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.gbfmgbfm said:robphy states, "Relative-velocities are defined between particles." As you have shown, this is not true.
That question doesn't make any sense. It is geometrically equivalent to asking for the angle between a line and a point.gbfmgbfm said:Suppose we define a point (x1=0, x2=0, x3=0, x4=0). What is a photon's velocity relative to that point?
ghwellsjr said: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?
ghwellsjr said: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.
ghwellsjr said: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?
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.gbfmgbfm said: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, 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.gbfmgbfm said:Dear George,ghwellsjr said: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.
Many people say that time stops at the speed of light. Do you agree with this?
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?gbfmgbfm said: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.
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.gbfmgbfm said: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?
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.gbfmgbfm said: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 said: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 said: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.
PAllen said: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.
PAllen said: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'.
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.gbfmgbfm said:If, as you say, we cannot measure the speed of photons, how do we know that they travel the velocity of light?
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.gbfmgbfm said: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 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.gbfmgbfm said: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?
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.gbfmgbfm said:Dear George--you do realize that physics is a science of measurement, and if we can't measure something, it's not physics.
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):ghwellsjr said: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.gbfmgbfm said: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?
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 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.PAllen said: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).
Yes, but I am merely repeating what Einstein says. Read his 1905 paper or any of his other writings.PAllen said: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 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.PAllen said: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.
It's not merely the most practical way, it's the only way.PAllen said: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).
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.PAllen said: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.
Did I say something like that? Where is this quote from?PAllen said: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'.
PAllen said:Please note, that despite challenges, you have provide no definitions of velocity, while others have provided several that all lead to the same conclusions.
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.gbfmgbfm said: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?
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.ghwellsjr said: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".
Each of those books is a pop-sci book, not a mainstream scientific book.gbfmgbfm said:There are many, many more books stating thusly.
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.gbfmgbfm said:So why are you saying we cannot measure the speed of photons?
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.gbfmgbfm said:If, as you say, we cannot measure the speed of photons, how do we know that they travel the velocity of light?
Again, the issue is synchronization. The Δt that you measure using a pair of synchronized clocks depends on your synchronization convention.gbfmgbfm said:What? Now you're implying that ∆t is not a measured quantity? Why can't we measure time?
What I am getting at is simply that if you treat light as photons, a two way measurement is a measure of photon speed - the average speed of outgoing and incoming photons. The fact that it may not be the same photon is not really relevant.ghwellsjr said: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.
Of course I know this. The point (which I did not bother to elaborate because I thought it was understood) is that if you slow transport a clock in a round trip you can (in principle) measure time difference. You then still have to assume you can cut this in half for a one way slow clock trip synchronization (however, this is a different assumption than isotropy of light speed; it is an assumption of isotropy of time shift for clock transport). However, this remains an independent measurement, because in measuring the slow clock round trip shift, you have nowhere used light. You have measured c as a feature of spacetime. Then, in my view (with the noted isotropy assumption), you can measure that light travels at this c (if you synchronized clocks thus, and measured bullets, you would obviously not find they travel at c).ghwellsjr said:It's not merely the most practical way, it's the only way.
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.
ghwellsjr said:Did I say something like that? Where is this quote from?
No, you have presented no definition. The section you quoted is not definition of velocity. ghwellsjr has shown, in detail, how other sections of this book are consistent with other papers and books by Einstein, so I will not belabor this.gbfmgbfm said: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.
I agree with George that you can't measure the one way speed of photons without a bunch of additional assumptions. Thus, I definitely agree you cannot directly measure the one way speed of photons - because of the assumptions you have to make.gbfmgbfm said:PAllen--do you agree with George that, "I'm just saying that we can't measure thee speed of photons."
Yes, I agree with this. I would normally put it as: there is no such thing as the reference frame of a photon; or you can talk about speed of light relative to a material body, but you cannot talk about speed (or anything else) relative to light.gbfmgbfm said: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?"
This is an example of misleading poetic license. Time does not stop at a black hole horizon for a clock passing through it. A clock stationary at the black hole horizon is an impossibility. I guess, you call this sort of true if you took the sense to mean: it is no more possible to have a stationary clock at the event horizon than it is to have a clock moving at the speed of light.gbfmgbfm said: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. "
National geographic is not a source for physics.gbfmgbfm said: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. "
To me, this is just an argument about why you cannot talk about rockets or clocks moving at c, and why it is not meaningful to talk about such a frame. The sentence you chopped off suggests this is the beginning of a classic reductio at absurdum argument. You are taking the 'absurd' part of the argument and pretending it is meant as not absurd.gbfmgbfm said: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. . ."
gbfmgbfm said: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?
What I was objecting to was the insertion of the word "measured" in the second postulate. If the postulate was: "As measured in any inertial frame of reference, the speed of light in empty space is c and is independent of the state of motion of the emitting body", then I would agree this would be accurate, but redundant because that postulate is covered by the first postulate and does not need its own special enunciation. But it is not accurate to include the word "measured" in a postulate that refers to the propagation of light because we can neither observe nor measure the progress of light. If we could, we wouldn't need a second postulate. And remember, Einstein specifically made a point that his second postulate seemed to be at odds with the first and if he meant that it was referring to something about light that could be measured, there wouldn't be any issue of reconciliation.DaleSpam said: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.ghwellsjr said: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".
This is the first time I ever heard of anyone claiming that the slow transport of clocks involved splitting the difference in a round-trip. No matter, it still cannot be used to synchronize remote clocks or Einstein would have suggested it since he obviously knew about the possibility. It is only because Einstein has previously synchronized remote clocks that he can make a claim about how a clock loses time when it is transported from one location to another and that claim only holds true in that one frame. As viewed by another frame in motion with respect to the initial rest frame of the two clocks in question, the times on the two clocks are not any where near being synchronized when they remain separated even though when they are brought back together all frames agree on their difference.PAllen said:Of course I know this. The point (which I did not bother to elaborate because I thought it was understood) is that if you slow transport a clock in a round trip you can (in principle) measure time difference. You then still have to assume you can cut this in half for a one way slow clock trip synchronization (however, this is a different assumption than isotropy of light speed; it is an assumption of isotropy of time shift for clock transport). However, this remains an independent measurement, because in measuring the slow clock round trip shift, you have nowhere used light. You have measured c as a feature of spacetime. Then, in my view (with the noted isotropy assumption), you can measure that light travels at this c (if you synchronized clocks thus, and measured bullets, you would obviously not find they travel at c).ghwellsjr said:It's not merely the most practical way, it's the only way.
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.
Thus, another independent synchronization convention is possible: measure slow clock round trip shift, and assume isotropy of clock transport shift. There is no part of this convention that assumes light speed (one way or two way).
gbfmgbfm said: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 said: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.
ghwellsjr said:This is the first time I ever heard of anyone claiming that the slow transport of clocks involved splitting the difference in a round-trip. No matter, it still cannot be used to synchronize remote clocks or Einstein would have suggested it since he obviously knew about the possibility. It is only because Einstein has previously synchronized remote clocks that he can make a claim about how a clock loses time when it is transported from one location to another and that claim only holds true in that one frame. As viewed by another frame in motion with respect to the initial rest frame of the two clocks in question, the times on the two clocks are not any where near being synchronized when they remain separated even though when they are brought back together all frames agree on their difference.
DaleSpam said:Each of those books is a pop-sci book, not a mainstream scientific book.
PeterDonis said:The event of the lightning bolt striking is *not* the same thing as "where the bolt struck". The latter refers to the location in *space* of the bolt striking, not the event in *spacetime*. So your second sentence is talking about something different than your first: it's talking about the relative velocities of the photon's worldline and the worldline of the point in space where the bolt struck. It is *not* talking about the "relative velocity" of the photon and the *event* where the bolt struck, which doesn't make sense.
gbfmgbfm said:Actually this makes perfect sense, "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."
Where can refer to space and time, for we live in a 4d manifold where they are inseperable.
gbfmgbfm said:Many of you want to work the word "worldline" into your discussions like little boys flexing their muscles at the swimming pool, muddying the waters so as to appear deeper like Nietzsche said, but Einstein makes NO MENTION of worldlines in his seminal book on Relativity--The Meaning of Relativity.
gbfmgbfm said:Above someone accuses Brian Green of being a non-mainstream scientist. Is Einstein also a non-mainstream scientist because he doesn't use the word "worldline" in defining relativity?