Relativity of simultaneity and parthood?

[durant]

This question may be kind of metaphysical, but I don't understand the relativity of simultaneity and its implications. If the temporal order of two distant events varies depending on the reference frame, are the parts of the event (or a temporal object) simultaneous with it in all frames of reference? What kind of events are relatively simultaneous? I know causality is preserved but is the identity of the thing (except its temporal relations to other stuff)?

 

[ghwellsjr]

This question may be kind of metaphysical, but I don't understand the relativity of simultaneity and its implications. If the temporal order of two distant events varies depending on the reference frame, are the parts of the event (or a temporal object) simultaneous with it in all frames of reference?

What parts of the event are you thinking of? Are you thinking of the four coordinates?

When we are talking about simultaneity, we only mean the temporal coordinates of two events both in the same Inertial Reference Frame. If they have the same value the two events are simultaneous in that frame. After applying the Lorentz Transformation to the coordinates of the two events to see what they are in another IRF moving at some speed with respect to the original IRF, we look again at the two temporal coordinates of the same two events in the second IRF. If they have the same value the two events are simultaneous in that IRF.

What kind of events are relatively simultaneous? I know causality is preserved but is the identity of the thing (except its temporal relations to other stuff)?

Does my above explanation answer your questions? If not, explain why not. Otherwise, I think you are reading more into this than is necessary.

 

[durant]

What parts of the event are you thinking of? Are you thinking of the four coordinates?

When we are talking about simultaneity, we only mean the temporal coordinates of two events both in the same Inertial Reference Frame. If they have the same value the two events are simultaneous in that frame. After applying the Lorentz Transformation to the coordinates of the two events to see what they are in another IRF moving at some speed with respect to the original IRF, we look again at the two temporal coordinates of the same two events in the second IRF. If they have the same value the two events are simultaneous in that IRF.

Does my above explanation answer your questions? If not, explain why not. Otherwise, I think you are reading more into this than is necessary.

By the parts I ment spatial parts, for instance 'my car at a time t' has spatial parts, tyres, doors etc. Does it have the same parts in all frames of reference? If i got it right only its temporal relations change when we change the frame of reference from which it is being observed. This is why I said it's more like a metaphysical question but I need an expert's opinion because it's confusing me. My basic question is, can a thing change its properites or parts when switching the frames of reference, or it simply changes its temporal coordinates.

 

[Dale]

This question may be kind of metaphysical, but I don't understand the relativity of simultaneity and its implications. If the temporal order of two distant events varies depending on the reference frame, are the parts of the event (or a temporal object) simultaneous with it in all frames of reference? What kind of events are relatively simultaneous? I know causality is preserved but is the identity of the thing (except its temporal relations to other stuff)?

I am not 100% sure that I understand what you are asking. However, it seems that you have some concern about an extended object and how the relativity of simultaneity affects extended objects.

If so, then I think that it is important to understand the geometry of relativity. The geometry of relativity consists of a 4 dimensional spacetime which includes the usual 3 dimensions of space and the usual 1 dimension of time, but together in a single 4 dimensional "manifold".

An "event" is a single point in spacetime, i.e. something that happens for only an instant and only a single location requiring 4 coordinates to identify. So there are no "parts" of an event. In a sense events are "parts" of other things.

A point particle exists at a specific location at any instant in time, so in spacetime this corresponds to a line, called a worldline. The different "parts" of a particle's worldline are different events along the worldline. E.g. the particle colliding with another particle could be one event etc.

An extended object exists at multiple locations at any instant in time, so in spacetime this corresponds to a "worldsheet" or "worldtube". Different simultaneity conventions consist of different ways of grouping the events that make up the worldsheet into events which occur at the same time. However, none of the physics depends on those groupings.

 

[ghwellsjr]

By the parts I ment spatial parts, for instance 'my car at a time t' has spatial parts, tyres, doors etc. Does it have the same parts in all frames of reference? If i got it right only its temporal relations change when we change the frame of reference from which it is being observed. This is why I sad it's more like a metaphysical question but I need an expert's opinion because it's confusing me.

Usually, when we talk about an object like a car in Special Relativity, we "collapse" the entire object into a single point because we are lazy and because it usually won't matter. However, if you want, you can describe the entire car with as many spatial points as you want and then use the LT to see what the coordinates of all those points look like in another IRF. So if you have a point for each of the four tyres and for each of the doors and for each corner of the car, then all those parts will have their own coordinates in a new IRF and some will have different temporal coordinates for the different parts, depending on which way the car is going in the new IRF (forward, sideways, up, etc.).

But if you think about it, you really need a bunch of points to describe a tyre or a door, don't you? Where does it end?

You can use this technique, for example, to show that the car will be length contracted as it moves forward but you only need to have two spatial points, one at the front and one at the rear to do this (again, because we are lazy and it really won't matter much to illustrate the point). You will, however, need to assign those two spatial points to multiple temporal points which results in a series of events for each spatial point. And then you need to select events that are simultaneous in the IRF where the car is moving to properly assess its Length Contraction.

 

[durant]

Usually, when we talk about an object like a car in Special Relativity, we "collapse" the entire object into a single point because we are lazy and because it usually won't matter. However, if you want, you can describe the entire car with as many spatial points as you want and then use the LT to see what the coordinates of all those points look like in another IRF. So if you have a point for each of the four tyres and for each of the doors and for each corner of the car, then all those parts will have their own coordinates in a new IRF and some will have different temporal coordinates for the different parts, depending on which way the car is going in the new IRF (forward, sideways, up, etc.).

But if you think about it, you really need a bunch of points to describe a tyre or a door, don't you? Where does it end?

You can use this technique, for example, to show that the car will be length contracted as it moves forward but you only need to have two points, one at the front and one at the rear to do this (again, because we are lazy and it really won't matter much to illustrate the point).

Okay, but it's still a neccessity that when speaking of a car, no matter in what reference frame, that it consists of its parts. Which implies that a car and all of its parts exist simultaneously in all reference frames. That doesn't change despite its parts having different coordinates, right? The Car may exist before Obama in one frame, and simultaneously in another frame, but its parts will exist simultaneously with it no matter what frame is in question. I hope I'm on the good track for understanding this.

 

[HallsofIvy]

What are "parts" of an event depends entirely upon how you recognize something as being a "part". We would need to know that before we can give a competent answer. For example, you talk about a "wheel" being part of a "car". If the car is going at .1 c in one direction and the wheel is going at .1 c in another direction, how long will this wheel be a part of this car?

 

[ghwellsjr]

I edited my previous response to cover this issue. Does it help?

 

[durant]

What are "parts" of an event depends entirely upon how you recognize something as being a "part". We would need to know that before we can give a competent answer. For example, you talk about a "wheel" being part of a "car". If the car is going at .1 c in one direction and the wheel is going at .1 c in another direction, how long will this wheel be a part of this car?

That's the change of conditions you're speaking, I was wondering about normal, earth-like conditions. The parts of the car together make up the car, so if it's consider an event or an object, its parts mus exist simultaneously with it in all frames of reference, cause otherwise it would be very illogical (not counter-intuitive, but illogical).

 

[durant]

I edited my previous response to cover this issue. Does it help?

I still don't understand some things, I'm not really familiar with relativity so this may be an obstacle. When we take the car as a whole, we take all of its spacetime points combined together, right? Which implies that all of its spatial parts must exist simultaneously, otherwise it may not be a car.

 

[Ookke]

I still don't understand some things, I'm not really familiar with relativity so this may be an obstacle. When we take the car as a whole, we take all of its spacetime points combined together, right? Which implies that all of its spatial parts must exist simultaneously, otherwise it may not be a car.

So is there a reference frame where car is missing steering wheel, another frame where car has no bumpers, etc. If that's what you want to ask, answer is no.

But let's make it a bit more complicated. Suppose that other parts of the car was constructed 1st of January 1970, but steering wheel was put into place day later. Now there exists a reference frame where car doesn't have steering wheel, and there exists a frame where car isn't even constructed yet, and another frame where the car is complete. All this is just because the car state (i.e. what's happening to the car right now) depends on the frame we choose.

Note that relative simultaneity is something that is only calculated, not something we could directly observe and verify. And there is certain criteria about which kind of events can be considered simultaneous and which cannot, so it's not completely arbitrary. Spacetime intervals (comparing time-like vs. space-like separated events) might be of some help understanding this http://en.wikipedia.org/wiki/Spacetime#Spacetime_intervals

 

[durant]

So is there a reference frame where car is missing steering wheel, another frame where car has no bumpers, etc. If that's what you want to ask, answer is no.

But let's make it a bit more complicated. Suppose that other parts of the car was constructed 1st of January 1970, but steering wheel was put into place day later. Now there exists a reference frame where car doesn't have steering wheel, and there exists a frame where car isn't even constructed yet, and another frame where the car is complete. All this is just because the car state (i.e. what's happening to the car right now) depends on the frame we choose.

Note that relative simultaneity is something that is only calculated, not something we could directly observe and verify. And there is certain criteria about which kind of events can be considered simultaneous and which cannot, so it's not completely arbitrary. Spacetime intervals (comparing time-like vs. space-like separated events) might be of some help understanding this http://en.wikipedia.org/wiki/Spacetime#Spacetime_intervals

Thanks for the answer and the link, just what I was looking for. :)

 

[PeterDonis]

Suppose that other parts of the car was constructed 1st of January 1970, but steering wheel was put into place day later. Now there exists a reference frame where car doesn't have steering wheel, and there exists a frame where car isn't even constructed yet, and another frame where the car is complete.

This is actually not correct--at least, what I think you mean by it is not correct. But rather than try to deconstruct it, let me state what I know to be correct, and then you can compare.

Here's what I know to be correct: suppose the car is 10 feet long, and suppose the steering wheel is attached at one end. (This is a special experimental car design .) Light travels at 1 foot per nanosecond, so suppose that, in the frame in which all parts of the car are at rest, the event of the steering wheel being attached happens 5 nanoseconds after the event(s) of the rest of the car being assembled.

In other words, we have two coordinate times of interest in this frame: t = 0, when all the pieces of the car except the steering wheel are assembled and are simultaneously at rest at x-coordinates from x = 0 (the steering wheel attachment point) to x = 10 feet; and t = + 5 nanoseconds, when the steering wheel is attached at x = 0. Call the event of the steering wheel being attached event S; call the event at t = 0, x = 0 (the assembly of the steering wheel attachment point) event O (the origin of the frame), and call the event at t = 0, x = 10 feet (the assembly of the far end of the car from the steering wheel) event E. Also we'll label the event at t = 0, x = 5 feet (the assembly of the midpoint of the car) event M.

Given the above, the following will be true:

(1) In the car's rest frame, events O and M and E are simultaneous, and event S happens after events O and M and E. (This should be obvious by inspection of the coordinate values I gave above.)

(2) There is a frame in which event S happens before event E; in other words, in this frame, the steering wheel gets attached before the far end of the car is assembled. (This follows from the fact that events S and E are spacelike separated: and *that* follows from the fact that I set up the time interval in the rest frame, 5 nanoseconds, to be smaller than the space interval, 10 feet, divided by c; in other words, the space interval is 10 light-nanoseconds, and 10 > 5.)

(3) There is also a frame in which event S is simultaneous with event E. (This follows easily from #1 and #2 and the continuity of the Lorentz transformation.)

(4) There is *no* frame in which event S happens before event O; in other words, there is no frame in which the steering wheel gets attached before its end of the car is assembled. (This follows from the fact that events O and S are timelike separated, which is obvious from the fact that in the car's rest frame both events have the same space coordinate, x = 0, but S's time coordinate is later than O's.) There is also no frame in which event S is simultaneous with event O, for the same reason.

(5) There is also *no* frame in which event S happens before, or is simultaneous with, event M. In other words, the attachment of the steering wheel *must* happen after the assembly of all of the front half of the car, in *any* frame. Only the assembly of the rear half of the car can have its time ordering relative to the attachment of the steering wheel changed by a change of frames. (This is because events S and M are null separated; a light ray emitted towards the front of the car at event M will pass through event S--it will be seen at the front of the car at the same instant that the steering wheel is attached.)

Note that all of the changes in time ordering of events in the above are only possible because the car is long enough that the time it takes light to travel its length is larger than the time between events O and S. In your formulation, that is many orders of magnitude from being true (unless the car is more than a light-day long ).

 

[Ookke]

This is actually not correct--at least, what I think you mean by it is not correct. But rather than try to deconstruct it, let me state what I know to be correct, and then you can compare.

Thanks, I appreaciate your elaborate answer. We can agree on 1-5, here my short descriptions why (in somewhat layman terms)
(1) agreed by coordinate values already
(2) and (3): since S and E are spacelike separated, there is always a frame where S is first, a frame where E is first, and a frame where S and E are simultaneous
(4) O and S happen in the same location, so there must be definite order that all frames agree
(5) the information (which travels at light speed) from M is already available for S at the time and place where S occurs, so M must be definitely first according to all frames

If we keep the event names and distances, but set S happen after one day, S will be timelike separated from O, M and E with good margin. Hopefully I got these right.

I still cannot see what is wrong in my original idea, maybe I could specify it a little. Actually my intuition was based on quite well known "Andromeda paradox" which is one of my favorites. Here is a link so anyone can check: http://en.wikipedia.org/wiki/Rietdijk–Putnam_argument

So let's have three observers close to each other, but far away from Earth, somewhere in huge Andromeda perhaps. At distances this large, even small differences in the relative speed cause significant difference in relative time. Let observer A move away from Earth at small speed, B be at rest relative to Earth, and C move towards Earth with small speed. Some math could be thrown in, but it doesn't help if the basic idea is wrong.

Now let's say that observer B is in sync with Earth time January 1 1970. A is moving away, so it's in sync with past Earth time, say December 31 1969. C is moving towards, so it's in sync with future Earth time, let that be January 2 1970.

Isn't it so that in A-frame the car is not even constructed yet, in B-frame the car is there but without steering wheel, and in C-frame the car is complete.

 

[PeterDonis]

If we keep the event names and distances, but set S happen after one day, S will be timelike separated from O, M and E with good margin.

Yes. The easiest way to think of it is to think of the past light cone of event S. With the numbers as I gave them (S is 5 nanoseconds after O in the car's rest frame), the past light cone of S includes O, M is on its boundary, and E is outside it. With your numbers (S is 1 day after O in the car's rest frame), all three of O, M, and E are way, way inside S's past light cone.

I still cannot see what is wrong in my original idea

What I said just now: if the car is of any normal size, with your numbers, all three of O, M, and E are way, way inside S's past light cone. But what you said in your original post only appeared to me to make sense if E is outside S's past light cone, as it is with my numbers.

Actually my intuition was based on quite well known "Andromeda paradox"

I'm aware of this "paradox", but I didn't realize you were trying to describe it; your original post appeared to me to be describing something quite different.

Isn't it so that in A-frame the car is not even constructed yet, in B-frame the car is there but without steering wheel, and in C-frame the car is complete.

Yes, I see what you're getting at now. To be precise, though, you need to specify that all three of these claims are true *at the event at which A, B, and C meet*. At least, that's how I think you are imagining the scenario, and how it's described in what you linked to.

Also, it's worth pointing out that, at the event at which A, B, and C meet, *none* of them can have any information yet about the car; that event is spacelike separated from all of the events involved in the car's construction. All three of A, B, and C will have to wait a couple million years (assuming they're all somewhere in the Andromeda galaxy) before any light signals from the car's construction reach them. This also means that none of A, B, and C, at the event at which they meet, can causally affect anything about the car's construction--or, indeed, anything for a couple million years later, along the car's worldline. By the time any light signal from any of A, B, and C reaches the car, it will be way, way out of warranty.

 

[Ookke]

By the time any light signal from any of A, B, and C reaches the car, it will be way, way out of warranty.

Definitely so . Yes I had Andromeda "paradox" in mind, but others can see only what is written. I'm glad this looks good now, thanks again.

 

[ghwellsjr]

I edited my previous response to cover this issue. Does it help?

I still don't understand some things, I'm not really familiar with relativity so this may be an obstacle. When we take the car as a whole, we take all of its spacetime points combined together, right? Which implies that all of its spatial parts must exist simultaneously, otherwise it may not be a car.

Here's the part of my previous response that I edited and I'd like to follow up on that now:

You can use this technique, for example, to show that the car will be length contracted as it moves forward but you only need to have two spatial points, one at the front and one at the rear to do this (again, because we are lazy and it really won't matter much to illustrate the point). You will, however, need to assign those two spatial points to multiple temporal points which results in a series of events for each spatial point. And then you need to select events that are simultaneous in the IRF where the car is moving to properly assess its Length Contraction.

Let's consider a car that is 10 feet long and stationary in an Inertial Reference Frame (IRF). (Don't confuse this car with the one Peter Donis proposed in an earlier post.) The front of the car shown in red is at a distance of 10 feet from the spatial origin and the rear shown in blue is at the spatial origin:

https://www.physicsforums.com/attachment.php?attachmentid=58389&stc=1&d=1367415325

Please be aware that there are solid parts of the car everywhere between the blue and red lines but if we filled them all in it would look like a solid block of color and make the next drawing harder to understand.

Now we want to see what this car looks like in a frame where it is traveling forward. To do that, we use the Lorentz Transformation process with a negative speed, in this case -0.6c, which will make the car go forward at 0.6c in this second IRF:

https://www.physicsforums.com/attachment.php?attachmentid=58390&stc=1&d=1367415325

I believe your concern is that the parts of the car, specifically the front and rear, are no longer simultaneous so how do we make sense of this? You are right, and the way we make sense is to view the car in the new frame with its own sense of simultaneity which is established by the horizontal axis lines. So we can see that at the coordinate time of 10 nanoseconds, the front of the car is at the coordinate distance of 14 feet while the rear of the car is at 6 feet making the car 8 feet long, contracted to 80% of its rest length.

As one justification for doing this, we can take those coordinates and transform them back into the original IRF and we see that they will be at the Coordinate (and Proper) Times of 2 nanoseconds for the front (red) end of the car and 8 nanoseconds for the rear (blue) end of the car. Even though these events are a different times, it won't matter for the measurement of the length of the car (with a ruler) in its stationary frame since the ends of the car are not moving relative to each other.

There are other justifications for establishing the contracted length of the car when it is moving and they all agree.

Does this make sense to you? Does it address the issue you are concerned about?

 

[durant]

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, but my main question was quite simply defined. Are all of the parts of the object simultaneous with the object itself? For instance, the body of my cat in some interval, is its head (as a part of the body) simultaneous with the body of my cat as a whole in all frames of reference. Hope you understand my question.

 

[ghwellsjr]

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, but my main question was quite simply defined. Are all of the parts of the object simultaneous with the object itself? For instance, the body of my cat in some interval, is its head (as a part of the body) simultaneous with the body of my cat as a whole in all frames of reference. Hope you understand my question.

Like all issues of simultaneity, until you define what you mean, there is no way to answer the question. I was giving you the way Einstein's Special Relativity defines simultaneity. If your cat is one foot long, it takes 2 nanoseconds for a light signal to propagate from one end of your cat to the other end and back. How can you know if the signal reached the other end after 1 nanosecond? In other words, if you put a clock at the front of your cat and another one at its rear, how would you set them so that you would be satisfied that they are synchronized?

 

[Nugatory]

Are all of the parts of the object simultaneous with the object itself? For instance, the body of my cat in some interval, is its head (as a part of the body) simultaneous with the body of my cat as a whole in all frames of reference. Hope you understand my question.

They are not, but the worst possible non-simultaneity is limited by the speed of light which is so large as to make this effect irrelevant at the scales that you're talking about.

Let's say that your cat decides to twitch its tail. Something happens in its brain, a signal travels down through its nervous system to the tail-twitching muscles, and these muscles contract. It takes about a millisecond or so for the signal to make it from brain to tail, so the "cat decides to twitch tail" event and the "muscles twitch" events are separated by a few tens of centimeters in space and a few milliseconds in time - they are NEVER simultaneous, and this has nothing to do with relativity.

Different observers moving at different speeds will report different times between the two events, but no observer will ever report that they are simultaneous, nor that the muscle twitch event happened before the "cat decides" event; thus, the cause must always precede the effect.

In order for relativity of simultaneity to mess up the order in which the events happen, they would have to separated so widely in space and so narrowly in time that a light signal couldn't make it from one to the other. In the cat/tail/twitch example, let's say the events are separated by one millisecond as far as we at rest relative to the cat are concerned. In one millisecond light travels about 300 kilometers. So if your cat was 300 kilometers long and its nervous system were still capable of passing a signal from one end to the other in less than a millisecond, then there would be observers who would report that the tail received the twitch signal before the brain sent it, and that would be an intolerable contradiction... and it's contradictions like this that lead us to say that relativity prohibits faster-than-light signalling.

 

[PeterDonis]

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

Simultaneity as a concept does not apply to objects; it applies to events. Events are points in spacetime. Objects are extended in space and time, so they consist of multiple points. Asking whether two points in spacetime--two events--are simultaneous makes sense; asking whether two collections of multiple points are simultaneous does not.

 

[bahamagreen]

I think I understand what the OP is asking...

Imagine observing the car at rest (both the car and observer at rest).
The car has many little clocks placed all over it and inside it.
The clocks are all set to read the same time for the observer.
The observer notes that all parts of the car have clocks that read the same time.
The observer concludes that "right now, all parts of this car are here".

A second observer is moving with respect to the car.
That observer will see some clocks on and within the car reading ahead and behind others.

A third observer moving in a different direct with respect to the car will see a different configuration of time differences on the clocks of the car.

All three observers get together and describe what parts of the car showed what different times on the clocks.

The OP is asking about how this comparison appears to suggest that one observer appears to have seen the front bumper of the car as being "younger" than the back bumper, but the other observer seems to have seen the front bumper as "older" than the back bumper. In effect they are not agreeing that they all saw all the parts of the car at the "same time".

For example. if the car is four wheel drive and floating at rest in open space with the first observer, he can mark the tires and put the car in gear and watch the marks on the tires rotate in synchrony. The second observer might observe that the front tires appeared to be advanced ahead of the rear because the mark was rotated further, and the third observer might argue that he saw the front tire mark falling behind the rear one.

So I think, fundamentally, the OP is noticing that different reference frames will not agree on the "present moment" of the front and rear tires - the parts of the car as an extended object seem to exist a little ahead or behind each other in time, depending on your frame of observation.
The metaphysical aspect of the question is stemming from the idea of an absolute reference frame that requires that all the car's extended parts should exist in the present moment for any and all arbitrary frames of reference.
Because relativity does not have that, from a metaphysical absolute perspective this makes the car and it's parts, and all extended objects, seem to be uncomfortably "loose" in time with some parts ahead and some parts behind, depending on the observation frame.

 

[PeterDonis]

So I think, fundamentally, the OP is noticing that different reference frames will not agree on the "present moment" of the front and rear tires

More precisely, they will not agree on which particular events on the worldlines of the front and rear tires are taking place at "the present moment".

the parts of the car as an extended object seem to exist a little ahead or behind each other in time, depending on your frame of observation.

How does what was just quoted above (with my clarification) imply this? What does "exist a little ahead or behind each other in time" mean?

Or to put it another way: try rephrasing what you said in the more precise terms I used, i.e., referring only to events on each part's worldline instead of the "parts" themselves. Does the rephrased version still sound like there's a problem?

 

[Dale]

my main question was quite simply defined. Are all of the parts of the object simultaneous with the object itself? For instance, the body of my cat in some interval, is its head (as a part of the body) simultaneous with the body of my cat as a whole in all frames of reference.

The problem is that "parts" is not something physical. You have complete freedom to define what you consider your "system" and you also have complete freedom to partition that system into whatever "parts" you like. So "parts" is a property of the analysis, not the physics.

The previous is the same in relativistic and pre-relativistic physics. The only additional nuance added in relativity is that you need to define the temporal as well as the spatial boundaries of each part, and that the shapes of those boundaries will change from frame to frame.

 

[bahamagreen]

What does "exist a little ahead or behind each other in time" mean?

I look at the clocks on the rear bumper and the front bumper and observe they indicate the same time. A second observer agrees with me on the rear bumper clock but reads the front bumper clock as a different time.
I would think that we saw the rear bumper as it was at the time it's clock indicated.
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.

I've not worked with worldlines, but 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) 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.
That's about as precise as I can go... I don't see it as a "problem"; I think I understand that an inertial reference frame for SR observations is just one of many... each acting as the "basis" for how the geometric results of the worldlines will be observed.

What I was meaning to point out is that this is a "problem" for a metaphysics that assumes extended objects (or parts, or separate points) must always be homogeneous in time from all perspectives.

 

[PeterDonis]

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.

 

[Dale]

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.

 

[bahamagreen]

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?

 

[PeterDonis]

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.

 

[ghwellsjr]

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.

 

[durant]

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)?

 

[ghwellsjr]

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.

 

[ash64449]

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?

 

[durant]

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.

 

[ghwellsjr]

But doesn't different observers disagree on the timing of the events based upon their state of motion?

Of course.