# Redshift/blueshift and time dilation

• Quantumgravity
In summary, it is not possible to accurately calculate the time dilation of an object based solely on the redshift or blueshift of the light coming from it. This is because other factors such as relative speed, gravitational potential difference, and the expansion of space-time must also be taken into account. Without this additional information, the amount of time dilation cannot be determined conclusively. Further research and understanding of rapidities and the Doppler factor may provide more insight into this problem.

#### Quantumgravity

Would it be possible to calculate the time dilation of an object if you only knew how redshifted or blueshifted the light coming from the object was? For example, if you knew the wavelength was redshifted by a factor of 4, or by a certain number of meters, could you determine the time dilation of the object relative to you, the stationary observer?

doppler

Quantumgravity said:
Would it be possible to calculate the time dilation of an object if you only knew how redshifted or blueshifted the light coming from the object was? For example, if you knew the wavelength was redshifted by a factor of 4, or by a certain number of meters, could you determine the time dilation of the object relative to you, the stationary observer?
Those who teach relativity with human face start with the radar echo, and continue, in a logical order, with the adition law of velocities, the Doppler Effect and optical aberration. I recomend
Asher Peres, "Relativistic telemetry,"
Am.J.Phys. 55, 516 (1987)
Peter Kenny, "Time dilation in special relativity: an alternative derivation,"
Physics Education 41(4), 334-336 (2006).
I find the last paper very transparent.
Being intertested in the field, I will answer to any further question you may have,concerning the subject, which could clarify my own bewilderment! Have a look please at the thread I started "Radar echo and clock synchronization".

With rapidities, the answer is easily demonstrated.

The Doppler factor (not to be confused with the Doppler shift) is $$k=e^\theta$$, and the time-dilation factor $$\gamma=\cosh\theta=\frac{1}{2}(e^\theta+e^{-\theta})$$.
So, $$\gamma=\frac{1}{2}(k+k^{-1})$$. Similarly, it's easy to write down the velocity using $$v=c \tanh\theta$$.

Robphy, thank you for the formula. I will need to do some research to fully understand it however.

I enjoyed the reading very much. I understand the math a bit better now.

Quantumgravity said:
Would it be possible to calculate the time dilation of an object if you only knew how redshifted or blueshifted the light coming from the object was? For example, if you knew the wavelength was redshifted by a factor of 4, or by a certain number of meters, could you determine the time dilation of the object relative to you, the stationary observer?
When we measure a source that emits red or blueshifted light we have to take the following three factors into account:

1. The relative speed between the emmitted and absorbed source.
2. The gravitational potential difference between the emmitted and absorbed source.
3. The expansion of space-time.

So if we only know the actual red- or blueshift then we cannot conclusively determine the amount of time dilation.

MeJennifer said:
When we measure a source that emits red or blueshifted light we have to take the following three factors into account:

1. The relative speed between the emmitted and absorbed source.
2. The gravitational potential difference between the emmitted and absorbed source.
3. The expansion of space-time.

So if we only know the actual red- or blueshift then we cannot conclusively determine the amount of time dilation.
Explain please what do you mean by expansion of space-time and what is its connection with the discussed problem. Thanks.

I think MeJennifer means that if the object we were talking about was something like a galaxy, and the space between us and the galaxy was expanding, it would stretch the wavelenth of light along with it. I read about that in a Scientific American article. I'm not sure how the photons are able to 'stick' to the fabric of space-time, but somehow they do, and if space-time stretches, so does light.