Understanding Doppler Shift for Light in Special Relativity

In summary: Therefore, the wavelength and frequency of light can change in different inertial frames while keeping the speed of light constant. In summary, according to special relativity, the wavelength and frequency of light can change in different inertial frames while keeping the speed of light constant due to the invariance of the phase of the wave. The Doppler shift is a result of this invariance and explains the occurrence of redshift in stars.
  • #1
SteveDC
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How do Doppler shifts work for light if, according to special relativity, light is constant velocity for all observers? So if c is unchanged, then surely wavelength and frequency don't change.

I appreciate that I must be misunderstanding something, because redshift on stars occurs, but I am struggling to explain why.

Thanks in advance for any help :)
 
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  • #2
The frequency of a light wave corresponds to the time-like component of the wave 4-vector of a light wave, and components of 4-vectors are not invariant under non-trivial Lorentz transformations. More generally, energy is a frame dependent quantity. Why should wavelength and frequency of light waves be unchanged between inertial frames just because ##c## is unchanged between inertial frames? They can scale inversely under Lorentz transformations so as to cancel out any change in their ratio.
 
  • #3
## c=\lambda\nu## is the equation relating velocity and wavelength and frequency. So both can change while keeping c constant.

[edit. got it wrong first time]
 
  • #4
SteveDC said:
How do Doppler shifts work for light if, according to special relativity, light is constant velocity for all observers? So if c is unchanged, then surely wavelength and frequency don't change.
One thing which is the same in all rest frames is the phase of the wave. That is, for example, the wave crest always remains a wave crest. A typical wave is exp(i(kx - ωt), where the phase is kx - ωt, or equivalently since ω = ck, the phase is k(x - ct). This quantity must be an invariant.

Under a Lorentz transformation,

x' = γ(x - vt)
t' = γ(t - v/c2 x)

implying that x - ct just picks up an overall factor:

x' - ct' = γ(1 - v/c)(x - ct) = √((1 - v/c)(1 + v/c)) (x - ct)

Invariance requires that the wave vector k picks up the inverse factor:

k' = √((1 + v/c)(1 - v/c)) k

which represents the Doppler shift.
 
  • #5


I can understand your confusion about the Doppler shift for light in special relativity. It is a common misconception that the speed of light is constant for all observers in all situations. However, according to special relativity, the speed of light is only constant in a vacuum and for an observer in a stationary frame of reference.

When it comes to the Doppler shift for light, it is important to understand that it is not the speed of light that changes, but rather the perceived wavelength and frequency of the light. This is due to the relative motion between the source of the light and the observer.

For example, if a source of light is moving away from an observer at a high velocity, the perceived wavelength of the light will be longer and the frequency will be lower. This is known as a redshift. Similarly, if the source of light is moving towards the observer, the perceived wavelength will be shorter and the frequency will be higher, known as a blueshift.

This phenomenon occurs because the motion of the source of light affects the path that the light takes to reach the observer. In special relativity, this is known as time dilation and length contraction. The relative motion between the source and observer causes a difference in the time it takes for the light to reach the observer, resulting in a change in the perceived wavelength and frequency.

So, in short, the Doppler shift for light in special relativity is not due to a change in the speed of light, but rather a change in the perceived wavelength and frequency caused by the relative motion between the source and observer. I hope this helps to clarify your understanding of this concept.
 

1. What is the Doppler effect in special relativity?

The Doppler effect in special relativity is a phenomenon where the frequency and wavelength of light appear to change for an observer moving at a relative velocity. This is due to the time dilation and length contraction effects in special relativity.

2. How does the Doppler shift for light differ in special relativity compared to classical physics?

In classical physics, the Doppler shift for light is solely dependent on the relative velocity between the source and observer. However, in special relativity, the Doppler shift is also affected by time dilation and length contraction, making it more complex to calculate.

3. Can the Doppler shift for light be observed in everyday life?

Yes, the Doppler shift for light can be observed in everyday life. For example, the redshift seen in the light from distant galaxies is a result of the Doppler shift in special relativity.

4. How does the Doppler shift for light affect the perception of time and space in special relativity?

The Doppler shift for light affects the perception of time and space in special relativity by causing time to appear to pass at different rates for observers moving at different velocities. It also causes objects to appear contracted in the direction of motion.

5. How is the Doppler shift for light used in astronomy?

The Doppler shift for light is used in astronomy to measure the relative velocities of stars and galaxies. By analyzing the Doppler shift in the light from these objects, scientists can determine their distance and movement in the universe.

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