Doppler effect for light - how can it be explained ?


by fsoica
Tags: doppler, effect, explained, light
jtbell
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#19
Feb5-12, 01:03 PM
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If one observer measures an object's momentum and energy as p and E, then another observer who is moving with velocity v with respect to the first observer measures the energy and momentum as

[tex]p^\prime = \gamma \left( p - \frac{vE}{c^2} \right)[/tex]

[tex]E^\prime = \gamma (E - vp)[/tex]

where [itex]\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}[/itex]

This is the Lorentz transformation for momentum and energy, similar to the L.t. for position and time which you may have seen if you've studied relativity.

For a photon, these two equations are equivalent, as you can see by substituting E = pc and E' = p'c.
murdakah
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Feb5-12, 01:48 PM
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Aaah I see. Its what I thought but just didnt have a basis to explain it on. Thanks a lot! :)
harrylin
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Feb5-12, 03:47 PM
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Quote Quote by Drakkith View Post
Is there something wrong with posting a link to a website that causes you to question something in science? It seems obvious to me that this isnt a deliberate attempt to advertise the site or anything.
Yes that is not allowed, as any link has an effect on such things Google ranking. Thus I also once got a warning (and this explanation) when I referred to a site that the administrators don't want linked.
harrylin
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Feb5-12, 03:58 PM
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Quote Quote by fsoica View Post
tks. for your reply.
I don't even think of hoping tounderstand the relativistic Doppler effect, since relativity is not one of my forte's.
The relativistic approach only "tweaks" the classical one, the one I have trouble grasping.
If light speed is a constant regardless the reference frame, I understand the energy of a photon and so, its frequency, is not. This is, I think, the difficulty for the non-scientist, to understand the photon as a relative entity, to grasp the reality of a light photon, a quanta, being a variable quantity. How come a "green" photon in a reference frame could become red in another one ?

Assuming one understands relativity, it's ok. It's acceptable (I'm guessing here, of course).

But what becomes of the classical effect ? How could I explain this one in layman's terms ?
You are perfectly right: as you say, the relativistic approach only "tweaks" the classical one. The successful classical model on which relativity is based is that of light as a vibration of an invisible medium, and the classical Doppler effect as well as the relativistic corrections rely on that model of "light waves", similar to sound waves. Classically the Doppler equations for sound and light are identical. With that model, perhaps the best way to view a photon is as a kind of wave packet: a wave pulse of limited dimensions. That doesn't change the Doppler effect.

In laymen's terms, just as with the sound of the horn of a train passing by, also the colour of the light that you receive is affected by the velocity of the source as well as by your own velocity. And the tweaks of relativity make that it is always as if there is a light medium that is in rest with respect to the reference frame that you use; only the relative velocity matters for the Doppler calculation.
James_Harford
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Feb5-12, 04:17 PM
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Quote Quote by murdakah View Post
Sorry to necro this old thread, but ive been wondering the same thing. I understand the regular doppler effect so dont go on about that. My problem is with regards to light doppler shift.
According to relativity, light's speed is always c in every inertial reference frame, so how is it possible that it imparts less or more energy because of realative motion?
This is particulary difficult when bring particle nature into account.
If you understand the regular doppler effect, then you can apply that knowledge to the relativistic doppler effect as experienced by any one particular inertial observer. Within that observer's frame of reference, light waves are analogous to sound waves in air provided there is no wind! Anything you can conclude about the change in frequency and wavelength of a moving source of sound has its equivalent for light waves. Einstein's great insight was that any other observers moving at constant speed relative to the first will also find themselves "at rest in the medium".

Edit: I should mention that the analogy applies to frequency and wavelength. The energy of the light photons is the frequency times Plank's constant. Why so, is a question to be answered elsewhere.
Drakkith
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Feb5-12, 04:36 PM
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Quote Quote by harrylin View Post
Yes that is not allowed, as any link has an effect on such things Google ranking. Thus I also once got a warning (and this explanation) when I referred to a site that the administrators don't want linked.
Whoa! I made that post way back when I was but a fresh faced PFer new to the site. Now I am a grizzled old PFer with 5k+ posts under my belt and understand the rules much better. But you are correct in your post, such sites are not allowed to be linked here on PF.


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