# Are forces subject to the doppler effect?

1. Aug 22, 2010

### kmarinas86

I know that photons hitting a solar sail can add energy to that sail.

I know that photons are gauge bosons.

I know that gauge bosons are thought to be the carriers of fundamental forces.

If a solar sail were gaining speed to a point where it reached relativistically with respect to the power source, I know that an observer on a solar sail would observe a reduction of the force on that solar sail.

Is not the same essentially true for any massless gauge boson?

It seems that the work done on the sail by previous photons reduced the amount of work that future photons coming from the same source and direction could add to it, that is, from the frame of reference of the sail.

It would seem that the actual amount of work done on the sail, from the frame of reference of the sail, would be less than the energy expended by the source which produced the photons.

Is this all correct?

2. Aug 22, 2010

### bcrowell

Staff Emeritus
It's true for any massless particle. It's also true for massive particles, although the amount of reduction would be different.

Yes, this is correct in an inertial frame that's momentarily co-moving with the sail (but not in the earth's frame).

You could define three frames: E = the frame of the earth, C = an inertial frame that's momentarily co-moving with the sail at some later time, S = a frame accelerating along with the sail.

In C, there is no mismatch between the sun's energy output and the work done on the sail, since the sun is emitting photons that are Doppler-shifted to a lower energy.

In S, we have much bigger issues with conservation of energy than the ones involved in the solar sail. For instance, the sun is rapidly gaining huge amounts of kinetic energy.

3. Aug 23, 2010

### Austin0

In the earth frame wouldn't the acceleration derived from the photonic reflection energy also drop off as the sail approached c ,?? to the point where there would be no measurable increase in v from further light reflection???
On the increase in the Sun's relative kinetic energy isn't this a sort of ubiquitous problem??? Inherent in any accelerating system from a relativistic perspective?
Or am I just not getting your point??