The Doppler Effect and the Velocity of Light in Einstein's Theory

[David]

So you're saying that its natural to assume that the universe is infinitely old and has been collapsing for an infinite amount of time, but has a finite amount of life left before collapsing completely?

No.

I never said that.

 

[David]

At one time, it was believed that the unvierse was eternal and static. But throwing gravity into that universe would indeed cause contraction: therefore the universe cannot be static. It must either be expanding or contracting. (or both).

Newton had two other suggestions:

Rotation or infinite.

We see that he was right about “rotation” on the local level, since the galaxies and solar systems rotate.

He was also apparently right about the expansion too.

David, it appears I gave you too much credit before in assuming you were just arging points you knew to be wrong for fun: you appear now to have some major gaps in your knowledge/understanding and a simple unwillingness to learn. Though it may be more pathological: you abuse/distort/misrepresent/mischaracterize to cover your unwillingness to learn.

LOL, you are the guy who told me that Lorentz and Einstein couldn’t have been talking about atomic clocks in their early papers, because you said atomic clock weren’t invented until the 1950s. Then I told you about Maxwell’s mention of natural atomic clocks in 1873.

 

[geistkiesel]

Einstein said in his 1916 book:

”If an observer sitting in the position M1 in the train did not possesses this velocity, then he would remain permanently at M, and the light rays emitted by the flashes of lightning A and B would reach him simultaneously, i.e. they would meet just where he is situated. Now in reality (considered with reference to the railway embankment) he is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A. Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A.”

What Einstein means by “he is hastening towards the beam of light coming from B” is that the light beam from the flash at B is converging on the observer that is moving toward B at the relative velocity of c + v, with v being the velocity of the observer toward B. What he means by “he is riding on ahead of the beam of light coming from A” means the light from the A flash is converging on the observer at the velocity of c – v.

This is very simple. The observer-relative speed of the light, relative to the moving observer is NOT “c”, it is NOT constant. It is c + v in one direction and c – v in the other direction.

This is why the Earth sees a blueshift in the light of the star the Earth is moving toward in its revolution around the sun and this is why the Earth sees a redshift in the light of a star the Earth is moving away from during its revolution around the sun. This is caused by the Second Cause of the Doppler effects that I told you about earlier. This is a Doppler Law of Physics. It can not be revoked.

I agree David. Instead of using light use crawling ants for the photons. Einstein would still come up with a loss of simultaneity as he concluded the loss of simultaneity as perceived by the observer on the moving platiofrm was the detection of the ant coming toward him from the front and then the ants comin toward him from the rear, and this is it!.

Of course you will need to restrict your speed to a constant values less than that of the ants so as not to embarrass Professor Einstein, graduate advisor to a host of SR theorists.

 

[quantumdude]

Of course you will need to restrict your speed to a constant values less than that of the ants so as not to embarrass Professor Einstein, graduate advisor to a host of SR theorists.

There's no need for anyone to restrict the speed to something less than the Lorentz invariant speed. Nature will take care of that for you.

 

[geistkiesel]

I’m talking about “physics”, not “science fiction stories”.

Good for you.

The reason the guy on the moving train will see the B flash first is because he is moving toward B and thus he and the light beam from B are converging on each other at the additive light-speed velocity of c + v. That’s a basic law of physics and of nature, and it’s a basic Doppler Law.

Oops, you just slid into sci-fi. Your "basic law of physics" is only an approximation, valid at low speeds.

Oh so SR theory gets to corrupt the basic laws of physics? I thought that even in SR theory the laws of physics were equivalent in all inertial frames.

Prove that what is observed to be true, is false.

Prove that a postulate, a mental arrangement, is superior to a direct observation such as described by David.

Let me see , your proof will start out as "SR theory says . . . ", What was the comment? " ..ooops" , wasn't it?

 

[geistkiesel]

There's no need for anyone to restrict the speed to something less than the Lorentz invariant speed. Nature will take care of that for you.

Tom

I was referring to the substitution of moving ants for the photons, this is why I suggested the volunteered slowing to a speed lless than the ants.

 

[quantumdude]

Oh so SR theory gets to corrupt the basic laws of physics?

No, it does the opposite. It says that the basic laws of physics are the same everywhere, everywhen, for everyone. That stands in stark contradiction to your crackpot idea that the laws of physics in our Earthbound frame are special and somehow Divine.

I thought that even in SR theory the laws of physics were equivalent in all inertial frames.

Now yer getting it.

Prove that what is observed to be true, is false.

That's your objective, not ours.

Prove that a postulate, a mental arrangement, is superior to a direct observation such as described by David.

If you think that David's thought experiment is a "direct observation", then you are just as stupid as he is.

Let me see , your proof will start out as "SR theory says . . . ", What was the comment? " ..ooops" , wasn't it?

No. The proof will start out as, "SR theory says...and let's see what real experiments say in support or denial of that"

That's what all scientists do. You would do well to follow that example, as you don't seem to care if an experiment is real or imagined. All you seem to care about is whether the experiment agrees with your preconceived notions.

edit: fixed a quote bracket

 

[geistkiesel]

No, it does the opposite. It says that the basic laws of physics are the same everywhere, everywhen, for everyone. That stands in stark contradiction to your crackpot idea that the laws of physics in our Earthbound frame are special and somehow Divine.

So if an observation that two photons are emitted simultaneously in a stationary frame and a moving frames say from A and B where M is the midpoint of A and B, just at the instant that identical points on the moving frame are such that A = A', B = B' and M = M' that this simultaeous event in both frames is not a simultaneous event?

I know I have crackpot ideas, WYSIWYG, but the Earth bound frame is an inertial frame is it not? And is not the Earth bound frame a part of the "everywhere" you refer to above?

I would never utter any statement that something is "somehow Divine". If I mentioned anything regarding 'divinity' I might say something "is Divine" and I might say that the laws of physics are Divine, wherever encountered, as in everywhere, but I fail to see any logical thread or relationship, relevance is what I am discussing, that justifies your use of words as you expressed them above.

Is it an old intuitive threat to professional security considerations that motivates your rather unscientific mode of response?

Special relativity is your mantra isn't it?

If you think that David's thought experiment is a "direct observation", then you are just as stupid as he is.

The experiments being discussed are as real as Einstein's when he presented his gedunkens. I would rather be as stupid as David than to be as stupid as you. his mind seems to work as a mind. It has the characteristics of being free, or working to that end. I don't recognize the characteristics of mind iassociated with your post. Brat robot is more what I observe.

quoting geistkiesel
No. The proof will start out as, "SR theory says...and let's see what real experiments say in support or denial of that"

That's what all scientists do. You would do well to follow that example, as you don't seem to care if an experiment is real or imagined. All you seem to care about is whether the experiment agrees with your preconceived notions.

edit: fixed a quote bracket

So one gedunken cannot be used to counter another gedunken? That is the scientific rule where you come from? I would do well to follow that example?

So David's and Geistkiesel's observations don't wash in a mind soaked in SR theory? That doesn't sound like a Divine situation to me. I am going to speak to someine in authority about that, as soon as I can get 'his' attention, if you know what I mean. I'll get back to later on this.

When you wake up Tom everything will seem like a bad dream, but the bogie man will be gone, the things that go bump in the night will be no more and you can begin to live again, free at last.

 

[russ_watters]

The experiments being discussed are as real as Einstein's when he presented his gedunkens.

Tom pointed this out, but didn't explain (it really should be self-evident). Einstein's thought experiments were conceived as hypothetical examples in order to explain his theory, just as yours and David's are. The difference is that since it was concieved, Relativity has been substantiated by mountains of real, scientific evidence. Your ideas, on the other hand, exist only in your mind.

So one gedunken cannot be used to counter another gedunken? That is the scientific rule where you come from? I would do well to follow that example?

That's correct. Since a thought experiment isn't real, it doesn't prove or disprove anything.

 

[quantumdude]

So if an observation that two photons are emitted simultaneously in a stationary frame and a moving frames say from A and B where M is the midpoint of A and B, just at the instant that identical points on the moving frame are such that A = A', B = B' and M = M' that this simultaeous event in both frames is not a simultaneous event?

You're asking me if a statement if the form, "If p, then p" is true. Of course it is, because it is an empty tautology.

I know I have crackpot ideas, WYSIWYG, but the Earth bound frame is an inertial frame is it not? And is not the Earth bound frame a part of the "everywhere" you refer to above?

The Earthbound frame is not inertial, but it is close enough. And yes, it is part of "everywhere".

I would never utter any statement that something is "somehow Divine". If I mentioned anything regarding 'divinity' I might say something "is Divine" and I might say that the laws of physics are Divine, wherever encountered, as in everywhere, but I fail to see any logical thread or relationship, relevance is what I am discussing, that justifies your use of words as you expressed them above.

You fail to see a lot of things.

Insisting that the laws of physics take their "textbook form" on Earth and insisting that the Lorentz transformation is wrong is logically equivalent to insisting that the laws of physics are the way we know them only on Earth.

Is it an old intuitive threat to professional security considerations that motivates your rather unscientific mode of response?

Just how would you even know what a scientific mode of response is? You don't even know the difference between a thought experiment and a real experiment.

Special relativity is your mantra isn't it?

No, physics is.

The experiments being discussed are as real as Einstein's when he presented his gedunkens.

Well, we agree on that much: Neither one is real at all.

I would rather be as stupid as David than to be as stupid as you.

Suit yourself. Suffice it to say that you got your wish.

his mind seems to work as a mind. It has the characteristics of being free, or working to that end.

Yes, his mind is "free" alright. It is so "free" that it is unconstrained by logic, science, mathematics, or evidence.

I don't recognize the characteristics of mind iassociated with your post. Brat robot is more what I observe.

Your vision is obviously clouded then. As I said, there is a difference between real experiments and thought experiments, which you don't see.

So one gedunken cannot be used to counter another gedunken? That is the scientific rule where you come from? I would do well to follow that example?

You say that to mock me, but the statement is correct. Thought experiments cannot disprove theories. Period.

Scientific theories are deductive arguments built up from statements which are the conclusions of inductive arguments. Those inductive arguments are based on experimental evidence. Given that, you can disprove a theory in one of two ways:

1. Show that the theory is not deductively valid.
2. Show that one or more of the premises is false.

#1 can be done with mathematics and #2 can be done with evidence. Neither can be done with a thought experiment.

So David's and Geistkiesel's observations don't wash in a mind soaked in SR theory?

What observation?

That doesn't sound like a Divine situation to me. I am going to speak to someine in authority about that, as soon as I can get 'his' attention, if you know what I mean. I'll get back to later on this.

Don't bother. It won't be worth reading anyway.

When you wake up Tom everything will seem like a bad dream, but the bogie man will be gone, the things that go bump in the night will be no more and you can begin to live again, free at last.

Get a clue. You haven't referred to a single real experiment. All you have referred to are thought experiments, which you falsely believe are just as good. They aren't.

You know, you and David would both do well to read posts from people such as Wisp and Yogi. They aren't convinced of SR either, but they refer to real, actual, factual experiments that have taken place in the physical world, not in warped minds. While I don't agree with them, it's not as though I dismiss anti-SR posts out of hand. I don't. I acknowledge that there are competent critics of SR out there.

You and David just aren't among them.

 

[Michael F. Dmitriyev]

Velocity of light is absolute and SINGLE velocity existing in the universe at microlevel.
Relativity appears at macrolevel.

 

[ram2048]

but he's talking about some superluminal things emitting light back to earth, which i find intriguing

if something going 4c to the left "emits" a photon to the right isn't that photon still going 3c to the right?

this slowing down to 0 speed then accelerating towards the left until it hits c in that direction is just odd

i don't think i can buy that

how about the one theory where light has a wave component and a matter component? Using that one the matter part could be emitted to the left at c, but the wave part is stretched to the magnitude of 3c to the right (redshifting) due to superluminal emitter...

this seems consistant

btw: i believe in einstein's setup he WAS referring to doppler shift, not relativistic observation. it seems way more simple than relativity.

 

[geistkiesel]

Velocity of light is absolute and SINGLE velocity existing in the universe at microlevel.
Relativity appears at macrolevel.

Michael,
I have a problem. I am under the belief that an electromagnetic sphere whose radius is expanding at velocity c will have a diameter of 2c after 1 second. This sounds suspiciously close to the statement that the photons moving in opposite directions to each other are expanding at a rate of 2c. I was told in no uncertain terms that I erred, but I ws not given any direction to solving my dilemma.

I want to believe llike everybody else. What is the rroof? That the sphere is expanding at a rate of 2^1/2c?, which is what I was told. Do you know?

 

[Michael F. Dmitriyev]

A photon being a bit of matter can be rewriting at a new place with the maximal speed.
The particles, as a words, sentences and the combination of words and sentences demands a greater time of rewriting according to their length. It is a most simple way to understand why any material object cannot exceed the velocity of light.

 

[Michael F. Dmitriyev]

Michael,
I have a problem. I am under the belief that an electromagnetic sphere whose radius is expanding at velocity c will have a diameter of 2c after 1 second. This sounds suspiciously close to the statement that the photons moving in opposite directions to each other are expanding at a rate of 2c. I was told in no uncertain terms that I erred, but I ws not given any direction to solving my dilemma.

I want to believe llike everybody else. What is the rroof? That the sphere is expanding at a rate of 2^1/2c?, which is what I was told. Do you know?

Relativity cannot be applied to the light.

 

[Doc Al]

I have a problem. I am under the belief that an electromagnetic sphere whose radius is expanding at velocity c will have a diameter of 2c after 1 second. This sounds suspiciously close to the statement that the photons moving in opposite directions to each other are expanding at a rate of 2c. I was told in no uncertain terms that I erred, but I ws not given any direction to solving my dilemma.

As I mentioned in another thread, there is no problem whatsoever in having someone observe two photons separating at a rate of 2c. In fact, if the photons are moving in opposite directions, relativity insists that this be the case.

Note that the observed speed of each photon is still c.

 

[russ_watters]

As I mentioned in another thread, there is no problem whatsoever in having someone observe two photons separating at a rate of 2c. In fact, if the photons are moving in opposite directions, relativity insists that this be the case.

Note that the observed speed of each photon is still c.

Note also that an observer traveling just behind one of those photons, just under C, still sees each photon traveling at C.

"Separation velocity" isn't a velocity that has any SR implications. Its just geometry.

If I may change the thought experiment slightly to make it resolvable...

Take 3 observers, x, Y, & Z starting out next to each other:

XYZ

X and Z move away from Y at just under the speed of light.

X<----Y---->Z

Observer X measures both Y and Z to be moving away from him at just under the speed of light - Z is just a little closer to the speed of light than Y. Observer Z measures the same thing about X and Y. Observer Y measures both to be just under C.

Geometrically adding the speeds gives X and Z a "separation velocity" of just under 2C from the frame of reference of Y. But that doesn't in any way imply that Z or X will measure their own velocity with respect to each other at just under 2c.

 

[Doc Al]

"Separation velocity" isn't a velocity that has any SR implications. Its just geometry.

Right. Don't confuse this "separation velocity" with a relative velocity.

As another example: Someone (observer A) observes two rockets (B and C) traveling in opposite directions, each with speed 0.9c. The "separation velocity" of the two rockets, as observed by A, is 1.8c. But the speed of C as observed by B (the velocity of C with respect to B) is only 0.994c.

 

[David]

Note also that an observer traveling just behind one of those photons, just under C, still sees each photon traveling at C.

Einstein revoked his “constancy” postulate in 1912. Why don't you know this? Haven't you read his 1912 papers?

 

[David]

Right. Don't confuse this "separation velocity" with a relative velocity.

As another example: Someone (observer A) observes two rockets (B and C) traveling in opposite directions, each with speed 0.9c.

Lorentz said that based on electrodynamics, there is a “speed limit” in local gravity fields. You can’t accelerate a rocket in the solar system to .9c. What you are posting here is urban legend. Why does Bernhardt Media promote urban legends?

 

[David]

Michael,

I want to believe llike everybody else.

You want to be brainwashed about relativity “like everybody else”??

Go out and by the complete 8 Volume set of “The Collected Papers of Albert Einstein”, Paperback English edition, Princeton Press, and you will see that these “mentors” don’t know what they are talking about.

Einstein revoked his “constancy” postulate in 1912. In 1907 he said that objects really don’t “geometrically” contract due only to “relative motion”. The distant galaxies exhibit redshifts that indicate they are moving at 2c and 3c relative to the earth. What these guys here are pushing is a bunch of rumors and urban legends suitable for teenagers.

 

[David]

I agree David. Instead of using light use crawling ants for the photons. Einstein would still come up with a loss of simultaneity as he concluded the loss of simultaneity as perceived by the observer on the moving platiofrm was the detection of the ant coming toward him from the front and then the ants comin toward him from the rear, and this is it!.

Of course you will need to restrict your speed to a constant values less than that of the ants so as not to embarrass Professor Einstein, graduate advisor to a host of SR theorists.

When Einstein said, “Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity).”

But everybody knew that already. This is why the railroads divided the country up into four time zones in the 19th Century, to try to bring some simple form of “simultaneity” to the rail system. Before then, everybody was using local time set at noon by sundials in every city, and railroad conductors had to convert railroad time into local time, because the two lacked “simultaneity”.

In 1916 he said, “Now in reality (considered with reference to the railway embankment) he is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A. Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A.”

Everybody knew that already too. That’s about as obvious as saying, “The front of the train will arrive at the station before the rear of the train.”

If we are closer to one of two simultaneous events, we will receive light or sound signals from the closest event first. If we are right in between the two simultaneous events, we will receive light or sound signals from both events at the same time. Doh. People have known this for thousands of years. People have known that all kinds of clocks slow down due to different natural effects, and they've known that for thousands of years.

This Einstein stuff is over promoted by guys who like to think they are "as smart as Einstein". It's a cult.

This reminds me of the movie, “Being There”. Review comments: “It is hysterically funny to see how the always immaculately dressed, in formal attire, Chance rises to national prominence, due to people reading more into his stated "few simple truisms," and then giving the credit of a deep thinker to Chance, who is simply stating what he understands, in a calm, confident, positive, reassuring manner.”

“Benjamin Rand takes a shine to the person he believes is "Chauncey Gardner;" a simpleton he takes as an enigmatic and deeply contemplative thinker. Rich and powerful Ben introduces him to the President, to whom Chance makes cryptic comments that the president takes as a wise analogy of the seasons and the economy. A national TV appearance spreads "Chauncey's" fame. The only person who knows him, the "old man's" kindly maid, sizes up Chance's words: gobbledygook. The rich and powerful assume "Chauncey's" simple words imply great intelligence. Ben's doctor suspects that Chauncey may in fact have a child's mind, but is not certain.”

 

[David]

There's no need for anyone to restrict the speed to something less than the Lorentz invariant speed. Nature will take care of that for you.

Hey, Mr. X-Ray, look at this:

“Thus for the largest known redshift of z=6.3, the recession velocity is not 6.3*c = 1,890,000 km/sec. It is also not the 285,254 km/sec given by the special relativistic Doppler formula 1+z = sqrt((1+v/c)/(1-v/c)). The actual recession velocity for this object depends on the cosmological parameters, but for an OmegaM=0.3 vacuum-dominated flat model the velocity is 585,611 km/sec. This is faster than light.”

http://www.astro.ucla.edu/~wright/doppler.htm

Hey, the 99 year old hoax is over.

 

[David]

. In fact, if the photons are moving in opposite directions, relativity insists that this be the case.

No it doesn’t. Read Einstein’s 1911 and 1916 papers. Read his 1912 papers. He said light speed is slower than “c” inside a gravity field. He said that light speed is NOT “constant”.

Look, you’ve got to spend more money on relativity books than you spent on the two $9.95 books, “The Principle of Relativity” and “Relativity: The Special and General Theory”.

You’ve got to read some of Einstein’s subsequent papers. You’ve got a $19.90 “relativity” education, and it shows.

 

[ahrkron]

Hey, Mr. X-Ray, look at this:

“Thus for the largest known redshift of z=6.3, the recession velocity is not 6.3*c = 1,890,000 km/sec. It is also not the 285,254 km/sec given by the special relativistic Doppler formula 1+z = sqrt((1+v/c)/(1-v/c)). The actual recession velocity for this object depends on the cosmological parameters, but for an OmegaM=0.3 vacuum-dominated flat model the velocity is 585,611 km/sec. This is faster than light.”

http://www.astro.ucla.edu/~wright/doppler.htm

Hey, the 99 year old hoax is over.

The same page, from UCLA, has a link from the phrase "faster than light" that takes you to an explanation of why this does not violate SR. You just chose not to see it.

For others that may wonder how that works, here is the link.

 

[ahrkron]

No it doesn’t. Read Einstein’s 1911 and 1916 papers. Read his 1912 papers. He said light speed is slower than “c” inside a gravity field. He said that light speed is NOT “constant”.

Even assuming that you were not quoting papers from the time GR was under development, nowhere near its final form, where did Doc Al or geistkiesel mention anything about GR, or a gravity field?[/color]

Also, you would be much better off dropping your "$9.95" argument. As some of us have pointed out to you already, getting a real education on current physics takes quite a bit more (money, time and effort) than those involved in buying and reading the collected papers of AE, who died in 1954.

And, as you say, it shows.

 

[russ_watters]

Einstein revoked his “constancy” postulate in 1912. Why don't you know this? Haven't you read his 1912 papers?

What does this discussion have to do with Einstein? He's dead.

 

[ahrkron]

When Einstein said, “Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity).”

But everybody knew that already. This is why the railroads divided the country up into four time zones in the 19th Century, to try to bring some simple form of “simultaneity” to the rail system[/color]. Before then, everybody was using local time set at noon by sundials in every city, and railroad conductors had to convert railroad time into local time, because the two lacked “simultaneity”.

Wow! This is just beautiful. I'm sorry David, but as I said, "it shows". You do not seem to understand what the issue with simultaneity is.

 

[ahrkron]

In 1916 he said, “Now in reality (considered with reference to the railway embankment) he is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A. Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A.”

Everybody knew that already too. That’s about as obvious as saying, “The front of the train will arrive at the station before the rear of the train.”

If we are closer to one of two simultaneous events, we will receive light or sound signals from the closest event first. If we are right in between the two simultaneous events, we will receive light or sound signals from both events at the same time. Doh. People have known this for thousands of years.

Again, as you did with your quote of UCLA's page, you are stopping just before things get interesting.

Of course people knew about sound arriving first from the closest source. The thing that changes all else is the fact that, unlike sound, light will be measured to have the same speed[/color] by both observers. From there, a little algebra takes you to Lorentz transformations, showing, along the way, their logical linkage to a measured phenomenon (the constancy of the speed of light).

People have known that all kinds of clocks slow down due to different natural effects, and they've known that for thousands of years.

Sure, but nobody before the uderstanding of Lorentz Transformations was able to correctly predict[/color] the slowing down caused by relative motion.

Your (failed attempt of a) rebuttal is akin to this:

[someone] Mr. X has discovered that gene Y is the cause of cancer.

[you] Nay! People have known that all kinds of persons die due to different natural effects, and they've known that for thousands of years.

 

[geistkiesel]

David said:
In 1916 he said, “Now in reality (considered with reference to the railway embankment) he is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A. Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A.”

Everybody knew that already too. That’s about as obvious as saying, “The front of the train will arrive at the station before the rear of the train.”

If we are closer to one of two simultaneous events, we will receive light or sound signals from the closest event first. If we are right in between the two simultaneous events, we will receive light or sound signals from both events at the same time. Doh. People have known this for thousands of years.

Again, as you did with your quote of UCLA's page, you are stopping just before things get interesting.

Of course people knew about sound arriving first from the closest source. The thing that changes all else is the fact that, unlike sound, light will be measured to have the same speed by both observers. From there, a little algebra takes you to Lorentz transformations, showing, along the way, their logical linkage to a measured phenomenon (the constancy of the speed of light).

I agree with David!
The Einstein Train gedanken from another view. Read at your peril.
______________________________________________
All moving frame values are non-primed with the exception of M’, the consistent location of the observer O in the moving frame.

At no time is there an inference that M’ was at the midpoint of the A and B photons emitted in the stationary frame.

To demonstrate the following:

Einstein’s moving train calculation indicating when the oncoming B photon is detected at t1 the A photon was located at a position consistent with –t1. Said in other words, as t1 is determined from t0 which locates M’ at t0, the A and B were equidistant to M’(t0) when t = t1.

Proof:
A moving observer located at M’ on a moving frame passes through the midpoint M of photon sources located at A and B in the stationary frame just as A and B emit photons. M’ is moving along a line connecting A and B, toward B.

At this instant the moving source t = t0. Later the moving observer detects the photon from B at t1, and later the photon from A at t2. The observer has measured her velocity wrt the stationary frame as v. Determine the position of the A photon at tx in terms of t0, t1, t2, and v when the B photon was detected at t1.

The photon from A must reach the position of M’ when t = t2. Therefore, the distance traveled by the A photon during Δt = t2 – t1, is Δtc. This is equal to the distance cΔt = vΔt + vt1 + vtx . Now we rearrange somewhat to arrive at, vtx = vΔt – cΔt + –vt1. Now as vΔt - cΔt is just -vtx - vt1

vtx = -vtx - vt1 – vt1

2tx = -2t1

tx = -t1

Therefore, in the moving frame the photon from A and the photon from B were equidistant from M’(t0) at t1.