# Is the existence of a photon relative? [duplicate]

If an observer passes an electron, in such a way that the observer is accelerating, the observer would see photons because accelerating charges induce electromagnetic waves. But from point of view of the electron or an inertial observer there is no magnetic field nor an acceleration which could 'produce' an electromagnetic wave.

So for the first observer there exists a photon but not for the second observer. How is this possible, are photons relative?

The short answer is yes. When one tries to generalise the theory of quantum fields in Minkowski spacetime to more general spacetimes, one finds that several familiar features of the theory are absent or ambiguous. For instance, it is not generally possible to unambiguously define a vacuum state when studying QFT in a curved spacetime. That is to say, a state which one observer sees as a vacuum, another may see as a thermal bath of particles.

Of course, the spacetime of concern here is just Minkowski spacetime, not a curved spacetime. However, the same problems one faces with QFT in curved spacetime appear also when studying QFT in flat spacetime in some complicated coordinate system, such as accelerating coordinates. Minkowski spacetime in accelerating coordinates is sometimes called Rindler spacetime (although it is the same spacetime), and a lengthy QFT calculation reveals that if our system is in the vacuum state according to an inertial observer, then our accelerating observer will see a background of particles with a perfect black body energy spectrum, with temperature

$$T = \frac{\hbar A}{2 \pi c k_B} \,,$$

where $A$ is the magnitude of the proper acceleration. This is known as the Unruh effect.

Secondly electrons and photons are elementary particles and are described in a quantum mechanical framework, where everything is particles and interactions of particles.

The blanket term "observer" has to be defined in terms of interactions, in order to be able to write down the mathematics of the system.

For an electron to be accelerated , it has to interact with a field and lose energy emitting a photon, as an example, in this diagram it is the field of another electron with which the upper electron interacts and radiates a photon:

But from point of view of the electron

Here the lower electron may be considered to start in its rest frame.

The whole diagram is Lorenz invariant, and the only thing that will be changing if one goes to the center of mass of the other electron , is how the energy is supplied to the photons.

In general photons do not disappear in Lorenz transformations, they may increase or decrease in frequency, decrease to the point of huge wavelengths which means that the light beam emergent from zillions such photons may have a wavelength the size of the universe and in the limit represent a static field.

• Sorry, I do not follow. There is no need to accelerate the electron, OP is comparing the same electron in inertial vs accelerating frames (we can think of it as a field, if necessary). Lorentz transformations transform inertial frames into inertial frames, so they are of no help here. The question is essentially how QED explains "fictitious" radiation in accelerating frames. Does it assert that the number of photons is not an invariant? Commented Mar 22, 2017 at 23:39
• @Conifold In the classical framework to get radiation one needs acceleration, in the quantum mechanical underlying framework this is interaction, so not a classical acceleration of the whole system. I suppose that my underlying assumption is that one cannot have acceleration transfering energy unless it is broken down to interactions. In any case it seems that the conundrum may be solved only using the general relativity formalism, which I do not pretend to understand: Commented Mar 23, 2017 at 4:35
• arxiv.org/pdf/gr-qc/0507040.pdf Commented Mar 23, 2017 at 4:35