B Resolving the Relativity of Simultaneity: A Geometric Approach

[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.

 

[Bartolomeo]

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.

Australian physicist Leo Karlov showed, that Roemer actually measured two way speed. L. Karlov. Australian Journal of Physics, 23, 1970, p. 243-253
Good book by Max Jammer
https://www.amazon.com/dp/0801884225/?tag=pfamazon01-20

 

[Ibix]

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.

True but irrelevant. I can assign coordinates; that they are based on a convention is not problematic. Arguing otherwise is like doubting the existence of Berlin just because it's a convention that latitude and longitude are measured with respect to geographic north rather than magnetic north.

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.)

You seem to me to be using the common english definition of "event" - something happening. The physics definition is simply a time and a place. There are events (identifiable places and times) along your worldline whether you are doing anything or not.

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).

No. Two events are separated by a time-like interval or they are not. That is a frame-independent fact. In fact, time-like intervals can be measured with a single clock, so no synchronisation convention is needed in this case.

They can agree the phenomenon occurs in a different frame

Phenomena occur. They do not occur in a frame. A frame is a choice of coordinates to label events. Saying something occurs in a frame is like saying a road is on a map. No. The road is on the ground. It may be represented on paper, and it may be represented in many different ways depending on the map system used. Going back to the point I was criticising, you were insisting that a worldline belongs to a frame. That is exactly analogous to insisting that the road belongs to one map and not another.

Light "physical phenomenon" is different: "never local".

True. Although typically this would be phrased as "there is no rest frame for light".

It connects events that are the fartest as possible.

Not true. Events can easily be far enough apart that light cannot cross between them. Then they can be joined by a ruler in some particular state of motion.

This makes a nonsense to speak of a "duration" for an hypotetical phenomenon which connects two events by a light-type interval in spacetime.

Not nonsense - merely that it must include a convention somewhere. It's like saying I was driving at 30mph due north. A speed without reference to something is nonsense. But as long as we've agreed the convention that speeds are measured relative to the local Earth's surface then my velocity is perfectly well defined. So it's not nonsense - just dependent on a convention.

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.

The thing you say there is no way to do is exactly what the Lorentz transforms allow you to do - relate one set of conventional measurements to another set.

 

[Ibix]

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.

My understanding of this experiment is that Romer was essentially using Io as a clock and attributing its apparent rate change to light travel time over varying distance. In relativistic terms, this assumes the Einstein synchronisation convention, which is to say it assumes that the speed of light is isotropic. So it's a measure of the two-way speed of light, not the one-way speed.

Edit: I hadn't seen @Bartolomeo’s post and haven't read Karlov's paper.

 

[Rap]

This arguing over philosophy and the meaning of words is pointless. Tie down the setup in the minds of both sides. If that cannot be done, aguing over results is pointless. Then step by step, go thru the sequence of events. If there is any disagreement, that's where to focus attention.

So I ask again:

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?

 

[Ibix]

Tie down the setup in the minds of both sides.

Which has to be done by words - so some discussion of meanings where people apparently disagree is in order, I think.

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?

Agreed. I'd tend to say pulses rather than beams to keep in mind that they're short flashes of light, but I mightvjust be being awkward.

 

[Rap]

Which has to be done by words - so some discussion of meanings where people apparently disagree is in order, I think.
Agreed. I'd tend to say pulses rather than beams to keep in mind that they're short flashes of light, but I mightvjust be being awkward.

I agree on both counts, but the bottom line is that this is a problem in spacetime geometry, pure and simple. It’s a geometry problem, and our words should be constrained by that fact.

I don’t think you were being awkward, I think you were doing a better job than I was in paring the problem down to its geometric essentials. We lose nothing by considering the light emitted by the spark to be a set of light-speed point particles (“short flashes”) emitted in all directions at the spark event and then choosing a minimal set which serve to specify the essence of the situation so we can discuss and resolve it.

I think the problem is that Alfredo Tiki does not understand this and so we have to go through the problem step-by-step until we come to a disagreement and then we can focus on resolving it. My post was an attempt to do that. If he can agree on the setup then we take the next step. If not, then there’s no point in going any further.