Understanding Mass and Vectors in Quantum Mechanics: The Role of the Higgs Field

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  • #51
kye said:
Isn't it Stephen Hawking said information can't be lost even inside the event horizon? شركة تنظيف خزانات بالرياض

You mean the free Dirac field also use mass as parameter (from the kinetic-mass), without needing the Higgs? Won't this make it weigh less? But even for the Dirac equation, won't the symmetry would be lost if you introduce mass by force...



It's said that "mass tells spacetime how to curve... spacetime tells mass how to move".. so how do fields interact with geometry, what mathematical language do you use for the interface besides the General Relativity formula that makes it as given without giving the interaction details?

Then it doesn't make sense to contemplate how electrons don't have positions (before measurements) in the atoms yet have fixed mass? This is also ad hoc and the complete analysis can only be done in the quantum field theory interactions between the higgs field and leptics field via the higgs mechanism?
 
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  • #52
BruceW said:
no, it actually is the energy. It does not measure the energy. it is the energy. just like in F=ma, m is directly the mass, e.t.c. ##T_{\mu \nu}## is directly the energy (and those other things).

Bruce, just want to understand your context... do you consider spacetime as fundamental as force? Do you consider General Relativity to be describing real gravitational field?
 
  • #53
in GR, there is no gravitational field like there is in Newtonian gravity. Instead, stress-energy causes spacetime to curve (and the spacetime curvature tells matter how to move). There are forces between matter, and there is spacetime. In GR, there is no gravitational force, and this idea of spacetime curvature gives us Einstein's version of gravitation. So some object will both experience forces from other objects and the curvature of spacetime. So the motion of the object will be determined by the combination of both: forces from other objects and due to the curvature of spacetime. For example, a small charged object which is acted on by an electromagnetic force, and exists in a generally curved spacetime will have an equation of motion like this:
{d^2 x^\mu \over ds^2} =- \Gamma^\mu {}_{\alpha \beta}{d x^\alpha \over ds}{d x^\beta \over ds}\ +{q \over m} {F^{\mu \beta}} {d x^\alpha \over ds}{g_{\alpha \beta}}
So, the first term on the right hand side is due to the curvature of spacetime, and the second term is due to the electromagnetic force on the small object. Anyway, I hope this answered your question, I was not 100% certain what you meant about if I consider spacetime as fundamental as force.
 
  • #54
BruceW said:
in GR, there is no gravitational field like there is in Newtonian gravity. Instead, stress-energy causes spacetime to curve (and the spacetime curvature tells matter how to move). There are forces between matter, and there is spacetime. In GR, there is no gravitational force, and this idea of spacetime curvature gives us Einstein's version of gravitation. So some object will both experience forces from other objects and the curvature of spacetime. So the motion of the object will be determined by the combination of both: forces from other objects and due to the curvature of spacetime. For example, a small charged object which is acted on by an electromagnetic force, and exists in a generally curved spacetime will have an equation of motion like this:
{d^2 x^\mu \over ds^2} =- \Gamma^\mu {}_{\alpha \beta}{d x^\alpha \over ds}{d x^\beta \over ds}\ +{q \over m} {F^{\mu \beta}} {d x^\alpha \over ds}{g_{\alpha \beta}}
So, the first term on the right hand side is due to the curvature of spacetime, and the second term is due to the electromagnetic force on the small object. Anyway, I hope this answered your question, I was not 100% certain what you meant about if I consider spacetime as fundamental as force.

Thanks for the clarifications. I got your general point. But do you believe that space and time should truly be united as spacetime and this is not just for sake of modeling but is truly is fundamental like mass, acceleration where it is definite? By fundamental I mean not breakable into more constituent like temperature being statistical movement of the atoms?

Or let me rephrase my words so you'd understand my point. General Relativity is just a theory. Is it possible gravity can still be caused by a real field (such as weak, strong field) and General Relativity is due to the symmetry of the theory.. or more specifically being a gauge symmetry, the curvature is just due to the Lie group math and in the future there can be a new math where curvature is not necessary (akin to our QED being perturbative now and in the future a non-perturbative QED possibly existing?)

Or in short, do you believe like the others that we can only access reality by the math and physics is about the math and one shouldn't care what is truly behind the math because it is no longer physics.. like we don't need to know what is really the wave function (like Bohmian or MWI) as what is important is just a way to model systems via ensemble?
 
  • #55
right now, I believe that GR is 'truly fundamental'. I don't think there is a more fundamental principle which can explain GR. Like you say, statistical mechanics is a more fundamental way to explain things like temperature. And I think that GR is as fundamental as it gets, there is no underlying theory which is more fundamental than GR.

Having said that, if they ever create a quantum theory of gravity, then yes that would be more fundamental, because it would unify quantum principles with gravity. But since they are no-where near making such a theory, at the moment, GR is as fundamental as it gets.
 
  • #56
So you agree with the following analogy?

wave function deals with real Hamiltonian energy (in addition to others like spin)
spacetime curvature deals with real energy, stress and momentum.

wave function and spacetime are just models of reality and we don't even know if they are really physical or literal.

Do you agree with the analogy? Inside Planck scale, these two theories break down so it's good to contemplate on QM and GR at the same time to make our mind get used to roads to a final elegant theory of quantum gravity.
 
  • #57
the energy eigenvalues of the wavefunction are the possible results of a measurement of energy. That's why quantum concepts are different to the non-quantum concepts. If the wavefunction happens to be an energy eigenstate, then you can say that the system actually has energy of some definite value. But otherwise, the system does not have a definite energy.
 
  • #58
The original question has been resolved and this thread is now degenerating into philosophy.

This is the QM forum, not the existentialism forum. Some discussion about QM interpretations is permitted, but this current discussion is not even an interpretations discussion and is therefore not in keeping with the forum.
 
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