Quick Question about the Doppler Effect

[Bridgeboy]

Hi,

I'm confused about how Doppler effect shifts the wavelength of light depending on the speed of the emitter. It makes sense from a classical point of view that the wavelength should shift. However, when I consider that light comes from photons, quantized energy, any shift in frequency corresponds to a shift in energy. This seems to mean for the Doppler effect to work, energy cannot be conserved.

The best I've found on my own search for this is the following article, which says energy is not conserved in general relativity:
http://blogs.discovermagazine.com/cosmicvariance/2010/02/22/energy-is-not-conserved/

Is this the reason for the Doppler effect or am I missing something simple?

 

[Drakkith]

Well, if you think about it, the motion of an observer and another object doesn't conserve energy anyways. Or rather the energy will depend on the relative motion of the two. For example, if I shoot a bullet at you at 2500 ft/s but you are moving away from me at 2000 ft/s the bullet will have far less kinetic energy when it hits you that it would if you were stationary relative to me. The same applies to all types of waves, including EM waves.

 

[Bridgeboy]

That's right. What matters in that case is the relative motion of the two objects. The total energy in the system is defined by this relative motion.

The problem for me, is that, if you think about light, it doesn't behave like you'd expect. If I shoot a laser at speed c, it is speed c for the someone moving 2500 ft/s or stationary relative to me. It's strange to me that it's the frequency that changes, which (I think) implies that the space it's traveling through is different.

This helps a bit. Thanks.

 

[Drakkith]

Relative velocity has no effect on space. It is purely the result of changing between reference frames.

 

[Bridgeboy]

In the case of the bullet, yes. In the case of an individual photon, is that true? It seems that if the photon was produced by the same process in both cases, the only thing that would make it different is the space. Sean Carroll seems to corroborate this in the link I posted. He writes:

"The thing about photons is that they redshift, losing energy as space expands. If we keep track of a certain fixed number of photons, the number stays constant while the energy per photon decreases, so the total energy decreases."

So he's attributing the difference we see to the expansion of space. If I'm reading him correctly, we wouldn't see the redshift at all if space wasn't expanding. Meaning, in the example of the laser shooting above, there is no doppler effect because the relative motions aren't due to the expansion of space.

 

[SHISHKABOB]

he's talking about redshift due to the expansion of the universe, which is not exactly the same thing as redshift due to a relative velocity

 

[Bridgeboy]

Ok. So there's two ways we can see the redshift. How would we distinguish between the two in the case of stars? Still confused...

 

[SHISHKABOB]

there's actually a number of things that cause redshift

http://en.wikipedia.org/wiki/Redshift

 

[Drakkith]

In the case of the bullet, yes. In the case of an individual photon, is that true? It seems that if the photon was produced by the same process in both cases, the only thing that would make it different is the space.

Don't think in terms of "individual photons". Instead think in terms of an electromagnetic wave. The photon is only the quantized interaction of the EM wave.

Sean Carroll seems to corroborate this in the link I posted. He writes:

"The thing about photons is that they redshift, losing energy as space expands. If we keep track of a certain fixed number of photons, the number stays constant while the energy per photon decreases, so the total energy decreases."

So he's attributing the difference we see to the expansion of space. If I'm reading him correctly, we wouldn't see the redshift at all if space wasn't expanding. Meaning, in the example of the laser shooting above, there is no doppler effect because the relative motions aren't due to the expansion of space.

The doppler effect is not the same as redshift via the expansion of space.

Ok. So there's two ways we can see the redshift. How would we distinguish between the two in the case of stars? Still confused...

We can't. Not by measurements of redshift alone. Put simply, we look out and measure redshift and see that the further away galaxies are the more they are redshifted. This means that they are moving away from us. Now, when we use General Relativity to describe this expansion, it turns out that the redshift is due to it and not normal doppler shift from motion through space. Since the expansion only affects galaxies that are hundreds of millions of lightyears away and further, anything closer that has redshift can be attributed to normal doppler shift. Past that cosmological expansion starts to become the dominant cause of redshift. (Although since galaxies have random motions through space relative to us in addition to cosmological expansion, there will be a small component that is redshifted or blueshifted by normal doppler shift, but this is overwhelmed by the redshift due to expansion.)

 

[Chronos]

In the case of redshift, distance increases, but, the average energy density decreases commensurately, so, the total energy is conserved. In the case of bluehift, distance decreases, but, the average energy density increases commensurately, so, once again the total energy is conserved.

 

[cepheid]

In the case of redshift, distance increases, but, the average energy density decreases commensurately, so, the total energy is conserved. In the case of bluehift, distance decreases, but, the average energy density increases commensurately, so, once again the total energy is conserved.

It's possible I misunderstand you, but for photons, ##\rho \propto a^{-4}## and ##V \propto a^{3}##, so total energy in a box of constant co-moving volume decreases with time, no?
I thought energy was simply not conserved in GR


Edit: but in any case, I think the answer to the OP's question for the simpler Doppler effect case has been stated already, that energy may be conserved, but it is not invariant.

 

[Chronos]

Yes, my analogy is admittedly crude, but, useful to convey the general idea without invoking visions of 'lost' [redshift] or 'free' [blueshift] energy fairies. To say this implies conservation of energy in any classical sense is more complicated. A fielder racing back to catch a fly ball may perceive the ball has momentum towards home plate upon catching it. Obviously, the ball never has negative momentum with respect to home plate, only with respect to the fielder.

 

[Bridgeboy]

there's actually a number of things that cause redshift

http://en.wikipedia.org/wiki/Redshift

Thanks. Should have checked this earlier. Lots of useful info here, like the fact that CMB is redshifted.

Don't think in terms of "individual photons". Instead think in terms of an electromagnetic wave. The photon is only the quantized interaction of the EM wave.

I'll try. It's hard for me to do this easily because I'm usually considering them at the point of emission, at discrete energies, and detection, at discrete energies. Thinking of it as a wave while it is in transit seems to be only a semiclassical interpretation of light.

We can't. Not by measurements of redshift alone. Put simply, we look out and measure redshift and see that the further away galaxies are the more they are redshifted. This means that they are moving away from us. Now, when we use General Relativity to describe this expansion, it turns out that the redshift is due to it and not normal doppler shift from motion through space. Since the expansion only affects galaxies that are hundreds of millions of lightyears away and further, anything closer that has redshift can be attributed to normal doppler shift. Past that cosmological expansion starts to become the dominant cause of redshift. (Although since galaxies have random motions through space relative to us in addition to cosmological expansion, there will be a small component that is redshifted or blueshifted by normal doppler shift, but this is overwhelmed by the redshift due to expansion.)

Interesting. Before now, I was under the impression that everything is redshifted. I guess that's not true for local objects.

http://en.wikipedia.org/wiki/Blueshift

 

[SHISHKABOB]

the andromeda galaxy, for instance, is blue-shifted because at the moment it's approaching us

the local gravitational force is greater than the expansion of space in this case, so the Andromeda galaxy and the Milky Way are both headed for a collision in like... 3-5 billion years?

 

[flinky]

if photons lose energy when redshifted due to the expansion of space, then space must gain the energy so why isn't this a candidate for dark energy, or is it?

and a little off topic but curious - when light (a single photon) leaves a distance star it behaves like a wave so does that mean it spreads out (like a wave on a pond) across the universe or it travels in a straight line? I'm thinking of the two slit experiment here which suggests to me light spreads out and across the vast distances of the universe it must be spread quite wide (or quite thin) and couldn't this be attributed to the loss of energy?

 

[Drakkith]

if photons lose energy when redshifted due to the expansion of space, then space must gain the energy so why isn't this a candidate for dark energy, or is it?

Why must space gain energy? What mechanism would it use to gain this energy? How would it use this energy? Remember that energy is the ability to do work.

and a little off topic but curious - when light (a single photon) leaves a distance star it behaves like a wave so does that mean it spreads out (like a wave on a pond) across the universe or it travels in a straight line? I'm thinking of the two slit experiment here which suggests to me light spreads out and across the vast distances of the universe it must be spread quite wide (or quite thin) and couldn't this be attributed to the loss of energy?

I think it is better to understand and think of light as an EM wave that propagates outwards from it's source. Once it interacts with something can you consider it to be photons. Individual photons do not spread out as the wave travels. If they did we would see it in everyday circumstances as EM waves expand outwards from their sources in antennas and such. (If i understand your meaning of "spread out" correctly)

 

[flinky]

Why must space gain energy?

dunno

What mechanism would it use to gain this energy?

dunno

How would it use this energy?

ah! to get bigger

I think it is better to understand and think of light as an EM wave that propagates outwards from it's source. Once it interacts with something can you consider it to be photons.

yeah I get this, but looking at the two slit experiment hypothetically speaking the wave propagates through the slit towards the wall and hits the wall at two separate points at exactly the same time, interacting in two different places at exactly the same time. does this mean two photons would be created from the one wave? taking into account the uncertainty of where the photon is in a wave and assuming there's only one photon per wave then a photon must be more than just interaction if this hypothetical situation could arise

 

[Bridgeboy]

the wave propagates through the slit towards the wall and hits the wall at two separate points at exactly the same time, interacting in two different places at exactly the same time. does this mean two photons would be created from the one wave? taking into account the uncertainty of where the photon is in a wave and assuming there's only one photon per wave then a photon must be more than just interaction if this hypothetical situation could arise

You seem to be treating this like photons are riding the wave. In the case of the two slit experiment, it is the wave function that is described as spreading to both points simultaneously. In other words, it describes the probability of finding a photon at once side or the other, not the photon's actual existence at both places at once.

 

[Drakkith]

yeah I get this, but looking at the two slit experiment hypothetically speaking the wave propagates through the slit towards the wall and hits the wall at two separate points at exactly the same time, interacting in two different places at exactly the same time. does this mean two photons would be created from the one wave? taking into account the uncertainty of where the photon is in a wave and assuming there's only one photon per wave then a photon must be more than just interaction if this hypothetical situation could arise

The EM wave, or wavefunction of the photon, travels through the two slits, interferes with itself, and makes a pattern on the wall or detector. A photon can be detected anywhere within this pattern, with the probability being greater or lesser depending on where in the pattern you are looking.