# Is the highest photon energy currently possible a Planck photon or based on space-time quantinization?

It makes sense that there could be an upper limit to the frequency/energy for individual photons if the universe as we know it is quantized.

But, the highest energy photons I've heard about have a frequency between $$10^{20} \ \text{Hz}$$ to $$10^{30} \ \text{Hz}$$. A Planck photon however would have around $$10^{35} \ \text{Hz}$$. If we assume a cosmological model wherein space-time is quantized to a fundamental metric such as a Planck length, is there any reason to think the highest possible energy of a photon would be higher or lower than that?

• The energy of a photon depends on the chosen reference frame, so it is not clear what you are asking. – A.V.S. Jun 21 '19 at 5:00
• Physics is invariant of the frame of reference though, so regardless of how you are moving, a photon will appear to move at the same speed, and space-time would still be quantized. The question is fundamentally related to what we assume as true of physics, so it doesn't really matter. Pick a frame of reference you feel comfortable with and use the same frame in both the Planck result and the other theoretical limitation, unless you have an argument for why none would exist. – askmathquestions Jun 21 '19 at 5:16
• A.V.S is talking about Doppler shift. – wcc Jun 22 '19 at 14:47

Due to Lorentz invariance, the spectrum of photon energy does not cut off, but goes all the way to infinity. So, photons much higher than the Planck energy would be possible.

Update: So, the notion of quantized spacetime is of course speculative at this point. It implies that there may be different ways in which one can try to do it. However, it needs to be consistent with our current understanding, which has been tested and shown to be working. One of these requirements is Lorentz invariance. So, unless we through out Lorentz invariance, any scheme to quantize spacetime that implies a violation of Lorentz invariance would not be correct.

Considering the role of photons in mediating force among particles, one can use the tried-and-tested quantum field theory calculations. Here one finds that integrals over what effectively comes down to the photon energy need to extend to infinity. If one were to introduce a cut-off for such an integral, the cut-off scale would appear explicitly in the result. If the cut-off is the Planck scale, the contribution of the Planck scale may be so small that it would not make an observable difference in observations that we are currently able to make. However, at the same time it also shows that there is no reason to introduce such a scale in the first place to match experimental observations. By implication, the Planck scale is at present only a hypothetical scale, one that cannot at present be observed in any experiments.

As a result, it becomes rather difficult to predict what the effect of some hypothetical scheme to quantized spacetime would be at some hypothetical scale. Our current understanding does not allow arbitrary modifications to the theories, unless we suspect that something is wrong somewhere.

• Is it possible that Lorentz invariance could be violated at values of $\gamma$ not yet achieved in controlled experiments? – garyp Jun 23 '19 at 11:28