The vacuum in QFT. What is it. Why have it. Does everyone believe in it?

[Mike2]

The frames are not accelerating through the space they occupy, so the Unruh effect does not apply. The acceleration relative to each other, caused by the cosmic expansion of space, is not factored into the Unruh effect at all, which is strictly about single frames moving through space. Look it up.

I beg to differ. All that is necessary to apply the Unruh effect is to have one frame accelerating with respect to another. Nothing is said about how far away that accelerating frame is from the inertial frame. We can imagine that our local inertial frame extends to infinity (along with its vacuum state). Then if some distant galaxy is accelerating with respect to that frame, we should be able to apply the Unruh effect to derive a temperature for that galaxy.

Those distant galaxies are not moving with respect their local space. But they are accelerating with respect to us. Since space is uniformly expanding (an assumption), distant galaxies recede from us, and with time they are farther away and thus receding even faster as time passes (since they are getting farther away as time passes). This is an acceleration. That acceleration is very slow, and the Unruh effect is probably negligeble. But we observe other accelerations effects, namely the expected increase in red shift as galaxies recede ever faster with time. So if this acceleration is real for other observable effects, it should be applicable to the Unruh effect as well.

So universal expansion gives us a rate of the increase in volume of space with time. And this is connected to the vacuum energy through the Unruh effect. Or has anyone come up with another theory to connect spacetime with vacuum energy (I mean apart from correlating observables, no theory there, that's just putting in a relationship by hand). Thanks.

 

[Haelfix]

"I beg to differ. All that is necessary to apply the Unruh effect is to have one frame accelerating with respect to another"

Yes so long as the frames are local with respect to one another, then you can convert to Rindler coordinates and apply the Unruh analysis.

This is not true for distant objects (there is no concept of a vacuum, in spacetimes without well behaved far fields and timelike killing vectors). Hence the Unruh effect cannot be applied to FRW cosmologies, its out of its domain of applicability.

 

[ueit]

Can you point out to me such experimental evidence, rather than theoretical constructs?

We have experimental evidence that mass (gravity) produces a time delay. Can you recover this from QM's equations?

But this is not where it "failed", which is the central argument of this thread. Thermodynamics does not "fail" just because it is a statistical theory. If it does, your combustion engine was designed using flawed principles and you have a tough time explaining why it works. Something fails if it cannot describe a phenomenon, not a hypothetical scenario that no one has verified. The latter is called 'speculation'.

If one claims that thermodynamics is a fundamental theory, then its incapacity to describe an atom can be seen as a failure even if the theory is still useful. An unstable particle/atom decays at a certain time after it is produced. I see QM's incapacity to predict this time point as a failure of the theory. It is usually argued that this uncertainty is somehow fundamental but I've never seen a good reason for that. I find this position unscientific.

 

[Mike2]

"I beg to differ. All that is necessary to apply the Unruh effect is to have one frame accelerating with respect to another"

Yes so long as the frames are local with respect to one another, then you can convert to Rindler coordinates and apply the Unruh analysis.

This is not true for distant objects (there is no concept of a vacuum, in spacetimes without well behaved far fields and timelike killing vectors). Hence the Unruh effect cannot be applied to FRW cosmologies, its out of its domain of applicability.

A couple points to consider. First, there needs to be some distance between the reference frame of the inertial measuring device and the accelerating body whose thermal state is being measured. This is necessary simply because particles need to be transferred from the accelerating object to the measuring device (through some distance) to even detect the thermal state of the accelerating object. The question then is how much distance is too much between the inertial measuring device and the accelerating objects whose thermal state is being measured? I suppose all that is required is that the measuring device be able to receive particles from the accelerating objects. And we certainly receive particles from distant receding galaxies.

Second, this ever faster recession velocity (with time) ultimately results in a cosmological event horizon where particles are receding faster than light. And some have calculated the usual thermodynamics of temperature and entropy associated with this horizon. There always seems to be an acceleration associated with horizons. Either you have the Rindler metric with a horizon that is a flat plane. Or you have the accelerating reference frame due to gravity in black hole event horizons, etc. And so there should be an acceleration for the cosmological event horizon.

And third, the FRW metric was not specifically ruled out in the calculations I saw for the Unruh effect. It was not even used. If it were in that context, it would be used to show that distant places were by definition accelerating referece frames compared to any measuring device.

R.M. Wald's book that calculates the Unruh effect states that particles are an undefined entity where the acceleration cannot be definitively defined. This can be due to very fast changes in acceleration or where various observers would not see the acceleration as the same. But universal expansion is the same everywhere for every observer. So a consistent acceleration can be defined. And we do have a very hot temperature and particle creation associated with the initial inflationary expansion of the universe. This seems to argue that expansion is associated with the energy density of thermal states. And this is exactly the kind of evidence we would use to confirm a quantum gravity theory. So I tend to think that the first thing a quantum gravity theory would predict is the relationship between expansion and the vacuum energy.

 

[ZapperZ]

We have experimental evidence that mass (gravity) produces a time delay. Can you recover this from QM's equations?

But QM says nothing regarding this. So there's no way to check if it fails here. Does the lack of description implies that it failed, or that it has not been formulated yet. Can you recover the band structure of a semiconductor from General Relativity? Using your logic, GR has failed!

If one claims that thermodynamics is a fundamental theory, then its incapacity to describe an atom can be seen as a failure even if the theory is still useful. An unstable particle/atom decays at a certain time after it is produced. I see QM's incapacity to predict this time point as a failure of the theory. It is usually argued that this uncertainty is somehow fundamental but I've never seen a good reason for that. I find this position unscientific.

See my point above. Use ANY other existing theory and derive the phenomena that currently only have a well-developed and tested description via QM. Does that mean that all of the other theories have failed, or have been falsified just because they can't? This is what you're trying to push using this kind of logic against QM.

Zz.

 

[ueit]

We have experimental evidence that mass (gravity) produces a time delay. Can you recover this from QM's equations?

But QM says nothing regarding this. So there's no way to check if it fails here.

I admit, I have no training in QFT. I've studied only non-relativistic QM as a part of my chemistry degree so I apologize if I make stupid claims. However, it seems to me that the time delay should appear as a prediction in QFT if it is correct (for example I'd expect that a pion would be predicted to decay faster when alone and the speed of its decay would be correlated with the matter density around it as predicted by GR)
Now, are you saying that it is only a computability problem? My understanding is that QM and GR are mathematically incompatible so there is no chance of QM predicting gravity in its present formulation, but I could be wrong.

Can you recover the band structure of a semiconductor from General Relativity? Using your logic, GR has failed!

Give me the mass/energy distribution at Planck level and we'll see if GR cannot predict the semiconductor properties. If GR fails then it fails. I'm not arguing that GR should replace QM or that it's better, but for the necessity of finding a deterministic model capable of giving an explanation for quantum phenomena.

See my point above. Use ANY other existing theory and derive the phenomena that currently only have a well-developed and tested description via QM. Does that mean that all of the other theories have failed, or have been falsified just because they can't? This is what you're trying to push using this kind of logic against QM.

No other theory (except maybe GR, see my answer above) is relevant. Every other branch of science reduces to these theories. Chemistry doesn’t claim to explain a particle’s decay, it points to QM for that. The problem is that QM is the final theory at this moment and therefore it is in a unique position. We cannot analyze its validity by comparing it with other theories. If it cannot explain a decay event we need to search for a new theory that can. That’s how science works.

 

[ZapperZ]

I admit, I have no training in QFT. I've studied only non-relativistic QM as a part of my chemistry degree so I apologize if I make stupid claims. However, it seems to me that the time delay should appear as a prediction in QFT if it is correct (for example I'd expect that a pion would be predicted to decay faster when alone and the speed of its decay would be correlated with the matter density around it as predicted by GR)
Now, are you saying that it is only a computability problem? My understanding is that QM and GR are mathematically incompatible so there is no chance of QM predicting gravity in its present formulation, but I could be wrong.Give me the mass/energy distribution at Planck level and we'll see if GR cannot predict the semiconductor properties. If GR fails then it fails. I'm not arguing that GR should replace QM or that it's better, but for the necessity of finding a deterministic model capable of giving an explanation for quantum phenomena.
No other theory (except maybe GR, see my answer above) is relevant. Every other branch of science reduces to these theories. Chemistry doesn’t claim to explain a particle’s decay, it points to QM for that. The problem is that QM is the final theory at this moment and therefore it is in a unique position. We cannot analyze its validity by comparing it with other theories. If it cannot explain a decay event we need to search for a new theory that can. That’s how science works.

I think you have a rather distorted view of why something is accepted to be valid, and when something is said to fail. We point to the fact that classical mechanics failed in some cases when there is empricial evidence in which classical mechanics PREDICT one way, and the emprical evidence results ANOTHER way.

QM says nothing about time dilation because that is not something it CAN. It is why relativistic effects were incorporated SEPARATELY into quantum mechanics! That is why we have "relativistic quantum mechanics"!

You example of "decay event" is puzzling. QM (via the Standard Model's weak interaction) is the ONLY theory that deals with such phenomena. To say that QM has failed implies that we have no clue on such processes since no other theories come even close.

So now, if we go by the criteria of when we can make a definitive statement on when something "failed", I again will ask you to point out where QM failed. If it isn't clear, I will emphasize that this evidence is the only thing that I care about.

Zz.

 

[ueit]

QM says nothing about time dilation because that is not something it CAN. It is why relativistic effects were incorporated SEPARATELY into quantum mechanics! That is why we have "relativistic quantum mechanics"!

First, I was speaking about GR time dilation, that is, time dilation produced by mass/energy. It seems that this effect cannot be incorporated in QM.
Sure, if you are careful enough when deciding what a theory should explain and what not, you could never falsify it. Like it or not the quantum particles have mass/energy and therefore are subject to gravitational interaction. If QM doesn't predict this interaction it cannot be correct, it is simple as that. Near a neutron star you could experimentally falsify it. Now, do you propose to wait until such an experiment is done before starting to develop another theory?

You example of "decay event" is puzzling. QM (via the Standard Model's weak interaction) is the ONLY theory that deals with such phenomena. To say that QM has failed implies that we have no clue on such processes since no other theories come even close.

QM cannot predict the exact timing of such an event, and given its probabilistic structure, never will. Now, what word would you use when a theory cannot predict an observed phenomenon which is clearly inside its domain even if perfect knowledge of the system is assumed?
Perhaps "failed" is too strong. Is "incomplete" better?

 

[ZapperZ]

First, I was speaking about GR time dilation, that is, time dilation produced by mass/energy. It seems that this effect cannot be incorporated in QM.
Sure, if you are careful enough when deciding what a theory should explain and what not, you could never falsify it. Like it or not the quantum particles have mass/energy and therefore are subject to gravitational interaction. If QM doesn't predict this interaction it cannot be correct, it is simple as that. Near a neutron star you could experimentally falsify it. Now, do you propose to wait until such an experiment is done before starting to develop another theory?

But I asked you before to use GR and arrive at the band structure of, say, GaAs, something that you are currently using in your electronics. What did you say? GR doesn't know how to deal with "Planck scale" stuff yet? Well tough! According to your logic, GR cannot be correct. Hell, classical mechanics and classical E&M can't be correct either because they can't describe even one of the most common family of material that everyone uses!

QM cannot predict the exact timing of such an event, and given its probabilistic structure, never will. Now, what word would you use when a theory cannot predict an observed phenomenon which is clearly inside its domain even if perfect knowledge of the system is assumed?
Perhaps "failed" is too strong. Is "incomplete" better?

I would strongly suggest you look for experiments that have the HIGHEST DEGREE OF CERTAINTY currently. In fact, some of them are held in such confidence that several of our fundamental constants such as "e" and "h" are obtained from those experiments. You will find that these are "quantum mechanics" experiments, in which the quantum description of the phenomena are so accurate and so robust that we rely on them. Now tell me how many GR experiments are even remotely close to such certainty?

I mean, these are not "speculative experiments" such as "near a neutron star"! How many observations do we have for those, and what is the degree of certainty there? You would compare that to how well we know the properties of a semiconductor so much so that we make USE of it daily?

I'm sorry, but this discussion is getting more absurd by the minute.

.. and I am STILL waiting for this "experimental evidence".

Zz.

 

[ueit]

But I asked you before to use GR and arrive at the band structure of, say, GaAs, something that you are currently using in your electronics. What did you say? GR doesn't know how to deal with "Planck scale" stuff yet? Well tough! According to your logic, GR cannot be correct. Hell, classical mechanics and classical E&M can't be correct either because they can't describe even one of the most common family of material that everyone uses!

I didn't say that "GR doesn't know how to deal with "Planck scale" stuff", I said that we don't have the required data, that is, the detailed mass/energy distribution in a semiconductor so that we could apply GR to it. We need to know first how the gravitational field of a quark and an electron looks like before we can ask GR for an answer. If we input the correct data and GR gives wrong answers then GR fails.

I would strongly suggest you look for experiments that have the HIGHEST DEGREE OF CERTAINTY currently. In fact, some of them are held in such confidence that several of our fundamental constants such as "e" and "h" are obtained from those experiments. You will find that these are "quantum mechanics" experiments, in which the quantum description of the phenomena are so accurate and so robust that we rely on them. Now tell me how many GR experiments are even remotely close to such certainty?

Why do you assume that I advocate GR against QM? I'm not saying GR is better, only that QM is limited and we have enough evidence to start looking for a better theory. I'm not saying that theory has to be GR. Even so, I remember reading on Spacedaily.com (one year ago or something like that) that GR was better verified than QM using a pair of pulsars. I don't have the reference though, but I don't think this type of comparison is even relevant. QM makes great predictions when working on flat spacetime but fails in other situations. Now, you say that strong gravity is outside of QM's regime but who establishes this regime in the first place? The universe is as it is with lots of gravity around. A correct theory of our universe must not fail in this situation. You asked for experimental evidence. I said time delay near a massive body, or the photon's curved path when passing a massive body. Now, something happens with those particles. If not QM then what theory should explain these observed facts at a quantum level?

What accuracy has QM when predicting the decay of a radioactive atom? 1% probability it will happen in the next 1000 years. That's really impressive! And it's not that we lack the necessary data, even perfect knowledge (at least from QM's point of view) doesn't help. True, there is no other theory to give better predictions but this is exactly the reason why the physicists should start looking for one. I know, you said that this is not a failure because QM is probabilistic, but let's not hide behind words. Probability implies lack of knowledge, in other words, failure to describe exactly the object of study.

 

[ZapperZ]

I didn't say that "GR doesn't know how to deal with "Planck scale" stuff", I said that we don't have the required data, that is, the detailed mass/energy distribution in a semiconductor so that we could apply GR to it. We need to know first how the gravitational field of a quark and an electron looks like before we can ask GR for an answer. If we input the correct data and GR gives wrong answers then GR fails.

Why do you assume that I advocate GR against QM? I'm not saying GR is better, only that QM is limited and we have enough evidence to start looking for a better theory. I'm not saying that theory has to be GR. Even so, I remember reading on Spacedaily.com (one year ago or something like that) that GR was better verified than QM using a pair of pulsars. I don't have the reference though, but I don't think this type of comparison is even relevant.

Riiiiiiight. This is what you call "evidence". For some odd reason, I have been wasting my effort in trying to explain to you the "degree of certainty" of various experimental FACTS.

I believe that your inability to comprehend the importance of such things rather dictates that I would be wasting my time pointing out to other well-verified, high-degree-of-certainty type experiments, such as the neutron drop experiments that showed evidence of quantum mechanical gravitational effects. And unlike you, I didn't read it off "sciencedaily".

And oh, before you keep harking towards the "probabilistic" nature of QM, maybe you ought to troll some more of PF and see all the various formulation of QM in terms of Bohm's Pilot Wave and MWI. I'm would bet you the people who advocates such view of QM would completely disagree with you on that pictures.

I am still waiting for this "experimental evidence" that showed where QM fails.

Zz.

 

[DrChinese]

... because QM is probabilistic, but let's not hide behind words. Probability implies lack of knowledge, in other words, failure to describe exactly the object of study.

You have dived off the deep end again, by use of the words "describe exactly". What theory "describes exactly" anything? There are none!

1. A theory is a useful description of some domain of patterns/pattern exceptions. QM is useful. (GR is useful too.) You somehow describe QM in terms of failure, which is laughable. If a better theory were found tomorrow, that would hardly lessen the benefit of QM because its utility would still be evident. If a better theory comes along, so be it. There are strong indications that cannot happen, because QM incorporates the Uncertainty Principle (which has significant experimental support).

2. GR and QM operate in different domains. They are not competing theories. Both are useful, and both can co-exist without any difficulty whatsoever. There is an open questions of whether a so-called Theory of Everything can be found which includes elements of both QM and GR. So we'll see...

But in the meantime, your attempt to compare these two great theories is sadly misplaced.

 

[Farsight]

Any good references on the meaning of the vacuum in QM? What were you taught in school? What made sense? What did not? What did you discuss with the other graduate students? Any paradoxes regarding the vacuum? Any thoughts on why string theory is inundated with them? Bring em on. I want to hear.

I can't give any good references. But for what it's worth: I've always been bothered by the separation of particles and vacuum. I have this Einstein "pure marble" preference which goes way back, and says that particles aren't billiard balls made out of hard stuff, they're topological, like knots. But they're made out of "properties" rather than string, so they have no surface or edge. Which means there aren't any distinct gaps in between to label as "vacuum". So when people talk about "the vacuum", I kinda go blank, and think Are we talking about space?