# A shot in the dark

1. Aug 6, 2013

### arnesinnema

The following is a shot in the dark.

Say we have two perfectly reflecting mirrors with equal mass. Which are perfectly parallel to each-other, initially at a ‘close’ distance of each other. Say that one photon is bouncing between these mirrors perpendicular to these mirrors. Also assume these two mirrors are places in an infinite large vacuum container which walls are cooled to absolute zero, i.e. the single photon bouncing between the two mirrors is the only photon within this container.
Than each time the photon is reflected by one of the mirrors it will apply some momentum however I would expect that since energy has to be conserved the increase in velocity of the mirrors has to be compensated for by the energy of the photon.

Than if this is correct this would result in a red-shift of the photon. Which could be interpreted as the photon being attracted by the mirror. Might this be what we know as gravity?

Regards Arne Sinnema

2. Aug 6, 2013

### Bill_K

No, it's just conservation of energy and momentum.

Note that if there really was for some reason an attraction between mirror and photon, the photon would be blue-shifted as it approached the mirror, then red-shifted as it moved away, the net effect cancelling out.

3. Aug 6, 2013

### Staff: Mentor

Definitely not. The redshift is larger the less mass the mirror has, the opposite of gravity.

4. Aug 6, 2013

### arnesinnema

hmmmm, it seems logical indeed that the redshift would increase with a decrease in the mass of the mirror. Okay, so no Nobel price this time then ;).

5. Aug 6, 2013

### Staff: Mentor

Not this time, but keep learning and thinking!

6. Aug 8, 2013

### arnesinnema

Gravity conserves energy?

However you might say that the role of gravity here is to conserve energy, i.e. when there would be no gravity than it seems to me there would be no reason why this single photon (with time going to infinity) could not bring both mirrors to lightspeed (assuming for now both mirrors have the same mass).

In other words since the accelaration of the object does lead to a red-shift of the photon, but this redshift is indeed inversely proportional with the mass of the mirror therefore another additional something has to be there so as to assure energy is conserved which we know as gravity.

Does this make sense?

7. Aug 8, 2013

### Leveret

The photon initially has some finite amount of energy, E. Even given an infinite number of reflections, the photon can transfer no more than E energy to the mirrors. This, the mirrors can ultimately have no more than E/2 kinetic energy each, as opposed to the infinite kinetic energy of a massive particle moving at the speed of light.

8. Aug 8, 2013

### arnesinnema

Flaw in thinking?

There's probably a flaw in my thinking. I'm assuming the energy transfer from photon to mirror ONLY depends on the surface of the mirror and that the photon does not know the mass of the mirror but ONLY sees the accelaration of the mirror surface.

But of course we should look at the microscopic scale between the photon and the (mirror) atom it impinges on. If the photon and atom together make sure that mass, energy and momentum is conserved than indeed there is no additional something (such as gravity) needed to correct things. I.e. is the total energy of the photon and atom before and after the reflection the exactly the same?