Relativity of simultaneity and parthood?

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  • #26
PeterDonis
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I look at the clocks on the rear bumper and the front bumper and observe they indicate the same time.
How do you look at them? And when (by your own clock)?

A second observer agrees with me on the rear bumper clock but reads the front bumper clock as a different time.
How does he look at them? And when (by his clock)?

Note, particularly, that for both observers, what you are thinking of as "the object at some instant of time" is *not* what you actually see. The light arriving at your location at some particular instant of time by your clock was emitted by the object at *different* instants of time by your clock. You do not see a "snapshot" of the object at a single "instant of time" by your clock; you have to *construct* that "snapshot" from observations that you make at different times by your clock.

I would think that we saw the rear bumper as it was at the time it's clock indicated.
Sure, and that will be as it was one light-travel time ago by your clock (assuming that your clock and the bumper's clock are synchronized). But note that if you and the second observer are in relative motion (which I assume you meant), it is impossible for *both* of your clocks to be synchronized with the rear bumper's clock; at least one of your clocks must be ticking at a different rate than the rear bumper's clock. This means you have to be really careful interpreting what the clock readings you see "mean".

I would think that we saw the front bumper as it was at different times, one ahead of the other by the difference between the two different times shown on the clocks.
Here it gets even more important to be precise. Note that for you and the second observer to see different clock readings from the front bumper, you must be spatially separated; if you were spatially co-located at the instant you observed the front bumper, you would have to see the *same* clock reading (because you would both have to be observing the same light beam from the front bumper). Since you are spatially separated, you can see different clock readings from the front bumper even if you both are at rest relative to each other; your spatial separation means the light travel time to you from the front bumper is different than the light travel time to the second observer. So in order to interpret what you are seeing, you have to separate this effect from the effect of your relative motion.

I've not worked with worldlines
I strongly advise becoming familiar with them; it's much harder to correctly analyze relativity scenarios if you don't understand them.

I would think that the nature of a particular inertial rest frame defines a kind of local plane through the spacetime (a certain orientation of the plane). The geometric result is intersecting the plane through multiple worldlines (parts of things, or multiple things)
Yes. The "local plane" is often called a surface of simultaneity.

determining time sequence - another orientation would "cut" the worldlines at a different "angle" and present a different sequence.
As long as the events in question are spacelike separated, yes. Changing frames can't change the time ordering of events along a single worldline, and it can't change the time ordering of events on different worldlines that are timelike or null separated (i.e., one event is within the other event's past or future light cone, so they can be causally connected).

So before you can even figure out what a change of frame can do to the time ordering of events, you have to figure out how they are causally related to each other (i.e., are they timelike, null, or spacelike separated). But if you know how they are causally related to each other, you can figure out *all* of the physics; you don't even have to go through the extra step of figuring out the time ordering in a particular frame. The main reason we still talk about inertial frames, IMO, is interpretation: it helps to put the physics in terms we can grasp intuitively.

I suppose this would also determine the shape configuration, too.
Yes, in the sense that the 3-D geometric shape of the intersection of an object's "world tube" (the set of all worldlines of points within the object) with a particular surface of simultaneity can depend on the orientation of the surface of simultaneity (i.e., on the state of motion of the inertial frame that defines the surface of simultaneity). But note, once again, that because of light travel time delays, this "shape" will *not* in general be the same as the shape that you actually see when you observe the object. Google "Penrose-Terrell rotation" to see an example of how this works.
 
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The geometric result is intersecting the plane through multiple worldlines (parts of things, or multiple things) determining time sequence - another orientation would "cut" the worldlines at a different "angle" and present a different sequence. I suppose this would also determine the shape configuration, too.
Yes. If you imagine a worldsheet which is a rectangle in some frame where it is parallel to the time axis then you will have a worldsheet which is a parallelogram in other frames where it is not parallel to the time axis.
 
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The reason I specified that the car is covered in clocks was so:

The local observer at rest wrt to car would see all the clocks set to the same time.
Consider that a given. He can make his observation during any time period.

This allows the second observer moving wrt the car to report a difference between two clocks - it does not matter what the specific times are.

Just to be clear, if both observers' record keeping periods are long enough, one may imagine that they will find one clock reading that matches - even if the reading by the second observer occurs "long after" the reading by the first observer due to propagation.

The point is that they compare notes later and find a match and a discrepancy (probably one plane of matches in a whole car volume of discrepancies). The match indicates that these readings are of that car clock as it was indicating locally at that time.

For the first observer, all his readings match each other, indicating the same time.
For the second observer, the different readings indicate different local times on the clocks of the car. Since the readings of both observers were performed in what each would consider a single moment, the conclusion they must draw is that they observed different "times" of the car, except for the plain of the car in which their readings of the car clocks matched.

Using clocks, and especially letting them show the same time for one observer but not another may be misleading (might make one think the synchronized clock IRF is the "right"one). Think of it this way...

Instead of clocks with faces, replace them with clocks that change geometric shape through time. This makes it more clear what observing the car's parts at different "times" means, because one observer can observe the differential change in shapes across the body of the car while the other sees the same pattern of shapes throughout - it is more clear that one or the other is seeing what the other has already observed or is about to observe... not just the whole car, but the different parts of the car - they are not seeing the same parts of the same car wrt time.

That said, Peter, your question about "How is he seeing them?" seems trivial at first, but as I consider it there may be something here... the "snapshot" term is a photography term. One way to "look" at something is to take a picture (snapshot), and another way is to just use your eyes. I'm wondering about a potential difference between them.
The snapshot is a brief timed exposure, but the eyes are receiving an integrating constant input. The data captured by the snapshot represents a plane of light (maybe a fat plane) whose thickness may be less than the object being observed... whereas observation by eye (or long snapshot exposure) may be longer than the light time line of sight depth of the same object. I wonder if in that case there is a difference between the fast image and the slow image with respect to what is going on at the near and far ends of the object?

As far as "By whose clock?", I don't think it matters in this case - the clocks are on the car and the observations are of the times indicated on the clocks.

I think both observers can get at least one like clock reading - they may each have to take a long period of readings... if the local observer reads the back bumper as 15:00, then there is a period for the second observer within which that reading can also be observed, he may just have to have started later (both observers are within each others light cones).

What areas of math are you using to work with these concepts?
 
  • #29
PeterDonis
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The local observer at rest wrt to car would see all the clocks set to the same time.
Only if you define "see" to mean he *constructs* this. It is *not* what he actually sees, as in the light actually reaching him at a given instant by his own clock.

For the first observer, all his readings match each other, indicating the same time.
Only if you specify *which* readings match each other. Once again, the clock readings the first observer actually sees (as in, the light signals actually reaching the first observer at a given instant by his own clock) are *not* all the same. He has to construct a surface of simultaneity in which all the clock readings match "at the same time" by correcting for the light travel time from different parts of the object to him.

For the second observer, the different readings indicate different local times on the clocks of the car.
Different compared to what? The clock readings actually seen by either observer at a given instant (as in, the light signals actually reaching the observer at a given instant) are different simply because of light travel time delay. Each observer has to correct for that; and each observer will have to correct *differently*. Once again, there are two reasons for the difference: the observers can be spatially separated, and they can be in relative motion.

Since the readings of both observers were performed in what each would consider a single moment, the conclusion they must draw is that they observed different "times" of the car
*If* they correct their actual observations for light travel time delay (as above), *and* if they interpret the resulting readings that way.

except for the plain of the car in which their readings of the car clocks matched.
There won't be any such plane if they are in relative motion. There will be one instant by each observer's clock in which what they actually see (as in, the light signals actually reaching them at that instant) is the same; this is the instant at which they pass each other. But they construct *different* simultaneity planes even at this instant, because they have to correct differently for light travel time delay due to their relative motion.

As I said before, all this gets a lot clearer if you draw a spacetime diagram of the scenario. If you don't currently know how to do this, I strongly recommend learning how. IMO it really helps to understand what's going on in scenarios like this.

Instead of clocks with faces, replace them with clocks that change geometric shape through time.
I think we're in agreement on what "clock readings" mean, and how they can change from event to event along the worldline of a given object (or part of an object).

the "snapshot" term is a photography term.
I shouldn't have used that term, since the way I was using it is not really the right way. You're using in the right way in what follows, so let me correct my own terminology. Instead of the word "snapshot" for what I was talking about, I'll use the word "slice". A "slice" of an object is the intersection of its world-tube (i.e., the set of worldlines of all parts of the object) with a particular 3-D surface of simultaneity; i.e., it is the set of events within that object that happen at some particular coordinate time according to a particular inertial frame.

The snapshot is a brief timed exposure, but the eyes are receiving an integrating constant input.
But the input received by the eyes is just a series of snapshots (where now I'm using that word in your sense, the proper sense). What the brain does with the data provided by the series of snapshots is a separate question, and it's not a question of physics, it's a question of neurobiology and cognitive science. The physics of light reaching the eye is prior to all that, and IMO we should be very careful not to confuse them.

The data captured by the snapshot represents a plane of light (maybe a fat plane)
Actually the usual way a "snapshot" is modeled is as a sphere (or section of a sphere). More precisely, it's the intersection of a 2-sphere (or section of a sphere) in space at a given instant of time in some frame, with a set of light rays that just reach that 2-sphere at that instant of time in the same frame.

For example, think of the intersection of a set of light rays that all pass through the focal point of your eyeball with your retina (which is more or less a section of a sphere). Ideally, the focal point of the light rays is the center of the sphere, so light rays that all pass through the focal point at some instant in the retina's rest frame will all reach the retina at the same instant in the retina's rest frame (the second instant will be delayed by the light travel time from the focal point to the retina).

So over time, the data collected by the eye is a series of snapshots, taken at a series of instants in the retina's rest frame. For an idealized thought experiment, we can think of this series as continuous (i.e., the series of instants is continuous), but of course a real retina does not take continuous snapshots; it takes a snapshot roughly once every 20 ms or so (the recovery time of the neurons in the optic nerve, IIRC--i.e., the time it takes for a neuron to be ready to fire again after it has fired once).

whose thickness may be less than the object being observed
A snapshot, as defined above, doesn't have a "thickness", if by that you mean a thickness in time (or in space). It is taken at a single instant.

I wonder if in that case there is a difference between the fast image and the slow image with respect to what is going on at the near and far ends of the object?
I don't think so; or rather, I think that if we're going to talk about how we actually consciously perceive objects, we are no longer talking about physics but about neurobiology and cognitive science, as above. The physics itself is as I described it above.
 
  • #30
ghwellsjr
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My primary concern is about objects at rest relative to the earth. I'm not familiar with Lorentizan transformations so I don't understand them...
Unless you are willing to understand the Lorentz Transformation process, you're never going to make sense out of Special Relativity. And it's not hard, especially if you use the standard configuration with units where c=1 which is what I always do. The concept is simple, just a little bit of algebra, but it's cumbersome unless you have an automated process to do all the work for you.
 
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But does this mean that different observers can have different descriptions about the same event (regarding what it is, what parts is it made of)? Doesn't that contradict the causality preservation where all the timelike events are the same for all observers (and their temporal order)?
 
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ghwellsjr
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But does this mean that different observers can have different descriptions about the same event (regarding what it is, what parts is it made of)? Doesn't that contradict the causality preservation where all the timelike events are the same for all observers (and their temporal order)?
The Lorentz Transformation process takes care of all the coordinates for all events correctly for you when you go from one Inertial Reference Frame to another and it preserves everything that every observer can see or measure. No exceptions.
 
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The Lorentz Transformation process takes care of all the coordinates for all events correctly for you when you go from one Inertial Reference Frame to another and it preserves everything that every observer can see or measure. No exceptions.
But doesn't different observers disagree on the timing of the events based upon their state of motion?
 
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The Lorentz Transformation process takes care of all the coordinates for all events correctly for you when you go from one Inertial Reference Frame to another and it preserves everything that every observer can see or measure. No exceptions.
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)?

So, to sum up, will different observers see different states of the same event/state of the object depending on their reference frame? This sounds really contradictory and non-objective.
 
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ghwellsjr
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But doesn't different observers disagree on the timing of the events based upon their state of motion?
Of course.
 
  • #36
ghwellsjr
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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.
 
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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?
 
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ghwellsjr
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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.
 
  • #39
DevilsAvocado
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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:

Relativity_of_Simultaneity_Animation.gif
 
  • #40
DevilsAvocado
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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...)
 

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