Does time exist in quantum gravity? by Claus Kiefer

A wonderful essay and beautifully written. (You must have lived for years in an English speaking country, ah, University of Alberta!)

I like that you hang your analysis on linear superposition and the requirement that GR be reached in the limit. Some comments.

(a) The simplest GR situation is the non rotating black hole. By saying "classical limit" do you mean to make a choice of coordinates? If so which? (I like Gullstrand-Painleve.)

(b) The presence of the imaginary unit i in Schroedinger's equation is sometimes said to go away when the situation is made relativistic with Dirac's gamma matrices. But I think David Hestenes' geometric arguments in that case apply and agree that it is significant; the imaginary unit does not go away.

Of your arxiv papers, I like most gr-qc/0406097, on the quasinormal modes of black holes. Lubos Motl proposed that "tripled Pauli statistics" as an explanation for this, you wrote "It could turn out, for example, that the entanglement of the (quantized) gravitational QNMs with the black-hole quantum state gives rise to the Bekenstein-Hawking entropy ..."

I wanted to point out that the mutually unbiased bases (MUBs) of the Pauli algebra are used by quantum information people to define the maximally entangled states (and also complementary states in the sense that knowing the results of one measurement destroys all information about the other). And that, sure enough, the maximum number of MUBs for the Pauli algebra is 3. This is just what is needed to triple Pauli statistics.

Dear Dr. keifer,

i read the essay as an experimentalist and found your presentation logical. describing nature is a difficult job, as we individually have our background bias. i feel that concepts and precepts that we happen to choose initially more or less decide what outcome of results we will get.Time invariance and reversability are important in Physics. Thus linearity in time is important. However, we also from the conjugative nature of time with energy that only distortion in time results in energy release, as also distortion in space results in creation of mass. Universe to begin with must have had such space-time distortions. As creations more or less stabilised and subsequently just evolved further, we had a period of steady state. Thus, both change and conservation are the features of the Universe. Chaos has lead to the randomness of the physical processes on a time averaged scale. Order contains chaos but not vice-versa. Thus, somewhere behind the probabilistic considerations of the physical phenomenon lies an unknown order! The non-physical concept of ' consciousness ' appears to arise in the horizon as human behaviour is not entirely governed by physical features. thus, we as observer or cognizer of the process, start invoking this aspect. Duality of quantum mechanics itself provides the basic resistance to approach the Truth. Thus, the later remains a relative quantity in sciences. Measurements restrict science. How to solve such dellima!

Sorry, the last word in my posting 'dilemma' that was wrongly spelled!

It seems to me this essay is simply a rehash of the same ideas as those of Carlo Rovelli (see his essay here earlier), Julian Barbour and others, namely that if the Wheeler-DeWitt equation holds, then time is illusory in a very real sense. But does the Wheeler-DeWitt equation holds in reality, at least at scales larger than the Planck length, as the author claimed? Unfortunately, there's no experimental evidence one way or another, so the author's claim of the Wheeler-DeWitt equation being "the most reliable equation of quantum gravity,

even if it is not the most fundamental one", must be taken with a large grain of salt. The unfortunate fact is that despite decades of research, quantum gravity is still a purely theoretical research with little or no connection to empirical evidence, and even its internal consistency cannot be demonstrated convincingly, so while researchers may have come up with formalisms and theories that are beautiful and elegant as mathematical theories, none of these theories can claim to be closer to reality than any other. It seems to me a bit premature to dictate the physical properties of Time using any of these untested theories.

Quantum Gravity + Time = $$$$$

Do a search at NSF on "time quantum gravity."

http://nsf.gov/awardsearch/piSearch.do;jsessionid=7F7E1A09E64B392775A7855BA8211E51?SearchType=piSearch&page=1&QueryText=time+quantum+gravity&PIFirstName=&PILastName=&PIInstitution=&PIState=&PIZip=&PICountry=&Search=Search#results

You will see that using quantum gravity to understand time is nothing new.

The research has received millions upon millions of dollars, and yet has produced abosolutely nothing but for aging quantum gravity regimes. NSF is just the tip of the iceberg.

All these millions upon millions, and yet, there is no:

1) graviton

2) consistent theory of quantum gravity, nor anything even close

3) any reason to go on

And yet, as the purpose of fqxi is generally to

1) fund well-funded, institutionalized crackpottery &

2) recreate physics in old physicists' image,

I imagine any essay that mentions time and quantum gravity will receive an award or two from the ruling pseudo-physicists.

Quantum Gravity + Time = $$$$$

Dear Dr. Kiefer,

the canonical quantization of General Relativity certainly leads to a loss of time. Canonical quantization and Schrödinger equation however rely on Newtonin notion of time. Hence it is not too surprising that 4-D general coordinate invariance paradoxically leads to the disappearence of time in general relativity.

I think that 4-D general coordinate invariance (no loss of time!) must be the starting point and dictate the formalism. For instance, my own work originated as a modification of general relativity based on the assumption that space-times are 4-D surfaces in certain higher dimensional space possessing the symmetries of empty Minkowski space and explaining standard model symmetries in terms of isometries and holonomies.

In this framework time is not lost and general coordinate invariance has amazingly strong and unexpectred consequences and leads to a formulation of quantum theory using the counterpart of super-space of Wheeler having strong resemblances to the loop spaces appearing in string models (in the sense that it decomposes to a union of infinite-D symmetric spaces with Kahler metric possessing maximal isometry group).

Thank you for a nice essay,

Matti Pitkanen

- Time is absolute in Quanta Physics that is to say 'algebraic', but in Einstein's Theories too. Algebraic time, wether it is vectors or arcs of time is always 'absolute'.

- Aristotle in his 'Physics' (III) does explain that there seem to be no reason to deduce a discontinuous Time from Natural phenomenon of Time. Infinity postulate in 'distance', infinity postulate in 'quantity' AND infinity postulate in Time too are just 'approximations' for Aristotle. So the idea of 'non discontinuous' Time is not new.

Hello Claus,

Thanks for the paper "Does time exist in quantum gravity?"!

But might not a better title be, "Does quantum gavity exist in time?"

I know it is fashionable to make the real unreal, and the unreal real, in the realm of fundraising, but after awhile money gets boring, and a man's soul yearns for truth, beauty, and physics!

I would have to agree with Ming, "It seems to me this essay is simply a rehash of the same ideas as those of Carlo Rovelli (see his essay here earlier), Julian Barbour and others, namely that if the Wheeler-DeWitt equation holds, then time is illusory in a very real sense. But does the Wheeler-DeWitt equation holds in reality, at least at scales larger than the Planck length, as the author claimed? Unfortunately, there's no experimental evidence one way or another, so the author's claim of the Wheeler-DeWitt equation being "the most reliable equation of quantum gravity, even if it is not the most fundamental one", must be taken with a large grain of salt. The unfortunate fact is that despite decades of research, quantum gravity is still a purely theoretical research with little or no connection to empirical evidence, and even its internal consistency cannot be demonstrated convincingly, so while researchers may have come up with formalisms and theories that are beautiful and elegant as mathematical theories, none of these theories can claim to be closer to reality than any other. It seems to me a bit premature to dictate the physical properties of Time using any of these untested theories."

It is curious that three out of the four papers receiving "restricted" votes deal with well-funded "quantum gravity" approaches that are a couple decades old, at least; and which have borne no fruit. I know some people argue that string theory is a forver-young theory deserving infinite funding, as it never succeeds at anything, but c'mon now--let's not go there. Let's get back to asking and answering foundational questions, while reading the foundational papers!

Furthmore, it is interesting that while there is no theoretical nor empirical evidence for quantum gravity, it is yet being used as a "tool" to explore time by "profssionals." This would be like conducting a heart-transplant with an imaginary scapel. All the doctors would stand around, talking and arguing about how beautiful and elegant their imaginary scapels are, and how each one is holding the best and desrves the most funding, while their patient died on the table. This is pretty much what has happened to physics over the past forty years, expect the imaginary theories haven't been elegant nor beeautiful. They have been non-finite, unwieldy, snarky, vast and confusing, obfuscating the subtle, convoluting the simple, confounding the honest soul, and exalting the illusionaist and hypester. This type of "beauty" is better relegated to postmodern literature departments.

Might it not be dangerous to let something that does not exist--quantum gravity--inspire and/or dictate our contemplations on time? I mean theoretical physics is hard enough, even when it is built on reality. But to build theoretical physics upon the unreal--is this not the very "Trouble With Physics" Lee Smolin writes about, which is better suited to building sociological movements, even when begun with the best intentions?

Do we have to quantize gravity? Could it be that nature is as it is, and that God or the Prime Mover/Creator came up with both QM and GR, which seem to coexist perfectly well in their current forms? For instance, this laptop computer is powered by quantum phenonema, and too, it is held on my lap by gravity. Each one has a role, and each seems perfectly content to play it. Perhaps both mathematical predictions and the experimental search for gravitons has fallen short because gravitons do not exist. Now this is no reason to stop looking, but too, it is not exactly a reason to keep looking, and it is certainly not a reason to get rid of time, which does seem to exist, as my laptop's clock tells me I am running late, yet again. :)

A book you would enjoy is Freeman Dyson's THE SCIENTIST AS REBEL. On page 219 Freeman Dyson writes,

"(Brian) Greene takes it for granted, and here the great majority of physicists agree with him, that the division of physics into seperate theories for large and small objects is unacceptable. General relativity is based on the idea that space-time is a flexible structure pulled and pushed by material objects. Quantum mechanics is based on the idea that space-time is a rigid framework within which observations are made. Greene believes there is an urgent need to find a theory of quantum gravity that works for large and small objects alike. . . As a conservative, I do not agree that a division of physics into separate theories for large and small is unacceptable. I am happy with the situation in which we have lived for the last eighty years . . . The question I am asking is if there is conceivable way we could detect the existence of individual gravitons. I propose as an hypothesis that it is impossible in principle to observe the existence of individual gravitons." --Freeman Dyson, THE SCIENTIST AS REBEL, pp 219-220

Perhaps we should found our contemplations on time not upon the unreality of quantum gravity, but on the reality of *physical* theories represnting *physical* phenomenon.

Instead of being built on the unreal, my simple theory--Moving Dimensions Theory--is built upon the rock-solid empirical evidence supporting widely-accepted theories of relativity, quantum mechanics, and statistical mechanics.

And MDT tells us a lot about time and its arrows across all realms, showing that they are phenomena that emerge from a common, deeper principle--a fundamental universal invariant--dx4/dt=ic.

MDT views time as a phenomenon that naturally emerges because the fourth dimension is expanding relative to the three spatial dimenions at the rate of c. Change is fundamentally woven into the fabric of spacetime via dx4/dt = ic, which makes sense, because change is fundamentally woven into our everyday existence, empirical observations, and all branches of physics! Indeed--it would not be possible to make a measurement without change! A great thing about MDT is that it allows us to keep all of relativity while unfreezing time and liberating us from the block universe, which is yet a meaningful artefact that arises from certain interpretations of relativity. And who knows, perhaps MDT will tell us something about quantum time, which will tell us something about quantum gravity. For MDT also provides a *physical* framework for quantum entanglement and nonlocality, and thus it provides a *physical* model underlying qm's inherent nonlocal, probabilistic nature.

Think about MDT as a simple *physical* unification of relativity and QM--both entanglement and nonlocality can be accounted for via the same principle--the same hitherto unsung univeral invariant of dx4/dt=ic--that ensures a photon does not age, no matter how far it travels. A photon's timelessness, implied by relativity, represents a nonlocality in time. Both quantum entanglement and the agelessness of a photon descend from a common principle--a fundamenatl, universal invarinat: dx4/dt = ic. A photon is matter that "surfs" the fourth expanding dimension, and thus it remains in one place in the fourth dimension, while traveling through the three spatial dimensions at c. Ergo the fourth dimension is expanding relative to the three spatial dimensions. Perhaps this is MDT's simplest proof: The only way to remain stationary in the fourth dimension is to move at c through the three spatial dimensions: egro, the fourth dimension is expanding relative to the three spatial dimensions.

And a great thing about MDT is that it also presents a *physical* model for entropy, as briefly elaborated on in my paper:

http://fqxi.org/community/forum/topic/238

MDT represents the kind of theory we have not seen for awhile--a simple postulate and a simple equation that present a novel, hitherto unsung aspect of the universe--the fourth dimension is expanding relative to the three spatial dimension: dx4/dt=ic. This fundamental invariance underlies the invariance of the speed of light--both the constant velocity of c meausred by all inertial observers and, the constancy of c that is independent of the source. MDT also underlies relativity's two postulates, and all of relativity may be derived from MDT's simple principle of a fourth expanding dimension.

When we look at Einstein's 1912 Manuscript, we see that time plays a different role from position. x1, x2, x3 represent the three spatial dimensions, which we generally use to demarcate position. And then along comes x4, which Einstein equates with ict. So as t progresses on our watches, x4 must progress. Time is very, very different from the three spatial dimensions! Perhaps it is not a dimension after all, but a parameter that emerges because the fourth dimension is expanding relative to the three spatial dimensions, as suggested by x4=ict.

MDT and dx4/dt=ic also underly time's thermodynamic arrow, and in my paper I account for and unify all of time's arrows and assymetries with MDT's simple postulate and equation. And in addition to this, all of relativity may be derived from MDT, while qm's entanglement and nonlocality are explained with a *physical* model, along with entropy.

Thanks for the paper! I just think it would be prudent to wait for a consistent theory of quantum gravity, or some experimental evidence, before using quantum gravity as a tool to probe time's great and vast mystery. It would be like hanging something on a sky hook, or shifting smoke with a left-handed smoke shifter.

http://www.urbandictionary.com/define.php?term=left%20handed%20smoke%20shifter

As a new boy scout on my first campout back in sixth grade, I was sent forth to other campsites to go find a left-handed smoke shifter (to shift the smoke from the breakfast campfire) and a sky hook. Of course, this is a big inside joke to everyone but the youngest scouts, so people at the next campsite always smile and nod and say, "We just lent our sky hooks and left-handed smoke shifters to that troop down yonder." And so it would go, as we ran from campsite, to campsite, to campsite, looking for that which did not exist.

This pretty much sums up postmodern academia, where a postdoc might be sent from campus, to campus, to campus, looking for things that do not exist, as the elders get a good laugh. All the postdoc can really hope is that someday they'll be allowed to fund others to seek out their left-handed smoke shifters, to keep the cash flowing.

The big difference is that the joke only lasted a couple hours in boy scouts. When you returned to the campsite after running a few miles, scouting all the neighboring campsites for the left-handed smokeshifter, you were let in on it, and then taken on a snipe hunt that same night:

http://en.wikipedia.org/wiki/Snipe_hunt

It was all good fun, but in academia we are talking about entire careers and hundreds of millions of taxpayer dollars, so all this snipe hunting kindof loses its humor after a day or two.

I understand that you are probably receiving orders from the centralized Ministry of Curiosity to not discuss MDT, as it is not proper to ask foundational questions without an offical permit. But I have heard that the times are a changin', as MDT has liberated us from the Block Universe while unfreezing time and progress in theoretical physics!

Best,

Dr. E (The Real McCoy)

What is true in this quoting of F. Dyson is that theoretical Science is dangerous. In my opinion, the LHC Experience is the next coming soon big Scandal in Science: nothing will be discovered and how can you justify to spend billions for nothing?

One can observe that the Scientists who are working on this experience are afraid by the scandal themselves because they try to avoid it already, explaining that if the 'Higgs Boson' does not exist, no matter, the experience would have been a good experience although!!

But what is wrong in Dyson's explanation is that there are two different reasonings. 'Quanta Physics' and Einstein's Theory are both based on the same Idea of Time, seen as an 'event' that one can measure. And obviously simultaneity, events, instants, speed, coincidence can only be measured AFTER and not BEFORE. If Time-Space is relative 'a posteriory', one need before a non-relative Space to measure the simultaneity.

I want just add this: Leon Lederman recently in a French-TV documentary was linking beauty and symmetry: this is a very special idea of 'beauty' coming from music; no human beautiful face or body is symmetric. The sphere is not symmetric too.

FLR,

Negative results are meaningful. Would you think that money spent on the Michelson-Morley experiment was wasted? Without that negative result, no one would give a second thought to special relativity.

Tom

In 'Special Relativity', Einstein is translating the discrete motion of a train (on a railway that looks like a scale) in a speed continuous ratio.

One can observe here that 'Time' is in the 'arrow' or 'vector' of speed, in other words that Time is the reference of the translation in algebraic 'ratio', which is always 'a posteriori' (See Zeno's cheap experience with a tortoise and a famous athlete.)

In this mood, Achilles cannot rejoin the tortoise and 'a posteriori' is becoming 'a priori' that is becoming 'a posteriori' at its turn on a binary rythm until the 'Absolute' or the 'Infinity' (Same principle in 'Quanta physics' based on statistics and probability theories).

So the paralogism, either the 'Special Relativity' paralogism -two speed vectors for one train-, or the paralogism of Michelson and Morley -limited/absolute speed of light- are possible in 'cognition' or in an 'a posteriory' Time-reference. The question is: does cognition comes from Matter or Matter from Algebra?

Because the Paralogism of Scientists that are driving the 'LHC experience' is obviously the same kind of paradox: splitting the particle in two come from the reflexion, especially the waves coming from trigonometry and 'surfacing'.

(To answer T. Ray I did not say negative results are not meaningful but that Scientists who do doubt of the positive result of their tree billion experience before it started is meaningful too.)

Just finished reading this essay a second time, and I love it. With few words, Dr. Kiefer is able to reduce the argument to distinct foundational principles (universality and superposition principle of quantum theory), and comes to very intriguing conclusions: The direction of time is defined by the direction of increasing (!) entanglement; and decoherence results in classical appearance of nature. This is quite surprising, to understand the quantum arrow of time this way (as compared to the more traditional irreversibility of observation). IMHO, achieving this simplicity of argument gives the conclusions and their interpretation a lot of weight. I'll be sure to read it again.

This is not 'intriguing'. The entanglement in non-observable phenomenons is the result of an 'ideology of matter'. Water and wave? No, just water.

There is no physical reason to change Space in Time or Time in Space but only a rational one. 'Algebraic geometry' is subjectivity and subjectivity allows every kind of illusion such as travelling in the Future, the Past, or standing on a Present dot.

Why do we think now that motion is real Dynamics? This is the good but awkward question.

Dear Claus,

Really nice presentation of the problems of time in Quantum Gravity, and ingenious solution for regaining it. Congratulations!

Best regards,

Cristi Stoica

"Flowing with a Frozen River",

http://fqxi.org/community/forum/topic/322

Is this a competition or a wedding-party?

Dear Klaus,

I can not see how is clock time related to the directional derivative you define in Eq- 4 and 5. Indeed, you can not forget that time is defined by means of macroscopic clocks, and clocks are not able to define any space derivative.

I believe it is your charge to demonstrate how clock (macroscopic) time is connected to (microscopic) directional derivative. Please clarify this point in order to restore the meaning of the paper.

John

Hi Claus,

You wrote: "Time emerges from the separation into two different subsystems: one subsystem (here: the gravitational part) defines the time with respect to which the other subsystem (here: the non-gravitational part) evolves."[footnote 2]

Footnote 2: "More precisely, some of the gravitational degrees of freedom can also remain quantum, while some of the non-gravitational variables can be macroscopic and enter the definition of time."

May I ask you to elaborate on the GR dictum -- 'matter tells spacetime how to curve and spacetime tells matter where to go' -- in the framework of your ideas, as clarified in footnote 2. Thank you very much in advance.

As to the "problem of time", check out a simple Gedankenexperiment in Wikipedia and its discussion here.

Regards,

Dimi

Dear Professor Kiefer,

While you very convincingly explained your problem with time, thank you, I am worried by your reference to Schroedinger. You gave Ann. Phys. VI 384, 489-527 (1926). Is this correct?

If I recall correctly, I found that Schroedinger wrote the famous equation in his 4th Mitteilung Quantisierung als Eigenwertproblem in Ann. Phys. (1926), not in vol. 384 but already in vol. 81 (4), 109-172.

In order to make sure we refer to the same text, I quote what he wrote below the equation I refer to: "... one may

consider the real part of psi the real wave function, if necessary."

Notice, according to 100 years of Planck's Quantum by Duck and Sudarshan, p. 176, Heisenberg wrote in Z. Phys. 33, 879 (1925): Re{A(n,n-alpha)exp(i omega(n,n-alpha)t}. The authors added a note: The erroneous 'Re' - real part - immediately vanished from Heisenberg's work.

Everybody knows, the also real squared magnitude psi psi* has been preferred instead of the real part. Can you tell me please who introduced this twist from real part to magnitude?

What about your effort to reestablish an arrow of time, do you consider it enough to have a directed time, and do you share Einstein's belief that there is no difference between past and future?

Sincerely,

Eckard Blumschein

Hi Claus,

I very much hope to hear from you. To explain my request posted on Dec. 3, 2008 @ 11:47 GMT, may I quote from your essay (p. 2): The Schrödinger equation (1) is, with respect to t, deterministic and time-reversal invariant. As was already emphasized by Wolfgang Pauli, the presence of both t and i are crucial for the probability interpretation of quantum mechanics, in particular for the conservation of probability in time."

But if we accept your belief that time emerges only as some "semiclassical time", and is (p. 6) "only an approximate concept", how would you address the Hilbert space problem? In your words: "What is the appropriate inner product that encodes the probability interpretation and that is conserved in time?" (C. Kiefer, arXiv:gr-qc/9906100v1, p. 15)

I wonder if you can solve the Hilbert space problem with some "semiclassical time", given your speculation that (Essay, p. 6): "... the Hilbert-space structure, too, is an approximate structure and that different mathematical structures are needed for full quantum gravity."

For if you can't solve the Hilbert space problem, your prerequisites from the Schrödinger equation (p. 2) may not be relevant at all, and you will have to start from scratch, by replacing the Hilbert-space structure with ... well, something else (perhaps "different mathematical structures", as you put it).

I believe Schrödinger provided a viable hint to this 'something else' in November 1950; check out 'Quantum Mechanics 101'.

Regards,

Dimi