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On the Lighter Side => New Theories => Topic started by: the_roosh on 10/06/2019 12:05:36

Title: How is this explained in Special Relativity?
Post by: the_roosh on 10/06/2019 12:05:36
In the classic thought experiment to explain "time dilation", two observers - good ol' Alice and Bob - are moving relative to each other. Each is carrying a single light clock. From her perspective on the platform, Alice sees Bob's clock ticking slowly, because the photon travels a longer, diagonal distance between tick and tock.

Now, imagine that each are carrying 2 light clocks, oriented at a right angles to each other; one is oriented perpendicular to the x-axis, while the other is oriented perpendicular to the y-axis i.e. one perpendicular to the direction of motion and one in-line with the direction of motion.

From Alice's perspective, as normal, she will see "time slow down" for the clock oriented perpendicular to the direction of motion. For the other clock, however, shouldn't she see the "time" speed up in one direction - because it travels a shorter distance between tick and tock - while seeing it slowdown in the other direction bcos it travels a longer distance between tick and tock. This is because in one direction the mirror is moving towards the photon, while in the other direction - after reflection - the mirror is moving away from the photon. This is the same reason why Alice would see Bob's clocks fail to synchronise. Length contraction would only serve to make time speed up even more in the given direction.

Also, if the clocks are set up so that 2 of the mirrors are side-by-side i.e. the top mirror of the perpendicular-to-the x-axis-clock is beside the left mirror of the perpendicular-to-the y-axis-clock, and we imagine the photon in each clock starting from the opposite mirror. Add to this that the clocks makes a click every time it reflects off a mirror.

In the rest frame of the clocks, the photons in each clock would arrive at the opposite mirror simultaneously combining to make one louder click, while according to the observer on the platform, the photons should not arrive in sync and should therefore make 2 distinct clicks.

Is that correct?
Title: Re: How is this explained in Special Relativity?
Post by: Janus on 10/06/2019 16:50:12
You are coming up against the relativistic effect known as the "relativity of simultaneity".  Bob, if he sends light pulses to two mirrors, parallel to the relative line of motion and opposite each other, then, for Bob, those pulses will reach those mirrors at the same time.  For Alice, the light will reach the trailing mirror first and then the leading mirror.  Bob and Alice will not agree as what event are simultaneous if they are separated along the line of motion.   
But now consider the reflections.  Again according to Bob, they take an equal time to return and meet back up with him again at the same time.  For Alice, the trailing refection takes longer to catch up to Bob than the leading reflection take to run into Bob.  The end result is that both pulses return to Bob as the same time.
The upshot is that One "tick" must be a round trip and it makes no sense to only consider only one leg of the trip.
Length contraction come into play in that it assures that the parallel pulses make the round trip in the same time as the perpendicular ones do. 

The end result looks like this from Alice's frame:

* length_con2.gif (127.71 kB . 640x100 - viewed 777 times)
( I only am showing one of the parallel mirrors here, as this is an existing animation I had already made, but adding the other mirror would not change the end result.)
From Bob's frame, His clock would behave like the stationary one in this animation, while Alice's clock moved off to the Left, being length contracted and ticking slow.
Title: Re: How is this explained in Special Relativity?
Post by: the_roosh on 10/06/2019 18:16:19
You are coming up against the relativistic effect known as the "relativity of simultaneity".  Bob, if he sends light pulses to two mirrors, parallel to the relative line of motion and opposite each other, then, for Bob, those pulses will reach those mirrors at the same time.  For Alice, the light will reach the trailing mirror first and then the leading mirror.  Bob and Alice will not agree as what event are simultaneous if they are separated along the line of motion.   
But now consider the reflections.  Again according to Bob, they take an equal time to return and meet back up with him again at the same time.  For Alice, the trailing refection takes longer to catch up to Bob than the leading reflection take to run into Bob.  The end result is that both pulses return to Bob as the same time.
The upshot is that One "tick" must be a round trip and it makes no sense to only consider only one leg of the trip.
Length contraction come into play in that it assures that the parallel pulses make the round trip in the same time as the perpendicular ones do. 

The end result looks like this from Alice's frame:

* length_con2.gif (127.71 kB . 640x100 - viewed 777 times)
( I only am showing one of the parallel mirrors here, as this is an existing animation I had already made, but adding the other mirror would not change the end result.)
From Bob's frame, His clock would behave like the stationary one in this animation, while Alice's clock moved off to the Left, being length contracted and ticking slow.
Thanks Janus, I am familiar with the Relativity of Simultaneity. That is why I posted the question, because of an issue with it.

If we consider the scenario with just one light clock first. Alice on the platform observes Bob's clock to be ticking slowly because the photon traces a longer, diagonal path between tick and tock. The conclusion in Einstein's interpretation of relativiity is that "time slows down for the relatively moving observer".

Now, conider the same clock turned on it's side. What does Alice see. Well, she sees the clock tick faster in one direction than in the other - your gif demonstrates it clearly. So, she sees "time" speed up in one direction and slow down in the other.

Now, put the two clocks in together. For the floor to ceiling clock "time slows down", but for the end-to-end clock, time speeds up as the photon goes to the rear of the train (because the mirror is moving towards it) while time slows down when the photon is going in the opposite direcction (because the mirror is moving away from it).

Surely pardoxical, no?
Title: Re: How is this explained in Special Relativity?
Post by: Janus on 10/06/2019 20:06:23
You are coming up against the relativistic effect known as the "relativity of simultaneity".  Bob, if he sends light pulses to two mirrors, parallel to the relative line of motion and opposite each other, then, for Bob, those pulses will reach those mirrors at the same time.  For Alice, the light will reach the trailing mirror first and then the leading mirror.  Bob and Alice will not agree as what event are simultaneous if they are separated along the line of motion.   
But now consider the reflections.  Again according to Bob, they take an equal time to return and meet back up with him again at the same time.  For Alice, the trailing refection takes longer to catch up to Bob than the leading reflection take to run into Bob.  The end result is that both pulses return to Bob as the same time.
The upshot is that One "tick" must be a round trip and it makes no sense to only consider only one leg of the trip.
Length contraction come into play in that it assures that the parallel pulses make the round trip in the same time as the perpendicular ones do. 

The end result looks like this from Alice's frame:

* length_con2.gif (127.71 kB . 640x100 - viewed 777 times)
( I only am showing one of the parallel mirrors here, as this is an existing animation I had already made, but adding the other mirror would not change the end result.)
From Bob's frame, His clock would behave like the stationary one in this animation, while Alice's clock moved off to the Left, being length contracted and ticking slow.
Thanks Janus, I am familiar with the Relativity of Simultaneity. That is why I posted the question, because of an issue with it.

If we consider the scenario with just one light clock first. Alice on the platform observes Bob's clock to be ticking slowly because the photon traces a longer, diagonal path between tick and tock. The conclusion in Einstein's interpretation of relativiity is that "time slows down for the relatively moving observer".

Now, conider the same clock turned on it's side. What does Alice see. Well, she sees the clock tick faster in one direction than in the other - your gif demonstrates it clearly. So, she sees "time" speed up in one direction and slow down in the other.
No, As I said before, is doesn't you really can't think of it that way when considering  the one way travel for light.
 Let's put it this way,   Let's say we put ideal clocks at Bob's mirrors.  According to Bob's frame, those clocks are synchronized to each other.  and to a clock at with Bob, halfway between those clocks.  If, as measured by Bob, those mirrors are 300 meters apart, then according to him if the pulses leave his clock when it reads 0, then will arrive at the mirrors when all three clocks read 0.5 microsec (we'll round c up to 300,000,000 m/sec), and returns to Bob when all three clocks read 1 microsecond.  However, according to Alice, All three of those clocks are not in sync, the Lead clock lags behind the middle clock and the trailing clock runs ahead.  So even though it takes less time for the pulse to reach the trailing clock, its "head start insures that it reads 0.5 microsec when the pulse reaches it, and while it takes longer for the pulse to reach the leading clock, the fact that lagged behind the other clocks means that it will also read 0.5 microseconds when the pulse arrives, even though this pulse arrived later than the pulse arrived at the trailing clock.  If you were to run a string of clocks between the mirrors,  each one recording its time when a light pulse passed it, Both Alice and Bob would agree as to what time was on any given clock when that light pulse passed it, even though they would not agree as to which two clocks pulses fired in opposite directions where passing at any given moment.   
Quote

Now, put the two clocks in together. For the floor to ceiling clock "time slows down", but for the end-to-end clock, time speeds up as the photon goes to the rear of the train (because the mirror is moving towards it) while time slows down when the photon is going in the opposite direcction (because the mirror is moving away from it).

Surely pardoxical, no?

No.  It doesn't make any sense to say that Time "speeds up" for a pulse going one way, as Bob and Alice will not agree on the simultaneity of events that are separated along the line of relative motion.  while one pulse takes less time going in one direction according to Alice, you cannot make a one for one comparison between this and Bob's measured rate of time.
Title: Re: How is this explained in Special Relativity?
Post by: the_roosh on 11/06/2019 05:08:44
No, As I said before, is doesn't you really can't think of it that way when considering  the one way travel for light.
 Let's put it this way,   Let's say we put ideal clocks at Bob's mirrors.  According to Bob's frame, those clocks are synchronized to each other.  and to a clock at with Bob, halfway between those clocks.  If, as measured by Bob, those mirrors are 300 meters apart, then according to him if the pulses leave his clock when it reads 0, then will arrive at the mirrors when all three clocks read 0.5 microsec (we'll round c up to 300,000,000 m/sec), and returns to Bob when all three clocks read 1 microsecond.  However, according to Alice, All three of those clocks are not in sync, the Lead clock lags behind the middle clock and the trailing clock runs ahead.  So even though it takes less time for the pulse to reach the trailing clock, its "head start insures that it reads 0.5 microsec when the pulse reaches it, and while it takes longer for the pulse to reach the leading clock, the fact that lagged behind the other clocks means that it will also read 0.5 microseconds when the pulse arrives, even though this pulse arrived later than the pulse arrived at the trailing clock.  If you were to run a string of clocks between the mirrors,  each one recording its time when a light pulse passed it, Both Alice and Bob would agree as to what time was on any given clock when that light pulse passed it, even though they would not agree as to which two clocks pulses fired in opposite directions where passing at any given moment.   
I'm not disputing that they will agree on the clock times.

No.  It doesn't make any sense to say that Time "speeds up" for a pulse going one way, as Bob and Alice will not agree on the simultaneity of events that are separated along the line of relative motion.  while one pulse takes less time going in one direction according to Alice, you cannot make a one for one comparison between this and Bob's measured rate of time.
Why doesn't it make sense? In the traditional thought experiment with the floor-to-ceiling-clock the observer in "the stationary system" - let's call her Alice - observes the photon in Bob's clock traveling a longer, diagonal path between the mirrors - meaning a longer time betweeen "tick" and "tock". Alice concludes that "time has slowed down for Bob".

Now, we simply turn the clock at a right angle, so that it is no longer oriented floor-to-ceiling but instead end-to-end, with the train moving from left to right (from Alice's perspective). Imagine the photon leaving the mirror on the right hand side as Bob passess Alice.

Alice will see the mirror (closest to the back of the train) moving towards the photon, meaning that the photon travels a shorter distance between the mirrors i.e. from "tick" to 'tock". Just as the photon traveling the longer distance, in the first case, lead her to conclude that "time has slowed down for Bob", so too the shorter distance traveled by the photon, in the second case, should lead her to conclude that "time has sped up for Bob".

Length contraction only serves to exacerbate this.
Title: Re: How is this explained in Special Relativity?
Post by: Janus on 11/06/2019 20:03:50
If you are considering A "tick" as when the light pulse leaves the central source and a "tock" as when the pulse reaches an end mirror,  Then you have to consider how Bob measures the time between "tick" and "tock".   Measuring the time between "ticks" or between "tocks"  is straight forward, because the interval is being measured by a single clock (either at the source or end mirror).    When Bob measures the interval between "tick" and "tock", he has to use two clocks, One that measures the time at the source when the pulse leaves, and one at the end mirror when the pulse arrives.  Now as long as Bob can consider these clocks as being synchronized to each other, then he can also assume that the time measured by an end mirror clock at a "tock" is the same as the time measured by the clock at the source.   

So according to Bob, a tick can start at zero for all clocks like this.
 [ Invalid Attachment ]
And and a tock occurs when all clocks read one, like this:
 [ Invalid Attachment ]

Now according to Alice,  A tick starts like this:
 [ Invalid Attachment ]
The horizontal leg is length contracted ( we are assuming a 0.5 c relative velocity between Bob and Alice)
And while the both the source clock and vertical leg end clock both read zero., the horizontal end clock already reads 0.5 ( relativity of simultaneity).   

A tock for the horizontal leg occurs when the end clock runs into the expanding light pulse.  In between tick and tock, all clocks will have advanced by 0.5.  The source and vertical end clock read 0.5 and the horizontal clock reads 1.
 [ Invalid Attachment ]
Both Bob and Alice agree that the pulse leaves the source when the clock there reads 0 and reaches the end clock when the clock there reads 1,  but they disagree as to what time it is on the other two clocks when that happens.  if Bob is located at the source clock, He will say that the end clock reading 1 and his clock reading 1 are simultaneous, while Alice will say that those events are not simultaneous.

Thus according to Alice, a tock ( the pulse reaching the end mirror) occurs when Bob's source clock reads 0.5, however according to Bob, when his source clock read 0.5, a tock has yet to occurred.   You can't make a direct comparison between the Tick-tock interval for the two frames because a tock represents different pairs of events for the Two frames ( end clock reading 1 and source clock reading 0.5 for Alice, End clock reading 1 and source clock reading 1 for Bob.)    The only way to make a proper comparison is to deal with a round trip for a pulse, either leaving the Source at a tick and returning on the successive tick, or measuring between tocks at the end clocks.  This way both Bob and Alice agree as which events the interval is being measured between.

When dealing with a vertical pulse, to be strict, you should also only consider the total round trip.  However, since both Bob and Alice will agree that both source clock and end clock remain in sync with each other, we can "cheat" and only consider just the one way trip and not encounter any problem.   And while this "cheat" works in this case, it is technically a cheat, one that only works in this particular case and can not be applied to the horizontal light clock.


Title: Re: How is this explained in Special Relativity?
Post by: the_roosh on 13/06/2019 09:20:57
If you are considering A "tick" as when the light pulse leaves the central source and a "tock" as when the pulse reaches an end mirror,  Then you have to consider how Bob measures the time between "tick" and "tock".   Measuring the time between "ticks" or between "tocks"  is straight forward, because the interval is being measured by a single clock (either at the source or end mirror).    When Bob measures the interval between "tick" and "tock", he has to use two clocks, One that measures the time at the source when the pulse leaves, and one at the end mirror when the pulse arrives.  Now as long as Bob can consider these clocks as being synchronized to each other, then he can also assume that the time measured by an end mirror clock at a "tock" is the same as the time measured by the clock at the source.
Introducing more clocks doesn't help the situation. The light clock is the clock. It is used bcos it represents an "ideal" clock. If you introduce a clock at each mirror, then we may as well introduce a clock at each mirror for those clocks and so on ad infinitum.

The emboldened part above is the subject of debate in this thread:
https://www.thenakedscientists.com/forum/index.php?topic=77116.0

When dealing with a vertical pulse, to be strict, you should also only consider the total round trip.  However, since both Bob and Alice will agree that both source clock and end clock remain in sync with each other, we can "cheat" and only consider just the one way trip and not encounter any problem.   And while this "cheat" works in this case, it is technically a cheat, one that only works in this particular case and can not be applied to the horizontal light clock.
This is the key point here - I understand about observers agreeing on clock readings.

The idea that we should only consider the total round trip is entirely arbitrary. If a clock can be said to "measure time" then it is "measuring time" at every moment in the process. Time is not suddenly measured at the end of the round trip. If we label the mirrors "tick" and "tock" then the path traveled from "tick-to-tock" and the path traveled from "tock to tick" are just as valid a "measurement of time" as "tick-tock-tick" or "tock-tick-tock".

The same goes for the horizontal clock. If it is a clock which "measures time" then it is always measuring time and it's "tick-to-tock" and "tock-to-tick" must be measurements of time.
Title: Re: How is this explained in Special Relativity?
Post by: Colin2B on 13/06/2019 12:41:18
The emboldened part above is the subject of debate in this thread:
https://www.thenakedscientists.com/forum/index.php?topic=77116.0
@Janus is answering the question in the OP, not the one you referenced.
Please read https://www.thenakedscientists.com/forum/index.php?topic=66954.0 which explains how we manage new/alternative/variations-of theories on this site.
Title: Re: How is this explained in Special Relativity?
Post by: the_roosh on 13/06/2019 15:49:42
@Janus is answering the question in the OP, not the one you referenced.
Please read https://www.thenakedscientists.com/forum/index.php?topic=66954.0 which explains how we manage new/alternative/variations-of theories on this site.
Yes, I was linking him to that thread to avoid starting a discussion on it in this one because his statement seemed to beg the question.