# Quantization of Energy

1. Jun 9, 2005

### SeReNiTy

Since energy only exists in quanta, does this mean mass is also quantized according to einstein's famous equation?

2. Jun 9, 2005

### dextercioby

Who said energy is always quantized/exists only in quanta...?

Daniel.

3. Jun 9, 2005

### SeReNiTy

I thought this was what plank discovered, damn i must of been very wrong!

4. Jun 9, 2005

### dextercioby

Not wrong,just unaware of the fact that a Hamiltonian operator may have a continuous spectrum as well.

Daniel.

5. Jun 9, 2005

### SeReNiTy

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?

6. Jun 9, 2005

### dextercioby

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 and i've never seen the latter in any of the books i've read or lectures i've taken.

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.

EDIT:Yes,Pete,of course we do,i just blanked for a while...

Last edited: Jun 9, 2005
7. Jun 9, 2005

### SeReNiTy

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!

8. Jun 9, 2005

### pmb_phy

Huh??? Of course we have mass in GR. Mass is fully described by that tensor. Recall what Einstein said
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.

9. Jun 9, 2005

### dextercioby

Here's Einstein's equation

$$E^{2}=\vec{p}^{2}c^{2}+m^{2}c^{4}$$.

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.

10. Jun 9, 2005

### James Jackson

The energy is quantised in some systems, not all. Planck quantised the energy levels for stable electromagnetic equilibrium modes inside a cubical cavity - analogous, in a way, to the quantised energy levels of a 3D harmonic oscillator. Note 'stable equilibrium modes', which are of course a function of wavelength, box dimensions and 'quantum numbers' $n_{1,2,3}$. The quantisation comes as a result of the system being looked at.

11. Jun 9, 2005

### James Jackson

Indeed, he (or she) who unifies GR and QM gets a big pat on the back!

12. Jun 9, 2005

### pmb_phy

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 at

http://www.imath.kiev.ua/~fushchych/papers/1968_1.pdf

13. Jun 9, 2005

### James Jackson

Do you know any of the mathematics behind QM? Measureable quantitied (position, momentum, energy) are represented by certain mathematical objects, called operators. They 'operate' on the wavefunction to describe it's evolution when a measurement of that operator is performed.

What DexteroIforgettherest is saying is that you can not construct one of these operators which when applied to the wavefunction, yields the mass.

Essentially you can realise this as the mass is a fundamental part of the wavefunction description (the Hamiltonian, which is an operator which decribes the total energy of the system, contains the mass as a fixed quantity, so the system is defined, in part, by the mass).

14. Jun 9, 2005

### SeReNiTy

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?

15. Jun 9, 2005

### dextercioby

@Pete:It was an interesting reading,but i dunno,the fact that such theories have not transpired into books and college textbooks makes me kinda skeptic.

People are being taught worldwide that spin angular momentum is the perfect example for a quantum observable with no classical analogus,which comes from viewing rotation symmetry through the eyes of group theory representations and the axioms of quantum mechanics.

Since,classically,mass is neither a Lagrangian nor a Hamiltonian observable,i dunno what to think...

Daniel.

Last edited: Jun 9, 2005
16. Jun 9, 2005

### dextercioby

We can very simply merge GR & QM,it's just that we don't get a sound theory.
If it's ever done,maybe a lot of new things may come into the arena,not only the quantum description of mass.

Why wouldn't space-time be quantized ?

Daniel.

17. Jun 9, 2005

### SeReNiTy

Well if mass is quantised then space can only curve at certain values, no?

Hmmm, if space is quantised, can that explain HUP? For example i'm thinking if space only exists in certain quanta, then the infomation holds must exist in finite values, hence a compromise between the infomation on momentum and displacement must be made? Is this reasoning wrong?

18. Jun 9, 2005

### dextercioby

Not wrong,just speculative.I won't pursue it.

Daniel.

19. Jun 9, 2005

### James Jackson

Surely the HUP is explained by the non commutativity of the two observables, unless, of course, you're looking for a 'deeper' (metaphysical?) explaination.

20. Jun 9, 2005

### SeReNiTy

Nope, i'm looking for a physical explanation and trying to derive certain princples from physical reality not maths...