This article has been updated many times: 120 well-known thinkers and scientists were asked the exciting "*2005 annual Edge question*"

The answer of Lenny Susskind was probably one of the most entertaining ones: Lenny's answer was a conversation with a stupid (or "slow", as he says) student of him who wanted Lenny to explain rigorously what probability is. The student wants clear statements: if something has a 50% probability, it will happen exactly in 500 cases out of 1000. Lenny tries to refine his viewpoint. Lenny knows that very unlikely things won't happen, but he can't prove it. Well, it's because it's not *exactly* true, is it?

The beliefs of many other people are even more bizarre: Carlo Rovelli is convinced that time does not exist, but he can't prove it. Similarly, Lee Smolin believes that quantum mechanics is not the final theory, but he can't prove it. I will discuss these two opinions below. Also, Philip Anderson believes that string theory is a "futile exercise" in physics, but he can't prove it.

**Global warming**

Stephen Schneider - the co-author of models of global cooling, nuclear winter, and global warming - is convinced that there exists global warming, but he can't prove it. Incidentally, 5200 years ago there was probably an abrupt climate change. According to the global warming theory, the major climate variations in the presence of humans are not natural (for example, effects of solar variations), but they're rather caused by the humans. Well, then it's not hard to deduce that Krishna together with the Egyptians who just discovered the first hieroglyphs in 3200 BC started to produce too many SUVs and power plants. This would normally lead to a destruction of the humankind, but fortunately the Minoan civilization established Greenpeace and saved the day.

Steve Giddings is more reasonable and says that the black holes conserve information, but he can't prove it. Anton Zeilinger says that the real lesson of quantum mechanics is to abandon the difference between reality and information, but he can't prove it. Lawrence Krauss believes that there are many universes. John Barrow adds that the universe must be infinite. Martin Rees believes that intelligent life has the power to spread throughout the galaxy. Paul Steinhardt believes that our universe is not coincidental. Richard Dawkins says that all "design" in the universe follows from the Darwinian selection, but he can't prove it.

**Brain and consciousness**

Roger Shank believes that people can't decide rationally about important things. Steve Pinker, on the other hand, believes that the brain contains circuits that are able to do much more than what has been useful for the humans so far. (Incidentally, I liked his lecture about the evolution theory behind religion.) Also, Christine Finn believes that the modern humans use their brains very efficiently. Alison Gopnik claims that the children have more consciousness than adults.

Rupert Shaldrake, the inventor of the **morphogenetic field**, claims that there are no fixed laws of nature - everything is just about the "*memory*" of the Universe. The things we believe are the natural laws are actually just "*habits*" that survived the natural selection. Unfortunately he does not say what are the physical *laws* that govern the natural selection of the *habits*, and therefore I predict that his theory is just a *habit* that will not survive the process of natural selection between the candidate *theories*. ;-)

And so on, and so on. You should look at it.

Neither of these beliefs is tremendously new, but in my opinion most of them are strange. I am an "atheist" concerning most of these belief systems.

If I were asked the religious question, I would probably answer that

- All continuous dimensionless parameters in fundamental physics may be calculated from a theory that does not need any dimensionless continuous parameters as input. The future scientists will view this theory of everything as refined string theory, but I can't prove it.

**Lee Smolin vs. quantum mechanics**

This also answers what I think about Lee Smolin's belief. Well, I believe that Lee is completely wrong, but I can't quite prove it. I should try anyway. Physics has undergone many revolutions in the 20th century - but the quantum revolution remains the most brutal one. It's just hard for most people - which, of course, includes the physicists in the most radical cases - to accept the big lessons of these important discoveries. But these 20th century insights just seem to be completely true and we will never "undo" them - but I can't prove it.

The Lorentz symmetry will remain as important as the rotational symmetry, for example, and any deep theory that deals with high velocities will have to explain why. There is no indication whatsoever that special relativity - as a constraint on physical laws in small enough regions of spacetime in which the space looks flat - is wrong. There is no indication of a violation of basic principles of quantum mechanics - by which I mean roughly the following:

- only the probabilities of various events may be calculated from the fundamental theory
- the probabilities must be calculated as the squared modulus of some "complex amplitudes", or as a sum of such terms (to allow for the density matrix)
- the complex amplitudes are matrix elements of some linear operators
- observables - such as the momentum - are given as linear operators on a Hilbert space
- the evolution operator is what determines the evolution, and it is another linear operator
- because the sum of all probabilities equals one, the evolution operators (or the S-matrix) must be unitary

I think that there is an overwhelming evidence that the theories based on these principles - quantum theories - are excellent in describing the real world. There exists a circumstantial evidence that no "deformation" of quantum theory may lead to a meaningful theory. It is possible that a particular physical theory only allows you to work with a subset of the concepts that appear in another quantum theory - for example, it only has the S-matrix or only the squared amplitudes i.e. the probabilities are directly expressed using density matrices. But in all these cases, the objects in the truncated theory must exactly satisfy the same rules that also follow from the quantum postulates above.

It seems to me that this picture may describe

- all ordinary experiments we've ever seen
- all mind-blogging experiments involving entanglement (David Goss has pointed out that these experiments used to be called "mind-boggling" in the pre-blog era, but you should not misunderstimate these experiments because of the typo haha)
- all quantum gravity experiments that we have not seen yet - string theory allows the black hole to be described within the postulates explained above

Because of these reasons, I think that insisting on the viewpoint that this basic quantum structure is inaccurate, approximate, incomplete is a kind of misconception. A result of prejudices from classical physics. And I don't think that the models and ideas proposed by various physicists today - e.g. Gerard 't Hooft or Lee Smolin - are better in any sense than the old failed attempts of Schrödinger, de Broglie, Einstein, Bohm, Bell, and others. It's still the same classical prejudice that drives this machinery. No pretty mathematics. No signs of an agreement with reality. Useless superconstruction trying to supersede quantum mechanics which is what really works. Aether.

Note that I tried to formulate the postulates in such a way that they should be acceptable by all physicists who work on actual physics as opposed to philosophy, regardless of their preferred interpretation of quantum mechanics. These "allowed" interpretations include:

- Feynman's neutral interpretation "shut up and calculate"
- the Copenhagen interpretation, regardless how you exactly answer the unphysical question "what is happening with the wavefunction before you measure and how should you interpret it"
- the Copenhagen done right, i.e. the Consistent Histories - which is the interpretation I choose
- the Many-Worlds-Interpretation

Of course, the forbidden interpretations are those that actually want to modify physics:

- de Broglie-Bohm's interpretation that adds new degrees of freedom (classical positions of particles) and tries to argue that some observables (such as position) are more fundamental than others (such as momentum). This interpretation has too many other problems and I don't have enough space to list them
- Penrose's interpretation of the wavefunction collapse in the brain induced by quantum gravity ;-). I am not sure whether it is constructive to comment on this idea
- Other attempts to imagine that the wavefunction is real and there are additional "nonlinear" effects that sometime induce a wavefunction collapse. I think it's extremely easy to prove that all these pictures are incompatible with physics we know, but I can't prove it right now
- Transactional representation in which one travels back and forth in time
- Wolfram's interpretation of quantum mechanics that says that we should forget not only quantum mechanics, but also other physics that we've learned since the 16th century - for example all physics that deals with continuous numbers. Instead, we should return to some trivial combinatorial games with stones - the cellular automata (CA) - and
*believe*that these games have something to do with physics because Wolfram's book shows that they generate pictures reminiscent of a piece of tiger's skin, and therefore they undoubtedly must include the whole biology and physics

Lee Smolin repeats many times that quantum mechanics "makes no sense" to him regardless of the interpretation one chooses, and he has tried many. I apologize, but I see no other way to interpret these sentences than to say that Lee Smolin does not quite understand quantum mechanics and with this limited understanding he probably thinks that it's inconsistent. I am deeply convinced that it is *not* a religious question whether quantum mechanics is an internally consistent theory that moreover agrees with reality. It is a completely well-defined, scientific question and the answer is, of course, "it is", and Lee Smolin must be doing something seriously wrong if his answer is different.

**Does time exist?**

Carlo Rovelli believes that time does not exist. That's a kind of vague statement. One would have to define what "time" means in the most general theory, and what does it mean for this time to exist. I *might* agree if he said that time is not an exact concept after all. There is a simple yet powerful argument composed of two parts supporting the viewpoint that time is not an exact concept:

- the progress in string theory shows that space is emergent, approximate concept - it is just the manifestation of some particular light modes in your theory, but there can be many other light and heavier modes. T-duality is able, in fact, to exchange the translations in space with a phase redefinition of fields depending on their winding number. Whether something is space or not is a matter of convention, especially if this space is small
- special relativity that is still exactly preserved by local physics - at least if the space is large - says that "whatever holds for space, holds for time as well". This means that if space is emergent and approximate, time should be emergent and approximate, too

This is a nice exercise in logic, but it may be a futile one. Unlike Carlo Rovelli, I think that all theories that will ever be accepted to have something to do with physics will have to show that time emerges from them - because we simply know that time exists. Perhaps, time won't be an exact observable - and there won't probably be any general exact Hamiltonians in quantum gravity. On the other hand, a Hamiltonian could always exist with an appropriate gauge-fixing. But even if you work with the S-matrix that does not allow you to study the evolution "moment by moment", you can still exactly distinguish the future from the past. Time will always have to "reappear" in one way or another. Physics only emerges if we have time, at least some time. There is no physics without time.

When Rovelli tries to clarify his point of view in detail, I think that this clarification makes his proposal even more obsolete. He literally compares spacetime to the "surface of the water". The latter is eventually made of atoms, and so forth. Jesus Christ, this is not just analogous - it is exactly the 19th century idea of luminiferous aether. Everything that can carry waves must be made of "atoms", they thought. Einstein with his special relativity had to throw away this garbage of luminiferous aether - and it's exactly what makes Einstein so special. I believe that in the 22nd century, only a few very specialized historians of science will remember these specific "discrete" attempts to revolutionize physics, and they will consider these physicists as late 20th century followers of the wrong 19th century ideas of aether - who had nothing new to offer. But I can't prove it.

**Smolin, Rovelli, and relationism**

Both Rovelli as well as Smolin also talk about "relations" - everything must be given in terms of "relations". Such ambitious philosophical statements escape from my left ear as soon as they enter the right ear. I don't understand how these statements can mean anything new. One must have a Hilbert space (or whatever replaces it in your framework) and some degrees of freedom, and the physical Hilbert space may be constructed from a larger one, imposing some gauge symmetries. Maybe, instead, we will have some "bootstrap" mechanism to define the degrees of freedom - but Rovelli and Smolin don't seem to be talking about this approach. Until you say which gauge symmetries you want to include and which global symmetries should survive, you have not said anything. Some guesses can lead you somewhere, other guesses are useless. But it's not a scientific approach to convert one conceivable symmetry into a "religion".

Rovelli and Smolin obviously talk about the independence of physical laws on some large set of operations - a symmetry. But which symmetry it exactly is?

They seem to talk both about some ambitious "large" symmetry between all possible objects, but at the same moment it also seems that they are speaking about something as trivial and discredited as Mach's principle. Those who want to return us before general relativity to the age of Mach's principle in which "space" (or the metric tensor) did not exist without the presence of "objects", also seem to misunderstand the steps that Einstein had to do before 1916 in order to convert some vague philosophical ideas to a physical theory. Some of these steps have definitely invalidated many details of Mach's principle. These insights cannot be undone either: the metric tensor, in one approximation or another, will always exist as a legitimate physical entity even in vacuum, although its short-distance structure can become more complicated. Do they really want to revive Mach's principle? I think that the 20th century has brought us no new evidence - neither experimental nor theoretical - that would indicate that physics should return to the 19th century when Mach was promoting a similar idea with a similar lack of evidence.

**Cumrun and Edward on foundations of QM**

There were some comments about well-known physicists who believe that we still don't understand the real logic behind the foundations of quantum mechanics. I guess that the person talked about the Chapter 15 of *The Elegant Universe*, right? I don't actually think that Edward Witten and Cumrun Vafa would seriously question that the probabilities will be calculated as the squared complex amplitudes - which are matrix elements of linear operators. In Cumrun's recent attempts to re-explain Bell's inequalities using a "classically" looking framework that allows for negative probabilities, he still works with the partition sum of the black holes that equals Z_{top}^2 where Z_{top} is the topological string partition sum.

From a calculational point of view, even these radical approaches seem to satisfy the principles above. My feeling is that neither Cumrun nor Edward want to deform the structure of quantum mechanics to something inequivalent. My impression is that they want something that I also want - to find an equivalent way of looking at quantum mechanics that will also include the emergence of all other conceivable classical limits in different contexts. You know, the quantum postulates are not yet a theory of everything. They're just a framework and you must add a definition of your Hilbert space and your Hamiltonian or the S-matrix. String theory requires all postulates of quantum mechanics to be taken seriously, but the reverse does not hold: you cannot derive string theory from the postulates. It would be, of course, nicer to find a generalized form of the quantum postulates that would actually imply the whole string theory - or at least that would imply some unification of quantum mechanics and geometry.

**Freeman Dyson and math**

Freeman Dyson interpreted the question "what do you believe but can't prove" as a real mathematician, and he wanted to offer something even more interesting than Kurt Gödel. Kurt Gödel was able to construct a statement that is true, but cannot be proved using the pre-determined axiomatic system as long as this system contains the axioms about integers. Gödel's unprovable statement is essentially a convoluted, encoded version of the statement

- I am a happy statement that cannot be proved within the system you talk about.

Is this statement true, or false? Obviously, if it were false, then its opposite would have to hold:

- The statement can be proved within the system.

But if it were so and if the statement were provable, then it would have to be true - only true statements can be proved in a consistent system - and therefore you get a contradiction with the assumption that the statement was false. By assuming the consistency of the system, we proved that the statement can't be false. So it must be true. It's true and it says that it's unprovable within the system. Well, so it means that it is true and it is not provable within the original axiomatic system. Of course, it is however provable in a system that transcends the original axiomatic system - any system. What is this stronger system that transcends any older system? Well, it's called *Luboš Motl's reference frame* - because we just proved that the statement was correct. Thanks to my fellow, German Czech (these words are combined just like in "African American") Kurt Gödel for helping me with the technical part. ;-)

Back to Dyson. He wants to be better than Gödel. Dyson believes that Gödel's particular unprovable statement is not comprehensible to normal people. Well, maybe it is, but it is certainly not a useful statement - rather a sophisticated version of the liar's paradox.

Dyson's example is simple indeed:

- Write down all powers of two - 1,2,4,8,16, ... 1024 ... and write them backwards in the decimal system - 1,2,4,8,61, ... 4201 ... You will never find a power of five (5,25,125,625...) among these numbers.

Of course, there is a trivial possible error in Dyson's statement: you must eliminate "1" from the powers of two because it is also a power of five. ;-) But I don't want to be picky. Dyson argues that his statement should be true because the probability that a large random number - such as a large inverted power of two - decreases rapidly with the exponent. Because the few first examples are not powers of five, none of them will be a power of five assuming that the reverted numbers are kind of random.

For a mathematician, Dyson suddenly adds a very non-mathematically looking step:

- you see that I used some probabilistic argument which is not rigorous, and therefore there is no proof

Freeman Dyson apparently neglected one fact - namely that he is not the only mathematician in the world. If Dyson can't prove it, it does *not* imply that no one can prove it! If there is no proof based on the divisibility by 3,7, and 11, it does not mean that there is no proof whatsoever: but I can't prove it right now. Concerning Dyson's example, my belief has always been just the opposite:

- any well-defined and interesting statement in mathematics that deals with the "real" finite, countable objects - for example the objects that you can write on the paper (such as Dyson's integers) - can either be proved, or its negation can be proved, using "legitimate" mathematical logic, not necessarily constrained to some possibly insufficient axiomatic system

This would also mean that someone can either find a counterexample that is a power of two that reads like a power of five backwards, or someone can find a rigorous proof that such a thing can't happen. I believe that imagining that the human intelect may be insufficient to deal with some well-defined questions is just a defeatist prejudice without any justification, but I can't prove it. ;-) As far as I know, it's not possible to show that my religion about provability is incorrect.

I also believe, much like CIP, that Dyson's family got a little bit too much room in this happening, but I can't prove it.

## snail feedback (56) :

And Phillip Anderson thinks string theory is a crock - but can't prove it.

I discuss a few in Religious Science

Good post Lumo - but do you any idea why every living human named Dyson, or at least Freeman and all his kids - are represented?

Hey Lubos - what is your opinion on Smolin's belief that quantum mechanics is wrong (he says that it doesn't make 'sense'), and needs to be replaced by a hidden variables theory? 't Hooft has also worked on such things: hep-th/0104219. He states that you may be able to get around the Bell inequalities if certain assumptions (say the freedom of choice of the measurement direction in Stern-Gerlach type experiments) don't hold at the Planck scale. 't Hooft came by Chapel Hill a while ago and gave a talk on this stuff, he suggested that the fundamental laws could be like Wolfram's discrete cellular automata at the Planck scale, and he hinted at connections with black hole entropy.

It seems to me that at least some of the motivation for these speculative ideas is the desire for a deterministic theory of nature. But there already is such a theory - pure quantum mechanics where there is no collapse of the wave function, i.e. Everett's Many World's Interpretation (MWI), which follows very quickly from the fact that our brains are composed of atoms that evolve in time according to the unitary time evolution operator. Presumably they reject the MWI since it disagrees with their intuitive belief that there is only one 'world' - one history, one version of themselves...

But in fact, I think the MWI can be intuitive. If you make the perfectly reasonable assumption that mathematics describes the universe so well because indeed the universe actually is a mathematical structure(*), then we in turn are nothing more than particular permutations of some 10^29 basic mathematical objects. Quantum mechanics - which is the particular type of mathematical structure we find ourselves to be embedded in - then allows us to deduce that many other permutations of atoms similar to ourselves are being constantly split off from us into separate branches of the global wavefunction (say as we walk around playing with a geiger counter, being split by cosmic rays and radioactive decays in the ground...). While quantum mechanics describes all these other permutations and histories and their respective amplitudes according to precise rules, it is not so surprising, in general, that they exist: that is, if we also make the natural assumption that all mathematical structures exist (and you agree with this right?).

Thoughts on Smolin & 't Hooft's hidden variables and/or MWI as an alternative?

* actually you can argue that anything is a mathematical structure, although usually I'd change terminology and state that anything that can exist is just a type of information (saving the term 'mathematical structures' for information that can be highly compressed - as our universe is, and most random strings of integers are not). This is somewhat similar to Anton's suggestions.

To previous poster on The Future of Quantum Mechanics Your link reminded me of this as well on Gerard T Hooft views.

Hey Lumo, here's a puzzle for you:

In which book were Ed Witten and Cumrun Vafa BOTH cited as being of the opinion that we don't really understand the foundations of quantum mechanics yet?

You get one guess.

I tend to believe that an anthropic principled mensch, who achieves a successfully circular and most accurately uncertain rational thinking possible about the mathematical infinity of What Is in_ evolving patterns of _formation, risks immediate mental collapse from self-exhaustion.

It seems that LuMo might soon provide us with an illuminating proof of whether or not this belief is correct. %}

Best wishes to Lubos and you all!

P

Lee Smolin is just bizarre! I still can't get over the fact that he got his PhD with the great Profs. Sidney Coleman and Stanley Deser. (I guess I don't have to explain here how wonderful both of them are!)

The best way of silencing crackpots like Smolin is to make progress in string theory and just prove them wrong. I just wish he didn't besmear the reputation of his advisors by making embarassing statements. Surely, none of the weird anti-QM statements Smolin makes today stem from either Coleman or Deser.

Best, Michael

Lubos said he believes:

"All CONTINUOUS dimensionless parameters in fundamental physics may be calculated from a theory that does not need any dimensionless continuous parameters as input. The future scientists will view this theory of everything as refined string theory, but I can't prove it."

Could you elaborate on what do you mean "CONTINUOUS" dimentionless parameters? You seem to consistently have a difficult time understanding what continuity really means, both here and in the mistake you made in your 4*ln(3) paper.

You mean dimentionless numbers like PI, e, alpha, The dimentions of the real world 4, the count of dimentions in popular string theories, 11, etc., all are varying, and varying in a continuous fashion? Vary against what? Against position or against time? Are you saying the value of PI would change continuously over time?

I really do not think you know what you are talking about when you say "continuous dimentionless numbers"! Dimentionless numbers, being what they are for good reasons, are unique and do not change. So there is no continuity or discreteness in those numbers.

What you also fail to understand, is any computation process takes inputs to produce outputs. To calculate PI you probably don't need to punch an input on the keyboard, but your math reasoning of how PI should be obtained from certain Taylor expansion would be used as inputs. To obtain the fine structure constant, you would also need an input paremeter. It is impossible to obtain alpha from pure math reasoning alone, the way you obtain PI. The string theory takes no input at all so far, so all can speculate at this stage, is to speculate there are 10^122 different possible "landscapes" depending on the input, but you know none of them.

Again you seem to have a difficult time understanding the concept of continuity. The mistake you made in your 4*ln(3) paper, is you implied continuity of spacetime, by writting down differential equations which take derivatives against position and time, at the Planck Scale where continuous position and time simply no longer exist. That is a fatal mistake rendering the rest of you paper total rubbish.

Have you nothing to say about it or at least try to defend your self? Or you feel so defeated that the only response you could have is to simply delete this message of mine, without being able to say a word?

Quantoken

Dear Quantoken with Baez's crackpot index exceeding 1000,

the word "dimension" is spelled without any "t". Continuous parameters are those that take values in reals. Dimensionless are those that can be written down without any units. And parameters of Nature are those that are found in the real Universe, i.e. Nature.

Be sure that I am explaining it to you only because other readers definitely know what a dimensionless continuous parameter of Nature is. Pi is not a parameter of Nature - Pi is a mathematical (not a physical) constant. An example of a parameter of Nature is the fine-structure constant alpha=1/137.03604... that determines the strength of the electromagnetic interaction or the proton/electron mass ratio 1836.1515... The number 4, the spacetime dimension, is not a continuous parameter of Nature either because it is discrete, not continuous.

Your comments that every calculation needs continuous inputs to produce outputs just shows your stupidity, and I don't think it's constructive to waste time with such a statement. The same applies to the collapse of your brain concerning the number 4.log(3).

Best

Lubos

Travis said:

"'t Hooft came by Chapel Hill a while ago and gave a talk on this stuff, he suggested that the fundamental laws could be like Wolfram's discrete cellular automata at the Planck scale, and he hinted at connections with black hole entropy."

People like 't Hooft and Smolin etc. are indeed searching in the correct general direction, but they are not quite getting closer yet, since they missed a few key points. I have reached much further than them by realizing that few key points, and I come very close to the ultimate answer that I see it already. I just don't have the right math tool to grab it in hand.

It does have something to do with blackhole entropy, and stuff like Bekenstein Bound. But they all get it wrong by assuming it's porportional to the surface area of the 3-D space, and totally forget there is also a time dimention. The entropy should be proportional to the surface area of the 4-D spacetime, not the 3-D space-only. Just think about Lorentz invariant, stupid! Also, the discreteness does not happen at Planck Scale, it already happen at a scale much higher, the elementary particle scale.

Quantoken

Justifiably Anonymous Michael said -

The best way of silencing crackpots like Smolin is to make progress in string theory and just prove them wrong. I just wish he didn't besmear the reputation of his advisors by making embarassing statements. Surely, none of the weird anti-QM statements Smolin makes today stem from either Coleman or Deser...Oh goody, more of the physics of thought control. Where do you guys come from anyway? Why has the outcry of the Boetians become so shrill lately? I hear this stuff and wonder if you learned nothing from Feynman.

More substantively, last time I heard, consistent histories still had some serious problems of its own. Like the inability to predict the future or deduce the past. Any breakthroughs on that point that I haven't heard about?

Come on, CIP, what you say is completely ridiculous.

First of all, Feynman would be exploding by anger if he saw all these people claiming that quantum mechanics does not make sense to them etc. - he was very sensitive about this kind of doing "physics". He kindly, but intensely explained Einstein's inability to understand quantum mechanics. Einstein also thought that there was something wrong with QM - Feynman's interpretation of this attitude of Einstein is demonstrated in the last volume of Feynman's lectures where he explains the EPR effect.

Second, the whole point of a the Consistent Histories interpretation of quantum mechanics is to predict the (probabilities of different outcomes in the) future. What you say is simply a nonsense. The prescription of Consistent Histories to achieve this goal is completely straightforward. Just see a page on wikipedia about it. It's kind of trivial and it's obvious that it works. All these valid interpretations of course imply the same practical conclusions about any doable experiment, and they would not really surprise Bohr in this aspect.

I totally agree with Michael that the anti-QM statements indicate a completely forgotten wisdom and power to calculate that Coleman and Deser represented.

And yes, I think it's wrong to use quantum mechanics to "predict" the past. What you can do is to start with some reasonable initial conditions - like the moment when Earth was formed - and evolve this into the "future" relatively to that moment, and then argue about the past.

But evolving the present state to the past is something that will only give you meaningful results for dynamics that is inherently time-symmetric, like the motion of planets. Every time you generate entropy, it becomes impossible to deduce anything about the past. If you mix blue and red colors, you get a purple mixture, but you won't be able to deduce when the mixing started, for example.

If you just evolved a generic state to the past, you would obtain another generic state - yet, we know that the entropy in the past was probably smaller. There's just no way to get this counting right. The only way to deduce something reasonably about the past is to figure out what initial conditions in the past look reasonable and which of them may have evolved into the known present.

I've erased a text of "Quantoken" - who was complaining how science discriminates against the crackpots like him, and listing some irrelevant precise data values of some constants plus attacks against me - because he is a obnoxious type of insect and I don't want the quality of the discussions here to deteriorate to his level. You're not welcome here, Quantoken. Thank you for your understanding.

Re Rovelli and time:

Actually, it is possible to prove rigorously that time does not exist, even in Newtownian mechanics. Consider a nonrelativistic particle of mass m at a position x and at time t. The action is:

S = \int ds 1/2m (dx/ds)^2/(dt/ds)

This action is invariant over reparameterizations of s, therefore the Hamiltonian vanishes on the constraint surface: H=0. Therefore there is no dynamics and time does not exist. Furthermore, neither x nor t commutes with the Hamiltonian:

[H,x] , [H,t] \neq 0

since they are not invariant under reparameterizations of s. Therefore neither the particle's position nor its time are gauge invariant observables. Niether time nor space exist, and there is no physics to be described. A trivial extension of this idea holds for General relativity and quantum gravity since they are also diffeomorphism invariant systems; therefore there is no space, no time, and no physics at all in the field of physics. Rovelli may be right after all.

-Ted

Hi Ted, excellent example.

Do you agree that I can gauge-fix the s-reparameterization symmetry of your action by the "s=t" gauge and get a completely equivalent description that obviously HAS time? And if you agree that I can do it, do you agree that my description is more physical? Do you agree that because there is apparently a nice way to formulate the same physics that has a time, then morally even your theory HAS time and your formulation of the theory using "s" was just a sleight-of-hand to hide the time?

What I say mostly applies to GR, too.

Lubos,

I was being a little bit tongue-in-cheek... As you say, gauge fixing is really the answer to this conundrum. In fixing a gauge all first class constraints are eliminated and, virtually by definition, the resulting formalism only describes gauge invariant physical degrees of freedom. It seems that this type of confusion infects a lot of the philosophy of LQG people, resulting in their problems with time, quantum mechanics, and "relationalist" ideas.

-Ted

Re: Consistent Histories. I was talking about the (to me) very bothersome Dowker and Kent results, apparently realized also by Hartle and Gell-Mann, that an arbitrarily large number of utterly non-classical histories are just as consistent with the familiar world as the classical history we imagine. If our theory doesn't tell us that the classical history of our world is any more likely than the possibility that all our thoughts, memories, and artifacts are chance illusions created by a completely accidental non-classical concatenation of events, how can we deduce anything about the past? The same reasoning appears to show that an arbitrarily non-classical future (in which, say, Susskind gets a google-plex of heads in a row is just as probable as a more classical one.

Since my perception is derived originally from one of your favorite villains, Lee Smolin, I would be interested in your critique.

About Feynman: I had in mind a couple of Feynman ideas and expressions - first his exhortation to physicists not to always follow the beaten path in physics. I was also thinking of his statement that "I think I can safely say that no one understands quantum mechanics."

CIP!

Feynman's quote about QM is an expression that QM is much more mind-boggling and revolutionary than general relativity (which was in the first part of this quote). I completely agree with this semi-joke, and he certainly did not intend to say that the predictions of QM didn't make sense. On the contrary, Feynman always emphasized that all these questions - and complaints - about the interpretation just don't belong to science but rather philosophy and the real men don't study them. This is where the Feynman dictum "shut up and calculate" comes from. It is directed against these interpretational philosophers.

Feynman would also disagree with your statement that quantum mechanics is the beaten path while the crying for a "classical" description is not. It's the other way around. Classical physics has been developed for 3 centuries, and it's a path beaten to death. Quantum mechanics is the original, sexy, shocking path, and it's the only path that is compatible with the quantum experiments. Your ad hominem argument works in the opposite direction than what you wanted, and even if it worked the right way, it certainly can't be used as an argument in science.

Googolplex is spelled like this, not with the company in the name - the company name is just a pun. There is nothing non-classical about a googoplex of heads in a row. More about your particular paper on consistent histories in the next comment.

Dowker and Kent don't show anything that I would consider a problem. Moreover, I think that you also misunderstood their argument.

Also, I think that you are mistaken if you think that Gell-Mann and Hartle share the concerns of Dowker and Kent.

See e.g.

http://arxiv.org/abs/quant-ph/0401108which says that "Some people feel uneasy about approximate medium decoherence" and where Hartle shows that you can also count the medium-decohering histories in such a way that all decoherence that you count is accurate.

I can't answer your particular concerns because I think that you have even misunderstood what the word "consistent" means in the term "consistent histories" - i.e. you misunderstood the very definition of the CH interpretation. It is not "consistent with the real world" or what exactly you write. "Consistency" of the histories is a particular mathematical constraint - kind of orthogonality of the states that you get by acting with the projectors describing the histories.

There cannot be anything wrong about it, and be sure that this criterion is extremely constraining. You won't be able to find non-classical histories that decohere, and you certainly have not found an example - the history with the googolplex is completely classical and of course that it is an OK history to include into a set of consistent histories. Every rational person would include this history into the set - it's just a very unlikely classical history, but a completely classical one that decoheres from others. I just think that you're confused, and you did not even reproduce the concerns of Dowker and Kent faithfully.

Another reason QM can be thought of as nonintuitive is that (for some reason) there are quite many postulates compared to some other general physical theories. (Thermodynamics, statistical physics, classical mechanics, et cetera.)

lumo makes a great job of presenting them in a coherent form which should help the postulate impaired. "Quantum Mechanics" by Powell and Crasemann is an example of the bungled mess one may otherwise meet.

To travis garret: the latter part of your posting posting, about MWI, doesn't make much sense to me. And the part about structure and information seems plain wrong - nonrandom strings are not compressed, compressed strings look random.

Hello guys!

I barely remember having looked at that paper by Dowker and Kent, and as far as I know, the approximate decoherent - and approximately consistent histories - is the only complaint they really had. Very unrelated to what you were saying, CIP.

I have personally no problem whatsoever with approximate decoherence. In some sense, the decoherence functional allows you to interpret the probability as a matrix on the space of your chosen alternatives of history. The set selection criterion of the CH interpretation amounts to the diagonalization of the decoherence functional, roughly speaking.

The probabilities of the alternatives are the eigenvalues. In this sense, probability itself behaves as a "quantum operator", and it is obvious that that its values only become exact once you approach the classical limit - which is guaranteed for big objects in which you only study some observables etc.

What I want to say is that a single Hydrogen atom is never "quite sure" about its own probabilities. We can only assign the probabilities to "classical" outcomes if the outcomes are really classical. For finite systems, they're never exactly classical and the decoherence is never perfect for finite systems and finite time intervals. "Small" objects will never be able to measure themselves. On the other hand, this "problem" does not occur for the large objects where the classical limit becomes usable.

There's no problem with working with approximately decoherent histories - i.e. set of histories where the "addition rules" are slightly violated. These violations describe how exactly we're able to define the answers, and they go abruptly to zero with the increasing size of the system. This "error" is equivalent to the errors in predicting the probabilities - the eigenvalues - and it can simply be neglected if it is some weird plex-exponential number like exp(-10^23). You can't never measure the probabilities this exactly if you're a finite object.

Some people just want to be more exact about physical predictions than physics actually allows. This is much like the uncertainty principle. In the uncertainty principle, the error of X times the error of P is never smaller than the Planck constant (over 4.pi). In the decoherence, the errors in predicting the probabilities of classical outcomes - and the violations of the consistency of the histories - only go to zero only when the histories decohere completely - for big systems measured over sufficient times.

Neither of these topics is an issue that would cripple our ability to predict a doable experiment, I think.

Sure, but then there is a fundamental inconsistency in the global theory, which is only slightly less bad than violating experiment =)

AFAIK, virtually everyone who works in quantum measurement theory, agrees that there are still conceptual problems and inescapable paradoxes in QM. Decoherence is a wonderful theory, in the sense that it gets rid of the rather anthropomorphic 'human observer' nonsense. Good! Progress! It should not be regarded as the last word though, since it still fundamentally has the same problems as other parts of QM. Like the fuzzy ill understood transition from classical to quantum.

Since you work in Quantum gravity, you should know much better than me that the whole measurement problem in curved spacetime just becomes a tremendous conceptual mess. Thats why you guys work with physics at infinity (SMatrix and so on), so you can get rid of the annoying problems of time evolution. Thats not entirely satisfactory though, which is why a lot of non crackpot physicists still believe there is something deeper in the endgame.

Yes, I agree that the interpretation of quantum mechanics in the quantum gravity context of fluctuating geometry (and causal structure) is much more subtle, and the S-matrix - which only consists in some simple backgrounds and cosmologies - is the only observable we really understand. Predicting the odds of histories that take a finite time requires some sort of gauge fixing - or measuring the space and time relatively to some other observables.

Godel's theorem is about countable objects, so the "finite, countable" in Motl's conjecture is presumably really "finite" only.

http://icl.pku.edu.cn/yujs/MathWorld/math/r/r286.htm

hey everybody, happy new year of physics btw :)

Just a simple question, lubos said:

"Do you agree that I can gauge-fix the s-reparameterization symmetry of your action by the "s=t" gauge and get a completely equivalent description that obviously HAS time? "

To which I agree as far as a classical description of time is concerned. This gauge fixing process is rather arbitrary but compelling as far as some gauges are physically reasonables. (In addition using "x=s" as the 'time' has very interesting features and goes also into the core of the problem).

May I ask you lubos how do you expect to extend this idea into the quantum world?

In other words, how do you expect to treat time quantum mechanically if you previously fixed it to be a classical parameter? (the "s=x^0" condition holds strongly without change after quantization in the usual approach since it become a second class constraint. The Sch. representation thus follows as the WdW equation or the Heis. one for the X(s) operators.)

Relational quantum mechanics is an attempt to overcome this 'problem' (time isnt external and should also behave quantum mechanically) and I agree with Carlo and Lee an others that it is a very attractive one, not just philosophically but practically. It has been recently shown indeed that relational time might lead to observable effects and indeed render the BH information paradox unobservable: Phys.Rev.Lett.93:240401,2004

It would be very interesting to have also a consistent quantum description of time emerging from string theory as well, I just can't see it so far.

It is still not clear to me how the a theory which is apparently described in a fixed background, as string theory seems to be, could describe fluctuations in the geometry as well. I'm glad I'm not the only one who struggles with this, as Ed once answered to my question:

"....though string theory was discovered historically in

the context of a fixed spacetime background, it turns out that the string describes fluctuations in the geometry, though we don't understand very fully how this happens."

I certainly admire many of the theorist nowaday involved in this enterprise (I actually find Ed's honesty remarkable). However, I agree in part with Empty Kangaroo et al.,

http://insti.physics.sunysb.edu/~siegel/parodies/next.html

that string theory has become the everything of theory rather than the theory of evertything, yet to be proven. This is unhealthy for the field and discouraging for young phycisists trying to persue a different path.

(Incidentally, Lubos, QCD as you know was 'formally' born and proved 'right' as a theory for the strong interactions almost imidiately (like probably Frank would say) once asymptotic freedom was shown. Could you find such an equivalent landmark in the history of physics in string theory? ).

I am not against string theory as I am in favor of exploring new roads to understand nature, it would be very sad if we find tomorrow string theory is wrong and that's all we got to bet the 'money' on. I'd be very happy nonetheless if in the contrary it is proved right, at least it would be testable.

best regards,

R

Lubos - Here is a fragment of the Smolin interpretation of Dowker and Kent: "Dowker and Kent showed that there had to be an infinite number of other worlds ... an infinite number of consistent worlds that have been classical up to this point but will not be naything like our world in five minutes' time. Even more disturbing, there were worlds that were classical now that were arbitrarily mixed up superpositions of classical in the past." He adds that Dowker concluded this invalidates deductions from the existence now of fossils "that dinosaurs roamed the planet a hundred million years ago."

He also adds that Hartle later told him that he and Gell-Mann "were fully aware that their proposal imposed on reality a radical context dependence: one cannot talk meanifully about the existence of any object or the truth of any statement without completely specifying the the questions that are to be asked. It's almost as if the questions bring reality into being."

In all this he's talking about a talk Dowker gave (based on the paper) and private conversations with Hartle, so I have no idea how reliable a reporter he is. Anyway, it's enough to make me prefer to shut up and calculate, or would be if I knew how to calculate anything very interesting :-)

I don't understand or endorse anybodies speculations about something "beyond quantum mechanics," but to quote Feynman on quantum one more time: "I cannot define the real problem, therefore I'm not sure there is a real problem, but I'm not sure there's no real problem."

I'd like to understand all this better if I had the time, that is, if time actually existed. Anyway, to digress further, it always seems to me that the real problem with time in physics is recognition about what is special about this "now" that is always rushing though spacetime at the speed of light (as Brian Greene puts it).

Cheers,

CIP

As one German Czech* to another, Lubos, I think your version of Godel's proposition needs some revision. You say

I am a happy statement that cannot be proved within the system you talk about...But I think a fairer rendering would be: I am a happy arithmetic statement about a real, finite, integer number that cannot be proved true from the axioms of arithmetic.

*Actually, I am only 1/16 Czech and about 3/16 German.

Cheers,

Pig

Dowker and Kent again: If you check out p. 79-80 Of the D&K paper (PDF version) I cited above, I think you will find concerns expressed about deduceability and predictability equivalent to those Smolin attributed to Dowker in her talk.

CIP... First of all, what Smolin says about Dowker and Kent may be described by the same words as your comments about Dowker and Kent; well, it's probably not an accident because you just copied and pasted. It does not make much sense.

Second of all, Dowker and Kent may have written a review, but they certainly did not start to think in the CH framework. On the pages 79-81, they propose a lot of conjectures that are in direct contradiction with the CH formalism. Of course that they can't find any evidence for their claims because their claims are wrong.

For example, they say that one needs to construct a special theory of consciousness to make the picture complete. This is rubbish. CH was exactly designed to solve this biggest problem - CH decide what is a "good history" and what is a "bad history" purely in terms of the actual dynamics - roughly speaking, a history emerges as a legitimate description once the objects are large and interacting enough. It is kind of always OK to assume that the Moon's center of mass is sharpy in one of the regions defined plus minus a micrometer, and use it as an extra splitting to make the histories finer. One can prove it.

Also, Gell-Mann and Hartle showed how can you show that quasiclassical physics emerges in the right limit, and the complaints of Dowker and Kent are too vague. Incidentally, such an isolation of a quasiclassical limit in a given theory is the closest replacement for a "unique" set selection mechanism, and whoever looks for an even more unique one, is misled.

Next, Dowker and Kent seem to call for a unique set of fine histories, once again. But that's a basic misunderstanding of the structure. CH are not meant to provide one with a unique fine-graining. There is no unique fine-graining and only Bohm-like people who have not gotten what quantum mechanics is may continue to look for "unique fine-graining". In real quantum mechanics, one can possibly define different sets of histories, and as long as they're consistent or approximately consistent up to the errors one can tollerate, these histories are equally fine. One may formulate one set of questions about the future history, and if the set is consistent, QM+CH answers it. One can do it with other consistent set, too.

This has nothing to do with personal consciousness or solipsism. Even objectively, taking all other people and computers into account, we are able to define various slightly differing sets of consistent histories.

If this conclusions violates someone's religion, it's his or her problem, but definite not Gell-Mann, Hartle, or Omnes' problem.

Also, there can't be any unique statements about the past. Many macrophenomena are "irreversible" - entropy increases. Consequently, there is no reliable way to reverse them "deterministically". This distinction between the past and the future is very important in a correct interpretation of QM, too - simply because decoherence is a phenomenon very analogous to friction and dissipation. And it's reality.

If you ask the question whether dinosaurs were around, and you construct a set of consistent histories - some of them with dinosaurs, some of them without dinosaurs - be sure that QM+CH will unambiguously answer that the dinosaurs were most likely around. It's the very same reasoning that we would use otherwise. If Dowker believes that there will be another answer, then he probably believes that fossils and science can't be trusted. But it's his belief, not mine.

On the other hand, we can possibly construct consistent histories that DON'T talk about dinosaurs et al. - very different sets of histories (I don't know exactly how to do it). And conceivably, they can be consistent. But the resulting probabilities can't be interpreted as "dinosaurs were not there" because this was not the question. Someone is confusing two situations: "answering a question by NO" and "not asking the question at all". These are two very different things.

OK, I think that the main proposals of Dowker and Kent are misled - the proposed search for a "unique" set selection criterion; the proposed necessity to construct a theory of consciousness; and so forth. I don't want to read it anymore because it's no physics.

CIP - questions vs. answers. First, be sure that my private communication with Hartle show that he's not aware of any serious problem with CH either, as of 2004.

Second. You and others seem to feel uneasy about the fact that one must first ask a question before the theory can calculate an answer for her. Yes, it's so. You can't uniquely calculate what are the questions, especially if you go away from the quasiclassical limit. If someone imagines that the theory must eventually give him a deterministic model that knows what the variables are and what their values were, then he's misled.

The emergence of the "right" questions is not something that is statically encoded into the structure of the theory. The main point of CH is that it reveals dynamically which sets of questions may be asked. Dynamics decides what's a forbidden interference among the outcomes we want to decide between. Dynamics determines how fast decoherence is. If anyone wants to decide about the right questions without dynamics, then he's doing it wrong.

All the discussed differences between the interpretation of the actual history are academic - and none of the critics ever derived a "wrong" conclusion from the CH. I use a very different thinking than constructing the literal decoherence functionals to decide whether the dinosaurs were around - because there would be just too many histories and too many projectors to take into account. And I am convinced that this this thinking is compatible with CH. It's simply because every step, every process that we know physics predicts - like reproduction of DNA - occurs with the same probability in CH.

Dear R, happy new year to you, too!

I expect - more precisely: we know - that gauge-fixing extends to a quantum theory if this theory is consistent. It is often difficult to say what a quantum theory, defined in terms of its classical limit, means - and gauge-fixing is often kind of necessary to make sense out of the theory. The Nambu-Goto action is really hard to quantize: it's not clear what it would mean. The Polyakov action is better, and the simplest way to get the spectrum is to gauge-fix.

The light cone gauge is a good gauge choice for any theory on a background that admits it. Other gauge-fixings are more problematic, at least according to string theory - they don't allow us to solve the theory easily and they have also other problems.

According to the Wheeler-deWitt equation, we *must* kind of gauge-fix - to choose the time as a function of some other, gauge-invariant degrees of freedom - if we want to make any contact with observable physics. These connections partly depend on conventions; they can't always be done exactly, and so forth. But I believe that this is just the truth: if your correct physical theory tells you that some objects are relative - they depend on your conventions, reference frames and other choices - you must accept it. Also, if it tells you that some observables are inaccurate, they can't be defined exactly, you must accept it as well.

This is my viewpoint. If someone wants to claim that some things may be defined exactly and/or uniquely even though it does not look so, he or she must have some evidence unless he or she wants to leave the scientific approach. Every nontrivial statement must have some evidence - either a direct experimental proof, or evidence that it follows from the consistency of any acceptable theory. I reject all statements about the physical world that are done purely on the philosophical grounds, especially if they seem to contradict our experiments and the knowledge that we've obtained from these experiments.

Philosophy is usually a wrong guide in physics and this philosophical approach is usually just a manifestation of people's prejudices and misconceptions.

There are simply many people who have some strongly held prejudices or beliefs - that things must be certain, the uncertainty principle must be wrong after all, that it must be possible to derive uniquely what are the right questions one can ask, that there must be an "objective reference frame", that geometry must be an exact notion, and so forth. They have these prejudices, they don't allow anyone to question them, and they insist that the physical theories will be constructed in order to agree with their prejudices.

One should not be surprised that the theories that are constructed to match these prejudices will usually be junk. The valuable theories in physics are constructed to agree with experiments and the natural mathematical beauty that the real Nature displays.

I don't think that the Mach-principle-like relational approach is something up-to-date because it is an approach that might say that only the relative positions of objects and events are physical, but it still assumes that the relative positions form an absolute set of observables that are "more fundamental" than other observables (such as the values of various fields). It just goes against the 20th century physics. General relativity as well as string theory show that the "indifferent podium" is never indifferent after all. All features of reality that influence other objects tend to be dynamical and "equally fundamental", so to say. It's just a wrong approach to imagine that a theory is defined in a two step process - one defining the background where things take place (or the relations that the objects can have), and then defining some objects assuming the first assumption. In reality, the objects influence each other in both ways.

This is a very vague chat, but once someone defines a particular theory that is meant to satisfy these medieval prejudices - such as loop quantum gravity - one can show why this theory is rubbish much more factually.

You ask me "What is the string theory equivalent of asymptotic freedom". Well, if you really want an "equivalent", I can tell you an exact equivalent, of course. It's the dilaton going to zero at the boundary of anti de Sitter space. This is the string theory equivalent of the gauge theory statement about asymptotic freedom, according to the AdS/CFT correspondence. ;-)

Sincerely

Lubos

My impression is that they want something that I also want - to find an equivalent way of looking at quantum mechanics that will also include the emergence of all other conceivable classical limits in different contexts.-----------------------------You think anything, that might even hint of philosophy, should travel through the space of your ears?:)In planck time, this could not hold very much information for you:)The matter distinctions of your brain would require a finer apprehension of time?:)

In respect of Smolin and Hooft and their requirements you are speaking about, are the realizations that they all have to recogized, is a viable means to measure what is illucive.

This world that NIMa and others look at in dimensional parameters is limited as you know by high energy realizations. At supersymmetrical levels how would you measure time, seems a useless question when you do not have this measure to look at in terms of classical solutions in regards to gluon interactions?

Smolin understood that quantum gravity would have these limitations, and you would be very happy to know that quantum gravity has a couple of roads that lead to it.:)

I would not quickly dismiss the thoughts of the Penrose and Smolins, and others who also recognized the limitations and had to devise methods of determination.

It is very problematic that they would seek a deeper meaning and maybe "reject time" as a fundamental measure in gluon perception that they would have to approach it someway else?

That we could have taken blackhole from the ideas of GR interpetation led too, in one parameter of thnking, and reduce to it to blackhole manufacturing at high energy considerations, would have sounded very nice by what you speak of from Steve Giddings.

As a philosopher, the mathematical you encounter, is very much derive from some

basis of thinkingthat you like to reject. Sometimes looking at there methods of apprehension of limiations drives many to create what is lacking in the question of what do we know.Even if I think Smolin has limited himself as well, I have been most appreciative of the roads he has lead many through.

My answer is that your comments are absolutely silly. What I solved was a limit of a differential equation that describes the quasinormal modes because they were claimed to be related to some weird, but ambitious discrete speculations about quantum gravity. The differential equations are the only well-defined things about this picture and everything else is just a speculation. The only hope for the speculation would have been that there would be some support for it coming from the continuous differential equations - there is no other support that these ideas are related to gravity. If you don't like the fact that important phenomena in this Universe are described by differential equations which are continuous structure, you should definitely try to move into another Universe and make all of us happier.

It is regrettable the quantity of discussions around the net based in this false antagonism continuous<-->discrete. After two millennia and half, people does not learn, even with all the modern research on scaling and renormalisation group. Or perhaps, people is just lazy to do the homework (Lubos, here you have your insult for Quantoken and similar: lazy. Lazy as every man with a faith).

As for Smolin, I will not hold a opinion, but I find funny the Anonymous remark about being a disciple of Coleman. Actually, Lee Smolin was a disciple of Sidney Coleman, who was a disciple of Murray Gell-Mann, who was a disciple of Victor Friedrich Weisskopf, who was a disciple of Max Born, who was a disciple of Carl Runge.Did you read DaVinci Code (Holy blood, holy graal)?

Leucipo said:It is regrettable the quantity of discussions around the net based in this false antagonism continuous<-->discrete.There is no doubt that this is the root of all "evil?:)Discrete structures, are like my platonic solids, and nodal points flips sought in monte carlo methods, sound very nice.:

But at high energy considerations, it asks you to think a little different and in topological forms. Here, there is no tearing which would to me imply dscrete structures?

I might need help here as the evolving mind in the brain and the coverings, have vastly been changed from what it once was of my lizard brain:) That such fine structures might be viewed, in a more generalized visualization from such focused evolutions?:)

Maybe the brains form is like the Doctor crossing the room, that it brings to it such abstractions, most appropriate for such visualizations. We'll see what next math is developed out of philosophical discussion.

Hi guys,

I think that in actual physics, there is no tension between the discrete structures and the continuous structures. Both of them are clearly necessary, and there are lots of relations between them. For example, L^2(R) has both a continuous as well as discrete bases.

Having said this, I think that most technical progress in physics has always been about finding a continous explanation of some qualitative observation - and qualitative observations are often discrete.

Let me say a couple of examples:

The ancient Greeks often thought that the world was continuous. Fortunately, they also discovered Euclidean geometry with its continuous rules, but they never directly thought that the continuous rules would govern Nature.

The real physics started with Newton who could have only described motion of planets by simultaneously inventing the calculus, derivatives - highly continuous structures. This mechanism was then expanded to partial differential equations, field theory - which is in some sense even more continuous.

Then there was a UV catastrophe, and attempts to discretely truncate the high energy frequencies. Planck was smarter and he truncated them continuously - and found a continuous formula for the black body and its continuous derivation.

Bohr had the old theory of an atom that was discretizing the energies etc. - but only when Schrodinger and others constructed the continuous equations that implies the discreteness of the eigenvalues, things became convincing. Feynman reformulated quantum mechanics using path integrals - which involve continuous functionals on the space of continuous configurations - which is, in some sense an even more continuous concept.

I could continue, but the lesson seems clear to me. The discrete rules are either a qualitative motivation for something that must eventually be justified by some continuous physics done properly, or they're just small subtleties that are added to the continuous rules.

The dogma that the whole world should be discrete goes against most of the lessons that science has taught us in the last 500 years - it's just a naive, protoscientific viewpoint.

All the best

Lubos

Hi leucipo!

What exactly do you find funny about my remarks defending Coleman and Deser? You did say that you are not willing or capable of having your own opinion, but if you know anything about physics, the importance of Coleman's and Deser's contributions can't have escaped you. And that's exactly where my criticism of Smolin begins: As a student of them, he should know, too, yet his work is a string of misinformed sub-standard speculations, more often than not in open conflict with the foundations laid by his former advisors.

I know that those people who have felt the thrill and excitment of reading and understanding a quality physics-paper will understand where I'm coming from. The really important contributions are typically very transparent insightful explanations of things that were thought to be too difficult to solve.

Let me name an example: Coleman and collaborators realized that the Schwinger model contained a new parameter that is clearly absent in the classical theory. This must have seemed mystifying to everyone involved, try to imagine how difficult a problem this must have seemed to be! Yet, a short time later, Coleman was able to provide (see his paper "More about the massive Schwinger model") an explanation so clear and obviously correct, even a layman could understand the essence of his argument. (The parameter is the theta-angle which, in 1+1 dim, corresponds to a constant electric background.)

Or look at Deser's "Topologically massive gauge theory". Mass terms typically spoil gauge invariance -- Deser in no uncertain terms showed how to give the gauge fields a mass anyway. This is real understanding of important issues.

Name one paper of Smolin's that lives up to these standards...!

Work in areas like loop quantum gravity is almost always different. A complicated formalism usually hides purported insights, and the arguments given are hardly ever summarized in understandable terms -- or they are just wrong. Even worse, the justification for introducing the formalism in the first place is shaky at best. What *is* the justification for assuming that the phase space of 4d gravity is in 1:1 correspondence with its QM counterpart? There is none. In fact, any smart grad student in 2005 can show that it's wrong.

I agree with one thing you said. There is a long tradition of smart people educating smart people. It's truly sad if such tradition is broken by a crackpot who didn't care to listen.

To those who are not physicists (and there are plenty here it seems, certainly including this idiot quantoken), I would like to say: If you care about physics, you are right; there are few things as exciting and important. But don't try to have your own opinion too soon. It's like listening to an opera performed by professionals and starting to sing loud and wrong. No one is going to like it. And no one is going to mistake you for an artist. It makes you a heckler, nothing else. Listening, by contrast, is quite an enjoyable and reasonable thing to do.

Best,

Michael

lubos said:I could continue, but the lesson seems clear to me. The discrete rules are either a qualitative motivation for something that must eventually be justified by some continuous physics done properly, or they're just small subtleties that are added to the continuous rules.--------------------------I must thank you for the history lesson, with a slightly different view of the Lubos Framework:)

Why discard the measure of the ole view of Q<->Q measure, and continue it, as a relevant move to a higher significance? You no longer fixate upon the metric view, but look to the fields around it:)

That is part of that evolution I see you are talking about in this history lesson. Thanks from my laymen, heart of hearts.

As well your differences of opinions on Peter's Woits might have been looked at, for consideration?

I would like to be able to see better with the higher faculties, of my new brain attachment:)My third eye, is developing fine?:)

Hi Torbjorn -

Yeah, I did write that at 3 a.m. - let me try to be a little more clear. There are two general issues:

#1 Say we want a deterministic theory of nature, and QM in particular. The original Copenhagen interpretation is obviously no good (it describes a very incompressible type of universe!), so that leaves us with the MWI (which is highly compressible - all you need are the initial states, and you can then evolve forward, producing lots of different histories in the classical limit) (*). But the existence of all these different decohered histories jars with some people's intuition of how the universe should be, so they conjecture about cellular automata rules at the Planck scale that would determine, for instance, precisely when a radioactive atom will decay. I am arguing their gut level rejection of the MWI was wrong however, and a many different histories universe can be perfectly intuitive.

This requires a bit of a detour:

#2 I am going to make 2 natural assumptions about the universe to build the case that many worlds can be intuitive. First I assume that the universe actually is a mathematical structure, i.e. we can form a complete mathematical model of reality so that the model and reality are one to one. This claim is bolstered by every successful prediction in physics. It is fun to think about which result best supports this worldview - the spin-statistics theorem perhaps?

2nd assumption: Now accepting that our universe is a mathematical structure (and we are particular permutations of atoms within it), it is then reasonable to assume that all mathematical structures exist - there is no distinction between possible and realized mathematical structures (**). That is, what basis could there be for only our universe existing when it is just another particular type of information?

But then we and our histories are just permutations of basic mathematical building blocks, and so by the 2nd assumption all the other permutations would exist as well. Otherwise it would be as if you were saying that only 1,4,3,2 existed, and not 1,2,4,3 or 4,2,3,1 and so on ( - switching the large numbers of spherical harmonics and Laguerre polynomials for a couple integers...). More concretely, say the universe was of a classical Newtonian billiard ball type - so that all of the future history, including how we now find ourselves, was based on some particular initial conditions. The second assumption would then hold that all other sets of initial conditions would exist as well, giving rise to a huge family of completely disjoint histories. As it turns out we live in a quantum mechanical world which is even more interesting - from one set of initial conditions it effectively splits into many different almost completely disjoint histories in the classical limit. In general, if you accept both assumptions, then you shouldn't expect that only precisely one history and version of yourself exists. If you are nothing more than a permutation of mathematical objects, it is reasonable that all other permutations exist as well. Even in the dubious cellular automata universes, you could start with different initial conditions and get other histories, just like in the Newtonian case.

Is that any clearer?

*and perhaps this CH interpretation. I still need to look at it a lot closer, but I am betting that you will still have branching of worlds, such as when you measure the left-right spin of an electron that has already been determined to be spin up. So far I have read that the CH demands that you use commuting basis functions for describing your states, which is how it should be, and which is perfectly compatible with the MWI.

** At first glance it would appear that there would be serious problems with this - how could one make any predictive theories when all information exists? I don't think it is quite that bad however. First you can rank the information by it's complexity - if you reduce everything to integer strings which can be thought of as programs, then there are many more complex programs than simple ones. It would also seem at first that the 'noise' programs which contain no patterns would dominate the counting, but I think you can eliminate them by only considering representation independent programs - i.e. a 'real' program on one computer would be linked unambiguously to another version on a different computer (representation independence), while on the other hand there would be no reason to link a particular 'noise' program on one computer to any other program on another computer. It's vaguely reminiscent of getting rid of the infinite contributions to path integrals by gauge invariance - you separate it out via Fadeev & Popov and only count over the important stuff - in this case you only count over the representation invariant programs, i.e. the real ones that actually describe something (hmm, I wonder if you could get ghosts... ;-).

Even still, there are going to be many more complex programs than simple ones, which I think makes the 2nd assumption testable - that is you don't ever expect an end to physics. If perhaps string theory is verified at some point, you would still then expect to find new surprising phenomenon (like we found with dark energy and neutrino mass) that would necessitate reinterpreting string theory as a particular limit of some yet more complex theory (add more stuff to the lagrangian? Higher derivatives and larger solution spaces? ...) - simply because statistically there are many more complex theories possible than the simple one where just string theory would turn out to be eternally valid and complete. We'll see!

Hi Michael,

I agree that results such as Coleman-Mandula, or books as the one of Aspects of Symmetry, are clearly more illuminating for physics that the works of Smolin I know of. I reserved my oppinion because on one hand I have never worked (just read) over Smolin shoulders, and on the other hand I feel that some level of debate is needed in our overspecialised age.

I found funny your remark because just yesterday I was drawing some genealogies and I found also this surprising heritage from Coleman to Smolin. By the way, it is probably the longest known pedigree in theoretical physics, going up to Otto Mencke, the cofounder of Acta eruditorum.

"some continuous physics done properly" Yes, the kind of proper work that is reflected in the renormalisation groups methods, in Kadanoff or in Wilson-Kogut: that a proper work with the continuous limit is basically to keep track of the process. The need of a renormalisation point, movable but undisposable, in the deepest clue we have nowadays about the communion between the discrete and continuous.

hey lubos, thanks for your answer, I have still some remarks....

you said:

"It is often difficult to say what a quantum theory, defined in terms of its classical limit, means - and gauge-fixing is often kind of necessary to make sense out of the theory.......Other gauge-fixings are more problematic, at least according to string theory - they don't allow us to solve the theory easily and they have also other problems."

Is it true that gauge fixing is 'necessary'? Dirac's approach, if I'm correct, was to construct observables in term of gauge invariant objects. It is certainly true that we can talk of observables in any gauge and therefore, in principle, have the same answer.

Now you are telling me that some gauges are problematic in string theory, does this mean that there is not a consistent gauge invariant way of quantize string theory? If so, what does it mean that some gauges are 'better' than others in physical terms? (in other words, why QM picks certain gauges over others and what would that tell about the theory. This has a very simple example in standard QM with the choice of canonical pairs and factor ordering issues I never completely understood. That's a good one actually, how do you treat factor ordering in the path integral approach?)

another thing, you said:

"According to the Wheeler-deWitt equation, we *must* kind of gauge-fix - to choose the time as a function of some other, gauge-invariant degrees of freedom - if we want to make any contact with observable physics."

Firstly, the choice 'x^0=s' doesn't look like a function of gauge invariant degrees of freedom, in fact in a totally covariant framework gauge invariant objects are frozen, they don't evolve at all. I agree that WdW is gauge fixed, my question was more related of how this equation, which represents 'the physics', will account for time-fluctuations if now time is an external parameter in it. I disagree though that to make contact with observable physics we have to gauge-fix, the basics of a relational construction lies in totally the opposite, namely, to construct gauge invariant objects that will represent 'evolution' in a relational way, like a gauge invariant answer to the question: what's the value of q_1 'given' q_2=t. This translate into QM as: "what's the probability of q_2=x 'given' q_1=t". I found this approach remarkably in that now q_1 plays the role of the clock but it is in the same footing that all the other variables contrary to the gauge fixing process where I can't see how can you treat time as a quantum object. That's why quantum mechanically the difference between to gauge or not to gauge become, I think, physically relevant.

I like this:

"But I believe that this is just the truth: if your correct physical theory tells you that some objects are relative - they depend on your conventions, reference frames and other choices - you must accept it. Also, if it tells you that some observables are inaccurate, they can't be defined exactly, you must accept it as well."

We all have some degree of belief in this business, 'the truth' is an strong statement I will hesitate to use. I agree that if the theory is correct, namely, explains nature, you have to learn to live with it whatever it tells you about 'her'. So far it is not clear what the final theory of gravity is, I will save here my words for the future. I disagree that observables depend on conventions, I do agree that observables are relational objects and therefore depend upon choices, our choices. If that's what you meant, you are close to relational ideas as well :)

This is even more interesting:

"Every nontrivial statement must have some evidence - either a direct experimental proof, or evidence that it follows from the consistency of any acceptable theory. I reject all statements about the physical world that are done purely on the philosophical grounds, especially if they seem to contradict our experiments and the knowledge that we've obtained from these experiments."

It would take days to discuss this, but let me just make a few remarks. String theory so far doesnt have any direct experimental proof, and the consistency of an acceptable theory is a source of debate. I am curious about 'the knowledge that we've obtained from experiments' and the birth of string theory. As far as I know string theory was ruled out as a description of the strong interaction and suddenly promoted to a theory of everything without any ground but the belief that the spin-2 massless particle is the 'graviton'. Gravity has been always based on philosophical insights, look Newton's idea that it had to be universal, and Einstein construction of GR without any clue but it's equivalence principle. String theory claims to fulfill Einstein's dreams, I'm afraid that most of his dream were based on philosophical grounds and beliefs.

In addition, physicists, like for instance Glashow, claim we won't be ever able to rule out string theory. How do you handle a theory that can't be confronted with nature?

I am not against following philosophical beliefs but I agree with you that we should make contact with Nature ocasionally.

You also said:

"General relativity as well as string theory show that the "indifferent podium" is never indifferent after all. All features of reality that influence other objects tend to be dynamical and "equally fundamental", so to say."

I agree with that and so does the LQG people. The very heart of relationism is that: " All features of reality that influence other objects tend to be dynamical and "equally fundamental", so to say." The problem with this is how do you treat time and it 'equally fundamental' status. We can't treat it as an external classical parameter and that's why relational ideas are necessary.

In addition you said:

"It's just a wrong approach to imagine that a theory is defined in a two step process - one defining the background where things take place (or the relations that the objects can have), and then defining some objects assuming the first assumption. In reality, the objects influence each other in both ways."

Totally agree, but historically, as pointed out by Witten to me, string theory was more a two step theory that a background independent one. What you just said here is again the core of relationism to which I totally agree.

I agree this is a very vague chat and I appreciate the time you take in answering my quesions.

I disagree that lqg ideas are totally rubbish as I also believe string theory is a beautiful mathematical construction as far as I know. However, there are a lot of beautiful constructions (subjective topic btw) which do not represent our world.

The type of argumentation between the two is not good for our physics society nor for young students. Saddly it doesn't look like is gonna be better.

With respect to QCD, I was asking you for an equivalent landmark of asymptotic freedom not how does it come from string theory. Incidentally, talking about ADS/CFT, holography was originally proposed by thooft who is a nonlocal hiden variables advocate by now if I understood him clearly.

We can also discuss about leny's landscape and the anthropic principle, but I guess that there is too much information here so far, it might create a BH :)

best regards,

R

Hi travis-

It's clearer now, except that I don't make head or tails of your concept of 'compressible'.

Anyhow, to make this shorter and possibly correct I will use lumo's replies. Since I elsewhere saw a statement that 'Consistent histories' was an interpretation of QM I haven't looked into it before. lumo tells us that in fact you have QM+CH, consistent with QM, but with larger scope (histories).

In lumos CH reference (http://en.wikipedia.org/wiki/Consistent_histories) there are two more postulates. Histories Hi are defined as a product of projection operators and they are consistent, ie Tr(HioHj') = 0 and Pr(Hi) = Tr(HioHi'). No branching, no MWI.

Lubos,

The De Broglie-Bohm interpretation does not add extra variables to describe quantum mechanics, and neither does it place treat either momentum or position specially. All it does is mathematically reformulate Schrodinger's equation, and interpret

the phase of the quantum mechanical wavefunction as a classical action and the amplitude as a classical real space density, and then treat the corresponding momentum and position as the true classical variables underlying the quantum system. Since, the formulation is mathematically exact and equivalent to the schrodinger equation, one does not have to buy into its interpretation to use it to solve various, concrete problems, involving the treatment of some variables as quantum objects and others as classical ones.

Of course that the Bohm interpretation adds extra variables that don't exist normally; it has BOTH the wavefunction as well as CLASSICAL coordinates and velocities of particles.

You don't have to use a correct interpretation of quantum mechanics unless you need to make correct predictions. In the simple models, one can construct an "awkward superstructure" (as Einstein called the theories of hidden variables) that is equivalent to the correct quantum mechanics, but it can't be generalized to other systems - such as relativistic systems - and even if it can, all the correct predictions of these bizarre theories are those copied from quantum mechanics, and all the new predictions are incorrect.

The Bohm picture picks priviliged observables which is highly unacceptable especially in quantum field theory - which is the real picture we've been used to describe the real world already from the 1930s. In quantum field theory, one can talk about configurations with well-defined classical values of the fields, or about configurations with well-defined numbers of particles with well-defined positions. These bases are different, incompatible, and there is no physical sense in which one basis is better than another basis. There are also many other bases one can choose.

However, in the Bohmian picture you HAVE to make a choice which variables will be treated as the extra classical degrees of freedom, and whatever choice you will make, you will eventually be in trouble. Also, the Bohmian picture will always violate Lorentz invariance and it will always have problems to incorporate spin etc.

The de Broglie pilot wave theory could have been a serious research direction in the 1920s when people started to understand the framework behind quantum mechanics, but today the research of the Bohm theory is just an artifact of poor knowledge of physics - the Bohmian theories have nothing to do with the actual quantum physics of the last 60 years: spin, quantum field theory, gauge theory, renormalization, Higgs mechanism - but it's also un-helpful for entanglement, quantum computing, and understanding of quantum decoherence which is really the main piece of progress in the interpretation of QM in the last 25 years.

Lubos,

That is not quite true. Mathematically, there are no additional variables. One has a phase, and an amplitude, the derivatives of which are called "momentum" and "position" in the Bohmian theory. One does not need to accept this assignation. However, by solving the quasi-newtonian equations for this "position" and "momentum" one is actually calculating the wavefunction of the system. So this is an interesting

calculational technique, which is still being worked on today. While you may consider this irrelevant because it applies only to non-relativistic situations, and does not have any use in QFT or any such thing, there are still several problems in physics which involve non-relativistic quantum mechanics, and

involve the calculation of wavefunctions and densities. The equations of motion due to Bohm's trick do have a limited use there. No one really believes that the pilot wave interpretation is correct, but the mathematics of the Bohmian theory is natural to the Schrodinger equation and can be thought of as a way of rewriting the same.

From a different point of view, any theory of hidden variables or otherwise which tries to supplant quantum mechanics is fundamentally pointless, unless it can predict all the set of things that QM does, and in addition make predictions that go beyond the QM framework. The Bohmian view fails this test, and so do all other substitutes for QM that I know of.

You must have confused Bohm's theory with some completely different theory, or perhaps you misunderstood the very basic points of it.

Bohm's theory is a key example of a theory of hidden variables. What do you think that the term "hidden variables" mean? It's the whole point of this problematic approach to quantum physics that it involves a lot of new variables - in the simplest case, it includes both the classical position and momentum of a particle, as well as a "physical" wave function whose "quantum potential" affects the motion of the particle. These new degrees of freedom can't be directly seen, and if they could be seen, the usual symmetries of Nature and causality would be violated.

Incidentally, hidden variables and Bohmian theory are "lost causes in physics number 1 and 11" of Streater. I endorse his text 1 and 11, which does not imply that I endorse all of this texts.

http://www.mth.kcl.ac.uk/~streater/lostcauses.html

More interesting beliefs, IMHO:

-Carlo Rovelli (and see also Donald Hoffman) "Time does not exist"

-Jesse Bering "I do never die" approach. A Linguist here, Agustin Garcia-Calvo, has a close one.

-Maria Spiropulu use of no-thing, just because it remembers me of "my disciple" Democritus.

-John McWorter about the language on Flores island

-and Rudy Rucker multiverse "Reality is a novel"

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