You're absolutely right, although we must qualify what that means a bit and give some examples.
The first example is the easiest, but the force carriers are real,
not virtual. If an atom emits a photon, it can propagate through space
and be absorbed by another atom, effectively conveying a force. The
frequency of the photon of course obeys the normal reference frame
rules for Doppler shifting. A beautiful example of the effects of
Doppler shifting of photons with very slow relative velocities between
the emitter and absorber is the Mossbauer effect, which takes advantage
of a wonderful property of solids in that a the recoil momentum against
the photon is picked up by the entire crystal lattice and not just by
the emitting atom. Photons are quite real, not just "conjectured".
If the force is carried by "virtual" photons (or other force
carriers like W bosons, Z bosons or gluons), then there is no single
frequency which characterizes the state of these particles. Instead,
they occupy localized regions of space and have wavefunctions that fall
off exponentially with distance. You still can doppler-shift them, but
the rules are now a little more complicated. Fourier showed that any
reasonably well-behaved function can be expressed as a sum of sine and
cosine functions. So you can take these arbitrarily shaped
wavefunctions for virtual particles and express them as sums of waves,
each with a different wavelength. Then the frequencies of each
component will obey the usual Doppler-shifting rules and you have to
add up the shifted components back to get the total. If you want to do
it all relativistically (which is the only way it makes consistent
sense, even with just photons in the mix), you have to do a Lorentz
transformation to view each of the components in the frame you'd like
to work in.
I always think it's easiest to do all the physics in one frame of
reference, but if you want to look at fields in other frames of
refernece, then the Lorentz transformation describes how to do this.
Tom
(published on 10/22/2007)
