# Can the Doppler effect account for the increase in an object's energy with velocity?

I am aware that the relativistic mass can be expressed in terms of rest mass and momentum, which seems to be the canonical explanation, but I am looking at an alternative way of visualising the increase in mass of a system with velocity.

My understanding is that the mass of a system (e.g., a particle) is accounted for by the energy of the force-carriers within it (plus the Higgs interaction, but ignoring that for now).

These being considered as waves, it seems that the frequency of these waves would be observer dependent and that a moving observer would measure (at least conceptually) the frequencies of the forces in the system differently than a stationary observer. I also note that the energy changes would be asymmetric depending on the relative direction of motion of the force-carrying particle being observed. So a particle moving directly towards the observer at 0.5C would have double the frequency and therefore twice the energy, whereas one moving directly away at 0.5C would have two-thirds the frequency and the energy, and so the net change would be an increase in energy. (These figures may be approximations).

My question is whether this simple re-accounting of the observed wave frequency and energy in the system in the new inertial frame would lead to a correct calculation of the energy of the moving system, or whether there is something else going on?

I realise that the question "is it a good model" is a matter of opinion, so that is not what I am asking. What I am wondering is whether it is fundamentally flawed, and if so, why?

The relativistic mass is an obsolete concept. What SR (special relativity) states is a relation between the energy $E$ of a particle and its rest mass $m$ and momentum $p$, that is
$E^2 = p^2 c^2 + m^2 c^4$
The rest mass represents the internal energy of a particle due to motion and interactions of its constituents.

If you assume a massless particle, e.g. a photon, you have the nice relation
$E = pc$

As the momentum depends on the velocity of the particle with respect to the observer, the energy depends on the relative motion, of course.

However, seems you are referring to the relativistic Doppler effect which states that the frequency of a photon is depending on the relative motion of the source vs. the observer. As the energy and the frequency $\nu$ of a photon are related by $E = h \nu$, where $h$ is the Planck constant, the energy is depending on the relative motion as well.

The SR relations show consistency when describing a particle or a photon in different reference frames.

• Thanks. I was aware of the equations including momentum, but I was trying to get away from that and was wondering what the equations looked like using the wave model. In effect, I was looking for confirmation that the last paragraph you wrote was correct. In effect, your last paragraph (with a question-mark added) is my question. – rghome Mar 5 '18 at 16:21