Doppler Effect & Einstein's Theory: Explained & Proven?

[physicsignoramus]

Got to start somewhere...

Light is supposed to travel at c regardless of the motion of the source, right? Then how do you explain the Doppler effect? The shift in frequency should occur not because the wavelength changes, but because we are gaining or receding (c+v or c-v), and therefore percieve a different frequency.

In Einstein's example of a railway embankment, with simultaneous flashes of light at points A and B, there is an observer on the rail car midway between points A' and B' who sees one flash first because she is moving toward it, and the other flash second as she recedes from it. I don't understand why our observer would not have some tools with her, and notice that there is a Doppler shift on each of these two flashes, and do some simple additive and subtractive calcuations to verify that the two flashes did indeed occur at the same time, but were in motion relative to the observer. What am I missing? (a brain?)

I tried to find an explanation of DeSitters observations of binary stars that proves light travels at c regardless of the motion of the source, but no luck. Help? Other proofs?

Since my math is stale, I also tried to find a layman's explanation of the Maxwell-Lorentz equation and Lorentz transformation. Help?

 

[MeJennifer]

Light is supposed to travel at c regardless of the motion of the source, right?

Not supposed so, but a fact.

Then how do you explain the Doppler effect?

Consider object X and observer Y approaching each other. Object X sends light to observer Y.

With regards to the general Doppler effect: remember that light speed is not infinite, it takes time for a light beam to go from X to Y and because the distance between X and Y decreases while the light was going from X to Y the wavelength appears to be shorter for Y. Also the distance between X and Y has to be adjusted by relativistic length contraction since they are approaching each other.

With regards to the relativistic Dopppler effect: since X and Y approach each other each will measure relativistic time dilation in the other object, hence the frequency of the wave of the light sent from X and observed by Y is lower than as it was measured by X .

You can imagine that it gets really cute if X and Y accelerate toward each other with constant acceleration or even with non constant acceleration. Then calculating the frequency of the wavelength becomes a non-linear calculation. Imagine at t1 the speed was A, then at t2 the speed was B etc, so for each new t one has to calculate the time dilation.

 

[physicsignoramus]

Don't the effects of length contraction and time dilation cancel each other out?

 

[Doc Al]

Light is supposed to travel at c regardless of the motion of the source, right? Then how do you explain the Doppler effect? The shift in frequency should occur not because the wavelength changes, but because we are gaining or receding (c+v or c-v), and therefore percieve a different frequency.

The relativistic Doppler effect combines two factors: the "normal" Doppler effect plus time dilation.

In Einstein's example of a railway embankment, with simultaneous flashes of light at points A and B, there is an observer on the rail car midway between points A' and B' who sees one flash first because she is moving toward it, and the other flash second as she recedes from it. I don't understand why our observer would not have some tools with her, and notice that there is a Doppler shift on each of these two flashes, and do some simple additive and subtractive calcuations to verify that the two flashes did indeed occur at the same time, but were in motion relative to the observer. What am I missing?

The fact that the "moving" observer would see a Doppler shift does not change the fact that she measures the flashes to occur at different times according to her clocks.

Don't the effects of length contraction and time dilation cancel each other out?

Why would you think that?

 

[russ_watters]

Depends on what you mean by "cancel each other out". Obviously, they are different things so one can't make the other not exist, but they do interact in such a way as to make C always constant (or rather, C is always constant, so...).

 

[physicsignoramus]

So I am stretching a point here, but when an astronomer looks at a star that is 50 million light years away, and she is looking into the past 50 million years, does she ever calculate where that star would be today, 50 million years after the observed position? Do astronomers extrapolate in that fashion to the observable universe and estimate what the size of the universe is today? I know that the calculations for each of the billions of galaxies would be nearly impossible, but using the most distant observable galaxies in each sector (8 sectors? 32? 3200?) of the universe, maybe estimates have been made with this method? If I have strayed too much from the subject of relativity, please forgive. Something tells me it is not completely irrelevant to my question...probably fundamentally intertwined?

 

[BoTemp]

I'm not an astronomer, but I believe the answer to all those questions is yes. Relative velocity can be calculated by the doppler shift, and so position can be extrapolated. Look up Hubble's Law; it's a fairly straightforward application of this fact. I'm not sure if the size of the universe has been estimated, but I've seen estimates on total mass, and lifetime is fairly well known (13.7 billion).

Calculations have been done using GR to determine the overall http://en.wikipedia.org/wiki/Density_of_the_universe" of the universe.

 

[chroot]

Due to the finite age of the universe and the finite speed of light, we cannot (necessarily) see everything in the universe. What we see is in a sphere centered on us. The actual size of the universe may be much larger than the part of it that we can actually see. The universe may, in fact, be infinite in extent, but we'll never directly know what's outside our spherical observable universe.

- Warren

 

[BoTemp]

Due to the finite age of the universe and the finite speed of light, we cannot (necessarily) see everything in the universe. What we see is in a sphere centered on us. The actual size of the universe may be much larger than the part of it that we can actually see. The universe may, in fact, be infinite in extent, but we'll never directly know what's outside our spherical observable universe.

- Warren

Very true. In fact, gravitational effects mean we'd never be able to see the whole universe, just the http://en.wikipedia.org/wiki/Cosmic_light_horizon" , at least if we only viewed from Earth. Should be good enough though, nothing outside the observable universe affects our planet in any way.

 

[physicsignoramus]

Great replies. Thank you. I found an excellent description of the Michelson-Morley Experiment, and seem to be heading in the direction of the Maxwell-Lorentz equation.