On The Flow of Time by George F R Ellis

Dear Professor Ellis,

Thank you for your reply. You are quite right. Nonetheless I do not share your aversion towards complex numbers. My point is:

Complex plane is in general assumed to contain much more data as compared to the real line. That's why quantum mechanics run into the trouble of Schroedinger's cat, entanglement, decoherence, etc.

If I am correct then only past time relative to any process of concern counts and analytical continuation just creates redundant data. Is there nobody who either refutes or supports this?

Sincerely, Eckard Blumschein

Dear Prof. Ellis,

So far, I assume that Hilbert and his pupil J. v. Neumann were at least among the first who declared the flow of time an illusion. Do you know earlier ones?

Sincerely,

Eckard Blumschein

Dear Eckard Blumschein

The idea is very much older than Hilbert. According to the Wikipedia article on Plato, "Plato, like so many other Greek philosphers, was stymied by the question of change in the physical world. Heraclitus had said that there is nothing certain or stable except the fact that things change, and Parmenides and the Eleatic philosophers claimed that all change, motion, and time was an illusion. Where was the truth? How can these two opposite positions be reconciled? Plato ingeniously combined the two" [in his theory of forms].

Sincerely

George Ellis

Thank you for the reminder that toy models of reality are just that -- toys -- and that any theory which hopes to explain the real world must reflect that reality.

Thanks for that, Tevian. I think your point is crucial: theoretical physicists tend to get totally caught up in their very simplified models of reality, and then start to confuse them with reality. We have attained a huge sucess in terms of our progress in fundamental physics (apart from the open question of quantum gravity). The problem now is to get a more realistic relation of this body of foundational theory to physical and biological reality, specifically the nature and functioning of truly complex systems. They too provide data about the nature of the real world; if necessary, the fundamental theories must be modified to take this data into account. And whatever one says about microphysics, it seems clear that the flow of time is not an illusion at the macro scale. I suggest, for example, that it is not yet determined who will win the fqxi essay prizes. This will be determined eventually, as part of the overall historical process, as the flow of time rolls inevitably on.

Prof. Ellis: "I suggest, for example, that it is not yet determined who will win the fqxi essay prizes."

Perhaps also not after the prizes are awarded and you forgot who won?

About your essay, do you think that one can do experiments to find deviations of standard quantum mechanics, e.g. decoherence in isolated systems that are not due to interactions with the environment?

't Hooft has worked on models in which quantum mechanics is not fundamental. He is led to models in which information loss has to be present at the fundamental level, see e.g. here:

http://arxiv.org/abs/gr-qc/9903084

http://arxiv.org/abs/hep-th/0105105

http://arxiv.org/abs/quant-ph/0212095

http://arxiv.org/abs/quant-ph/0604008

http://arxiv.org/abs/quant-ph/0701097

Dear Saibal Mitra

Your essay starts "Assuming the validity of the Many Worlds Interpretation of quantum mechanics (MWI), we examine the possibility of changing the past by memory erasure". I have problems with the many worlds assumption, as I have for example never had an answer from those I consulted as to how often the wave function branches, and what decides when it happens. I do not grasp the utility of the idea, which appears to be untestable. But maybe I will be persuaded some day. Your essay then carries on "In the future our descendents will probably be machines". I cannot concur with this assumption, indeed I am not sure that it makes sense. Then I cannot see any reality in your proposals about reloading and erasing memory: I do not believe this is remotely practicable. So I do not think there is any reality to the proposal that the identity of those who won the prizes can be altered after they have been won. I cannot see that this is a profitable line of speculation to pursue. However T'Hooft's ideas on quantum mechanics are surely worth consideration. Yes those kinds of experiments are certainly worth considering.

Dear Prof. Ellis,

thanks for your comments. I'll write a detailed reply to your criticism on my essay on the comments page of my essay:

http://www.fqxi.org/community/forum/topic/354

to prevent the discussion here from going off topic.

I think the following points are appropriate to mention here:

1) It is legitimate to investigate the consequences of purely unitary time evolution. As of yet, there is no evidence that time evolution does not proceed in a unitary way. In my essay, I just considered a hypothetical (machine) observer who can erase his/her/its memory, I didn't speculate about new fundamental physics.

2) If it is proposed that time evolution is not unitary, then this has to be supported by experimental evidence. Because then a more complicated theory is proposed and, as of yet, it hasn't been shown that the purely unitary time evolution is not sufficient to account for all experimental data.

Dear Professor Ellis,

Thank you for pointing me to Plato (427-348) and Aristoteles (384-322) who claimed: Numbers are basic to anything.

Ancient mathematicians did not have negative numbers. They certainly did not have the notion negative time.

After Descartes and Fourier necessarily obeyed the usual notion of what clocks putatively show, maybe, it was Minkowski who invented world-lines thought to range from minus infinity to plus infinity, Hilbert denied the arrow of time, and Einstein called the division between past and future an illusion. They all did so for mixed mathematical, religious, and speculative reasons, which are still dominating fund-raising including its reflection in the votes of this contest.

Mathematics claimed to generalize anything, and scientists are still considering most abstract and most general models as the deepest ones. Benefits for science, technology and economy seem to be more or less occasional spin-offs.

Regards,

Eckard Blumschein

Dear Saibal Mitra

every time a quantum measurement is made the evolution does not proceed in a unitary way. Please see for example Roger Penrose: The Emperor's New Mind, pages 250-251, which makes explicit aspects of what is for example in Isham's book Lecturs on Quantum Theory, pages 71-73 and 82-85. You state "It is legitimate to investigate the consequences of purely unitary time evolution. As of yet, there is no evidence that time evolution does not proceed in a unitary way." You are talking of quantum theory without any measurements taking place, and hence no outcomes of any experiments and no evidence of anything. The many worlds picture does not change the abundant experimental proof that what we verify by experiment in the unverse domain we actually experience is measurements that proceed in a non-unitary way.

Dear Prof. Ellis,

I think we would need evidence that a completely isolated system undergoes non unitary time evolution. If you are locked up in a hypthetically perfectly isolated box and you perform measurements in tat box then, if you are right, the wavefunction of the entire box would not evolve according to the unitary time evolution. Then, since you are a large collection of particles, one should expect that unitary time evolution is violated in general (apart form the, wavefunction collapse associated with measurements, which in the MWI is explained as the observer becoming entangled with the system).

Dear Sabal Mitra

You say "I think we would need evidence that a completely isolated system undergoes non unitary time evolution." The whole point of my article is that there do not exist any completely isolated systems in the real world (except perhaps the universe itself). They are a fiction. The best you can do is partially isolate particular systems for limited times. But for example, the matter of which they are now composed was not isolated 14 billion years ago when they were part of the primeval soup. And the whole point about living systems is that they cannot function if isloated: they are open systems. The "hypothetically perfectly isolated box" you invoke is just that: hypothetical. It cannot exist in physical reality.

Dear Prof. Ellis,

Yes, I agree with you here. I think 't Hooft also argued in a similar way in defense of his ideas. You have to assume that the fact that you cannot isolate a (macroscopic) system from the rest of the universe is (also) due to fundamental physics in such a way that assuming you could do so would lead to flawed conclusions.

Suppose that quantum gravity is given by noncommutative geometries (plural) according to unitarily inequivalent groups. Further let there be associator maps between these groups. This would then be nonassociative QM, which is nonunitary. However, it can preserve quantum bits if described by E_8 or some sporadic group with an error correction capacity. A coarse grained description of this system, which eliminates nonassociative graphs, will then give a thermal description similar to Bogoliubov transformations used in black hole radiation.

This system might then be the entire universe, maybe more compactly described in it earliest fractions of femptoseconds of existence. Any supposedly closed system an experimenter might set up suffers from a number of problems. The system can't be kept completely away from the boundaries of the box, except for a black hole in the AdS spacetime. So there is no procedure for arriving at a perfect fine grained description for a system. Hence all systems we observe are ultimately open on some scale of frequencies, time or space.

Lawrence B. Crowell

Dear Lawrence B. Crowell

thanks for that interesting elaboration.

Dear George,

In response to my first posting from Dec. 2, 2008 @ 07:02 GMT above, on Dec. 3, 2008 @ 16:47 GMT, you wrote:

"... the outcome of quantum events is unknown until they happen. That is a key feature on which I build my proposal; so there is no conflict."

I'm glad to notice that you can surf the Web, so please check out the link to my essay 'Quantum Mechanics 101', in my first posting above. The crucial issue is *not* that the outcome of quantum events is "unknown until they happen".

We aren't talking epistemology here. The puzzle is know since 1935. To quote from Erwin Schrödinger's "Die gegenwärtige Situation in der Quantenmechanik":

"... measuring it does not mean ascertaining the value that it (the quantum system - D.C.) has."

As to whether there is conflict in your reasoning, I think it is too early to say anything conclusive. You haven't yet elaborated on the so-called Dynamic Dark Energy -- the driving force of 'the flow of time'.

I wish you best of luck in placing this perfectly smooth "dark stuff" on some Cauchy surface.

Dimi

Dear Dimi Chakalov

you correctly note that my statement "... the outcome of quantum events is unknown until they happen. That is a key feature on which I build my proposal; so there is no conflict." is not as strong as it could be, and indeed should be. It must have been penned in haste, or late at night. I should have made it much stronger, as follows: "... the outcome of quantum events is unknown and indeed undetermined until they happen." Then I am no longer talking just epistemology: I am talking about the way things actually occur, as emphasized for example by Feynmann. This is what I in fact intended, amd is meant throughout my paper.

I have not related my paper to dark energy, as usually understood, because in my view that is a completely different puzzle from what is considered here. I do indeed have views on that issue, but see no reason to post them here.

Dear George,

Good to see you (and your essay) here.

"The most important property of time is that it unfolds. The present is different from both the past and future, which in turn are completely different from each other, the past being fixed and the future changeable. The present is the instant of transition between these two states. The time that is the present at this instant will be in the past at the next instant."

I feel like I may be begginning to repeat myself a little in this essay contest, but it can be shown that if instants (and instantaneous magnitudes) existed, motion and change would be impossible. Furthermore, as instants would constitute the building blocks of time, if they can't/don't exist, neither can time.

"But one thing is clear: both the entire Darwinian process of evolution through which we come into existence, and the processes by which we read this article, depend on the flux of time. You would not exist and have the ability to read this article if the view proposed here (and expounded in more detail in Ref. [6]) was not a correct description of the way things are."

That's not the case. Indeed, it would only apply if instants (and time) did exist. I agree that it does apply to the standard interpretation of block time, but this is also because of its assumption of the physical existence of instants, spatial points and space-time points (and as such, the resulting assumption of the existence of time, space, and space-time). As soon as one recognizes that instants, instantaneous magnitudes, space-time points etc, do not exist, however, motion and change become possible, and can be seen to be completely compatible with gr and the block view, with all times (those shown by a clock) sharing equal footing.

Also, in order for change to be possible, one does not need time to exist, as one only need motion. Indeed, I think that if one thinks carefully about it, it becomes apparent that it is motion that enables the hands of a clock to rotate and for one to represent an interval, rather than the other way around (the existence of time enabling motion). My essay (and notes) go into this further. I naturally agree that certain processes are not time reversible, but this is completely compatible with a timeless block view (if interpreted correctly). Moreover, it does not suggest at all that time flows.

Best wishes

Peter

Dear Peter Lynds,

Thank you for your response. You state "it can be shown that if instants (and instantaneous magnitudes) existed, motion and change would be impossible. Furthermore, as instants would constitute the building blocks of time, if they can't/don't exist, neither can time." I presume you are referring to the Zeno's paradox argument, presented in your own fqxi essay and elsewhere. However I do not accept that argument, for the following reason: many discussions of quantum gravity conclude that at the very smallest scale, space-time will be discrete, for this is how the basic quantum theory principle will manifest itself in the context of the nature of space-time (quantized area and volume operators are one of the main deductions from loop quantum gravity, and there are 701,000 web-pages identified by a Google search for "discrete space time").

I concur in this view both because of quantum principles, and because this rids physics of the profound problem of the uncountable infinities of numbers that occur in the real line of mathematics. Indeed David Hilbert in a famous passage [D Hilbert (1964), ``On the Infinite". In Philosophy of Mathematics, ed. P Benacerraf and H Putnam (Englewood Cliff, N. J.: Prentice Hall), pp 134-151] stated that "Our principal result is that the infinite is nowhere to be found in reality. It neither exists in nature nor provides a legitimate basis for rational thought . . . The role that remains for the infinite to play is solely that of an idea . . . which transcends all experience and which completes the concrete as a totality." On this view, infinities are mathematical entities that never occur in physical reality; this may be taken as applying to the nature of space in a profound way. Incidentally, at a stroke this gets rid of many of the divergences that plague theoretical physics.

If space-time at its foundations is discrete, then the Zeno's paradox argument falls away. In this case it is not time that is an illusion, it is space-time continuity that is an illusion, generated by the coarse graining that underlies all macroscopic physics and hence also chemistry and biology. Furthermore, you state that most people believe that Zeno's paradox is resolved by calculus; but this ignores that fact that one of the great advances in mathematics was the transition from calculus to analysis, where the taking of limits is replaced by the use of bounding methods (utilising the famous `epsilons' and `deltas' of analysis) and the associated characterisation of solutions in terms of Sobolev spaces. Mathematical physics got rid of those troublesome limiting processes decades ago.

So my position is that continuity is an illusion, and your argument does not apply to the real physical world. Finally you state "in order for change to be possible, one does not need time to exist, as one only needs motion. Indeed, I think that if one thinks carefully about it, it becomes apparent that it is motion that enables the hands of a clock to rotate and for one to represent an interval, rather than the other way around (the existence of time enabling motion)." I cannot understand how you conceptualise motion without the flow of time to underpin it. Motion is identified by something being in a different position at a later time than at an earlier time. Perhaps your view is related to a relative rather than absolute view of the nature of space and time; that is a further interesting argument, which I will not enter here, except to comment that I believe there may be a fundamental duality between absolute and relative views of the nature of space and time. But adopting a relative view of space or time will still leave one with change taking place as relative time flows.