Relativity of simultaneity and parthood?

[ghwellsjr]

Again, you're referring to pure mathematical calculations, I know this is a physics forum, but can you be more concrete perhaps. If my parts aren't simultaneous with me, that means that different observers may see me as a sum of different parts, depending on what my state is in one frame and what it is in another. Or for example, an part of an apple changes from being green to being brown (therefore the whole apple changes its color as a whole), will all observers agree on the state of the apple as a whole no matter what the reference frame is (and no matter if some parts exist before or later than others)?

No, but when you are talking about a small object like an apple, the possible ranges of differences in timing are fractions of a nanosecond. But if you were talking about the Earth and the moon, then it can make a substantial difference.

So, to sum up, will different observers see different states of the same event/state of the object depending on their reference frame?

I'm not sure what you're asking. Different observers see different things because they are in different places and the images or the signals of the events propagate to them differently depending on how far away they are from each event.

So, for example, when the men walked on the moon and were communicating with mission control, if a man on Earth spoke at the same time as a man on the moon spoke (according to their common rest frame), they would each hear the other one speaking later and not at the same time. Another IRF may not determine that they spoke at the same time, but it will still have the same delay from the time each one spoke until they heard the other one spoke, in terms of each man's own Proper Time.

Different IRF's will assign different coordinates to the same event. Different observers will see things differently from each other. But the different IRF's preserve what the different observers see and measure. In other words, whatever any observer sees or measures as determined by one IRF, they will see and measure identically in any other IRF.

This sounds really contradictory and non-objective.

Maybe it does but it's not. We have to deal with the reality of light propagation time and SR does it in a simple and consistent way. I doubt that you could improve on it.

 

[durant]

So, for example, when the men walked on the moon and were communicating with mission control, if a man on Earth spoke at the same time as a man on the moon spoke (according to their common rest frame), they would each hear the other one speaking later and not at the same time. Another IRF may not determine that they spoke at the same time, but it will still have the same delay from the time each one spoke until they heard the other one spoke, in terms of each man's own Proper Time.

So you mean like when one observer sees two thunders hitting the ground simultaneously, and another sees one hitting before another, the only thing that will differ between different frames will be the temporal order. The identity and the parts of each thunder will be identical in all inertial reference frames?

 

[ghwellsjr]

So you mean like when one observer sees two thunders hitting the ground simultaneously, and another sees one hitting before another, the only thing that will differ between different frames will be the temporal order. The identity and the parts of each thunder will be identical in all inertial reference frames?

What differs between frames is the assignment of coordinate values, both temporal and spatial, to each event. Think of all the events you described:

1) A thunder occurs somewhere
2) Another thunder occurs somewhere else at a later time
3) Observer 2 sees one of the thunders
4) Observer 1 sees both thunders
5) Observer 2 sees the other thunder

This is just one possible temporal order that would fit your description even if the observers were at rest with respect to each other. Although different IRFs can change a lot of coodinates, they can never change the Proper Times on the observers' clocks when they see the thunders.

 

[DevilsAvocado]

What areas of math are you using to work with these concepts?

For basic understanding, trigonometry would be sufficient, but I think you could do just fine with common sense and visualizing. After all, it’s just straight lines we’re talking about in Relativity of Simultaneity:

 

[DevilsAvocado]

Are all of the parts of the object simultaneous with the object itself?

Don’t want to hijack this thread, however I have a similar thought but in a different 'setup', that hopefully will answer your question (with a Yes in the video).

Relativity Paradox – RoS: Trains, Tunnels & Guillotines
https://www.physicsforums.com/showthread.php?t=689692

(Hope this is okay with PF policy...)