Redshifting Help - Understand the Doppler Effect of Light Waves

[Evolver]

Okay, I understand the principle of redshifting, but I feel I am missing an element to it's comprehension because as is it doesn't make complete sense to me.

I understand the Doppler effect of sound waves, as in a train passing by; the waves in front are of a higher frequency due to the motion of the train producing them and subsequently lower frequency as the train passes.

Now, the redshifting of light from distant galaxies traveling away at high speeds is where I am confused. I am lead to believe that the galaxies are generating a similar effect in that the light waves are lower frequency behind the moving body and thus appear redshifted (and if the galaxies were heading towards us would appear blueshifted.)

But this makes no sense to me. According to relativity, light in a vacuum travels at a constant speed regardless of the motion of the body that it is emitted from. Therefore, indicating that light is affected by the motion of galaxy is not consistent with this line of thinking.

I do realize it probably has something to do with time dilation, but I am not aware of how. Please someone help me grasp this concept.

Thanks!

 

[nutgeb]

According to relativity, light in a vacuum travels at a constant speed regardless of the motion of the body that it is emitted from. Therefore, indicating that light is affected by the motion of galaxy is not consistent with this line of thinking.

First, you need to distinguish between two kinds of light redshifting, SR Doppler and Cosmological.

SR Doppler redshift occurs as between two inertial frames - think of one as being stationary and the other moving. SR Doppler redshift is the combination of two components (which actually are inseparable). In the case of redshift, the light photons lose energy as a result of the need to accelerate themselves such that they travel at exactly c relative to the observer. This is classical Doppler redshift. You are correct that the speed of light - c- does not vary in any inertial frame. But the energy of a photon does decrease when observed in frame that is receding away from the emitter. The lower the energy of a photon, the longer its wavelength. Longer wavelength = redshift.

The second component of SR Doppler redshift is time dilation. From the perspective of the observer, the emitter is time dilated because it is in motion relative to the observer. Dilated time = slower clock = lower frequency of wavecrests = longer wavelength = redshift. The SR Doppler formula simply multiplies the classical Doppler redshift by the emitter's time dilation.

Cosmological redshift is a different but related phenomenon which occurs in an expanding, gravitational universe. At a simple level, cosmological redshift is exactly proportional to the distance of the emitting object at the time of observeration. Another way to say it is that the cosmological redshift is exactly proportional to the amount by which the scale factor of the universe has expanded in the interval between emission and observation.

But these descriptions of the cosmological redshift do not explain HOW it occurs. It is fairly certain that the 'expansion of space' does not itself directly cause the distance between wavecrests to expand. The 'expansion of space' is inherently incapable of causing an increase in separation between any two things unless those things were already moving apart in the initial condition, and retain some sort of separational momentum (like physical objects such as galaxies have). Over a small time period, all of the wavecrests emitted by a receding emitter have exactly the same fixed wavelength, so the crests cannot be said to be in motion relative to each other in the initial conditions. In addition, the concept of retained separational momentum cannot be meaningfully applied to intangibles such as wavecrests.

SR Doppler redshift does not occur in a cosmological context between galaxies which are receding away from each other exactly at the pace of their local Hubble flow, because no time dilation exists as between fundamental comovers in the FRW metric, which models cosmological expansion.

 

[sylas]

Okay, I understand the principle of redshifting, but I feel I am missing an element to it's comprehension because as is it doesn't make complete sense to me.

I understand the Doppler effect of sound waves, as in a train passing by; the waves in front are of a higher frequency due to the motion of the train producing them and subsequently lower frequency as the train passes.

Now, the redshifting of light from distant galaxies traveling away at high speeds is where I am confused. I am lead to believe that the galaxies are generating a similar effect in that the light waves are lower frequency behind the moving body and thus appear redshifted (and if the galaxies were heading towards us would appear blueshifted.)

But this makes no sense to me. According to relativity, light in a vacuum travels at a constant speed regardless of the motion of the body that it is emitted from. Therefore, indicating that light is affected by the motion of galaxy is not consistent with this line of thinking.

Think about your train example again. The sound waves are also traveling at the same speed with respect to you, no matter whether the train is approaching or receding.

You are also correct about blue shift for an approaching galaxy. Andromeda, for example, is approaching us, and is blueshifted as a result.

I do realize it probably has something to do with time dilation, but I am not aware of how. Please someone help me grasp this concept.

Time dilation does mean that the formulae used are a bit different; but you still get a Doppler shift even without any time dilation effects -- as the train example shows.

Cheers -- sylas

PS. This is not a question for which you need to worry about all the details of large scale cosmology. For nearby galaxies, there's no meaningful difference between cosmological redshift and Doppler redshift. The cosmological factors of large scale spacetime become important on very large scales; but not for small redshift galaxies.

 

[javierR]

The speed of light is indeed a constant here, but the doppler effect has to do with observed frequencies of the light, and these can change from observer to observer. I haven't checked the quality of the wikipedia entry, but I'll assume it's alright:
http://en.wikipedia.org/wiki/Relativistic_Doppler_effect

 

[JesseM]

SR Doppler redshift occurs as between two inertial frames - think of one as being stationary and the other moving. SR Doppler redshift is the combination of two components (which actually are inseparable). In the case of redshift, the light photons lose energy as a result of the need to accelerate themselves such that they travel at exactly c relative to the observer. This is classical Doppler redshift. You are correct that the speed of light - c- does not vary in any inertial frame. But the energy of a photon does decrease when observed in frame that is receding away from the emitter. The lower the energy of a photon, the longer its wavelength. Longer wavelength = redshift.

The second component of SR Doppler redshift is time dilation. From the perspective of the observer, the emitter is time dilated because it is in motion relative to the observer. Dilated time = slower clock = lower frequency of wavecrests = longer wavelength = redshift. The SR Doppler formula simply multiplies the classical Doppler redshift by the emitter's time dilation.

SR Doppler redshift has nothing to do with photons "losing energy as a result of the need to accelerate themselves", it's just time dilation plus the effect of the source moving away from you (or towards you in the case of blueshift), which means that each successive wave peak is emitted at a greater distance from you and thus has longer to travel to reach your eyes than the previous peak. See my post #12 on this thread for a numerical example.

 

[nutgeb]

SR Doppler redshift has nothing to do with photons "losing energy as a result of the need to accelerate themselves", it's just time dilation plus the effect of the source moving away from you (or towards you in the case of blueshift), which means that each successive wave peak is emitted at a greater distance from you and thus has longer to travel to reach your eyes than the previous peak.

I agree that each wave has longer to travel.

But are you disagreeing that a redshifted photon has less energy than a non-redshifted one?

 

[nutgeb]

SR Doppler redshift has nothing to do with photons "losing energy as a result of the need to accelerate themselves", it's just time dilation plus the effect of the source moving away from you (or towards you in the case of blueshift), which means that each successive wave peak is emitted at a greater distance from you and thus has longer to travel to reach your eyes than the previous peak.

I agree that each wave has longer to travel, which can be correctly described as causing the longer wavelength.

But, of course, a redshifted photon has less energy than a non-redshifted one, and my description is equivalently correct.

 

[JesseM]

I agree that each wave has longer to travel.

But, of course, a redshifted photon has less energy than a non-redshifted one, and my description is equivalent.

How is it equivalent? For one thing the relation between energy and wavelength depends on quantum mechanics, whereas my explanation works for classical EM waves too. And I don't see how you'd actually derive the relativistic Doppler shift from the QM energy/wavelength relation (or from the energy/wavelength relation + time dilation--you appear to have said the energy change has to be considered separately from the time dilation effect)...can you provide an actual derivation of the Doppler shift equation in this way, or a numerical example showing how you can get the correct shift using the energy/wavelength relation? If not I am doubtful that your statement makes any sense at all.

 

[nutgeb]

can you provide an actual derivation of the Doppler shift equation in this way, or a numerical example showing how you can get the correct shift using the energy/wavelength relation?

Of course the energy of light is proportionally reduced, as measured by an observer in relative motion away from the emitter, compared to the energy measured by an observer stationary in the inertial frame of the emitter.

If you disagree with that statement, please state simply, "I disagree."

 

[JesseM]

Of course the energy of light is proportionally reduced, as measured by an observer in relative motion away from the emitter, compared to the energy measured by an observer stationary in the inertial frame of the emitter.

If you disagree with that statement, please state simply, "I disagree."

I do not disagree with that statement on its own. But I see no way to derive the Doppler shift equation from the fact that the energy is lower in the frame where the emitter is moving, and that is what you were saying when you said "In the case of redshift, the light photons lose energy as a result of the need to accelerate themselves such that they travel at exactly c relative to the observer. This is classical Doppler redshift." Unless you can show how to derive the Doppler shift from the different energy in the two frames, then this statement is a complete non sequitur, akin to saying "the length of the emitter is contracted in the frame where the emitter is moving. This is classical Doppler redshift". The first sentence is of course true on its own terms, but it has nothing to do with the explanation for the Doppler shift.

 

[nutgeb]

Jesse, I'm not going to get into an extended argument on this point. I agree with your terminology for describing how the classical redshift applies to light, it's a good description.

The classical Doppler formulas, based on velocity and wavelength, are as follows (where outward relative velocity has a positive sign):

Moving emitter, stationary observer: $$\lambda _{o} = \lambda _{e} (1 + v_{e})$$

Moving observer, stationary emitter: $$\lambda _{o} = \lambda _{e} / (1 - v_{o})$$

 

[JesseM]

The classical Doppler formulas, based on velocity and wavelength, are as follows (where outward relative velocity has a positive sign):

Moving emitter, stationary observer: $$\lambda _{o} = \lambda _{e} (1 + v_{e})$$

Moving observer, stationary emitter: $$\lambda _{o} = \lambda _{e} / (1 - v_{o})$$

OK, and these formulas don't seem to be derivable from energy considerations as you were suggesting--that's the only point I was making.

 

[nutgeb]

[Edit: Upon further consideration, I revised the first sentence as follows: The classical Doppler shift is required by energy conservation considerations, and the redshifted energy of a photon in an observer's frame can be calculated in theory by measuring the emitter's atomic recoil in the observer's frame.]

Consider a hydrogen atom that emits a photon, which subsequently is absorbed by an observer moving away from the atom. The atom will recoil away from the observer. The sum of the atom's recoil energy and the photon's redshifted energy, both as measured in the observer's frame, must equal the energy of the atom's motion (relative to the observer) just before the photon was emitted. Classical Doppler shift of the photon is required in the observer's frame in order to avoid violating the conservation of energy.

The energy of a photon in a frame is equal to the Planck Constant times the photon's frequency as measured in that frame.

 

[JesseM]

The classical Doppler shift can be derived from energy considerations alone.

Consider a hydrogen atom that emits a photon, which subsequently is absorbed by an observer moving away from the atom. The atom will recoil away from the observer. The sum of the atom's recoil energy and the photon's redshifted energy, both as measured in the observer's frame, must equal the energy of the atom's motion (relative to the observer) just before the photon was emitted. Classical Doppler shift of the photon is required in the observer's frame in order to avoid violating the conservation of energy.

The energy of a photon in a frame is equal to the Planck Constant times the photon's frequency as measured in that frame.

First of all, a classical or relativistic derivation of the Doppler shift shouldn't depend on knowing formulas from quantum mechanics. Second, even if we assume we know the relation between energy and frequency from QM, it's not clear this is actually helpful in getting the Doppler equation, which is supposed to deal with the case of an emitter moving at constant velocity, not an emitter that recoils and changes velocity each time it emits a photon. The Doppler equation compares the frequency in two frames, the emitter frame and the observer frame, it's not clear what you want the equivalent of the "emitter frame" to be in the above argument--the rest frame of the atom after it has emitted the photon, or before?

If you want to continue to defend the claim that the Doppler equation can be derived from energy considerations, you need to actually provide a derivation with equations--or at least provide a numerical example--the verbal arguments above are much too handwavey.

 

[nutgeb]

Second, even if we assume we know the relation between energy and frequency from QM, it's not clear this is actually helpful in getting the Doppler equation, which is supposed to deal with the case of an emitter moving at constant velocity, not an emitter that recoils and changes velocity each time it emits a photon.

Every emission of every photon involves a recoil. This is not QM in any specialized sense, it's basic physics.

The Doppler equation compares the frequency in two frames, the emitter frame and the observer frame, it's not clear what you want the equivalent of the "emitter frame" to be in the above argument--the rest frame of the atom after it has emitted the photon, or before?

As you know, the Doppler equation compares the redshift to the emitter frame before the effect of recoil is considered. The atom's recoil frame is brought into the analysis specifically as a way to derive the redshift from energy conservation. As you know, it is most straightforward to analyze energy conservation with regard to a complete system rather than by reference to pieces of the system in isolation.

... you need to actually provide a derivation with equations--or at least provide a numerical example--the verbal arguments above are much too handwavey.

This is simple energy conservation. The momentum p_tot of the total atom+photon system remains exactly constant before and after emission. Therefore the momentum of the redshifted photon must be p_tot - p_atom, where the latter is the momentum of the recoiled atom as measured in the observer's frame. {Edit: In order to balance the total system momentum to compare vectors in both the +x and -x directions, the atom's momentum needs to be expressed as a negative number, so the redshifted photon's momentum should be expressed as p_tot + p_atom.} Obviously the recoiled atom's momentum (in the observer's frame) is simply the atom's mass times its [initial velocity + recoil $$\Delta$$ velocity].

 

[sylas]

This is simple energy conservation. The momentum p_tot of the total atom+photon system remains exactly constant before and after emission. Therefore the momentum of the redshifted photon must be p_tot - p_atom , where the latter is the momentum of the recoiled atom as measured in the observer's frame. Obviously the recoiled atom's momentum (in the observer's frame) is simply the atom's mass times its [initial velocity + recoil $$\Delta$$ velocity].

That is not a derivation with equations. It's still hand wavey. Try giving an actual mathematical derivation using equations. Derivations means you express the assumptions as equations (not as English) and get your result with algebra (not with an English declaration that it is "simple").

 

[JesseM]

Every emission of every photon involves a recoil. This is not QM in any specialized sense, it's basic physics.

I was talking about the quantum relationship between the energy of a photon and its frequency/wavelength, which you seem to be assuming (otherwise how are considerations of energy/momentum supposed to tell us anything about frequencies?)

As you know, the Doppler equation compares the redshift to the emitter frame before the effect of recoil is considered.

Typically I think the Doppler equation just assumes the effects of recoil can be treated as negligible because the momentum of the emitted waves are very small compared to the momentum of the emitter. In any case, if you want to think in terms of the frame where the atom is at rest before emitting the photon, then actually show how it works using this frame and the fame of the observer. If you don't want to do a general derivation, just give a specific numerical example where we consider an atom in motion at some specific velocity relative to an observer, consider it emitting a photon of some specific frequency, and then (somehow, because you have in no way explained it) use energy considerations to figure out both the frequency in the frame where the atom was at rest before emission, and the frequency in the observer's frame. If you can't even provide a simple numerical example, then it's obvious you don't have an actual well-defined argument in mind.

The atom's recoil frame is brought into the analysis specifically as a way to derive the redshift from energy conservation.

Huh? You just said you wanted to consider the emitter's frame "before the effect of recoil is considered". Just tell me, what frame are you using for the "emitter frame" in the standard Doppler equation? Is it the frame where the atom is at rest before emitting the photon, or the frame where it is at rest afterward?

This is simple energy conservation. The momentum p_tot of the total atom+photon system remains exactly constant before and after emission. Therefore the momentum of the redshifted photon must be p_tot - p_atom , where the latter is the momentum of the recoiled atom as measured in the observer's frame. Obviously the recoiled atom's momentum (in the observer's frame) is simply the atom's mass times its [initial velocity + recoil $$\Delta$$ velocity].

All of this is pretty obvious, but it gives me no idea of how you intend to derive the redshift equation, which relates frequency in the observer's frame to frequency in the emitter's frame. In the above you appear to be talking solely about the momentum of the photon and atom in the observer's frame before and after the emission, with no reference to any other frame.

Please, no more vague verbal arguments. If you have a well-defined idea about how to derive the Doppler equation from energy considerations, it should be exceedingly simple to give a numerical example where you actually use energy considerations to calculate the frequency of the photon in the observer's frame and some other frame (what that other frame is, you still haven't made clear) and show that they match what's predicted by the Doppler equation (classical or relativistic, I'm not sure...if it's not relativistic, does that mean you won't assume the photon moves at c in both frames?) If you don't have any clear idea of how to do this, that's fine, but then please acknowledge that your ideas are tentative and don't confidently assert that the Doppler relation can be derived from energy considerations if you don't have a definite procedure in mind.

 

[nutgeb]

The photon recoil analysis is a way of relating a photon's redshifted energy to the total system energy, and to demonstrate that Doppler shift is required for energy conservation. But beyond that, I don't think it is the easiest path to analyze the workings of classical redshift. I have the recoil analysis written out in mathematical terms but sharing it will not advance this discussion.

Let me return to what I intended in my original post. You have used a lot of words to characterize a simple statement of mine, most of which are twisting my words.

A photon's energy in an observer's frame is trivially derived from its momentum in that frame: E = pc.

Further, it is a basic element of the classical Doppler shift that a photon's momentum is reduced by the factor of (1-v)/c if the observer is moving away from the emitter.

It is absurd to challenge these basic propositions or demand that I provide proof of something else. I never intended to suggest that a photon's redshifted energy shift derives from anything other than the decrease in its momentum due to chasing a moving observer. That's why I was perfectly willing to accept the way you described it.

 

[JesseM]

The photon recoil analysis is a way of relating a photon's redshifted energy to the total system energy, and to demonstrate that Doppler shift is required for energy conservation. But beyond that, I don't think it is the easiest path to analyze the workings of classical redshift. I have the recoil analysis written out in mathematical terms but sharing it will not advance this discussion.

By "recoil analysis" do you mean a derivation of the redshift starting from considerations of energy and/or momentum? If so, providing it would certainly advance the discussion--it would either show you do have the derivation I've been asking for, or myself and others could point out any flaws we found in the analysis.

Let me return to what I intended in my original post. You have used a lot of words to characterize a simple statement of mine, most of which are twisting my words.

Your "simple statement" was: In the case of redshift, the light photons lose energy as a result of the need to accelerate themselves such that they travel at exactly c relative to the observer. This is classical Doppler redshift. Then in a subsequent post you said The classical Doppler shift can be derived from energy considerations alone. Is it "twisting your words" to understand these as claims that the correct value for redshift can be derived from considerations of energy or momentum?

If you do think I am twisting your words, the solution is simple: say something like "no, I do not claim the Doppler equation can be derived just from considerations of the energy/momentum in both frames." On the other hand, if my interpretation of your words was correct and you do claim such a derivation is possible, then all you need to do is provide it (as I said, a numerical example rather than a full derivation would be convincing too). But if you won't do either of those things, you're just being evasive, and probably running afoul of the forum rules about not using the forum to advance original claims that are not part of mainstream physics (or that aren't demonstrably derivable from mainstream physics).

A photon's energy in an observer's frame is trivially derived from its momentum in that frame: E = pc.

Strictly speaking you can only "derive" that by starting from the relativistic equation $$E^2 = m^2*c^4 + p^2*c^2$$ and then including the fact that a photon has zero rest mass. Didn't you say you wanted to talk in classical terms rather than relativistic ones? In relativistic terms your earlier statement about the atom's momentum just being its mass times its velocity would be incorrect, for example.

Further, it is a basic element of the classical Doppler shift that a photon's momentum is reduced by the factor of (1-v)/c if the observer is moving away from the emitter.

What are you talking about? The classical Doppler shift equation says absolutely nothing about a photon's momentum, it deals with frequency of a wave in different frames. In a classical universe, if a wave is sent out at c relative to the emitter, and the emitter is moving away from the observer at v, then the observer will see the frequency reduced by 1/(1 + v/c). In quantum physics we also know that momentum is proportional to frequency according to the formula p = h*frequency/c, so if we carelessly combine the quantum formula with the classical one (though this would be physically dubious since the classical formula assumes the wave has a speed c-v in the observer's frame, while the quantum formula assumes photons move at c in whatever frame the formula is being used) then we could conclude the momentum is also reduced by 1/(1 + v/c), which is different from your equation (1-v)/c (a formula that doesn't even seem to make sense dimensionally since v and c have units of distance/time while 1 is dimensionless).

It is absurd to challenge these basic propositions or demand that I provide proof of something else.

Your (1-v)/c formula for momentum reduction, which supposedly comes from "classical Doppler shift", is not a basic proposition. And it's not absurd to demand that you provide proof of what you asserted at the beginning about Doppler shift coming from energy considerations which got this whole debate going, something you appeared to continue to assert when you said "The classical Doppler shift can be derived from energy considerations alone." If you wish to back off from this claim, then do so.

I never intended to suggest that a photon's redshifted energy shift derives from anything other than the decrease in its momentum due to chasing a moving observer.

The debate was never about a photon's "redshifted energy", it was about the Doppler equation which deals with the frequency of a wave (of photon if you prefer) in both frames. Do you or do you not claim this is derivable from considerations of momentum/energy? If you do not, please state that clearly, and if you do, please provide a derivation or a numerical example.

 

[nutgeb]

This is my last post on this subject. It is impossible to have a rational dialogue with you when you are twisting my words and spraying arguments in all directions. You can post whatever you want on this topic as long as you direct it to the OP or others, and leave me and my words out of it.

For the sake of clarity, the following will clarify and REPLACE ALL prior statements I've made on this subject:

A photon's energy as measured locally in the observer's frame is a direct function of its momentum. From Wikipedia article "Photon":

"In empty space, the photon moves at c (the speed of light) and its energy and momentum are related by E = pc, where p is the magnitude of the momentum vector p. For comparison, the corresponding equation for particles with mass m is: $$E^2 = m^2 c^4 + p^2 c^2$$"

Classical Doppler effect causes an observer moving away from the emitter to measure a photon to have a lower momentum than it had in the emitter's frame. This is true regardless that the simple form of the classical Doppler formula does not include a momentum term.

Energy, momentum, frequency and wavelength are all directly related and go hand-in-hand with respect to redshift. Whether the reduction in momentum is caused fewer wave crests hitting the observer in a given period of time, or by an increase in the wavelengths between received crests, or simply from being received in a moving frame, is not crucial to the OP's question. As a practical matter it amounts to the same thing. Various "hand-waving" descriptions can reasonably describe the outcome.

The recoil of an emitter atom demonstrates that the classical Doppler shift of the photon complies with energy conservation.

*** FINIS ***

 

[JesseM]

This is my last post on this subject. It is impossible to have a rational dialogue with you when you are twisting my words and spraying arguments in all directions.

Again, I simply quoted your words, explained what I thought was the obvious interpretation, and asked you to clarify if I was misunderstanding. If you are not willing to give me a straightforward answer to the question of whether "The classical Doppler shift can be derived from energy considerations alone" meant that you think the standard Doppler equations (which involve frequencies, not energies or momenta) can be derived from considerations of energy and momentum, then it seems like it is you who are not interested in "rational dialogue", but in any case the accusation of twisting your words when I gave you ample opportunity to clarify is quite unfair.

Classical Doppler effect causes an observer moving away from the emitter to measure a photon to have a lower momentum than it had in the emitter's frame. This is true whether or not the simple form of the classical Doppler formula includes a momentum term.

Since there is no form of the Doppler formula other that the "simple form" that deals only with frequency (or wavelength), the burden is on you to explain how the formula implies anything whatsoever about momentum. Since you petulantly refuse to give derivations of any of your strange claims, I can only speculate that you are wanting to combine the Doppler formula with the quantum formula relating frequency to energy (or momentum) for photons, but this is not really a legitimate move physically for reasons I explained earlier (the classical formula would assume a wave moving at c in one frame is moving at c-v in another, whereas the quantum formulas always assumes photons move at c in whatever frame you're using them). If that isn't what you meant, once again you are invited to clarify.

Energy, momentum, frequency and wavelength are all directly related and go hand-in-hand with respect to redshift.

They only "go hand-in-hand" in quantum physics, as far as I know. Classical physics does not postulate any set relationship between the energy/momentum of a wave and its frequency/wavelength.

The recoil of an emitter atom demonstrates that the classical Doppler shift of the photon complies with energy conservation.

No it doesn't, because classically the Doppler equation tells us nothing whatsoever about energy or momentum.

 

[nutgeb]

I need to correct 2 points:

Strictly speaking you can only "derive" that by starting from the relativistic equation $$E^2 = m^2*c^4 + p^2*c^2$$ and then including the fact that a photon has zero rest mass.

For the photon, as Wikipedia says:

"In empty space, the photon moves at c (the speed of light) and its energy and momentum are related by E = pc, where p is the magnitude of the momentum vector p. For comparison, the corresponding equation for particles with mass m is: $$E^2 = m^2 c^4 + p^2 c^2$$."

I agree that the atom's momentum should follow the relativistic formula.

... we could conclude the momentum is also reduced by 1/(1 + v/c), which is different from your equation (1-v)/c.

I agree that I made a typo, and forgot to reverse the sign compared to the way it's used in some other contexts. $$p = h / \lambda$$, so I should have said the photon's momentum is decreased (divided) by a factor of (1+v/c).

 

[JesseM]

I need to correct 2 points:

Strictly speaking you can only "derive" that by starting from the relativistic equation $$E^2 = m^2*c^4 + p^2*c^2$$ and then including the fact that a photon has zero rest mass.

For the photon, as Wikipedia says:

"In empty space, the photon moves at c (the speed of light) and its energy and momentum are related by E = pc, where p is the magnitude of the momentum vector p. For comparison, the corresponding equation for particles with mass m is: "$$E^2 = m^2 c^4 + p^2 c^2$$

That's not a "correction", it's exactly what I was saying in the section you quoted! I said that you can only "derive that"--"that" referring to the equation E=pc for a photon which you had stated in the post I was responding to--by starting from the equation $$E^2 = m^2*c^4 + p^2*c^2$$, "and then including the fact that a photon has zero rest mass", i.e. plugging m=0 into that equation, which leaves you with $$E^2 = p^2*c^2$$, which of course reduces to E=pc for a photon (or any other particle with zero rest mass).

I agree that the atom's momentum should follow the relativistic formula.

But you can't then combine formulas derived from relativistic physics with formulas from classical physics (the classical Doppler equation) willy-nilly.

I agree that I made a typo, and forgot to reverse the sign compared to the way it's used in some other contexts. $$p = h / \lambda$$

That's a formula from quantum mechanics, which confirms that you are trying to combine the formula from quantum mechanics with the classical Doppler equation, a physically dubious move for reasons I already explained--the classical Doppler formula assumes that a photon with a speed of c in one frame would have a speed of c-v in another, whereas the quantum formula assumes a photon always has a speed of c in whatever frame you're using.

Basically you are trying to make original arguments based on combining formulas from different domains of physics that aren't really compatible (something you've done a few times on older threads too). Again, please reread what the rules say about not using these forums as a platform to advance your own novel arguments, their purpose is to teach people about what are accepted claims and derivations in mainstream physics.

 

[nutgeb]

You have repeatedly mischaracterized my words and ideas, and not satisfied with that, now you are attacking my verbatim quote from Wikipedia regarding $$p = h / \lambda$$, which you assert is not allowed to be discussed in the context of classical Doppler shift. I hope someone else will weigh in on that point.

I am not trying to make original arguments here, I am trying to explain that it was never my intention to claim anything other than what standard physics provides for classical Doppler shift. You are the one who recklessly insisted from your very first post, and continued doing so relentlessly thereafter, that I have intentions to prove something outside of standard physics, taking my statements out of context, and putting words in my mouth.

You are the one who came up with the terminology "derived from energy considerations", which is so broad and meaningless that anyone could drive a truck through it. Which I subsequently did with the recoil analysis, although I admitted it didn't add much substantively to the understanding of classical Doppler shift, other than demonstrating how classical Doppler shift complies with energy conservation. Since you disagree with that characterization as well, again I hope someone else will weigh in. I wish I hadn't brought that point up because it just played into your game of empty shadowboxing.

Harassment is a violation of forum rules, and I respectfully request that you stop. For my part, I will discontinue contributions to this thread.

 

[JesseM]

You have repeatedly mischaracterized my words and ideas,

You keep throwing around this accusation, and it's unfair. I just give my interpretation of what you say and then invite you to clarify if I've got it wrong, which you have no reason not to do if you are interested in rational debate.

now you are attacking my verbatim quotes from Wikipedia.

In no way did I "attack" it! I agreed with it, I just disagreed with your idea that it somehow contradicted what I had said in the post of mine that you quoted, when as I explained I had been saying exactly the same thing in that quote: that the equation E=pc for photons is derived from the more general relativistic equation $$E^2 = m^2*c^4 + p^2*c^2$$.

I am not trying to make original arguments here, I am trying to explain that it was never my intention to claim anything other than what standard physics provides for classical Doppler shift.

You may not be trying to make original arguments, but your arguments are not part of standard physics, regardless of whether you understand this fact or are ignorant of it; in particular, the classical Doppler shift equation says nothing about the energy or momentum of waves, and it is incorrect to combine the classical Doppler shift equation with the equation $$p = h / \lambda$$ which comes from quantum mechanics. For this reason, your claim that "the photon's momentum is decreased (divided) by a factor of (1+v/c)" is also incorrect, since it is based on an illegitimate combination of equations from different branches of physics (you would probably be OK if you combined the quantum equation with the relativistic Doppler equation, assuming the equation $$p = h / \lambda$$ for photons is valid in the context of relativistic quantum theory).

You insist on claiming I have intentions I do not have, and putting words in my mouth.

I say nothing about your "intentions", I only say that the actual claims you are making are incorrect and not a part of standard physics, regardless of whether you understand this or not. As always, if I have misunderstood anything you are claiming, then if you are interested in constructive debate then you should clarify and explain what I have misunderstood. On the other hand, if you're not interested in rational debate and just want to vent your hostility at me, then by all means continue to refuse to clarify anything and keep throwing out those broad accusations without explaining what specifically I have gotten wrong.

Harassment is a violation of forum rules, and I respectfully request that you stop.

It is not "harrassment" to argue about physics with people when they are making claims you think are incorrect! I'm not going to stop pointing out where I think you have gone wrong in your arguments, since bad arguments are potentially misleading to readers. And if you continue to make these arguments without being willing to discuss them, I will report your posts to the mods.

 

[nutgeb]

It is not "harrassment" to argue about physics with people when they are making claims you think are incorrect! I'm not going to stop pointing out where I think you have gone wrong in your arguments, since bad arguments are potentially misleading to readers.

Argument becomes harrassment when you (a) repeatedly take my statements out of context, (b) insist I am trying to claim something I'm not despite my attempts to correct your misimpression, (c) threaten me with sanctions for not admitting that something was incorrect which I didn't claim in the first place, (d) characterize any error I make as evidence of my ignorance, and (e) hijack this thread with unrelated issues that were not resolved to your personal satisfaction in other threads about other topics.

And if you continue to make these arguments without being willing to discuss them, I will report your posts to the mods.

I see, if I don't continue arguing with you ad nauseum and ultimately agree that you are right and I am wrong about every point you want to debate, then you will "report" me. Gosh now that's an invitation to rational discussion if I ever heard one.

Let me help you out. I hereby withdraw and disavow ALL statements I made in this thread, as well as all statements I didn't actually make but was accused of making, as well as all statements I made in a different context than I was accused of making them, as well as all implications that may or may not follow from things I did or didn't say, as well as any implication that I might disagree in the slightest with anything Jesse said.

Now please stop harassing me.

 

[JesseM]

Argument becomes harrassment when you (a) repeatedly take my statements out of context,

Not intentionally, I don't. And you refuse to explain which particular statements I am taking out of context, or what you actually meant by them--all you do is throw around broad, hostile accusations like "you take my statements out of context" and "putting words in my mouth" without giving any specifics. If you're going to make hostile accusations like that, then you need to give specifics about what I am getting wrong, otherwise it seems you are more interested in painting me an unpleasant light than in having a constructive dialogue.

(b) insist I am trying to claim something I'm not despite my attempts to correct your misimpression,

Please show me a single instance on this thread where you have corrected me about any specific claim you made. I asked you what you did mean by various claims, such as:

--"The classical Doppler shift can be derived from energy considerations alone." (I hadn't noticed until now that you later edited this to say 'The classical Doppler shift is required by energy conservation considerations', but this statement appears equally wrong to me unless you can show specifically how the classical Doppler shift equation is 'required' by energy conservation)

--"Classical Doppler effect causes an observer moving away from the emitter to measure a photon to have a lower momentum than it had in the emitter's frame." (the classical Doppler effect says nothing whatsoever about momentum, so this looks wrong too)

--"Energy, momentum, frequency and wavelength are all directly related and go hand-in-hand with respect to redshift." (energy and momentum do not go hand-in-hand with frequency and wavelength unless you refer to quantum equations)

--"I agree that I made a typo, and forgot to reverse the sign compared to the way it's used in some other contexts. $$p = h / \lambda$$, so I should have said the photon's momentum is decreased (divided) by a factor of (1+v/c)." ($$p = h / \lambda$$ is a quantum equation, am I incorrect that you derived the factor (1+v/c) by combining it with the classical Doppler shift equation? If so I would say this is an incorrect combination of two different domains of physics, and the factor (1+v/c) would not be justifiable in either classical physics or relativity)

In not a single one of your posts have you clarified what you meant by these statements, or told me specifically how I am supposedly misinterpreting you. I really am making a good-faith attempt to understand what you are talking about by quoting your words, giving my interpretation and requesting clarification if I've gotten it wrong, but all I get from you is unremitting hostility and venom.

(c) threaten me with sanctions for not admitting that something was incorrect which I didn't claim in the first place

More totally broad and nonspecific accusations. What did I threaten you with sanctions for not admitting which you didn't claim in the first place? In my last post I listed various claims of yours I thought were incorrect, like the claim that the momentum would be reduced by (1+v/c), and said "if you continue to make these arguments without being willing to discuss them, I will report your posts to the mods." Did you not, in fact, say that the momentum would be reduced by (1+v/c)? If not, what was the meaning of your statement "$$p = h / \lambda$$, so I should have said the photon's momentum is decreased (divided) by a factor of (1+v/c)"?

(d) characterize any error I make as evidence of my ignorance,

Instead of throwing around hostile accusations based on who knows what, could you please provide examples of posts where I do the things you accuse me of? I certainly don't think anyone who looks back on this thread will find that I have characterized "any error" you make as evidence of ignorance--for example, I never said you were ignorant for saying the momentum was reduced by "(1-v)/c", an equation which you later corrected to (1+v/c). But I did tell you that the corrected equation was still wrong because it is based on an incorrect combination of a classical equation and a quantum equation, and since you never retracted that equation even after I explained this, I said "the actual claims you are making are incorrect and not a part of standard physics, regardless of whether you understand this or not" (which I immediately followed by a suggestion that I might still be misunderstanding you, and if so requested that you clarify).

(e) hijack this thread with unrelated issues that were not resolved to your personal satisfaction in other threads about other topics.

Again, examples please. I think I made one brief and nonspecific reference to the fact that you had wrongly combined equations from different domains in previous threads, but since I didn't even refer to a specific past thread I obviously wasn't trying to hijack the discussion or actually revisit those previous topics.

I see, if I don't continue arguing with you ad nauseum and ultimately agree that you are right and I am wrong about every point you want to debate, then you will "report" me.

Nope, I never said anything like that. Just said that if you continued to repeat incorrect claims (like the one about momentum being reduced by (1-v)/c ) and aren't even willing to debate them in a rational way, then I will report that, because it goes against the rules of the forum. If you are willing to have a rational debate like an adult, then I wouldn't report you even if you continued to disagree with me and say your original claims were correct. Likewise, if you simply stop repeating these claims that's fine with me too, it's the fact that you kept sticking by claims and being unwilling to actually discuss the reasoning behind them that tempted me to report you.

Gosh now that's an invitation to rational discussion if I ever heard one.

Like I said, as long as you are willing to actually discuss things rationally I'm not going to report you.

Let me help you out. I hereby withdraw and disavow ALL statements I made in this thread

Then I guess we're done with this thread, although on a personal level I'm not happy about all the nasty accusations you've thrown my way.

Now please stop harassing me.

Again, it is not "harrassment" to try to correct claims of yours about physics I think are mistaken on a thread in a physics forum. Likewise it is not "putting words in your mouth" to quote things you have said, explain what I think you meant and why I think you'd be wrong under that interpretation, and invite you to clarify if my interpretation is wrong. Please stop with the baseless, nonspecific accusations of unfair debating tactics on my part, you have never pointed to any specific post where I have actually done any of the things you accuse me of doing.

 

[nutgeb]

It turns out Jesse's debating style is appropriate and that my use of the "h word" is inappropriate, in fact it violates a forum policy against obscenity. Once again I stand corrected.

Jesse, I withdraw that claim and apologize.

I look forward to vigorous future debates on other subjects.

 

[JesseM]

Thanks nutgeb, I appreciate it.

 

[nutgeb]

Section 11 of http://arxiv.org/abs/physics/0605204" , cited in the Wikipedia article "Relativistic Doppler Shift", includes the following:

"In deriving the mass-energy relation we show, as a by-product, that the energy of radiation suffers a Doppler shift too, without having to resort to the energy-frequency relation of elementary quantum mechanics. This will allow us to introduce the “four-momentum” of a particle in a quite natural way."

 

[JesseM]

Section 11 of http://arxiv.org/abs/physics/0605204" , cited in the Wikipedia article "Relativistic Doppler Shift", includes the following:

"In deriving the mass-energy relation we show, as a by-product, that the energy of radiation suffers a Doppler shift too, without having to resort to the energy-frequency relation of elementary quantum mechanics. This will allow us to introduce the “four-momentum” of a particle in a quite natural way."

Thanks for the link. It looks to me like they are saying that they can derive the difference in energy for an electromagnetic wave in two frames, not the traditional Doppler shift equation which gives the difference in frequency/wavelength in two frames...even if one chooses to call this a "Doppler shift in energy", they are deriving a relativistic formula $$E' = E((1+ \beta )/(1- \beta ))^{1/2}$$, whereas you were saying that some sort of classical Doppler shift equation could be derived from energy/momentum considerations. Also note that they specifically avoid using the quantum rules relating momentum and wavelength which you had invoked at certain points. I wasn't arguing that it was definitely impossible to find some derivation of a Doppler shift from energy considerations (I wasn't sure either way, and I'm still not sure whether one could derive the frequency/wavelength relation from energy/momentum in relativistic electromagnetism), I was just arguing that you didn't seem to have a derivation yourself so your confident statements that it was possible were unjustified, and that some of your stabs in the direction of a relation between the two were based on incorrectly combining quantum formulas with classical ones.

 

[nutgeb]

I had read Moriconi's paper long before I made my first post in this thread. Took me a while to remember the source and refresh on the details.

 

[JesseM]

I had read Moriconi's paper long before I made my first post in this thread. Took me a while to remember the source and refresh on the details.

And as I said, I think what the paper was saying was fairly different from what you were saying...you seemed to be arguing we could get the classical Doppler shift as opposed to the relativistic one from energy/momentum considerations, and you also seemed to be making use of quantum rules involving frequency/wavelength like $$p = h / \lambda$$ as a basis for your statement that the momentum would be reduced by a factor of (1+v/c) in the observer frame (whereas the Moriconi discussion avoided invoking any quantum rules, and in fact had nothing to do with frequency or wavelength whatsoever). As always, if this is a misunderstanding of what you meant please clarify.

 

[nutgeb]

A relativistic formula can only be used with respect to relativistic Doppler shift.

I think we've beat this topic to death. Thanks for the thoughts about QM and relativity, which are consistent with Moriconi.

 

[JesseM]

A relativistic formula can only be used with respect to relativistic Doppler shift.

Of course. But you seemed to be saying earlier that the classical (non-relativistic) Doppler shift can be derived from energy/momentum considerations, which is not supported by the Moriconi paper. Anyway, if you're done with this topic then I'm fine letting it be.