous decay. A new Gravity Nullification Model for Universe Expansion (GNMUE) is proposed that integrates the missing physics of the spontaneous mass-energy conversion into a simplified form of general relativity. The model predicts the observed expansion of the universe and galaxies and other data. The model provides answers to key fundamental questions and resolves paradoxes among general relativity, quantum mechanics, and cosmology. It also bridges the gap between quantum mechanics and relativity theories via revealing relativistic understanding of the inner workings of quantum mechanics. The impact of the new understanding on widely-accepted fundamental assumptions is discussed and a new wholesome perspective on reality is provided.
I would greatly appreciate your comments on my paper. Please feel free to get in touch with me at avsingh@alum.mit.edu.
Best Regards
Avtar Singh
Dear Ken
Nice essay. I hadn't before given much thought as to why most physicists do not
like the idea of future boundary conditions. I like your anthropic explanation.
From reading some of your other work it seems you are mostly interested in Lagrangian field theory rather than Lagrangian mechanics. For this reason, I'm curious to know how you imagine describing an electron?
If you imagine the electron as being a soliton, then we agree on that. On the other hand, I think that looking for a nonlinear field theory of the electron is jumping way too far ahead in terms of our current knowledge of physics because the length scales are too small. The experimental bounds on detecting internal structure of the electron charge-center suggest it would be a rather small soliton (< 10^(-19)m), which is an awful lot smaller than the electron Compton wavelength and I think too small to be relevant in quantum mechanics.
So the way I imagine future boundary conditions most directly playing a role is through Lagrangian mechanics (2nd or higher order) not field theory. I touch on this in my essay (briefly in Section 2.1). Hope you find it interesting.
Good luck with the essay!
Andrew
Ken.
To simplify; I found mapping abstraction back to reality does not describe nature using present mathematics. Substituting the strict disciplines of logic however allowed a model which appears to give far more consistent results.
The model challenges a few assumptions which I identify. I assume you haven't yet read the essay? It's quite dense but mainly conceptual. Too many and too little time I know. (I'm mainly in astronomy and quantum optics so speak different languages anyway).
Your rationalisation of the theoretical background to my work is none the less very helpful and encouraging. I hope to cite your work.
I do hope you can read mine and comment, and forgive the Shakespearian metaphors to help kinetic visualisation!
Best wishes
Peter
Ken
I like your paper, and think that this issue of the universe being or not being a computer is important. I don't think there is any conflict if we say that evolution of the wave function is deterministic. So its not so much that there are future boundary conditions, its that we can know some probabilities with certainty. We know that we are mortal for instance. We can not escape the unbearable certainty of some outcomes. There are certain two state systems.
Determinism is a tricky thing. There are two types that I can articulate, one is cold determinism of the classical, and the other is the warm determinism of the quantum. Determinism is a foundation it seems, but the universe seems to prefer the latter over the former.
In any case, it seems that you would agree with the statement that quantum universe is certainly more relevant than the classical one, would you agree?
Hi Ken,
First, regarding your essay. Title not withstanding, you are not really arguing against the universe as literally a computer a la Lloyd or Wolfram. You only indirectly argue against them by positing a block universe, which certainly can't be computed. So my questions were about trying to pin down your main conclusion. Now, you admit in your reply to me that you don't have a novel argument for block universe, though I assume you want that to be a distinguishing feature of LSU. Another possibility is that you are really arguing for a new time-symmetric interpretation of QM but again, merely being a block universe is neither necessary nor sufficient for that. In other words, there can be block worlds without local time-symmetric processes and there are time-symmetric accounts of QM that are not block world. Yet another possible interpretation of your essay is that you see some necessary connection between LS and LSU or some ontological fact about reality, but of course any such inference would require extra premises not given in the essay. And finally, since we already knew that a time-symmetric psi-epistemic account of the QM could deflate the MP and provide a local picture of entanglement, that can't be your novel conclusion. I think the answer to what is novel in your essay comes at the end and again in your reply to me:
"In an LSU model, once you work backward to fill in the 4D spacetime, you can translate that 4D description to a 3+1D *description* of what is going on between measurements. But I do not think it will be "Newtonian", in that it will not always be a solution to some master differential equation, and I do not think it will be an "explanation", just a movie-like description of what actually happened. For an *explanation*, one will have to consider the whole 4D-LSU picture."
If you could find such a formalism, that might lend some extra credence to a block universe and could constitute a novel time-symmetric interpretation of QFT. If this is indeed the heart of your essay, here's my challenge to you. If the lagrangian density L is a function of the field f and its derivatives, S is stationary wrt to f (LS formalism), and f satisfies the boundary conditions (LS formalism), then L satisfies a differential eqn (NS formalism). If you want your LS soln to allow for a continuously mediated (3+1)D story, then I don't see how L won't be a function of f and its derivatives, thus allowing for an NS counterpart. Can you explain how you plan to avoid this LS-NS correspondence? Isn't there a theorem to this effect? See http://en.wikipedia.org/wiki/Lagrangian for example.
Of course what's interesting about our account http://fqxi.org/community/forum/topic/1393 with the SCC at bottom, is that it's exactly what you are looking for except you would have to give up the continuously mediated (3+1)D description. Even though you say such a description wouldn't be explanatory, you think the lack of such a description entails instrumentalism. An understandable worry, but our view isn't instrumentalism. The key to understanding why is seeing that our "fields" are such that matter/sources and spacetime (the metric) are inextricably connected. So it isn't that some independent dynamical QM entity disappears at one point in some spacetime arena and re-appears at another point in that arena. Our "fields" are spacetimematter fields, not some continuous medium between events. Spacetimematter fields on the graph are the fundamental ontological elements and these are not dynamical entities in some (3+1)D sense, they are inherently 4D. In other words, for you "between" necessarily means "between time-evolved entities." To see what we're saying just flip that perspective, i.e., let "between" give rise to "time-evolved entities involved in processes." Then you'll be asking the right questions, e.g., "What is happening between measurements?" becomes "What is between for measurements?" [Answer: spacetimematter fields on a graph.]. When you take spacetimematter seriously, you have to re-think what you mean by "between", "duration", "distance" and so on, in such situations. This is as big a difference in what it means to "explain" as when we went from Aristotelian to Newtonian physics. You worry that our model is needlessly extreme, but that depends on the pay off right? Gauge fields on links allow us to discharge the mysteries of QM with a psi-epistemic account that explains interference, entanglement, discrete outcomes, all consistent with SR and no MP. It also allows us to explain so-called dark energy and unify GR and QFT. Nor do we give up spacetime as you accuse in your reply, we simply give up the differentiable manifold as fundamental. You are so close to us in spirit, if only you can throw off the remaining chains of dynamism.
Ken,
Thanks for the detailed response. You have provided me with several pieces of information I didn't know, and several other ideas I will have to carefully consider. I share your preference for GR and its few simple principles. However, coming from a math background and working mostly with very nice things like algebraic schemes and complex manifolds, it is hard for me to believe that the physical world is based on similarly nice things. I expect successful theories beyond GR and the SM to still be based on simple principles, but possibly involving arbitrarily messy mathematics. Take care,
Ben
