The number of photons may change between inertial frames: a new "Unruh effect"

Let us work in semiclassical physics. Let us have a monochromatic laser beam which is reflected or is refracted by a small object (is scattered by the object). Let us assume that the object is smaller than the wavelength.

        laser beam

        ~~~~~~~~~~~~~~~~~~~

        ~~~~~~~~~~~~  ● object

        ~~~~~~~~~~~~~~~~~~~

                                          <o> measuring device

What kind of photons an observer may measure in the scattered light?

If the system and the measuring device are fixed in the laboratory frame, then the observer will see all oscillation of fields having the same frequency f as the laser. He will see photons whose energy matches the photons in the laser beam.

But let us then make the measuring device to move at a constant speed v relative to the laboratory frame.

The waveform close to the object has a complex form. The Fourier decomposition of the signal received by the measuring device will have many frequencies, some of them very high.

The observer may see a photon which has much higher energy than the photons emitted by the laser.

How do we interpret this? If the laser sends, say, one photon of energy E in a second, how can the observer see a photon with a much higher energy E'? Is energy conserved?

Seeing a high-energy photon has an extremely low probability, though.

We have discussed the analogous problem in the context of an accelerating laser, or an accelerating observer. There is no obvious way to match individual photons in emission to photons in absorption. We have called this problem the "real Unruh effect".

In purely classical physics there is no problem. Energy in a wave of frequency f can be transformed to energy in a wave of much higher frequency f'. It is quantization which poses the problem here.

The length scale problem is ubiquitous

We have been studying bremsstrahlung in the past weeks. The "length scale" problem is that an electron passing very close to a proton should classically emit photons of very high energy. What wipes away these photons? Our new observation in this blog post shows that a similar problem exists in very mundane scattering of laser light.