# How Does Expansion Effect the Frequency of Light

1. Feb 21, 2012

### Staff: Mentor

I have a question. I've been told that expansion "stretches" the light out and causes the redshift. However, the frequency of the light is the number of oscillations in its fields per second correct? How does "stretching" the wave affect the frequency? I know that v=fλ is the equation relating frequency to wavelength, and that increasing the wavelength should decrease the frequency, but is that really all there is too it? Or is it due to the recession velocities similar to normal doppler shift? (Which, for an EM wave still doesn't make sense to me)

Perhaps a better question is how does red/blue shift (for whatever reason) change the frequency of the light? Is it simply in the math and the above equation? I can understand the doppler effect of sound, as each wavefront takes longer to arrive if something is heading away from you, and quicker if it's heading towards you, but I have a hard time understanding this effect on light.

Last edited: Feb 21, 2012
2. Feb 21, 2012

### salvestrom

the wavelength is the distance, in a straight line, between the start and end of a full oscillation. it can be measured from any point on the wave as long as the end is in the same place relatively speaking as the start point, just one oscillation over. stretching the wavelength is therefore a direct reduction in the number of oscillations in a second since the velocity is fixed.

3. Feb 21, 2012

### mathal

red and blue shift of light frequency in genera is analogous to Doppler in sound waves. The frequency is adjusted in precisely the same way as sound waves with the relative velocity being the factor determining the change in frequency. However with light to get a precise value especially when objects are moving at even a small fraction of the speed of light you need to use SR to adjust the frequency. With SR it doesn't matter whether the object is moving rapidly away or rapidly towards you, the effect is the same. There is a just a difference in velocity. SR treats the observer as not moving and ascribes the velocity to the other object. The effect is that the frequency is factored to a lesser value than it would be without SR.

The radar police use to catch speeders used the doppler effect on light reflected back from the vehicle to determine it's velocity-no SR is required because of the tiny relative velocities.
The light (radar frequency) from approaching vehicles will have a higher frequency than sent, receding vehicles will have a lower frequency. The difference in frequencies when 'played' together creates a pulse-the faster the pulse the greater the difference in velocity between the officer and the speeder.

I won't speculate on why red shift isn't quite so simple to explain in cosmological distances and times. I will say that the relative velocity of galaxies away from us appears to have been accelerating for 5 or 6 billion years. I don't think any definitive explanation of all aspects of the redshift of galaxies is absolutely accepted by many physicists. -It's an open question.
mathal

Last edited: Feb 22, 2012
4. Feb 22, 2012

### Bobbywhy

"Cosmological Redshift in FRW Metrics with Constant Spacetime Curvature"

By: Fulvio Melia

ABSTRACT

Cosmological redshift z grows as the Universe expands and is conventionally viewed as a third form of redshift, beyond the more traditional Doppler and gravitational effects seen in other applications of general relativity. In this paper, we examine the origin of redshift in the Friedmann-Robertson-Walker metrics with constant spacetime curvature, and show that—at least for the static spacetimes—the interpretation of z as due to the “stretching” of space is coordinate dependent. Namely, we prove that redshift may also be calculated solely from the effects of kinematics and gravitational acceleration. This suggests that its dependence on the expansion factor is simply a manifestation of the high degree of symmetry in FRW, and ought not be viewed as evidence in support of the idea that space itself is expanding.

See: arXiv:1202.0775v1

Last edited: Feb 22, 2012
5. Mar 2, 2012

### clamtrox

Assuming the universe is homogeneous and isotropic, then the energy density of photons drops like a-4 while their number density goes down as a-3 -> single photons energy decreases as a-1, where a is now the scale factor of the universe.

If you want to be less model-dependent, you can explicitly foliate the spacetime into 3 spatial and 1 temporal dimension (choose your coordinates) and then calculate the photon redshift in this frame, and you get something like
$1+z(t) = \exp \left[ \int^{t_0}_t dt \theta/3 \right]$
where theta is now related to the metric connection in the coordinates you chose.