The Line That Seperates QM and Relativity?

[3CKPilot]

What is the consensus about the line that separates objects governed by quantum mechanics and those governed by relativity? What property(ies) do physicists look at when determining if something is governed by relativity or quantum mechanics? Is it a firm line or is it rather blurred?

 

[Demystifier]

The consensus is that such a line does not exist at all. Some phenomena may be both relativistic and quantum.

 

[sirchasm]

Check out relativistic electronic devices on the Googler

 

[Naty1]

Some areas are blurred..others quite distinct...

Try reading Wikipedia Quantum Mechanics especially http://en.wikipedia.org/wiki/Quantum_mechanics#Relativity_and_quantum_mechanics

to get a feel for the circumstances...some things, like black body radiation,electron oribits and entanglement have no good classical explanation...in other areas there is some overlap...see,also, the correspondence principle a few sections further along...

 

[LaserMind]

What is the consensus about the line that separates objects governed by quantum mechanics and those governed by relativity? What property(ies) do physicists look at when determining if something is governed by relativity or quantum mechanics? Is it a firm line or is it rather blurred?

I believe that Bohmian interpretaion fails the special relativity analysis, because his pilot wave is required to travel faster than light.

 

[vanesch]

As per special relativity, there are no serious problems. Well, there are some mathematical difficulties, but special relativity + quantum theory and some assumptions of particles leads to quantum field theory (that's what Weinberg tells us in his book). Now, quantum field theory is mathematically not 100% sound, but it does work in practice. So for the working physicist, special relativity and quantum theory go together. It is true that some *interpretations* of quantum theory violate the spirit of relativity (such as Bohmian mechanics), but the purely unitary quantum theory can be made entirely Lorentz invariant.

It is even true that, as per an extension of this, quantum theory also works fine in a *given* general-relativistic spacetime. If you *give me* the spacetime, even if it is not a flat minkowski spacetime such as in special relativity, one can still apply locally quantum field theory.

However, the serious problem comes in when one considers quantum fields to be the sources of spacetime curvature, as it should be. One then runs into the "problem of time". Quantum theory requires time to be a real parameter (which plays a role in the evolution of the quantum state), but through the action of gravity, time itself should be treated as an operator acting upon the quantum state. This gives one a very difficult problem, because about all of dynamics in quantum theory is based upon the fact that there exists a unitary operator which maps the state psi(t1) onto the state psi(t2): psi(t2) = U(t1,t2) psi(t1).

The derivative of U wrt t2 is the hamiltonian, which is supposed to be a hermitean operator.

However, if time itself is not a real number anymore, but an operator, this blows up the most basic structure of the quantum formalism.

People have tried to get around this, and that's the whole domain of quantum gravity, but I'm out of my depth there.

 

[Demystifier]

I believe that Bohmian interpretaion fails the special relativity analysis, because his pilot wave is required to travel faster than light.

This is a very common misconception about special relativity. The truth is that special relativity, by itself, does not forbid velocities faster than light. The best known counterexample is a tachyon - hypothetic particle obeying special relativity and moving only faster than light.

Concerning the Bohmian interpretation, it can be formulated in a completely relativistic form:
http://xxx.lanl.gov/abs/0811.1905 [accepted for publication in Int. J. Quantum Inf.]

 

[Demystifier]

It is true that some *interpretations* of quantum theory violate the spirit of relativity (such as Bohmian mechanics), but the purely unitary quantum theory can be made entirely Lorentz invariant.

Would you say that THIS
http://xxx.lanl.gov/abs/0811.1905
variant of Bohmian mechanics violates the spirit of relativity?

 

[FredericGos]

This made me think (again) about Bekenstein-Hawking radiation. I've read numerous times that they/he 'combined quantum field theory with classical general relativity and predicts that black holes radiate through particle emission'.

In light of what you wrote Vanesh, how did he do it?

I know this result is widely accepted as true, but without a widely accepted theory of quantum gravity, how did he circumvent the problems you mention? Did he somehow invent a model that is ONLY valid in the specific context and that everybody can adhere to?

Just curious and something I've thought about numerous times, but never asked ;) Sorry if i somehow hijacked the thread.

 

[Demystifier]

However, if time itself is not a real number anymore, but an operator, this blows up the most basic structure of the quantum formalism.

Would you consider
http://xxx.lanl.gov/abs/0811.1905
to be a first step?

 

[Demystifier]

This made me think (again) about Bekenstein-Hawking radiation. I've read numerous times that they/he 'combined quantum field theory with classical general relativity and predicts that black holes radiate through particle emission'.

In light of what you wrote Vanesh, how did he do it?

I know this result is widely accepted as true, but without a widely accepted theory of quantum gravity, how did he circumvent the problems you mention? Did he somehow invent a model that is ONLY valid in the specific context and that everybody can adhere to?

Just curious and something I've thought about numerous times, but never asked ;) Sorry if i somehow hijacked the thread.

The Hawking radiation also suffers from a sort of the problem of time. Namely, in curved spacetime the notion of quantum particles depends on the choice of the time coordinate. Thus, the existence of Hawking radiation seems to depend on the choice of time. It is usually interpreted that Hawking radiation is an observer dependent concept, but such an interpretation is far from being completely satisfying.

Furthermore, there is an even more serious problem with Hawking radiation, because it seems to violate unitarity of quantum mechanics (the so called black-hole information paradox). It is widely believed that this problem cannot be solved without an explicit theory of quantum gravity.

 

[FredericGos]

Furthermore, there is an even more serious problem with Hawking radiation, because it seems to violate unitarity of quantum mechanics (the so called black-hole information paradox). It is widely believed that this problem cannot be solved without an explicit theory of quantum gravity.

How come then that Hawking radiation is so widely accepted? And again, since we don't have 'an explicit theory of quantum gravity', how can hawking even begin to speak about things in the domain that GR and QM have in common (very high gravitational field & very small distance) ? Is it just because we actually CAN do it and that the results are somewhat full of holes (no pun intended ^^) and conflict in some parts with GR or QM?

 

[Fra]

What is the consensus about the line that separates objects governed by quantum mechanics and those governed by relativity?

I guess this question belongs more to the BTSM section but I personally think a much more constructive and interesting question is to ask what unites them.

There are various non-mainstreamd thinkers sniffing in this direction.

See for example "Why things fall" by Olaf Dreyer, he has some ideas ha labels "internal relativity",

"...In internal realtivity matter and spacetime cease to exist as distinct entities, rather, they arise simultaneously from an underlying quantum system. It is through the emergent matter degrees of freedom that geometry is inferred. We have termed our program Internal Relativity to stress the importance of looking at the system from the point of view of an internal observer. We argue that special relativity is then a natural consequence of this viewpoint. The most important new aspect of Internal Relativity involves how gravity appears..."
-- http://arxiv.org/PS_cache/arxiv/pdf/0710/0710.4350v2.pdf

He has not taken any major steps in that paper but he lines out a viewpoint that is better than the average paper IMHO.

I don't share his reasoning all the way but I think some parts are good. One idea is that relativity does not just apply to spacetime transformations, it can also apply to internal transformations, and at that point interesting connections to quantum mechanics and the microstructure of matter becomes closer.

It may well be a deeper principle that unites not only SR but also GR first principles with some of the QM first principles.

/Fredrik

 

[Demystifier]

How come then that Hawking radiation is so widely accepted? And again, since we don't have 'an explicit theory of quantum gravity', how can hawking even begin to speak about things in the domain that GR and QM have in common (very high gravitational field & very small distance) ? Is it just because we actually CAN do it and that the results are somewhat full of holes (no pun intended ^^) and conflict in some parts with GR or QM?

Ultimately, the question "Why Hawking radiation is so widely accepted?" belongs to sociology, not physics. But, in my opinion, the main physical reason is the fact that various variants of the Hawking effect have been derived in MANY different and seemingly inequivalent ways. Each of these derivations has its own weaknesses, but it is hard to explain why all these different approaches lead to the same final result, unless this final result is actually correct (even if the derivations of it are not). For a brief overview, see, e.g., the Introduction in
http://lanl.arxiv.org/abs/gr-qc/0502074 [Phys.Rev.Lett.95:011303,2005]

 

[FredericGos]

But, in my opinion, the main physical reason is the fact that various variants of the Hawking effect have been derived in MANY different and seemingly inequivalent ways.

ah, ok. That makes sense. I didn't know that others have reproduced the result.

 

[jamesmaxwell]

I think there is no boundary between Relativity and QM.
Any physical thing is both quantum mechnical and relativistic.

But in case we analysis an object, for our convenience, we can assume some physical law not follow QM or Relativity but classcial mechnics' laws which are not right more. In General, CM is more easy and simple to treat object.

If a particle's velocity is low, we can use CM instead of Relativity. If mass is so light, we can also exclude quantum mechanical effect and just discuss object by CM law.
It's possible cause classical mechanics is good approximation to real world.

I guess you deceive these kinds of approximation as boundary between QM and Relativity.
To treat quantum mechnical and relativistic effect at once is sooooo difficult and never ouccurs unless you study QFT. That's why we generally consider only one of them.

It's so awkward and impossible that physical law changes depending on obecject's speed or mass.

 

[vanesch]

Would you say that THIS
http://xxx.lanl.gov/abs/0811.1905
variant of Bohmian mechanics violates the spirit of relativity?

I have to say that I've got too many other things to do than to study your paper, sorry. Such things take time when done properly. When I was saying that Bohmian mechanics was violating the spirit of relativity, I was talking about the standard BM with the non-local quantum potential. I'm not saying either that the problem is unsurmountable or anything.

 

[vanesch]

This made me think (again) about Bekenstein-Hawking radiation. I've read numerous times that they/he 'combined quantum field theory with classical general relativity and predicts that black holes radiate through particle emission'.

In light of what you wrote Vanesh, how did he do it?

I know this result is widely accepted as true, but without a widely accepted theory of quantum gravity, how did he circumvent the problems you mention? Did he somehow invent a model that is ONLY valid in the specific context and that everybody can adhere to?

I'm not an expert on this, but - in as far as I understand how this is done - Hawking radiation is nothing else but Unruh radiation, as applied to a classical solution of a black hole.

Now, Unruh radiation is something rather weird, and can even be found in flat spacetime. It comes about by doing quantum field theory in an accelerated coordinate frame. I don't know the details, honestly, but the thing comes down to the following: if you transform the vacuum state as seen in an inertial frame, into the Rindler frame (the frame of an accelerated observer in flat spacetime), then this shows up as a state with a thermal population of particles. This comes about because of the time-varying doppler shift that one gives to each of the modes of the vacuum state.

I think you can read such a derivation here: http://arxiv.org/abs/quant-ph/0401170
But - as I said - don't ask me the details, I'm no expert.

 

[LaserMind]

I'm not an expert on this, but - in as far as I understand how this is done - Hawking radiation is nothing else but Unruh radiation, as applied to a classical solution of a black hole.

Now, Unruh radiation is something rather weird, and can even be found in flat spacetime. It comes about by doing quantum field theory in an accelerated coordinate frame. I don't know the details, honestly, but the thing comes down to the following: if you transform the vacuum state as seen in an inertial frame, into the Rindler frame (the frame of an accelerated observer in flat spacetime), then this shows up as a state with a thermal population of particles. This comes about because of the time-varying doppler shift that one gives to each of the modes of the vacuum state.

I think you can read such a derivation here: http://arxiv.org/abs/quant-ph/0401170
But - as I said - don't ask me the details, I'm no expert.

Well, a collapsing wave function spread over a large space area collapses FTL. In fact it collapses instantly everywhere and ignores special relativity. But the particle could have been found a great distance from where it was actually found. So how can it manage to do that? ummmm...

 

[Ilja]

I believe that Bohmian interpretaion fails the special relativity analysis, because his pilot wave is required to travel faster than light.

No, the wave function does the same as it does in any quantum theory, namely to follow the Schroedinger equation of that theory.

The nonlocality is caused by the fact that the wave function is a function on the configuration space, not on usual space. The QM probability current is nonlocal as well.

Of course, there is a conflict between BM and fundamental relativity. But BM is a realistic explanation of quantum theory, and relativity has no such explanation (using the EPR-Bell notion of realistic explanation). I'm a realist, therefore I prefer realistic explanations, as far as they are available. I'm not a dogmatic - if there would be no possibility for a realistic explanation, I would possibly even give up realism. But in a situation where such a realistic explanation is already well-known, I see not the slightest reason to give up realism.

 

[Dmitry67]

Of 13 interpretations, http://en.wikipedia.org/wiki/Interpretation_of_quantum_mechanics#Comparison
7 are realistic and only 4 are not.

 

[Bob S]

Look at my recent post under the Klein Gordan equation. The negative pion in an atomic orbit of titanium was relativistic, and I had to use a relativistic form of the reduced mass calculation.

 

[feynmann]

I believe that Bohmian interpretaion fails the special relativity analysis, because his pilot wave is required to travel faster than light.

Per John Bell, any quantum theory must be non-local, so not just Bohmian interpretaion fails the special relativity, even Copenhagen interpretation fails the SR. Any quantum theory must fail the SR

 

[Demystifier]

Per John Bell, any quantum theory must be non-local, so not just Bohmian interpretaion fails the special relativity, even Copenhagen interpretation fails the SR. Any quantum theory must fail the SR

Wrong! Per John Bell, any quantum theory must be non-local, but it may still save special relativity. See, for example,
John Bell, Speakable and Unspeakable in Quantum Mechanics, Sec. 22.4