Understanding the Dressed Particle Approach to Quantum Field Theory

[spidey]

If there is uncertainty in energy,then there should also uncertainty in mass..is this correct?

if that is correct,since there are uncertainties in energy and mass,is it true that the gravity also has uncertainty..i.e.we cannot measure gravity accurately? Does gravitation also affected by uncertainty principle?

 

[meopemuk]

If there is uncertainty in energy,then there should also uncertainty in mass..is this correct?

if that is correct,since there are uncertainties in energy and mass,is it true that the gravity also has uncertainty..i.e.we cannot measure gravity accurately? Does gravitation also affected by uncertainty principle?

Yes, you are absolutely right. Gravity must be affected by the uncertainty principle just like any other force. However this doesn't fit well with the classical Einstein's general relativity. This is the main reason why nobody was able to build a quantum theory of gravity by "quantizing" general relativity.

 

[spidey]

Yes, you are absolutely right. Gravity must be affected by the uncertainty principle just like any other force. However this doesn't fit well with the classical Einstein's general relativity. This is the main reason why nobody was able to build a quantum theory of gravity by "quantizing" general relativity.

Why GR doesn't fit with UP? It should fit i think. GR also requires mass or energy for curved space-time.

 

[Dmitry67]

What I don't understand is why virtual particles, while they have some energy and momemntum (manifesting in the Casimir effect, for example), do not produce the gravitational field. The should be no difference how normal and virtual particles interact with the gravitons. However, if we assume that they do interfact, then to density of vacuum becomes too high and inconsistent with the observations.

 

[meopemuk]

Why GR doesn't fit with UP? It should fit i think. GR also requires mass or energy for curved space-time.

The distribution of mass in QM is probabilistic, i.e., it is described by a wave function or by a vector in the Hilbert space. Then the space-time curvature around this mass should be probabilistic too. Instead of usual c-number metric tensor components you should have some probabilistic quantities: quantum amplitudes or something like that. There can be no fixed curved space-time manifold, but some kind of "linear combination" of different manifolds. I think that nobody was able to build a successful mathematical formalism on these ideas. So, we do not have a quantum version of GR yet.

 

[meopemuk]

What I don't understand is why virtual particles, while they have some energy and momemntum (manifesting in the Casimir effect, for example), do not produce the gravitational field. The should be no difference how normal and virtual particles interact with the gravitons. However, if we assume that they do interfact, then to density of vacuum becomes too high and inconsistent with the observations.

This is just another confirmation that "virtual particles" and "density of vacuum" are completely unphysical notions. They are just mathematical artefacts of some ill-formulated theories and have no relevance to experimental observations. I wouldn't consider Casimir effect as an "experimental proof" of virtual particles.

 

[Dmitry67]

Well, there are 1000 ways of explaining the QM (and all they will be wrong, the only right thing is the mathematics behind it) but at least agree with me that QM is not mathematically compatible with the gravitation.

To be more precise, what is an energy density (not in QM sense but the gravitation sense) between the Casimir plates?

 

[spidey]

One more question related to UP..
what does UP tell about big bang?

 

[ueit]

The distribution of mass in QM is probabilistic

QM gives the probability to find a certain mass distribution. It does not make the ontological claim that mass distribution is fundamentally probabilistic.

 

[meopemuk]

QM is not mathematically compatible with the gravitation.

I would rather say that QM is not compatible with GR (theory) rather than with gravitation (physical effect)

To be more precise, what is an energy density (not in QM sense but the gravitation sense) between the Casimir plates?

My best guess is that energy density between Casimir plates is zero.

 

[meopemuk]

QM gives the probability to find a certain mass distribution. It does not make the ontological claim that mass distribution is fundamentally probabilistic.

Thank you for the correction. That's what I meant.

 

[Dmitry67]

I would rather say that QM is not compatible with GR (theory) rather than with gravitation (physical effect)

My best guess is that energy density between Casimir plates is zero.

Why?
Between plates energy density is LOWER then in a 'usual' vacuum

So if it is ZERO (for what distance between the plates?) then you have to assign a positive energy for a usual vacuum

 

[mn4j]

is it true that the gravity also has uncertainty..i.e.we cannot measure gravity accurately?

No! Uncertainty means we are unable to predict accurately NOT that we unable to measure accurately.

 

[meopemuk]

Why?
Between plates energy density is LOWER then in a 'usual' vacuum

So if it is ZERO (for what distance between the plates?) then you have to assign a positive energy for a usual vacuum

I just don't buy the idea that vacuum has any energy associated with it. Vacuum is just empty space (no particles), so the energy should be zero. If some theory tells otherwise, then there is a problem with that theory.

 

[Dmitry67]

>Vacuum is just empty space (no particles), so the energy should be zero

Ha-ha. It is not true in QM
And how would you explain the Casimir effect?
It is not a 'theory', it is an EXPERIMENT

 

[meopemuk]

>Vacuum is just empty space (no particles), so the energy should be zero

Ha-ha. It is not true in QM

There is a variant of quantum field theory, which does not require the presence of "vacuum energy". You can search the web for "dressed particle" or "clothed particle" approach.

And how would you explain the Casimir effect?
It is not a 'theory', it is an EXPERIMENT

I guess that the "dressed particle" approach should be able to provide the explanation (though I haven't seen any works in this direction). Also, take a look at

R. L. Jaffe, "The Casimir effect and the quantum vacuum", http://www.arxiv.org/abs/hep-th/0503158

 

[Dmitry67]

I know what a dressed particle is. So far I don't see how you can avoid a problem with energy in the Casimir effect.

Suppose you have 2 parralel plats on a distance 1mm. Mass of both plates is exactly 1kg.
Now you wait until very small but increasing Casimir force attracts 2 plates... faster and faster.

As they accelerate their mass and energy increases.
Now the question: from where the additional mass comes from?
Answer: from a vacuum.

 

[meopemuk]

I know what a dressed particle is. So far I don't see how you can avoid a problem with energy in the Casimir effect.

In the dressed particle approach there are no fluctuating particle-antiparticle pairs in the vacuum. The vacuum is a state where the number of (dressed) particles is strictly zero. The energy of this state is zero too.

Suppose you have 2 parralel plats on a distance 1mm. Mass of both plates is exactly 1kg.
Now you wait until very small but increasing Casimir force attracts 2 plates... faster and faster.

As they accelerate their mass and energy increases.
Now the question: from where the additional mass comes from?
Answer: from a vacuum.

I am not an expert on the Casimir effect, but I was always interested if somebody tried to advance a less exotic explanation of it? Something that does not involve "vacuum energy". For example, why the attraction cannot be explained by London dispersion forces (e.g., forces between induced dipoles on atoms) or something like that. Is there a 100% proof that regular explanations do not work and only "vacuum energy" explanation works.

 

[Dmitry67]

1
In the dressed particle approach there are no fluctuating particle-antiparticle pairs in the vacuum. The vacuum is a state where the number of (dressed) particles is strictly zero.

2 The energy of this state is zero too.

3
I am not an expert on the Casimir effect, but I was always interested if somebody tried to advance a less exotic explanation of it? Something that does not involve "vacuum energy". For example, why the attraction cannot be explained by London dispersion forces (e.g., forces between induced dipoles on atoms) or something like that. Is there a 100% proof that regular explanations do not work and only "vacuum energy" explanation works.

1 dressed particle = pure particle surrounded by the cloud of virtual particles.
2 why? QM does not define a vacuum energy, it can not be derived from any low-energy local experiment without gravity
3 well, just do it and get a noble prize :)
otherwise it sould like 'i don't like it'. Like people don't like QM, or Relativity and invent their own theories. Casimir effect is an old thing, lots of experiments, all consistent with QM

 

[meopemuk]

1 dressed particle = pure particle surrounded by the cloud of virtual particles.

In the dressed particle approach I am talking about

O. W. Greenberg, S. S. Schweber, "Clothed particle operators in simple models of quantum field theory", Nuovo Cim. 8 (1958), 378.

there are NO "virtual clouds". The whole idea of this approach is to avoid confusion and divergences associated with "virtual clouds"

2 why? QM does not define a vacuum energy, it can not be derived from any low-energy local experiment without gravity

In the dressed particle approach the vacuum state is an eigenstate of the full Hamiltonian with the lowest eigenvalue - zero. I think this is in full agreement with experiment: A particle counter in vacuum will never click. Any massive particle in vacuum moves with constant velocity along straight line, which indicates that the "gravitational field" is absent.