Resolving the Relativity of Simultaneity: A Geometric Approach

[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
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[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.