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FQXi FORUM
CATEGORY: Essay Contest
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TOPIC: What if Time Really Exists? by Sean Carroll
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The voting deadline has been extended to January 1, 2009.
Please vote for your favorite essays soon!
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Essay Abstract
Despite the obvious utility of the concept, it has often been argued that time does not exist. I take the opposite perspective: let's imagine that time does exist, and the universe is described by a quantum state obeying ordinary time-dependent quantum mechanics. Reconciling this simple picture with the known facts about our universe turns out to be a non-trivial task, but by taking it seriously we can infer deep facts about the fundamental nature of reality. The arrow of time finds a plausible explanation in a "Heraclitean universe," described by a quantum state eternally evolving in an infinite-dimensional Hilbert space.
Author Bio
Sean Carroll is a Senior Research Associate in theoretical physics at the California Institute of Technology. He obtained his Ph.D. from Harvard University in 1993, and has held positions at MIT, the Institute for Theoretical Physics at UC Santa Barbara, and the University of Chicago. He is the author of Spacetime and Geometry, a graduate-level textbook on general relativity. His research interests include cosmology, field theory, particle physics, general relativity, quantum gravity, quantum mechanics, and thermodynamics.
Download Essay PDF File
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Sean,
If time is eternal, what would be the consequence of space being infinite?
As a consequence of fluctuation([long link]), space expands, but since the universe would be infinite, this would only cause a form of opposing instability and pressure, resulting in the gravitational collapse and atomic spin of mass. Therefore explaining how order arises from chaos, thus creating low entropy states. Which eventually break down and radiate their energy back out, in a convection cycle of expanding energy and collapsing structure?
Hasn't Complexity Theory shown order does arise from chaos anyway?
Regards from the gallery,
JM
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Dear Sean,
I realise that there could be an element of wanting to play devil's advocate in your essay, but with all respect, what if God or the aether really exist? As is the case with those two, there is just no physical or logical reason to invoke the existence of time. Moreover, if time did exist, one can show that a Heraclitean universe and change would not be possible. Lastly, in relation to the idea of time being infinite, you seem reluctant to take on board a certain point!
Best wishes
Peter
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Sean,
I think it's great that somebody is finally standing up for time. I think the line of reasoning that time is illusory is significantly flawed. My belief stems from the fact that I feel that there is a yet to be articulated semi-radical revision of our view of the fundamental nature of reality which incorporates the flow of information as intrinsic in the fabric rather than as a byproduct or adjunct to that nature. As such I think time is a real and critical element in such a formulation.
Cheers,
Elliot
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PS: With my previous comment, I should have probably been more specific in relation to your arguments. For example, if one assumes the existence of time via the Schrodinger equation, through the resulting necessary assumption of the existence of instants in time underlying the equation, it follows that change would be impossible.
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Sean,
A very nice essay, and I agree with much of what you say in it. A few thoughts:
a) Thank you for tracking down this quote of Eddington, however you did it: it is a great statement of the Boltzmann's brain paradox! I will henceforth steal and employ it at every appropriate opportunity.
b) The conclusion of p. 7 is that the basic sensibility of the world requires the universe to have an infinite dimensional Hilbert space. This is an amazing thing: I can pick out a dimensionality that is *as large as I like*, and instantly rule it out via this argument. Doesn't this bother you? That is, we have a case where a physical infinity is qualitatively and observationally different from any arbitrarily large number. This is either amazing, or something is wrong with the argument (though it is not clear to me what, I only have some hunches.)
c) I'm not sure I would really agree that `baby universe' creation via the 'Recycling universe' mechanism (the reverse Coleman-DeLuccia process) should count as creating low-entropy regions while increasing overall entropy. In fact, I'm fairly convinced that this process is precisely what a downward entropy fluctuation in the thermal system of dS would look like. It's not at all clear that it really helps with the B-Brain problem.
Anthony
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Hi Anthony--
a) I have to give credit to Don Page for the Eddington quote. There are also some great collections of original papers by Boltzmann and contemporaries, which are often surprisingly readable.
b) Yes it is remarkable! Which is why I tried to make the assumptions behind the argument as clear as possible. (There is one fuzzy point I didn't have time space to explore in this essay: the connection between the time parameter in the assumed Schrodinger equation and the time we use in our spacetime description of cosmology.)
c) I'm not sure about this myself, I was just trying to keep options open. You might very well be right. Recycling has the advantage of being better understood than Farhi-Guth baby-universe creation, but it's not clear that it really addresses this problem.
Sean
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Nice essay, I enjoyed reading it. A couple of quick comments:
I see nothing to preclude the possibility that dual time in all of its eternity covers just the period after the big bang. After all we have examples where the boundary time covers only a patch of the dual spacetime (say the case of AdS black holes, where it covers the region outside the horizon). More generally, that dual time is probably not simply related to any clock reading in some semiclassical bulk spacetime.
As for Anthony's question b), this coincides with my prejudice: infinity is not a number, it is a limiting process, and anything which depends on any quantity being strictly infinite should be viewed with suspicion.
Now, if you replace your infinite Hilbert space by a finite one, you'd have recurrences, but by making the Hilbert space larger and larger you'd make them appear later and later. Seems to me that you insert the infinity by demanding that the universe *always* looks like ours for all eternity. We have no evidence for that, and by definition we never will. If we demand that the universe has interesting things going on for the first 15 billion years, or any other finite period of time, we can live with a finite Hilbert space, no?
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I think that the argument that unitarity implies that time must be infinite is *extremely* weak. Unitarity can be stated loosely as "the amount of information at any time [that exists] is the same as the amount of information at any other time [that exists]." Clearly that can be true if time is finite. SC's argument is like saying that the Big Bang [as classically understood] violates the law of conservation of energy, and is therefore incompatible with the Einstein equations. Of course this is wrong. But then the whole argument falls to the ground.
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Moshe, I agree with the importance of that loophole, as I alluded to in my answer to Anthony's point b). I probably could have made that clear in the essay, but I was feeling the pressure of the word limit. I would personally bet against the possibility that dual time only covers the post-big-bang universe, because I doubt that the whole universe is Robertson-Walker, and that the BB is a boundary stretching through all of space -- but it's certainly a logical possibility.
About the infinity, I think this is a good example of where "infinite" is very different from "really big." For the simple reason that, by hypothesis, time itself is infinite. If time is finite, you can always make the Hilbert space big enough to avoid recurrences/ergodicity; but if time is infinite, you can't, and the argument goes through. If you like, the assumption that time is infinite is where the importance of infinity enters the argument.
anonymous, I don't think it's unitarity that implies time must be infinite, it's the Schrodinger equation. There is nothing about the wave function that would ever stop it from evolving; it's always just a ray in a Hilbert space, all of which are essentially created equal.
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On page 4: "and brining to life Friedrich Nietzsche’s image of eternal return": Is that supposed to be "bringing to life", or is the image actually immersed in salt water?
But if you have an infinite dimensional Hilbert space, doesn't that get you all kinds of quantum weirdness? Or, is that what you want?
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A very interesting essay! Personally I'm not persuaded that our own failure to be Boltzmann Brains tells us anything about the number of observers in the whole history of the universe who *are* Boltzmann Brains (surely that was Hartle and Srednicki's point?) but nonetheless it's an attractive prospect to banish such entities completely.
A few minor typos:
page 2, last sentence of first paragraph:
"by acting the Hamiltonian operator on that state"
page 6, last sentence:
"and brining to life Friedrich Nietzsche’s image of eternal return"
page 8, second-last paragraph (missing reference here?):
"This is a very different scenario from the various forms of eternal cosmologies that feature a low-entropy “bounce” that replaces the Big Bang [?];"
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Hello Sean,
Fun paper and great to see a fan of time here!
"Our conclusion that the Hilbert space of the universe needs to be infinite-dimensional might not seem
very startling; the universe is a big place, why should we be surprised that it requires a big Hilbert space?"
Moving Dimensions Theory can provide an infinite number of dimensions. As the fourth dimension is expanding relative to the three spatial dimensions at the rate of c, manifesting itself of spherically-symmetric expanding spheres of locality, each tiny sphere of expansion can be considered a brand new, compactified dimension. Have you ever wondered why photons never, never interact? Because each one travels in its own dimension, as photons are but matter surfing the fourth expanding dimension.
Picture every point becomeing a sphere in the fourth dimension, which yet defines a single locality--the very source of Huygens' principle, which pervades of all nature, from Feynman's many paths to Young's double slit to classical wave pools.
http://jac_leon.club.fr/gravitation/images/kaluza-klein.gif
Feel free to use MDT as a *physical* mechanism to provide your theory with the infinite dimensions you need.
http://fqxi.org/community/forum/topic/238
MDT already provides a *physical* mechanism for entropy, quantum entanglement and nonlocality, all of relativity, all the dualities--space/time, mass/energy, and space/time--so you might as well use it too. :) MDT also accounts for the graviational slowing of light and time, as well as the gravitational redshift, while showing why there is no need to quantize gravity, which will save us all a lot of dead-end work. Please find MDT's treatment of the gravitational slowing of light and time attached.
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."
In your essay, you write, "But the proof of the pudding is in the tasting, and right now the best taste we have of quantum gravity comes from string theory."
This is kind of like saying the best taste we have of traveling faster than light comes from the Millenium Falcon in Star Wars. Since string theory has no equations and is not a finite theory of anything, and since quantum gravity exists neither in theory (nobody has one, nor has come close) nor in reality (nobody has ever seen a graviton, nor knows how we might look for one), I guess it makes sense that the best way to taste quantum grvaity (which does not exist) is with string theory (which isn't a theory). But going after what might not exist with what never works in finding what might not exist just doesn't seem fun anymore. Even John Baez is leaving his pursuit of quantum gravity behind ( http://www.edge.org/q2008/q08_5.html ), and perhaps the time is nigh for all of us focus on Movindg Dimensions Theory with multi-million dollar initaitves, as MDT provides a *physical* mechanism and model for time and all its arrows and assymetries, as well as entropy, relativity, and quantum mechanics's entanglement and nonlocality.
I enjoyed the sentence, "(Juan Maldacena) discovered that a four-dimensional supersymmetric gauge theory defined on Minkowski space, in the limit of a large number of colors and strong coupling, is equivalent to ten-dimensional supergravity compactified on a fivesphere, with anti-de Sitter boundary conditions at spatial infinity."
Well Newton dicovered gravity, and Einstein discovered relativity, and it seems Shakespeare was right--brevity is the soul of wit.
Do you not long for the heroic age of physics, whence physics was explained in terms of simple, physical concepts, with simple mathematical equations?
Do you not long for simple postulates reflecting *physical* truth: the fourth dimension is expanding relative to the three spatial dimensions at c, with simple equations: dx4/dt=ic, and far-reaching conseuqences, as diverse physical phenomena spanning all realms are united with a simple model?
You write, "When quantizing gravity, spacetime itself becomes part of the quantum description, and time seems to disappear according to the Wheeler-DeWitt equation."
Well, actually, nobody has ever quantized gravity. So how would we know what happens when gravity is quantized?
You write, "But the Schr¨odinger equation, on which this is all purportedly based, is perfectly reversible."
Actually, if one uses the Schrodinger equation to describe radiation, it does not describe a reversible process, as radiation in its simplest case appears as spherically-symmetric waves that are expanding, not shrinking. this is because photons surf the fourth dimension, which is expanding, not shrinking.
wiki page
http://en.wikipedia.org/wiki/Photon
You write, "But the reason why we ever had access to a low-entropy configuration such as an egg is ultimately because the environment of the Earth is a low-entropy place."
Actually the creation of the egg in the chicken increased the entropy of the universe. I'm not sure I agree that the solar system is a low-entropy place--compared to who's absolute rule/measuring stick of entropy? It might have lower entropy than other places, but does that it make it a low entropy place? It is what it is. What should it be if not what it is? And cans such questions be answered by science?
You write, "But the fact that we ever began with a low-entropy is not natural at all." Did not the solar system and earth evolve from a swirling cloud of dust over billions of years? Was the entropy of the swirling cloud of dust so very low?
All these quotes are great, but are they science?
Is expressing and re-expressing the anthropic principle science? We are here because we are here and if we weren't here we woudln't be, so there must have been a statistical deviation. This is nothing new. Had our parents nver met, nor theirs, nor theirs, nor theirs--what are the chances? We owe our DNA to a vast improbability. OK, now let's move on to asking and answering foundational questions about *physical* reality.
Are tautological witticisms science?
"A universe containing mathematical physicists will at any assigned date be in the state of maximum disorganization which is not inconsistent with the existence of such creatures."
You write, "In fact, entropy can grow both into the far future and into the far past; the overall multiverse can be
completely symmetric with respect to time."
Can entropy really grow into the past?
MDT shows that the past isn't real, as the block universe does not exist.
And if you suppose a block universe, the past is frozen, so its entropy can't change there either.
Have to run! Thanks for the words!
Best,
Dr. E (The Real McCoy)
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6_MOVING_DIMENSIONS_THEORY_EXAMINES_THE_GRAVITATIONAL_REDSHIFT_SLOWING_OF_CLOCKS.pdf |
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Hi Sean,
I've really enjoyed your essay.
However, I have one comment. I think that quantum gravity does not necessarily imply Wheeler-DeWitt equation
H |psi> = 0
For example, even if you do NOT take into account dualities of string theory, it is still true that string theory is a theory of quantum gravity without the Wheeler-DeWitt equation.
Do you agree?
Best,
Hrvoje
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Hello Hrvoje,
I'm not sure you have noticed, but string theory isn't actually a theory, in the traditional sense, like MDT.
MDT's postulate: The fourth dimension is expanding relative to the three spatial dimension at the rate of c: dx4/dt=ic.
But what are string theory's postulates and equations? Is it not amazing that not even Sean knows string theory's postulates and equation?. That is why, although Sean says string theory gives us the best "taste" of quantum gravity, he doesn't provide us with any of string theory's postulates nor equations, nor does he ever show us how they quantize gravity, because nobody has ever quantized gravity, and because string theory has no postulates nor equations. Not even in Sean's essay, nor in the 10^99 papers on String Theory, all of which reference Ed Witten, who never even majored in physics as an undergrad, but in politics.
Do not take my word for String Theory's failure and not even wrongishness:
The first page of String Theory in a Nutshell states in a footnoted sentence:
THE CASE FOR STRING THEORY:
String Theory has been the leading candidate over the past two decades for a theory that consistently unifies all the fundamental forces of nature, including gravity. It gained popularity because it provides a theory that is UV finite.(1)
The footnote (1) reads: "Although there is no rigorous proff to all orders that the theory is UV finite, there are several all-orders arguments as well as rigorous results at low-loop-order. In closed string theory, amplitudes must be carefully defined via analytic continuation, standard in S-matrix theory. When open strings are present, there are diveregences. However, they are interpreted as IR divergences (due to the exchange of massless tsates) in the dual closed string channel. They are subtracted in the "Wilsonian" S-matrix elements." --STRING THEORY IN A NUTSHELL
So you see, String Theory is not a finite theory, but this is generally kept to the footnotes, when mentioned at all.
A lot of Nobel Laureates have vast problems with String Theory:
""WE DON'T know what we are talking about." That was Nobel laureate David Gross at the 23rd Solvay Conference in Physics in Brussels, Belgium, during his concluding remarks on Saturday. He was referring to string theory. . ." --http://www.newscientist.com/channel/fundamentals/mg18825293.700
"It is anomalous to replace the four-dimensional continuum by a five-dimensional one and then subsequently to tie up artificially one of those five dimensions in order to account for the fact that it does not manifest itself." -Einstein to Paul Ehrenfest
(Imagine doing this for ten dimensions! Or forty! Just to spite Einstein!)
"String theorists don't make predictions, they make excuses." -Richard Feynman, Noble Laureate
"String theory is like a 50 year old woman wearing too much lipstick." -Robert Laughlin, Nobel Laureate
"Actually, I would not even be prepared to call string theory a "theory" rather a "model" or not even that: just a hunch. After all, a theory should come together with instructions on how to deal with it to identify the things one wishes to describe, in our case the elementary particles, and one should, at least in principle, be able to formulate the rules for calculating the properties of these particles, and how to make new predictions for them. Imagine that I give you a chair, while explaining that the legs are still missing, and that the seat, back and armrest will perhaps be delivered soon; whatever I did give you, can I still call it a chair?" -Gerard `t Hooft, Nobel Laureate in String Theory
"It is tragic, but now, we have the string theorists, thousands of them, that also dream of explaining all the features of nature. They just celebrated the 20th anniversary of superstring theory. So when one person spends 30 years, it's a waste, but when thousands waste 20 years in modern day, they celebrate with champagne. I find that curious." -Sheldon Glashow, Nobel Laureate
"I don't like that they're not calculating anything. I don't like that they don't check their ideas. I don't like that for anything that disagrees with a n experiment, they cook up an explanation-a fix-up to say, "Well, it might be true." For example, the theory requires ten dimensions. Well, maybe there's a way of wrapping up six of the dimensions. Yes, that's all possible mathematically, but why not seven? When they write their equation, the equation should decide how many of these things get wrapped up, not the desire to agree with experiment. In other words, there's no reason whatsoever in superstring theory that it isn't eight out of the ten dimensions that get wrapped up and that the result is only two dimensions, which would be completely in disagreement with experience. So the fact that it might disagree with experience is very tenuous, it doesn't produce anything; it has to be excused most of the time. It doesn't look right." -Richard Feynman, Nobel Laureate in Physics
"But superstring physicists have not yet shown that theory really works. They cannot demonstrate that the standard theory is a logical outcome of string theory. They cannot even be sure that their formalism includes a description of such things as protons and electrons. And they have not yet made even one teeny-tiny experimental prediction. Worst of all, superstring theory does not follow as a logical consequence of some appealing set of hypotheses about nature. Why, you may ask, do the string theorists insist space is none-dimensional? Simply because string theory doesn't make sense in any other kind of space." --Sheldon Glashow, Nobel Laureate in Physics
Even String Theory's founder, Michio Kaku, has problems with the theory: "The great irony of string theory, however, is that the theory itself is not unified. To someone learning the theory for the first time, it is often a frustrating collection of folklore, rules of thumb, and intuition. (IN OTHER WORDS IT IS NOT PHYSICS!!!) At times, there seems to be no rhyme or reason for many of the conventions of the model. For a theory that makes the claim of providing a unifying framework for all physical laws, it is the supreme irony that the theory itself appears so disunited!!"
Chapter 1. Path Integrals and Point Particles: Why Strings?
" --"Introduction to Superstrings and M-Theory," page 5. -Michio Kaku
"If Einstein were alive today, he would be horrified at this state of affairs. He would upbraid the profession for allowing this mess to develop and fly into a blind rage over the transformation of his beautiful creations into ideologies and the resulting proliferation of logical inconsistencies. Einstein was an artist and a scholar but above all he was a revolutionary. His approach to physics might be summarized as hypothesizing minimally. Never arguing with experiment, demanding total logical consistency, and mistrusting unsubstantiated beliefs. The unsubstantial belief of his day was ether, or more precisely the naïve version of ether that preceded relativity. The unsubstantiated belief of our day is relativity itself. It would be perfectly in character for him to reexamine the facts, toss them over in his mind, and conclude that his beloved principle of relativity was not fundamental at all but emergent-a collective property of the matter constituting space-time that becomes increasingly exact at long length scales but fails at short ones. This is a different idea from his original one but something fully compatible with it logically, and even more exciting and potentially important. It would mean that the fabric of space-time was not simply the stage on which life played out but an organizational phenomenon, and that there might be something beyond." -A Different Universe, Reinventing Physics From The Bottom Down, Robert B. Laughlin, Winner of the Nobel Prize in physics for his work on the fractional quantum Hall effect.
"[String Theory] has no practical utility, however, other than to sustain the myth of the ultimate theory. There is no experimental evidence for the existence of strings in nature, nor does the special mathematics of string theory enable known experimental behavior to be calculated or predicted more easily. Moreover, the complex spectroscopic properties of space accessible with today's mighty accelerators are accountable in only as "low-energy phenomenology"-a pejorative term for transcendent emergent properties of matter impossible to calculate from first principles. String theory is, in fact, a textbook case of Deceitful Turkey, a beautiful set of ideas that will always remain just barely out of reach. Far from a wonderful technological hope for a greater tomorrow, it is instead the tragic consequence of an obsolete belief system-in which emergence plays no role and dark law does not exist."
-A Different Universe, Reinventing Physics From The Bottom Down, Robert B. Laughlin, Winner of the Nobel Prize in physics for his work on the fractional quantum Hall effect.
MDT delivers an ultimate theory, whereas Loop Quantum Gravity and Sring Theory only sustain a myth of an ultimate theory. And thus we are commanded from on high--from the pinnacles of the ani-theory regimes--to ignore MDT and Nobel Laureates such as Robert Laughlin, F.A. Hayek, Feynman, Einstein, Planck, Glasgow, and others I quote above. Welcome to the dark ages of physics, where progress in physics is frozen in a block universe tied together with tiny, vibrating strings.
I apologize for the length of this post, but I am working on a book: HERO'S JOURNEY PHYSICS & MOVING DIMENSIONS THEORY: FROM COPERNICUS, TO BRUNO, TO GALILEO, TO NEWTON, TO EINSTEIN--AND YET IT MOVES!
Best,
Dr. E (The Real McCoy)
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Sorry for not reading your reply carefully enough. I'm still confused about the logic though, so with the risk of making the same mistake again: what phenomenological issues prevent us from having recurrences in the asymptotic future? Granted, we haven't seen eggs unscrambling, but maybe that's because we have not been around long enough to sample significantly the Hilbert space.
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Hrvoje-- Again, I could have been more precise. Even in GR, you don't necessarily get the WdW equation; it depends on your boundary conditions. (And in string theory you can get the equivalent of it.) My only point was that it is a common starting point for many investigations of quantum gravity.
Moshe-- The point is just that most "people like us" will have been around long enough. Given any macrostate you like, including one in which you are absolutely convinced you arose from a low-entropy past with a Big Bang etc, it is extremely likely (in a finite-dim Hilbert space where the state evolves ergodically through a specified torus) that you actually fluctuated out of a higher-entropy past, and that the next observation you do will reveal the thermal equilibrium all around you. All of your memories are completely unreliable, etc.
It's just the Boltzmann Brain argument, but this is a context in which it really works rigorously, not just at a hand-wavy level. If you are evolving eternally in a finite-dim Hilbert space, there is a very well-defined measure on the space of configurations. You have no right to put yourself in a part of the evolution which you deem to be thermodynamically sensible; all you can do is restrict attention to moments in the evolution resembling your macrostate. And the overwhelming majority of those will be thermodynamically crazy.
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OK, that's the part I missed, thanks.
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Dear Author,
Your simple view about the reality of Time and the description of all the known processes to be dealt with using Time-dependent Quantum physics treating the Universe to exist in a unique quantum state, appears to signify that only quantum physics can lead us to the reality. The scientific facts about the Universe known do not conform to such a simplification. What about the birth of the Universe via Big Bang and what existed before, is an enigma still. We all know that there is awareness of the humans that crosses beyond the body senses and scientific instruments. A term 'consciousness' has been admitted as a non-physical entity that covers all the different levels of human awareness. Even famous neurologists have seen the neurons in the Supplementary Motor Area of the brain to become active when no activity was expected from within the body senses. A non-physical covering is considered to surround the SMA, to understand the neuron activity due to external interactions that leave an impression in this covering permanently even after the death of the human concerned. Thus, it appears that the universe and things therein, including the humans need to concern themselves with such an entity 'consciousness' and the same is not open to model on current scientific knowledge.
In my own essay, i have mentioned some aspects that indicate non-constancy of the Physical constants and also possibility of force-field strengths variation with time, in order to understand the Universe from its birth itself. Currently, the tendency to project the Physics evolved in past few hundred years to explain all the observed facts seen about the universe evolution( WMAP data)appears to be insufficient!
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I am curious of your opinion about some other weird speculations by Carlos Rodriguez on the "nature" of (space)time and reality: Are We Cruising a Hypothesis Space?
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so is he a Boltzmann Brain?
I don't quite see why "we" shouldn't be the fluke among flukes - given infinite time there will be infinite Brains.
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Sean, I'm a little confused by how the duality argument bears on the frozen-time problem. In what sense is time really part of the quantum description in the bulk? How do we know that the time parameter in the bulk is not just the time parameter on the boundary? That is to say, do the dynamics truly generate a internal notion of time or are we still just presuming time from the outset?
Does assuming the validity of the Schrödinger equation beg the question (of eternal time)?
George
P.S. The analogy of two straight lines, with a point of closest approach, is very elegant.
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George, it's probably not a good idea to think in terms of "bulk" and "boundary" here. I'm not proposing some specific duality between the complicated real-world spacetime and a dual theory; I'm just using the successful examples of duality to motivate the idea that there exists some description of the universe that takes the form of an ordinary time-dependent quantum system. As Moshe points out, there is an additional assumption that "time" in our universe is at least somewhat related (although it might only be approximate) to the time parameter in the quantum-mechanical theory.
The assumption is that the Schrodinger equation is right, but that certainly implies that time goes forever.
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I want to thank you for writing a straightforward essay despite having impressive credentials. I have found a correlation, the more impressive the credentials the harder and more intelligent sounding the author made their essay. The less impressive the credentials the more references there are to energy being anything except a conserved number. I'm going to give you one of my restricted votes since you have written a clear and straightforward essay. I agree with you that time does exist; however, I believe your approach can be made more rigorous. I know you have an idea that is probably right but I want your mathematics to lead to deeper insight and not frustration.
When discussing real time try to avoid equations with imaginary numbers. A Hilbert space by definition is an infinite dimensional space. In quantum mechanics a finite number of the terms have non-zero coefficients. It may seem like splitting hairs but it is an important distinction. A Hilbert space is also a mathematical fantasy that helps with calculations it is not physically identical to the universe. Explaining time by only focusing on the time evolution of the wavefunction without including collapse is not possible. Entropy can only be measured after the wavefunction collapses. In equation 5 obtaining an infinite TAUab is only possibly if 2pi is divided by zero. Lastly, infinite eigenvalues with the same E means infinite degeneracy for everything in the universe.
Having written that I do know that you are smarter than me and an FQXI member. This is why I have been hesitant to comment on your essay and other members. I only ask that you please avoid wrath in your reply because we are on the same side.
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Dear Sean Carroll,
i am requesting you to see my post of yesterday, Nov., 26. Of course it is certainly your choice to ignore response to the same.
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Dear Sean,
I salute your well written essay defending the reality of time.
I have two questions about the infinite dimensionality of the Hilbert space, which you consider to be required for conciliating the idea of a Universe undergoing unitary evolution with the observed level on entropy.
1) Let us consider a Universe with a finite number of particles at a given time. If a particle evolves influenced only by its interaction with a finite number of particles (all others), wouldn't it stay within a finite dimensional Hilbert subspace of the (possible infinite dimensional) particle's Hilbert space? Therefore, if the system starts with a finite number of interacting particles, the total Hilbert space, as a tensor product of finite dimensional Hilbert spaces, should be finite dimensional.
2) Since the time period increases exponentially with the dimension of the Hilbert space, which, in turn, increases exponentially with the number of particles, isn't it possible that even a finite dimensional Hilbert space be enough?
In this case, the Universe will have a finite period, although very long.
Best wishes,
Cristi Stoica
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Dear Sean,
it seems that you ignore the discussion about the intrinsic unobservability of the quantity time, and how do clock work.
The point is exacly to recognize that there is no real time meters, because the definition is self-recursive, and to find a way to break such recursivity, or to show how you can do without time. Starting with the assumption that time exists and hoping that further consistency works reminds to the description of the solar system with the epicycles: it works very well but it assumes very wrong principles...
John
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Cristi-- Even if it were possible to describe a system with a finite number of particles using a finite-dimensional subspace of an infinite-dimensional Hilbert space, that doesn't necessarily mean that the subspace would be spanned by a finite number of *energy eigenstates*. If it were, then the evolution would be identical to that of a finite-dimensional Hilbert space.
And an exponentially large number is still not good enough -- compared to infinity, even a large number is still small.
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Dear Sean,
You are definitely right, if we represent the states in terms of energy eigenstates, there is a probability of 0.(9) to need an infinite dimensional eigenbasis.
Cristi Stoica
“Flowing with a Frozen River”,
http://fqxi.org/community/forum/topic/322
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Dear Sean,
Very clear essay. My concerns are addressed to you and all other wave function (Hilbert space) fundamentalists. I know you want to table this question for the most part and explore a toy QM model but one can't resist asking: whence spacetime? Starting with infinitely dimensional Hilbert space, how are you going to derive spacetime (GR, Lorentz invariance, etc.). Furthermore, how are you going to explain the illusion that we live in a 3D world? My understanding is that those background independent models of QG that do "recover" spacetime either assume a global notion of time or causality (the light-cone structure). In either case, why isn't this cheating? And of course in order for your Heraclitean view to prevail, background independence is essential otherwise you just have a "quantum-block" world of the sort defended by Saunders and other Oxford-Everettians who are likewise wave function fundamentalists. So obviously, the Everett move alone doesn't entail the fundamentality of time and change, on the contrary, the most sophisticated Everettians (on this branch anyway) are block-worlders.
I get that somehow duality and de Sitter space are part of your answer here, but I don't fully follow the logic, how exactly do these two answer my questions? I look forward to your reply.
Cheers,
Michael
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An elegant argument that infinite time requires an infinite dimensional Hilbert space. This really brings home the difference between "infinite" and "arbitrarily large".
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Sean, I fully agree with your conclusion of time evolution in an infinite dimensional Hilbert space and the relation to quantum mechanical unitarity.
I want to suggest an alternative, however, to your statement:
"Think of two particles moving on straight lines in an otherwise empty three-dimensional space. No matter how we choose the lines, there will always be some point of closest
approach, while the distance between the particles will grow without bound sufficiently far in the future and
the past."
I think that the distance between the two points is bounded in the past by a 1-dimension information channel, and grows without bound in the future. I realized this in replying to another entrant, Ryan Westafer:
"Suppose one draws a squiggly vertical line to represent a singularity. Curved lines drawn over the top and bottom of the singularity form a convex-lens shape (gravitational lensing). Label the area left of the singularity, "present," and the area to the right of the singularity, "past." If the past is assigned a negative value and the present a positive value, the singularity would be the zero-valued future. The past area is empty; information from the past is channeled along the 1-dimensional edges of the "lens;" the present area is filled with events. An observer from the present cannot look back into the past without staring into the future of the black hole event horizon. Connecting with my own theory:
Because we live in a 10 dimension event space, which as I calculated and explained is identical to the 4-dimension horizon, our only access to the past is in the one-dimensional time parameter. The asymptotic lines trailing to the right where the "lens" closes (but not quite) is the d >= 11, n-dimension Hilbert space. The "emptiness" of the past space is handled analytically in my mathematical model by calculation in the complex plane for reasons that I think should be obvious--the 2-dimensionality of the information channel (the surface of the lens' edge) is a negatively valued space, and the ratio of two negative complex numbers is real and positive."
The reference is to my essay, "Time counts." Note that I agree with Maldacena holography, as you mention, that finds equivalence between a complete theory of quantum gravity in 10 dimensions and quantum field theory in 4 dimensions. I construct from first principles the identity between the 4 dimension horizon and the 10 dimension boundary.
All best,
Tom
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Dear Sean, yers time exists, time is a "coordinate of motion".
yours amrit
| | attachments:
3_In_The_Theory_of_Relativity_Time_is_a_Coordinate_of_Motion__Sorli_2009.pdf |
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The existance of a photon or any other single harmonic oscillator is enough to prove that hilbert space is infinite dimensional
[a,a*] = 1
Take the trace of either side to show that this cannot have any finite dimensional representations.
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i often wonder who can quantify 0 and infinity. To me these two are mere 'elative'nature. The experimental observations (facts) decide when we can take a physical parameter to be 0 or tending to 0. The same is true for 'infinity'. Purely,the significance comes with data and not on purely mathematical considerations. Does it appear proper to say that time can have an infinite range just because time-dependent Schroedinger equation so demands to maintain the sanctity of 'sia'. The physical reality comes only from the product 'sia-sia*'. The very duality of wave/particle nature comes from the necessity of'uncertain' space/time picture. The reality can only be provided through the multiplicity of events and probablistic considerations as individual event can no longer be persued with classical determinacy.
May be i am just repeating background already well known. mathematics of quantum physicshthen explains the significance of multiple events probalistic reality in measurement, in contrast with classical individual event study.
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