C as the speed of light and the speed of sound in Michelson-Morley.

[Dale]

The philosophical problem is, to which reference frame does the still air belong, in an intuitive sense.

We don't generally do philosophy here. There is no theoretical or experimental sense in which an object belongs to a particular reference frame. Any philosophical problems are tangential to the physics.

Can we say that one person can mathematically claim an air molecule is at rest, and another observer claim one and the same molucule is in motion in mathemaical terms

Yes, that is exactly what the principle of relativity implies, not just in mathematical terms, but in terms of the laws of physics.

 

[PeterDonis]

Let us say that the train and whistle (source) are approaching the stationary platform observer (receiver). The classical Doppler formula which the platform observer would use is:

ƒ = [c / (c + v_s)]ƒ₀

No, this would be the formula if the train and whistle were moving *away* from the platform observer. If they are moving *toward* the platform observer, the formula is

ƒ = [(c + v_s) / c]ƒ₀

Which is the same as the formula for the case of a stationary train and whistle and a moving observer, since v_s = v_r.

 

[Dale]

Let us say that the train and whistle (source) are approaching the stationary platform observer (receiver). The classical Doppler formula which the platform observer would use is:


ƒ = [c / (c + v_s)]ƒ₀


If the platform and the non-walking observer (as well as the entire earth) were approaching a stationary train and blowing whistle, then the classical Doppler formula would be:

ƒ = [(c + v_r) / c]ƒ₀

Clearly these two frequency values are different. So the platform observer can distinguish between the platform moving towards the train whistle, versus the train moving towards the platform.

The velocity in the classical Doppler is the velocity wrt the medium. You can distinguish between source moving wrt the medium and receiver moving wrt the medium according to the classical formula. However, you cannot distinguish between a moving and a stationary medium even classically.

 

[Simon Bridge]

Well Simon, we seem to be moving from physics into philosophy. Are you saying that the train observer and the platform observer measure different speeds for the sound wave from the train whistle?

No.
The quoted passage makes two assertions:
1. the doppler shift is different for moving but stationary observer vs moving observer stationary source. The actual equations are different in galilean relativity - which is what you want to use.
2. the speed of sound in a medium is not invarient like the speed of light in a vacuum is.

Well Nugatory, creating wind on a "windless day" seems to be more of a philosophical problem than a physics problem.

Nope - it is a well known and tested physical phenomenon - to make wind on a windless day you just have to have some speed wrt the air.
Try this yourself - drive in a car with the window down. Notice the wind?

A passenger will experience a "breeze" through an open window on a moving train. The wind has been created by the train moving through the air molecules, not the air moving past train.

Makes no difference to the physics - these two situations are physically identical from the POV of the passenger.

Even by the classical Doppler equations, these are not equivalent scenarios. The air and platform moving to meet a resting train is not philosophically equivalent to the train moving towards the stationary platform.

Can you provide an experiment that the Newtonian equivalence principle does not hold in these two circumstances?

We can demonstrate that galilean relativity does not hold at high speeds though - which is why we need to modify the doppler effect equation for special relativity.

 

[GerryB]

No, this would be the formula if the train and whistle were moving *away* from the platform observer. If they are moving *toward* the platform observer, the formula is

ƒ = [(c + v_s) / c]ƒ₀

Which is the same as the formula for the case of a stationary train and whistle and a moving observer, since v_s = v_r.

In any science text I have read on the classical Doppler effect, there is one set of formulas for the source approachig the receiver, or moving away from the receiver. There is another set of formulas for the receiver approaching the source, or moving away from the source. And they are noticably different.

 

[Dale]

Here is a good source on Doppler, which presents the acoustic and light in a reasonably well unified framework.
http://www.mathpages.com/rr/s2-04/2-04.htm

 

[GerryB]

Things don't "belong" to a reference frame. A reference frame is just a convention for using numbers to describe the position of an object at any given moment. We have this air molecule, and you might say that it's two meters east of you while I say it's five meters west of me - it's the exact same air molecule in the exact same place and we're using different reference frames to describe its position. There's no reason why it's more "my" air molecule at position -5 than it is "your" air molecule at position +2.

As my buddy once said while drinking some beers at a local bar, "Mathematics is not Reality."

The galilean transformation offers up two different values for one and the same particle (velocity, position, etc.) Which value is the truth, which is the REAL value?

 

[PeterDonis]

In any science text I have read on the classical Doppler effect, there is one set of formulas for the source approachig the receiver, or moving away from the receiver. There is another set of formulas for the receiver approaching the source, or moving away from the source. And they are noticably different.

The formulas for approaching vs. moving away should certainly be noticeably different, yes. For approaching, the observed frequency at the receiver should be higher than the emitted frequency at the source; but for moving away, the observed frequency should be lower. The formula you wrote down for the moving source case (the one with v_s) says the opposite.

But the formulas for source moving vs. receiver moving should be the same once you specify approaching or moving away. That's a simple consequence of the principle of relativity, and classical physics obeys the principle of relativity. Classical physics uses Galilean transformations instead of Lorentz transformations to mathematically realize the principle of relativity, but for speeds much less than the speed of light the two are the same.

I suspect that you have misread whatever reference you used. Can you give a specific reference that you are interpreting the way you describe?

 

[GerryB]

The velocity in the classical Doppler is the velocity wrt the medium. You can distinguish between source moving wrt the medium and receiver moving wrt the medium according to the classical formula. However, you cannot distinguish between a moving and a stationary medium even classically.

Certainly these formulas are with respect to the medium. On a windless day, the medium is connected to the stationary observer, which is connected to the stationary earth. So if the medium is moving towrds the source, then the platform and the Earth are also moving towards the stationary source, at the same velocity. So the receiver will use one set of formulas.

Again on a windless day, if the train is moving with a certain velocity relative to the medium, then the train is also moving at the same velocity with respect to the platform and the earth. This requires a different set of Doppler formulas.

The classical Doppler formulas do account for the scenario you have described.

Here is a good source on Doppler, which presents the acoustic and light in a reasonably well unified framework.
http://www.mathpages.com/rr/s2-04/2-04.htm

This is an excellent link. It shows the usage of c as the symbol for sound. It also shows how the STR Doppler is negligible at the slow speeds of a train as compared to light.

 

[GerryB]

The formulas for approaching vs. moving away should certainly be noticeably different, yes. For approaching, the observed frequency at the receiver should be higher than the emitted frequency at the source; but for moving away, the observed frequency should be lower. The formula you wrote down for the moving source case (the one with v_s) says the opposite.

But the formulas for source moving vs. receiver moving should be the same once you specify approaching or moving away. That's a simple consequence of the principle of relativity, and classical physics obeys the principle of relativity. Classical physics uses Galilean transformations instead of Lorentz transformations to mathematically realize the principle of relativity, but for speeds much less than the speed of light the two are the same.

I suspect that you have misread whatever reference you used. Can you give a specific reference that you are interpreting the way you describe?

Well Peterdonis, I first read this in Tipler Physics, but I have seen it in many other places as well, as I mentioned above:

http://en.wikipedia.org/wiki/Doppler_effect[/QUOTE]

Here is a good source on Doppler, which presents the acoustic and light in a reasonably well unified framework.
http://www.mathpages.com/rr/s2-04/2-04.htm

 

[Dale]

The classical Doppler formulas do account for the scenario you have described.

Yes, they do account for the scenario, and they do not support the idea that the speed of sound is frame invariant. Do you understand that now?

This is an excellent link. It shows the usage of c as the symbol for sound.

No it doesn't. It never once shows that. It is very consistent in using $c_s$ for the speed of a signal and c for the invariant speed.

 

[PeterDonis]

Well Peterdonis, I first read this in Tipler Physics, but I have seen it in many other places as well, as I mentioned above:

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

Ah, sorry, I was misinterpreting $v_r$ and $v_s$ as relative velocities of the source and receiver, instead of velocities relative to the medium.

I agree with DaleSpam's responses to you, though. The mathpages article he linked to makes clear the distinction between the speed of propagation of sound (or any other signal) in a medium ($c_s$) and the invariant speed dictated by relativistic kinematics ($c$).

 

[Nugatory]

The galilean transformation offers up two different values for one and the same particle (velocity, position, etc.) Which value is the truth, which is the REAL value?

There is no single true value. Go back to the example I proposed earlier, where an air molecule is two meters east of you and five meters west of me. Both "two meters east" and "five meters west" are accurate and true statements about its position, but they are not frame-invariant. Indeed, it is because they are frame-dependent that they can both be true; allow me to move around enough and I an make the statement "The air molecule is X meters from me" true for any value of X.

Compare those statements with the equivalent frame-independent invariant statement "The distance between us is seven meters and the air molecule is five/seventh of the way from me to you". That statement is true in all frames and for all observers, and if you change either of the numbers it will be false in all frames for observers - so that's a reasonable candidate for what you're calling a REAL truth.

Of course that's just position, not velocity. But again, there are frame-dependent and frame-independent ways of describing a velocity problem. We can say "You are approaching me from the north at ten meters per second", or we can say "I am approaching you from the south at ten meters per second"; they both can be true because they're both frame-dependent so if we look long enough we'll find some frame in which one of them is true. Again, however, there's an equivalent frame-independent statement that is true for all observers: "The distance between us is shrinking by ten meters per second".

 

[GerryB]

Now we have come back around to my original question. What properties do sound waves and light waves share such that scientists use the symbol c to represent the wave velocity of both?

 

[Dale]

The symbol j is used for the imaginary number and current density. The symbol $\Omega$ is used both for electrical resistance and the spatial part of a metric. The symbol f is used for both frequency and function. The symbol x is used for space and for an arbitrary unknown quantity. The symbol $\phi$ is used for potentials and for phase angles. And so forth.

Sound and light are both waves, so they share many substantive similarities (propagation, reflection, refraction, diffraction, energy, phase, frequency, amplitude, etc.). The use of the same symbol is not substantive, it is mere trivia or semantics.

Can you phrase your question in terms of physics, or are you actually interested in such trivia/semantics as the symbols used.

 

[GerryB]

The symbol j is used for the imaginary number and current density. The symbol $\Omega$ is used both for electrical resistance and the spatial part of a metric. The symbol f is used for both frequency and function. The symbol x is used for space and for an arbitrary unknown quantity. The symbol $\phi$ is used for potentials and for phase angles. And so forth.

Sound and light are both waves, so they share many substantive similarities (propagation, reflection, refraction, diffraction, energy, phase, frequency, amplitude, etc.). The use of the same symbol is not substantive, it is mere trivia or semantics.

Can you phrase your question in terms of physics, or are you actually interested in such trivia/semantics as the symbols used.

I do science, and I write poetry, so words are very important to me. In the examples you mentioned, certainly different branches of science or mathematics may, by happenstance, use the same symbol to describe very different properties. But in physics I would expect that there are some very specific reasons that physicists have chosen certain terminologies to communicate with other physicists.

 

[Dale]

But in physics I would expect that there are some very specific reasons that physicists have chosen certain terminologies to communicate with other physicists.

Sometimes there is, but often there is not. For instance color charge or the names of the quark and its flavors. Regardless of the reasons for the choice of a symbol, it is semantics, not physics. Experimental results don't care what symbols we use nor why we use them. "A rose by any other name..."

If you change your mind and decide later that you would like to have a conversation about propagation and interference in sound and light waves, then I would be glad to participate.

 

[Nugatory]

But in physics I would expect that there are some very specific reasons that physicists have chosen certain terminologies to communicate with other physicists.

Nope, it's purely historical accident. "P" for momentum probably comes from the Latin "petere", for example.

When you're writing down your ideas for others to read, it's advantageous to use whatever convention will be most familiar to the largest number of your potential readers, so once a convention is established it tends to become dominant.

 

[GerryB]

"A rose by any other name..."

When you're writing down your ideas for others to read, it's advantageous to use whatever convention will be most familiar to the largest number of your potential readers, so once a convention is established it tends to become dominant.

The ink on paper, the symbols, may not be important, but the meanings behind those symbols is of life and death importance. If the service engine light comes on in your car, the little light cannot harm you, but if you disregard the warning, you will have to suffer the consequence of having to pay for an engine that catches fire because it has no oil in it.

We as scientists must strive to agree on the meanings of the words and symbols we use to communicate with each other, how ever they may have started. If we do not make this agreement, then civilization will cease to exist.

 

[Dale]

The ink on paper, the symbols, may not be important, but the meanings behind those symbols is of life and death importance.

So we agree. Then please ask your question in terms of the meanings rather than the symbols. So far, it seems as though you are asking about the ink on paper rather than the physics.

 

[GerryB]

So we agree. Then please ask your question in terms of the meanings rather than the symbols. So far, it seems as though you are asking about the ink on paper rather than the physics.

Yes we agree on the importance of the meanings of words, but we seem to disagree on the meaning of invariance as it applies to sound, which is a key aspect of my question. So it seems pretty unresolvable.

 

[Dale]

To my knowledge "invariance" has only one meaning in special relativity. It means that a quantity or an equation does not change under the Lorentz transform. Is that not your understanding also?

 

[GerryB]

To my knowledge "invariance" has only one meaning in special relativity. It means that a quantity or an equation does not change under the Lorentz transform. Is that not your understanding also?

Well I agree with your definition of invariance in STR, but I think invariance has meanings beyond that. Since gallean transformations are contained within STR, but whose effects are negligible at the speeds of an average train, we can still use the old formulas. In classical galilean transformations, acceleration, distance intervals, and time intervals are also invariant (unchanging) quantities. So I am speculating that the observers in two reference frames moving relative to one another will measure the same velocity c for the sound wave, then I speculate that the equation I presented in my first post is valid. But it is only speculation, which is why I have asked the question.

Will these two observers use the same formula: L = ct + vt? This formula describes the idea that as the sound wave (velocity, c) travels rearward, it meets the caboose (velocity, v) traveling forward during the sane time. Each begins at the endpoints of the distance, L. This formula can be rearranged to the MM form: L / (c + v) = t; v = [L / t] - c, to find the velocity of the train relative to the earth.

 

[Dale]

Well I agree with your definition of invariance in STR, but I think invariance has meanings beyond that. Since gallean transformations are contained within STR, but are negligible at the speeds of an average train, we can still use the old formulas. In classical galilean transformations, acceleration, distance intervals, and time intervals are also invariant quantities. So I am speculating that the observers in two reference frames moving relative to one another will measure the same velocity c for the sound wave, then I speculate that the equation I presented in my first post is valid. But it is only speculation, which is why I have asked the question.

Even in Galilean relativity it is clear that the speed of sound is frame variant. In fact, in Galilean relativity ALL finite speeds are frame variant.

Let $v=dx/dt$ be any velocity. Then by the Galilean transform:

$t'=t$
$x'=x+ut$
$y'=y$
$z'=z$

then

$v=dx/dt=d(x'-ut)/dt=d(x'-ut')/dt'=dx'/dt'-u=v'-u \ne v'$

 

[Dale]

Closed pending moderation.

Edit: after discussion with the other mentors, the thread will remain closed. The idea that the speed of sound is frame variant has been succinctly proven here (for Galilean relativity) and is not a controversial topic (for either Galilean or special relativity) in the professional literature.