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FQXi FORUM

April 19, 2021

CATEGORY:
The Nature of Time Essay Contest (2008)
[back]

TOPIC: What if Time Really Exists? by Sean Carroll [refresh]

TOPIC: What if Time Really Exists? by Sean Carroll [refresh]

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.

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.

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

this post has been edited by the forum administrator

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

this post has been edited by the forum administrator

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

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

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

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

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.

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

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

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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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?

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?

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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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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Hi Sean,

I find your lack of response to my comment/challenge a little bit unfortunate.

Best wishes

Peter

I find your lack of response to my comment/challenge a little bit unfortunate.

Best wishes

Peter

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?

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?

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 [?];"

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 [?];"

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...

view entire post

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...

view entire post

attachments: 6_MOVING_DIMENSIONS_THEORY_EXAMINES_THE_GRAVITATIONAL_REDSHIFT_SLOWING_OF_CLOCKS.pdf

this post has been edited by the forum administrator

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

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

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...

view entire post

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...

view entire post

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.

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-- 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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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.

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.

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!

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!

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?

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.

I don't quite see why "we" shouldn't be the fluke among flukes - given infinite time there will be infinite Brains.

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.

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.

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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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.

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.

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.

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.

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

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

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.

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

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

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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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

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

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

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

An elegant argument that infinite time requires an infinite dimensional Hilbert space. This really brings home the difference between "infinite" and "arbitrarily large".

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...

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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...

view entire post

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

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

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

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

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...

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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...

view entire post

attachments: Moving_Dimensions_Theory__Heros_Journey_Physics.pdf

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

yours amrit

attachments: 3_In_The_Theory_of_Relativity_Time_is_a_Coordinate_of_Motion__Sorli_2009.pdf

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.

[a,a*] = 1

Take the trace of either side to show that this cannot have any finite dimensional representations.

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.

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.

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.

(...[-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.

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...

view entire post

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...

view entire post

attachments: 2_2_wheeler_recommendation_mcgucken_medium2.jpg, 1_retina2.jpg

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

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

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

Horwitz, L.P. (2005) On the significance of a recent experiment demonstrating quantum interference in time. http://arxiv.org/abs/quant-ph/0507044

Dear Dr. Carroll,

Here's a post that tries to comment on FQXi's 2008 essay contest (The Nature of Time) as well as its 2010 essay contest (Is Reality Digital or Analog?)

We have to wonder if the Large Hadron Collider was worth all the time and money it took to build. It won't find the Higgs boson. It may well "prove" that strings exist but this will only deceive the world because...

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Here's a post that tries to comment on FQXi's 2008 essay contest (The Nature of Time) as well as its 2010 essay contest (Is Reality Digital or Analog?)

We have to wonder if the Large Hadron Collider was worth all the time and money it took to build. It won't find the Higgs boson. It may well "prove" that strings exist but this will only deceive the world because...

view entire post

I know I can't submit another essay. I don't plan to - these are just some comments that came to mind after thinking about my essay. They don't seem very relevant to the topic "Is Reality Digital or Analog?" but writing them has given even more satisfaction than writing the essay, and I'm in the mood to share them with the whole world. So if you've got time to read them...

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According to the Community Ratings, my essay in the 2011 Essay Contest is sliding further down the ratings each day. But I'm having more luck with a science journal called General Science Journal - comments of mine inspired by the essay (which are nearly 20,000 words long and include comments about "The Nature of Time" as well as "Is Reality Digital or Analog?") were published in the Journal on Feb. 6 and may be viewed at http://gsjournal.net/ntham/bartlett.pdf

I didn't have time to submit my essay for reality but the approach of theoretical sociophysics would lay out four layers of time: the changing state of the universe, physics understanding this change as the underlying character of temporal sequence, timing and tempo and then with the emergence of behaviourally modern humans a new kind of causation where humans can frame the changing world around...

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Connections

The binding of existence

This is a story, built upon knowledge, intuition, and speculation. In the end, it is built upon some known theoretically successfully tested truths, and some unknowns conveyed in a formula that I consider trumps any objections – as we ponder the scope of existence. First we know of existence, by way of our self-awareness, coupled with scientific...

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The binding of existence

This is a story, built upon knowledge, intuition, and speculation. In the end, it is built upon some known theoretically successfully tested truths, and some unknowns conveyed in a formula that I consider trumps any objections – as we ponder the scope of existence. First we know of existence, by way of our self-awareness, coupled with scientific...

view entire post

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