Redshift/blueshift and time dilation

[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?

 

[bernhard.rothenstein]

doppler

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".

 

[robphy]

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 $$v=c \tanh\theta$$.

 

[Quantumgravity]

Thanks, rothenstein. Your thread was enlightening.

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

 

[robphy]

In another thread, neutrino alerted us that part of the first edition of Taylor/Wheeler's Spacetime Physics is available at http://www.eftaylor.com/download.html#special_relativity
Rapidity is developed in part 3 of Chapter 1.

 

[Quantumgravity]

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

 

[MeJennifer]

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.

 

[bernhard.rothenstein]

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.

 

[Quantumgravity]

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.