Proper Frequency
Mike Helland
object like a rod, but for an electromagnetic wave is there such a
thing as proper frequency and proper wavelength?
Obviouslly, a red-shifted light wave is going to have a frequency that
appears lower because the growing amount of space in between, but is
there a "proper" frequency for the light, that represents its frequency
indepedent of the doppler shift?
Dirk Van de moortel
"Proper" is an attribute given to a quantitative property
of an observer as measured the observer himself.
Since light is modeled as something no observer can
be travelling with, no attribute of light can carry the
attribute 'proper'.
See also the answers given in sci.physics.
Dirk Vdm
David Park
news:1135106736.0...@g47g2000cwa.googlegroups.com...
I am going to wade in and see if I am corrected by my betters. Proper time
for a particle is the time measured by a clock traveling with the particle.
But we can't arrange for any clocks, or frequency meters to travel with a
light wave. So it couldn't have a proper frequency. But I suppose we might
define a proper frequence of zero.
I would also like to ask a related question. Special relativity says that if
two observers moving relative to each other exchange light signals they will
both measure the same doppler shift. This is often used in proofs and
covered by "the laws of physics are invariant and there are no preferred
frames." I would like to know if there are any experimental tests of the
reciprocal doppler shifts?
David Park
dj...@earthlink.net
http://home.earthlink.net/~djmp/
markp...@wideopenwest.com
Since the proper length and proper time are defined as the length of an
object and the amount of time that passes in a comoving frame, we can't
really define a proper frequency for an electromagnetic wave. If we
talk about an observer comoving with the wavefront, his proper time is
zero and we can't define a frequency (not to mention the fact that
frequency doesn't really mean much when you're travelling with a wave
front, and the wave would carry zero energy from a comoving frame).
Another way of looking at it is by defining "poper energy" in the same
way as for any object, that is to say, the length of the energy
momentum four vector - which is the mass energy. Obviously, EM waves
(or photons if you prefer) have no mass, so E = pc, and the length of
the four vector is zero, so in a comoving frame (if such a thing could
meaningfully exist) the light would have no energy or frequency.
Igor Khavkine
The answer is No. One way to see it is the following. A time-like
vector in Minkowski space-time selects a preferred frame (coordinate
system) in which the t-axis points along the vector and the spacial
coordinates are orthogonal to it. In this special coordinate system,
the t-component of the vector is called its proper length (or proper
energy/mass when talking of a 4-momentum vector).
OTOH, a light-like vector points along one of the directions contained
in the light cone. But the light cone is unvariant under all Lorentz
transformations. Thus, a light-like vector is simply unable to pick a
preferred coordinate system, so we can't make any "proper" measurements
of a photon's 4-momentum.
Hope this helps.
Igor
Murat Ozer
> I know there is such a thing as proper length and proper time for an
> object like a rod, but for an electromagnetic wave is there such a
> thing as proper frequency and proper wavelength?
Since photons cannot be brought to rest there is no rest frame for
them. This means that proper frequency and proper wavelength
does not make sense for photons. However, a local energy and
hence local frequency as opposed to laboratory energy and
frequency can be defined for them. See, for example, Landau and
Lifshitz 'The Classical Theory of Fields', p.249 after Eq. 88.5, and
Okun et al. arXiv:physics/9907017 'On the Interpretation of the
Redshift in a Static Gravitational Field'.
Regards,
Murat Ozer
Tom Roberts
> Special relativity says that if
> two observers moving relative to each other exchange light signals they will
> both measure the same doppler shift. This is often used in proofs and
> covered by "the laws of physics are invariant and there are no preferred
> frames." I would like to know if there are any experimental tests of the
> reciprocal doppler shifts?
I know of no such experiments in the literature, and I have been looking
for experimental tests of SR (I am slowly working on updating the FAQ
page on experimental tests of SR).
I believe the common usage of police radar guns could be turned into a
~1% verification of this (two approaching cars each measure the other's
speed).
It might be possible to turn Vessot's "gravity probe A" experiment into
a test of this (they used a Doppler-canceling technique that might be
usable, there would be thorns...).
It might be possible to turn Pound and Snider into a test of this for
gravitational redshifts (I believe they interchanged source and detector
at the top and bottom of the tower and got appropriate results).
There are surely other possibilities, but those are the ones that come
to mind.
Tom Roberts tjro...@lucent.com