The Foundational Questions Institute is sponsoring an essay competition on “The Nature of Time.” Needless to say, I’m in. It’s as if they said: “Here, you keep talking about this stuff you are always talking about anyway, except that we will hold out the possibility of substantial cash prizes for doing so.” Hard to resist.
The deadline for submitting an entry is December 1, so there’s still plenty of time (if you will), for anyone out there who is interested and looking for something to do over Thanksgiving. They are asking for essays under 5000 words, on any of various aspects of the nature of time, pitched “between the level of Scientific American and a review article in Science or Nature.” That last part turns out to be the difficult one — you’re allowed to invoke some technical concepts, and in fact the essay might seem a little thin if you kept it strictly popular, but hopefully it should be accessible to a large range of non-experts. Most entries seem to include a few judicious equations while doing their best to tell a story in words.
All of the entries are put online here, and each comes with its own discussion forum where readers can leave comments. A departure from the usual protocols of scientific communication, but that’s a good thing. (Inevitably there is a great deal of chaff along with the wheat among the submitted essays, but that’s the price you pay.) What is more, in addition to a judging by a jury of experts, there is also a community vote, which comes with its own prizes. So feel free to drop by and vote for mine if you like — or vote for someone else’s if you think it’s better. There’s some good stuff there.
My essay is called “What if Time Really Exists?” A lot of people who think about time tend to emerge from their contemplations and declare that time is just an illusion, or (in modern guise) some sort of semi-classical approximation. And that might very well be true. But it also might not be true; from our experiences with duality in string theory, we have explicit examples of models of quantum gravity which are equivalent to conventional quantum-mechanical systems obeying the time-dependent Schrödinger equation with the time parameter right there where Schrödinger put it.
And from that humble beginning — maybe ordinary quantum mechanics is right, and there exists a formulation of the theory of everything that takes the form of a time-independent Hamiltonian acting on a time-dependent quantum state defined in some Hilbert space — you can actually reach some sweeping conclusions. The fulcrum, of course, is the observed arrow of time in our local universe. When thinking about the low-entropy conditions near the Big Bang, we tend to get caught up in the fact that the Bang is a singularity, forming a boundary to spacetime in classical general relativity. But classical general relativity is not right, and it’s perfectly plausible (although far from inevitable) that there was something before the Bang. If the universe really did come into existence out of nothing 14 billion years ago, we can at least imagine that there was something special about that event, and there is some deep reason for the entropy to have been so low. But if the ordinary rules of quantum mechanics are obeyed, there is no such thing as the “beginning of time”; the Big Bang would just be a transitional stage, for which our current theories don’t provide an adequate spacetime interpretation. In that case, the observed arrow of time in our local universe has to arise dynamically according to the laws of physics governing the evolution of a wave function for all eternity.
Interestingly, that has important implications. If the quantum state evolves in a finite-dimensional Hilbert space, it evolves ergodically through a torus of phases, and will exhibit all of the usual problems of Boltzmann brains and the like (as Dyson, Kleban, and Susskind have emphasized). So, at the very least, the Hilbert space (under these assumptions) must be infinite-dimensional. In fact you can go a bit farther than that, and argue that the spectrum of energy eigenvalues must be arbitrarily closely spaced — there must be at least one accumulation point.
Sexy, I know. The remarkable thing is that you can say anything at all about the Hilbert space of the universe just by making a few simple assumptions and observing that eggs always turn into omelets, never the other way around. Turning it into a respectable cosmological model with an explicit spacetime interpretation is, admittedly, more work, and all we have at the moment are some very speculative ideas. But in the course of the essay I got to name-check Parmenides, Heraclitus, Lucretius, Augustine, and Nietzsche, so overall it was well worth the effort.
CarlN, I don’t think there is an actual limit moment you can ID as “infinity”. Just think again of relations like x x’ transformation and the weird time issues about black holes. Maybe *I* can’t ever notice a calendar moment when “infinitely many years” since whenever, but *someone else* operating through mappings might be able to go past all of my infinite time or distance (with my “infinity” like the open circle on “one” at x < 1.)
Neil B, I agree I put it too broadly – what I meant is that infinity has its place in math, is part of the system. And from my layman perspective it looks like in physics infinity needs to be avoided at all cost.
I know that there are good reasons for this – it just seams (maybe better would be feel) strange.
Physics has problems with infinities associated with an observable. These crop up with electric potentials V(r) = qq’/r, where r —>0 at a point charge you get an infinite potential. There are of course ways around this, but singularities regularly crop up as troublesome. However, infinite time is not the same problem. A two body problem in Newtonian mechanics is ideally eternal. Of course we accept that for two stars in a mutual orbit other external factors will probably at some time end it, but there is nothing which causes physicist hair to stand up over the prospect of a two body system ticking away forever.
The issue Neil B with the black hole is one example. If you fall into a black hole you will cross the event horizon in a short finite period of time. An external observer will see you slow down and never reach the horizon. This has a relationship called the tortoise coordinates, where you never can witness anything cross the horizon. Of course it becomes incredibly redshifted so that you can’t observe much except Planck scale modes. This gets into the whole matter of the stretched horizon, black hole holography and AdS/CFT. The curious thing which happens of course is that the external observer in principle can witness you, or Planck modes (strings etc) associated with you, right up to the moment the black hole quantum evaporates.
In the case of cosmology there is no evaporation point of the same type. So with respect to some conformally mapped coordinates. So the “infinity” is reduced to something finite. In the Anti de Sitter cosmology, a sort of strange twin of the more physical de Sitter cosmology, the boundary of the space is in Fermat coordinates a finite boundary. Yet particles leave and exit this boundary at +/- infinity along great arcs similar to a Poincare disk. So something which is infinite in one definition (time) is mapped to something finite in Fermat metric coordinates. Of course you can put a black hole in this space and have all sort of fun with dilated times and coordinates for particles on paths between the boundary and horizon.
Lawrence B. Crowell
I am not able to follow the discussion, but it comes to my mind, the issue at least to lay people is whether time is an illusion. It seems the scientific discussion focuses on that it is not. ( at least that is what I gather )
Wanting to get a better grip of whether time is an illusion, I decided to search readable sources— and gather that from New Scientist. http://www.newscientist.com/article/mg19726391.500-is-time-an-illusion.html
“… Physicists have long struggled to understand what time really is. In fact, they are not even sure it exists at all. In their quest for deeper theories of the universe, some researchers increasingly suspect that time is not a fundamental feature of nature, but rather an artefact (sic) of our perception. One group has recently found a way to do quantum physics without invoking time, which could help pave a path to a time-free “theory of everything”. If correct, the approach suggests that time really is an illusion, and that we may need to rethink how the universe at large works.”
I thought this is cute, that the holy grail quest for the “theory of everything” will or could soon be a “time free” theory of everything ( smile) (smile) (smile) So to get around, with a time free theory of everything, it seems to get back or return to or come home to square one with the suggestion time really is an illusion.
So is time an illusion?
I am a bit rushed for time so did not read the entire 7 page article if the fonts are expanded to size 12 Roman Times font style ( saved for a later day), so I cannot tease out the writer’s suggestion (if any) time is an illusion. http://www.newscientist.com/article/mg19726391.500-is-time-an-illusion.html
Ok. So Neil, as an immortal local observer, will not ever turn the calendar page “Year Infinite”. But LC, via some “conformally mapped co-ordinates” probably, will actually see that Neil wraps around to the page “year infinite”. LC, via a strong telescope can actually read “Year Infinte” on Neils calendar.
Guys, this is not general relativity, this is general inconsistency. You seriously need to get your spacetime straight.
My apologies, for being insensitive to many great , serious , & genuine attempts at the theory of everything, something dear to the heart, soul & mind of those professionally & scientifically engaged in that worthy pursuit.
Such efforts are to be commended whether they bear immediate fruit or not. It may be there are several or more baskets of paradigms, and to reconcile the different baskets seem herculean now, with our current perception of separate and distinct baskets with their own self contained logic.
This comment on New Scientist’s Is time an illusion?” echoes in my being … “It is not reality that has a time flow, it is our very approximate knowledge of reality that has a time flow,” says Rovelli. “Time is the effect of our ignorance.”…. because it comes close to home of ancient buddhist teachings that ignorance is the greatest taint, on the perception of the world as real, when it is not. Science view of and on time, gives a small window to introduce concepts of perception versus fundamental or non fundamental ( of which time is said to be a non fundamental) that seems to defy human understanding based on perception & experience, a rare & unique occasion of possible interface or criss crossing of views or worldviews. But the explanation given by the author is distinctly and admittedly different, “Imagine gas in a box. In principle we could keep track of the position and momentum of each molecule at every instant and have total knowledge of the microscopic state of our surroundings. In this scenario, no such thing as temperature exists; instead we have an ever-changing arrangement of molecules. Keeping track of all that information is not feasible in practice, but we can average the microscopic behaviour to derive a macroscopic description. We condense all the information about the momenta of the molecules into a single measure, an average that we call temperature.” And THUS “According to Connes and Rovelli, the same applies to the universe at large. There are many more constituents to keep track of: not only do we have particles of matter to deal with, we also have space itself and therefore gravity. When we average over this vast microscopic arrangement, the macroscopic feature that emerges is not temperature, but time. ..”
This brings to my mind somewhere where it is said that time is connected or related to gravity, and the higher we go up a high rise building, and live there, we age faster because of weaker gravity as compared to another who lives on ground level. It also brings to mind something about travelling at speed of light and ?? not aging? Or something odd (forgotten), and so, it is not the usual perception of the clock ticking time as we ordinarily experience.
What comes to my mind is the similarity between the thermodynamic partition function and the QM path integral. By “Wick rotation” of the time you get a temperature.
I guess Rovelli is right by saying that time does not really exist. Classically the present is encoded in the particles positions. The past exists only as encoded in the particles present momenta. And the future does not exist at all.
Only the present really exist. Any spacetime geometry that allows some kind of time travel is fundamentally wrong.
Interested: The problem is somewhat beyond whether time exists, but how is it that time in general relativity and quantum mechanics can ever be made to agree with each other about time. In general relativity time is a symmetry of the theory, or in the su(1,1) part of the sl(2,C) group. One can in ADM relativity consider spatial surfaces as foliating a spacetime. How these spatial surfaces link together is chosen by the analyst in a manner similar to a gauge choice. This is of course curious, for we can think of time as some one dimensional space with a fibration given by spatial surfaces. So “choosing” how time acts is equivalent to choosing a section in a fibration of spatial surfaces over a real line which parameterized time.
Quantum mechanics in the other hand treats time as more concrete. The Schrodinger equation
holds time as an evolutionary parameter which is not a symmetry of the Hamiltonian. In relativistic quantum theory one must assign fields on a spatial surface of simultaneity (equal time commutators of fields etc), and from there time acts as a parameter which fixes a Hamiltonian, but is not a symmetry of the Hamiltonian. Things get somewhat odd when the space or spacetime is curved. In particular the distinction between a vacuum and a particle state breaks down.
General relativity does not derive a Schrodinger equation per se, but in the “space plus time” ADM approach the canonical quantization of variables give the above equation with the left hand side zero. This Wheeler-DeWitt equation is then not a wave equation of evolution, but a constraint type of equation which specifies a wave functional on metric configuration variables.
This dichotomy between how general relativity and quantum mechanics treat time still obtains. The big theory of unification is string theory, which is more particle based based. There general relativity is treated with a background, which adulterates some aspect of gravitation. The other theory called Loop Quantum Gravity is more general relativity oriented, but this theory has difficulty in deriving particle or quantum physics in a workable manner. At the core of this problem is that GR and QM simply regard time in basically different ways.
In euclidean gravity time is related to a temperature as
which indicates that on a microscopic level time is the phase description of spinor fields (or whatever substructure there is) to gravitation. There may then be a time, or equivalently a temperature, where the physics is scale invariant, which will occur for some very low temperature (T goes to zero) or equivalently a long time parameter. This is I think a quantum critical point, similar to the “breakdown” of electrons or quasi-particle Fermions in a Landau fluid.
In this setting time appears to be emergent, but at the critical temperature T = 0 time does “go to infinity,” if you will.
Lawrence B. Crowell
CarlN, there will not be a way to read the “year infinite” on my calendar since as I have repeatedly said, remapping makes the limit to infinity a “closed” point like the “one” in x < 1. But you may well be right that there is no way for any entity to physcially relate to another one in that remapped way which seems to "include" the limit to infinity within it's own finite coordinates. I could be just a math notion that has no real physical enactment. This is all part of the question, what is really real, wave functions, time itself, "curved space" and "so then, what does it curve into" etc. I think the universe isn't fundamentally real or self-sufficient in itself anyway. It's just a "Matrix" like scheme for generating phenomenal existence, i.e. for "a purpose" as hinted through anthropic fine tuning.
It is hard to know if the universe expands to its attractor point in an infinite time period for sure. The cosmological horizon, just as with a black hole horizon, might produce exceedingly long wavelength radiation and decay. The following article arxiv.org/abs/0803.1987 discusses this, though I am not sure about part of this. However if this occurs the cosmological horizon at r = sqrt{3/Lambda} will have some temperature T ~ Lambda, and over an immense period of time the cosmological constant (parameter) will approach zero and the horizon will retreat off to “infinity.” The final state of this is an empty Minkowski spacetime. Whether this takes a literal “infinity time” or not is somewhat academic. It might be that as with BEC’s there is some tiny temperature T > 0 where the process stops. So the final state of the universe might then be at some finite time, though enormously large, in the future. Again we are in a domain of great uncertainty, and because of the nature of this subject we obviously will never do an experiment or make any observations!
It is also curious that the final state might be a Minkowski spacetime, which would be an eternal void with no clock or anything else in it.
Lawrence B. Crowell
Neil, I guess you took the point. You can’t remap infinite time, since it will not ever exist.
On what is “real” you can only rely on what does not introduce inconsistency. A “thing” that is in conflict with itself cannot exist. It cannot exist more than 2=3.
Certain spacetime geometries will in fact give rise to inconsistency or “incomputability” like GR regarding the BH singularity or time travel.
However, the most important point is that “time” is invariably finite. The impossibility of future infinite time means that there is no infinite time in the past. The infinite simply takes too long for time to pass. So the beginning of time is finite in the past. This is of course the BB. And this is creation from nothing.
Of course one can think about something “before” the BB, that has caused the BB. But the same logic applies. That needs a beginning too. As we have discussed before, you cannot explain anything using eternal (outside of time if necessary) concepts, since there is no way of explaining the properties of eternal “things”. There is no way of explaining something eternal has this set of properties instead of that set of properties. If you go that way all you have is wishful thinking and no explanation.
You already know that creation “from” nothing is logical. That is simply logically possible.
And also, it is of course impossible for something not self-consistent to start to exist.
This is why our physics books is full of math!
But still there are things to be said. On what it means to exist, for example.
🙂
LC, time (or the size of the universe) will always be finite, but increasing. This is just a mathematical fact. You can’t reach infinity by finite increments applied one after the other. You just move from one finite value to another for ever. That is just the way it is. And how it must be. Physically it is impossible to measure anything infinite.
Whether or not an alarm clock will ever ring once time reaches infinity is besides the point. Of course that can’t happen. That still does not mean that time can’t continue endlessly. In effect what you are saying is that because there is not the infinite register space for information required to enumberate that infinite time it then must not exist.
Again one can consider a Zeno type of argument. Suppose that in one second I or some oracle machine counts 1, and then in the next 1/2 second it counts 2, and the in the next 1/4 it counts 3 and so forth. Then this is an infinite sequence of performed in 1 + 1/2 + 1/4 + 1/8 + … = 2 seconds. Now I have invoked a bit of “magic” here, but this does indicate that in a finite time an infinite number of counting steps is possible, at least mathematically.
So for the universe being infinite in spacial extent, that is of course an interesting question. It indeed could be infinite! Inflation expanded a region the size of an atom to about 1 meter in the first 10^{-20} seconds or so of the universe. Suppose the universe tunnelled out of the vacuum from a wormhole with the Reissnor Nordstrom F(r) = 1 – 2M/r – /r^3/3, for
ds^2 = -F dt^2 + F^{-1}dr^2 + r^2 dOmega^2
Suppose the cosmological constant / = /(f, f-dot), for f a Higgian field, this for small scales, such as with a virtual wormhole near the Planck scale, this / might be very large. This will then act to inflate the two 3-balls in the interior of the wormhole boundaries, which compose a three sphere S^3. Now suppose that this Higgsian field is dynamical, say it is composed of gauge particles or quark-like particles. Then there is a theorem by Fred Taubs which says that such fields can be concentrated at a pole on the sphere, associated with a Chern class. This could not only inflate the sphere, but puncture it and push the boundary “off to infinity!” So inflation might not have just blown up a three sphere with a small radius of curvature to one with 10^{-20} that curvature, it might have literally “popped it” and stretched it out to infinity.
I am not saying this happened with any certainty, but who knows. The universe looks awfully spatially flat, so it could be indeed infinite!
Lawrence B. Crowell
LC, you are almost there. Time can indeed continue endlessly, while always remaining finite. The “transition” from a finite to an infinite value cannot happen by finite steps. Making the steps ever smaller can also prevent you from going past a certain value as your example shows.
Anything infinite cannot be measured. Any theory involving infinities is impossible to verify.
There are certain infinities which are more troublesome in physics than others. Physics is really about local principles, so if there is an infinte cosmology in either space or time which permits finite measurements in any local region this is not that troublesome. Infinities which are troublesome in theories is where you get infinite masses for particles or other divergences which would be locally observable.
Again, I think the problem you raise is somewhat artificial. If there is a Cauchy-like sequence of energy eigenvalues, similar to what Sean argues for, which permit the endless occurrence of time increments to be “measured” by quantum transitions, then just because this will never register the “number” infinity, this does not mean there is not infinite time. By the same token just because there is no meter stick large enough to measure the real number line does not mean there is some consistency problem with the idea of the reals, or infinte spaces, or their application in physical or cosmological models.
Lawrence B. Crowell
Interesting stuff.
Any attempt to deny the real existence of time breaks the physicalist notion of the correspondence between brain states and mental states. We subjectively experience the passage of time as a succession of mental states; physicalism assumes, amongst other things, that you cannot have a change of mental state without a change of brain state; hence there is an objective succession of brain states.
Sean, I think your classification of Parmenides as belonging to ‘presentism’ is incorrect. He would actually belong the the school of thought called ‘eternalism’.
http://plato.stanford.edu/entries/spacetime-bebecome/
Parmenides might be the first person to advance something similar to block time, which is the viewpoint in general relativity from a purist perspective.
L. C.
The classification was only a loose one, as noted in the essay — given the word limit, I couldn’t get into the various specific schools of thought.
CarlN Says: “Only the present really exist. Any spacetime geometry that allows some kind of time travel is fundamentally wrong”
I do not personally know, having little maths, but if there is something to this below ( same comment above about this funny script), then time travel might be fundamentally right, albeit progress in this area is slow.
” Prof RICHARD GOTT: The greatest time traveller so far is an astronaut, cosmonaut named Sergei Abediev who spent 748 days aboard the Meer space station travelling over 17000 miles per hour. And when he came back because of this he had aged a 50th of a second less than he would have if he had stayed home. In other words when he got back to the earth he found it to be a 50th of a second to the future of where he expected it to be, he has time travelled a 50th of a second into the future.
NARRATOR (DILLY BARLOW): Admittedly a 50th of a second may not sound dramatic but the cosmonauts of Meer could have travelled much further into the future, all they’d have needed to do was travel even faster.
Prof PAUL DAVIES: Imagine if I go off in a rocket ship at very close to the speed of light and perhaps I’m gone for about a year whizzing around our part of the galaxy and I come back to earth and I find that you’re ten years older. I’ve been away one year but ten years have elapsed here on earth, and so in effect I’ve just nine years into your future.
Prof DAVID DEUTSCHE: This sounds like an extremely weird and unbelievable property of nature. It’s actually one of the best corroborated physical effects that we know of. People who build satellites have to routinely take into account the fact that time travels at a different speed in different states of motion.” http://www.bbc.co.uk/science/horizon/2003/timetriptrans.shtml
Lawrence Crowell ,
You attempted to explain to me, but I think it had more science than I could manage or chew off. I read this http://www.bbc.co.uk/science/horizon/2003/timetriptrans.shtml It seems like a pretend script, a made up story or dialogue but it also seemed to have some content . Yes ? / No?
The ending of the script was surprising for it echoes what I felt at the onset of knowing the big question about time, if it exists.
“Prof FRANK TIPLER: Inside the simulation you can’t tell any difference between the simulated environment, the virtual reality and the real environment. In fact this environment we need find ourselves in could be just a simulation.
NARRATOR (DILLY BARLOW): Three hundred years ago science set out on a quest to master time, to control it. People didn’t like time being controlled by a super intelligent superior being, we do it for ourselves instead. But every time we made a break through there was a downside. Now we’re told we may not even be real. Instead we may merely be part of a computer program, our free will as Newton suggested is probably an illusion. And just to rub it in, we are being controlled by a super intelligent superior being, who is after all the master of time.
Prof DAVID DEUTSCHE: From the point of view of science it’s a catastrophic idea, the purpose of science is to understand reality. If we’re living in a virtual reality we are forever barred from understanding nature.
Prof PAUL DAVIES: Our investigation of the nature of time has lead inevitably to question the nature of reality and it would be a true irony if the culmination of this great scientific story was to undermine the very existence of the whole enterprise and indeed the existence of the rational universe.”
Back to me – If it were to turn out that, we would walk down the road where, we realize we are not real, and that we are some virtual reality, then it will/could/might open door to other ancient knowledge of what type of virtual reality our rational being and rational universe is. It would/could/might be knowledge converging at some point in future, through the scientific pursuit of the scientific understanding of time, and thus of real nature of reality.
Interested, you refer to relativistic time dilatation. This is not time travel in the usual sense. You can slow your time (and aging) with respect to earth (for example) by taking a rocket trip.
Time travel is stepping into a stationary machine and find that
you have moved back in time or forward in time more than the time you spent in the machine. I tend take the absence of time travelers as empirical “proof” of the impossibility of this.
LC, Sean is not using the accumulation point(s) of eigenvalues to “generate” time by quantum transitions. Instead he says nothing about time and uses the superposition of eigenstates to make sure the universe never repeats itself (given time from the outset). However, he does not explain in this setup how an omelet turning into eggs is less probable than eggs turning into an omelet.
The idea is to provide a large enought a Hilbert space, which has energy gaps small enough for any future cold condition, so that a quantum Poincare recurrence does not set in. An elementary example of a recurrence is a two state atom and photon in a cavity described by the Janes-Cummings Hamiltonian.
Lawrence B. Crowell
LC, what in this setup make sure the future cold condition?
As the universe expands things get colder. The 3K CMB temperature is a remnant of the period about 380,000 years after the big bang where radiation and matter existed in a plasma. The end of that age released the radiation which is now redshifted and “cooled” to the feeble microwave background we see today. This will continue as the universe expands into a sort of void that approaches absolute zero temperature.
Lawrence B. Crowell
I know, but what about what my question?