Red/blue shift question.

[Severian]

Would that negate the shifting effect in light then?

 

That would depend on which direction they are moving and how fast. I think in most cases it is not a very big effect.

[Daecon]

Depend on the direction? I wasn't aware there could *be* a difference depending on anything. Wouldn't that imply that the laws of physics are not constant with respect to your frame of reference?

 

However phrases like "in most cases" make me slightly uncertain...

[Saint]

But the important velocity difference is that between the source and the observer - not the signal propagation speed. As long as the observer isn't travelling at relativistic speeds relative to the source, it is exactly the same phenomena as it is for sound.

 

No, that's not the important velocity difference. The differences that matter are the difference between the source and the medium, or the observer and the medium. If you choose to model the doppler shift of sound in a laboratory setting, with no medium velocity, that's great, but it doesn't change the reality of the shifting mechanism.

 

Why are you holding onto a model for doppler shifting that relies entirely on additive velocities and propogation mediums to explain doppler shift in a theory that doesn't allow either?

[Severian]

Depend on the direction? I wasn't aware there could *be* a difference depending on anything. Wouldn't that imply that the laws of physics are not constant with respect to your frame of reference?

 

The laws of physics are always independent of your reference frame, but what you measure may not be. If I measure your speed relative to me, I will get an answer dependent on my reference frame. If an ambulance is moving away from you, it has a lower frequency siren than if it was moving towards you - that is the whole point of the doppler effect.

[Severian]

No' date=' that's not the important velocity difference. The differences that matter are the difference between the source and the medium, or the observer and the medium.

[/quote']

 

When discussing the doppler effect one normally assumes that the medium is at rest with respect to the observer. But it doesn't really matter - for sound travelling through air, the wind may speed up or slow down the propagation of the sound wave but this alone will not cause a frequency shift because the wave peaks are all slowed down (or speeded up) by the same amount, so the time between peaks stays the same. For light, there is no medium anyway.

 

Why are you holding onto a model for doppler shifting that relies entirely on additive velocities and propogation mediums to explain doppler shift in a theory that doesn't allow either?

 

You seem to have this ass-backwards. You are the one insisting that the medium is important - not me.

 

Here is a nice explanation:

http://archive.ncsa.uiuc.edu/Cyberia/Bima/doppler.html

[Daecon]

The laws of physics are always independent of your reference frame, but what you measure may not be. If I measure your speed relative to me, I will get an answer dependent on my reference frame.[/b'] If an ambulance is moving away from you, it has a lower frequency siren than if it was moving towards you - that is the whole point of the doppler effect.

(my bolding)

 

But isn't the speed of light independent of anyone's reference frame?

[MetaFrizzics]

Depend on the direction? I wasn't aware there could *be* a difference depending on anything. Wouldn't that imply that the laws of physics are not constant with respect to your frame of reference?

However phrases like "in most cases" make me slightly uncertain...

The idea that the laws of physics are the same in every reference frame is of course simply absurd.

 

In every mainline theory of Electromagnetisim or Gravity there are a unique set of preferred frames in which the laws take a simple and invariant form providing the laws themselves refer to coordinate systems at all. This unique and related set of frames are related by the fact they have constant relative velocities' date=' and none are undergoing absolute acceleration of any kind.

 

[b']Some theories have a 'coordinate-free' expression [/b]which then becomes 'invariant' but this is hardly meaningful in the context of relative measurements of distance, time, and motion, which are the only kinds one can make in the real world, i.e., from some actual reference frame. Thus while certain formalisms of General Relativity may appear to be 'coordinate-free' they are useless in this form for applying to real world problems.

 

Interestingly, there is a unique formulation of laws of motion and gravity which actually *does* offer an exact identical form of the laws in every reference-frame regardless of relative motion or absolute acceleration. It's called Relational Mechanics, and was formulated by A.T. Assis. However in this system inertial mass and gravitational mass are not defined but derived from the theory, and Einstein's Equivalence Principle is unnecessary.

[Severian]

(my bolding)

 

But isn't the speed of light independent of anyone's reference frame?

 

Yes, but the speed of light is not relevant here - it is the speed of the source with respect to the observer which is relevant.

[Severian]

The idea that the laws of physics are the same in every reference frame is of course simply absurd.

 

The only absurd thing around here is your belief that you know any physics.

 

In every mainline theory of Electromagnetisim or Gravity there are a unique set of preferred frames in which the laws take a simple and invariant form providing the laws themselves refer to coordinate systems at all. This unique and related set of frames are related by the fact they have constant relative velocities' date=' and none are undergoing absolute acceleration of any kind.

[/quote']

 

These frames are called inertial frames, and for the purposes of this discussion they are the only relevant frames (since the doppler shift has nothing to do with gravity).

 

Einstein's first postulate of Special Relativity is:

The laws of physics are the same in all inertial frame.

 

I think it is fairly amazing that classical electromagnetism, written down in 1856, is relativistically invariant, ie. it has the same form in all inertial frames. We had a relativistic theory of elctromagnetism almost 50 years before relativity!

 

Some theories have a 'coordinate-free' expression which then becomes 'invariant' but this is hardly meaningful in the context of relative measurements of distance, time, and motion, which are the only kinds one can make in the real world, i.e., from some actual reference frame. Thus while certain formalisms of General Relativity may appear to be 'coordinate-free' they are useless in this form for applying to real world problems.

 

Since I can make measurements in different frames of reference and compare the results, relativistic invariance is hardly useless.

 

Interestingly, there is a unique formulation of laws of motion and gravity which actually *does* offer an exact identical form of the laws in every reference-frame regardless of relative motion or absolute acceleration. It's called Relational Mechanics, and was formulated by A.T. Assis. However in this system inertial mass and gravitational mass are not defined but derived from the theory, and Einstein's Equivalence Principle is unnecessary.

 

I find it amusing that you support a Machian 'theory' which has the very property that you called 'absurd' in the first line of the very same post!

[MetaFrizzics]

The only absurd thing around here is your belief that you know any physics.

Wow, that seems harsh.

Have I attacked anyone else in such an extreme manner over differences of opinion or minor errors in phraseology? But I know you secretly like me. Spank me if you must. I am going to send you some pics from my latest 'glamour' photo-shoot you saucy, virilent, hairy-chested Sean Connery look-alike!

 

We had a relativistic theory of electromagnetism almost 50 years before relativity!

Actually, we had two. But only Heaviside, Weber, Poincaire, and Lorentz knew about it.

 

I find it amusing that you support a Machian 'theory' which has the very property that you called 'absurd' in the first line of the very same post!

You misread me: I said it was absurd to think that conventional theories suggest either that we have, or need invariant physical laws in *every* frame. It's not absurd to prefer a theory which offers formally invariant laws in every frame, whether accelerated or not.

 

But of course I am here to amuse and please you. That is why you love my contributions to the threads. I am your foil, your doppleganger, your alter-ego, your arch-criminal enemy, your greatest challenge. Your platonic life-partner: your intellectual match in the fields of your own expertise, and more than enough woman for you.

[Thomas Kirby]

Shouldn't resident experts hold themselves to a higher standard of behavior? I don't think that was called for, Severian.

[Severian]

Shouldn't resident experts hold themselves to a higher[/i'] standard of behavior? I don't think that was called for, Severian.

 

Which bit? Pointing out that Metafizzics doesn't know any physics or pointing out the fallacy of his statements?

[MetaFrizzics]

Just look at your avatar:

I know I can soften you up once you've been milked properly.

[Daecon]

The speed of light is irrelevent to a doppler-like effect? That's something I'd never have thought.

 

Could gravity not have anything to do with it at all? After all, if gravity affects even light, maybe it would "stretch" the light being emmited by a star into a slightly lower frequency, red-shifting it...? (As opposed to the source moving away, I mean.)

 

Is that theory even plausable?

[Severian]

The speed of light is irrelevent to a doppler-like effect? That's something I'd never have thought.

 

Let me qualify that statment. The speed of light does not effect the qualitative description of what is happening' date=' although it does effect the quantitative description.

 

Lets take a simple example:

 

My friend and I are standing a distance [math']d[/math] apart and he throws a ball at me, with velocity [math]v[/math] at intervals of time [math]\Delta t[/math]. Asuming we can neglect air resitance, the ball takes time [math]d/v[/math] to reach me, so the first ball hits me at time [math]t_1=d/v[/math], and the second ball hits me at time [math]t_2=d/v + \Delta t[/math]. The frequency of balls is [math]\frac{1}{t_2-t_1} = \frac{1}{\Delta t}[/math] and is independent of [math]v[/math]. So far so good.

 

Now, while still throwing the balls, my friend walks away from me with speed [math]u[/math] but still throws the ball at me with speed [math]v[/math] in my frame. (We are interested in the frequency in my frame, and since we will want to make the ball light later on, it makes sense to stay in my frame. Also, for sound, since the air is at rest, we should keep the same speed in the 'air's rest frame.) As before, the first ball (which he throws just as he starts to move backwards) hits me at time [math]t_1=d/v[/math]. By the time he throws the second ball, he is a distance [math]d+u \Delta t[/math] away, so the ball takes time [math]\frac{d+u \Delta t}{v}[/math] to cover the distance and hits me at time [math]t_2=\frac{d+u \Delta t}{v}+\Delta t[/math]. The frequency with which balls hit me is now [math]\frac{1}{t_2-t_1} = \frac{v}{u+v} \frac{1}{\Delta t}[/math]. So if he moves away from me, the frequency decreases.

 

This is exactly the doppler effect for sound. notice that the expression is dependant on the speed of sound [math]v[/math]. My point was that this formula is also completely valid for the doppler effect with light. This is because all of the quantities are defined in my frame of reference and relativity only effects the comparison of quantities in different frames.

 

To be fair though, we should point out (as I mentioned earlier) that if my friend is moving away at a relativistic speed, then [math]\Delta t[/math] is better to be defined in the 'ball thrower's" frame, since he is the one who decides when to throw. In this case, the time between his throws in my frame is time dilated to [math]\gamma \Delta t[/math], with [math]\gamma = \frac{1}{\sqrt{1-u^2/c^2}}[/math] so the frequency becomes: [math] \frac{v}{u+v} \frac{\sqrt{1-u^2/c^2}}{\Delta t}[/math]. This equation is now fully general and works for any situation.

 

Further, if the 'ball' is made of light, ie. [math]v=c[/math] this becomes [math] \frac{c}{u+c} \frac{\sqrt{1-u^2/c^2}}{\Delta t} = \sqrt{\frac{c-u}{c+u}} \frac{1}{\Delta t}[/math]

 

(I hope I haven't made any silly mistakes, since I did this on the fly without looking anything up....)

[MetaFrizzics]

Well, to prevent misleading anyone, a few things should be pointed out:

 

The Doppler Effect for sound and light differ in one important respect.

 

(1) Sound waves propagate in a medium. Motion of the source and of the observer are therefore distinguishable: "moving source" and "moving observer" signify motion relative to the medium. A different formula applies to each case.

 

(2) In the case of light however, one cannot distinguish between motion of the source and motion of the observer: only their relative velocity is defined, and there can be only one Doppler formula.

 

For source & receiver receding (expansion):

 

[math] f' = f \sqrt{\frac{1 - V/c}{1 + V/c}}[/math]

 

and for source & receiver approaching (contraction):

 

[math] f' = f \sqrt{\frac{1 + V/c}{1 - V/c}}[/math]

 

These are the relativistic Doppler formula(s). The radicals of these equations can be expanded using the binomial theorem: the result is the series,

 

[math] f' = f[1-\frac{V}{c}+\frac{3}{4}(\frac{V}{c})^2 - ...] [/math]

 

To a first order in V/c, the equation takes the simple form

 

[math] \frac{\Delta f}{f} = \frac{f' - f}{f} = - \frac{V}{c} [/math]

 

Where the minus signs refer to receding and are replaced with plus signs for the approaching case.

[MetaFrizzics]

Thus for Approaching objects,

 

[math] f' = f[1+\frac{V}{c}+\frac{3}{4}(\frac{V}{c})^2 - ...] [/math]

 

To a first order in V/c, the equation takes the simple form

 

[math] \frac{\Delta f}{f} = \frac{f' - f}{f} = + \frac{V}{c} [/math]

[Saint]

Severian - in your last example, say your friend throws a string of balls at time interval delta t while you are both standing still wrt one another and you are separated by some large distance. He then stops throwing the balls. You then start moving toward him. Will you see an increase in the frequency of the balls you receive? That is, in the frequency of the balls he has already thrown and are currently in transit? Basically, I want to know if you can influence the frequency of an existing beam of light (string of balls), or if the frequency shift can only be generated based on changing the relative distance from the source to the receiver.

 

Sorry if this is unclear. Hopefully you see what I'm getting at.

[MetaFrizzics]

The nonrelativistic Doppler formulas which apply to sound, for a stationary source and moving reciever is:

 

[math] f' = f(f-\frac{V}{c}) [/math] ....(receding: change to + sign for approaching)

 

and for the stationary receiver, moving source, you get:

 

[math] f' = \frac{f}{1 + V/c} [/math] ....(change + sign to minus for approaching)

 

(i.e., four equations instead of two.)

[Severian]

The Doppler Effect for sound and light differ in one important respect.

 

(1) Sound waves propagate in a medium. Motion of the source and of the observer are therefore distinguishable: "moving source" and "moving observer" signify motion relative to the medium. A different formula applies to each case.

 

Yes' date=' that is right. I did mention this in my post too. In the case I derived, the medium was at rest with respect to the observer. However, as long as you quote the propagation speed with respect to the observer (rather then with respect to the medium), you can use one formula (the one I wrote down). The motion of the medium relative to the observer would of course change this speed.

 

(2) In the case of light however, one cannot distinguish between motion of the source and motion of the observer: only their relative velocity is defined, and there can be only one Doppler formula.

 

Agreed, but again if one quotes the velocity of propagation with respect to the observer, this should be the same formula as you would use for sub-light propagators.

 

For source & receiver receding (expansion):

 

[math] f' = f \sqrt{\frac{1 - V/c}{1 + V/c}}[/math]

 

This is the same as the expression that I derived (the last equation of my post). The other equations can all be derived from this.

[MetaFrizzics]

Basically, I want to know if you can influence the frequency of an existing beam of light (string of balls), or if the frequency shift can only be generated based on changing the relative distance from the source to the receiver.

The short answer is no. Once the signal has been released it is independant of source, if it is in fact discrete packets of energy travelling through space.

[Severian]

Severian - in your last example' date=' say your friend throws a string of balls at time interval delta t while you are both standing still wrt one another and you are separated by some large distance. He then stops throwing the balls. You then start moving toward him. Will you see an increase in the frequency of the balls you receive? That is, in the frequency of the balls he has already thrown and are currently in transit?

[/quote']

 

In my example, I was assuming completely separate cases (so resetting the clock when he starts to move), but to answer your question: yes, you will increase the frequency for the balls in motion aswell as the ones he hasn't yet thrown.

[Saint]

Severian - this might be a clearer way to ask the question. If are in a space ship located 10 light-years from a star, and stationary wrt the star, when we start moving toward the star, will we immediately notice the bluse shift (asuming we are moving fast enough to produce an appreciable shift)? Or will we have to wait until the light from the star being emitted right now reaches us in order to notice the shift.

[MetaFrizzics]

Shouldn't resident experts hold themselves to a higher[/i'] standard of behavior? I don't think that was called for, Severian.

Well, to be fair, my sense of humour can be provocative sometimes.

As long as no one else is offended, I certainly am not offended by Severian's wry witty comments. It is important for those with smaller appendages to compensate by playfully attacking intellectual giants such as myself. It is the highest form of flattery, and I have a responsibility to take young physicists like Severian under my wings like a huge free-range fighting-hen would defend her chicks.

[MetaFrizzics]

Severian - this might be a clearer way to ask the question. If are in a space ship located 10 light-years from a star, and stationary wrt the star, when we start moving toward the star, will we immediately notice the bluse shift (asuming we are moving fast enough to produce an appreciable shift)? Or will we have to wait until the light from the star being emitted right now reaches us in order to notice the shift.

(1) The FREQUENCY (not the speed) of the light is dependant upon where the source is when it releases each pulse.

 

(2) If you haven't received a given pulse yet, you can change the time you receive it by travelling toward or away from the pulse (which is in transit).

 

(3) So yes, you can cause a red or blue shift in a stream of light which has already technically (Absolute time wise) been released by the distant star.

 

(4) Although Relativity forbids us to posit a fixed plane of 'Absolute Simultaneity', we can get around this by talking about whether or not a given event is inside or outside the 'light-cone' of the observer or receiver, and whether or not and when a signal will be received on the observer's timeline.

 

If you think about it, of course you can cause a red/blue shift by independantly changing your speed relative to a source. The times between release of light and our reception of it are so great (measured in hundreds or thousands of light-years!) that we might as well view all light available to us as 'already been released'. The red/blue shifts we observe are actually due to our motion relative to planes of propagation of EM waves now. If you couldn't create a shift by motion, we would never see any observable shifts now. All the shifts we see are based upon the earth's / solar system's current speed.

 

It is worthwhile to distinguish between the absolute frequency released by the burning star (which will reflect the elements present in it, creating a spectral thumbprint of frequency spikes) and the perceived frequency that the observer records. The observer moves through the 'peaks' and 'troughs' of a spherical expanding wavefront which is moving in a fixed manner. the observer darts in and out of these troughs and peaks in any way they desire (if sufficient acceleration is available).

 

The limits on 'shifts' are practically determined by the ability of the observer to accelerate in given directions. We could create a red/blue shift, but it would be awfully expensive fuel-wise!