- #31
SiennaTheGr8
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I think @SiennaTheGr8 likewise had a good point in #26. 
B Resolving the Relativity of Simultaneity: A Geometric Approach
- Thread starter Andrew1955
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The discussion centers on the relativity of simultaneity as illustrated by Einstein's thought experiment involving two observers: one on a moving train and one stationary on the embankment. Both observers perceive the timing of two simultaneous lightning strikes differently due to their relative motion, leading to the conclusion that simultaneity is not absolute. The moving observer sees the flashes at different times because they are moving towards one flash and away from the other, while the stationary observer sees them simultaneously. This discrepancy raises questions about how Einstein connects these observations to the broader concept of time passing at different rates. Ultimately, the conversation emphasizes that both observers are correct in their respective frames of reference, highlighting the non-absolute nature of time and simultaneity.
- #32
FactChecker
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There is more than one "time". Each reference frame judges the time that events occur by its own set of clocks synchronized within its reference frame. But if two frames in relative motion try to synchronize between the two at one point, they are forced to be unsynchronized at other points in the direction of relative motion. So they can never agree on whether two events which are separated in the direction of relative motion are simultaneous. If one reference frame thinks that they are simultaneous, then the other can not agree.Andrew1955 said:
I couldn't disagree more. It helps one understand how it all fits together. It helps one to understand how each reference frame can think that the other's clocks are running too slow. -- Because each reference frame is moving toward the other reference frame's trailing clocks, which people in the first frame thinks were synchronized incorrectly.
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- #33
pixel
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SiennaTheGr8 said:I think @SiennaTheGr8 likewise had a good point in #26.
@pixel missed your post #26 and would have otherwise referenced it.
- #34
craigns
The question I would add to this discussion is what is time? I would stress that it is not a thing itself but rather a measurement or snapshot of the state of the relationship of things (atoms) at a particular moment. Personally I think Einstein treats time too much as a thing.
- #35
A Lazy Shisno
Mister T said:
Sorry, I'm still trying to learn some of the finer details of SR, but why doesn't the ball have the initial velocity of the train? If I'm on a train and I have a ball in my hand, it has the same velocity as the train. So when I throw it in the direction of the train's motion, it has the velocity of the train plus the velocity I imparted on it (from the perspective of an outside observer). I thought the special thing about light is that its speed doesn't depend on the velocity of the thing it's being emitted from?
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- #36
Dragon27
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Yeah, the special thing about light is its speed. Any object that has the speed of light in one inertial FoF moves at the speed of light in any other inertial FoF. The velocity of light (or any object moving at the speed of light), though, unlike speed, can change with the change of the FoF (inertial). And it does so according to the laws of SR (velocity addition formulas). E.g. if you shoot a photon perpendicular to the movement of the train (from your point of view), while you on the train, the photon will have the additional velocity of the train along the direction of its movement (from the ground point of view).A Lazy Shisno said:
- #37
A Lazy Shisno
Dragon27 said:
No, I know what happens when you fire the light perpendicular, but what I'm talking about it that the speed doesn't depend on the speed of the source. When you (on a moving train) throw a ball in the direction of the train's motion, it has the speed of the train plus the speed you threw it at (from the perspective of an outside observer). The point is that light is different, it doesn't have a speed of c plus the velocity of the train, it just has a speed of c in both frames.
- #38
Wes Tausend
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For humans, time actually is a thing or rather, rotation event. Time is always, always a real rotation of "something". There is no other way to measure a periodic event but to count the clicks as the "merry-go-round" comes around again.craigns said:
Although confined to a roundy-ness in all clocks, time can be proportioned to any other motion direction within geometries, a length or temperature change as simple examples. It is even true for the "bouncing ball clock" in the relativity animation I tried to promote above in post #25 (so Andrew1955 could finally 'get it'). The ball on Einstein's train is made to bounce in continuous sine-wave-like fashion as it passes... which is merely a set of stretched-out circle-like rotations.
Wes
- #39
Dragon27
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Define "plus". If you're saying that the speed of ball changes (in this case, increases), then yes, the speed of light is special (as Mister T has pointed out in his original post). Because it stays the same. But the amount by which the speed of ball changes is not the exactly the same as in classical non-relativistic mechanics.A Lazy Shisno said:
- #40
A Lazy Shisno
Dragon27 said:
Yeah, that's what I was trying to get at in my original post. I'm aware that relativistic phenomena obviously apply to the ball, but I was trying to explain that the light doesn't act like a ball being thrown to either end of the traincar because it is independent of the speed of its source, hence why the relativity of simultaneity was realized.
- #41
Dragon27
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But there's nothing special about the light (except for its speed). The relativity of simultaneity is realized, whether we're talking about the light, or the balls. Light is affected by the movement of its source. Only the speed of the light is absolute (not even velocity in general).A Lazy Shisno said:
- #42
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Yes. The only complication for the thrown ball is that an outside stationary observer will not add the same velocity numbers. He would think that the person on the train is wrong about the ball's speed because of the distortion of distance and time.A Lazy Shisno said:
- #43
Herman Trivilino
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A Lazy Shisno said:
Yes, it does.
No, adding is not the right way to combine speeds. If you have two wedges and you stack them to make a steeper wedge, you wouldn't add the slopes of the wedges to get the slope of the stacked wedge. That's not the right way to combine slopes.
Because light travels at a special speed, the fastest speed possible. So when you combine it with the speed of something else you get the same speed. Again, adding speeds is not the right way to combine them.
- #44
GrayGhost
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Andrew1955 said:
Hello Andrew. I've been looking through your thread here. The problem as I see it, is that you do not yet understand the theory, and so as is often the case, you challenge the validity of the relativistic effects. And until one understands the theory, one has no other choice but to lean toward absolute time and absolute simultaneity, because that's the casual everyday experience for the average person. To know whether the relativistic effects are real or not, one must first come to master the LTs and their meaning. Takes awhile. One will never understand it by a collection of relativistic buzz words and buzz phrases from relativists. If you are truly interested, pay close attention to what the experts on the forum here say, and take your own time to start the process of deriving the LTs. And if you wish to learn the theory much sooner than much later, then look at how Minkowski spacetime diagrams are designed, and draft some of your own. Their geometric presentation is very intuitive. It may well save you months to years in the learning process. It did for me.
Andrew1955 said:
SR is not about illusionary effect. Its about real relativistic effects, per the LTs. They have been verified by measurement. It is also not about brain processing. The LTs hold for all, and no matter the brain considering them. They held long before the first man walked the earth. For example ... a driver traveling 60 mph wrt the road holds another driver at 30 mph wrt himself, if that driver is 30 mph wrt the road (same direction) ... we do not assume this an illusionary effect simply because we do not know if everyone sees the exact same shade or color of (what we all call) blue.
Andrew1955 said:
If it is compelling enough, certainly. The question is ... what does the math say? Then, is our physical description of the math compelling? The answer is yes, if many tests and their repeat-ability support the math and its interpretation as true. And, that has certainly been the case wrt relativity theory.
Best Regards,
GrayGhost
- #45
Sorcerer
Andrew1955 said:
My take on this thorny issue:
Easy way to vaguely understand:
(1) Every timed measurement is pair of simultaneous events (the hand of your clock arriving at a certain tick mark coinciding with the event you are looking at, e.g., the simultaneous events of the hand of your clock moving to a point and, say, the racer you are timing arriving at a point).
(2) If every timed measurement is at minimum a pair of simultaneous events, and simultaneity is not universal, then timed measurements cannot be universal either.
(3) Since everything that moves in a periodic way can be used as a clock (including the motion of the atoms that make you), it seems to follow that time itself cannot be universal as well.
Hard way to vaguely understand:
How fast are you moving right now?
When you are finished considering that question, hopefully you will realize the question is completely meaningless. You are sitting still, on a spinning earth, which is orbiting the sun, which is orbiting the milky way, which is moving with respect to other galaxies, which are themselves moving in a large galaxy cluster, and so on and so on.
In my humble opinion, the first step to figuring this "paradox" out is understanding this concept. Galileo figured it out some time ago: the principle of relativity. So when you get that down, you'll truly realize there is no inherent difference between the person at rest on the train and the person who sees the train fly by (or from the perspective of the train passenger, the person who flies by the train).
That's a big Step 1, I believe.After that, all you have to do is incorporate the idea that all the fastest signals used for communication move at the same maximum speed for all uniformly moving observers (conveniently, the speed of light is this speed). So what happens when you combine "Step 1" with the fact that there is a maximum speed which all observers agree on regardless of how "fast" (remember the question is meaningless in and of itself) they are moving?
Then you can turn to the good old fashioned light clock (and realize that what applies to a light clock must apply to any type of clock as well, because there is nothing magical about them that makes them unique with respect to the laws of physics). This little cognitive tool really does the trick. So, we have both observers agreeing on the speed of light, and we have the principle of relativity. So we can imagine a pulse of light bouncing vertically between two mirrors, and each trip up is a tick, each trip down is a tock. And we can further imagine the clock being held steadily by one observer (so that the other one sees the clock moving). You end up with a straight up and straight down path of the light for the observer holding it, and a triangle shape for the path of light for the other observer. This will actually give you a right triangle if you combine the two. You can use t and T to represent the time that each measures, and it MAY be that the times are the same, and it MAY be that they are not. Don't make the assumption yet.
So, looking at the triangle, you have a hypotenuse of ct, a horizontal line of vt (v is the relative speed between the two observers), and a vertical line of cT. Use the Pythagorean theorem to find the ratio of t to T, i.e., t/T. (c in both cases because all observers agree on the speed of light, and ct and cT because speed times time is distance). Just basic middle school stuff.
(ct)2 = (vt)2 + (cT)2
First divide everything by (ct)2(1)2 = (v/c)2 + (T/t)2
Now, subtract (v/c)2
1 - (v/c)2 = (T/t)2
Now take the root
√[1 - (v/c)2 ]= T/t.
We could stop right there and see that the only way T = t is if v is 0, but just to make things look standard, divide by T/t and then divide by √[1 - (v/c)2 ]:
t/T = 1/√[1 - (v/c)2 ]
Then multiply by T to get your standard time dilation formula:
t = T/√[1 - (v/c)2 ] ****
So yeah, if you assume the principle of relativity and the constancy of the maximum speed (which conveniently matches with the speed of light), and then use simple thought experiments like a light pulse clock, you see rather clearly that the two observers are going to disagree on time. Then if you are clever enough to realize that, because of the principle of relativity, this result applies universally, in all similar instances regardless of where the observer is and how fast s/he is moving, it is clear that anything that can be used to measure time will give measurements of time that depend upon frame of reference. And if you are super clever, you will note that the atoms your body is made of, the electrical pulses in your brain as you think, and every other thing that moves in a way that could conceivably be used as a clock, will have the same property of time depending on frame of reference, and then you can make the next logical leap to realize that time itself depends on frame of reference, rather than merely clocks.
Then you can make the next logical leap and consider how you would measure the length of something moving past you, and realize you'd be depending on some sort of signal coming from the edges of the object to your eye, taking a finite amount of time to get there, and once again depending upon simultaneity (to get an accurate length, you need to measure the two ends simultaneously, since the object is moving). From there you will realize that length contraction will occur according to observers measuring the length of a moving object. And once again, if you understand Galileo's principle of relativity, you will note that your particular frame of reference is not special, and thus the measured length will also necessarily depend on frame of reference (since it depends on simultaneity, which is not universal).Or you could go the simple route and realize that if simultaneity is not absolute than neither can time be absolute.
(****on a somewhat unrelated note, this works for pre-special relativity time as well. All you have to do is assume that c is infinity, and you end up with t = T, like it was in the old days. Or you could assume that v is approximately zero compared to c, making v/c zero in the limit, reducing the thing to t = T again. But of course we know that c is finite and that all inertial observers agree on it, meaning you are stuck with t not being equal to T when v is not equal to zero).
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- #46
Herman Trivilino
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Sorcerer said:
A long as the two occurrences are in the same location (co-located) when they occur then they are a single event.
If they occur at the same place and at the same time according to one observer, then that will be true for all observers. This is an event. This kind of simultaneity is absolute. But if the two events are separated along the line of relative motion, then simultaneity is relative.
- #47
GrayGhost
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Andrew1955 had asked ... how did Einstein make the leap of faith that time must pass more slowly in a moving frame, based on his train thought-experiment alone?
Before Maxwell, there was absolute time, absolute simultaneity, and a variable light speed. As such, the train passenger must agree with the embankment observer (and all observers) that the 2 remote flash events occurred simultaneously. Maxwell's 1864 EM theory required light speed be invariant, but this was not supported by experiment until the MMX experiment in 1887. So from about 1887 onward, great physicists first began tackling compatibility issues associated with an invariant light speed, with Einstein succeeding in 1905. Einstein's train scenario assumed an invariant light speed c. As such, the train passenger could no longer agree that the 2 remotely located flash events were simultaneous. So absolute simultaneity was in need of revision. If absolute simultaneity required revision, so too did absolute time. So the train thought-experiment presented the requirement for relative simultaneity (RoS), and also revealed that absolute time was insufficient. If time is not absolute, then it must be relative in some way. However the precise manner in which the measure of space and time needed change required a complete derivation process, which is over-and-above the train thought-experiment.
Andrew mentioned he had read through Einstein's 1905 OEMB paper. Near the beginning of Section 3, Einstein relates the 3 events of the 2 frames (emission, reflection, and reception) in what is often referred to as his 3 Taus Eqn. In particular, the reflection event in system K which DOES NOT occur at the midpoint of the ray's round trip, is related to the reflection event in system k which DOES occur at the midpoint of the ray's round trip. RoS is introduced right there, and that in-and-of-itself gives rise to the relativistic effect of "time-desynchronization of moving entity". The relative measure of space and time (ie LTs) was determined by all that follows (the 3 Taus Eqn) in Section 3, which includes a partial differentiation of his 3 Taus Eqn, a subsequent integration of that result to establish a frame-to-frame relation for time in a general form, then followed by a number of assumptions, substitutions, and algebraic manipulations to attain the LTs in their final form. There was in fact "a dance of sort" between RoS and the relative measure of space & time, such that all observers agree on all LT solns, even though they disagree as to what are simultaneous events and the relative measure of space and time.
OEMB for reference ... https://www.fourmilab.ch/etexts/einstein/specrel/www/
Best Regards,
GrayGhost
Before Maxwell, there was absolute time, absolute simultaneity, and a variable light speed. As such, the train passenger must agree with the embankment observer (and all observers) that the 2 remote flash events occurred simultaneously. Maxwell's 1864 EM theory required light speed be invariant, but this was not supported by experiment until the MMX experiment in 1887. So from about 1887 onward, great physicists first began tackling compatibility issues associated with an invariant light speed, with Einstein succeeding in 1905. Einstein's train scenario assumed an invariant light speed c. As such, the train passenger could no longer agree that the 2 remotely located flash events were simultaneous. So absolute simultaneity was in need of revision. If absolute simultaneity required revision, so too did absolute time. So the train thought-experiment presented the requirement for relative simultaneity (RoS), and also revealed that absolute time was insufficient. If time is not absolute, then it must be relative in some way. However the precise manner in which the measure of space and time needed change required a complete derivation process, which is over-and-above the train thought-experiment.
Andrew mentioned he had read through Einstein's 1905 OEMB paper. Near the beginning of Section 3, Einstein relates the 3 events of the 2 frames (emission, reflection, and reception) in what is often referred to as his 3 Taus Eqn. In particular, the reflection event in system K which DOES NOT occur at the midpoint of the ray's round trip, is related to the reflection event in system k which DOES occur at the midpoint of the ray's round trip. RoS is introduced right there, and that in-and-of-itself gives rise to the relativistic effect of "time-desynchronization of moving entity". The relative measure of space and time (ie LTs) was determined by all that follows (the 3 Taus Eqn) in Section 3, which includes a partial differentiation of his 3 Taus Eqn, a subsequent integration of that result to establish a frame-to-frame relation for time in a general form, then followed by a number of assumptions, substitutions, and algebraic manipulations to attain the LTs in their final form. There was in fact "a dance of sort" between RoS and the relative measure of space & time, such that all observers agree on all LT solns, even though they disagree as to what are simultaneous events and the relative measure of space and time.
OEMB for reference ... https://www.fourmilab.ch/etexts/einstein/specrel/www/
Best Regards,
GrayGhost
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- #48
Sorcerer
Thanks for the insight. But there would by necessity be a distance separating them, would there not? If you are timing when a train arrives, your clock is close to the train, but not on the train. That is, your measurement is comparing two events: the event of the second hand hitting a number, and the event of a train pulling into a certain location. Is that right?Mister T said:
- #49
Ibix
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Yes. But there are two caveats.Sorcerer said:
First, the Lorentz transforms only do "funny" things in the direction that the other frame is moving. We usually pick that to be the x direction. Two events with equal x coordinates will be simultaneous (or not) for all frames moving in the ±x direction, regardless of their y and z coordinates.
Secondly, if the two clocks are a lot closer together than the length of the train then any error introduced by a failure to consider clock synchronisation between those two clocks becomes small compared to the relativistic effects you're measuring along the train. That idea of things being close enough together that you can neglect some effects is important throughout relativity.
- #50
FactChecker
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There will be agreement on the simultaneity of two events that are not separated in the direction of relative motion. They may be separated in other directions with no problem.
- #51
Herman Trivilino
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Sorcerer said:
It's negligible. Note that this is what we do in all of physics, it's part of the modelling process. In practice the distance between the objects involved is very very small compared to the other distances involved in the analysis.
- #52
SiennaTheGr8
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Ibix said:
At the risk of being pedantic: Lorentz transforms of some quantities (e.g., velocity) will be "funny" even in the y and z directions.
- #53
Alfredo Tifi
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So it is the time of passenger - as evaluated by a platform observer - which slows down (and vice versa); not the time as evalued by the passenger himself.jartsa said:
Nobody experiments a change in his local-personal-time. In the inertial motion the two observers can evaluate each other's clock only during the short time instants of crossing in front of each other. They will never meet again. What is hard to accept is the time change of clocks as an objective fact when one of two twins has returned back home after a relativistic journey or after an atomic clock orbitated in a reduced gravitational field. These are both experimental facts. We would like to correlate these actually relented time lines to the inertial reciprocal evaluation of clocks' rate, in such a way to merge the evaluation and the fact into one coherent thing.
- #54
Alfredo Tifi
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I want to propose a more symmetrical setting. A single event "Spark" is caused by friction in the same time and place: when M and M' are passing in front of each other and sratch two flints, causing a single spark. Both M and M' stand in the middle between two hyperbolic mirrors which reflect a converging light onto an electronic detector which reveals the reflecting light and causes a chime everytime light strikes the detector.Dragon27 said:
M's expects his detector will reveal two chime events simultaneously, as M' expects the same, two chime' events simultaneously emitted by his own detector. The chimes are events occurring in the same place. I believe (but maybe I'm wrong) that for the symmetry of the situation M and M' will actually register two simultaneous chimes from their device. There is no problem with simultaneity here. But I think we have another issue with "light" as a physical phenomenon: what is clear to me is that we can't describe light as something unique travelling.
If the light emitted in the spark were a unique propagation physical phenomena, we couldn't have double simultaneous chimes from both the observers.
Once light has been "emitted" in the single event spark, every frame owns its "copy" or "version" of light causing a total of four distinct chime events. We can't speak of light as one and the same thing during the propagation towards each couple of mirrors for both observers.
To speak of light as something (one thing) traveling works only from the POV of a single observer which experiments two separate (in time) events in the same place (1. spark; 2. chime). By dividing distance by time we always find c. But if we speak of light event phenomena as a propagation phenomena, each event as the same phenomenon for every observer, we are misunderstanding the true nature of light and the meaning of light type distances in our relativistic Universe.
- #55
Rap
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Alfredo Tifi said:
@Dragon27
M and M' will not experience simultaneous chimes. Let's say M is motionless with respect to the detectors, M' is not. Then M will experience simultaneous chimes, M' will not. M' will not, because to him, the detectors are moving. One detector is moving towards where the spark happened, the other is moving away, and so, to him, the distances the two light beams have to travel are different, and since the speed of light is constant, the chimes cannot be simultaneous.
M will say the time interval between the chimes is zero. M' will say it is t. (time dilation). Classically they would both agree it was zero.
M will say the distance between the two detectors is L. M' will say the distance between the two detectors is L', which will be smaller than L. (Lorentz contraction). Classically, they would both agree it was L.
M will say the distance between the two chime events is L. M' will say the distance between the two chimes is X where X is greater than L, because the detectors moved during the time interval between the chimes (despite the fact that they were closer together). Classically they would both agree it was L, since there was no such time interval, and no disagreement about the distance between the detectors.
Both will agree on the value of the distance squared minus the time interval squared. In other words L^2 = X^2-t^2.
- #56
Alfredo Tifi
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This could be true only if referred to the evaluation of one's and other's detector: M and M' both say their own detector receive two light signals simultaneously, coming from their own mirrors, provided they hear two simultaneous chimes (and see two simultaneous LED blinkings into their own detector hold in their hand). But if B watches the detector of B' faraway (or if B' looks at the detector of B), he could even expect two LED blinks arriving at different times from there, because he imagines a light beam as traveling from a mirror moving forward and another beam traveling from an escaping mirror; thus he presumes those beams will reach the other observer's detector in different times. But this nice fable is only based on the assumption that light is travelling and that that light is "one and the same thing-ball" for everybody. The cruel reality is that we have never seen a beam of light travelling. We can see, at most, a light beam standing in between a distance, if we put some smoke there. So, everything can "travel" but light, is my tenet. The other reality is that the light of both detectors will blink simultaneously from the pov of each owner. And this simultaneous blinks will correspond to another event-signal which will be perceived by the other observer faraway. No matter of time lapse and distance, a double simultaneous blink event in the hands of B' is a fact, independently from the original scratch and spark. Whatever it will reach B, that event will conserve and vehicle the image of a far detector in which two LEDs are simultaneously blinking. So both observers will observe a double simultaneous chime and LED light blink in their own detector, and also a double simultaneous blink (obviously retarded) into the far observer's detector.Rap said:
This is manifestly wrong. No observer is motionless. In our Universe doesn't exist something like "rest". Everything is in relative motion respect to a myriad of other things. In this case M and M' are both in motion one respect to the other, because of the perfect symmetrical setting. The pitfall is even more evident because you are considering the spark and the spark-event place as standing there, somewhere, maybe in front of M. If you want imagine a spatial location for that spark-event with any short-time duration, then you'd better imagine that place is - at any time - exactly midway between M and M'. In this case M and M' are both in motion respect to the light source at same (opposite) speed. This will reestablish a clear image of the symmetry. And you maybe want to put there a third observer too: the one sitting at the spark-place, i.e. the POV of M°. Like M and M', M° has two mirrors and a chime-LED detector pointed towards the two mirrors equidistant in opposite directions. He will observe two chimes and LED light emissions from his detector in his hands, and, after a short time lapse, M° sees two double simultaneous LED blinks coming from M and M', from opposite directions, but simultaneously.Rap said:
If you think to light as something connecting events in different points of spacetime, instead of something "travelling in space", you could start re-thinking and re-writing all concepts. I am not able to do that at this moment, but I have no doubts on the results and implications of this thought experiment of mine.
I hope somebody more expert than me and open minded would take in account these analyses of the issue.
Many years ago I read PW Bridgman didn't like to think of light as something travelling. Now, I know why, or I presume to know why.
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- #57
Rap
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Alfredo Tifi said:
@Dragon27
Maybe we aren't talking about the same scenario here. What I am saying is that there is a frame (the detector frame) in which the two detectors are motionless, separated by a distance L. Observer M is midway between the two, and also motionless with respect to the frame, and so he is motionless with respect to the two detectors. He's in the middle, and stays in the middle.
Observer M' is in a frame (the prime frame) that is moving with respect to the detector frame. Before the spark, M' is moving towards M. The spark occurs the instant they meet, when they are at the same position. After the spark, M' is moving away from M.
When the spark occurs, observer M says the two detectors are equidistant from him, and motionless. When the spark occurs, observer M' says one detector is moving away from him, the other detector is moving towards him and both will agree they are midway between the two detectors. To both observers, the detectors light up at certain times later. Observer M in the detector frame sees them light up at times t1 and t2 after the spark, and we agree that t1=t2. To the observer in the prime frame, the detectors light up at times t1' and t2' after the spark. You say t1' equals t2', I say they are not equal.
Can we agree on all of the above? We have to agree on the setup before we can go any further, right?
- #58
FactChecker
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If
1) each reference frame is using it's own synchronized clocks to record the times of events and
2) the clocks are at the positions where the events happen and
3) the events are separated in the direction of relative motion,
then they will not agree on whether events are simultaneous.
If all those conditions are satisfied, t1=t2 forces t1'≠t2'.
1) each reference frame is using it's own synchronized clocks to record the times of events and
2) the clocks are at the positions where the events happen and
3) the events are separated in the direction of relative motion,
then they will not agree on whether events are simultaneous.
If all those conditions are satisfied, t1=t2 forces t1'≠t2'.
- #59
Rap
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FactChecker said:
1) Yes, but only one clock per observer is needed. The time of the detection event can be inferred if both observers know their relative velocities and the detector positions, by observing the light flash from the detector.
2) Yes, but not necessary (see above)
3) Yes
And yes, the conclusion follows. I just want to make sure that Dragon27 agrees with the setup or else it’s apples and oranges.
- #60
FactChecker
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As long as the times recorded are identical to the multiple-clock setup.Rap said:
The simplest, most basic situation is that the times recorded in each frame are the times in that frame at the location of the events. Anything else is a complication. You must be careful that your method gives the same time as the multiple clocks or the results will not be the same.
I was under the impression that the situation being discussed was fundamentally different.