Resolving the Relativity of Simultaneity: A Geometric Approach

[Dragon27]

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?

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]

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).

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.

 

[Wes Tausend]

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.

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.

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

 

[Dragon27]

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).

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]

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.

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.

 

[Dragon27]

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.

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).

 

[FactChecker]

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?

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.

 

[Mister T]

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.

Yes, it does.

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).

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.

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?

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.

 

[GrayGhost]

I understand a lazy shisnos example alright. I am still not clear why peculiarities about the speed of light must mean time and length must also change.

If light causes us to perceive weird stuff does this mean that weird stuff is really happening?

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.

If we see wave lengths of light as red is red really out there or is there just colourless energy which we interpret and imagine as being red? Do you think the sky is actually blue? The grass is green? These things are only illusions created by the human visual system.

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.

We use light to help us perceive reality. If light tells us time has changed, should we believe that just because 'light says its true'.?

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

 

[Sorcerer]

I understand a lazy shisnos example alright. I am still not clear why peculiarities about the speed of light must mean time and length must also change.

If light causes us to perceive weird stuff does this mean that weird stuff is really happening? If we see wave lengths of light as red is red really out there or is there just colourless energy which we interpret and imagine as being red? Do you think the sky is actually blue? The grass is green? These things are only illusions created by the human visual system.

We use light to help us perceive reality. If light tells us time has changed, should be believe that just because 'light says its true'.?

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).

 

[Mister T]

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).

A long as the two occurrences are in the same location (co-located) when they occur then they are a single event.

If every timed measurement is at minimum a pair of simultaneous events, and simultaneity is not universal, then timed measurements cannot be universal either.

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.

 

[GrayGhost]

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

 

[Sorcerer]

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.

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?

 

[Ibix]

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?

Yes. But there are two caveats.

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.

 

[FactChecker]

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.

 

[Mister T]

Thanks for the insight. But there would by necessity be a distance separating them, would there not?

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.

 

[SiennaTheGr8]

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.

At the risk of being pedantic: Lorentz transforms of some quantities (e.g., velocity) will be "funny" even in the y and z directions.

 

[Alfredo Tifi]

A passenger on the train does not notice that, so he must have a slow wristwatch or a slow atomic clock, as observed from the platform.

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.
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.

 

[Alfredo Tifi]

Yes, that's from the point of view of the ground observer. From the point of view the train observer he's not moving at all, so the flashes of light ARE non-simultaneous.

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.
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.

 

[Rap]

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.
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.

@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.

 

[Alfredo Tifi]

@Dragon27
M and M' will not experience simultaneous chimes.

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.

@Dragon27Lets 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.

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.
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.

 

[Rap]

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.

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.
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.

@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?

 

[FactChecker]

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'.

 

[Rap]

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) 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.

 

[FactChecker]

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.

As long as the times recorded are identical to the multiple-clock setup.

2) Yes, but not necessary (see above)

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.

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.

I was under the impression that the situation being discussed was fundamentally different.

 

[Alfredo Tifi]

@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.
...
We have to agree on the setup before we can go any further, right?

Absolutely YES: we are not talking of the same scenario. My scenario is the following (perfectly symmetric): 2 spaceships, four mirrors, two detectors (one for each spaceship and observer)
M and M' are sitting in the middle of two transparent spaceships. The two spaceships are equal and are moving one towards the other. There are two mirrors inside, one in front and the other back, equidistant from M in M's spaceship and equidistant from M' in his spaceship. M keeps his own detector as M' holds his detector in his hands. Both detectors point to both mirrors, emitting a signal (a sound or chime and a led lamp blinks) from the light received from each mirror.
You can imagine to observe the scene from the pov of a third observer M° who is constantly midway between M and M'
When the the two spaceships are getting so close to slide one onto the other, M and M' put a flint out of window and the scratch of the two flints will provoke a spark exactly were M° is sitting. Obviously, M° sees and listens at the two chimes simultaneously, because he sits where the two spaceships meet.
The spark event occurs in the point where the spacetime lines of M and M' cross each other. Same x position but slightly different z position (level).
M, M' and M° have the same right to consider the spark event as belonging to their reference system, as if they were motionless respect to the spark. Then they hear a simultaneous double chime and see two simultaneous LED light blinks in their own detector. After some nanosecond they will also see the image of the other's detector faraway corresponding to a double simultanous blink.
Don't try to solve the paradox saying that the spark event "belongs" only to M°. Also M and M' consider their own image of the spark as belonging to their system.
This is the reason why their detectors will receive the signals from both mirrors simultaneously. the paradox exists ony if you consider light as a single thing propagating.

 

[Rap]

Absolutely YES: we are not talking of the same scenario. My scenario is the following (perfectly symmetric): 2 spaceships, four mirrors, two detectors (one for each spaceship and observer)
M and M' are sitting in the middle of two transparent spaceships. The two spaceships are equal and are moving one towards the other. There are two mirrors inside, one in front and the other back, equidistant from M in M's spaceship and equidistant from M' in his spaceship. M keeps his own detector as M' holds his detector in his hands. Both detectors point to both mirrors, emitting a signal (a sound or chime and a led lamp blinks) from the light received from each mirror.
You can imagine to observe the scene from the pov of a third observer M° who is constantly midway between M and M'
When the the two spaceships are getting so close to slide one onto the other, M and M' put a flint out of window and the scratch of the two flints will provoke a spark exactly were M° is sitting. Obviously, M° sees and listens at the two chimes simultaneously, because he sits where the two spaceships meet.
The spark event occurs in the point where the spacetime lines of M and M' cross each other. Same x position but slightly different z position (level).
M, M' and M° have the same right to consider the spark event as belonging to their reference system, as if they were motionless respect to the spark. Then they hear a simultaneous double chime and see two simultaneous LED light blinks in their own detector. After some nanosecond they will also see the image of the other's detector faraway corresponding to a double simultanous blink.
Don't try to solve the paradox saying that the spark event "belongs" only to M°. Also M and M' consider their own image of the spark as belonging to their system.
This is the reason why their detectors will receive the signals from both mirrors simultaneously. the paradox exists ony if you consider light as a single thing propagating.

I'm sorry I misinterpreted the scenario. As you describe it, yes, M and M' will both experience simultaneous returns of the light from the spark, and Mo will see both detection events as simultaneous. But there is a problem - If everything is happening on one axis, then some mirrors will block each other, there will be situations where one mirror receives light, and so the mirror behind it does not. This does not destroy the scenario, however. We can just use half-mirrors which transmit half the incident light and reflect the other half, no need to offset the detectors either. But now there is not a single light beam, every time a beam hits a mirror, it splits into two beams. So I do not understand the paradox.

 

[Ibix]

@Rap - I think the ships are supposed to be slightly out of the plane so they don't collide. As long as the offset is very small compared to the length of the ships I think that's fine.

I agree with you that I can't see a paradox anywhere. The light is emitted at one event. There are four reflection events splitting the (initially) single forward-moving and single rearward-moving pulses into two, and two reception events. Or more if we add in M°.

I'm not sure what the stuff about one observer (frame?) "owning" an event is supposed to mean. That's no part of relativity, or at least is highly non-standard terminology, so may be the source of the belief that there is some kind of paradox here. Perhaps @Alfredo Tifi can explain what he means a bit more.

 

[Alfredo Tifi]

@Rap - I think the ships are supposed to be slightly out of the plane so they don't collide. As long as the offset is very small compared to the length of the ships I think that's fine.

Exactly, the spark-event occurs at the same time in the same X position where M° is sitting, but there is an offset in the Y axis: M is at +Δy° whereas M' is at -Δy° with Δy° << Δxₘ (distance between mirrors). M and M' have zero speed in the y° direction, from the POV of M°'s frame. So they won't collide.

@Rap I agree with you that I can't see a paradox anywhere. The light is emitted at one event. There are four reflection events splitting the (initially) single forward-moving and single rearward-moving pulses into two...

1. I don't want complicate the experiment with half-mirrors. I only want parabolic mirrors to capture and reflect more radiation energy and make the detector capable to detect something.
2. There are NOT "reflections events" physically detectable, with measurable or demonstrable precise positions in spacetime. Only the spark is such an "event", as is a physical event the observable response of a detector (chime + light blink). These are not imagineering, but doable phenomena.
3. If we think light pulse associated to the spark-event as a "unique some-thing" flying or traveling towards the mirrors we have a paradox: the detection of the same "flying thing" occurs into three different points of M°'s spacetime frame (and from any else reference frame). Ergo, we cannot think that pulse as a unique thing propagating. Light speed is completely different from any other speed.

@RapI'm not sure what the stuff about one observer (frame?) "owning" an event is supposed to mean. That's no part of relativity, or at least is highly non-standard terminology, so may be the source of the belief that there is some kind of paradox here. Perhaps @Alfredo Tifi can explain what he means a bit more.

I am not speaking of the spark event, the sole event M, M' and M° agree in settling into a precise point in spacetime. If I try to imagine light propagation as a single phisical phenomena emanating from that spark-event, I must place its spacetime line in one frame, but neither M, M', nor M° or any other observer will ever agree on the final-detection physical-event of that propagation, meant as a unique and the same physical phenomenon with duration. I don't know what could mean for an observer-frame to own a "copy" or "portion" of a "propagation phenomena", but I believe this kind of physical phenomena, if exists, is not the same and unique phenomena for all inertial observers. It seems as a "splitted" or "replicated" propagation, or it is not at all a physical phenomena such as "a propagation phenomena" as for material objects.
Summarizing: We don't know what happens to the light between the two initial (spark) and final physical-detection events. The final detection events are separate events in spacetime. So, they aren't the "same" event (in the same sense the spark was). If they have a "cause" in some-thing propagating, this cause is not common: they are not causated by the same-unique propagation phenomena. We can only suppose they are causated by the unique spark event, but this is not useful to speak about what happens to the light between the two physical events. So, I am only sure that light propagation is not a physical duration phenomena in the classic sense. I can't say what it is (I hope somebody more expert will say!)
PS: only within a single frame an observer can think (but, to think is not to let "be") to light as some-thing propagating from the spark towards the mirror and after a while returning back to the detector (second event) and calculate the speed of such a propagation phenomena from the time lapsed between the two events, disinterested to the other observers.
This propagation phenomena is incompatible with a multiple-observer POV. We are not authorized to think light as some-thing propagating only due to the existence of a time lapse in our reference frame, as occurs for sound waves echo.

 

[Ibix]

2. There are NOT "reflections events" physically detectable, with measurable or demonstrable precise positions in spacetime.

What? Put a light meter with a clock synchronised to whatever frame at each mirror. It'll detect the light reflection event no trouble.

3. If we think light pulse associated to the spark-event as a "unique some-thing" flying or traveling towards the mirrors we have a paradox:

An event is a place and a time. For example, you getting out of bed this morning is an event - the place is your bed, the time is whenever you set your alarm. Thinking of "you getting out of bed" being something that could fly or travel somewhere is silly. So any apparent paradox following from this statement is due to you having a wrong idea of what an event is.

If I try to imagine light propagation as a single phisical phenomena emanating from that spark-event, I must place its spacetime line in one frame

Here you seem to misunderstand what a frame is. It's just a choice of coordinates, like a choice of which direction on a map corresponds to north. So your statement is like saying "if I try to imagine a road, I must draw it on one map, and then no other map will agree on the road". Or something like that.

A frame isn't a physical thing. It's literally just a choice of how you, personally, have chosen to synchronise clocks. How you choose to synchronise clocks has no bearing on what physically happens, and in no way renders any other choice of how to synchronise clocks invalid or inconsistent.

 

[Rap]

I am not speaking of the spark event, the sole event M, M' and M° agree in settling into a precise point in spacetime. If I try to imagine light propagation as a single phisical phenomena emanating from that spark-event, I must place its spacetime line in one frame, but neither M, M', nor M° or any other observer will ever agree on the final-detection physical-event of that propagation, meant as a unique and the same physical phenomenon with duration.

There are four beams - Two that bounce off the M-mirrors, two that bounce off M'-mirrors. There are two detection events - the simultaneous arrival of the light from the two M-mirrors, at the M-detector, and the simultaneous arrival of the light from the two M'-mirrors, at the M'-detector. Do we agree on that?

 

[Dale]

2. There are NOT "reflections events" physically detectable, with measurable or demonstrable precise positions in spacetime. Only the spark is such an "event", as is a physical event the observable response of a detector (chime + light blink). These are not imagineering, but doable phenomena.

The reflections are certainly valid events and, as mentioned above, are easily detectable. An event is a “point” in spacetime. Just like a single point may have diferent coordinates in different coordinate systems, so a single physical event may have different coordinates in different reference frames.

3. If we think light pulse associated to the spark-event as a "unique some-thing" flying or traveling towards the mirrors we have a paradox: the detection of the same "flying thing" occurs into three different points of M°'s spacetime frame (and from any else reference frame). Ergo, we cannot think that pulse as a unique thing propagating. Light speed is completely different from any other speed.

The light pulse from the spark forms a light cone. That is the set of all events in a frame such that $c^2(t-t_0)^2=(x-x_0)^2+(y-y_0)^2+(z-z_0)^2$. So it is not just one or even three events, it is an infinite number of events

 

[Alfredo Tifi]

What? Put a light meter with a clock synchronised to whatever frame at each mirror. It'll detect the light reflection event no trouble.

The trouble is the following: nobody was yet able to measure the one way travel time of flight and the light speed because this kind of time synchronisation requires apriori assumptions on the speed which ought to get measured.

An event is a place and a time. ... you having a wrong idea of what an event is.

Don't know who has a wrong idea of an event. Time and space in the event cone can only be flagged if something (e.g. an observable change) happens. If I remain on the bed and no alarm clock is ringing we can say I'm moving along time-type distance, but there are no events (assuming my heart does not beat, flat breath, no biochemical reaction etc.)

Here you seem to misunderstand what a frame is. It's just a choice of coordinates, like a choice of which direction on a map corresponds to north. So your statement is like saying "if I try to imagine a road, I must draw it on one map, and then no other map will agree on the road". Or something like that. A frame isn't a physical thing. It's literally just a choice of how you, personally, have chosen to synchronise clocks. How you choose to synchronise clocks has no bearing on what physically happens, and in no way renders any other choice of how to synchronise clocks invalid or inconsistent.

This is exactly what I mean with a frame. We need a frame of this kind to describe a duration-phenomenon. For normal-true duration phenomena different observers agree on the duration or time lapse between the initial and final events because these events are local in one frame at least (i.e. a frame can be chosen to make the two events separated by just a time-type interval). Then the different observers have an evidence to affirm these are one and the same phenomenon for everybody. They can agree the phenomenon occurs in a different frame where a cause and and effect are recognizable, a start and an end of a process, what we call duration. Light "physical phenomenon" is different: "never local". It connects events that are the fartest as possible. This makes a nonsense to speak of a "duration" for an hypotetical phenomenon which connects two events by a light-type interval in spacetime. They can't be local for any observer. Different observers have no evidence to affirm the inter-time between spark event and detection of mirror light are connected by the same phenomena which the other observers detect and describe.

 

[FactChecker]

The trouble is the following: nobody was yet able to measure the one way travel time of flight and the light speed because this kind of time synchronisation requires apriori assumptions on the speed which ought to get measured.

This is wrong. The very first estimate of the speed of light was obtained by observing a peculiarity in the orbit of moons of Jupiter (https://en.wikipedia.org/wiki/Rømer's_determination_of_the_speed_of_light). When Jupiter is closer to Earth, eclipses happen earlier than expected (if light travel was instantaneous) and when Jupiter is farther away, eclipses are later than expected. That's allowed an estimate of the speed of light. It is one-way travel time. And the only "apriori assumption" was to compare it with instantaneous travel. Since then, the speed of light has been measured with incredible accuracy.

 

[Dale]

nobody was yet able to measure the one way travel time of flight and the light speed because this kind of time synchronisation requires apriori assumptions on the speed

This is completely true, but does not contradict the point that @Ibix made. The conventionality of synchronization does not change the fact that the reflection is a valid event and can be detected and assigned valid coordinates in a given reference frame.

If I remain on the bed and no alarm clock is ringing we can say I'm moving along time-type distance, but there are no events (assuming my heart does not beat, flat breath, no biochemical reaction etc.

Do you have a professional scientific reference supporting this claim? It seems highly speculative to me.

Light "physical phenomenon" is different: "never local". It connects events that are the fartest as possible. This makes a nonsense to speak of a "duration" for an hypotetical phenomenon which connects two events by a light-type interval in spacetime.

This is essentially correct. The duration you speak of here is called “proper time”, and only applies for timelike worldlines. A light like worldline does not have a proper time.

However, a lightlike worldline can be parameterized by an affine parameter which separately identifies each event and also provides a unique ordering. Thus, different events on a light like worldline are still distinct “points” in spacetime even though the interval is 0.