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Utwo
2009-Mar-20, 07:07 PM
I'm reading Relativity and Common Sense by Hermann Bondi, and at first he explained the Doppler effect when it comes to sound waves, which is pretty straight-forward for most post-high school people, but I'll explain what I think I know about it anyway:

http://i67.photobucket.com/albums/h298/cdesign_proponentist/dop1.gif

So, lets just say that the speed of sound is 2 units per second, and the emitter (the red dot) is emitting one pulse per second, while moving to the right at a speed of 1 unit per second (half the speed of sound).

In front of the emitter, the pulses are bunched together such that they're only one unit apart. Since the pulses move at 2 units per second, the listener on the right will hear the pulses every 0.5 seconds, or twice the frequency that they are emitted.

Behind the emitter, the pulses are spread apart such that they're three units apart. Since the pulses move at 2 units per second, the listener on the left will hear the pulses every 1.5 seconds, or 2/3rds the frequency that they are emitted.

I was surprised to find out that it isn't the same in reverse; that is, if the emitter is sitting still and the listeners are moving at 1 unit per second, the effect won't be precisely the same:

http://i67.photobucket.com/albums/h298/cdesign_proponentist/dop2.gif

In that diagram, the listener on the right is moving towards the light emitter at a speed of 1 unit per second. So, the relative velocity between this listener and the emitter is the same as the relative velocity between the emitter and the right-side listener in the first diagram. Therefore, one couldn't be blamed for thinking that, in this second diagram, the right-side listener would hear the pulses at the same frequency as the right-side listener in the first diagram: 1 pulse per 0.5 seconds.

However, that isn't true. Every second, the listener moves towards the left 1 unit, and the sound wave moves to the right 2 units. So, the relative velocity between the listener and the wave is 3 units per second in this second diagram. Since the sound waves are 2 units apart, the listener will hear a pulse every 2/3rds of a second.

This was counter-intuitive to me, but when I draw the diagram, I can see that it is true. What matters most is the relative velocity between the sound waves and the listener, and the distance between the pulses, not the emitter and the listener. The motion of the emitter only changes the distance between the pulses.

And this is made even more obvious when you consider super-sonic travel. If the emitter emits one pulse per second, but is moving faster than the speed of sound, then by the time it emits its second pulse, it will have traveled past the wave of the first pulse. So, the listener will actually hear the second pulse first. However, no analog of this is possible when the emitter is stationary and the listener is moving. No matter how quickly the listener moves towards the emitter, it can't hear the second pulse before the first pulse. It will always hear them in order. As the listener's speed approaches infinity, the time between the pulses, from the listeners point of view, approaches zero.

Now comes light.

The book goes on to explain that light doesn't work this way. With pulses of light waves, it doesn't matter which is moving; whether it's the emitter moving or the listener moving, or both, it doesn't matter. All that matters is the relative velocity between the emitter and the listener (or "seer" in this case).

I am having a difficult time grasping this. All the book seems to say about it is that sound wave propagation takes the medium (air) into account. Since light has no medium, the apparent lack of relativity between the emitter's motion and the listener's motion doesn't exist.

But this is a confusing explanation to me, because the medium doesn't seem to have anything to do with it. The waves still have to travel through space, whether there is a medium or not. If I were to re-interpret the above diagrams as pulses of light instead of sound, and emitters and listeners that move at 0.5c instead of half the speed of sound, then the result is exactly the same.

Now, I understand that, with relativity, space can be stretched and squashed. I suspect that the real explanation for this has to do with relativistic notions of space not being totally constant.

But the whole purpose of this book is to explain relativity in a way that makes sense to the layperson, and it seems weird that they would just move along with the assumption that space is somehow not constant; that is, to explain relativity by assuming relativity. I feel like I have a hump I have to get over before I can move on.

peteshimmon
2009-Mar-20, 10:54 PM
Well done! I did a thread a few years ago,
First glimmerings of Relativity where I
put a worked out description of how a
moving observer will see the same doppler
shift of light as fixed observers watching
the mover. Funnily enough I did not know
then that sound was different! I worked that
out a few months later.

I think it would make a great physics
demo. Play the sound of crossing bells
heard from a railway carriage as featured
in numerous films. Then mount the bells on
the train and listen while they pass at the
same speed. Seems surprising when the
situation seems logically the same.
But it aint!

nauthiz
2009-Mar-20, 11:23 PM
I believe it has to do with the different nature of sound and light waves.

A sound wave is a pressure wave in a medium. It's something that's created by pushing/pulling on material in that medium over a period of time. Since it happens over a period of time, if you're moving while you emit the sound, that is going to have an effect on the pattern of pressure waves because you're at different locations as you create each little bit of the wave.

In light waves, on the other hand, each photon carries its own intrinsic wavelength (ignoring important details about relativity, of course). And each photon is emitted instantaneously - so the entire wave is created at that one instant. That means that from the light wave's perspective it doesn't really matter whether the object that's emitting it is in motion or stationary.

mugaliens
2009-Mar-21, 02:00 AM
The best way I know to wrap your noggin around light doppler effects is to consider the spacetime energy difference between the sender and the receiver. So long as it's the same, there is no doppler shift. But if the sender is at a higher potential than the receiver, such as when the sender is moving towards the receiver, or when the receiver is at stationary at the bottom of a gravity well, blue-shifting occurs.

Jerry
2009-Mar-23, 05:01 PM
The difference between the light and sound examples is also amplified because velocities we experience are relatively high compared to the speed of sound; but very low compared to the speed of light; so most of the time, you can neglect the effect of the medium on light, but you must include it when addressing sound.

Also from the example; when a vehicle exceeds the speed of sound, the 'second emitted pulse' does not always pass the first pulse: as the craft travels towards the first pulse, the density of the medium is compressed and the speed of sound increases. Like the wake in front of a boat, the first pulse speeds up and the second pulse is trapped behind it...or right on top of it: This is the sonic boom: Compressed waves at the leading edge of a aircraft; and the second boom is the release of the compressed envelope at the rear of the plane.

nauthiz
2009-Mar-23, 05:08 PM
most of the time, you can neglect the effect of the medium on light

I didn't think light was carried by a medium. Do you mean the luminiferous aether (http://en.wikipedia.org/wiki/Luminiferous_aether)?

HenrikOlsen
2009-Mar-23, 09:25 PM
But this is a confusing explanation to me, because the medium doesn't seem to have anything to do with it. The waves still have to travel through space, whether there is a medium or not. If I were to re-interpret the above diagrams as pulses of light instead of sound, and emitters and listeners that move at 0.5c instead of half the speed of sound, then the result is exactly the same.
The thing that's different from the sound example is that the moving "listener" experiences time at a different rate when moving at different velocities1 and that the relative velocity between the "listener" and the light is 1c no matter how fast he's moving.