Michelson-Morley experiment, speed of speed, c

[Geryllax Vu]

Can the speed of sound,c, be substituted for the speed of light,c, in the formula:

t = [L/(c-v)] + [L/(c+v)]

from the Michelson-Morley experiment to detect the aether?

[JulianO]

It could, but you'd be detecting the movement of the carrying body - such as the air, or wind speed.

[Geryllax Vu]

Exactly my line of thinking, "relative to what?". To expand my question, suppose that a sound pulse is emitted in a moving closed compartment (sealed door and windowless), then does doppler effect get cancelled out, thus making the sound a wave with constant velocity, like light?

[JulianO]

Exactly my line of thinking, "relative to what?". To expand my question, suppose that a sound pulse is emitted in a moving closed compartment (sealed door and windowless), then does doppler effect get cancelled out, thus making the sound a wave with constant velocity, like light?

Pretty much, after the initial effects of acceleration, box, air within, and emitter are all travelling at the same speed. It depends where your ear/microphone/detector is though. If it's in the box, no doppler. The same is true of light, thanks to M&M.

[andrew s]

The difference is that the speed of light c in free space is constant for all observers irrespective of there relative motion. The speed of sound in a medium (e.g. sound in air) is not constant and will be measured differently by observers with different relative velocities with respect to the medium (and each other). Light also shows a Doppler effect but the speed remains constant as the frequency and wavelength change together to keep c constant.

Regards Andrew

[Geryllax Vu]

ROFL, there is an observer in box -- with Schrodinger's cat. The box is moving with constant velocity, not accelerating. I've only peeked at that chapter. The M&M experiment was done in Cleveland, which is just up the North Coast from Toledo (Lake Erie). The more I read, the crazier they get.

[Geryllax Vu]

The difference is that the speed of light c in free space is constant for all observers irrespective of there relative motion. The speed of sound in a medium (e.g. sound in air) is not constant and will be measured differently by observers with different relative velocities with respect to the medium (and each other). Light also shows a Doppler effect but the speed remains constant as the frequency and wavelength change together to keep c constant.

Regards Andrew

I think that is the question I'm working towards. Is it possible for the observer in the box, not moving relative to the box, nor relative to the medium, to measure a constant velocity for sound? I think your last point leads to an even stranger idea I hadn't even thought of, what restraints are keeping the velocity of light constant, even when there are relative motions involved (source, receiver, medium)?

[andrew s]

I think that is the question I'm working towards. Is it possible for the observer in the box, not moving relative to the box, nor relative to the medium, to measure a constant velocity for sound? I think your last point leads to an even stranger idea I hadn't even thought of, what restraints are keeping the velocity of light constant, even when there are relative motions involved (source, receiver, medium)?

First question yes - provided the sound source is also not moving wrt the box,medium & you.

Second question - we don't know, it is just an observational fact that c is constant and is now built into the definition of our fundamental units - time, lehgth etc.

Andrew

[JulianO]

First question yes - provided the sound source is also not moving wrt the box,medium & you.

Second question - we don't know, it is just an observational fact that c is constant and is now built into the definition of our fundamental units - time, lehgth etc.

Andrew

Constant C also drops out of the Maxwell equations for light. That's what Einstein latched onto to come up with the special theory of relativity.

[Geryllax Vu]

First question yes - provided the sound source is also not moving wrt the box,medium & you.

Second question - we don't know, it is just an observational fact that c is constant and is now built into the definition of our fundamental units - time, lehgth etc.

Andrew

So to address your first point, is it possible for an observer in a box not moving relative to the sound source, nor the box, nor the medium, to measure a constant velocity for sound? This would then mean a yes to my original question of a valid substitution? As to your second point, this a bit of the old sticky wicket! To say that a value is constant is equal to saying that a value is neither increasing, nor decreasing. Light must have some mechanism by which it resists both acceleration and braking. This in itself might be evidence of an aether !!

[JulianO]

So to address your first point, is it possible for an observer in a box not moving relative to the sound source, nor the box, nor the medium, to measure a constant velocity for sound?

It's not possible for an observer in a fixed frame of reference to determine anything about absolute velocity of anything. Their motion and that of the box, provided it is constant is undetectable by any means. All you can say is you are moving relative to something else, and whether you are both moving, or one of you is fixed, is not determinable. This applies to light and sound and people.

This would then mean a yes to my original question of a valid substitution? As to your second point, this a bit of the old sticky wicket! To say that a value is constant is equal to saying that a value is neither increasing, nor decreasing. Light must have some mechanism by which it resists both acceleration and braking. This in itself might be evidence of an aether !!

You're into the realms of special relativity, and normal addition rules don't apply. Light always moves at the c for every observer, even those moving at 99.99% of c. How other observers view each other is the subject of the relativity equations. See http://stargazerslounge.com/topic/161113-travelling-at-the-speed-of-light/

[andrew s]

Constant C also drops out of the Maxwell equations for light. That's what Einstein latched onto to come up with the special theory of relativity.

Absolutly and the Maxwell equations transform with the Lorentz rather than the Galilean transformations which is why velocities don't just add in special relativity.

Andrew

[Geryllax Vu]

Absolutly and the Maxwell equations transform with the Lorentz rather than the Galilean transformations which is why velocities don't just add in special relativity.

Andrew

Absolutly and the Maxwell equations transform with the Lorentz rather than the Galilean transformations which is why velocities don't just add in special relativity.

Andrew

How far down the rabbit hole do you want to go?

Suppose a windowless train car is travelling on a high speed rail with a constant velocity (v = 200 m/s). An observer is locked within holding a single clock (stopwatch). A light emitter is affixed to the rear wall. The observer on the train car flips a switch to emit a light pulse towards the front wall along the length the length of the train car (L= 100 m).

When this light pulse reaches the forward wall it activates a sound emitter directed back towards the rear wall and the observer. Now when the observer had activated the light emitter he or she also started the stopwatch.

In this scenario the light pulse is effectively an instantaneous signal. Its travel time can't be measured by a stopwatch over this short distance. Thus, the only time that can be measured is the return trip for the sound pulse:

speed = distance / time

Using the Galilean transformation with a constant velocity:

L - vt = ct

L /(c+v) = t

v = [L / t] - c

v = 200 m/s L = 100 m c = approx. 300 m / s

[JulianO]

Using the Galilean transformation with a constant velocity:

L - vt = ct

I'm not sure what you're writing here, but it cant be right. The two t's aren't the same. It takes an unmeasureably short time for ct₁ and a measureable time for vt₂. I'm not sure what L is doing in there either.

So its

vt₂ = ct₁ = L

Nothing very mysterious going on.

[Geryllax Vu]

I'm not sure what you're writing here, but it cant be right. The two t's aren't the same. It takes an unmeasureably short time for ct₁ and a measureable time for vt₂. I'm not sure what L is doing in there either.

So its

vt₂ = ct₁ = L

Nothing very mysterious going on.

The two t's are the same!!! Hey, I got freaked out when i first saw it, TOO!!

I should have written it out but I was getting lazy, lol.

In most relativity books when they mention the mention M&M they show the algebra, but watch out they go over it very quickly:

speed = distance / time

c = L - vt₁ / t₁ As seen by an outside observer the train car is moving forward while sound pulse is travelling toward rear wall thus sound pulse travels shorter distance than length of train car, L

vt₁ Is how much distance the train car travels forward

ct₁ But during same time the sound pulse goes the opposite way, it's an algebra word problem when do they meet?

ct₁ = L - vt₁ Solve for t₁ first

ct₁ + vt₁ = L

t₁(c +v) = L

t₁ = L / (c + v) This is the classical formula from M&M. You can do a similar solution if train car goes in opposite direction t₂ = L /(c - v)

v = [L / t₁] - c Solving for v. observer can find absolute uniform motion from within his or her own reference frame, based only on info available within that reference frame

[JulianO]

The two t's are the same!!! Hey, I got freaked out when i first saw it, TOO!!

I should have written it out but I was getting lazy, lol.

In most relativity books when they mention the mention M&M they show the algebra, but watch out they go over it very quickly:

speed = distance / time

c = L - vt₁ / t₁ As seen by an outside observer the train car is moving forward while sound pulse is travelling toward rear wall thus sound pulse travels shorter distance than length of train car, L

But you said the observer is in the box. That changes everything!

vt₁ Is how much distance the train car travels forward

ct₁ But during same time the sound pulse goes the opposite way, it's an algebra word problem when do they meet?

ct₁ = L - vt₁ Solve for t₁ first

ct₁ + vt₁ = L

t₁(c +v) = L

t₁ = L / (c + v) This is the classical formula from M&M. You can do a similar solution if train car goes in opposite direction t₂ = L /(c - v)

v = [L / t₁] - c Solving for v. observer can find absolute uniform motion from within his or her own reference frame, based only on info available within that reference frame

No - still wrong, you're mixing up your frames of reference. The sound pulse sets off from one wall at ct. It travels at c through the air which is stationary as seen from the person in the carriage (as anyone who's ridden in a car, train, or aircraft will agree), but moving at v to an external observer . To the person in the carriage it will take time ct to reach the other end.

To someone outside watching this through a one way mirror, the sound wave would come up with your formula, and if they could hear it it would be doppler shifted too, but they can tell one of you is moving anyway!

The only way you could get your scenario is to have the air moving at v inside the carriage too,

You would then know something is happening as the air rushes past you, but whether you were moving, or just standing in a wind tunnel you wouldn't be able to tell.

[Geryllax Vu]

But you said the observer is in the box. That changes everything!

No - still wrong, you're mixing up your frames of reference. The sound pulse sets off from one wall at ct. It travels at c through the air which is stationary as seen from the person in the carriage (as anyone who's ridden in a car, train, or aircraft will agree), but moving at v to an external observer . To the person in the carriage it will take time ct to reach the other end.

To someone outside watching this through a one way mirror, the sound wave would come up with your formula, and if they could hear it it would be doppler shifted too, but they can tell one of you is moving anyway!

The only way you could get your scenario is to have the air moving at v inside the carriage too,

You would then know something is happening as the air rushes past you, but whether you were moving, or just standing in a wind tunnel you wouldn't be able to tell.

Precisely! I am mixing reference frames. As my buddy Ryan said over a couple beers at the bar, "Mathematics is not reality."

I think Reality is always mixing reference frames and not worrying about how we feel about it. She is like the ghost you see from the corner of your eye, but when you turn to look, you see nothing. But when the hair stands up on your neck, your skin gets the gooseflesh, and you break out in a cold sweat, you suddenly feel, you are not alone in the house.

In the windowless carriage, Time is the clue.

In my thought experiment, you don't need gravity, or wind, or visual cues from outside to tell you about your state of motion, or rest

If the measured time, t < L / c you are moving forward

If the measured time, t > L / c you are going in reverse

If the measured time, t = L / c you are at rest

You can then find the magnitude of the velocity of the train car, v, from the formulae shown above

[JulianO]

If the measured time, t < L / c you are moving forward

If the measured time, t > L / c you are going in reverse

If the measured time, t = L / c you are at rest

You can then find the magnitude of the velocity of the train car, v, from the formulae shown above

Try it - I think you'll find its always t = L / c whether your stationary or moving at a constant velocity.

[Geryllax Vu]

Suppose a hi- speed train car (L = 100m) is travelling on a long, straight, level, portion of track. It is windowless, on a windless day (to cancel Doppler Effect and galilean transformation, outside air molecules, medium, at rest relative to train car).

An open tube (a sort of waveguide open at either end to the ouside air) is constructed along a central axis running the length of the train car from the front wall to the rear wall. The tuibe is of sufficient diameter to allow the free flow of air without much turbelence.

At the rear wall is affixed a light emitter that is directed toward the front wall. It activates a sound emitter, by the phooelecteric effect. This sound emitter is suspended rigidly along the central axis of the tube so that it can direct a sound pulse back towards the rear wall where a sound receiver, a single clock , and a single observer are at rest at the other end of the tube.

The light emission is effectively an instantaneous signal, so the only time that can be measured by a typical clock is the time for the sound pulse to to return to the initial light emmision point.

However, while the sound pulse (c, constant velocity approx. = 300 m/s) is on its rearward flight, during the same time, the train car is moving forward at the constant velocity, v (v = 200 m/s). So, setting up an algebra word problem, the total distance travelled until they meet:

L = ct + vt

L = t(c + v)

L/t = c + v

[L/t] - c = v

Can the observer within the train car solve for his or her velocity, v?

[JulianO]

Can the observer within the train car solve for his or her velocity, v?

I'm not sure I fully understand the setup, but I think the answer is the observer can solve for the speed of the air passing through the tube.

However, there are lots of solutions to this.

The train could be moving at 200 m/s, the air could be blown down the tube at 200 m/s and the train stationary, it could be moving at 300m/s and a fan blows air 100 m/s the other way etc etc.

The observer can tell the air is moving relative to them, but that's all they an tell.

[Geryllax Vu]

-This thought experiment proposes an acoustic definition of absolute motion and simultaneity utilizing the Michelson-Morley interferometer formula and the violation of Galilean invariance by any type of waves:

T = [L /(c-v)] + [L /(c+v)] = [2Lc] / (c²-v²)

-On a windless day an archetypical flatbed train car of length, L, is in motion with the velocity, v. This velocity, v, can be solved for by rearranging the above formula and adding the total time, T, from two synchronized clocks. Also by a comparison of the times on the two clocks, simultaneity can be determined.

-Since the poles are at rest relative to each other but each is in motion (at the same velocity) relative the air, this dynamic of the experiment can lead to a means of determining the motion of the train car relative to the air.

-At either end of the train there are vertical poles (approx. 1m tall). Also at the midpoint of the train car is another pole of the same height. Mounted at top of the end poles is a light activated sensor electrically connected to a sound emitter directed back towards the central location. At the central location are a light emitter, two sound receivers (microphones), two synchronized clocks, and a single observer.

-Now at the speed of a typical train car (v << c) there should be no measurable or observable Relativistic effects; but the speed of sound waves could be easily measured by typical clocks. Thus, the time of travel for the returning sound signals are the only times that can be measured by the clocks. The experiment then begins.

-From the central location a split beam light emitter sends a light pulse to the fore and aft pole sensors. This light signal is effectively instantaneous in terms of travel time through the air, and by logical extension, each light signal arrives at either end pole simultaneously. Thus the fore and aft sound emitters are activated, each sending a sound pulse back towards the central location.

-If the time for each returning sound signal is measured on each clock, then the times can be added to get a total time, T. Then the velocity of the train car relative to the still air can be solved for. If the times are the same then the signals will arrive at the central location simultaneously, and the train car is at rest relative to the air. If the times are different then the train car is in motion in the direction of the lesser time. Thus this experiment finds the magnitude and direction of the train car velocity or absolute motion relative to the air (medium).

T = [.5L] / (c-v) + [.5L] / (c+v) = 2[.5L]c / (c² - v²)

- (Times and distances to and from the central location).

[michael.h.f.wilkinson]

The problem with the speed of sound is that sound travels through air. The air is the medium. You cannot have the medium not being at rest inside the train, without a 200 m/s gale blowing through the train. Now for a moment suppose there is a 200m/s wind blowing inside the train. Suppose I speak in the train, and somebody further "down-wind" hears me. With my voice I produce a 100Hz sound. The speed of the sound as detected by the listener (provided he can hear above the racket of a 200m/s = 720 km/h hurricane (hypercane?)), is 340+200m/s.The frequency remains the same, because each pulse travelling from my mouth to his ear takes the same time, because our relative distances do not change. The measured wavelength does change from 3.4m to 5.4m, but the ear is sensitive to frequency, not wavelength.

BTW, the ether was in trouble before Michelson-Morley: It's supposed physical properties were weird: incompressible to allow massive speed of travelling waves, but totally frictionless at the same time (or else planets would plunge into the sun).

[Geryllax Vu]

In a book I read online with Planck in the title, I will try to remember it. It spoke about how waves (sound and light) violate galilean invariance. So Im trying to exploit this in my analogy.

I moved to a flat bed train car from an enclosed train car. I realized that the reason the echo formula works is because the earth drags a layer of atmospherewith it as it moves through space. So T will always equal 2L / c. Thus staying with invariance. But if the object is moving and the medium is stationary (windless day), or the object is stationary and the medium is moving (gale force wind) then I think the MM formula will fit.

Im trying to find a simple principle first then add on foam density and energy transfer. I avoid Doppler altogether because the fore and aft poles on the train car are at rest relative to each other (hopefully) but each is moving in tandem relative to the air (medium). I dont think that the interactions on the molecular level are important yet.

This violation of invariance aspect is what I want. Thnx for your inputs.

[Geryllax Vu]

This is the book I was talking about: Physics Meets Philosophy at the Planck scale, violation of galilean invariance page 103:

http://books.google.com/books?id=NugSt4i2-KIC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q=galilean%20invariance&f=false