Speed of light is constant because of doppler effect?

[linklink]

Doppler effect told us that the frequency and wavelength changed but not the speed of wave if the transmitter or receiver is moving. Could I interpret Doppler Effect as follow:
Frequency/wavelength change for different observers, however, the speed of wave is constant for all observers.

If it is true, why is it so special that Einstein picked the constancy of speed of light as the postulate of SR? Could I use sound instead and then do the Lorentz transformation by using sound wave and say that "speed of sound is constant, nothing can travel faster than the speed of sound"?

 

[Quinzio]

Doppler effect told us that the frequency and wavelength changed but not the speed of wave if the transmitter or receiver is moving. Could I interpret Doppler Effect as follow:
Frequency/wavelength change for different observers, however, the speed of wave is constant for all observers.

You're messing up things a bit.
IF, and only IF, the speed of the wave is equal to the speed of light, then the speed of the wave is the same for all observer (because speed of light is the same for all observer).
If the speed of the wave is not the speed of light then the other observer will have to relativistically add their own speed.

Frequency you perceive is another thing:
A fat guy is sitting at the end of a conveyor belt. The conveyor carries him Coca-Cola bottles he drinks.
Speed of wave = speed of the conveyor belt
Wavelength = distance between the Coca bottles
Frequency = how much Coca bottles the guy drink in a second /hour (or the inverse of the time between two Coca bottles drinking).
I could make the conveyor move faster, and increase the distance between the bottles so the frequency will remain the same.

The guy could decide he wants to drink more bottles in an hour. so he moves towards the beginning of the conveyor, in order to pick up more bottles in a unit time, so he increases the drinking frequency (doppler effect).

As you can see, the speed of light here has nothing to do.

If it is true, why is it so special that Einstein picked the constancy of speed of light as the postulate of SR?

Speed of light is a fact of the universe, non a postulate. Einstein could do nothing else than acknowledge that nothing will travel faster than light, and other facts...

Don't call it speed of light. Call it maximum speed of the universe.
It happens that light is traveling at the max speed so we called it speed of light, but light is only one of the things that travel at max speed.
We could have called it speed of electromagnetic waves.

Could I use sound instead and then do the Lorentz transformation by using sound wave and say that "speed of sound is constant, nothing can travel faster than the speed of sound"?

Not really.
As I exaplained before speed of light is a bad name because it seems it depends on light or any other means that happens to travel at max speed.
Out there there is a max speed, then there are objects that travels at or near that speed. Other things, like sound waves, are turtles in comparison to the max speed, so Lorentz has little to do with them.
Of course you can apply Lorentz transform to that but you will yeld negligible effects.
:)

 

[linklink]

I guess I misunderstand the meaning of doppler effect...

Let's say Alan is stationary with respect to the air and Bill is moving towards him at 30m/s. The distance between Alan and Bill is 360m, and speed of sound in air is 330m/s. So if Bill speaks with frequency f, what Alan perceived is that the frequency increased to (11/10)f.
But then could I say the speed of sound Alan perceived is still 330m/s while the actual relative speed of sound to Alan is 360m/s and Alan will hear Bill's voice at exactly t=1s?

 

[ZealScience]

Doppler effect told us that the frequency and wavelength changed but not the speed of wave if the transmitter or receiver is moving. Could I interpret Doppler Effect as follow:
Frequency/wavelength change for different observers, however, the speed of wave is constant for all observers.

If it is true, why is it so special that Einstein picked the constancy of speed of light as the postulate of SR? Could I use sound instead and then do the Lorentz transformation by using sound wave and say that "speed of sound is constant, nothing can travel faster than the speed of sound"?

I think you got some misunderstanding here. If wave length or wavelenght changes how can speed be constant? So it has nothing to do with doppler effect in changing frames, the effect is more on GR which deals with gravitational doppler shift. Speed of light is derived by Maxwell's equations and it is correct, to fit it space-time must follow lorentz transformation. Also notice that doppler effect of sound is non-relativistic, which deviates a little bit from that of light.

 

[linklink]

If wave length or wavelenght changes how can speed be constant?

what I think is if the receiver is moving towards the wave, the frequency appears higher and the wavelength appears shorter so that their product(speed) remain the same, is true for EM wave or any other wave?

 

[ZealScience]

what I think is if the receiver is moving towards the wave, the frequency appears higher and the wavelength appears shorter so that their product(speed) remain the same, is true for EM wave or any other wave?

If you mean that, it is true. But that phenomenon is more on gravitational effect as I posted. If you observing object approaches event horizon of the black hole, they would become redder. However, the doppler effect is a "side effect" of time dilation (which comes from the property of speed of light), not the doppler shift causing c to be constant.

 

[ghwellsjr]

If you do doppler experiments with sound, you can determine the speed of the sources and emitters with respect to the stationary medium that carries the sound waves and you can figure out the speed of that medium with respect to the observers. This is because the doppler shifts are not always reciprocal between the two observers. The forumla for calculating the doppler frequency involves the speed of the two observers with respect to the medium.

If you do doppler experiments with light, you will find that the frequency shifts depend only on the relative speed of the two observers and does not depend on their actual speed through any fixed medium. So the propagation of light is different than the propagation of sound and you cannot make your idea work.

You could postulate that the speed of sound is constant for all observers but then you could not also postulate that the laws of physics are the same for all observers. What Einstein did was show that by giving up the notion of absolute time and absolute space, you could postulate that the speed of light is constant and that the laws of physics are the same for all observers in relative motion.

 

[linklink]

You could postulate that the speed of sound is constant for all observers but then you could not also postulate that the laws of physics are the same for all observers. What Einstein did was show that by giving up the notion of absolute time and absolute space, you could postulate that the speed of light is constant and that the laws of physics are the same for all observers in relative motion.

So...I could say that speed of any wave is constant. However, the properties of EM wave is different from other kinds of wave and light happens to be the only choice for SR to be correct. That's the idea, right?

 

[ghwellsjr]

Right.

 

[linklink]

Thanks guys.
I guess I got a better understanding about doppler effect now~

 

[Dale]

Could I use sound instead and then do the Lorentz transformation by using sound wave and say that "speed of sound is constant, nothing can travel faster than the speed of sound"?

No, the speed of sound is not frame invariant.

 

[harrylin]

So...I could say that speed of any wave is constant. However, the properties of EM wave is different from other kinds of wave and light happens to be the only choice for SR to be correct. That's the idea, right?

Sorry that's not really correct: SR models EM waves just like classical waves, and obeying Maxwell's laws - that was rather well established at that time (ignoring quantum effects).

Nevertheless, an increasing number of measurements also suggested that in vacuum the speed of light and radio waves as we measure it (following a certain calibration procedure) is like a law of nature: it is always the same.

SR is based on those two seemingly contradictory observations; the solution is that our measurements of "time" and "length" depend on our system ("relative to the observer").

As a result, the observed Doppler effect is also a little affected (due to "time dilation").

Harald

 

[ghwellsjr]

SR is based on those two seemingly contradictory observations;

SR is based on two seemingly contradictory postulates, not observations.

Linklink asked if he could postulate that the speed of sound is constant, which I said he could, but then he could not also postulate that the laws of physics would be the same for all observers in relative motion. Light is the only wave for which this works. I think he understood that.

So I don't understand why you are saying that his summary of my statement is incorrect.

 

[grav-universe]

The speed of sound is constant in all directions, isotropic, in one frame only, that which is stationary to the medium. In all other frames it cannot be measured isotropically, so does not have the same measured speed in all directions. Clocks can be synchronized along a particular line in order for a frame to measure the speed of sound isotropically in either direction along that line, but it will be measured at different speeds in other directions. This because SR is not based upon the effects of the aberration of a medium alone, the effect of which is stated in part of the second postulate, but also the results of the M-M experiment, whether or not Einstein specifically acknowledges that about his paper, as it is still demonstrated in the same way as that of the M-M experiment.

In order for a frame to measure the speed of sound isotropically in every direction, without the need for introducing clocks, then sound pulses sent simultaneously from a point of origin to the same distance in any direction, along rods of equal lengths when laid end to end and then rotated to other directions, when the sound pulses reflect off something at the end of the rods and travel back to the origin, they must be received at the point of origin simultaneously. Clocks can then be applied by synchronizing so that the same one way speed is measured in every direction as a direct consequence of the two way time being the same in all directions away and back to a single clock at the origin, over distances that are considered equal within the frame of the rods. As has been found by working through the equations that would require this of any such M_M type experiment with a null result for a medium, in order for the pulses to be emitted and likewise received simultaneously, which all frames must agree upon, then another frame that is moving relative to the M-M type experiment but is stationary to the medium so itself measures an isotropic speed, then in order for the observed frame to measure the medium isotropically as well, the stationary frame must measure the apparatus to be contracted in the line of motion, Lx, as compared to any contraction perpendicular to the line of motion, Ly, by a factor of Lx / Ly = sqrt(1 - v^2 / V^2). According to a frame of reference that measures a medium isotropically at V and the apparatus is moving by a relative measured speed v, that particular observed apparatus can only be measured to contract by a factor with one specific value V, which is determined to be the speed of light, so we cannot have V = c and at the same time have V equal to the speed of sound.

 

[harrylin]

SR is based on two seemingly contradictory postulates, not observations.

Einstein explained that those postulates are based on the observations that I described.

Linklink asked if he could postulate that the speed of sound is constant, which I said he could, but then he could not also postulate that the laws of physics would be the same for all observers in relative motion. Light is the only wave for which this works. I think he understood that.

So I don't understand why you are saying that his summary of my statement is incorrect.

It's not a difference of "the properties of EM wave" with other waves that matters.
What matters is that the differences in measurements of time and distance have much more impact on waves (or whatever) that propagate at the speed of light, than on waves that propagate at the speed of sound.

PS: I tried to clarify that SR does not propose something weird about the properties of light; what is special is the speed of light, which is a limit speed.

 

[linklink]

Linklink asked if he could postulate that the speed of sound is constant, which I said he could, but then he could not also postulate that the laws of physics would be the same for all observers in relative motion. Light is the only wave for which this works. I think he understood that.

Let me confirm that :)

Let's say Alan is stationary with respect to the air and Bill is moving towards him at 30m/s. The distance between Alan and Bill is 360m, and speed of sound in air is 330m/s. So if Bill speaks with frequency f.

If Alan measures the wave, he will find:
v' = 330+30 = 360
f' = f*330/(330-30) = (11/10)f
λ' = v'/f'

But if Bill sends out a light signal instead of speaking, Alan will measure the EM wave as follow:
v' = v = c
f' = f*c/(c-30)
λ' = v/f'

So Alan and Bill will both find the speed of light is c but they will find a different speed of sound wave, and that's why SR works only for c.

SR is based on two seemingly contradictory postulates, not observations.

I don't understand this, why is the postulates seemingly contradictory?

 

[ghwellsjr]

The speed of sound is constant in all directions, isotropic, in one frame only, that which is stationary to the medium. In all other frames it cannot be measured isotropically, so does not have the same measured speed in all directions. Clocks can be synchronized along a particular line in order for a frame to measure the speed of sound isotropically in either direction along that line, but it will be measured at different speeds in other directions. This because SR is not based upon the effects of the aberration of a medium alone, the effect of which is stated in part of the second postulate, but also the results of the M-M experiment, whether or not Einstein specifically acknowledges that about his paper, as it is still demonstrated in the same way as that of the M-M experiment.

In order for a frame to measure the speed of sound isotropically in every direction, without the need for introducing clocks, then sound pulses sent simultaneously from a point of origin to the same distance in any direction, along rods of equal lengths when laid end to end and then rotated to other directions, when the sound pulses reflect off something at the end of the rods and travel back to the origin, they must be received at the point of origin simultaneously. Clocks can then be applied by synchronizing so that the same one way speed is measured in every direction as a direct consequence of the two way time being the same in all directions away and back to a single clock at the origin, over distances that are considered equal within the frame of the rods. As has been found by working through the equations that would require this of any such M_M type experiment with a null result for a medium, in order for the pulses to be emitted and likewise received simultaneously, which all frames must agree upon, then another frame that is moving relative to the M-M type experiment but is stationary to the medium so itself measures an isotropic speed, then in order for the observed frame to measure the medium isotropically as well, the stationary frame must measure the apparatus to be contracted in the line of motion, Lx, as compared to any contraction perpendicular to the line of motion, Ly, by a factor of Lx / Ly = sqrt(1 - v^2 / V^2). According to a frame of reference that measures a medium isotropically at V and the apparatus is moving by a relative measured speed v, that particular observed apparatus can only be measured to contract by a factor with one specific value V, which is determined to be the speed of light, so we cannot have V = c and at the same time have V equal to the speed of sound.

I think you're missing the point. Linklink was asking why he couldn't reject Einstein's notions of physics and establish his own notions based on a constant speed of sound. If he were to do that, even if an experiment showed that round-trip echoes did not arrive simultaneously from different directions, he could still postulate that the speed of sound were constant but that would require him to have a weird sort of physics that would claim that time progressed at different rates based on direction and on speed through the medium. And that's the point--he could not also postulate that the laws of physics were the same for all observers, as there would be one set of laws for observers stationary in the medium and other sets of laws for observers that were traveling in different directions and at different speeds.

 

[ghwellsjr]

SR is based on two seemingly contradictory postulates, not observations.

Einstein explained that those postulates are based on the observations that I described.

I am not aware that Einstein ever explained that his second postulate was based on any observation. Could you provide a reference please?

Linklink asked if he could postulate that the speed of sound is constant, which I said he could, but then he could not also postulate that the laws of physics would be the same for all observers in relative motion. Light is the only wave for which this works. I think he understood that.

So I don't understand why you are saying that his summary of my statement is incorrect.

It's not a difference of "the properties of EM wave" with other waves that matters.
What matters is that the differences in measurements of time and distance have much more impact on waves (or whatever) that propagate at the speed of light, than on waves that propagate at the speed of sound.

Maybe so, but that is not what is significant in this thread. What is significant in this thread is the issue of doppler and why the doppler effect for sound is fundamentally different than the doppler effect for light and it's not merely because sound is so much slower than light. It's because the in-line doppler effect for light has only one variable in it, the relative speed between the two observers, whereas the in-line doppler effect for sound has more than one variable in it because it needs to take into account the relative speeds of the observers through the medium. Because of this, the doppler effect for light is given a special name, Relativistic Doppler.

 

[ghwellsjr]

Let me confirm that :)


If Alan measures the wave, he will find:
v' = 330+30 = 360
f' = f*330/(330-30) = (11/10)f
λ' = v'/f'

Your equation for the frequency is correct but I don't know why you are including the other two equations. Doppler is normally only concerned with frequencies, not velocities, wavelengths or distances. We do use velocities to calculate doppler but not the other way around. And we normally are comparing the same frequency emitted by both observers and seeing how they are shifted differently when received by the other observer. So in your example, we should also calculate what frequency Bill measures of the same frequency f coming from Alan. In this case, the answer is

f'' = f*(330+30)/330 = (12/11)f​

And so you can see that they both hear a different frequency from the other one even though they are both emitting the same frequency.

But if Bill sends out a light signal instead of speaking, Alan will measure the EM wave as follow:
v' = v = c
f' = f*c/(c-30)
λ' = v/f'

So Alan and Bill will both find the speed of light is c but they will find a different speed of sound wave, and that's why SR works only for c.

No, this is not correct. I don't know what you are doing. You need to use the Relativistic Doppler factor when considering light.
For observers moving toward each other, it is:

√[(1+ß)/(1-ß)] where ß is the speed as a fraction of the speed of light or v/c.

Now in your example, v is so much smaller than c that the Doppler factor is essentially 1. Nevertheless, it yields the same frequency shift for both observers. In fact, it doesn't matter how fast they are approaching each other, they will both measure the Doppler frequency shift to be the same as the other one measures.

I don't understand this, why is the postulates seemingly contradictory?

Prior to Einstein, everyone believed that time and space were absolutes and that makes it impossible for the laws of physics and the speed of light to be the same for all observers no matter their relative speeds. By absolute, we mean that there is one universal "clock" by which the entire universe ticks and one universal standard for distance. Under those conditions, it appears that the laws of physics and the constant speed of light could not both be true for all observers.

 

[grav-universe]

I think you're missing the point. Linklink was asking why he couldn't reject Einstein's notions of physics and establish his own notions based on a constant speed of sound. If he were to do that, even if an experiment showed that round-trip echoes did not arrive simultaneously from different directions, he could still postulate that the speed of sound were constant but that would require him to have a weird sort of physics that would claim that time progressed at different rates based on direction and on speed through the medium. And that's the point--he could not also postulate that the laws of physics were the same for all observers, as there would be one set of laws for observers stationary in the medium and other sets of laws for observers that were traveling in different directions and at different speeds.

Nothing that can be done with clocks alone (without changing how we consider distances to be measured in different directions) will ever allow all inertial frames to measure an isotropic speed of sound. This is because in order to be able to measure an isotropic speed of a medium, pulses must travel the lengths of the rods of equal length in every direction and back along the same rods to reach the origin simultaneously, thereby gaining a null result in every inertial frame for an M-M type experiment. We can see then that the same distances are traveled in the same times, so clocks can be synchronized within the frame to measure the speed isotropically. If a null result is not gained, then the same times are not measured by the single clock at the origin, whereby isotropic speeds in different directions is not gained according to that single clock, so neither can it be gained regardless of how we set the timing rates or synchronize other clocks throughout the same frame.

Two inertial frames can only measure an isotropic speed for a particular speed V, based upon what must be true if both gain a null result for the M-M experiment. Since a frame that is synchronized to measure the isotropic speed V of a particular medium will measure a contraction of another frame that also measures an isotropic speed of the same medium as Lx / Ly = sqrt(1 - (v / V)^2), which can only be observed with that specific contraction for one particular value V, then only that speed V is isotropic to both frames. We gain a null result for light, and since the light medium fills the universe and our frame is arbitrary, all inertial frames should then gain a null result for light, so V = c only (although with a different timing rate another frame might measure c', but still isotropically only for light).

 

[ghwellsjr]

Nothing that can be done with clocks alone (without changing how we consider distances to be measured in different directions) will ever allow all inertial frames to measure an isotropic speed of sound.

I didn't say that it could be done with clocks alone, I agree it would also require changing the meaning of distance measurements and a whole lot of other things, that's why I called it "a weird sort of physics". It's not worth spending a lot of analysis on. My only point is that you couldn't postulate that the speed of sound was a constant in every frame and postulate that the laws of physics would be the same in every frame and I think you are pointing out more reasons why the physics would be of a weird sort, not only being frame-dependent, but also being direction-dependent. It seemed pretty obvious to me without going into all these details.

 

[harrylin]

I am not aware that Einstein ever explained that his second postulate was based on any observation. Could you provide a reference please?

OK, in his 1905 paper he merely hinted at where he got it from:

These two postulates suffice for the attainment of a simple and consistent theory of the electrodynamics of moving bodies based on Maxwell's theory for stationary bodies.

http://www.fourmilab.ch/etexts/einstein/specrel/www/

And in 1907 he clarified it a little better:

[this] "principle of the constancy of the velocity of light," is at least for a coordinate system in a certain state of motion [..] made plausible by the confirmation through experiment of the Lorentz theory [1895]

- Uber das Relativitatsprinzip und die aus demselben gezogenen Folgerungen
http://www.soso.ch/wissen/hist/SRT/E-1907.pdf

He explained the same (that the light postulate is based on the success of the Maxwell-Lorentz theory) in one or two other papers but I don't have an index in my head. :tongue2:

Maybe so, but that is not what is significant in this thread.

Indeed! I just wanted to make sure that the OP doesn't think that SR works because light is weird. What matters is that light propagates at the limit speed.

What is significant in this thread is the issue of doppler and why the doppler effect for sound is fundamentally different than the doppler effect for light and it's not merely because sound is so much slower than light. [..]

Right - the observed Doppler effect is only symmetrical for signals that propagate at the speed of light. What matters for this thread is that the Doppler effect is not the cause of a property of light or the speed of light.

Cheers,
Harald

 

[harrylin]

[...]
Prior to Einstein, everyone believed that time and space were absolutes and that makes it impossible for the laws of physics and the speed of light to be the same for all observers no matter their relative speeds. By absolute, we mean that there is one universal "clock" by which the entire universe ticks and one universal standard for distance. Under those conditions, it appears that the laws of physics and the constant speed of light could not both be true for all observers.

To elaborate a little more, along the lines that Einstein explained it:

Suppose that you measure with a loudspeaker and a microphone on the road the speed of sound as 350 m/s in all directions. Now, if you assume that sound is made up of waves, you will expect that someone with such equipment on the roof of a car will measure the speed of a sound wave as for example 350+30=380 m/s for a frontal wave. You will be greatly surprised if you hear that from the car the speed of sound is also measured as 350 m/s in all directions. That would be normal for bullets, but unexpected for waves. So, postulating light as a wave seems contradictory to postulating that the speed of light will be measured the same wrt relatively moving systems.

 

[Naty1]

too many imprecise statements posted ...for the OP, as a starter:

"For waves that propagate in a medium, such as sound waves, the velocity of the observer and of the source are relative to the medium in which the waves are transmitted. The total Doppler effect may therefore result from motion of the source, motion of the observer, or motion of the medium. Each of these effects is analyzed separately. For waves which do not require a medium, such as light or gravity in general relativity, only the relative difference in velocity between the observer and the source needs to be considered."

see here:
http://en.wikipedia.org/wiki/Doppler_shift

[There ARE differences in the exact Doppler effect for light and for sound because for sound the medium determines the wave speed.]

You might find the astronomy secton of the above reference of interest...