CATEGORY:The Nature of Time Essay Contest[back] TOPIC:What if Time Really Exists? by Sean Carroll[refresh]
Sean Carroll wrote on Nov. 24, 2008 @ 09:32 GMT
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.
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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Peter Lynds wrote on Nov. 24, 2008 @ 18:24 GMT
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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Elliot Tarabour wrote on Nov. 24, 2008 @ 19:53 GMT
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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Peter Lynds wrote on Nov. 24, 2008 @ 21:11 GMT
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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Member Anthony Aguirre wrote on Nov. 24, 2008 @ 21:31 GMT
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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Member Sean Carroll wrote on Nov. 24, 2008 @ 21:51 GMT
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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Moshe wrote on Nov. 25, 2008 @ 00:46 GMT
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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Anonymous wrote on Nov. 25, 2008 @ 01:00 GMT
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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Member Sean Carroll wrote on Nov. 25, 2008 @ 01:25 GMT
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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Peter Lynds wrote on Nov. 25, 2008 @ 01:38 GMT
Hi Sean,
I find your lack of response to my comment/challenge a little bit unfortunate.
Best wishes
Peter
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Kaleberg wrote on Nov. 25, 2008 @ 02:28 GMT
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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Greg Egan wrote on Nov. 25, 2008 @ 02:49 GMT
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"
"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.
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.
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.
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Hrvoje Nikolic wrote on Nov. 25, 2008 @ 13:04 GMT
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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Dr. E (The Real McCoy) wrote on Nov. 25, 2008 @ 14:58 GMT
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...
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/mg1882529 3.700
"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!
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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Member Sean Carroll wrote on Nov. 25, 2008 @ 17:45 GMT
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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Moshe wrote on Nov. 25, 2008 @ 18:56 GMT
OK, that's the part I missed, thanks.
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F. Le Rouge wrote on Nov. 25, 2008 @ 19:36 GMT
Contrary to yours my French opinion is that Time is worshiped as a God in US culture in law, music, movies, science, economy, more than in the German romantic one if it is possible… The difference with Greek religion is that Chronos is not such a positive God.
Subtle Time even enables US Scientists to build highways with space-time blocks to travel until the Infinity or the Big-Bang. Or to predict the Future from Past informations.
(Just tell me WHO is fighting against Time invasion of Physics here in this forum because I am looking for this person for a while.)
I am the only one here to say that the Travel is in Einstein’s Mind, that the ‘wave’ in Quanta Physics has nothing to do with matter, so let me please defend the idea that Time does not exist that you are caricaturing in your essay.
In a few words:
- Saint Augustine is not the best pleader for ‘Present Time’ but the European Middle-age or Aristotle.
- Time ‘does not exist’ for Aristotle in Matter/material things, but he does not deny its existence in the ‘concepts’ at all (‘Physics’, III-VI). Aristotle’s idea is that one must be careful and not give to material things the ideas’ properties that matter does not have. Eternity, Infinity, the ‘Standard conceptual model of Time’ in other words, made basically with a dot and a line or a circle (including both ideas of Infinity in quantity and in distance/time).
- Parmenide and Eleates in general are not sort of French ‘agents provocateurs’ as you are insinuating; they are not far away from Aristotle’s idea that Time is an accident. Difference is that Aristotle wants to avoid binary language to fight against binary language.
- Your mistake, Sean Carroll, is due to this: Infinity, wave, eternity, dots, circles, arrows, music are still part of the reality which is so ‘made of virtuality’ or ‘potentiality’ for you. And this specific opinion, you do loan it to everybody! (Clinton K. Miller on this forum for instance who is trying to strengthen Time too was surprised that one could have another idea about Time than he does.)
- To sum up: Aristotle, saint Thomas Aquinus or K. Marx, to take famous followers examples are denying the utility of Time-concept for sure, but not arguing that time does not exist in ideas or language.
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Narendra Nath wrote on Nov. 26, 2008 @ 13:34 GMT
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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Kevembuangga wrote on Nov. 26, 2008 @ 18:03 GMT
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?
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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George Musser wrote on Nov. 26, 2008 @ 21:18 GMT
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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Member Sean Carroll wrote on Nov. 27, 2008 @ 00:29 GMT
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.
post approved
Brian Beverly wrote on Nov. 27, 2008 @ 08:09 GMT
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.
post approved
Narendra Nath wrote on Nov. 27, 2008 @ 15:10 GMT
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.
post approved
Cristi Stoica wrote on Nov. 28, 2008 @ 21:28 GMT
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
post approved
Dimi Chakalov wrote on Dec. 2, 2008 @ 05:54 GMT
How can you talk about the Heraclitean time (footnote 4), and not address the issue of 'elementary timelike displacement', as created (?) by the so-called dark energy? Five years ago, in your astro-ph/0310342, you were musing on "a problem, a puzzle, and a scandal." Regarding the latter, may I suggest to check out some well known, since 1918, facts here.
post approved
J. Smith wrote on Dec. 2, 2008 @ 19:56 GMT
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
post approved
Member Sean Carroll wrote on Dec. 3, 2008 @ 18:08 GMT
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.
post approved
Cristi Stoica wrote on Dec. 4, 2008 @ 12:15 GMT
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
post approved
Michael Silberstein wrote on Dec. 6, 2008 @ 00:17 GMT
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
post approved
Tevian Dray wrote on Dec. 8, 2008 @ 06:46 GMT
An elegant argument that infinite time requires an infinite dimensional Hilbert space. This really brings home the difference between "infinite" and "arbitrarily large".
post approved
Dr. E (The Real McCoy) wrote on Dec. 8, 2008 @ 18:04 GMT
Hello Sean,
I was hoping for a bit of a dialogue, but too, the lack of dialogue will be useful to historians of science in understanding and characetrizing why our era has seen no progress in theoretical physics, despite unprecedented funding and resources.
Never before have so many been paid so much to advance physics so little. Indeed, future historians will see that overfunding...
I was hoping for a bit of a dialogue, but too, the lack of dialogue will be useful to historians of science in understanding and characetrizing why our era has seen no progress in theoretical physics, despite unprecedented funding and resources.
Never before have so many been paid so much to advance physics so little. Indeed, future historians will see that overfunding tends to lead to sociological constructs that exalt consesus building rooted not in logic, reason, and physics--not in foundational questions; but in fashion and politics which obscure the foundational spirits, papers, and questions.
So it is that the Anthropic Principle and tiny, little vibrating strings are exalted over *physical* contemplations and questions, *physical* principles, and *physical* models such as MDT: the fourth dimension is expanidng relative to three spatial dimensions, or dx4/dt=ic. For the first time in the history of relativity, change is woven into the fundamental fabric of spacetime; and a deeper physical invariant is shown to underly relativity and quatum entanglement and nonlocality, in addition to time and all its arrows and assymetries, and entropy, as well as Huygens' and Heisenbergs' principles.
In many ways Galileo had it easy, because at least the Inquisition in his day wasn't posing as physicists interested in science.
And Max Planck had it easy too, as he noted, "A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it."
But in Plancks' time, the opponents were generally a generation of successful scientists who had risen to the pinnacles of their profession via science--not by politics. So today's non-opponents of MDT are anti-theorists bolstered by state-funded crackpot indexes and anthropic principle politics--"we have tenure/funding because we are smarter than you because if we weren't smarter than you, we wouldn't have tenure/funding. Ergo we are smarter than you," is what they announce at their lavish conferences, reformulating the anthropic principle to fit the latest "flavor of the week" of their unchanging anti-theory regimes, which have frozen physics in a block universe.
Max Born wrote, "All great discoveries in experimental physics have been made due to the intuition of men who made free use of models which for them were not products of the imagination but representations of real things."
And yet, today, the quantum gravity regimes have rejected simple physical models along with the belief that the math ought represent *real* things. And now, they are even willing to forget time, space, reason, words, dialogue, physics, and physicists--to keep their perpetual motion funding apparati moving--even as time remains frozen. And thus, despite hundreds of millions in funding, there is no quantum gravity. There is no graviton, nor any consistent theory of quantum gravity. Instead, there are literally an infinite number of string theories, and a fair amount of loop-quantum theories, none of which quantize gravity in any finite, consistent way; let alone in any way that makes predictions that can be tested. There is no proof whatsover for tiny, vibrating strings, nor atoms of space and time, nor twistors, nor tiny little loops, nor multiverses, nor hyperspace, nor parallel universes, nor bouncing universes--all of which grace the cover of Scientific American as sycophant students are trained to call true physicists seeking *physical* models and *physical* truths crackpots. And the Greats themselves--Nobel Laureates--both living and dead, have spoken out against such pseudo-science and snarky mathematical handwaving, which has become a religion that has replaced physics, thusly bringing progress to a halt.
"Books on physics are full of complicated mathematical formulae. But thought and ideas, not formulae, are the beginning of every physical theory." --Einstein/Infeld, The Evolution of Physics
Instead of classical, rugged physics on the higher plain of physical reality, we get communal, political efforts which end up opposing progress in physics, as they oppose the individual heroic spirit by which all higher physical truths are ultimately apprehended.
Science is more of an art than a science, and it always seems to advance in manners never before anticipated by the establishment, as Planck stated. One cannot legislate, nor vote on, nor dictate the advancement of science by fiat. Do not take my word for it.
"One cannot pray a lie," as Mark Twain once said.
"New scientific ideas never spring from a communal body, however organized, but rather from the head of an individually inspired researcher who struggles with his problems in lonely thought and unites all his thought on one single point which is his whole world for the moment." --Max Planck
And again we see the primacy of the honest individual in the classic, epic hero's journey!
"A hero ventures forth from the world of common day into a region of supernatural wonder: fabulous forces are there encountered and a decisive victory is won: the hero comes back from this mysterious adventure with the power to bestow boons on his fellow man." --Joseph Campbell
http://en.wikipedia.org/wiki/Monomyth
And the Nobel Laureate eocnomist F.A. Hayek agrees!
"The tragedy of collectivist thought is that, while it starts out to make reason supreme, it ends by destroying reason because it misconceives the process on which the growth of reason depends. It may indeed be said that it is the paradox of all collectivist doctrine and its demands for “conscious” control or “conscious” planning that they necessarily lead to the demand that the mind of some individual should rule supreme—while only the individualist approach to social phenomena makes us recognize the superindividual forces which guide the growth of reason. Individualism is thus an attitude of humility before this social process and of tolerance to other opinions and is the exact opposite of that intellectual hubris which is at the root of the demand for comprehensive direction of social purpose." –F.A. Hayek, The End of Truth, The Road to Serfdom
Along comes a scientist who agrees with the philosophy of Einstein and Max Born and Planck. Along comes a physicist who agrees with Wheeler, and Feynman, and Glasgow, and Godel, and Bohr, and Gamow--wishing that he could watch old Westerns with Bohr and Gamow. Along comes a scientist who agrees with Nobel Laureate Robert Laughlin and Nobel Laureate F.A. Hayek, with Newton and Dirac, with Heisenberg and Minkowski, with the great mythologist Joseph Campbell. Along comes a scientist with simple theory that has a simple postulate and equation from which all of relativity may be derived; from which entropy naturally arises, and which accounts for time and all its arrows and assymetries across all realms, while also providing a *physical* model for entanglement and nonlocality, as well as a *physical* model for Huygens' principle and the Heisenberg Uncertainty principle. Not only does the multi-billion-dollar physics establishment ignore it, but they have so much funding, that they can hire grad students and profesors to snark the theory, so as to defend their perptual-motion NSF money machines and religions of wormholes, time warps, quantum gravity, multiverses, tiny, vibrating strings, and geometric mysticism/PR/hype, which Moving Dimensions Theory has no need for, as it concerns itself with physics and physical reality--with logic, reason, and simple postulates and equations that represent a hitherto unsung universal invariant--the fourth dimension is expanding relative to the three spatial dimensions at c.
What we have here is a modern-day Inquistion, except that it is even more dangerous, as at least Galileo's Inquistion weren't claiming sience's throne.
Where it is reported: "In 1633, physicist Galileo Galilei was brought before the Roman Inquisition. Tried on "vehement suspicion of heresy," Galileo was forced to swear that he "abjured, cursed and detested" the errors of his work, which extended the findings of the Polish astronomer Nicholaus Copernicus that the Earth Moves."
Now I have postulated that the fourth dimension expands relative to the three spatial dimensions, and not one person in the entire quantum gravity regime has ever, ever, taken the time to comment on my theory. It's not like MDT is a secret, so their silence puzzles the will.
It would be one thing if quantum gravity/string theory were smashing successes--then, naturally, Rovelli/Carol et al. would all be busy partying like rock stars and flying to conferences and awards ceremonies in Aspen and Hawaii. But with the utter failure of the anti-theory regimes, for decade after decade, surely they ought have a few moments to assess the great and natural success of the brand new directions proposed by MDT.
"Insanity: doing the same thing over and over again and expecting different results." --Albert Einstein
But I realize, that with tenure and titles to worry about in thier aging anti-tehory regimes; perhaps before commenting on MDT, they are all waiting for a confession, so as to make the theory "safe" for discussion in polite circles. I even thought of emailing Ed Witten and asking him to come out with a press release in which he states that the M in M-Theory stands for Moving Dimensions.
Well, here is my confession, based on Galileo's, which can be enjoyed here:
I, Dr. E, son of the late Vincenzio Galilei of Florence, aged 70 years, tried personally by this court, and kneeling before You, the most Eminent Antitheorists and Reverend Lord Cardinals of M-Theory Multiverses, Inquisitors-General throughout the Quantum Gravity Republic against heretical depravity, having before my eyes the Most Holy Gospels of an Elegant Universe, Not Even Wrong, and The Trouble With Physics, and laying on them my own hands; I swear that I have always believed, I believe now, and with Ed Witten's help I will in future believe all which the Holy Quantum Gravity and M-Theory Church doth hold, preach, teach, and hype to the press, including E-8 and next year's E-9 anti-theory.
But since I, after having been admonished by this Holy Office entirely to abandon the false opinion that the fourth dimension expands relative to the three spatial dimensions, and that quantum mechanics' entanglement, nonlocality, entropy, relativity itself, time and all its arrows and assymetries across all realms, the gravitational slowing of clocks and time, Huygens' Principle, Heisenberg's Uncertainty Principle, probability, and all the dualities (space-time, wave-particle, mass-energy) derive from this simple principle of MDT and its equation dx4/dt=ic, and that I was neither to hold, defend, nor teach in any manner whatever, either orally or in writing, the said false doctrine; and after having received a notification that the said doctrine is contrary to the Holy Writ of Hyperspace, I did write and cause to be printed a blog and forum in which I treat of the said already condemned MDT doctrine, and bring forward arguments of much efficacy in its favour, without arriving at any solution: I have been judged vehemently suspected of heresy, that is, of having held and believed that the fourth dimension's expansion is the universe's fundamental invariant and teh cause of all time and motion, and that the block universe does not exist and time is not the fourth dimension, but that time is a parameter that emerges because the fourth dimension is expanding relative to the three spatial dimensions at c, that change is and ought be woven into the fundamental fabric of spacetime with dx4/dt=ic, and that the fourth dimension, like the earth, does move.
Nevertheless, wishing to remove from the minds of your Tenured Eminences and all faithful LQGers and String Theorists this vehement suspicion reasonably conceived against me, I abjure with sincere heart and unfeigned faith, I curse and detest the said errors and heresies, and generally all and every error and sect contrary to the Holy Quantum Gravity Regimes, and I am ready to foregt time, forget space, and forget physical reality, while embracing multiverses and tiny, vibrating stirngs. And I swear that for the future I will neither say nor assert in speaking or writing such things as may bring upon me similar suspicion; and if I know any heretic who speaks out against tiny, vibrating branes, anti-theories, or atoms of space and time, or one suspected of heresy, I will denounce him to this Holy Office of Time Travel, or to the Inquisitor of Wormholes and Ordinary of the place in which I may be, which will of course be in the block universe, which MDT falsely liberated us from, while falsely grangting us free will and free thought, as it falsely unfroze time. I hereby remit all future free will, as I return to the block universe with the hopes of receiving the funding that is a part of my pre-Ordained future, as a member of the Quantum Gravity Church in this mulitverse--this subset of the landscape--that the Gods of the Anthropic Principle granted us, while declaring that we should receive infinite funding for our fortitude in service to teh Lords of the Landscape.
I also swear and promise to adopt and observe entirely all the penances which have been or may be by this Holy Office of Loops imposed on me. And if I contravene any of these said promises, protests, or oaths, (which Ed Witten forbid!) I submit myself to all the pains and penalties which by the Sacred Canons of String Theory and other Decrees of D-branes general and particular are against such offenders imposed and promulgated. So help me God and the Holy Warped Passages/The Trouble With Physics/10^99 indecipherable arxiv.org papers--which I touch with my own hands.
I, Dr. E, aforesaid have abjured, sworn, and promised, and hold myself bound as above; and in token of the truth, with my own hand have subscribed the present schedule of my abjuration, and have recited it word by word. In America, at the Convent della M-Theory, this 8th day of December, 2008, in this parallel universe.
I, Dr. E, have abjured as above, with my own hand."
And as I'm walking away to serve out my house arrest and exile form the academy after this confession, I turn to the crowd that had gathered to hear me read it and smile.
And I say, "And yet it--the fourth dimension--moves! Eppur si muove!"
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
post approved
Dimi Chakalov wrote on Dec. 10, 2008 @ 21:29 GMT
Sean:
To quote from your essay (p. 9), you take "a very reasonable, if far from unimpeachable, set of assumptions -- a quantum state evolving in time according to the conventional Schrodinger equation with a time-independent Hamiltonian", and set your goal (p. 4) as "it is worth our effort to pursue their ramifications and see where we end up."
I have a simple suggestion. Five years ago, in your arXiv:astro-ph/0310342v2, you were musing on the “smooth tension” of the "dark energy", and acknowledged "a problem, a puzzle, and a scandal".
To clarify what kind of "time" may be implied in the set of assumptions in your recent essay, try to embed the “smooth tension” into some Cauchy surface, as explained in your graduate-level textbook "Spacetime and Geometry".
If you fail, I hope you will have a much better idea of "where we end up" with your essay, and how to fix your problems.
Good luck.
Dimi Chakalov
post approved
Dr. E (The Real McCoy) wrote on Dec. 21, 2008 @ 19:04 GMT
Hello Sean,
I think Lee Smolin has some words of wisdom regarding the nature of physical theory, and I was wondering what you might think of them. Smolin's words seem to harken back to those of Galileo/Einstein--the traditional heroes who advanced physics by rugged ingenuity.
In a table inthe attached paper, I present a table which shows how MDT adheres to the more heroic...
I think Lee Smolin has some words of wisdom regarding the nature of physical theory, and I was wondering what you might think of them. Smolin's words seem to harken back to those of Galileo/Einstein--the traditional heroes who advanced physics by rugged ingenuity.
In a table inthe attached paper, I present a table which shows how MDT adheres to the more heroic principles underlying all successful *physical* theories.
In light of the recent tragic failures of the anti-theory regimes, which has brought physics to a standstill and exiled physicists and *physical* theories from the academy, I think it would be healthy to discuss what physics *ought* strive for in the future, so as to get it on a better path--so that we can join the greater journey on that higher road that we see by standing on the shoulders of giants--not by ignoring them and their philosophies.
Lee Smolin states in a BBC video, "We've forgotten how audacious science is and how it rages sometime -- how the ideas that turn out to be true are so often outrageous... we've forgotten the lessons of the people like Einstein, who come from the outside but have exactly the right insight and right idea." --http://www.youtube.com/watch?v=3bLwqnIfLRA&feature=related BBC Hard Talk
"Openness, the inclusion of different points of view, like in anything else, is essential to progress." --Lee Smolin http://www.youtube.com/watch?v=3bLwqnIfLRA&feature=related BBC Hard Talk
This contest has demonstarted that too, too many established professors and researchers refuse to partake in collegial dialogue, and this grates against the spirit of greats such as Wheeler, Einstein, and Galileo. Well-funded, tenured professors have time to administer crackpot indexes on their univeristy's servers, but no time to talk about physics and physical reality.
"I have never met a man so ignorant that I couldn't learn something from him." --Galileo Galilei
"Curiosity is more important than knowledge." --Einstein
Lee Smolin also says that a theory should "come in a coherent whole--it should start with a beautiful principle, like the principle of indeterminacy of quantum mechanics or the principle of relativity, and there then should be a beautiful equation that flows out from that principle to a myriad of consequnces." --Lee Smolin, BBC Video
MDT's beautiful principle: The fourth dimension is expanding relative to the three spatial dimensions at c with a wavelength of the Planck Length.
MDT's beautiful equation: dx4/dt=ic
MDT's myriad of consequences: all of relativity, time and all its arrows and assymetries, entropy, quantum nonlocality and entanglement, wave-particle/space-time/mass-energy duality, the gravitational slowing of light and time, and the single velocity for all entities through spacetime--c.
The resounidng silence from the establishment on MDT (after having promised to read the paper) has lead me to believe that they see nothing wrong with MDT, as unlike LQG and Sring Theory, MDT passes Dr. Smolin's criterion for a good theory (please see the attached paper). And too, MDT predicts all of relativity along with quantum nonlocality and entanglement, as well as entropy, by proposing a novel, deeper feature of our *physical* reality. (Please see the table in the attached document.)
Soon these comments will be frozen for all time, while the fourth dimension yet marches on at the rate of c!
Well, Best Wishes for the New Year!
I look forward to sending you & anyone a copy of my book, HERO'S JOURNEY PHYSICS & MOVING DIMENSIONS THEORY: FROM HERACLITIS, TO PLATO, TO ARISTOTLE, TO COPERNICUS, TO BRUNO, TO KEPLER, TO GALILEO, TO NEWTON, TO PLANCK/EINSTEIN/BOHR/BORN--AND YET IT MOVES! Unifying relativity, quantum mechanics, entropy, and time's arrows and assymetries with a new universal invariant: dx4/dt=ic."
Eppur si muove!
Dr. E (The Real McCoy)
"Books on physics are full of complicated mathematical formulae. But thought and ideas, not formulae, are the beginning of every physical theory." --Einstein/Infeld, The Evolution of Physics
I promise that my upcoming book will be filled with thought and ideas, just like the atached paper:
Moving Dimensions Theory & Hero’s Journey Physics
Overcoming the Tragic Anti-Theory Leviathans that No Longer Teach Foundational Papers nor Ask Foundational Questions
By Dr. E (The Professor in Black)
“In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual.” –Galileo Galilei
Moving Dimensions Theory—which regards time as an emergent phenomena—was inspired in part by Einstein’s words pertaining to the higher purpose of physical theories: “Before I enter upon a critique of mechanics as a foundation of physics, something of a broadly general nature will first have to be said concerning the points of view according to which it is possible to criticize
physical theories at all. The first point of view is obvious: The theory must not contradict empirical facts . . . The second point of view is not concerned with the relation to the material of observation but with the premises of the theory itself, with what may briefly but vaguely be characterized as the "naturalness" or "logical simplicity" of the premises (of the basic concepts and of the relations between these which are taken as a basis). This point of view, an exact formulation of which meets with great difficulties, has played an important role in the selection and evaluation of theories since time immemorial.”
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.
post approved
Narendra Nath wrote on Jan. 2, 2009 @ 07:48 GMT
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.
post approved
Brian Beverly wrote on Jan. 21, 2009 @ 00:59 GMT
Does it make sense to order imaginary numbers?
(...[-itn,...,-it2,-it1,0,it1,it2,...,itn]...)
The mathematical axioms tell us that complex numbers can not be ordered.
Order Axioms:
1) A number can not be less than itself
2) x > y, x < y, or x = y
3) if x > 0 and y > 0, then xy > 0
4) if x < y, then for all z, x + z < z + y
5) if x < y, then for all z, xz < yz
set x = i and y = 2i and z= 2 + i
1) makes sense
2) i < 2i makes sense
3) a bit tricky:
0 = 0 + 0i and i = 0 +1i therefore i>0 and 2i>0
(i)(2i) > 0 ---> -2 > 0 FALSE!
4) 2 + 2i < 2 + 3i (complex # is of the form a + bi)
5) This is the key axiom!
xz = what exactly? xz or x*z (* is complex conjugate i*=-i)
If we distribute xz as we do for real numbers then axiom 5 is false. If we take the complex conjugate x*z then axiom 5 is true.
Quantum mechanics relies on C* algebra which is ordered. What is the big idea of C* algebra? C*C, multiply a complex number by a complex conjugate and you end up with a real ordered/countable number.
post approved
Dr. E (The Real McCoy) wrote on Feb. 15, 2009 @ 19:00 GMT
Hello Sean! Hope all is well! I was wondering what your take might be on Lee Smolin's most recent comments-- reflecting his epic change of heart & mind--that time is indeed now real.
What do you make of this?
It is great that Lee is coming around and seeing time as a *physically* real entity. MDT goes a step further in seeing time as a *physically* real entity that emerges...
Hello Sean! Hope all is well! I was wondering what your take might be on Lee Smolin's most recent comments-- reflecting his epic change of heart & mind--that time is indeed now real.
What do you make of this?
It is great that Lee is coming around and seeing time as a *physically* real entity. MDT goes a step further in seeing time as a *physically* real entity that emerges because of a more fundamental, universal, hitherto unsung *physical* invariant--the fourth dimension is expanding relative to the three spatial dimensions at c:
In January 2009 Smolin wrote at The Edge, "THE LIBERATION OF TIME: I would like to describe a change in viewpoint, which I believe will alter how we think about everything from the most abstract questions on the nature of truth to the most concrete questions in our daily lives. This change comes from the deepest and most difficult problems facing contemporary science: those having to do with the nature of time." --http://www.edge.org/q2009/q09_9.html
On Thu Jan 25, 2007 11:07 am, I used the word "liberate" in writing, "MDT unfreezes time, liberating us all with free will-the free will to move beyond ST & LQG, which are not inextricably locked into the fixed future of the block universe as Brain Green and Paul Davies would have you suppose. Neither the future nor the past exists. Motion is inherent in the underlying four-dimensional space-time geometry, as the fourth dimension is expanding relative to the three spatial dimensions. Einstein noted that all objects are moving through space-time at the velocity c. This never changes. An object stationary in the three spatial dimensions is translating through the fourth dimension at the rate of c. An object stationary in the fourth dimension-a photon-is translating through the three spatial dimensions at the rate of c. Hence it is obvious that the fourth dimension is expanding relative to the three spatial dimensions. String Theory's greatest contribution to physics has been the utter rejection of the obvious, the denial of common sense, and the institutionalization of thousands of mediocrities to ignore or shout-down any physics that might get in the way of their vast commercial industries which must trump truth-their salaries, benefits, and science-fiction books. Indeed, ST gives full license to make one's ignorance one's arrogance, and thus it is the breeding ground for those with ambitions overshadowing their talents." --http://www.groupsrv.com/science/about204630.html
In January 2009, Smolin writes "There is also no past. The past only lives as part of the present, to the extent that it gives us evidence of past events. And the future is not yet real, which means that it is open and full of possibilities, only a small set of which will be realized. Nor, on this view, is there any possibility of other universes. All that exists must be part of this universe, which we find ourselves in, at this moment."
--http://www.edge.org/q2009/q09_9.html
In January, 2007, I wrote, "Neither the future nor the past exists. Motion is inherent in the underlying four-dimensional space-time geometry, as the fourth dimension is expanding relative to the three spatial dimensions. Einstein noted that all objects are moving through space-time at the velocity c. This never changes. An object stationary in the three spatial dimensions is translating through the fourth dimension at the rate of c. An object stationary in the fourth dimension-a photon-is translating through the three spatial dimensions at the rate of c. Hence it is obvious that the fourth dimension is expanding relative to the three spatial dimensions. "
All of this was posted in an amazon.com forum on 11/13/2006 for Lee's Book: The Trouble With Physics: The Rise of String Theory, The Fall of Science, and What comes Next:
"Lee Smolin's Great Book : A Dialogue with Lee Smolin / Moving Dimensions Theory"
Over the years I have shared several emails with Lee, Including this one from 9/26/07--I have yet to hear back, but now that he thinks time is real, perhaps he might find some :):
to lsmolin@perimeterinstitute.ca
date Wed, Sep 26, 2007 at 11:56 AM
subject Hello Lee: The Curious Nature of the Photon, Einstein's Annus Mirabilis, and Moving Dimensions Theory
Hello Lee,
Hope all is well with you--just bought a second copy of TTWP to read while in the server room, recovering some lost data. :) Loved it even more the second time around.
If you ever get a moment, would be grateful for any comments on MDT.
Keep up the great work!
Elliot
INTRODUCTION TO MDT
As the hallmark of Moving Dimensions Theory is a simple postulate reflecting an underlying physical reality, let us begin with the simple postulate:
The fourth dimension is expanding relative to the three spatial dimensions.
That is it. This postulate underlies relativity--length contraction, time dilation, and the equivalence of mass and energy. It underlies quantum mechanics--wave interference, tunneling, entanglement. It underlies statistical mechanics--entropy and time's arrow.
The great power of Moving Dimensions Theory is that the simple postulate, representing an underlying physical reality, explains curious physical phenomena in every realm-from relativity, to quantum mechanics, to statistical mechanics. MDT accounts for quantum entanglement and relativistic length contraction. It accounts for entropy and action-at-a-distance. MDT unifies all of time's arrows, and it shows that all the curious dualities-wave/particle, space/time, and mass/energy, derive from the same source. MDT resolves both the paradox of Godel's block universe/block time and the Einstein, Rosen, and Podolsky paradox.
MDT--a simple sentence brought forth by a single individual--is what physics ought to be all about--descriptions of physical reality that unify and explain physical phenomena with simple, concise underlying physical models. And, as MDT predicts relativistic length contraction, entanglement, the constant velocity of light, and wave interference, it is one of the best-tested theories of all time, in addition to being a most fundamental theory regarding the emergent nature of time.
The Curious Nature of the Photon, Einstein's Annus Mirabilis,
and Moving Dimensions Theory
As the contemplation of the photon lead to both quantum mechanics and relativity, let us also begin the presentation of Moving Dimensions Theory by contemplating the photon. Einstein's revolutionary 1905 papers included one devoted to the photoelectric effect—which considered the quantized nature of the photon—and a paper devoted to the electrodynamics of moving bodies—which considered electromagnetic radiation, relativity, and the wave properties of the photon as embodied by Maxwell's Equations. Another 1905 paper discussed statistical mechanics in the form of Brownian Motion, and Einstein's final three-page paper that year commented on the equivalence of mass and energy, as denoted with his famous equation, E=mc 2. Moving Dimensions Theory underlies and unifies all of Einstein's 1905 papers with its simple postulate—the fourth dimension is expanding relative to the three spatial dimensions.
Consider the emission of a photon in free space. One second later, the photon has equal probability of being found anywhere upon a sphere with a radius of 186,000 miles, as the velocity of light, c, is 186,000 miles per second. If we covered the surface of said sphere with detectors, one, and only one, would click. And the photon, although having traveled 186,000 miles through space, will not have aged one iota, for time stops at the speed of light. The photon will have traveled 186,000 miles through the three spatial dimensions, and yet it will not have moved one iota in the fourth dimension. And there lies our first clue to moving dimensions theory. For how can a photon propagate 186,000 in the three spatial dimensions, and yet not budge an inch in the fourth dimension, unless that fourth dimension is expanding, right along with it? Ergo, the fourth dimension is expanding relative to the three spatial dimensions. A photon, as we shall see time and again, is matter surfing the fourth expanding dimension.
Consider two interacting photons that are directed to propagate in opposite directions, as in experiments conceived by Bell and conducted by Aspect et al. One second later, each photon's polarization is measured at detectors separated by 372,000 miles. According to the laws of quantum mechanics and numerous supporting experiments, the measurement at one detector instantaneously affects the measurement at the second detector. It is as if the photons are yet side-by-side for all intents and purposes. This "spooky action-at-a-distance," as Einstein called it, is not so spooky in the context of Moving Dimensions Theory, for MDT states that although separated by 372,000 miles, the photons are yet in the exact same place in the fourth dimension, as the fourth dimension is expanding relative to the three spatial dimensions. So it is that quantum phenomena on the photonic level, as well as relativistic phenomena on the photonic level, are both accounted for with simple elegance via MDT: the fourth dimension is expanding relative to the three spatial dimensions.
Another paper Einstein penned in 1905 was devoted to Brownian motion and statistical mechanics. Drop a thimbleful of food coloring in a pool. The laws of statistical mechanics dictate that there is a high probability that the coloring will spread throughout the entire pool, and never again reassemble in a localized region. That all systems tend towards random disorder is a fundamental law of physics and condition of physical reality, and this too can be accounted for by Moving Dimensions Theory. As the fundamental motion of the universe is the expansion of the fourth dimension relative to the three spatial dimensions, two photons originating from a common origin will harbor a vast probability of being found at great distances from one another one second later—distances far greater than the distance that separates them at their emission. This is because each one has an equal probability of being found anywhere upon the surface of a spherically-symmetric wave front of probability, corresponding to the wave front of the fourth expanding dimension. Recall our system of detectors placed everywhere upon the surface of a sphere with a radius of 186,000 miles—each photon has an equal chance of being found at any detector after one second after they were emitted at a common origin, and chances are that the detectors will be farther apart than the distance of zero that defines the separation between photon's common origin. Hence entropy. Entropy arises because the fourth dimension is expanding relative to the three spatial dimensions. All particles undergoing thermal vibrations interact with photons, and all photons reside in the fourth expanding dimension, dragging all of entirety into random disorder.
Yet another paper published by Einstein in his "Miraculous Year" (annus mirabilis), was devoted to the equivalence of mass and energy. Think about the fascinating physical reality implied by Einstein's most famous equation—E=mc2. A kilogram of gold or lead or feathers sitting on a desktop is the same thing as 9x10 16 joules of energy—an exorbitant amount of energy—enough to power, or to destroy, a major city. How is it that a stationary mass possesses such a great energy? It is because the mass, which is stationary in the three spatial dimensions, is yet propagating through the fourth dimension at the rate of c. This is because the fourth dimension is expanding relative to the three spatial dimensions. Matter surfing the fourth expanding dimension appears at photons. Furthermore, as noted earlier, the photons will propagate at the rate of c through the three spatial dimensions, and yet they will never age—they will stay in a fixed place in the fourth expanding dimension. The primary invariant is c—all matter and/or photons—be it propagating through space or time, or some combination thereof, always, always moves at the rate of c. To be stationary in the three spatial dimensions means to propagate at the rate of c through the fourth dimension. To be stationary in the fourth dimension means to propagate at the rate of c through the three spatial dimensions. Ergo the fourth dimension is expanding at the rate of c relative to the three spatial dimensions. Most objects share motion between space and time, but the overall velocity of propagation through space-time is fixed at c— this primary invariance can never change, and this reality arises because of the deeper physical reality of Moving Dimensions Theory.
And so it is that Moving Dimensions Theory underlies and unifies the papers Einstein Published during his Annus Mirabilis—his "miraculous year." I highly recommend Harvard University Press's Einstein 1905: The Standard of Greatness by John S. Rigden, about wcich Publisher's Weekly writes, "The year 2005 will be the centenary of Einstein's annus mirabilis, when he published the five papers that marked him as one of the greatest scientists of all time. Washington University professor Rigden (Hydrogen: The Essential Element) sits readers down in front of his white board and explains what Einstein said in each of these papers, what was significant in them and how the scientific community reacted (not very well, in most cases—for a while). Einstein started off with a bang: in March he proposed that light was not a continuous wave, but was made up of particles. In April he finished what became his dissertation, on how to determine the size of molecules in a liquid (that may not sound very exciting, but this is one of Einstein's most cited papers). In May he wrote his paper on Brownian motion, and then in June came the summit of his achievements that year: the paper proposing his principles of relativity and the consistency of the speed of light (commonly known as the Special Theory of Relativity). Finally, almost as an afterthought, in September came the three-page paper that unleashed his now-famous equation, e=mc2, upon an unsuspecting world. Rigden writes with a rare felicity, free of jargon and with everyday metaphors that Einstein himself would no doubt have appreciated."
I encourage everyone to read Einstein's and Bohr's and Heisenberg's and Dirac's original papers, and contrast their majestic elegance, eloquence, reason, and logic to the snarky death threats and crackpot indexes manufactured by today's "best and brightest," and the accompanying silence from their established elders—the founders of string theory's oppressive regime and hand-waving, reason-subjugating, PBS miniseries. The future book on Moving Dimensions Theory will look back to the giants of yesteryear with deep honor and reverence, so that tomorrow's physics might advance in the spirit of simple Truth and Beauty. Every effort will be maintained to demonstrate that true physics is marked by grace and simplicity, as opposed to obfuscation and bullying. Moving Dimensions Theory is an idea whose time has come, and ideas are bulletproof.
The fourth dimension is expanding relative to the three spatial dimensions. Moving Dimensions Theory accounts for the aetherless aether.
This simple postulate offers a physical model underlying and unifiying:
RELATIVITY:
1) length contraction
2) time dilation
3) the equivalence of mass and energy
4) the constant velocity of light
5) the independence of the speed of light from the velocity of the source
QUANTUMN MECHANICS
1) action at a distance
2) wave-particle duality
3) interference phenomena
4) EPR paradox
THERMODYNAMICS
1) Time's arrow
2) Entropy
STRING THEORY'S MANY DIMENSIONS / KALUZA/KLEIN THEORY
1) a fourth expanding dimension can be interepreted as many dimensions, each time it expands
THE UNITY OF THE DUALITIES
1) wave/particle duality
2) time/space duality
3) energy/mass duality
4) E/B duality
GENERAL RELATIVITY
1) Gravitational redshift
2) Gravity waves
3) Gravitation attraction
THE SPACE-TIME BACKGROUND
1) quantum foam
2) the smearing of space and time at small distances
3) Hawking's imaginary time
PARADOXES
1) MDT explains away Godel's Block Universe
2) MDT unfreezes time
3) Resolves Zeno's Paradox
ONE GETS ALL OF THIS FROM A SIMPLE POSTULATE:
The fourth dimension is expanding relative to the three spatial dimensions in a spherically symmetric manner, in units of the Planck length, at the rate of c.
--dr. e's email to lsmolin@perimeterinstitute.ca
date Wed, Sep 26, 2007 at 11:56 AM
subject Hello Lee: The Curious Nature of the Photon, Einstein's Annus Mirabilis, and Moving Dimensions Theory)
I also sent other emails regarding Moving Dimensions Theory, including one sent on 4/19/07 which was cc'd to a dozen other physicists.
Lee writes at The Edge, "The view that time is real and truth is situated within the moment further implies that there is no timeless arbiter of meaning, and no transcendent or absolute source of values or ethics. Meaning, values and ethics are all things that we humans project into the world. Without us, they don’t exist."
Yes--while time is real, I will yet agree with Einstein over Lee--Einstein writes, "Yes, we have to divide up our time like that, between our politics and our equations. But to me our equations are far more important, for politics are only a matter of present concern. A mathematical equation stands forever."
Yes--I will have to stick with dx4/dt=ic from here on out to eternity, just as Ludwig von Boltzman has s=klogw on his tombstone and Max Born has xp-px=ih on his.
Gaetano Barbella wrote on Mar. 17, 2009 @ 07:17 GMT
Sono l’autore di un E-Book edito a dicembre scorso dalla Macro Edizioni dal titolo “I due Leoni Cibernetici” e sottotitolo “L’alfa e l’omega di una matematica ignota, pi greco e la sezione aurea”.
Riporto l’indirizzo informatico che è questo: http://www.macroedizioni.it/libro.php?id_libro=1474&PHPSESSI D=112db27d7afaa901eaae76c25cabcb4d.
Questo E-Book lo presento sul mio sito a questo indirizzo: Il geometra pensiero in rete.
Cordiali saluti,
Gaetano Barbella
post approved
John wrote on Apr. 7, 2009 @ 14:58 GMT
Well, time does exist. See
Horwitz, L.P. (2005) On the significance of a recent experiment demonstrating quantum interference in time. http://arxiv.org/abs/quant-ph/0507044