Exploring the STR Argument: X & Y's Clocks

[Andy Lee]

I am hopeful someone can give me a quick lesson here. I have an idea that time does not slow as one's velocity increases (bear with me, please). I'll state this in familiar terms with a person on a train vs platform and the light beam traveling vertically from the ceiling (P1) to the floor of the train (P2). Let's just say that it stops at that point (P2).

X is a person on the train and Y is a person on the platform. Both X and Y have the same sort of clock (measuring distance, by the way, not time, but save that for another day). They each have an identical clock, however you wish to see it.

The STR argument is of course very familiar and of course X's clock runs slow blah blah blah so enough said.

But I wonder, is it true? (Again, please humor me for a minute)

Here is X looking at the light beam from P1 to P2. We'll say for the sake of argument that the light has traveled four units and X's clock has traveled four (different) units, so X determines c to be 1 (4/4).

Note, in all diagrams please ignore the "o" symbols as it is the only way I could get the diagrams to format correctly.

P1
.
.
.
.
P2
X

And here is Y looking at the light beam from P1 to P2.

P1
.
o .
ooo .
ooooo .
ooooo P2
Y

And since the light has traveled more than four units (diagonal distance), then Y's clock has traveled more than four (different) units in order for c to be constant. Hence Y's clock is faster than X. Or as more commonly reported, X's clock is slower than Y's. Even though the clocks were identical.

But wait a minute. Put X and Y in together now. The beam of light was emitted the moment the train passed Y (moving from left to right as you can see)

P1
o .
ooo .
ooooo .
ooooooo .
ooooooo P2
Y oooooo X

In the diagram above, Y has not yet seen the light as it terminates at point P2. This 'information' must still traverse the distance from P2 to Y before Y stops his clock and reports his time. And while this happens, the train still travels. So we have:

P1
.
ooo .
ooooo .
ooooooo .
P3 . . . . P2 . . . . P4
Y oooooooooooo X

So Y clearly has to stop his clock AFTER X has stopped her clock, since X stopped her clock at P2 and is already at P4 when Y stops his clock. So of course Y's clock has 'ticked' longer to report the same information (or, if you prefer, X's clock 'ticking' less).

But then it is not really a case of X's clock "running slow", is it?

Thanks in advance for your feedback.

 

[Janus]

The light clock example ignores any time delay caused by the distance the light has to travel between Y and X. Put another way, the difference in time rate between the two clocks is what is left over after you account for this light propagation delay.

 

[FactChecker]

You can set up the experiment so that here are no delays due to observing what happens. Suppose each person (moving and stationary) has observers all along the length of the experiment with clocks that are exactly synchronized with his. They are in position to instantly observe what happens anywhere and record the time according to their clock. Comparing the results recorded by the moving versus the stationary observers will show the time delay of relativity. The time delay is due to the fact that the moving and stationary observers disagree on the synchronization of their clocks along the length of the experiment.

 

[PeroK]

I am hopeful someone can give me a quick lesson here. I have an idea that time does not slow as one's velocity increases (bear with me, please). I'll state this in familiar terms with a person on a train vs platform and the light beam traveling vertically from the ceiling (P1) to the floor of the train (P2). Let's just say that it stops at that point (P2).

Yours is a common misconception that relativity depends somehow on the finiteness of the speed of light delaying observations for some observers more than others. This is not the case. In classical physics you also have this delay, which observers will have to take into account when taking their measurements.

Relativity, in fact, deals with the difference in elapsed time in two different "reference frames" moving with respect to each other.

Understanding reference frames and factoring out the delay in observations is an important first step to understanding relativity.

 

[Mister T]

The STR argument is of course very familiar and of course X's clock runs slow blah blah blah so enough said.

To say X's clock runs slow is meaningless. Y observes X's clock to be running slow. X observes Y's clock to be running slow. To say Y's clock runs slow is meaningless.

 

[Andy Lee]

"You can set up the experiment so that here are no delays due to observing what happens. Suppose each person (moving and stationary) has observers all along the length of the experiment with clocks that are exactly synchronized with his. They are in position to instantly observe what happens anywhere and record the time according to their clock."

Certainly these observers can record the termination at their respective P2's and this would appear to cancel the P2P3 argument. But would there not then be an identical argument, this time placed at the beginning rather than the end of the experiment? It seems there would be an equivalent delay, now a result of the need to communicate the first passing of the train at Y to each observer. And since the repective observers then subtract this delay from their measurements there is no reason to suggest their clocks have anything more to contribute than Y's clock alone - thus reintroducing the P2P3 argument.

 

[PeroK]

"You can set up the experiment so that here are no delays due to observing what happens. Suppose each person (moving and stationary) has observers all along the length of the experiment with clocks that are exactly synchronized with his. They are in position to instantly observe what happens anywhere and record the time according to their clock."

Certainly these observers can record the termination at their respective P2's and this would appear to cancel the P2P3 argument. But would there not then be an identical argument, this time placed at the beginning rather than the end of the experiment? It seems there would be an equivalent delay, now a result of the need to communicate the first passing of the train at Y to each observer. And since the repective observers then subtract this delay from their measurements there is no reason to suggest their clocks have anything more to contribute than Y's clock alone - thus reintroducing the P2P3 argument.

Here's how I would do the experiment.

Two posts are placed next to the track, a certain distance apart. An observer stands at each post. These two observers synchronise their watches.

A third person boards a train that travels at high-speed along the track. He starts his light clock when he passes the first post and stops it when he passes the second. Thus, he measures the elapsed time in his frame for the train to travel between the two posts.

Meanwhile, each observer on the track notes the time the train passes their post. They, between them, therefore measure the elapsed time in their frame.

Afterwards, they all get together and compare notes. No one observed anyone else's clock during the experiment. They find that the clock on the train measured less time than that measured by two observers on the track. And, they can all work out why that happened by analysing the path the light beam must have taken in the track's reference frame. You do not, in fact, have to observe a light clock in order to calculate the elapsed time it reads.

You could alter the experiment by having the two observers on the track share a clock, perhaps located half-way between them. Each just reads the time: the delay is the same for both so the two readings give the correct elapsed time.

In either case, the delay in seeing clocks is irrelevant to the argument.

 

[Andy Lee]

Thanks PeroK. That will certainly help me.

If you could humor me for one more minute, I would like to raise a question about the nature of time.

It is clear that if person A is in an environment with no motion exhibited by any object in A's frame of reference, then it is impossible for A to measure the passing of time. I prefer to go one step further and say that time for A does not exist, rather than 'it cannot be measured.' And so time is (relative) motion of objects - much different than saying time is measured by relative motion of objects. And since relative motion of objects can be measured within the confines of three dimensions, why do people view time as some phenomenon beyond these three dimensions? Is time not just an artificial construct of human consciousness? I'll say that when you look at SR in this light it changes things a bit.

 

[PeroK]

Thanks PeroK. That will certainly help me.

If you could humor me for one more minute, I would like to raise a question about the nature of time.

It is clear that if person A is in an environment with no motion exhibited by any object in A's frame of reference, then it is impossible for A to measure the passing of time. I prefer to go one step further and say that time for A does not exist, rather than 'it cannot be measured.' And so time is (relative) motion of objects - much different than saying time is measured by relative motion of objects. And since relative motion of objects can be measured within the confines of three dimensions, why do people view time as some phenomenon beyond these three dimensions? Is time not just an artificial construct of human consciousness? I'll say that when you look at SR in this light it changes things a bit.

There is no such environment where motion is impossible and no environment where you cannot measure time. Things change and decay as well as move so time is not just an aspect of motion. There was, for example, a time before you asked your question and now there is a time when you have an answer.

 

[Andy Lee]

"There was, for example, a time before you asked your question and now there is a time when you have an answer."

But the only measurable difference between these two "times" is the configuration of particles in our three dimensional universe. The only change between the two times was change in relative position of particles (I say particles but I mean any measurable objects). So time is change in three-dimensional position and not any entity in its own right.

 

[PeroK]

"There was, for example, a time before you asked your question and now there is a time when you have an answer."

But the only measurable difference between these two "times" is the configuration of particles in our three dimensional universe. The only change between the two times was change in relative position of particles (I say particles but I mean any measurable objects). So time is change in three-dimensional position and not any entity in its own right.

If you have only 3 dimensions with no time, you cannot have change. You can only have one static configuration of the universe.

 

[Dale]

This thread has veered off into speculation and philosophy and is now closed.