What is the velocity of a photon?

[PeterDonis]

If you saw this question on an exam, what would you answer? "Suppose we define a point (x1=0, x2=0, x3=0, x4=0). What is a photon's velocity relative to that point?"

I would object that the question is not well-posed, because velocity relative to an *event* in spacetime makes no sense. It would be like me asking what is your "velocity" relative to the specific event "the Empire State Building at precisely noon last Tuesday". What does that even mean?

A 3-velocity (velocity in 3-dimensional space) is defined using the *worldline* of one object relative to another, not a single event.

A 4-velocity ("velocity" in 4-dimensional spacetime) is defined as the tangent vector of an object's worldline at a given event, but says nothing, by itself, about that object's relationship to any other objects; for that, you have to know the other objects' 4-velocities as well, meaning you have to know their worldlines, as above. For example, if I take object A as being at rest (I assume all objects are moving inertially here), then its worldline defines the "time" axis of an inertial frame, and if I then pick a particular time t in that frame, I can calculate the 3-velocity of object B at that time using B's 4-velocity at that time (meaning, at the event on B's worldline which has time coordinate t in A's frame); I just square each spatial component of the 4-velocity, add them, and take the square root of the sum. (Edit: Left out a step at the end, dividing by the time component of the 4-velocity. For a photon it would be the time component of the tangent vector.)

Technically, a 4-velocity is supposed to be a unit vector, which is why PAllen said you can't define one for a photon, since the tangent vector to a photon's worldline is always null. But a photon's worldline does have a tangent vector, and I can use it to calculate the photon's 3-velocity in a given inertial frame using the same procedure as I described for a timelike object like B above. If spacetime is flat, I will always get the answer c when I do this. If spacetime is curved, there are complications, of course.

 

[ghwellsjr]

1. First postulate (principle of relativity)
The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of coordinates in uniform translatory motion.
2. Second postulate (invariance of c)
As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body.

This is not an accurate statement of Einstein's second postulate because of your inserted first phrase, "As measured in any inertial frame of reference". The rest of it is an exact quote from Einstein's 1905 paper. You should read some more of his paper to clear up your confusion.

As Einstein points out, we can measure the speed of light by using a single timing device colocated with a light source and detector, and a remote mirror some measured distance away. We start the timer when the light source sets off a flash of light and we stop it when the detector receives the reflected flash. Now we know how long it took the light to make the round trip and how far it was and we can calculate the overall speed of light, but we cannot know how long it took for the light to get to the mirror or how long it took to get back. Einstein's second postulate says to make those two times equal and so know we have to basis for defining time on a remote clock. This is the mechanism by which we create the simultaneous times throughout a Frame of Reference.

So now when you ask about the speed of a photon, can't you see that it is nothing more than the definition of how we devise a Frame of Reference? All light, including photons, travel at c within a Frame of Reference because that is how we defined the Frame of Reference.

You ask about the point (x1=0, x2=0, x3=0, x4=0) but that is not a point, it's an event because it includes x4, the time coordinate, the part of the Frame of Reference that uses the speed of light in its definition. So in any Frame of Reference, light travels at c because that is how we define it and how we define time in the Frame of Reference.

Can you also see why it's meaningless to talk about measuring the speed of a photon?

 

[PAllen]

A 4-velocity ("velocity" in 4-dimensional spacetime) is defined as the tangent vector of an object's worldline at a given event, but says nothing, by itself, about that object's relationship to any other objects; for that, you have to know the other objects' 4-velocities as well, meaning you have to know their worldlines, as above. For example, if I take object A as being at rest (I assume all objects are moving inertially here), then its worldline defines the "time" axis of an inertial frame, and if I then pick a particular time t in that frame, I can calculate the 3-velocity of object B at that time using B's 4-velocity at that time (meaning, at the event on B's worldline which has time coordinate t in A's frame); I just square each spatial component of the 4-velocity, add them, and take the square root of the sum.

Technically, a 4-velocity is supposed to be a unit vector, which is why PAllen said you can't define one for a photon, since the tangent vector to a photon's worldline is always null. But a photon's worldline does have a tangent vector, and I can use it to calculate the photon's 3-velocity in a given inertial frame using the same procedure as I described for a timelike object like B above. If spacetime is flat, I will always get the answer c when I do this. If spacetime is curved, there are complications, of course.

This is why definitions are good. Peter is using:

4-velocity: Tangent vector to world line; may use arbitrary affine parameter (thus, not uniquely defined). Normalized to a unit vector for a timelike path (thus unique, in this case).

I was using:

4-velocity: derivative by proper time along a world line; inherently undefined for null paths.


Both definitions are defensible. For timelike paths, they are the same.

 

[ghwellsjr]

Another way of thinking about the 4-velocity of something that is not accelerating is to realize that it is the spacetime interval (a frame invariant value) divided by the proper time interval (another frame invariant value). Proper time is what a clock measures. A clock must be made of particles with mass. Therefore a clock cannot travel at the speed of light. Therefore there is no meaning to proper time for a photon. Therefore there is no meaning to the 4-velocity of a photon.

 

[PeterDonis]

Peter is using:

4-velocity: Tangent vector to world line; may use arbitrary affine parameter (thus, not uniquely defined). Normalized to a unit vector for a timelike path (thus unique, in this case).

Just to make a minor clarification, I wasn't actually insisting that the tangent vector to a photon's worldline be called a "4-velocity"; that depends on how comfortable one is attaching that term to a null vector, for which important properties of timelike tangent vectors do not apply (such as the property ghwellsjr describes in post #34). The key point is that you can use the components of that tangent vector, in any inertial frame, to compute the photon's "3-velocity" in that frame, as I described. In the case of inertial frames in flat spacetime, you will always get c when you do this.

 

[Dale]

robphy states, "Relative-velocities are defined between particles." As you have shown, this is not true.

Relative velocities are defined between worldlines. That is a minor clarification of robphy's comments, not a contradiction. Usually you are interested in worldlines which correspond to particles, so the distinction is a minor nitpick not any essential disagreement.

 

[Dale]

Suppose we define a point (x1=0, x2=0, x3=0, x4=0). What is a photon's velocity relative to that point?

That question doesn't make any sense. It is geometrically equivalent to asking for the angle between a line and a point.

 

[gbfmgbfm]

This is not an accurate statement of Einstein's second postulate because of your inserted first phrase, "As measured in any inertial frame of reference". The rest of it is an exact quote from Einstein's 1905 paper. You should read some more of his paper to clear up your confusion.

As Einstein points out, we can measure the speed of light by using a single timing device colocated with a light source and detector, and a remote mirror some measured distance away. We start the timer when the light source sets off a flash of light and we stop it when the detector receives the reflected flash. Now we know how long it took the light to make the round trip and how far it was and we can calculate the overall speed of light, but we cannot know how long it took for the light to get to the mirror or how long it took to get back. Einstein's second postulate says to make those two times equal and so know we have to basis for defining time on a remote clock. This is the mechanism by which we create the simultaneous times throughout a Frame of Reference.

So now when you ask about the speed of a photon, can't you see that it is nothing more than the definition of how we devise a Frame of Reference? All light, including photons, travel at c within a Frame of Reference because that is how we defined the Frame of Reference.

You ask about the point (x1=0, x2=0, x3=0, x4=0) but that is not a point, it's an event because it includes x4, the time coordinate, the part of the Frame of Reference that uses the speed of light in its definition. So in any Frame of Reference, light travels at c because that is how we define it and how we define time in the Frame of Reference.

Can you also see why it's meaningless to talk about measuring the speed of a photon?

Dear George,

You write, "Can you also see why it's meaningless to talk about measuring the speed of a photon?"

When James Clerk Maxwell noted that the velocity of electromagnetic waves and light was c in a vacuum, was this a meaningless statement?

 

[gbfmgbfm]

Another way of thinking about the 4-velocity of something that is not accelerating is to realize that it is the spacetime interval (a frame invariant value) divided by the proper time interval (another frame invariant value). Proper time is what a clock measures. A clock must be made of particles with mass. Therefore a clock cannot travel at the speed of light. Therefore there is no meaning to proper time for a photon. Therefore there is no meaning to the 4-velocity of a photon.

Dear George,

Many people say that time stops at the speed of light. Do you agree with this?

Thanks.

 

[gbfmgbfm]

This is not an accurate statement of Einstein's second postulate because of your inserted first phrase, "As measured in any inertial frame of reference". The rest of it is an exact quote from Einstein's 1905 paper. You should read some more of his paper to clear up your confusion.

As Einstein points out, we can measure the speed of light by using a single timing device colocated with a light source and detector, and a remote mirror some measured distance away. We start the timer when the light source sets off a flash of light and we stop it when the detector receives the reflected flash. Now we know how long it took the light to make the round trip and how far it was and we can calculate the overall speed of light, but we cannot know how long it took for the light to get to the mirror or how long it took to get back. Einstein's second postulate says to make those two times equal and so know we have to basis for defining time on a remote clock. This is the mechanism by which we create the simultaneous times throughout a Frame of Reference.

So now when you ask about the speed of a photon, can't you see that it is nothing more than the definition of how we devise a Frame of Reference? All light, including photons, travel at c within a Frame of Reference because that is how we defined the Frame of Reference.

You ask about the point (x1=0, x2=0, x3=0, x4=0) but that is not a point, it's an event because it includes x4, the time coordinate, the part of the Frame of Reference that uses the speed of light in its definition. So in any Frame of Reference, light travels at c because that is how we define it and how we define time in the Frame of Reference.

Can you also see why it's meaningless to talk about measuring the speed of a photon?

Dear George,

It is not my confusion, but rather I copied the postulates from wikipedia.

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

"Postulates of special relativity

1. First postulate (principle of relativity)
The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of coordinates in uniform translatory motion.
2. Second postulate (invariance of c)
As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body."

Should we fix wikipedia? Let me know and I will do it, if you do not want to.

Thanks.

 

[gbfmgbfm]

Is wikipedia wrong about the photon? Here they write, "In empty space, the photon moves at c (the speed of light)."

http://en.wikipedia.org/wiki/Photon
"In empty space, the photon moves at c (the speed of light)."

Does this need to be corrected? What should it be changed to say?

 

[gbfmgbfm]

In Einstein's Meaning of Relativity, Einstein writes,

"Further, let a ray of light pass from one point P1
to another point P2 of K through a vacuum. If r is the measured distance between
the two points, then the propagation of light must satisfy the equation
r = c.∆t."

Above George states that "it's meaningless to talk about measuring the speed of light."

And yet Einstein's entire MEANING of relativity is centered about the speed of light and measuring the speed of light.

Who is right, Einstein or George?

 

[ghwellsjr]

Dear George,

You write, "Can you also see why it's meaningless to talk about measuring the speed of a photon?"

When James Clerk Maxwell noted that the velocity of electromagnetic waves and light was c in a vacuum, was this a meaningless statement?

No, and because of his equations, Maxwell believed that it would be possible to detect the absolute rest state of the ether by measuring the one-way speed of light. He proposed a method and wrote about it in a letter which Michelson read and which inspired him to devise and perform his famous MMX. But Maxwell died before the experiment was carried out so he never learned that his equations, rather than providing support for a way to measure the one-way speed of light, instead adhered to the Lorentz Transformation of Special Relativity.

 

[ghwellsjr]

Another way of thinking about the 4-velocity of something that is not accelerating is to realize that it is the spacetime interval (a frame invariant value) divided by the proper time interval (another frame invariant value). Proper time is what a clock measures. A clock must be made of particles with mass. Therefore a clock cannot travel at the speed of light. Therefore there is no meaning to proper time for a photon. Therefore there is no meaning to the 4-velocity of a photon.

Dear George,

Many people say that time stops at the speed of light. Do you agree with this?

Thanks.

No, it's not that time stops at the speed of light, rather, there is no such thing as time at the speed of light. I tried to make that easy to understand by pointing out that time is what a clock measures and since no clock can travel at the speed of light, time doesn't exist at the speed of light.

Many people say that the faster something goes the more time slows down (which is true) but then they add, until it reaches the speed of light at which point time comes to a standstill and stops (which is not true). No matter how fast something is going, the speed of light is still c and just as far away as it was before it starting going close to c in the first place. People need to understand that c is no more approachable at 99.999%c than it is at 0%c.

There are many other ways of stating the concept that time doesn't exist for light but I'm just trying to make it simple.

 

[ghwellsjr]

Dear George,

It is not my confusion, but rather I copied the postulates from wikipedia.

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

"Postulates of special relativity

1. First postulate (principle of relativity)
The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems of coordinates in uniform translatory motion.
2. Second postulate (invariance of c)
As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body."

Should we fix wikipedia? Let me know and I will do it, if you do not want to.

Thanks.

I don't have a wikipedia account so I'll let you do it. Make sure you understand and believe what you are doing though. Have you looked up Einstein's 1905 paper to see the difference?

 

[ghwellsjr]

Is wikipedia wrong about the photon? Here they write, "In empty space, the photon moves at c (the speed of light)."

http://en.wikipedia.org/wiki/Photon
"In empty space, the photon moves at c (the speed of light)."

Does this need to be corrected? What should it be changed to say?

Nothing wrong with this quote. Photons do move at c. Did you think I was saying something other than that? I said they move at c because we define them and the propagation of all light to be c. I'm just saying that we can't measure their speed, unless you consider making a measurement of something you just defined to be a valid measurement.

 

[ghwellsjr]

In Einstein's Meaning of Relativity, Einstein writes,

"Further, let a ray of light pass from one point P1
to another point P2 of K through a vacuum. If r is the measured distance between
the two points, then the propagation of light must satisfy the equation
r = c.∆t."

Above George states that "it's meaningless to talk about measuring the speed of light."

And yet Einstein's entire MEANING of relativity is centered about the speed of light and measuring the speed of light.

Who is right, Einstein or George?

I'm explaining what Einstein promoted, I take no credit for any of this. I would like to see a link to the quote so I can read the context.

In the meantime, note that Einstein is talking about a measured distance but he didn't say ∆t was measured, did he?

Maybe you could read the context and figure it out on your own.

 

[gbfmgbfm]

Nothing wrong with this quote. Photons do move at c. Did you think I was saying something other than that? I said they move at c because we define them and the propagation of all light to be c. I'm just saying that we can't measure their speed, unless you consider making a measurement of something you just defined to be a valid measurement.

If, as you say, we cannot measure the speed of photons, how do we know that they travel the velocity of light?

A lot of people have come up with (and performed) a lot of experiments to measure the speed of photons with great precision. Google it if you do not believe me. So why are you saying we cannot measure the speed of photons? Curious, no?

 

[gbfmgbfm]

I'm explaining what Einstein promoted, I take no credit for any of this. I would like to see a link to the quote so I can read the context.

In the meantime, note that Einstein is talking about a measured distance but he didn't say ∆t was measured, did he?

Maybe you could read the context and figure it out on your own.

What? Now you're implying that ∆t is not a measured quantity? Why can't we measure time? Above you say we cannot measure the speed of photons. Then how do we know they travel at c? Dear George--you do realize that physics is a science of measurement, and if we can't measure something, it's not physics.

 

[PAllen]

At risk of putting words in ghwellsjr's mouth, I'll try to explain some of what I think he is saying. ghwellsjr is interested in precisely understanding the assumptions and definitions behind measurement, and clearly separating what was measured versus what we might say based on measurement plus definitions and model (I am much less precise in these matters).

1) ghwellsjr would (I think) say that if you measure the round trip time of light using a mirror and a measured distance, you have measured the two way speed of light and this cannot be a direct measurement of one photon's speed, because you can't say that a returning photon is the same as the emitted photon. I would be inclined to say that this is a measurement of the speed of photons (plural), and that is good enough to say, for ordinary purposes, that we have measured the speed of photons.

2) You cannot measure one way speed of light without having two separated clocks that are synchronized. The most practical way of synchronization, which Einstein used in his papers, is based on light. If you use this synchronization, you cannot independently measure the one way speed of light. Your synchronization ensures that it is 1/2 the two way speed of light, and cannot distinguish anisotropy of light speed (of the right sort).

3) You can use slow clock transport to synchronize two clocks separated by a distance. This has been done to measure one way speed of light. Then you enter philosophy: have you shown only that slow clock transport produces the same synchronization light synchronization, or have you measured the one way speed of light? To me, there is no a priori reason to expect slow clock transport to be equivalent, therefore I interpret the explanation for the match as the actual isotropy of lightspeed.

However, independent these issues of measurement philosophy, ghwellsjr's points are consistent with what everyone else has said in response to you, in particular, the meaninglessness of 'speed of a photon relative to an event in spacetime'.

Please note, that despite challenges, you have provide no definitions of velocity, while others have provided several that all lead to the same conclusions.

 

[gbfmgbfm]

At risk of putting words in ghwellsjr's mouth, I'll try to explain some of what I think he is saying. ghwellsjr is interested in precisely understanding the assumptions and definitions behind measurement, and clearly separating what was measured versus what we might say based on measurement plus definitions and model (I am much less precise in these matters).

1) ghwellsjr would (I think) say that if you measure the round trip time of light using a mirror and a measured distance, you have measured the two way speed of light and this cannot be a direct measurement of one photon's speed, because you can't say that a returning photon is the same as the emitted photon. I would be inclined to say that this is a measurement of the speed of photons (plural), and that is good enough to say, for ordinary purposes, that we have measured the speed of photons.

2) You cannot measure one way speed of light without having two separated clocks that are synchronized. The most practical way of synchronization, which Einstein used in his papers, is based on light. If you use this synchronization, you cannot independently measure the one way speed of light. Your synchronization ensures that it is 1/2 the two way speed of light, and cannot distinguish anisotropy of light speed (of the right sort).

3) You can use slow clock transport to synchronize two clocks separated by a distance. This has been done to measure one way speed of light. Then you enter philosophy: have you shown only that slow clock transport produces the same synchronization light synchronization, or have you measured the one way speed of light? To me, there is no a priori reason to expect slow clock transport to be equivalent, therefore I interpret the explanation for the match as the actual isotropy of lightspeed.

However, independent these issues of measurement philosophy, ghwellsjr's points are consistent with what everyone else has said in response to you, in particular, the meaninglessness of 'speed of a photon relative to an event in spacetime'.

Please note, that despite challenges, you have provide no definitions of velocity, while others have provided several that all lead to the same conclusions.

I define velocity in the same way Einstein does in The Meaning of Relativity. Einstein, unlike you, doesn't provide three different definitions of velocity.

PAllen--do you agree with George that, "I'm just saying that we can't measure thee speed of photons."

Do you agree with George that, "No, it's not that time stops at the speed of light, rather, there is no such thing as time at the speed of light?" Do both of you disagree with Dr. Brian Greene who wrote, "Time stops when traveling at the speed of light through space." --http://books.google.com/books?id=MfQDBKHgMxkC&pg=PA49&dq=time+stops+speed+of+light&hl=en&ei=InzYTofYJoHciQKQ1amLCg&sa=X&oi=book_result&ct=result&resnum=1&ved=0CDUQ6AEwAA#v=onepage&q=time%20stops%20speed%20of%20light&f=false

Do you disagree with Nigel Calder?
http://books.google.com/books?id=_8...ook_result&ct=result&resnum=6&ved=0CE4Q6AEwBQ
"Just as time stops completely on the very edge of a black hole, so time would stop if you could travel at precisely the speed of light. "

Do you disagree with National Geographic?
http://books.google.com/books?id=BB...k_result&ct=result&resnum=2&ved=0CDMQ6AEwATgK
" At the speed of light itself, time stops. "

Is Michio Kaku wrong too?
http://books.google.com/books?id=ub...v=onepage&q=time stops speed of light&f=false
"In fact, if the rocket were traveling at the speed of light, time would apparently stop inside the rocket, the rocket would be compressed to nothing, and the mass of the rocket would be infinite. Since none of these observations make. . ."


http://books.google.com/books?id=87...&q=time stops speed of light einstein&f=false
"Time stops at the speed of light."

There are many, many more books stating thusly.

Are you prepared to write letters to all the authors and editors, stating they are wrong?

Are you going to help George correct all those errant wikipedia pages too?

 

[gbfmgbfm]

However, independent these issues of measurement philosophy, ghwellsjr's points are consistent with what everyone else has said in response to you, in particular, the meaninglessness of 'speed of a photon relative to an event in spacetime'.

If a lightning bolt strikes, this causes an event in spacetime. The photons will travel away from where the bolt struck at the rate of c to an observer. What is so difficult about this?

https://www.amazon.com/dp/9569569069/?tag=pfamazon01-20

 

[ghwellsjr]

If, as you say, we cannot measure the speed of photons, how do we know that they travel the velocity of light?

Photons are light so we know their speed the same way we know the speed of any ray of light, we define it to be the same as the two-way speed of light.

Have you ever thought about how you would measure the speed of anything? Normally, you start a timer when the thing starts to move from point A to point B and you stop the timer when it reaches point B, correct? This works fairly well for things traveling rather slowly because we can use light to see when the thing reaches point B. But if the thing we are trying to measure is a photon or a flash of light, then we cannot use a single timer and start it when we see it leave point A and stop it when we see it reach point B because we will actually be including in our measurement the time it takes for the light to return to us and therefore we will be using the round-trip time and dividing that into the one-way distance and get a value that is much smaller than it should be, correct?

You might think that we could get around this problem by using electrical signals and detectors and/or triggers, etc. to make the measurement very precise, but it will still have the same problem because electrical signals cannot travel faster than light.

So what else can we do? Well we can use two clocks instead of one timer and we simply note the time on the first clock at point A when the photon(s) left point A and note the time on the second clock at point B when the photon(s) arrived at point B and then just subtract their times, correct? Well this will work perfectly well if we can make sure that the time on the two clocks is exactly the same.

Now that you see the problem, I would like you to see what Einstein said about this problem in his 1905 paper:

If at the point A of space there is a clock, an observer at A can determine the time values of events in the immediate proximity of A by finding the positions of the hands which are simultaneous with these events. If there is at the point B of space another clock in all respects resembling the one at A, it is possible for an observer at B to determine the time values of events in the immediate neighbourhood of B. But it is not possible without further assumption to compare, in respect of time, an event at A with an event at B. We have so far defined only an “A time” and a “B time.” We have not defined a common “time” for A and B, for the latter cannot be defined at all unless we establish by definition that the “time” required by light to travel from A to B equals the “time” it requires to travel from B to A.​

Einstein them proceeds to establish his clock synchronization convention and then his concept of a Frame of Reference using 3 coordinates of space and one coordinate of time.

A lot of people have come up with (and performed) a lot of experiments to measure the speed of photons with great precision. Google it if you do not believe me. So why are you saying we cannot measure the speed of photons? Curious, no?

I'm not aware that anyone has ever attempted to "measure the speed of photons" and so I did Google it but didn't find one case in the first two pages. Why don't you just list some links where people did these experiments, please? But be aware, if anyone claims to be able to do this, then they are disagreeing with Einstein. And remember, I'm talking about doing this before synchronizing any clocks.

 

[ghwellsjr]

What? Now you're implying that ∆t is not a measured quantity? Why can't we measure time? Above you say we cannot measure the speed of photons. Then how do we know they travel at c?

I hope my previous post has cleared up why Einstein would not say that ∆t is a measured quantity when used with regard to the speed of light. It's the other way around, the speed of light is used to define ∆t, the time difference between two remotely located clocks. After you synchronize clocks this way, you can use them to measure any time intervals you want but, of course, if you're going to measure the speed of light, then you must get c as your answer because you set your clocks to make the measurement of the speed of light equal to c.

I really would like to be more definitive about this quote from Einstein but I need a link. Is the reference online?

Dear George--you do realize that physics is a science of measurement, and if we can't measure something, it's not physics.

Measurements are the easy part of science, coming up with a theory to summarize all those measurements is the hard part. And coming up with an elegantly simple one like Special Relativity was really hard, it took a real genius to do that.

 

[ghwellsjr]

In Einstein's Meaning of Relativity, Einstein writes,

"Further, let a ray of light pass from one point P1 to another point P2 of K through a vacuum. If r is the measured distance between the two points, then the propagation of light must satisfy the equation
r = c.∆t."

Above George states that "it's meaningless to talk about measuring the speed of light."

And yet Einstein's entire MEANING of relativity is centered about the speed of light and measuring the speed of light.

Who is right, Einstein or George?

I'm explaining what Einstein promoted, I take no credit for any of this. I would like to see a link to the quote so I can read the context.

In the meantime, note that Einstein is talking about a measured distance but he didn't say ∆t was measured, did he?

Maybe you could read the context and figure it out on your own.

I found an online reference to http://www.combat-diaries.co.uk/diary29/Link%2014%20Einstein.PDF and your quote which is found on page 30. Immediately before your quote are these words (emphasis mine):

To this end we think of space and time physically defined with respect to two inertial systems, K and K', in the way that has been shown.​

And that way is shown on the previous page where he says:

In order to measure time, we have supposed a clock, U, present somewhere, at rest relatively to K. But we cannot fix the time, by means of this clock, of an event whose distance from the clock is not negligible; for there are no ‘instantaneous signals’ that we can use in order to compare the time of the event with that of the clock. In order to complete the definition of time we may employ the principle of the constancy of the velocity of light in a vacuum.​

And then he proceeds to describe his clock synchronization convention. Note that he starts off this quote saying that you can use one clock to measure time at a single location, which is what you do when you measure the round-trip speed of light, but you cannot use that clock or that clock in conjunction with a second remote clock to measure the time of a remote event until you use the one-way speed of light to define the time on that second clock with respect to the time on the first clock. And that means you have assumed the one-way speed of light to be the same as the two-way speed of light without actually having measured it.

Einstein goes through this same explanation in all his books, lectures and papers on this subject so if you're still not convinced, just look it up in another one.

 

[ghwellsjr]

At risk of putting words in ghwellsjr's mouth, I'll try to explain some of what I think he is saying. ghwellsjr is interested in precisely understanding the assumptions and definitions behind measurement, and clearly separating what was measured versus what we might say based on measurement plus definitions and model (I am much less precise in these matters).

I am interested in promoting the simple explanation that Einstein consistently presented over and over again which many people seem to have missed and that is his first postulate covers the measured round-trip speed of light and his second postulate covers the unmeasurable one-way speed of light.

1) ghwellsjr would (I think) say that if you measure the round trip time of light using a mirror and a measured distance, you have measured the two way speed of light and this cannot be a direct measurement of one photon's speed, because you can't say that a returning photon is the same as the emitted photon.

Yes, but I am merely repeating what Einstein says. Read his 1905 paper or any of his other writings.

I would be inclined to say that this is a measurement of the speed of photons (plural), and that is good enough to say, for ordinary purposes, that we have measured the speed of photons.

I would not say this and neither did Einstein. Rather, you can use the assumed (not measured) speed of photons (if you can figure out exactly how to do it) to synchronize your remote clocks to a local clock.

2) You cannot measure one way speed of light without having two separated clocks that are synchronized. The most practical way of synchronization, which Einstein used in his papers, is based on light. If you use this synchronization, you cannot independently measure the one way speed of light. Your synchronization ensures that it is 1/2 the two way speed of light, and cannot distinguish anisotropy of light speed (of the right sort).

It's not merely the most practical way, it's the only way.

3) You can use slow clock transport to synchronize two clocks separated by a distance. This has been done to measure one way speed of light. Then you enter philosophy: have you shown only that slow clock transport produces the same synchronization light synchronization, or have you measured the one way speed of light? To me, there is no a priori reason to expect slow clock transport to be equivalent, therefore I interpret the explanation for the match as the actual isotropy of lightspeed.

Some people think that Einstein never thought of this supposed alternate way to synchronize clocks but he wrote about this in his 1905 paper and rejected it. In fact he gave the formula to show how much time, as defined in a Frame of Reference, a clock loses during the course of transporting it at a given velocity, v, over a period of time, t, as ½tv²/c² (near the end of section 4). The only way this could work is if the clock travels at a velocity of zero or takes zero time to get there meaning it is not possible.

However, independent these issues of measurement philosophy, ghwellsjr's points are consistent with what everyone else has said in response to you, in particular, the meaninglessness of 'speed of a photon relative to an event in spacetime'.

Did I say something like that? Where is this quote from?

Please note, that despite challenges, you have provide no definitions of velocity, while others have provided several that all lead to the same conclusions.

 

[ghwellsjr]

I define velocity in the same way Einstein does in The Meaning of Relativity. Einstein, unlike you, doesn't provide three different definitions of velocity.

PAllen--do you agree with George that, "I'm just saying that we can't measure thee speed of photons."

Do you agree with George that, "No, it's not that time stops at the speed of light, rather, there is no such thing as time at the speed of light?" Do both of you disagree with Dr. Brian Greene who wrote, "Time stops when traveling at the speed of light through space." --http://books.google.com/books?id=MfQDBKHgMxkC&pg=PA49&dq=time+stops+speed+of+light&hl=en&ei=InzYTofYJoHciQKQ1amLCg&sa=X&oi=book_result&ct=result&resnum=1&ved=0CDUQ6AEwAA#v=onepage&q=time%20stops%20speed%20of%20light&f=false

Do you disagree with Nigel Calder?
http://books.google.com/books?id=_8...ook_result&ct=result&resnum=6&ved=0CE4Q6AEwBQ
"Just as time stops completely on the very edge of a black hole, so time would stop if you could travel at precisely the speed of light. "

Do you disagree with National Geographic?
http://books.google.com/books?id=BB...k_result&ct=result&resnum=2&ved=0CDMQ6AEwATgK
" At the speed of light itself, time stops. "

Is Michio Kaku wrong too?
http://books.google.com/books?id=ub...v=onepage&q=time stops speed of light&f=false
"In fact, if the rocket were traveling at the speed of light, time would apparently stop inside the rocket, the rocket would be compressed to nothing, and the mass of the rocket would be infinite. Since none of these observations make. . ."


http://books.google.com/books?id=87...&q=time stops speed of light einstein&f=false
"Time stops at the speed of light."

There are many, many more books stating thusly.

Are you prepared to write letters to all the authors and editors, stating they are wrong?

Are you going to help George correct all those errant wikipedia pages too?

Does the phrase "time stops" mean that the clock quit working or does it mean the clock no longer exists? Could it mean "time stops being time"? I really don't know if each one of these authors is promoting the idea of time slowing down until you reach a point at which it stops but it's still time or if they are saying that it's an unreachable state.

I recently had to straighten out another poster who said, "I heard Penrose say that time for light is 0." See Is SOL infinite? (from its own point of view). I knew that Roger Penrose would not make any such statement and it took a while to get to the bottom of what he actually did say and what the context was. I am not inclined to track down all the people that you claim have misrepresented Special Relativity since you have already shown a propensity to misunderstand what Einstein said, even after repeated clarifications. My hope is that you will come to a correct understanding of Einstein's Special Relativity and that you will then be able to go yourself to these sources and figure out whether they are mixed up or not. I'm not saying that there aren't some mixed up ideas in popular books on Special Relativity because I see it all the time but many of these authors know that most people are confused about Special Relativity and find it convenient to make some money, whether or not they themselves understand what they are talking about.

 

[Dale]

This is not an accurate statement of Einstein's second postulate because of your inserted first phrase, "As measured in any inertial frame of reference".

I wouldn't go so far as this. I wouldn't say that it is not inaccurate, rather it is tautological. In any inertial frame of reference light goes at c because an inertial frame of reference is one in which light goes at c.

 

[Dale]

There are many, many more books stating thusly.

Each of those books is a pop-sci book, not a mainstream scientific book.

 

[Dale]

So why are you saying we cannot measure the speed of photons?

He is saying that we cannot measure the one-way speed of light, we define the one-way speed of light. We can measure the two-way speed of light.

The issue is synchronization of the clocks. In order to measure a two-way speed of light you can use a rod, a mirror, and a single clock. Since you are using a single clock there is no issue with synchronization.

In order to measure a one-way speed of light you need to use a rod and two clocks which are synchronized. The value that you obtain for the speed of light is dependent on your synchronization convention. Einstein's synchronization convention assumes that the one-way speed is isotropic and equal to the two-way speed. So if you measure the one-way speed of light using clocks that are synchronized using the Einstein convention then you are guaranteed to get c since that was assumed.

If, as you say, we cannot measure the speed of photons, how do we know that they travel the velocity of light?

Because we have defined it that way. They travel at c in inertial frames because inertial frames are defined to be frames where they travel at c.

What? Now you're implying that ∆t is not a measured quantity? Why can't we measure time?

Again, the issue is synchronization. The Δt that you measure using a pair of synchronized clocks depends on your synchronization convention.