Has quantum mechanics changed since the big bang?

[Loren Booda]

Has the Planck era, inflationary era or other intervals of cosmology affected the fundamental theory of quantum mechanics? For instance, is QM defined at all before the Planck time? During the Planck era, are there any non-trivial applications of the wavefunction? Did inflation change just the scale of spacetime, or was quantum mechanics transformed by relativity during such extreme expansion?

 

[vanesch]

For instance, is QM defined at all before the Planck time?

QM wasn't even defined in the 19th century, so go figure

 

[Anonym]

Vanesch:” QM wasn't even defined in the 19th century”

According to that logic QM was not defined before G.Gamow work also.

Loren Booda:” Has the Planck era, inflationary era or other intervals of cosmology affected the fundamental theory of quantum mechanics?”

I guess not, since QM existed before.

 

[reilly]

One can argue that the in and out states of QFT, defined at t =+/- infinity are incorrect. Formally they should be relative to t=0, and t=time since the bang. My sense is, however, that the usual S-Matrix, and the usual free particle states are extremely good approximations to reality. And anyway, there are many small perturbations acting on any system that could well wipe out any "finite universe" corrections.

As long as QM gives descriptions of nature as she is, then what's to worry? The worry is about what can't be correctly described.
Regards,
Reilly Atkinson

 

[Careful]

As long as QM gives descriptions of nature as she is, then what's to worry? The worry is about what can't be correctly described.
Regards,
Reilly Atkinson

So, then you must inform us about your solution for the cosmological constant problem (if you see no problems in QFT). Or let me guess, finetuning is all you need, right ?

Careful

 

[vanesch]

I think it is unproductive to talk about the applicability of quantum theory as we know it in areas where it is clear that we need the domain of applicability of general relativity, given that there is nobody yet who knows what is their common paradigm. You can just as well argue about the bending of light in Newtonian gravity.

Hence, the "problem of cosmological constant" which is something that pops up in GR falls outside the domain of applicability of the quantum theories we know of today. It is probably reasonable to assume that once we have the new paradigm which includes both the domains of applicability of quantum theory and GR, the answer to that question will be clear.

 

[Careful]

Hence, the "problem of cosmological constant" which is something that pops up in GR falls outside the domain of applicability of the quantum theories we know of today. It is probably reasonable to assume that once we have the new paradigm which includes both the domains of applicability of quantum theory and GR, the answer to that question will be clear.

Well, there would be people who claim there simply is no problem: that vacuum energy is observable in GR but not in QM is merely an inconvenience which can be corrected by finetuning. Then, some portion of physicists would say that QM is fine (substraction of infinite energy densities need not to be understood), but it is GR that fails.

All I wanted to say by this one line is that I do not understand why some people who are merely content to dispose of (different) algorithms which allow them to compute scattering processes in laboratories have to impose their ``hands-on'' attitude on a much smaller number of physicists who still know that big objects consist out of small ones and therefore are fascinated by the question how the laws of the very large are effective approximations to the laws of the very small for systems with a large number of particles.

 

[vanesch]

Well, there would be people who claim there simply is no problem: that vacuum energy is observable in GR but not in QM is merely an inconvenience which can be corrected by finetuning. Then, some portion of physicists would say that QM is fine (substraction of infinite energy densities need not to be understood), but it is GR that fails.

Well, all these (and others) are options. Given that as of now, we have no empirical discrimination which tells us what way to follow, I think it is silly to lose sleep over it...

All I wanted to say by this one line is that I do not understand why some people who are merely content to dispose of (different) algorithms which allow them to compute scattering processes in laboratories have to impose their ``hands-on'' attitude on a much smaller number of physicists who still know that big objects consist out of small ones and therefore are fascinated by the question how the laws of the very large are effective approximations to the laws of the very small for systems with a large number of particles.

And what I wanted to answer is that, given that there is no obvious clarification of the issue yet, and certainly not much empirical indication, that this is all hypothetical and speculative in any case ; in other words, a guess is as good as another...

 

[Careful]

Well, all these (and others) are options. Given that as of now, we have no empirical discrimination which tells us what way to follow, I think it is silly to lose sleep over it...

Euh, , the cosmological constant problem is a theoretical problem. Finetuning ``solves'' the issue entirely.

And what I wanted to answer is that, given that there is no obvious clarification of the issue yet, and certainly not much empirical indication, that this is all hypothetical and speculative in any case ; in other words, a guess is as good as another...

I disagree with this. The CCP is a direct clash between Einstein's energy based approach and Newton's force based theory, any real (local !) solution should result in a theory which removes this distinction (and that requires new physics). Actually, regarding your first comment, the CCP is like the Rosetta stone in the search for better laws of physics. So, it is not entirely stupid to lose some sleep over it :-)

 

[reilly]

So, then you must inform us about your solution for the cosmological constant problem (if you see no problems in QFT). Or let me guess, finetuning is all you need, right ?

Careful

Goodness gracious. Why should I say anything about the cosmological constant?

You have managed to miss my point(s) entirely. Indeed there are areas of physics, gravitation in particular, where physics is just plain stuck. Who knows about QM and the cosmological constant? Do you? I certainly do not, nor did I ever claim I did.

I'm just a humble, emprically based physicist, who calculated a lot of numbers( radiative corrections) that helped to discover and map out the E&M nucleon form factors from electron scattering experiments. And, dear me, while I used other people's algorithms -- Schwinger and Feynman -- I had to invent some myself. According to your views,as best I can figure, I should be contrite or even embarassed about what I did. But I'm not. Even though, I'm not sure why QED works so well -- as Dyson noted, the perturbation QED series does not converge -- bummer.

Why even that theorist of theorists, Einstein was a big numbers guy -- even had patents on torpedos and refrigerators, some with Leo Szilard.
Given the history of physics, chances are that new phenomena will be at the forefront of any success in putting QM and GR on the same page. And, worse yet, I taught QED. As best as I can remember, I did suggest that QED and QFT were less than perfect -- naturally, in a moment of weakness.

I agree with much of what vanesch has said in this thread. And, by the way, how might we do finetuning?

Do you have any suggestions on what I might do to get over my computational and empirical bent? Perhaps there's a 12-step program for 'shut up and compute" types. Do let me know if you are familiar with such a program.
Regards,
Reilly Atkinson

 

[Careful]

According to your views,as best I can figure, I should be contrite or even embarassed about what I did.

Absolutely not ! All I wanted to say is that there are people with different notions of ``doing physics'' and I do not understand why these cannot coexist with mutual respect.

But I'm not. Even though, I'm not sure why QED works so well -- as Dyson noted, the perturbation QED series does not converge -- bummer.

Right, and there are people who find that interesting.

Why even that theorist of theorists, Einstein was a big numbers guy -- even had patents on torpedos and refrigerators, some with Leo Szilard.

Well, science in that time was naturally much more prominent he Can you imagine that in basically 25 years, airplanes, flying bombs, an atomic bomb, sound recording, etc... came into the lives of people ? Anyway, apart from a big numbers guy, Einstein was also a respectable womanizer .

Given the history of physics, chances are that new phenomena will be at the forefront of any success in putting QM and GR on the same page.

I am rather sceptic here, but am more than interested in seeing how far QM can be pushed.

And, worse yet, I taught QED. As best as I can remember, I did suggest that QED and QFT were less than perfect -- naturally, in a moment of weakness.

Hehe, why should you not do so (albeit we both know there are more than enough scientists who do so) ?! I believe there are still lot's of things to be learned from the goods as well as the shortcomings of QFT.

And, by the way, how might we do finetuning?

Just finetune the bare cosmological constant so that it cancels the QFT vacuum energy density to the actual measured value.

Do you have any suggestions on what I might do to get over my computational and empirical bent? Perhaps there's a 12-step program for 'shut up and compute" types. Do let me know if you are familiar with such a program.

I have nothing against this mentality (actually I prefer it by large over those thinking about say anthropic scenario's). It is a perfectly legitimate choice of doing physics (which requires lots of creativity) as long as one does recognize there are other problems (such as Dirac did in his young years). So, we must have misunderstood each other here, my apologies for that.

 

[reilly]

Careful you said:
I have nothing against this mentality (actually I prefer it by large over those thinking about say anthropic scenario's). It is a perfectly legitimate choice of doing physics (which requires lots of creativity) as long as one does recognize there are other problems (such as Dirac did in his young years). So, we must have misunderstood each other here, my apologies for that.I agree, and please accept my apolgies. Maybe not on the same page, but certainly in the same chapter.
Regards,
Reilly Atkinson

 

[vanesch]

I disagree with this. The CCP is a direct clash between Einstein's energy based approach and Newton's force based theory, any real (local !) solution should result in a theory which removes this distinction (and that requires new physics).

My understanding is that the concept of energy in GR and in QFT is totally different: in QFT it is the inherited quantity of a "first integral" in CM of the equations of motion that corresponds to time translation, while in GR it is part of a source term like charge is. This implies that fundamentally, in QFT, energies can get "constant offsets", and this liberty can be used (like, say, a gauge fixing freedom) to solve formal problems. Normal ordering is one of those things. Clearly in GR you have no such freedom.
No wonder you run into troubles when you use the concept of energy in QFT and plug it into GR. That's not surprising: the basic principles on which these quantities were based are different.

Actually, regarding your first comment, the CCP is like the Rosetta stone in the search for better laws of physics. So, it is not entirely stupid to lose some sleep over it :-)

Yes, the indication is that the naive transfer of the "energy" concept in QFT, directly as the energy concept in GR, gives problems. But it would have been rather a surprise if this weren't so. And "finetuning" is then simply maybe the "easiest" trick to make the two "talk to each other".

At least, that's how I understand this issue.

 

[Careful]

My understanding is that the concept of energy in GR and in QFT is totally different: in QFT it is the inherited quantity of a "first integral" in CM of the equations of motion that corresponds to time translation, while in GR it is part of a source term like charge is. This implies that fundamentally, in QFT, energies can get "constant offsets", and this liberty can be used (like, say, a gauge fixing freedom) to solve formal problems. Normal ordering is one of those things. Clearly in GR you have no such freedom.

You have just repeated in detail what I said.

No wonder you run into troubles when you use the concept of energy in QFT and plug it into GR. That's not surprising: the basic principles on which these quantities were based are different.

Well, not quite. In (hamiltonian or perturbative) relativistic field theory, one starts from an inertial reference frame in Minkowski which gives rise to a natural notion of energy density (at least classically). The classical vacuum value of the latter is exactly zero, however we do know that quantum mechanically such thing like normal ordering destroys it all (giving rise to an infinite VEV). These mode dependent energy densities express that quantum mechanically, the vacuum state describes the nonvanishing thermodynamical zero point motion. Actually, the translation symmetry in the absolute value of energy density spectrum is what allows you to do the finetuning in the first place (and as such is a quantum mechanical ``saviour''). But what is the meaning of substracting infinite energy densities (or at least gigantic ones if you make a Planck scale cutoff) ? It would lead us again to a discussion about the reality of the quantum mechanical vacuum, virtual particle states and so on ... as I tried to explain once, our theories do strongly suggest that there are real (unobserved) processes underlying what we observe. This implies that gauge invariance is a property of the (effective?) dynamical laws, but not an aspect of the kinematical description (so gauge degrees of freedom represent real particles - albeit we cannot measure them (yet?)). If we give an absolute meaning to gauge degrees of freedom, we must also specify a gauge : it seems to me that in EM the Lorentz gauge is a pretty fundamental thing.

Many people do think that introducing as yet unobserved (but naturally suggested) real entities is ugly (blue dragons sitting on your shoulder). Unnecessary to say that I sharply disagree since it seems to be infinitely more ugly to have entities in your mathematical description which do not have any real significance at all, but still influence the measurements in a decisive way. That are blue dragons indeed ! On the other hand, you could try to do symplectic reduction and eliminate the gauge symmetries, but then: ``who understands the Coulomb potential´´? This would in my opinion destroy the entire idea of fields as force carriers between particles ; similar observations concern relativity and the issue of diffeomorphism invariance (NOT coordinate invariance).

 

[vanesch]

The classical vacuum value of the latter is exactly zero, however we do know that quantum mechanically such thing like normal ordering destroys it all (giving rise to an infinite VEV). These mode dependent energy densities express that quantum mechanically, the vacuum state describes the nonvanishing thermodynamical zero point motion.

What I wanted to say is, that formal manipulations that lead to shifts in the energy spectrum are "no problem" for a QFT because a priori we shouldn't attach any specific meaning to absolute energy values in the QFT paradigm. In a stupid way: H \rightarrow H + C is a symmetry of any quantum theory.

Actually, the translation symmetry in the absolute value of energy density spectrum is what allows you to do the finetuning in the first place (and as such is a quantum mechanical ``saviour''). But what is the meaning of substracting infinite energy densities (or at least gigantic ones if you make a Planck scale cutoff) ?

I think the error resides in thinking that this means anything at all. I think QFT has fundamentally no meaning ascribed to absolute energy values, and that, at a certain moment, "freezing" the expression for energy and taking it as absolute energy which enters GR is totally arbitrary. So weening why this doesn't come out right is a well-deserved spanking I'd say, for taking quantities beyond what they were intended to mean.

It would lead us again to a discussion about the reality of the quantum mechanical vacuum, virtual particle states and so on ... as I tried to explain once, our theories do strongly suggest that there are real (unobserved) processes underlying what we observe. This implies that gauge invariance is a property of the (effective?) dynamical laws, but not an aspect of the kinematical description (so gauge degrees of freedom represent real particles - albeit we cannot measure them (yet?)). If we give an absolute meaning to gauge degrees of freedom, we must also specify a gauge : it seems to me that in EM the Lorentz gauge is a pretty fundamental thing.

 

[Careful]

What I wanted to say is, that formal manipulations that lead to shifts in the energy spectrum are "no problem" for a QFT because a priori we shouldn't attach any specific meaning to absolute energy values in the QFT paradigm. In a stupid way: H \rightarrow H + C is a symmetry of any quantum theory.

Yes, I got that and what I added is that even when you have a natural notion of energy available which works well classically (in either C has been set to zero), it doesn't so quantum mechanically.

I think the error resides in thinking that this means anything at all. I think QFT has fundamentally no meaning ascribed to absolute energy values, and that, at a certain moment, "freezing" the expression for energy and taking it as absolute energy which enters GR is totally arbitrary. So weening why this doesn't come out right is a well-deserved spanking I'd say, for taking quantities beyond what they were intended to mean.

No, that is what I tried to argue before: special relativistic field theory *does* give an absolute notion of energy (relative to a Lorentz frame), however it is indeed so that the relevant observables in QFT involve energy differences rather than absolute energies (and that is why your class of Hamiltonians above can be considered to be equivalent).

from which I cannot understand whether you (a) do not get it (b) disagree.
Let me say briefly that if you do not consider the vacuum energy as real (neither as the virtual particles which make up the vacuum) then, there is no problem since you are allowed not to couple it to gravity.

 

[vanesch]

from which I cannot understand whether you (a) do not get it (b) disagree.
Let me say briefly that if you do not consider the vacuum energy as real (neither as the virtual particles which make up the vacuum) then, there is no problem since you are allowed not to couple it to gravity.

Indeed,...up to a constant.

We use "correspondence" at the macroscopic level to tune in that constant to the observed gravitational effects (empirical fitting!), which fixes the arbitrary relative energy scale of QFT to the absolute scale needed in GR. Some people call that "fine tuning" because indeed the numbers are so big to give a small difference.

 

[Careful]

Indeed,...up to a constant.

We use "correspondence" at the macroscopic level to tune in that constant to the observed gravitational effects (empirical fitting!), which fixes the arbitrary relative energy scale of QFT to the absolute scale needed in GR.

Well, we still disagree I guess. You seem to suggest that there must be some a priori, deep reason why one will never be able to speak meaningfully about an observable vacuum energy in QFT. It is just so that FAPP in laboratories we measure energy differences, and therefore the absolute energy spectrum doesn't really matter. True, up till now, our quantization procedures for free field theories lead to the same Hamiltonian up to a constant ; but that is a problem of infinities which shows up in our formulation(s) of QFT so far. It really just shows that we did not understand quantum field theory properly yet. If we were to find a canonical, mathematically consistent formulation of it which arrives at vanishing vacuum energy, our problem would be solved (a formulation without vacuum fluctuations would just do that : Jaffe, Barut and many others have contemplated this). So far, we have been discussing the old CC problem. The ``new'' CC problem is much more ambitious and definitely requires new physics; the issue people deal with here is the following. You may take the attitude that the CC is an integral part of gravity, a free parameter for which you would like to have a deeper reason why it is so incredibly small in our universe. In either you would like to know ``why does nature prefers a flat spacetime´´ ? This is of course even much more difficult.

 

[vanesch]

Well, we still disagree I guess. You seem to suggest that there must be some a priori, deep reason why one will never be able to speak meaningfully about an observable vacuum energy in QFT.

Not in the way we set up QFT today, starting with a hamiltonian formulation and a unitary time evolution resulting from it (or any equivalent formulation, via path integrals or the like), because this is fundamentally rooted in the "H = time translation generator" paradigm. What I mean is that QFT, as a starting point, has no fixed zero for H. Unless we complement it with a principle that somehow gives an absolute scale to H, there is no way to do so, unless empirically (= "finetuning"). I think it would have been a small miracle if this "free floating" H scale would correspond somehow to the correct absolute scale in GR.

True, up till now, our quantization procedures for free field theories lead to the same Hamiltonian up to a constant ; but that is a problem of infinities which shows up in our formulation(s) of QFT so far. It really just shows that we did not understand quantum field theory properly yet. If we were to find a canonical, mathematically consistent formulation of it which arrives at vanishing vacuum energy, our problem would be solved (a formulation without vacuum fluctuations would just do that : Jaffe, Barut and many others have contemplated this).

I'm affraid that the mathematical difficulties of the infinities have obscured the fact that EVEN WITHOUT these problems, there wouldn't be a reason a priori for any QFT hamiltonian to be of "absolute scale". This is like renormalization: the problem of infinities has nothing to do with the fact that the empirical quantities are not equal to the bare parameters in the Lagrangian.

You may take the attitude that the CC is an integral part of gravity, a free parameter for which you would like to have a deeper reason why it is so incredibly small in our universe. In either you would like to know ``why does nature prefers a flat spacetime´´ ? This is of course even much more difficult.

Yes, of course. I don't say that one shouldn't look for a reason. I'm only saying that one shouldn't be surprised that the numbers coming out of QFT have nothing to do with the CC, and that it would be a small miracle if it did. Even without any problems of infinities. Simply because the way QFT is set up, there is nothing that requires the "reasonable hamiltonian" to have any absolute scale. This needs an entirely new principle.

But we are blinded by the fact that the "reasonable hamiltonian" as we arrive at it by mechanically applying quantization procedures comes out infinite, and that we have to use the build-in freedom H -> H + C to get rid of that infinity. We think that it is this "trick" which has screwed up somehow the "natural" absolute energy scale. But no, even if this wouldn't have happened, there is no fundamental reason why the "natural hamiltonian" would have to be the absolute scale needed to find the correct CC, because the H -> H + C is a fundamental symmetry build into QFT as we know it today.
Of course it might have come out right, but then it would have been an ununderstood miracle of why the H that pops up "naturally" comes out exactly right in absolute scale, because there is no principle that requires this.

 

[Careful]

Not in the way we set up QFT today, starting with a hamiltonian formulation and a unitary time evolution resulting from it (or any equivalent formulation, via path integrals or the like), because this is fundamentally rooted in the "H = time translation generator" paradigm. What I mean is that QFT, as a starting point, has no fixed zero for H.

Sure it has, that is what I was arguing all along ! In a classical relativistic field theory, energy is fixed in the same way as it is fixed for a relativistic particle of rest mass m. Given an inertial frame, the energy of the particle with respect to the corresponding observer is an unambiguous concept. Quantum mechanically, this would be exactly the same provided one could uniquely and consistently quantize the corresponding Hamiltonian. Of course, you could say : ``ohw, but I can add any constant to the Lagrangian (density), still get the same equations of motion, but a different Hamiltonian (density)''. Sure you can do that, but the thing is that you want this Hamiltonian (density) to correspond to the correct energy (density) as given by special relativity. Similarly, you could add a constant to the Lagrangian density of the matter part of the action in GR without (obviously) modifying the form of the matter equations of motion while affecting the equations of motion for the metric field. If you know the correct inertial mass of a particle, as well as the particle content of your theory, then Einstein's special relativity gives you the unique energy momentum tensor, period. Quantum mechanically, you can ``simply'' demand that also the spectrum of the Hamiltonian has the correct ``classical limit''.

I'm affraid that the mathematical difficulties of the infinities have obscured the fact that EVEN WITHOUT these problems, there wouldn't be a reason a priori for any QFT hamiltonian to be of "absolute scale". This is like renormalization: the problem of infinities has nothing to do with the fact that the empirical quantities are not equal to the bare parameters in the Lagrangian.

You are mixing up two kinds of infinities here ! The self energy and vacuum polarization infinities are indeed corrections to the mass and charge of the electron in QED (or classically if you want to). But this has nothing to do with the infinities in the vacuum energy, but rather with the fact that Maxwell never took into account the physics of the charges as being a source term in the first place. Rather, his equations were developped from observing the action of a field *on* a charged object. So, one can indeed legitimately claim that those infinities should have been taken into account already in the mass/charge of the particle itself and that they should have no observable consequence for the rest of the physics. But the point is that I do not have to worry about self interactions, the vacuum energy infinities show up in the free theory. So, the physical nature of these divergences is obscure (while the mass/charge renormalizations have a clear physical origin), it seems to be more a problem of the mathematical formulation than anything else (as Schwinger and Jaffe amongst others argue).

So, I disagree with the rest too. It might be that your disagreement is rooted in the attitude that the QUANTUM Hamiltonian is an OBSERVABLE while the classical Hamiltonian is a beable (and GR is about beables), to use the lagauge of John Bell. In the former spirit, one can claim that only energy differences with respect to the ground state of the apparatus are measured. But the thing is, that nowhere in the QM calculations a physical description of the measurement apparatus has been taken into account ! The vacuum state, literally being the vacuum whose energy is *in principle* measurable (by some God like unmaterial observer, but hey that is quantum mechanics ).