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Relativity of simultaneity and parthood?

  1. Apr 30, 2013 #1
    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)?
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  3. Apr 30, 2013 #2


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    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.
  4. Apr 30, 2013 #3
    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.
  5. Apr 30, 2013 #4


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    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.
  6. Apr 30, 2013 #5


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    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.
    Last edited: Apr 30, 2013
  7. Apr 30, 2013 #6

    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.
  8. Apr 30, 2013 #7


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    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?
  9. Apr 30, 2013 #8


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    I edited my previous response to cover this issue. Does it help?
  10. Apr 30, 2013 #9
    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).
  11. Apr 30, 2013 #10
    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.
  12. Apr 30, 2013 #11
    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
  13. Apr 30, 2013 #12

    Thanks for the answer and the link, just what I was looking for. :)
  14. Apr 30, 2013 #13


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    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 :wink:.) 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 :wink:).
    Last edited: Apr 30, 2013
  15. Apr 30, 2013 #14
    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.
  16. Apr 30, 2013 #15


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    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.

    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.

    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.

    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. :wink:
  17. Apr 30, 2013 #16
    Definitely so :smile:. Yes I had Andromeda "paradox" in mind, but others can see only what is written. I'm glad this looks good now, thanks again.
  18. May 1, 2013 #17


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

    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:


    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:


    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?
  19. May 1, 2013 #18
    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.
  20. May 1, 2013 #19


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    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?
  21. May 1, 2013 #20


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    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.
    Last edited: May 1, 2013
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