Question about Relativity of simultaneity and light clocks

[obnoxiousris]

The example our lecturer uses to illustrate the relativity of simultaneity is a light clock, where a photon is bounced between a reflector and a detector. a tick in the clock means the light has made a round trip in the clock.

There are two clocks, one is orientated perpendicular to the motion and the other parallel to the motion, both going at the same speed, it is shown that the photons hit the two reflectors not simultaneously, even though they were synchronized when stationary. However they will still measure the ticks at the same pace (so the photons return to the detectors at the same time, despite the time taken to reach the reflector is different), hence not violating the first postulate.

But if we define a tick as the time the photon bounced off the reflector, then the two clocks will not measure the same time, even though going at the same speed, so the first postulate is violated?? How do I make sense of this? Help please?

 

[PAllen]

I wonder if you have understood your instructor properly. Let's simplify the experiment. Let's say, while 'stationary with respect to something, and inertial', you arrange that a pulsed light source has its pulses received simultaneously at two detectors. The two detectors are 90% apart from the point of view of the source. Now, boost this whole frame to be moving rapidly relative to the 'stationary something' - in the direction of one of the detectors, but still inertial. Nothing will change measured in the now 'moving frame'. The detectors will still receive the pulses simultaneously from the point of view of the moving frame.

Maybe your instructor meant they will not be simultaneous viewed from the 'stationary something'? But this is no mystery at all. The stationary observer sees moving observer claim simultaneity, but the stationary observer sees the pulses arrive non-simultaneously, and also the the the moving observers timepieces at different positions are not synchronized, so the moving observer's claim of simultaneous arrival is considered due to de-synchronization of clocks.

No aspect of this is in violation of any aspect of relativity principle.

 

[obnoxiousris]

I get the train example where the moving and stationary observers don't agree on things being simultaneous (because the speed of light is constant and the events are separated in space), but what about the two clocks? If they are both in the perpendicular direction to motion,having the same velocity then they will be syncd ( first postulate), both the moving observer and the stationary observer would agree the ticks occur at the same time, however when one of the clocks is in the parallel position (and counting the time the photon hit the reflector as a tick), then the ticks will not be in sync, so the moving observer would find two different times, doesn't this violate the first postulate?

 

[GrayGhost]

obnoxiousris,

Very good question, and it does have an answer, as PAllen posted. Disagreeing as to what are simultaneous events is actually not a violation of the first postulate. Many assume such at first, but usually realize differently later.

First, observers who move relatively are allowed to disagree as to what are simultaneous events. So consider an observer at rest with the lightclocks, and another in relative motion at luminal v. While they agree the 2 photons always return to the emitter simultaneously, they can disagree that they reflect off the reflectors simultaneously. It should be pointed out though, that in your stated scenario, each of said 2 observers will disagree on how long the round trips take ... the observer stationary wrt the lightclocks claiming it took less time (for roundtrip) than the fellow who moves relatively (who experiences time dilation). The fellow who moves relatively knows the 2 photons reflect non-simultaneously, however when considering it in terms of relativity (using the Lorentz transformations) he knows that the observer at rest with the lightclocks must hold the reflection events "as simultaneous".

Imagine wonder-clocks attached to the emitters and reflectors, clocks that both observers can always see. They are all synchronized in the lightclock frame. OK, so the emissions occur simultaneously at 12:00:00 am. Further, imagine that at each reflection event, 1 sec transpires by the attached clocks ... so 2 sec for a round trip. Now here's the really cool part ... Imagine you are the fellow who moves relatively wrt the lightclocks. One emitter/reflector pair being aligned wrt the axis of propagation. The 2 clocks attached to that pair will not be synchronised "per you", although they tick at identical rate. The forward clock will possesses a time readout that lags the aftward clock's readout in any instant of your time ... however the guy at rest with the lightclocks never sees it that way. So per you, the forward clock at the reflector will lag "to just the right tune" that it's time readout (upon reflection) will agree with the reflection-event's time readout of the reflector-clock that's aligned perpendicularly with the axis of motion. So even though the reflection events do not occur simultaneously per you, you will indeed note that the moving reflector-clocks always display "the same time readout" upon reflection ... consistent with what all observers of the cosmos will record, including the observer at rest with the lightclocks. This upholds the 1st postulate of relativity.

In your stated scenario there are no clocks with time readouts, but rather only events that occur simultaneously "or not". Therefore, while it's a great starter scenario to establish concepts in relativity, such as time dilation and the required disagreement of simultaneous events, it is insufficient ... and folks with keen insight recognize that your question needs asked. Each time you grasp the points at hand, you will have many new questions to ask, and it will likely go on and on for awhile (usually does). Keep up the good work!

GrayGhost

 

[harrylin]

I get the train example where the moving and stationary observers don't agree on things being simultaneous (because the speed of light is constant and the events are separated in space), but what about the two clocks? [..] doesn't this violate the first postulate?

I wonder is you really "got" the train example. Here:
http://www.bartleby.com/173/9.html

In more elaborate drawings there are also clocks on the station platform, next to clocks in the train, in the front and in the rear. The clocks on the platform have been synchronised for the platform as "rest" system, and the ones in the train for the train as "rest" system.
Do you see that the clocks of the two systems cannot all agree on what time it is?

And what do you think that the first postulate means?

Harald

 

[obnoxiousris]

GrayGhost:

sorry i have read your comment many times and it still doesn't really make sense, are you saying that the even tho the two photons hit the reflectors at different times, the clock on the first hit photon will somehow lag a bit so when the second photon hit the other reflectot the readouts would be the same? am i missing something here? how does this work?

harrylin:

you were right, i don't understand this at all D: i guess i get the bit where the simultaneity of events depends on the relative motion of the observer, but when time is concerned, i get all confused. i think the first postulate means the all the measurements performed in inertial frames will yield the same result. so the observer with the clocks will see them syncd, and the moving observer wrt clocks will also see them syncd, even tho they may not agree on the rate of time as one experiences time dilation. so its really hard for me to accept when time is measured by not simultaneous events, it can still give out the same time...

 

[harrylin]

[..] you were right, i don't understand this at all D: i guess i get the bit where the simultaneity of events depends on the relative motion of the observer, but when time is concerned, i get all confused. i think the first postulate means the all the measurements performed in inertial frames will yield the same result. so the observer with the clocks will see them syncd, and the moving observer wrt clocks will also see them syncd, even tho they may not agree on the rate of time as one experiences time dilation. so its really hard for me to accept when time is measured by not simultaneous events, it can still give out the same time...

The bug is in understanding the relativity principle. It doesn't mean that all the measurements performed in inertial frames will yield the same result.
To a lesser degree that's already not the case in Newton's mechanics ("Galilean relativity")! For example, the speed of a man walking on a boat is 5 km/h wrt the boat, but wrt the shore the same speed is 15 km/h. One says that such measurements are "relative".

The relativity principle is only that the laws of nature are the same in different (inertial) reference systems; and that forces a number of measurements to be different. In Special Relativity the speed of light is fixed.* As a consequence, also measurements of "space" and "time" are "relative". In particular, there is disagreement about synchronisation of distant "time".

Harald

*more precisely: the constancy of the two-way speed of light wrt an inertial frame is made a law of nature, and the one-way speed is defined as equal to the two-way speed.

 

[obnoxiousris]

yes, different experiments do give out different results, but since the two clocks are moving with the same speed, won't their rate of time be the same? i meant to say that the speed of the man is 15km/h wrt shore, and will also be 15km/h to an observer standing on the shore, they will not measure different speeds because there is no relative motion between them... i think lorentz transformation is important to understand this, thanks for the replies, I am going to read thru my notes again.

 

[harrylin]

yes, different experiments do give out different results, but since the two clocks are moving with the same speed, won't their rate of time be the same? i meant to say that the speed of the man is 15km/h wrt shore, and will also be 15km/h to an observer standing on the shore, they will not measure different speeds because there is no relative motion between them... i think lorentz transformation is important to understand this, thanks for the replies, I am going to read thru my notes again.

As there are different errors in the above, a short comment may still be helpful.

According to an "intermediate" reference system in which the man moves at a velocity of -7.5 km/h (to the left), and the shore +7.5 km/h (to the right), both move at 7.5 km/h.

But according to a reference system fixed on the shore, the man is moving wrt the shore at a speed of 15 km/h while the shore is moving at 0 km/h. And different for a reference system that is fixed to the boat - that is called relative motion.
Please read again my post #7.Harald

PS: I strongly advice to get familiar with the Galilean transformation before studying the Lorentz transformation!

 

[GrayGhost]

GrayGhost:

sorry i have read your comment many times and it still doesn't really make sense, are you saying that the even tho the two photons hit the reflectors at different times, the clock on the first hit photon will somehow lag a bit so when the second photon hit the other reflectot the readouts would be the same? am i missing something here? how does this work?

OK, so there are 2 pairs of clocks, an emitter and reflector each, one clock attached to each emitter and reflector. Each reflector is a proper distance X from their respective emitter. All clocks synchronised in their own frame, so all at rest with each other. Imagine their own frame of reference, where they assume themself the stationary. The clocks of pair 1 are spatial separated upon the y-axis, both at x=0, with one clock at x,y=0,0 (its origin). Pair 2 are spatial separated upon the x-axis, both at y=0, with one clock at x,y=0,0 (its origin). Hence, 1 clock of each pair are essentially considered co-located at the origin, both emitters (which can also act later as reflectors if they wish). All clocks travel parallel wrt the x-axis in the direction of +x.

Per the observer (A) who records the clocks to move luminally along +x, the time readout of the clock attached to the forward reflector always lags the time readout of the clock attached to the trailing reflector's time readout, even though both (all 4 actually) tick at the same rate. The 1st photon to obtain reflection strikes the aftward reflector (of pair 1), then the 2nd photon reflects at the forward reflector later (of pair 2). Because the forward reflector's clock always lags the aftward reflector's clock, that photon can take a longer time to reach reflection. When it eventually obtains reflection, the clock at that leading reflector must possess the same time readout of the clock attached to the trailing relector of the 1st reflection event.

Observer A records the reflection events as asynchronous. The clocks themselves record the events as simultaneous. So long as observer A agrees that the time readouts of clocks colocated AT each reflection event are the same, then there is no violation because he agrees that observers of the clocks-frame measure the reflection events simultaneously. Observers are allowed to disagree on the measure of space and time, however no one in the cosmos can disagree what a clock read at an event it was colocated with.

GrayGhost