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Wo Wala Moiz
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Will the probability density of a wave function be affected by length contraction due to special relativity?
The interpretation of the wave function as a probability density in position space comes from non-relativistic quantum mechanics so doesn’t apply when relativistic effects like length contraction are significant. For that you will need the methods of quantum field theory.Wo Wala Moiz said:Will the probability density of a wave function be affected by length contraction due to special relativity?
Is it necessary? This question relies on two physics basics- that particles have a wave function whereupon they have a range of probability of positions and momentum over a set volume, and that in high accelerations/velocities, length contraction takes place.berkeman said:Please post the valid references that you have been reading about this question. Thanks.
So how does the interpretation differ in QFT?Nugatory said:The interpretation of the wave function as a probability density in position space comes from non-relativistic quantum mechanics so doesn’t apply when relativistic effects like length contraction are significant. For that you will need the methods of quantum field theory.
Note that QM is based on the Schrodinger equation, which is manifestly non-relativistic. The equation has a first order time derivative and second order spatial derivatives. That rules out compatibility with relativity.Wo Wala Moiz said:So how does the interpretation differ in QFT?
So do the quantum fields experience length contraction?PeroK said:Note that QM is based on the Schrodinger equation, which is manifestly non-relativistic. The equation has a first order time derivative and second order spatial derivatives. That rules out compatibility with relativity.
By contrast, the Dirac equation is the upgraded relativitistic equation for the electron.
Full-blown QFT is a different approach altogether. With quantum fields replacing single particle wave functions.
Try to look it up, PF encourages users to look for themselves and show some intent to answer their question by themselves. Try something some search prompt like "Lorentz transformation for quantum fields" for example. That's what is asked when we ask for valid references. It also avoids multiplying the effort.Wo Wala Moiz said:So do the quantum fields experience length contraction?
Well, there’s no wave function to interpret. As @PeroK says, it’s a completely different approach.Wo Wala Moiz said:So how does the interpretation differ in QFT?
The question makes no sense. A field isn’t a thing that can contract.So do the quantum fields experience length contraction?
Nothing experiences length contraction. It's a coordinate effect. Like experiencing being looked at from a different angle.Wo Wala Moiz said:So do the quantum fields experience length contraction?
Why not?Nugatory said:The question makes no sense. A field isn’t a thing that can contract.
The fields of quantum field theory are not the classical field lines that you're thinking about here.Wo Wala Moiz said:Why not?
If we were to visualise the gravitational "force" as being made of field lines, the length contraction caused from the perspective of a moving observer would (intuitively, and of course I could be wrong) cause the field lines along the direction of travel to move closer together.
Newton's law of gravity is not compatible with relativity. Again the statement of the law is manifestly non-relativistic. That's why Einstein developed the general theory of relativity. In that theory, the laws of physics are coordinate independent. The basic concepts of time dilation and length contraction are subsumed into coordinate independent laws, which do not depend on a particular class of reference frame.Wo Wala Moiz said:Why not?
If we were to visualise the gravitational "force" as being made of field lines, the length contraction caused from the perspective of a moving observer would (intuitively, and of course I could be wrong) cause the field lines along the direction of travel to move closer together.
Then we are not doing relativity, because in relativity, gravity is not a force, and there is no such thing as "field lines" for gravity.Wo Wala Moiz said:If we were to visualise the gravitational "force" as being made of field lines
No, it would make them APPEAR to move closer together. You seem to still feel that things "experience" length contraction, whereas in reality this is purely an observational artifact. It is, as @PeroK said, like looking at something from a different angle. The thing itself doesn't change, just your observation of it does.Wo Wala Moiz said:Why not?
If we were to visualise the gravitational "force" as being made of field lines, the length contraction caused from the perspective of a moving observer would (intuitively, and of course I could be wrong) cause the field lines along the direction of travel to move closer together.
I put quotation marks around "force" for a reason. It is a pseudoforce like centrifugal force.PeterDonis said:Then we are not doing relativity, because in relativity, gravity is not a force, and there is no such thing as "field lines" for gravity.
No, it is not a "pseudoforce" in GR, it is no kind of force at all and pretending otherwise isn't going to get you anywhere. Gravity in GR is space-time curvature. Period.Wo Wala Moiz said:I put quotation marks around "force" for a reason. It is a pseudoforce like centrifugal force.
Is centrifugal force a real force?phinds said:No, it is not a "pseudoforce" in GR, it is no kind of force at all and pretending otherwise isn't going to get you anywhere. Gravity in GR is space-time curvature. Period.
Not in GR it isn't.Wo Wala Moiz said:I put quotation marks around "force" for a reason. It is a pseudoforce like centrifugal force.
In GR, there is no such thing as "centrifugal force". You need to stop using concepts from Newtonian gravity.Wo Wala Moiz said:Is centrifugal force a real force?