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CATEGORY: The Nature of Time Essay Contest (2008) [back]
TOPIC: Does time exist in quantum gravity? by Claus Kiefer [refresh]
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Claus Kiefer wrote on Oct. 6, 2008 @ 11:38 GMT
Essay Abstract

Time is absolute in standard quantum theory and dynamical in general relativity. The combination of both theories into a theory of quantum gravity leads therefore to a `problem of time'. In my essay I shall investigate those consequences for the concept of time that may be drawn without a detailed knowledge of quantum gravity. The only assumptions are the experimentally supported universality of the linear structure of quantum theory and the recovery of general relativity in the classical limit. Among the consequences are the fundamental timelessness of quantum gravity, the approximate nature of a semiclassical time, and the correlation of entropy with the size of the Universe.

Author Bio

CLAUS KIEFER is a professor of theoretical physics at the University of Cologne, Germany. He has earned his PhD from Heidelberg University in 1988. He has held positions at the Universities of Heidelberg, Zurich, and Freiburg, and was an invited visitor to the Universities of Alberta, Bern, Cambridge, Montpellier, and others. His main interests are quantum gravity, cosmology, black holes, and the foundations of quantum theory. He has published several books including the monograph "Quantum Gravity" (second edition: Oxford 2007). He is a member of The Foundational Questions Institute since 2006.

Download Essay PDF File

Carl Brannen wrote on Oct. 7, 2008 @ 20:24 GMT
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.

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Bob Foster replied on Dec. 24, 2016 @ 14:30 GMT
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Dr. NN wrote on Oct. 8, 2008 @ 06:22 GMT
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!

socratus replied on Feb. 9, 2010 @ 05:50 GMT
What is the Source of the Universe ?


In the book “Evolution of Physics” Einstein and Infeld wrote:

“ We have the laws, but we are not aware what the body

of reference system they belong to, and all our physical

construction appears erected on sand ”.

They are right. Why?

Because :

The Universe ( as...

view entire post

socratus replied on Apr. 1, 2010 @ 08:52 GMT
Time and Quantum of Light. / My opinion./

Can Time Exist Without Matter?


According to Newton the answer is “ Yes”.


According to SRT and GRT the answer is “ No”.


Who is right? Who is wrong?

What is the resolution of this apparent paradox?


There are two kinds of...

view entire post

attachments: 450pxSocrates_Louvre.jpg

Dr.NN wrote on Oct. 9, 2008 @ 23:46 GMT
Sorry, the last word in my posting 'dilemma' that was wrongly spelled!

Ming wrote on Oct. 10, 2008 @ 00:57 GMT
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 = $$$$$ wrote on Oct. 11, 2008 @ 04:11 GMT
Quantum Gravity + Time = $$$$$

Do a search at NSF on "time quantum gravity.";jsessionid=7

u 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 = $$$$$

Matti Pitkänen wrote on Oct. 23, 2008 @ 10:18 GMT
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

F. Le Rouge wrote on Nov. 4, 2008 @ 14:27 GMT
- 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.

Dr. E (The Real McCoy) wrote on Nov. 6, 2008 @ 18:42 GMT
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...

view entire post

F. Le Rouge wrote on Nov. 8, 2008 @ 11:15 GMT
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.

T H Ray wrote on Nov. 12, 2008 @ 11:51 GMT

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.


F. Le Rouge wrote on Nov. 12, 2008 @ 17:04 GMT
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.)

Jens Koeplinger wrote on Nov. 25, 2008 @ 01:46 GMT
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.

F. Le Rouge wrote on Dec. 1, 2008 @ 09:59 GMT
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.

Cristi Stoica wrote on Dec. 1, 2008 @ 11:08 GMT
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”,

F. Le Rouge wrote on Dec. 2, 2008 @ 16:46 GMT
Is this a competition or a wedding-party?

J. Smith wrote on Dec. 2, 2008 @ 19:48 GMT
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.


Dimi Chakalov wrote on Dec. 3, 2008 @ 11:47 GMT
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.



Eckard Blumschein wrote on Dec. 9, 2008 @ 18:03 GMT
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?


Eckard Blumschein

Dimi Chakalov wrote on Dec. 11, 2008 @ 14:01 GMT
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'.



Peter Morgan wrote on Dec. 11, 2008 @ 15:19 GMT
Although I like your essay very much -- I think, particularly, that it is very clear and set at almost precisely the level requested -- I am reluctant to vote for it because I cannot see that it has any novelty. A novelty of clear presentation is perhaps worthwhile enough -- indeed sometimes more to be cherished than anything technical -- but is there something in your paper that has a technical novelty that you have not emphasized?

Like many established academics who have submitted essays, you have preferred not to reply to any comments. I would be grateful if you would reply briefly to this. I think your essay could have more fully described in what way it is novel. Academics who specialize in QG will of course know full well in what your essay is novel, but for someone who specializes in QFT it is not obvious.

F. Le Rouge wrote on Dec. 18, 2008 @ 10:19 GMT
Godfather or the Engineer's Physics French R. Descartes is 'forgetting Time' in Ballistic Science for at least two reasons:

-Force of a burden on a string is the same two days after than two days before;

-Because Descartes knows too that 'Speed idea' cannot be cutted from Metaphysics and he does not think it is a good idea to put Metaphysics in an essay about Statics.

Contrarily Einstein and Poincaré decided to put Time again (H. Bergson too in Biology fighting against Descartes' method more frankly than Einstein.)

Today fluctuations in Algebraic Geometry between 'block Time' or 'Flow Time' or 'Vector Time', between two dimensions or n-dimensions are coming from this.

Obviously Descartes' Empiricism is too 'dry' for Einstein, Poincaré and Bergson. Their illusion is to think that the trigonometric wave is more fresh than Descartes' arrow although it is just a concave arrow (or a boomerang).

'Block Time' is just an arrangement between the arrow and the flow.

Worm is in the apple from the beginning because Descartes does not understand what some Scientists before him knew (Euclid for instance), i.e. that Time is the Frame of the Algebraic Geometry. Either you forget the Time AND the algebraic Geometry but you cannot split them as he did (and Rovelli on this fq(x)i forum after him).

After Descartes his followers Helmholtz or Beltrami, Riemann are not even aware that there is a difference between Geometry and Algebraic Geometry and that the difference is that there is no Time in Geometry.

Most of Euclid's laws have nothing to do with measurement or geolocalization as Riemann is ignoring it.

And the fight of Bergson, Einstein and Poincaré against Descartes is useless because they share the same paradox, they are catched in the same reference.

The only collision that the LHC experience can involve is the collision between real Physics and algebraic language.

Claus Kiefer wrote on Dec. 23, 2008 @ 17:05 GMT
Response from the author

First of all, I would like to thank all persons who

have commented on my essay. In the following I shall briefly try

to respond on some of the questions and comments

in a collective way.

Since I have published in the past various papers on time in

quantum gravity, the question arose what is novel in my essay.

Firstly, the...

view entire post

amrit wrote on Dec. 24, 2008 @ 13:11 GMT
Dear DR. Klaus

for time tu understand Einstein and Buddha are needed.

Time exists in quantum gravity when we measure it.

Until time is not measured, time do not exist.

yours amrit

attachments: Time_Searching_of_Einstein_and_Buddha___Sorli__2009.doc

Dimi Chakalov wrote on Dec. 26, 2008 @ 17:01 GMT
Dear Claus,

You wrote (Dec. 23, 2008 @ 17:05 GMT) that you "want to advocate a novel perspective on the interpretation of the Wheeler-DeWitt equation and its timeless nature: being very conservative and imposing only two principles (universal validity of the Schr"odinger equation and the semiclassical correctness of Einstein's theory)..."

The first principle you decided to employ, the alleged "universal validity of the Schr"odinger equation", may be wrong, as I tried to argue since I read Ch. 10, 'Quantum gravity and the interpretation of quantum theory', in the first edition of your monograph "Quantum Gravity" (May 2004).

Please check out my essay 'Quantum Mechanics 101'; the link was in my posting from Dec. 11, 2008 @ 14:01 GMT above.

You also wrote (Dec. 23, 2008 @ 17:05 GMT): "In the quantum theory, on the other hand, spacetime has disappeared completely as a consequence of the uncertainty relations, ..."

I believe it is safe to say that, while quantum theory has been empirically established, there could be many *artifacts* from the "filter" we impose on the quantum realm with the 'spacetime of facts' of STR: please check out the KS Theorem in the essay on QM mentioned above.

If you disagree, please explain your arguments.

If you agree, please notice that the Hilbert space problem (C. Kiefer, Quantum geometrodynamics: whence, whither?", arXiv:0812.0295v1 [gr-qc]) may be solved along with the 'problem of time' en bloc , as it should be done.

Looking forward to hearing from you,


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Jacek Dabrowski wrote on Oct. 7, 2012 @ 18:22 GMT
[Sorry for triple post, something cuts my text into parts]


I well am a complete ignorant in this field (as a number-theory mathematician, not a physicist), but I have some 'philosophical' questions regarding this matter:

Assuming general relativity holds, we know that there is no 'time', just event sequence ordering (causality).

Assuming quantum mechanics holds, we know that there is no 'event' without the act of observation, through which a concrete state emerges from probability distribution.

So.. if we speak about 'time', we speak about event sequence ordering, only if we have some events, only if we perform some observation.

I am pretty sure it makes quite no sense in physics, but here is my idea:

* Maybe inexistence of time parameter in Wheeler–DeWitt equation is coherent with the above.. in that direct observation of gravitons is not possible.

I might be wrong in so many ways with this primary-school understanding, so please explain it to me:

* How can time be defined without observation?

* Isn't event sequence ordering (causality) derived from event observation?

* Isn't time an emergent phenomenon caused by observation?

* Can't lack of time mean inability to observe something?

* Would the assumption that gravity can be observed only indirectly change the principles of QFT/QM?

I apologize for my ignorance.

Elizabeth wrote on Oct. 7, 2012 @ 18:27 GMT
Russ,Jacek, time cannot occur without gravity and space.

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