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Since energy only exists in quanta, does this mean mass is also quantized according to einstein's famous equation?
Ok the other day i heard they did experiments with a neutron that verified gravitational energy was indeed quantized, hence the neutron at the lowest graviational potential energy existed a certain distance above the ground...now would mass also exist in quantized levels?dextercioby said:Not wrong,just unaware of the fact that a Hamiltonian operator may have a continuous spectrum as well.
Daniel.
Hmmm, is there a problem with my reasoning? Step aside from the maths for a second and can you tell me is it wrong to think mass is quantised as well if energy is quantised, after all the two are related by a equation we all know!dextercioby said:There are tricks with mass generation in the Higgs mechanism,but that's one thing, claiming that mass is quantized (hence attributing a densly defined selfadjoint linear operator to it) is something totally different.
Usually,we see mass as in input parameter in QFT.In GR,we don't have mass,but the energy-momentum 4 tensor.That's the little bit i know.I won't comment on any experiments,it's not my domain.
Daniel.
Huh??? Of course we have mass in GR. Mass is fully described by that tensor. Recall what Einstein saidIn GR,we don't have mass,but the energy-momentum 4 tensor.
Mass is not a component of this tensor. One integrates the momentum density over the object whose mass we seek and then we divide by the speed of the object. The result is mass.The special theory of relativity has led to the conclusion that inert mass is nothing more or less than energy, which finds its complete description in a symmetrical tensor of second rank, the energy tensor.
I've seen the term "mass operator" many times. However that kind of thing I never learned and it appears over my head. There is an article on this point atdextercioby said:As i said,there's no QM observable for mass.
Ah i see now, so this is the problem why QM cannot merge with GR...dextercioby said:Here's Einstein's equation
[tex] E^{2}=\vec{p}^{2}c^{2}+m^{2}c^{4} [/tex].
As you may have heard,to this equation equation one cannot apply Dirac's quatization scheme (included in the second/quantization postulate),as it would give erroneous results when interpreting 0-th component of the probability current 4-vector.
So it shouldn't have to do with a possible mass quantization.As i said,there's no QM observable for mass.It is an input scalar parameter (or a finite dimensional square matrix,if one refers to quarks or some other particles) and just that.
I dunno what superstring theory has to say on a possible mass quantization.
Daniel.
We can very simply merge GR & QM,it's just that we don't get a sound theory.SeReNiTy said:Ah i see now, so this is the problem why QM cannot merge with GR...
So to unify GR with QM one has to come up with the maths that describes a quantised mass hence a quantised gravity field?
Well if mass is quantised then space can only curve at certain values, no?dextercioby said:Why wouldn't space-time be quantized ?
Daniel.
Nope, i'm looking for a physical explanation and trying to derive certain princples from physical reality not maths...James Jackson said:Surely the HUP is explained by the non commutativity of the two observables, unless, of course, you're looking for a 'deeper' (metaphysical?) explaination.
Hmmm, with QM i know its all about formulism and drop a physical interpretation, but i like have that interpretation since i understand better that way...James Jackson said:Unfortunately for you, QM is theoretical physics. The fact that it explains results with amazing accuracy doesn't make it 'physical'. People often forget that physics is only a model. It doesn't say "The world is like this because physics says so", it actually says "Physics is like this because the world says so". How one attaches physical meaning to the theories is generally the area of philosophy.