Measuring The Relative Velocity Of Light

[swansont]

The relative frequency of the light measured by the observer while in motion = 190,000 cycle per second

The relative distance traveled in one second, divided by the relative frequency, equals the relative wavelength, right?

So (186,000 + 4,000) divided by 190,000 equals the wavelength (1 mile) Agree?

No. Tell me how this doesn't imply that I am measuring the light to be moving at 190,000 miles/s

The part of the formula that you throw out is “the distance the observer has traveled relative to the source”.

...
THIS NUMBER IS CAUSED BY INCORRECT MATH; IT IS NOT CAUSED BY SR.

If you shine laser light of the right wavelength on an atom, it will absorb that light. If the atom starts moving, that absorption slows and stops as the light moves out of resonance - the color has changed. How is the atom "ignoring" the amount that it has moved? It isn't doing any math, AFAIK.

 

[grounded]

No. Tell me how this doesn't imply that I am measuring the light to be moving at 190,000 miles/s

That is exactly what I am saying.

If you shine laser light of the right wavelength on an atom, it will absorb that light. If the atom starts moving, that absorption slows and stops as the light moves out of resonance - the color has changed. How is the atom "ignoring" the amount that it has moved? It isn't doing any math, AFAIK.

I don't think the atom cares about the length of the wave, it only cares about the amount of time it takes to complete one wave.

 

[wespe]

EXACTLY

But nobody is making this mistake, only you imagine so!

By MEASURING the relative speed of light wrt ourself, we already account for the traveled distance.

Clasically, when approaching a light source with v, the value we measure should have been c+v. But experiments reveal it is really c.

You want to make it c+v again by adding v to the MEASURED RELATIVE speed c. Therefore you want to account for the traveled distance TWICE.

 

[quantumdude]

The distance light travels away from the source in one second = 186,000 miles
The distance the observer travels towards the source in one second = 4,000 miles
The wavelength of the light while at rest relative to the source = 1 mile
The above are known because we set up the experiment.

OK

The relative frequency of the light measured by the observer while in motion = 190,000 cycle per second

It is if you use the pre-SR Doppler formula.

The relative distance traveled in one second, divided by the relative frequency, equals the relative wavelength, right?

So (186,000 + 4,000) divided by 190,000 equals the wavelength (1 mile) Agree?

Right here is where you are directly contradicting both the experimental evidence, and SR. Please try to understand why.

According to pre SR theory, the wavelength will be 1 mile. That is because the speed that the light approaches the observer is 186,000 mps+4000 mps=190,000 mps. So, according to the observer, the wavelength is:

λ=(relative speed of light)/(relative frequency)=(190,000 mps)/(190,000 Hz)=1mile

But we now know that that is false. The Galilean velocity addition formula simply does not hold! Yet you keep happily applying it as though it does, and that’s why you go wrong.

Also, You don’t have to use the “relative distance traveled”. It’s the relative speed that counts. Your numbers for the relative distance and the relative speed happen to have the same magnitude because you are considering the motion over a time of 1 second. But the observer could have moved twice that distance in twice the time, and the above analysis would still give the same result.

What you should take away from this part:

1.Forget about relative distance traveled, and start thinking about relative speed.
2. You can’t simply add velocities like you have been doing.

The part of the formula that you throw out is “the distance the observer has traveled relative to the source”.
You throw it out by not including it into the scale of the equipment used to measure the speed or wavelength, which is why you will always measure the total relative distance traveled by the light and the observer to be 186,000 miles.
I agree that you are not consciously throwing this out; you just never realized it was missing.

I’m not throwing it out at all, because I don’t even work in terms of relative distances. As I keep telling you, relative distance is irrelevant to this analysis. What I do throw out is the increase in relative velocity between the detector and the light.

If you do not include the 4,000 miles the observer has traveled you will measure the following:
THIS NUMBER IS CAUSED BY INCORRECT MATH; IT IS NOT CAUSED BY SR.

No, you are mistaken. The discrepancy is due to the feature of SR that says that the relative speed between light and an observer is always the same.

(186,000 + 0) divided by 190,000 = .9789 miles

Is not that the wavelength you predict the observer will measure due to SR?

No, it isn’t. You are using the classical Doppler formula. When SR came along, the Doppler formula had to be rederived, and it is :

f=f₀((1+β)/(1-β))^1/2

when the source and detector are approaching.

If you tell me that you are dividing the frequency into 186,000 miles because that is what you measured, then I’m telling you that you are measuring it wrong.

I know what you are telling me. You are mistaken.

Since we set up the experiment, we know the observer is traveling towards the source at 4,000 miles per second. We also know that light will travel away from the source at 186,000 miles per second. We do not really even have to measure these values. We know the total relative distance traveled is 190,000 miles per second.

You have to be careful here, especially about the part in blue. First, relative distance is not measured in miles per second, it is measured in miles. What you mean is that the relative speed is 190,000 miles per second. And second, you are wrong about that: it is 186,000 miles per second. You will only get your result if you assume that SR is wrong, and that the Galilean velocity addition holds. It doesn’t.

The observer knows he is traveling towards the light source at 4,000 miles per second.
The observer knows the light will travel 186,000 miles away from the source in one second.

OK so far.

The observer knows the relative distance traveled is 190,000 miles per second, this is a fact.

No, it is a falsehood.

The rest of your post just seems to be more of the same, so I’m not going to continue. Grounded, please open your mind to the possibility that you are wrong. You say that you want us to listen to you , and I am. But you aren’t returning the favor.

edit: fixed quote bracket

 

[grounded]

By MEASURING the relative speed of light wrt ourself, we already account for the traveled distance.

Where? Can you tell me where the oscilloscope, or the interferometer, or what ever you used to measure the speed accounted for the distance traveled relative to the source?

 

[quantumdude]

Where? Can you tell me where the oscilloscope, or the interferometer, or what ever you used to measure the speed accounted for the distance traveled relative to the source?

The distance traveled relative to the source is irrelevant. What you are talking about is the relative speed (edit: between the source and the observer), but that is also irrelevant. When measuring the speed of light, all you need to do is measure the spacetime coordinates of absorption and emission.

 

[quantumdude]

Some observations on the corfrectness of information exchange re om_Mattson v Grounded.

It must be awfully hard to make any observations at all, with your head shoved so far up your hind end.

This post of yours contains such asinine misrepresentations of both SR and myself, that I find them unworthy of any detailed response.

You said:

You can use your theory all day long, but when you get to the "we can look from the train frame of the stationary frame equivalently, that I drop out of the conversation

I wish you would. Either that, or get your brain in gear, because you aren't helping, and you certainly aren't here to learn anything.

 

[svitenti]

Hum...

I'm anxious to see what could replace SR, but you known that all the dependent theories of it like QED, QCD, Eletroweak, GR, would fall, but remember that these theories give good results, and like i said one replacement to SR has to give THE SAME results to the energy used today.

 

[wespe]

Where? Can you tell me where the oscilloscope, or the interferometer, or what ever you used to measure the speed accounted for the distance traveled relative to the source?

What do you think relative speed is?

Consider please:

You are in a spaceship x meters long. There are windows on the front and back. Someone far away sends a light signal. You let the signal pass through your windows. You take note of the times when light enters the front window and exits from the back window. So you can calculate deltaTime. Now you can calculate speed of light as x/deltaTime. You find it to be 300.000 km/sec. That is the relative speed of light wrt you. Because all of them were your measurements. You don't care about the distances anyone traveled wrt something else, you just measure how long it took for light to pass the distance on your ship. So you measured the relative speed of light wrt you.

Now, you fire your thrusters, and start approaching the light source. You repeat the experiment. Oddly, you find the same relative speed of 300.000 km/sec! Light doesn't seem to care how fast you are approaching it!

Suppose, you wanted to measure the relative speed of a rock, instead of light. Same procedure. But, after you fire the thrusters, you find the relative speed of rock increased. For light, it does not increase, experimentally shown. Please do a google search how light speed was measured.

 

[wespe]

Where? Can you tell me where the oscilloscope, or the interferometer, or what ever you used to measure the speed accounted for the distance traveled relative to the source?

I guess you didn't like my answer above.

OK I try again: the distances traveled are accounted by the moving objects themselves, when relative speed is measured. Because, relative speed is the approach speed, if you will understand that term better. Approach speed is directly measured by the observer. If you try to calculate it by adding or subtracting speeds of the objects wrt something else, then the answer you get will not match the directly measured speed. This mismatch becomes more and more as the speeds approach c. And relativity describes why this mismatch occurs, and how to do it correctly. Is there anything not clear?

 

[grounded]

What do you think relative speed is?

Consider please:
You are in a spaceship x meters long. There are windows on the front and back. Someone far away sends a light signal. You let the signal pass through your windows. You take note of the times when light enters the front window and exits from the back window. So you can calculate deltaTime. Now you can calculate speed of light as x/deltaTime. You find it to be 300.000 km/sec. That is the relative speed of light wrt you. Because all of them were your measurements. You don't care about the distances anyone traveled wrt something else, you just measure how long it took for light to pass the distance on your ship. So you measured the relative speed of light wrt you.

This is a theoretical experiments created off SR, but if it was done it would agree with what I am saying. Currently we calculate the relative speed of light from measurements of the frequency or the wavelength, but we always divide them into 186,000 miles.

Relative speed is the sum of the distance traveled by both objects in one second.

The relative speed between car “A” and car “B” is equal to the sum of the distance car “A” has traveled in one second, added to the distance car “B” has traveled in one second.

60 miles in one second, added to 40 miles in one second, equals a relative speed of 100 miles per second.

How do you define relative speed?

People say we can’t measure the speed of light like this because of SR. Fine.

If that is so, we should be able to measure the speed of light, as done above, and clearly see the effect of SR. But we won’t.

We currently do not include the distance traveled by the observer (speed) when we calculate the relative speed (total relative distance traveled per second), which guarantees a constant speed of light, no matter what.

Don’t you think it’s odd that we have to change the formula in order to measure SR effect?
By change I mean, replace “relative speed” with “speed of light” as shown below.

SPEED OF LIGHT divided by RELATIVE FREQUENCY equals RELATIVE WAVELENGTH

Instead of:

RELATIVE SPEED OF LIGHT divided by RELATIVE FREQUENCY equals RELATIVE WAVELENGTH

If SR is valid, why can't we measure its effect using normal means.

 

[grounded]

the distances traveled are accounted by the moving objects themselves, when relative speed is measured. Because, relative speed is the approach speed, if you will understand that term better. Approach speed is directly measured by the observer. If you try to calculate it by adding or subtracting speeds of the objects wrt something else, then the answer you get will not match the directly measured speed.

Can you put this in a car "A" and car "B" perspective with math and show how the distance car "B" travels is accounted for?

 

[wespe]

Currently we calculate the relative speed of light from measurements of the frequency or the wavelength, but we always divide them into 186,000 miles.

Where did you get that idea? Relative speed is measured directly, similar to what I described. By letting light pass a known distance, and dividing the distance by the time it took light to pass it (of course, assuming speed of light does not vary while it passes the distance). There is an issue with one-way / two-way measurements, but you first have to understand these before you get to that point.

Google search "how is the speed of light measured"
http://216.239.41.104/search?q="how+is+the+speed+of+light+measured"&ie=UTF-8&hl=en

 

[quantumdude]

This is a theoretical experiments created off SR, but if it was done it would agree with what I am saying.

No, it wouldn't.

Currently we calculate the relative speed of light from measurements of the frequency or the wavelength, but we always divide them into 186,000 miles.

No, that is wrong. We can measure the speed of light just by knowing the times and places of emission and detection in our frame of reference. There is no need whatsoever to do speed of light measurements using either wavelength or frequency.

Relative speed is the sum of the distance traveled by both objects in one second.

The relative speed between car “A” and car “B” is equal to the sum of the distance car “A” has traveled in one second, added to the distance car “B” has traveled in one second.

"Distance traveled" according to whom? You keep ignoring the fact that I am not obliged to regard the observer as moving at all. I can consider him to be at rest if I want.

But in any case, the relative speed of a light pulse is simply its change in position divided by the time it took to cover the distance. It will come out the same no matter if I regard the observer as moving or stationary. This is true either in Galilean relativity, or in SR.

60 miles in one second, added to 40 miles in one second, equals a relative speed of 100 miles per second.

That is the Galilean velocity addition formula again. It doesn't apply in the real world.

How do you define relative speed?

I define it as the rate at which the distance between other objects and myself changes as a function of time.

People say we can’t measure the speed of light like this because of SR. Fine.

Nobody says that. We say that when we do measure it, it confirms SR and contradicts what you are saying.

If that is so, we should be able to measure the speed of light, as done above, and clearly see the effect of SR. But we won’t.

Of course we will. In fact, we have. The speed of light has been measured to be 'c', even from very fast moving sources.

We currently do not include the distance traveled by the observer (speed) when we calculate the relative speed (total relative distance traveled per second), which guarantees a constant speed of light, no matter what.

Right. We calculate it that way because it agrees with measurements.

Don’t you think it’s odd that we have to change the formula in order to measure SR effect?

Will you please try to open up and learn some actual physics? The whole point of my post on Maxwell's equations was to explain why it's not odd.

By change I mean, replace “relative speed” with “speed of light” as shown below.

SPEED OF LIGHT divided by RELATIVE FREQUENCY equals RELATIVE WAVELENGTH

Instead of:

RELATIVE SPEED OF LIGHT divided by RELATIVE FREQUENCY equals RELATIVE WAVELENGTH

We do that because the relative speed of light is the same for everyone.

If SR is valid, why can't we measure its effect using normal means.

This is a bogus question. SR is valid, we do make measurements with normal means, and the effect is observed.

 

[wespe]

Can you put this in a car "A" and car "B" perspective with math and show how the distance car "B" travels is accounted for?

But the correct math will have to be SR math. If you do it as Galilean, the answers will be different, but wrong. Wrong because experiments don't agree with it. So, math doesn't prove anything, only experiments can decide. But if you are just asking to see the SR math, I guess I can do it (if you give me some time, I'm a bit slow, or there are people here who can show it quickly, I'd appreciate their help)

Edit: With Galilean math, the traveled distance is still accounted for. When working with slow speeds, the answers are approximately correct. So if you want that, I can show it quicker. Please let me know.

 

[quantumdude]

Can you put this in a car "A" and car "B" perspective with math and show how the distance car "B" travels is accounted for?

Whether you are using Galilean relativity or SR, the equation is the same.

I can calculate the relative velocity between and a light pulse and myself by measuring the following:

Event 1: Pulse Emitted
x₁=Location of emitter on x-axis at time t₁.
t₁=Time of emission.

Event 2: Pulse Detected
x₂=Location of detector on x-axis at time t₂.
t₂=Time of detection.

The speed of the pulse relative to me is then:

v=(x₂-x₁)/(t₂-t₁).

For light, this will always come out to be c. And as you can see, that result is not "built in" to the way we calculate relative speed. It is a simple, undeniable experimental fact.

 

[wespe]

Whether you are using Galilean relativity or SR, the equation is the same.

Yes. I was thinking of first defining the scene from a third perspective, then transforming for A and B as Galilean. And show that the traveled distance is accounted for, despite approximately correctly for low speeds.

 

[grounded]

We currently do not include the distance traveled by the observer (speed) when we calculate the relative speed (total relative distance traveled per second), which guarantees a constant speed of light, no matter what.

Right. We calculate it that way because it agrees with measurements.

That is my whole point...

Whether you are using Galilean relativity or SR, the equation is the same.

v=(x2-x1)/(t2-t1)

The above formula has nothing to do with calculating relative speed. Integrate the formula. All this formula does is calulate the amount of time it takes light to travel from the source to the point it was detected. Your speed has nothing to do with anything in this formula except that it will alter the distance light can travel before you detect it.

 

[quantumdude]

That is my whole point...

What, that we construct our theories so that they agree with experiment? Guilty as charged!

Now the real question is, Why do you have a problem with that?

The above formula has nothing to do with calculating relative speed.

Wrong. That formula is the very definition of relative speed.

Integrate the formula.

What?

All this formula does is calulate the amount of time it takes light to travel from the source to the point it was detected.

Right. And the ratio of those two quantities is the speed of the light relative to me.

Your speed has nothing to do with anything in this formula except that it will alter the distance light can travel before you detect it.

That's because my speed is zero. I am always free to regard myself at rest if I am not accelerating.

 

[grounded]

Right. And the ratio of those two quantities is the speed of the light relative to me.

That formula is the very definition of relative speed.

No it isn't, it is the speed of light relative to the source. Can't you see that? It simply measures the amount of time it takes light to travel a specific distance determined by the location you detect the light.

If you run into the light at a distance of 100,000 miles from the source, what does your speed have to do with anything as long as the experiment ended at 100,000 miles form the source. Think about it... It doesn't matter how fast you are traveling when you end the test, all you are doing is marking a specific distance from the source and measuring how long it took light to get to that spot. If you traveled for two seconds, then no matter what your speed is, you will be 372,000 miles from the source.

Does that make sense?

 

[reilly]

Grounded -- Yes, I read #52. You will find your ideas expressed more clearly and succinctly in any freshman physics book -- or high school algebra book(Tom is going to Chicago at 90 mph. Phil is on the same road going the other direction at 59mph. At noon they are 247 miles apart. When do they meet? , going in the correct lanes. Feel free to incorporate the lengths of the cars if you wish. Why not check out the Doppler shifts for radio communication s between the two, and for sound communication -- this is in a world with frictionless planes. In other words, you are discussing Galillean transformations, well known to work in non-relativistic situations. You neglect the experimentally confirmed fact that the speed of light is the same in all inertial frames. given that Maxwell's eq's are invariant under Lorentz transforms(unknown to Maxwell) but not under Galilean transforms requires a very profound change in our notions of time and space and how they are measured. That is to say, your #52 is only true under limited circumstances -- again something known from countless experiments. Svitenti, above, points out that SR is more than messing around with frequencies and wavelengths, and has worked brilliantly for a century.

I ask you again to point out in my argument with a wave function, where i am wrong.
What about radiation theory, Cerenkov radiation, i.e. light going faster than the speed of light in matter, not vacuum, Larmour precession and the magnetic moment of the elctron, and on and on and on? These are all phenomena that require SR to be true (or, better, not false) I'll make you a deal. I taught SR quite a few times. If you can point out the flaws in my argument of a few posts ago, I'll send you my lecture notes so you can have a field day in pointing out my errors.

Just to give you a sense of how extraordinary Einstein's ideas were and are, refer to Bateman's Electrical and Optical Wave-Motion(Dover) written before Einstein's ideas were fully accepted. People did a lot of shucking and jiving over how best to deal with the electromagnetic fields of moving charges. Read some history, if only to see how widespread SR has become -- as I mentioned above, if you can come up with something better than SR, you will have your day in Stockholm.

Regards,
Reilly Atkinson

 

[grounded]

Tom

If you divide the distance light has traveled by the amount of time you let it travel, why would you expect to get any answer other than the speed of light?

 

[quantumdude]

No it isn't, it is the speed of light relative to the source.

Actually, it applies to both. If I use the values of x and t as measured by me in my frame, then it does in fact give me the speed of light relative to me, as I said. But if I use the values of x and t as measured in the frame of the source, then that will be the speed of the light relative to the source.

It simply measures the amount of time it takes light to travel a specific distance determined by the location you detect the light.

Slight correction: It simply measures the amount of time it takes light to travel the distance determined by the location of the detector and the location of the source at the time of emission. It takes two points to determine a distance.

But yes, the formula takes the ratio of that distance and the elapsed time between the two events.

And that ratio is the speed of the light relative to me.

If you run into the light at a distance of 100,000 miles from the source, what does your speed have to do with anything as long as the experiment ended at 100,000 miles form the source.

The distance to the source is irrelevant. Speed is not defined by a distance, it is defined by a change in distance divided by a change in time.

Think about it... It doesn't matter how fast you are traveling when you end the test, all you are doing is marking a specific distance from the source and measuring how long it took light to get to that spot. If you traveled for two seconds, then no matter what your speed is, you will be 372,000 miles from the source.

All I did was take the distance the light covered and divided by the elapsed time. That is the speed of the light in my frame.

Why is that so hard to understand?

Does that make sense?

Not one bit.

edit to add:

I don't want to leave you with the wrong impression. I don't say that your statements make no sense because they are unintelligible, or because I don't understand you. I say it because they make no sense in the framework of what we know to be true about the world.

Your posts are perfectly understandable. They just don't describe the real universe.

 

[quantumdude]

Tom

If you divide the distance light has traveled by the amount of time you let it travel, why would you expect to get any answer other than the speed of light?

For Pete's sake, just look at the formula. It is not devised to always return "c", regardless of the values of the distances and times. Indeed, those distances and times are determined by experiment. If the Galilean velocity addition formula is true, then the relative speed will be calculated (by that very same formula) to be something other than 'c'. But we don't observe that. We observe what SR predicts, as I'm sure you must be aware by now.

 

[grounded]

For Pete's sake, just look at the formula. It is not devised to always return "c", regardless of the values of the distances and times. Indeed, those distances and times are determined by experiment. If the Galilean velocity addition formula is true, then the relative speed will be calculated (by that very same formula) to be something other than 'c'. But we don't observe that. We observe what SR predicts, as I'm sure you must be aware by now.

I don't understand how we can get anything but 'c' if all we are doing is measuring the distance between us and the source, and dividing it by the amount of time it took the light to get there.

Being serious, are you saying that because of SR we have to change the times and distances?

Can't we use that formula from a third perspective with no reletivistic effects since the location of the source, the locations of the spot the test ended, and the time it took the light to get there the same for the observer or someone on the source?

 

[grounded]

All I did was take the distance the light covered and divided by the elapsed time. That is the speed of the light in my frame. Why is that so hard to understand?

All the formula says is that light travels from the source at the speed of light. So in one second the ray of light will be 186,000 miles from the source and the observers speed cannot change this.

 

[grounded]

If you run into the light at a distance of 100,000 miles from the source, what does your speed have to do with anything as long as the experiment ended at 100,000 miles form the source.

The distance to the source is irrelevant.

How can you say that since the only distance we are measuring is the distance to the source? In fact the only thing we are measuring is the distance from the front of your spaceship to the source, and dividing it by the time it took to get there.

 

[quantumdude]

I don't understand how we can get anything but 'c' if all we are doing is measuring the distance between us and the source, and dividing it by the amount of time it took the light to get there.

What's not to understand? The formula contains independent variables. It's not as though they cooperate to trick us by always working out to be 'c'.

Being serious, are you saying that because of SR we have to change the times and distances?

Yes, the times and distances do change, but it is not "because of SR", it is "because that's the way the universe works". The absoluteness of the speed of light gives rise to the phenomena of time dliation and length contraction. Moving clocks tick slower relative to your frame, and moving yardsticks are shorter in your frame.

Can't we use that formula from a third perspective with no reletivistic effects since the location of the source, the locations of the spot the test ended, and the time it took the light to get there the same for the observer or someone on the source?

There are no relativistic effects in the formula for relative speed. The relativistic effects don't show up until you do precisely what you hint at here: Consider a third point of view. But we can't add that third perspective without way to transform coordinates between frames. So let's do that, using both Galilean relativity and Special Relativity.

Let a light source S be moving towards observer O at v=0.5c. Let S emit a pulse. Furthermore, let observer O' be at rest with respect to the source. This implies that the speed of light u' relative to him is c.

Again, let Event 1 be the emission of the pulse, and let Event 2 be the detection.

Question: What is the speed of light u as measured by O?

Here are two different answers, one from Galileo and one from Einstein.

1. In Galilean relativity, the transformation between spacetime coordinates (x,t) that O assigns to events, and those coordinates that (x',t') that O' assigns to events, are related by the following transformation:

x'=x-vt
t'=t

If we take the difference in distance Δx and Δ'x;', as measured by each observer, and similarly take the differences in time Δt and Δt', then each can compute the velocity of light relative to himself:

Δx'/Δt'=Δx/Δt-v.

Since Δx'/Δt'=u' and Δx/Δt=u, we have

u'=u-v

This is the Galilean velocity addition formula, which you are so fond of. Recall that u'=c and v=0.5c. Inserting them into the formula, we come up with a prediction of u=1.5c.

That is, Galilean relativity predicts that x₂, x₁, t₂, and t₁ will all be measured in such a way that the ratio of (x₂-x₁) to (t₂-t₁) will be 1.5c.

2. In Special Relativity, the transformation between spacetime coordinates (x,t) that O assigns to events, and those coordinates that (x',t') that O' assigns to events, are related by the following transformation:

x'=γ(x-vt)
t'=γ(t-vx/c²)

where γ=(1-v²/c²)^-1/2

If we take the difference in distance Δx and Δ'x;', as measured by each observer, and similarly take the differences in time Δt and Δt', then each can compute the velocity of light relative to himself:

Δx'/Δt'=(Δx-vΔt)/(Δt-vΔx/c²)

Dividing the top and bottom of the right side by Δt, we get:

Δx'/Δt'=(Δx/Δt-v)/(1-v(Δx/Δt)/c²)

Since Δx'/Δt'=u' and Δx/Δt=u, we have

u'=(u-v)/(1-uv/c²)

This is the velocity addition formula in SR. Recall that u'=c and v=0.5c. Inserting them into the formula, and solving for u, we get u=c.

That is, Special Relativity predicts that x₂, x₁, t₂, and t₁ will all be measured in such a way that the ratio of (x₂-x₁) to (t₂-t₁) will be c.

The only way to find out which is correct is to do the experiment, and collect the information on x₁, x₂, t₂ and t₁.

As it happens, SR is correct. The simple velocity addition formula of Galilean relativity does not work.

 

[quantumdude]

All the formula says is that light travels from the source at the speed of light. So in one second the ray of light will be 186,000 miles from the source and the observers speed cannot change this.

No, you are wrong. The formula doesn't say that at all. The formula contains quantities that are determined by experiment. Given (x₂-x₁), there is no way to know ahead of time what (t₂-t₁) is going to be.

 

[quantumdude]

How can you say that since the only distance we are measuring is the distance to the source? In fact the only thing we are measuring is the distance from the front of your spaceship to the source, and dividing it by the time it took to get there.

I already explained this to you. I say that the distances themselves are irrelevant, because it is only the change in distance that goes into computing the speed.

Look at the formula again:

v=(x₂-x₁)/(t₂-t₁)

The values of x₂ and x₁ (the distances) don't matter. What matters is their difference.

 

[wespe]

If you run into the light at a distance of 100,000 miles from the source, what does your speed have to do with anything as long as the experiment ended at 100,000 miles form the source. Think about it... It doesn't matter how fast you are traveling when you end the test, all you are doing is marking a specific distance from the source and measuring how long it took light to get to that spot. If you traveled for two seconds, then no matter what your speed is, you will be 372,000 miles from the source.

Tom Mattson has explained well, but just in case you are still confused..

OK, if distance is 100,000 miles, what value will you divide this by? You have to divide it by (detection time - emission time). How will you know the emission time? You can't measure it directly, because you are in the ship. The distance is also contracted due to SR effects, and it is difficult to see what the ship would directly measure as distance. These are additional complexities. To avoid them, my example did not include light emission time. It included two time values that you measured inside your ship. And the distance was again measured inside the ship. Divide and find the speed, v=dx/dt, should be simple enough.

 

[grounded]

Just so you know Tom...I really appreciate the time you have given up to respond to all my posts. Even though we don't agree, you still respond, thanks.

I do however have yet another question.

Given (x₂-x₁), there is no way to know ahead of time what (t₂-t₁) is going to be.

If I am given the location of the source (x₁), and I am given the location of the detector (x₂), isn't (t₂-t₁) equal to the amount of time it takes to travel (x₂-x₁) at the speed of light?

 

[quantumdude]

Just so you know Tom...I really appreciate the time you have given up to respond to all my posts. Even though we don't agree, you still respond, thanks.

I don't mind, because you are obviously sincere.

I do however have yet another question.

If I am given the location of the source (x₁), and I am given the location of the detector (x₂), isn't (t₂-t₁) equal to the amount of time it takes to travel (x₂-x₁) at the speed of light?

It will return the speed of light relative to me. The definition of relative speed--by itself--does not prefer the SR velocity addition formula over the Galilean velocity addition formula. If you go back to my example with the light source moving at 0.5c towards me, where I work out the prediction using both Galileo and Einstein, you'll see that the exact same definition of velocity is used in both cases. If Galileo is correct, then the time elapsed (t₂-t₁) will be such that the speed of the light in my frame is 1.5c. And if Einstein is correct, then it will be such that the speed is c.

So the experimental question is: When does the pulse arrive?

Hopefully you now see that the result is not guaranteed to be 'c' just by virtue of the definition of relative velocity.

 

[grounded]

OK, if distance is 100,000 miles, what value will you divide this by?

When I see this:

v=(x₂-x₁)/(t₂-t₁)

I see this:

v=(The distance between the source and the detector) / (The amount of time it takes light to travel from the source to the detector)

From my perspective the observers speed only changes the position of the detector, but we are still only calculating the amount of time it takes light to travel from the source to the detector.

 

[quantumdude]

When I see this:

v=(x₂-x₁)/(t₂-t₁)

I see this:

v=(The distance between the source and the detector) / (The amount of time it takes light to travel from the source to the detector)

The part in red is not quite right. Remember that Event 1 was defined to be the emission of the pulse. That means that x₁ is the location of the source when the light was emitted. The source may move after time t₁, and so x₂-x₁ is not the distance between the source and the detector. It is the distance between the emission and the detection.

In other words, it is the distance that the light travels.