# Why can't their be zero-energy at the atomic scale

1. Jan 9, 2010

### noblegas

I know because E=(n+1/2)*h-bar*omega , and n is an integer , with the integers ranging from zero, to all positive values. Photons are said to be massless physical quantities and according Einstein's theory of special relativity (or general relativity) mass and energy are equivalent. So if a photon is massless, then why wouldn't the energy for a photon be zero? I know that in vacuum states, that their are still oscillations occurring, so technically there is no vacuous state ; is that the explanation for why there are zero energies states at the atomic level? Bose einstein condensate , says that an energy state can get close to a temperature equivalent to the absolute value of zero but not exactly at absolute zero. Could n0n-zero temperature be the explanation for a non-zero energies. Why do oscillations at the atomic level never cease?

Last edited: Jan 9, 2010
2. Jan 13, 2010

### noblegas

I really thought that I asked a straightforward question

3. Jan 13, 2010

### ZapperZ

Staff Emeritus

Zz.

4. Jan 13, 2010

### noblegas

Okay, I got my question answer about why photons are massless but I still don't understand why subatomic particles cannot have zero energy. Is it because electrons don't crash into the nucleus of an atom.

5. Jan 13, 2010

### ZapperZ

Staff Emeritus
The energy STATE of each situation is different and very dependent on the geometry of the situation. You also have to deal with one consequence of QM, which is the HUP. If you think that something will have less and less energy by making it moves even less, then you're confining it to a smaller region of space. At some point, the HUP kicks in and the entity can acquire a large energy (see de Boer effect in the specific heats of noble gasses).

Zz.

6. Jan 13, 2010

### humanino

Energy (outside general relativity) is defined up to a constant. By definition, zero energy is the vacuum. Particles are excitations of fields, and carry a certain amount of rest mass and a certain amount of kinetic energy, with the relativistic $E^2=p^2+m^2$ (with units such as the speed of light is equal to 1). So, a photon without rest mass could in principle have a vanishingly small energy. In practice, we always have a finite resolution for our detectors, so we cannot detect photons below a certain energy. If we theoretically insist to measure energies down to zero, we would find that the number of photons below a certain energy (integrated from zero to any finite value, no matter how small) is infinite. This is an example of "infrared (and collinear) divergence". Such infrared divergences are interpreted as real : in fact, we have to take into account the resolution of our detectors and make corrections to compare various experiments with different radiative corrections.

So the simple statement is that even in pure quantum electrodynamics, there is a cutoff in the lowest energy measurable, corresponding to the resolution of our detectors. It's not so much that the theory is inconsistent when we allow for zero energy photons, rather it's an unphysical situation which would be impossible to achieve experimentally.

7. Jan 13, 2010

### noblegas

So we have not yet developed the right detectors to detect and observed photons with zero energy?

8. Jan 13, 2010

### ZapperZ

Staff Emeritus
Do you not know what "unphysical" mean?

Zz.

9. Jan 13, 2010

### noblegas

Yes I do. But humanino said that we are in a situation were in a situation where we cannot experimentally detect particles with zero mass. By the same token, strings would be considered unphysical because our accelerators and detectors are not sophisticated enough to detect and observed such phenomena currently at such scales.

10. Jan 13, 2010

### humanino

Hold on, I detect photons with zero mass right now, with me eyes ! I meant that we cannot detect particles with an arbitrarily small energy in a finite amount of time/space. I hope my comments are not too confusing either. Radiative corrections are quite a tricky business.

11. Jan 13, 2010

Staff Emeritus
I think the issue of photons with undetectably low energies is not terribly helpful in answering the original question, which has to do with the minimum energies of quantum mechanical systems. It's a bit of a side track (albeit an interesting one).

12. Jan 13, 2010

### humanino

The reason I pointed in that direction is (apart from personal background) because I believe a photon in a cavity is about as simple a quantum system as it comes. It involves only QED, is almost the exact same as the harmonic oscillator, and one can easily conceive mental experiments. The OP shows an understanding of the HO energy spectrum including its constant term, and then directs the question to photons.

Otherwise, I'm not sure how to proceed with this question. One could go into criteria for the discreteness of the spectrum for compact operator. For now, I'm pretty much running out of steam, but I'm quite open to read an alternative approach to the original question. In particular, I did not want to prevent the development of Zz's approach (de Boer effect in the specific heats of noble gasses). I am not familiar with it all, and would not be able to feed this direction.

13. Jan 13, 2010

### Mentz114

This is the Hamiltonian for a system with no energy

$$\mathcal{H}=0 + 0$$

( The second zero is the interaction term )

14. Jan 14, 2010

### Count Iblis

The Casimir energy can be negative in certain geometries. The question is if the Casimir energy can be larger in magnitude than the total mass of the atoms at the boundary.