Is cheating going on in Relativity?

[Sam Woole]

Is cheating going on in Einstein’s theory of relativity? For instance, the textbook “Fundamentals of Physics” (6th edition, published by John Wiley and Sons, jointly authored by David Halliday, Robert Resnick, and Earl Walker, on pages 925, 926 and 927, where the relativity theory was briefly introduced) said specifically and repeatedly that clocks would be used to measure time intervals. But I did not find any time interval that was read from the clocks. Instead all the time intervals used in the instruction were computed by means of Newtonian physics.

 

[reilly]

Computing time intervals simply tells you what to expect when measuring the time. Indeed, time is measured by clocks; computations do not measure time. Not to worry, relativity is alive ,well and very robust, and has been so for roughly a century.

Regards,
Reilly Atkinson

 

[DrChinese]

Is cheating going on in Einstein’s theory of relativity?

Welcome to PhysicsForums!

Not sure exactly what you mean about cheating. Relativity (both SR and GR) has been very well tested through the years. John Baez has some good stuff at his physics site, including this:

What is the experimental basis of Special Relativity?

 

[Chronos]

The most important concept in SR is that all clocks are local. In other words, the only one that matters is strapped to your wrist. Clocks strapped to other observers wrists will not, and cannot be ever be expected to agree. There is no universal clock. Special relativity is basically a four dimensional solution to Pythagorem's theorem. Wrap your head around that and you've got it... at least until you woozily stumble into the GR minefield and realized why you always hated geometry deep down inside.

 

[Sam Woole]

Thanks to reilly, DrChinese, and Chronos for your replies to my question. I however think the problem was not so simple.

I wish all of you have access to the said textbook and then let us look into the thought experiment therein. The textbook authors claimed that the clocks will produce 2 different time intervals. But I believe otherwise and let me show you how.

If we simplify the graphics and ignore the light, the thought experiment can be shown as follows:

S__________R
P__________Q

where S, R, P, and Q are points on two reference frames. A clock will move from S to R. And at P and Q each there is another clock. When the clock at S departs, it must register a reading of time. Let me call it the departure
time "b". I believe the same departure time "b" will be recorded on another clock located at P. Don't you agree? (The textbook said, it was a light beam that departed. But it was all the same departure time, and that was why it was perfect all right not to mention the departure of light.)

Now the clock will record an arrival time when it arrives at R. Let us call it "e". And the other clock at Q certainly will record the same arrival time "e" according to the design of the thought experiment. To obtain the time interval t, it is to deduct the departure time from the arrival time:
t = e - b. This means that all 3 clocks would measure one identical time interval t, not two different time intervals claimed by the authors of the textbook.

Consequently the relativistic nature of time cannot be proven unless relativistic advocates resort to cheating.

 

[Doc Al]

I wish all of you have access to the said textbook and then let us look into the thought experiment therein. The textbook authors claimed that the clocks will produce 2 different time intervals. But I believe otherwise and let me show you how.

Why don't you scan it in?

If we simplify the graphics and ignore the light, the thought experiment can be shown as follows:

S__________R
P__________Q

where S, R, P, and Q are points on two reference frames. A clock will move from S to R. And at P and Q each there is another clock. When the clock at S departs, it must register a reading of time. Let me call it the departure
time "b". I believe the same departure time "b" will be recorded on another clock located at P. Don't you agree? (The textbook said, it was a light beam that departed. But it was all the same departure time, and that was why it was perfect all right not to mention the departure of light.)

To say "A clock moves from S to R" is very different from saying "A beam of light is emitted at S and arrives at R". Which is it? (I'll assume the latter.)

You have two frames in relative motion, I presume. I assume S & R are in the "moving" frame. At the moment that the light is emitted at S, the point P passes by point S. Let's define the time read by the clocks at S and P to read the same at the moment they pass each other, which is the moment that the light is emitted.

Now the clock will record an arrival time when it arrives at R. Let us call it "e". And the other clock at Q certainly will record the same arrival time "e" according to the design of the thought experiment.

Not true at all! I assume the experiment is that the light arrives at point R just at the moment that point Q passes R. Each frame has its own clocks, presumably synchronized in their own frame: the moving frame has clocks at S and R; the other frame has clocks at P and Q. When the light arrives at R and Q, those clocks will not read the same times.

To obtain the time interval t, it is to deduct the departure time from the arrival time:
t = e - b. This means that all 3 clocks would measure one identical time interval t, not two different time intervals claimed by the authors of the textbook.

You seem to just assume that the time of flight will be the same in both frames. But that ignores what is known about how time and distance measurements depend on the frame doing the measuring.

Consequently the relativistic nature of time cannot be proven unless relativistic advocates resort to cheating.

Where exactly is the cheating? You seem to have given your version of the thought experiment; why don't you describe the version in the book.

 

[JesseM]

Thanks to reilly, DrChinese, and Chronos for your replies to my question. I however think the problem was not so simple.

I wish all of you have access to the said textbook and then let us look into the thought experiment therein. The textbook authors claimed that the clocks will produce 2 different time intervals. But I believe otherwise and let me show you how.

If we simplify the graphics and ignore the light, the thought experiment can be shown as follows:

S__________R
P__________Q

where S, R, P, and Q are points on two reference frames. A clock will move from S to R. And at P and Q each there is another clock. When the clock at S departs, it must register a reading of time. Let me call it the departure
time "b". I believe the same departure time "b" will be recorded on another clock located at P. Don't you agree? (The textbook said, it was a light beam that departed. But it was all the same departure time, and that was why it was perfect all right not to mention the departure of light.)

Now the clock will record an arrival time when it arrives at R. Let us call it "e". And the other clock at Q certainly will record the same arrival time "e" according to the design of the thought experiment. To obtain the time interval t, it is to deduct the departure time from the arrival time:
t = e - b. This means that all 3 clocks would measure one identical time interval t, not two different time intervals claimed by the authors of the textbook.

Consequently the relativistic nature of time cannot be proven unless relativistic advocates resort to cheating.

What you are missing is the fact that in the rest frame of the clock which moved from S to R, the clocks that are resting at P and Q are out-of-sync, so the time interval between them is not the correct one in the first clock's rest frame (if you walked through a hallway and the clock on one end said 2:00 while the clock on the other end said 3:00, then you would not conclude it took you an hour to cross the hallway, you'd just conclude the second clock was ahead of the first one). This is known as "the relativity of simultaneity", and it's a pretty simple consequence of the idea that each frame should assume light moves at c. Just imagine a rocket going by you where a crewmember sets off a flash at the rocket's midpoint and synchronizes clocks on either end of the rocket by setting them to the same time at the moment the light from the flash hits them; since the rocket is moving forward in your frame, you will see that the clock at the front of the rocket is moving away from the point where the flash was set off while the clock at the back is moving towards it, so if you also assume light moves at c in all directions in your frame, you will conclude the light hit the back clock before the front clock, and thus that the two clocks are out-of-sync.

You might want to take a look at a detailed example I worked out (with diagrams) on this thread, involving two rulers with clocks mounted at regular intervals sliding alongside each other, showing how in each ruler's rest frame it is the clocks on the other ruler which are running slow (and which are out-of-sync).

 

[Sam Woole]

Thank you, Al Doc. I am sorry that I did not give you enough information because I don't have the scanning device. But in my opening post I have made it clear between [clocks] and [equation]. We used clocks to measure time intervals, or we used equations to compute time intervals. These are two distinctly different operations, clocks and equations. If someone told me he would use clocks to do something and he switched to equations, of course he cheated me. This was exactly what had happened in the said textbook.

In your reply to me you said: "When the light arrives at R and Q, those clocks will not read the same times."
S__________R
P__________Q

Why the clock at Q will NOT read the same arrival time as the clock at R did? You did not explain why. I believe otherwise, because this was a thought experiment. If all the clocks at S and P could be thought to read the same
departure time, the same "thought" logic must apply to the arrival point. Hence when the light beam arrived at R and Q, the clocks there would logically read the same arrival time.

Further, there could not be any synchronization problem either, simply because it was all a thought. In a thought an infinite number of clocks can be thought as synchronized perfectly. Imperfection can only happen in real experiments in the laboratory. If the clocks in different frames were synchronized in different ways, our thought can make compensations to them, adding or deducting a few nano-seconds to make difference disappear.

As a last argument of mine, even if the clocks at R and Q would not read the same arrival time as you alleged, the cheating was still here, simply because the textbook authors produced the different time intervals by means
of Newtonian physics. My logic was so glaringly clear that nobody could miss. Say I bought an orange and an apple from Mr. Newton's store, and I told my parents I bought them from Mr. Smith's store. There was no change
to the fact that there were an orange and an apple. But I cheated my parents about the source.

If my parents got sick after consuming the fruits, the blame would fall on Mr. Smith, not on Mr. Newton, as a result of my cheating.

As to JesseM's reply, I believe he had the same argument since he mentioned synchronization. My point was how to identify the cheat, not to tell what the light would do in different reference frames. As to your relativity of simultaneity, I shall respond separately after I have studied your details.

 

[JesseM]

Further, there could not be any synchronization problem either, simply because it was all a thought. In a thought an infinite number of clocks can be thought as synchronized perfectly. Imperfection can only happen in real experiments in the laboratory. If the clocks in different frames were synchronized in different ways, our thought can make compensations to them, adding or deducting a few nano-seconds to make difference disappear.

But whose clocks do you add or deduct time from? Each observer has a set of clocks which are at rest with respect to himself and which he defines as synchronized, while seeing the clocks of moving observers being out-of-sync. And each observer uses his own set of clocks to mark the time of events--so if I see an event happen next to clock A in my system when it reads 2:00, and another event happen next to clock B in my system when it reads 3:00, I'll say that the time-interval between the two events was 1 hour, even if other observers using their own set of clocks get a different answer. So if I say that my clocks are synchronized and your clocks are out-of-sync, while you say that your clocks are synchronized and my clocks are out-of-sync, the situation is perfectly symmetrical, there's no objective way to decide which set of clocks is measuring time-intervals "correctly".

Did you look at the diagrams of the two ruler/clock systems I provided on the other thread I linked to? They make the symmetry of the situation pretty clear.

As a last argument of mine, even if the clocks at R and Q would not read the same arrival time as you alleged, the cheating was still here, simply because the textbook authors produced the different time intervals by means
of Newtonian physics.

Where do textbook authors use Newtonian physics when justifying the ideas of relativity? I've never seen that before, can you quote the section you're talking about?

 

[Doc Al]

Thank you, Al Doc. I am sorry that I did not give you enough information because I don't have the scanning device. But in my opening post I have made it clear between [clocks] and [equation]. We used clocks to measure time intervals, or we used equations to compute time intervals. These are two distinctly different operations, clocks and equations. If someone told me he would use clocks to do something and he switched to equations, of course he cheated me. This was exactly what had happened in the said textbook.

You do realize that this is a thought experiment, don't you? We can't actually read what the clocks say, we have to deduce what they say according to the accepted laws of physics. One principle that was probably applied was that light travels at the same speed ("c") with respect to any frame.

In your reply to me you said: "When the light arrives at R and Q, those clocks will not read the same times."
S__________R
P__________Q

Why the clock at Q will NOT read the same arrival time as the clock at R did? You did not explain why. I believe otherwise, because this was a thought experiment. If all the clocks at S and P could be thought to read the same
departure time, the same "thought" logic must apply to the arrival point. Hence when the light beam arrived at R and Q, the clocks there would logically read the same arrival time.

The reason why the clocks at S and P read the same at the instant that they pass each other is because we agreed to set them to read the same time at that single instant. For two systems of coordinates, you can always set the origin to be the same. But what other clocks read at other times must be deduced from physics, not merely assumed. (If you just assume that all clocks read the same time, then you will get results that contradict known laws of physics.)

Further, there could not be any synchronization problem either, simply because it was all a thought. In a thought an infinite number of clocks can be thought as synchronized perfectly. Imperfection can only happen in real experiments in the laboratory. If the clocks in different frames were synchronized in different ways, our thought can make compensations to them, adding or deducting a few nano-seconds to make difference disappear.

You seem to have the wrong idea as to what a "thought experiment" means. It doesn't mean "just think whatever you want". It means that you set up a situation (one that may be impractical to do in real life) and apply real laws of physics to deduce what happens. You don't just assume whatever you want.

A clear application of the assumptions of relativity (that the speed of light is invariant, for one) will show that the two frames must disagree as to how the other frame's clocks are synchronized.

As a last argument of mine, even if the clocks at R and Q would not read the same arrival time as you alleged, the cheating was still here, simply because the textbook authors produced the different time intervals by means
of Newtonian physics. My logic was so glaringly clear that nobody could miss. Say I bought an orange and an apple from Mr. Newton's store, and I told my parents I bought them from Mr. Smith's store. There was no change
to the fact that there were an orange and an apple. But I cheated my parents about the source.

What "Newtonian Physics" was used? I suspect that what was used was something like: Distance = speed X time. That's just as true for Einstein as for Newton.

Once again: Where's the cheating? To show "cheating" you should lay out, step by step, the actual argument made in the textbook (not just your version) and point to the exact statements that you question.

 

[Sam Woole]

Doc Al and jesseM, and everybody else who have responded to my charge, I am sorry I could not copy and transmit the textbook's full text over here due to my computer skills. I shall drop the matter for good. If my charge had hurt any body, I apologize to them all. Sorry again.

 

[JesseM]

Doc Al and jesseM, and everybody else who have responded to my charge, I am sorry I could not copy and transmit the textbook's full text over here due to my computer skills. I shall drop the matter for good. If my charge had hurt any body, I apologize to them all. Sorry again.

No one was asking you to transmit the full text (which would be illegal anyway), just to quote a paragraph or two where they mentioned Newtonian physics in connection to relativity, or perhaps scan a page if you don't feel like typing it.

 

[Chronos]

Not at all Sam, you asked an honest question... and got gang banged! The best, and most honest part, was when you asked sincerely. I respect that, Sam. I rule in your favor.

 

[Chronos]

Footnote: I think you are profoundly wrong, Sam, but I like the way you think.

 

[jtbell]

Sam,

You may simply be one of those people who likes to learn things "by debate", so to speak, using an argumentative skeptical style. In many fields this is common, and you'll even find this sort of thing in physics, especially in true "cutting edge" areas.

The problem is that on the Net there are many anti-relativity cranks and crackpots who are convinced that they are right and mainstream scientists are all wrong, and who argue their views very aggressively and persistently. Anyone who comes onto an Internet discussion group and tries to discuss relativity in a similar style is likely to be treated like one of those people, regardless of their actual motives.

 

[Sam Woole]

Thanks to everybody. As JseesM suggested, I shall quote some from the said textbook. On page 925 of the textbook, under the title The Relativity of Time, there were these words: “If observers who move relative to each other measure the time interval between two events, they generally will find different results.
Why? Because the spatial separation of the events can affect the time intervals measured by the observers."

The textbook then gives a thought experiment involving an observer Sally on a train moving at v relative to another observer Sam on the ground, represented in two figures. I do not know how to draw these figures. Let me describe the first figure and see whether you can visualize.

Sally will send a light pulse from her clock toward the ceiling of the cabin where she is in. To her, the light travels along the height (D) of her cabin, and comes down along the same height (D) and arrives at her clock. The textbook says: "Sally measures a certain time interval t between the two events, related to the distance 2D from source to mirror by t = 2D/c."

The quote immediately above has two parts. The first part means Sally would obtain information from her clock, reading a departure time and an arrival time; the second part means she needs not read, because the time interval is related to the distance traveled by light.

Don't you think these two actions, saying one thing and doing a different thing, constituted a lie?

 

[robphy]

Sally will send a light pulse from her clock toward the ceiling of the cabin where she is in. To her, the light travels along the height (D) of her cabin, and comes down along the same height (D) and arrives at her clock. The textbook says: "Sally measures a certain time interval t between the two events, related to the distance 2D from source to mirror by t = 2D/c."

The quote immediately above has two parts. The first part means Sally would obtain information from her clock, reading a departure time and an arrival time; the second part means she needs not read, because the time interval is related to the distance traveled by light.

Don't you think these two actions, saying one thing and doing a different thing, constituted a lie?

Your passage described a light-clock.

The duration between emission and reception, t, represents "1 tick" of that clock... a perfectly good unit of time. One could regard the first emission as the time reading of "0 ticks".

Upon the first reception, if the source reflects back or re-emits a light signal, waiting for a second reception yields a second tick.

The duration of a tick is proportional to the separation, D, between the "mirror" on the ceiling and the source. That's what t=2D/c means... a relationship relating t and D.. not a definition of t. (If you want a clock with a finer resolution, reduce the separation D.)

 

[JesseM]

Thanks to everybody. As JseesM suggested, I shall quote some from the said textbook. On page 925 of the textbook, under the title The Relativity of Time, there were these words: “If observers who move relative to each other measure the time interval between two events, they generally will find different results.
Why? Because the spatial separation of the events can affect the time intervals measured by the observers."

The textbook then gives a thought experiment involving an observer Sally on a train moving at v relative to another observer Sam on the ground, represented in two figures. I do not know how to draw these figures. Let me describe the first figure and see whether you can visualize.

Sally will send a light pulse from her clock toward the ceiling of the cabin where she is in. To her, the light travels along the height (D) of her cabin, and comes down along the same height (D) and arrives at her clock. The textbook says: "Sally measures a certain time interval t between the two events, related to the distance 2D from source to mirror by t = 2D/c."

The quote immediately above has two parts. The first part means Sally would obtain information from her clock, reading a departure time and an arrival time; the second part means she needs not read, because the time interval is related to the distance traveled by light.

Don't you think these two actions, saying one thing and doing a different thing, constituted a lie?

Why is it a lie? It just says that the time interval she actually measures using her clock will in fact match up with what she would predict if she assumed light travels at c in both directions in her own frame. They're not saying that Sally "needs not read", they're just telling you what relativity predicts she will read on her clock. Predictions should match observations in any successful theory, no?

 

[Janus]

Sally will send a light pulse from her clock toward the ceiling of the cabin where she is in. To her, the light travels along the height (D) of her cabin, and comes down along the same height (D) and arrives at her clock. The textbook says: "Sally measures a certain time interval t between the two events, related to the distance 2D from source to mirror by t = 2D/c."

The quote immediately above has two parts. The first part means Sally would obtain information from her clock, reading a departure time and an arrival time; the second part means she needs not read, because the time interval is related to the distance traveled by light.

Don't you think these two actions, saying one thing and doing a different thing, constituted a lie?

I'm sorry, but I don't see anything wrong with this quote. All it says is that the time that Sally reads on the Clock and 2D/c will be the same amount of time. It's like saying that if I start a stopwatch as someone starts to drive away from me at 60mph, then that person turns around after 10 miles and comes back, my stop watch will read 20 min upon his return. If he turns around after 20 miles, my stopwatch will read 40 min, and if he turns around after 5 miles it will read 10 min. There is a direct relation to the time I read on my stopwatch and the distance he drives before turning around.

 

[Sam Woole]

It seemed that JesseM and Janus and most people believed that Sally's clock would produce a time interval equal to the one produced by Newton's equation.

First of all my allegation had nothing to do with the equality between time intervals. My allegation was, if the textbook authors eventually used Newton's equation to compute the time interval, they should not in the beginning have said they would use clocks to do the job. They need not set up any clocks at all. Too much ado about nothing. They should not use the word "measure". They should just say they will compute. As a result the first paragraph I quoted in the former post of mine should read like this:

"If observers who move relative to each other COMPUTE the time interval between two events, they generally will find different results. Why? Because the spatial separation of the events can affect the time intervals COMPUTED by the observers."

The change of one action to another (from measure to compute) has illogical consequences. When computation has produced a shorter time interval, the explanation we can give is that we have put in (into Newton's equation) a shorter distance. I believe we cannot say, the reason for the equation to have produced a shorter time interval is because the clock ticked too slow. Can we accept such a logic?

But in my view this was exactly what was happening in teaching the relativity theory. When a shorter time interval was obtained from Newton's equation, we were told the clock was malfunctioning, or time dilated.

Such a practice (a shorter distance producing a shorter time interval) means time dilation has been used to prove the existence of time dilation. Is this logic sound?

Secondly, if the textbook authors believed that the clocks would produce a time interval equal to the one computed from Newton's equation, they were obliged to demonstrate HOW. Or at least they should have said a few words
about it.

Let us represent your belief like this:

(e - b) = t = 2D/c...wherein e is the arrival time, b the departure time, shown on clocks; t is the resulted time interval, which equals the computed time interval 2D/c.

As is customary that two reference frames are moving at v relative to each other. As a result when the light pulse departs and arrives at the clocks, the two frames have created a distance. Let us call this distance g. This
means, to create the distance g the frames have taken the same time interval t as the light pulse has done. Don't you agree? If you do, the situation can be represented with this: t = g/v. This equation must be true especially if we
refer to Janus example of stopwatches and cars.

Since you believed that the measured time interval (e - b) is equal to the computed time interval 2D/c, it means
(e - b) = t = 2D/c = g/v. This equation means that
both frames have obtained the one and only time interval t, whether the observers used the measuring technique or the computation one.

But the textbook told us that there would be two "different results." So, there must be something wrong? Don't you agree?

 

[JesseM]

It seemed that JesseM and Janus and most people believed that Sally's clock would produce a time interval equal to the one produced by Newton's equation.

What are you talking about when you say "Newton's equation"? Do you just mean speed = distance/time? This equation is not specifically Newtonian, it's just as true in relativity as in Newtonian physics.

First of all my allegation had nothing to do with the equality between time intervals. My allegation was, if the textbook authors eventually used Newton's equation to compute the time interval, they should not in the beginning have said they would use clocks to do the job. They need not set up any clocks at all. Too much ado about nothing. They should not use the word "measure". They should just say they will compute.

Even if you feel the clocks and rulers are unnecessary, this hardly qualifies as "cheating" as long as the computed result matches what you'd actually get using clocks and rulers. In any case, the clocks and rulers are necessary, because if you have two observers in different reference frames, each observer uses his own clocks and rulers to determine speeds, and this explains how the two observers can both say the same light beam moved at c even if they disagree on the length of the path that the beam took; otherwise this wouldn't make any sense.

As a result the first paragraph I quoted in the former post of mine should read like this:

"If observers who move relative to each other COMPUTE the time interval between two events, they generally will find different results. Why? Because the spatial separation of the events can affect the time intervals COMPUTED by the observers."

But what they mean here by "compute" is "subtract the measured time of the first event according to that observer's clocks from the measured time of the second event", so clocks are still involved. If Sally is on the train and Sam is on the ground, and Sam uses his own clocks to mark the time that the light beam leaves the floor and the time it returns to the floor (he will need two separate synchronized clocks for this since the train is moving while the clocks need to be at rest relative to him, and each clock needs to be next to the event it's measuring so that you don't have to worry about delays due to the finite speed of light), then if he subtracts the measured time on his own clocks that the light beam left the floor from the measured time on his own clocks that it returned to the floor, he'll get a larger time interval between these two events than Sally got using her onboard clock (which means from his point of view, Sally's clock must have been ticking slow). But he also measures the light beam to have taken a longer path between the floor and the ceiling, since the train was moving horizontally and thus the light beam was moving diagonally in his frame rather than purely vertically; if he divides the distance he measured by the time he measured, he will also find that the light beam traveled at c in his frame.

edit: I should add that when Sam "synchronizes" his two clocks at different locations, he does so using the assumption that light always travels at c in his frame; if he made a different assumption then he wouldn't measure Sally's light beam to travel at c. So it is true that the idea that light always travels at c is a starting assumption of relativity rather than something found empirically; however, if each observer creates a coordinate system using a network of rulers and clocks synchronized using this assumption, then the laws of physics will have exactly the same equations in each observer's coordinate system, so there's no physical experiment that will distinguish one of these coordinate systems from another, and that is an empirical fact that would not be true if we lived in a universe with different laws of physics.

 

[Sam Woole]

What are you talking about when you say "Newton's equation"? Do you just mean speed = distance/time? This equation is not specifically Newtonian, it's just as true in relativity as in Newtonian physics.

Yes, I did mean that. I used to called t=d/v Newton's equation. I now realized I should not. I also apologize for the incorrect use of the word "compute". Anyway, reading clocks is an act very different from using the equation.

Let us make our discussion short. JesseM's language implied that he has access to the said textbook. If so, I believe he would be able to judge these 3 cases. (1) The two reference frames have created a distance; (2) A time interval will be obtained when this distance is put into the equation (t = d/v). (3) And the time interval so obtained is the time interval needed by the frames for creating that distance, and is equal to the one taken by light for its round trip. Do you think these 3 cases justified?

 

[JesseM]

Let us make our discussion short. JesseM's language implied that he has access to the said textbook.

I didn't mean to imply that, I just was inferring the textbook authors' meaning from the quotes you provided.

If so, I believe he would be able to judge these 3 cases. (1) The two reference frames have created a distance;

What do you mean they "created a distance"? Each reference frame measures the distance between events using their own set of rulers, I don't know if that has any relation to what you're talking about here.

(2) A time interval will be obtained when this distance is put into the equation (t = d/v).

If you know the object's velocity in your frame, I guess you could do this, but usually it's the other way around--you have clocks at two locations along the object's path, and you note the times on each clock at the moment the object passes them and subtract one from the other to get a time interval, then you divide by the distance between the two clocks.

(3) And the time interval so obtained is the time interval needed by the frames for creating that distance, and is equal to the one taken by light for its round trip. Do you think these 3 cases justified?

I still don't understand what it means for a time interval "create" a distance, a distance is just something you measure on a ruler. And the time interval for an object to cross a given distance will only be equal to the one for light to cross that distance if the object is traveling at light speed, if it's going slower then the time interval will be larger. But I'm probably misunderstanding what you're trying to say--maybe you could give me a numerical example of what you're talking about?

 

[vanesch]

Yes, I did mean that. I used to called t=d/v Newton's equation. I now realized I should not. I also apologize for the incorrect use of the word "compute". Anyway, reading clocks is an act very different from using the equation.

Sam, if I may jump in, as others have already argued, you may have a difficulty understanding what is mean to be a "thought experiment". In fact, a thought experiment is not an experiment at all, but a way of reasoning, which COULD eventually correspond to an experimental situation. It is, in a certain way, "armchair philosophy" But what's the purpose ? The purpose is to analyse the consequences of a certain set of (imagined or real) laws of nature. Now, in special relativity, we do the following:
1) we still assume that, for an observer, space is 3-dim Euclidean space (meaning, you can use all high school geometry), we call it E^3_observer
2) we still assume that LOCALLY an observer has a clock that gives him "time". Whether this is a real clock, or a mathematical variable you call t_observer, doesn't matter of course.

With points 1 and 2, we can now define of course things like "a trajectory" (for an observer), which is a mapping from t_observer into E^3_observer, and from such a trajectory, we can define a velocity which is de derivative of this trajectory to t_observer. All this makes sense WITH RESPECT TO AN OBSERVER.

Up to here we are on par with Newtonian physics, except that:

3-Newton) Newton assumes that for all observers, the t_observer are equal
3-Relativity) Relativity assumes that c is a constant for all inertial observers.

From the 3-Relativity point, you can now DEDUCE that the time seen on the watch of Sally, when her light pulse bounced up and down, MUST BE equal to 2 D/c
Indeed, the light pulse is going to cover a distance 2 D (this we can deduce, from Sally's point of view, because of 1) and because of 3-Relativity, we know that the speed of light is c, so we have to have that c = 2 D / time-seen-by-Sally

 

[Sam Woole]

I didn't mean to imply that, I just was inferring the textbook authors' meaning from the quotes you provided. What do you mean they "created a distance"? Each reference frame measures the distance between events using their own set of rulers, I don't know if that has any relation to what you're talking about here. If you know the object's velocity in your frame, I guess you could do this, but usually it's the other way around--you have clocks at two locations along the object's path, and you note the times on each clock at the moment the object passes them and subtract one from the other to get a time interval, then you divide by the distance between the two clocks. I still don't understand what it means for a time interval "create" a distance, a distance is just something you measure on a ruler. And the time interval for an object to cross a given distance will only be equal to the one for light to cross that distance if the object is traveling at light speed, if it's going slower then the time interval will be larger. But I'm probably misunderstanding what you're trying to say--maybe you could give me a numerical example of what you're talking about?

I am sorry it was all my fault due to lack of information, specifically lack of graphics about the thought experiment. Let us drop this very textbook and go to Einstein's writing available online.

I believe people cannot succeed in their attempt to prove that time is relative unless they cheat. This belief of mine included Einstein himself as the cheater. To find out whether there is cheating in the theory of relativity,
and whether Einstein cheated, we shall refer to Chapter 9 of Einstein's own book: Relativity, The Special and General Theory, available at http://www.ivorix.com/en/einstein/ .

With easy access to Einstein's own words, we are in a better position to exchange opinions than when I could not provide you enough information from the textbook Fundamentals of Physics named in my first posting.

In the said chapter, Einstein designed a thought experiment to prove that simultaneity is relative. He described it in these words:

"Up to now our considerations have been referred to a particular body of reference, which we have styled a railway embankment. We suppose a very long train traveling along the rails with the constant velocity v and in
the direction indicated in Fig 1. People traveling in this train will with advantage use the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train. " And the Figure looks like this:

Fig. 1.
v→
A ____________________m ____________________B
A ____________________M____________________ B

Einstein continued:
"Then every event which takes place along the line also takes place at a particular point of the train. Also the definition of simultaneity can be given relative to the train in exactly the same way as with respect to the embankment. As a natural consequence, however, the following question arises :
"Are two events (e.g. the two strokes of lightning A and B) which are simultaneous with reference to the railway embankment also simultaneous relatively to the train? We shall show directly that the answer must be in the negative.

"When we say that the lightning strokes A and B are simultaneous with respect to the embankment, we mean: the rays of light emitted at the places A and B, where the lightning occurs, meet each other at the mid-point M of the length AB of the embankment. But the events A and B also correspond to positions A and B on the train. Let m be the mid-point of the distance AB on the traveling train.

"Just when the flashes (as judged from the embankment) of lightning occur, this point m naturally coincides with the point M but it moves towards the right in the diagram with the velocity v of the train. "

Here I drew the following figure to represent Einstein's description, Figure 2:
A__________________m__________________B
A____________________M___________________B

In Einstein's book, there was no figure like this showing a total of 4 events A, A, B, B. But his description of the graphics implied explicitly that there were 2 events on the train and 2 events on the embankment. Yet the above graphics may or may not agree with Einstein's later ideas. We shall encounter this doubtful situation in the last paragraph of my post.

Einstein continued:
"If an observer sitting in the position m 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."

Here I believe a cheat has been committed: "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." To appreciate my charge, let me repeat Figure 2:

A__________________m__________________B
A____________________M___________________B

When Einstein said m is "hastening towards the beam of light coming from B", which B was he talking about?

If he was talking about the B on the train (m's reference frame), I think he lied against his light-speed principle. If he was talking about the B on the embankment (M's reference frame), I think he lied again, against his own regulation: " People traveling in this train will with advantage use the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train. "

I believe my thinking above is correct meaning Einstein did cheat.

Einstein continued his cheating by saying:

"Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A."

I believe otherwise. I believe observers taking the railway train as their reference-body cannot come to the conclusion as Einstein did, but rather they will conclude that lightning flashes A and B emitted simultaneously.
My belief can be justified like this:
Since Am = mB, so that Am/c = mB/c = t.

But Einstein continued and said:
"We thus arrive at the important result:
"Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity)."

To me this statement of Einstein's was a big lie. First of all the first word "events" was false or highly contradictory, because, according to Einstein's description of his thought experiment, there were a total of 4 events, two on the train frame and another two on the embankment frame. I believe we as students of his theory are entitled to be told which events he was talking about (again?). If he was talking about only two events, which two?

When you try to identify them, I believe you shall find that the entire sentence representing Einstein's "important result" does not make sense at all. If you do not find so, I am glad to learn from you and retract all my charges.

 

[Sam Woole]

Sam, if I may jump in, as others have already argued, you may have a difficulty understanding what is mean to be a "thought experiment". In fact, a thought experiment is not an experiment at all, but a way of reasoning, which COULD eventually correspond to an experimental situation. It is, in a certain way, "armchair philosophy" But what's the purpose ? The purpose is to analyse the consequences of a certain set of (imagined or real) laws of nature.
vanesch, welcome. You got it right regarding my difficulty in understanding the relativity theory. I am just a leisure reader, not a student of physics. If I am wrong, I am readily happy to change.
Certainly you are perfect right in saying that the thought experiment is a kind of reasoning. I think I do understand this point. But the point I was trying to make was, can we lie in the reasoning process. If we lied, of course truth was sacrificed in the reasoning process.

Now, in special relativity, we do the following:
1) we still assume that, for an observer, space is 3-dim Euclidean space (meaning, you can use all high school geometry), we call it E^3_observer
2) we still assume that LOCALLY an observer has a clock that gives him "time". Whether this is a real clock, or a mathematical variable you call t_observer, doesn't matter of course.


From the 3-Relativity point, you can now DEDUCE that the time seen on the watch of Sally, when her light pulse bounced up and down, MUST BE equal to 2 D/c
Indeed, the light pulse is going to cover a distance 2 D (this we can deduce, from Sally's point of view, because of 1) and because of 3-Relativity, we know that the speed of light is c, so we have to have that c = 2 D / time-seen-by-Sally

I think your deduction process is a lie, even though you obtained the same time interval as 2D/c. If you told your students you would use clocks to obtain the time interval but you did not do so, you lied. Whether you have obtained the true time interval or not, you lied in the reasoning or deduction process.

Secondly, I did challenge the truth of the time interval t = 2D/c. Due to my inability to quote enough information from the textbook, I was unable to demonstrate fully to my own satisfaction so as to support my challenge. I propose we move to Einstein's book which will let me quote enough information to facilitate our discussion. Please go to my new reply below.

 

[JesseM]

I am sorry it was all my fault due to lack of information, specifically lack of graphics about the thought experiment. Let us drop this very textbook and go to Einstein's writing available online.

I believe people cannot succeed in their attempt to prove that time is relative unless they cheat. This belief of mine included Einstein himself as the cheater. To find out whether there is cheating in the theory of relativity,
and whether Einstein cheated, we shall refer to Chapter 9 of Einstein's own book: Relativity, The Special and General Theory, available at http://www.ivorix.com/en/einstein/ .

With easy access to Einstein's own words, we are in a better position to exchange opinions than when I could not provide you enough information from the textbook Fundamentals of Physics named in my first posting.

In the said chapter, Einstein designed a thought experiment to prove that simultaneity is relative. He described it in these words:

"Up to now our considerations have been referred to a particular body of reference, which we have styled a railway embankment. We suppose a very long train traveling along the rails with the constant velocity v and in
the direction indicated in Fig 1. People traveling in this train will with advantage use the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train. " And the Figure looks like this:

Fig. 1.
v?
A ____________________m ____________________B
A ____________________M____________________ B

Einstein continued:
"Then every event which takes place along the line also takes place at a particular point of the train. Also the definition of simultaneity can be given relative to the train in exactly the same way as with respect to the embankment. As a natural consequence, however, the following question arises :
"Are two events (e.g. the two strokes of lightning A and B) which are simultaneous with reference to the railway embankment also simultaneous relatively to the train? We shall show directly that the answer must be in the negative.

"When we say that the lightning strokes A and B are simultaneous with respect to the embankment, we mean: the rays of light emitted at the places A and B, where the lightning occurs, meet each other at the mid-point M of the length AB of the embankment. But the events A and B also correspond to positions A and B on the train. Let m be the mid-point of the distance AB on the traveling train.

"Just when the flashes (as judged from the embankment) of lightning occur, this point m naturally coincides with the point M but it moves towards the right in the diagram with the velocity v of the train. "

Here I drew the following figure to represent Einstein's description, Figure 2:
A__________________m__________________B
A____________________M___________________B

In Einstein's book, there was no figure like this showing a total of 4 events A, A, B, B. But his description of the graphics implied explicitly that there were 2 events on the train and 2 events on the embankment.

I think the idea is that the train and the embankment are arbitrarily close in the vertical dimension--If you like, you could imagine that they are both 1-dimensional and that there is no distance at all between them. So at the moment the train and the embankment were lined up, there would be no separation between the two "As" in your picture or between the two "Bs", and there are only two events, the first lightning strike (which occurs at the same time and place as the two lined-up As) and the second one (which occurs at the same time and place as the two lined-up Bs).

Einstein continued:
"If an observer sitting in the position m 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."

Here I believe a cheat has been committed: "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." To appreciate my charge, let me repeat Figure 2:

A__________________m__________________B
A____________________M___________________B

When Einstein said m is "hastening towards the beam of light coming from B", which B was he talking about?

He's discussing things from the frame of the embankment (in the train's own frame it is at rest so it isn't 'hastening toward' anything), so it'd be the bottom B. Note that as time passes the top m will be moving to the right relative to the bottom M.

If he was talking about the B on the train (m's reference frame), I think he lied against his light-speed principle. If he was talking about the B on the embankment (M's reference frame), I think he lied again, against his own regulation: " People traveling in this train will with advantage use the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train. "

Huh? That quote only refers to how "people traveling in this train" will measure things, but clearly M is on the embankment, not on the train, so in M's frame it will appear that m is moving towards the location of the lightning strike on the right and away from the location of the lightning strike on the left.

Einstein continued his cheating by saying:

"Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A."

I believe otherwise. I believe observers taking the railway train as their reference-body cannot come to the conclusion as Einstein did, but rather they will conclude that lightning flashes A and B emitted simultaneously.

Impossible, since the light from lightning strike B will hit m before the light from lightning strike A does (as you can see by considering things from M's frame). So if m assumes that both signals traveled at the same speed, and if he also measures both to have happened at the same distance from him, he can only explain this by saying the strike at B happened before the strike at A.

My belief can be justified like this:
Since Am = mB, so that Am/c = mB/c = t.

I assume "Am" represents the distance from A to m, and "mB" represents the distance from m to B? It is indeed true that m will judge these distances to be equal, and will therefore judge both signals to have taken the same amount of time to reach him (that's what the 't' in your equation represents), but that's not the same as saying they both reached him at the same time. Indeed, we can see by considering things from M's perspective that the two signals do not reach him at the same time, therefore he is forced to conclude that one happened before the other.

 

[vanesch]

I think your deduction process is a lie, even though you obtained the same time interval as 2D/c. If you told your students you would use clocks to obtain the time interval but you did not do so, you lied.

A 'clock' in a thought experiment is a mathematical variable, of course.
If I say: let us imagine I throw a rock down from a 10m high tower, and I calculate what time this rock would take to fall from 10m (in Newtonian physics), are you going to accuse me of lying because I didn't use a rock, but white chalk on the blackboard ?

 

[Severian596]

Hi Sam, I have followed your discussion thus far and maybe I can help. Maybe not! But maybe...I'll quote your reply to Einstein.

I believe otherwise. I believe observers taking the railway train as their reference-body cannot come to the conclusion as Einstein did, but rather they will conclude that lightning flashes A and B emitted simultaneously.
My belief can be justified like this:
Since Am = mB, so that Am/c = mB/c = t.

Here you justify your belief by claiming that the individual on the train will measure his (or her) distance from event A and event B as the same distance (given by your Am = mB). This assumption is incorrect, and in fact Einstein's illustration hinges on the fact that Am does NOT equal mB as far as the individual on the train is concerned. Keep reading and I'll explain why with (yet another) analogy.

To me this statement of Einstein's was a big lie. First of all the first word "events" was false or highly contradictory, because, according to Einstein's description of his thought experiment, there were a total of 4 events, two on the train frame and another two on the embankment frame.

There were only TWO events total. Two lightning flashes observed by two observers does not create any new events. Do two lightning flashes observed by 4 observers result in 8 events? No. The events are what they are. If two observers hear a stone hit the pavement, it doesn't mean two stones hit the pavement. So the observer on the train and the observer on the embankment are in fact observing the same events.

Okay, here it goes, an analogy using balls. You and I are at the start of the 100m dash. You can run faster than I can. The starter fires his pistol and we're off and running! A person awaits us at the finish line, and he's got a baseball in his hand. At some point during the race he throws the ball towards us (opposite of our direction of motion). Who will the ball reach first? It will reach you first, because you're faster than me and you're closer to the finish line.

With that in mind, how do you measure WHEN an event takes place? The closest you can come is to measure the time that an event took place by observing when the light from that event reaches you. Prior to the moment when a beam of light that occurred AT THE LOCATION OF THAT EVENT, and at the SAME MOMENT AS THAT EVENT reaches you, you had no knowledge of the event. Your friend with his cell phone standing at the event couldn't call you on his cell phone, because radio waves travel at c, so his call would reach you after the event's flash of light. The fastest that information can travel is c.

How do you synchronize two clocks that are at rest with respect to each other? You put an LED light midway between the two clocks, and tell each clock to turn on when they "see" the LED turn on. The light beam from the LED travels one half of the distance between the clocks and hits each clock "simultaneously", and so the clocks are synchronized.

But what about us in our 100m dash? Let's dumb-down our ability to measure the time of event (the thrown baseball). Let's assume that we can't SEE the person throw the ball, let's say we can only feel the wind from the ball fly by our face. You end up measuring the time that the event occurred (the ball flew by your face) when you were at the 60 meter mark, I measure the time when I was at the 40 meter mark. It took you t seconds to reach the 60 meter mark and that's when you measure the event. It took me t seconds to reach some mark, and y more seconds to reach the 40 meter mark when I felt the ball go by. Here are the times when we measured the event of the thrown baseball:

You measured event time = t
I measured event time = t + y

The event was not simultaneous for us. According to you, the ball was thrown sooner (after less time). The lightning bolt analogy is the EXACT same idea, just with two balls traveling at the speed of light, one from the finish line and one from the starting line. Two events! Two observers traveling at different speeds, different measured times for the events.

 

[JesseM]

Here you justify your belief by claiming that the individual on the train will measure his (or her) distance from event A and event B as the same distance (given by your Am = mB). This assumption is incorrect, and in fact Einstein's illustration hinges on the fact that Am does NOT equal mB as far as the individual on the train is concerned. Keep reading and I'll explain why with (yet another) analogy.

Actually, in this thought-experiment Am does equal mB. Suppose the observer on the ruler is carrying a ruler, and he's sitting on the "0" marking of the ruler. If the observer on the embankment sees the lightning flash at B as occurring next to marking "x" on the train-observer's ruler, won't he see lightning flash A occurring next to marking "-x" on the train-observer's ruler? After all, the train-observer's ruler shrinks symmetrically, and you don't have to worry about how his clocks are synchronized when checking which markings the flashes occur next to.

You can check this using the Lorentz transform. Say that in the embankment-observer's frame, flash A happens at x = -10 light seconds, t = 0 seconds, while flash B happens at x = 10 light-seconds, t = 0. If the train is moving at 0.6c, then you can use the Lorentz transform to see the coordinates of these events in the train's frame:

x' = 1.25(x - 0.6c*t)
t' = 1.25(t - 0.6c*x/c^2)

Plugging in the coordinates of flash A, you get x' = -12.5 light seconds, t' = 7.5 seconds; plugging in the coordinates of flash B, you get x' = 12.5 light seconds, t' = -7.5 seconds. So, both flashes do occur 12.5 light-seconds away from the center of the coordinate system where the train-observer is sitting, although they occur at different times, 15 seconds apart. Since they both occur 12.5 light-seconds away, the light from both flashes will take 12.5 seconds to reach the train-observer in his own frame, so Sam Woole's equation is correct if t is understood to be a time-interval rather than an actual time-coordinate; in the train-observer's frame the flashes reach him at different times because they happened at different times, not because the time-interval between the flash happening and the light reaching him is different in the two cases.

 

[Severian596]

Ouch...thanks Jesse, obviously I only wish I was as good at this material as you are. What about the rest of my post? Please point out any other errors so they're not propagated.

Thanks very much for the correction.

 

[Sam Woole]

A 'clock' in a thought experiment is a mathematical variable, of course.
If I say: let us imagine I throw a rock down from a 10m high tower, and I calculate what time this rock would take to fall from 10m (in Newtonian physics), are you going to accuse me of lying because I didn't use a rock, but white chalk on the blackboard ?

Of course I could not accuse you so. If you have said you will use a clock to measure the drop (a departure time) and fall (arrival time) of the rock, and you did not use the clock, I and anybody else could accuse you of lying. Furthermore, if you tell your teacher you will use clock A to measure, and then you used clock B, and in your report to the teacher you wrote down clock A, I believe you lied, even though the two clocks were identical.

 

[JesseM]

Ouch...thanks Jesse, obviously I only wish I was as good at this material as you are. What about the rest of my post? Please point out any other errors so they're not propagated.

Thanks very much for the correction.

I looked it over, another possible confusion is that in your baseball analogy you seem to be mixing up the time that an event happens in a given observer's coordinate system with the time he receives a signal from an event. Each observer assigns times to events in ways that try to get around the delay in perceiving the event due to the finite speed of light--one way is to have an array of clocks which are at rest relative to you and synchronized in your rest frame (though they will be out-of-sync in other frames), and then the time-coordinate you assign to an event will be the reading on a clock that was right next to the event when it happened. Another way would just be be to take the time you perceived an event and then subtract the distance/c, so if I observer light from an exploding star 100 light-years away in 2005, I'll say that the explosion happened at time-coordinate 2005-100=1905. As long as two observers are at rest with respect to each other, these kinds of procedures insure they will both assign a given event the same time-coordinate, even if the light from the event takes longer to reach one than the other.

 

[robphy]

Sam,
in post #17 (just after your transcription of the text you first referenced),
I responded with "The duration between emission and reception, t, represents "1 tick" of that clock... a perfectly good unit of time. One could regard the first emission as the time reading of "0 ticks". "
Do you agree that this is a clock? and that the clock just measured a time of "1 tick"? Note: I am making no explicit references to the separation d.

 

[Sam Woole]

Let me apologize again for the Figure 2 I posted. It does not look like I wanted it, and as a result my language might be misunderstood. Let me try again and see whether it would keep the form I wanted.

Figure 2:
... A __________m__________B
A __________M__________B.

which shows the train has moved a distance to the right; it no longer coincides with the embankment.

Hi Sam, I have followed your discussion thus far and maybe I can help. Maybe not! But maybe...I'll quote your reply to Einstein.

I thank you for coming to help a novice.

Here you justify your belief by claiming that the individual on the train will measure his (or her) distance from event A and event B as the same distance (given by your Am = mB). This assumption is incorrect, and in fact Einstein's illustration hinges on the fact that Am does NOT equal mB as far as the individual on the train is concerned. Keep reading and I'll explain why with (yet another) analogy.

I think you were wrong. First, JesseM has shown by higher math that they do equal to each other. Second, Einstein's words were: "Let m be the mid-point of the distance A B on the traveling train." Please note, Einstein needed the midpoint, Am = mb, so as to deduce whether the departures of light were simultaneous. If Am does not equal mB, how can he deduce?

There were only TWO events total. Two lightning flashes observed by two observers does not create any new events. Do two lightning flashes observed by 4 observers result in 8 events? No. The events are what they are. If two observers hear a stone hit the pavement, it doesn't mean two stones hit the pavement. So the observer on the train and the observer on the embankment are in fact observing the same events.

Here my Figure 2 will play a part. The foregoing words of yours changed my figure 2 into a new one as follows:
Figure 2:
... __________m__________

A __________M__________B.

where observer m on the train frame would use the two events A and B in the embankment frame to deduce whether the events A and B are simultaneous. I do not believe any deduction from such a situation would make sense.

Furthermore, Einstein expressly said: "People traveling in this train will with advantage use the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train. Then every event which takes place along the line also takes place at a particular point of the train." Observers cannot jump fences.

I have read another demonstration online where the author used meteors instead of lightnings used by Einstein. He said two meteors would strike simultaneously on both ends of the train and the embankment resulting in two damages on both ends of the train, for the observers on the train to see; and two damages on the embankment for the observers on the ground to see. This demonstration means, other people were understanding Einstein's thought experiment in the same way like me, 4 events, not 2.

 

[JesseM]

I have read another demonstration online where the author used meteors instead of lightnings used by Einstein. He said two meteors would strike simultaneously on both ends of the train and the embankment resulting in two damages on both ends of the train, for the observers on the train to see; and two damages on the embankment for the observers on the ground to see. This demonstration means, other people were understanding Einstein's thought experiment in the same way like me, 4 events, not 2.

As long as you assume the bottom line and the top line of your diagram are arbitrarily close together (again, just imagine both the train and the embankment as 1-dimensional, and imagine there is no separation between the two lines), it doesn't make any difference whether you consider these to be 2 events or 4, because even if you consider them to be 4 it will still be two pairs of events which occurred at exactly the same point in spacetime. Regardless of which frame you choose, the event of the meteor hitting the right side of the train will happen at the same position and time as the event of the meteor hitting the right side of the embankment, and the same for the meteor hitting the left side of the train/embankment. Do you disagree?

 

[Sam Woole]

Sam,
in post #17 (just after your transcription of the text you first referenced),
I responded with "The duration between emission and reception, t, represents "1 tick" of that clock... a perfectly good unit of time. One could regard the first emission as the time reading of "0 ticks". "
Do you agree that this is a clock? and that the clock just measured a time of "1 tick"? Note: I am making no explicit references to the separation d.

Certainly I do. I shall read your post again.

 

[JesseM]

Here my Figure 2 will play a part. The foregoing words of yours changed my figure 2 into a new one as follows:
Figure 2:
... __________m__________

A __________M__________B.

where observer m on the train frame would use the two events A and B in the embankment frame to deduce whether the events A and B are simultaneous. I do not believe any deduction from such a situation would make sense.

Furthermore, Einstein expressly said: "People traveling in this train will with advantage use the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train. Then every event which takes place along the line also takes place at a particular point of the train." Observers cannot jump fences.

What do you mean they "cannot jump fences"? Are you saying he can't assign coordinates to events A and B because they didn't occur on the train? The whole idea of a "coordinate system" in SR is that if fills all of spacetime, and can be used to assign coordinates to any event anywhere and anytime. The fact that the train observer "regards all events in reference to the train" doesn't mean his coordinate system is only defined inside the train! It just means that he uses a coordinate system where the train is at rest (ie the train's position coordinates don't change as the time coordinate changes). So he can still assign coordinates to the events of the lightning flashes, and anyway, as I've said a few times now you can just consider the vertical distance between m's line and M's line to be negligible and then it doesn't even matter whether an event occurred on one line or the other since the two lines won't have different y-coordinates.

 

[Sam Woole]

Your passage described a light-clock.

The duration between emission and reception, t, represents "1 tick" of that clock... a perfectly good unit of time. One could regard the first emission as the time reading of "0 ticks".

Upon the first reception, if the source reflects back or re-emits a light signal, waiting for a second reception yields a second tick.

The duration of a tick is proportional to the separation, D, between the "mirror" on the ceiling and the source. That's what t=2D/c means... a relationship relating t and D.. not a definition of t. (If you want a clock with a finer resolution, reduce the separation D.)

robphy, I agree to what you have said here.

 

[Sam Woole]

I am sorry I did not know how to use the QUOTE feature. Some of my responding language were included in the quote. Please find them on your own. Tell me how to separate my response from the quote, please.

I think the idea is that the train and the embankment are arbitrarily close in the vertical dimension--If you like, you could imagine that they are both 1-dimensional and that there is no distance at all between them. So at the moment the train and the embankment were lined up, there would be no separation between the two "As" in your picture or between the two "Bs", and there are only two events, the first lightning strike (which occurs at the same time and place as the two lined-up As) and the second one (which occurs at the same time and place as the two lined-up Bs).

I agree to all the above.

He's discussing things from the frame of the embankment (in the train's own frame it is at rest so it isn't 'hastening toward' anything), so it'd be the bottom B. Note that as time passes the top m will be moving to the right relative to the bottom M. Huh? That quote only refers to how "people traveling in this train" will measure things, but clearly M is on the embankment, not on the train, so in M's frame it will appear that m is moving towards the location of the lightning strike on the right and away from the location of the lightning strike on the left.

Yes again I agree to your description above. But what did you mean by the sententce of yours: [That quote only refers to how "people traveling in this train" will measure things,] To me, both you and Einstein were saying, people traveling in the train will measure things happening on the train; people on the train will not measure things happening on the embankment. Did you mean this?

Impossible, since the light from lightning strike B will hit m before the light from lightning strike A does (as you can see by considering things from M's frame). So if m assumes that both signals traveled at the same speed, and if he also measures both to have happened at the same distance from him, he can only explain this by saying the strike at B happened before the strike at A. I assume "Am" represents the distance from A to m, and "mB" represents the distance from m to B? It is indeed true that m will judge these distances to be equal, and will therefore judge both signals to have taken the same amount of time to reach him (that's what the 't' in your equation represents), but that's not the same as saying they both reached him at the same time. Indeed, we can see by considering things from M's perspective that the two signals do not reach him at the same time, therefore he is forced to conclude that one happened before the other.

As I requested, here you were trying to identify which events Einstein was talking about. You identified them to be the two events on the embankment. If so, we do not need the long train specified by Einstein. We need only one reference frame. Two observers M and m are located at the midpoint of AB, the embankment. When lightning strikes on both ends, m starts to run toward B; from M's perspective, m will see light B first and light A later. It would be this simple and easy. We don't have to bother about the long train.

Even if so (two events on the embankment), m still cannot be forced to conclude that "one happened before the other", simply because from M's perspective m is no longer located midpoint of the two events A and B in his (M's) frame (embankment).

To identify the events like that, we have made Einstein's events into traffic signs. When train passed, signs would be left behind.

I do not think you can identify them like this because of Einstein's stipulation that observers on the train would use events on the train to measure things, not the signs left behind on the embankment. Please consider, if there were no events on the train, why he stipulated so? Was Einstein too much ado about nothing?

 

[JesseM]

As I requested, here you were trying to identify which events Einstein was talking about. You identified them to be the two events on the embankment. If so, we do not need the long train specified by Einstein. We need only one reference frame. Two observers M and m are located at the midpoint of AB, the embankment. When lightning strikes on both ends, m starts to run toward B; from M's perspective, m will see light B first and light A later. It would be this simple and easy. We don't have to bother about the long train.

Sam, I don't think you understand the concept or purpose of a "reference frame". A reference frame is a coordinate system that assigns coordinates to any point in spacetime--it's not like if you're in the frame where the train is at rest you can only talk about events that take place onboard the train, you can analyze events taking place on Jupiter from the train's reference frame if you want. And of course you can analyze any physical situation from any reference frame you want. We could analyze the events of the lightning strikes solely from the embankment's frame, or we could analyze them solely from the train's frame, or any other possible frame. The point of this thought experiment is just to see how the coordinates of two different reference frames are related to each other, under the assumption that each reference frame will say that light signals move at c within that frame.

Even if so (two events on the embankment), m still cannot be forced to conclude that "one happened before the other", simply because from M's perspective m is no longer located midpoint of the two events A and B in his (M's) frame (embankment).

Yes, in M's frame the two events happen at the same time, of course. It is only when you try to analyze the same events from the perspective of m's frame that you are forced to conclude that one happens before the other. There is no objective truth about whether they really happened at the same time or one happened before the other--it depends on which frame you choose, and there's no reason to say one frame's perspective is better than the other's.

I do not think you can identify them like this because of Einstein's stipulation that observers on the train would use events on the train to measure things, not the signs left behind on the embankment. Please consider, if there were no events on the train, why he stipulated so? Was Einstein too much ado about nothing?

Again, you're not understanding the concept of a "reference frame". When he says they use the train to measure things, he just means they measure things using a coordinate system where the train's position is assumed to be fixed (the train's rest frame), he doesn't mean that they only measure events that take place onboard the train.

 

[Doc Al]

Einstein's simple argument

Was Einstein too much ado about nothing?

You seem to be missing the point, which is a shame since Einstein's train argument for the relativity of simultaneity is delightfully simple. (You wouldn't be lying to us, would you Sam? ) I'll give it one more shot.

For one thing, there are just two events--the two lightning strikes--and these events are viewed from two different frames of references (as JesseM tried to explain). One frame is the "stationary" platform; the other, the moving train. Events don't "belong" to a frame; they just exist. They can be observed from any frame.

It may be useful to think of the lightning strikes as making burn marks on the train and the platform. Call the location of the burn marks on the platform A and B; the locations of the burn marks on the train, A' and B'. A diagram showing how things appear at the instant the lightning strikes--according to the platform observers--would look something like this:

Fig. 1.
v→
A' ____________________m' ___________________ B'
A ____________________M____________________ B
(1) ............(2)

To avoid confusion, I'm going to refer to the two lightning strikes as #1 and #2, as labeled on the diagram.

According to the platform observers, both lightning strikes #1 & #2 occur simultaneously. What can we deduce from this? Looking at things from the platform frame, we have no choice but to conclude that the light from lightning strike #2 must reach the moving observer at m' before the light from lightning strike #1. This is a fact that everyone must agree occurs; even folks on the train will agree with this. (I'll refer to this as proposition #1.)

Another fact that both frames will agree with is that the lightning strikes occur at equal distances from the midpoint observers. By this I mean that observer M (on the platform) is at the midpoint of the two burn marks A & B; similarly, observer m' (on the train) is at the midpoint of the two burn marks at A' & B'. (I'll refer to this as proposition #2.)

Now let's view things from the train frame. Observer m' knows that the lightning strikes occurred equally distant from him (see proposition #2) and he also knows (after all, he was there!) that the light from strike #2 reaches him first (see proposition #1). From this simple fact, and the relativistic premise that the speed of light is the same for all observers (whether on the train or on the platform), he must deduce that lightning strike #2 must have occurred before lightning strike #1. (I'll refer to this as the conclusion.)

This is Einstein's simple argument that events that are observed to occur simultaneously in one frame (the stationary platform frame, in this example) will be observed to occur at different times in another frame (the moving train frame). Simultaneity is not absolute; it depends on the frame doing the measuring.

 

[pervect]

Don't know if it will help the discussion any, but there's a longish peer-reviewed article publically downlowdable for the next 30 days from the iop website that covers essentially the same material as being discussed here.

http://www.iop.org/EJ/article/-ffissn=0143-0807/-ff30=all/0143-0807/26/6/017/ejp5_6_017.pdf

 

[Doc Al]

Thanks, pervect! I totally missed that one. (And I've corresponded with the author of that article on other matters.)

 

[ZapperZ]

Oh sure! Now pervect gets all the credit!

:)

Zz.

 

[Sam Woole]

Thank everybody and especially to Doc Al. You might have thrown a fatal blow on me. I agree I do have difficulty in understanding the workings of reference frames. But I still have a few last throes. Let me quote a paragraph from Doc Al.

"Now let's view things from the train frame. Observer m' knows that the lightning strikes occurred equally distant from him (see proposition #2) and he also knows (after all, he was there!) that the light from strike #2 reaches him first (see proposition #1). From this simple fact, and the relativistic premise that the speed of light is the same for all observers (whether on the train or on the platform), he must deduce that lightning strike #2 must have occurred before lightning strike #1."

In the above quote there were these words: "...he also knows that the light from strike #2 reaches him first..." Besides this knowledge of m', I believe he (m') also has this knowledge: he (m') was no longer aligned with M. This latter knowledge should mean to him (m'), motion has taken place and he (m') was no longer midpoint between #1 and #2. Was I right?

I think I was right because this non-alignment was specifically pointed out by Einstein, m' hastening toward the light from #2. Hence how would an observer not located on the midpoint between #1 and #2 deduce?

....A'_________________m'_______________B'
#1,A_______________M_______________B#2

Since I do have difficult in understanding the workings of coordinate systems, I will not deduce myself. Please tell me how would m' (not midway between the two events) deduce non-simultaneity in such a situation.

 

[JesseM]

Thank everybody and especially to Doc Al. You might have thrown a fatal blow on me. I agree I do have difficulty in understanding the workings of reference frames.

It might help you to understand that each observer's coordinate system can be thought of as the readings on a set of rulers and clocks which are at rest with respect to that observer, and which fill all of space. I can't just use one clock, I need to have separate clocks sitting on each marking on the ruler so that I can assign times to events based on the local reading on the clock that was right next to the event at the moment it happened--if I only had a single clock I'd have to worry about the fact that signals from events at different distances from me would take different amounts of time to reach me and my clock, but if you always rely on local readings from clocks next to the event you don't have to worry about signal delays. So say I see a lightning flash which occurs next to the 15-meter marking of my ruler, and at the moment it happens, the clock sitting on the 15-meter mark reads 19 seconds. Then I would assign this event coordinates x=15 meters, t=19 seconds. The one tricky part of all this is that if I use multiple clocks, I have to make sure they're "synchronized", but how do I tell if clocks at different locations are synchronized without moving them? (moving them would cause them to slow down due to time dilation) Einstein suggested a simple procedure--each observer should synchronize his clocks under the assumption that light moves at exactly c in his own frame, so if you set off a flash at a point that's an equal distance from two clocks, they are defined as "synchronized" if they both read the same time at the moment the light hits them. The only catch is that if all observers assume this, then each observer will see other observer's clocks as out-of-sync! Suppose I have two clocks at either end of the train and I set off a flash at the midpoint of the train, and set them to read the same time when the light hits them, as Einstein's procedure suggests. From the point of view of another observer who sees the train moving, it will appear that the back clock is moving towards the point where the flash was set off while the front clock is moving away from it, so from his point of view the light will reach the back clock before the front clock, and thus if I set the clocks to read the same time at the moment the light hits them, they'll appear out-of-sync in his frame.

"Now let's view things from the train frame. Observer m' knows that the lightning strikes occurred equally distant from him (see proposition #2) and he also knows (after all, he was there!) that the light from strike #2 reaches him first (see proposition #1). From this simple fact, and the relativistic premise that the speed of light is the same for all observers (whether on the train or on the platform), he must deduce that lightning strike #2 must have occurred before lightning strike #1."

In the above quote there were these words: "...he also knows that the light from strike #2 reaches him first..." Besides this knowledge of m', I believe he (m') also has this knowledge: he (m') was no longer aligned with M. This latter knowledge should mean to him (m'), motion has taken place and he (m') was no longer midpoint between #1 and #2. Was I right?

No. m agrees that he is not aligned with M, but he considers himself to be at rest and M to be moving, so in his frame this non-alignment is caused by the fact that M is hastening toward the location of strike #1.

I think I was right because this non-alignment was specifically pointed out by Einstein, m' hastening toward the light from #2.

But in that quote he was only talking about how things looked in M's frame, not m's frame.

Hence how would an observer not located on the midpoint between #1 and #2 deduce?

....A'_________________m'_______________B'
#1,A_______________M_______________B#2

Since I do have difficult in understanding the workings of coordinate systems, I will not deduce myself. Please tell me how would m' (not midway between the two events) deduce non-simultaneity in such a situation.

Remember, the lightning strikes aren't objects that persist in time so you can see whether you're getting closer to one as time passes, they are discrete events which only happened at a single moment in time. In M's frame, they both happened at the same moment that m and M were lined up. In m's frame, they happened at two different times, but the distance of each strike from him at the moment they happened was equal. Imagine both M and m were carrying their own rulers, and they were each sitting at the 0-meter mark of their rulers. If each lightning strike left a burn mark on both rulers, then both M and m would observe the burn marks to be equal distances from the 0-meter mark where they are sitting. For example, if m was moving at 0.6c relative to M, and M saw the burn marks at -10 meters and 10 meters on his own ruler, then m would see the burn marks at -12.5 meters and 12.5 meters on his ruler. And remember that it is only in M's frame that m is moving towards the location of strike B and away from the location of strike A (because m is getting closer to the burn mark at 10 meters on M's ruler); in m's frame, he is standing still while M is moving towards the location of strike A and away from the location of strike B (because M is getting closer to the burn mark at -12.5 meters on m's ruler). And if m assumes that light travels at c in his frame, then since the light from both strikes has to travel 12.5 meters to reach his eyes, both light beams must have taken the same amount of time to reach his eyes, so if he sees one before the other, that must mean one strike happened before the other.

 

[Doc Al]

In the above quote there were these words: "...he also knows that the light from strike #2 reaches him first..." Besides this knowledge of m', I believe he (m') also has this knowledge: he (m') was no longer aligned with M. This latter knowledge should mean to him (m'), motion has taken place and he (m') was no longer midpoint between #1 and #2. Was I right?

It's certainly true that m' knows that he's moving past M, so their alignment is only momentary. But that's not what's important. What's important is where m' was when the lightning struck the train. m' knows that he was right in the middle between A' and B' (he can verify this because the lightning left burn marks). Remember: As seen by the train frame, the lightning hit points A' and B'; As seen by the track frame, the lightning hit points A and B.

According to the track frame A & A', B & B', and M & m' were all perfectly aligned at the instant that lightning strikes #1 and #2 occurred. (But, it turns out, the train frame will not agree!)

I think I was right because this non-alignment was specifically pointed out by Einstein, m' hastening toward the light from #2. Hence how would an observer not located on the midpoint between #1 and #2 deduce?

....A'_________________m'_______________B'
#1,A_______________M_______________B#2

Since I do have difficult in understanding the workings of coordinate systems, I will not deduce myself. Please tell me how would m' (not midway between the two events) deduce non-simultaneity in such a situation.

This non-alignment (according to the track frame) as m' moves past M after the lightning has struck is used to deduce that the light from strike #2 must arrive at m' before the light from strike #1. Note: We deduce this by viewing things from the track frame. But a fact like this is true for all observers, even m'. So we are free to use this fact and combine it with the fact that A' and B' are equi-distant from m'. From this we are forced to conclude that according to the train frame strikes #1 and #2 could not have happened at the same time.

This last deduction is just common sense. If two light bulbs are the same distance away from me. And I see one light up before the other, then I have to conclude that one was turned on before the other. No choice! (Key point: It doesn't matter if I am moving towards the bulbs. All that matters is that I was equally distant from the bulbs when they were turned on.)

Yes, these results are counter-intuitive. The bit of physics that forces us to these conclusions is the strange fact that the light is seen by both M and m' as moving at the same speed with respect to each of them! This is not how ordinary, slow-moving things behave. Let's say you can throw a baseball at 90 miles an hour. If you were to throw the ball from a car moving towards me at 50 miles an hour, I would see (and feel) the baseball moving towards me at 90 + 50 = 140 miles/hour. (Ignore air resistance.) This is not how light (or anything else that moves fast) works. If you shine a flashlight towards me from a moving car (or rocket ship), it doesn't matter how fast that car moves...I will measure the light as moving towards me at the same speed.

 

[Sam Woole]

I am sorry I must drop the discussion as I just could not understand what you people have said, including the demonstration brought to me by pervect. Thanks to all and please trust that I have tried my best.

 

[Charvell]

I have heard of experiments using atomic clocks but I wonder if the same experiments can be done with non atomic clocks? I have reason to suspect the atomic clock may not be the most appropriate mechanism for this. Has anyone considered this?