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Trying to clear up some confusion (clock synchronization)

  1. Jul 23, 2015 #1
    I was trying to understand a few of the relativity basics that seem to have me confused. Below is a thought experiment and some questions, I would really appreciate any help to improve my understanding. Thanks

    Imagine a large, circular, tube like space station. Free to spin around the inside diameter of the space station is a large rigid ‘pointer’ (As in diagram below) So the set up is a bit like a compass.


    image.jpg

    There are two clocks at points A and points B, which are exactly 180 degrees apart. When the ends of the pointer line up exactly with points A and B, they do so simultaneously (as seen from the centre of the space station) and both clocks synchronise.

    Say the distance between points A and B is 360,000 km and assume 300,000 km per sec as the speed of light.

    Scenario 1

    The space station turns the pointer until the points align and clocks synchronise. A rocket ship travelling at 0.6c passes over points A and B in a straight line. As it passes over point A, (event 1) it starts a clock on the rocket ship and the time of the clock at Point A is taken by the space station.

    When the rocket ship passes over point B, (event 2) the clock on the rocket ship stops and the space station makes a note of the time on the clock at point B

    The rocket ships signals the elapsed time on its clock to the space station, which was 1.6 seconds. The space station then compares this with the time difference between the two clocks A and B, which was 2 seconds.

    So both the space station and the rocket ship agree that time on the rocket ship ran slower between the two events, as it was moving relative to the space station.

    However as there are no special frames of reference, then it is equally valid for the rocket ship to say it was at rest and the space station was moving. However even if this was the case, the clock on the rocket ship would still have shown less time pass between the two events then the two clocks on the space station. (Due to length contraction I am assuming?)

    Is this correct? If so I am confused as to how the rocket ship’s clock will always show less time between the two events than the space station.

    Scenario 2

    Remove the clocks, but this time when the pointer aligns at points A and B, A and B send light signals to each other, which are reflected back to a receiver at the centre point of the pointer. So each light source travels 360,000 km from its origin in one direction and 180,000 km back to the centre point.

    If the receiver at the centre point receives both light signals at the same time, (same time wrt to the centre point) then doesn’t this suggest that the one way speed of light is the same in both directions?

    Thanks.
     
  2. jcsd
  3. Jul 23, 2015 #2

    PeterDonis

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    Yes, but you have to be careful in interpreting what that means. See below.

    No, that's not correct. What is correct is that the difference between the reading on clock A at the first event, and the reading on clock B at the second event, would be greater than the difference in readings on the rocket ship's clock between those two events. But in the rocket's rest frame, clock B and clock A are not synchronized; clock B is ahead of clock A. So the difference in those two clock readings does not give the "elapsed time on the space station" according to the rocket's rest frame; you have to first correct for the lack of synchronization. Once you make that correction, you find that in the rocket's frame, the elapsed time on the space station between the two events is less than that on the rocket, by the appropriate time dilation factor.
     
  4. Jul 23, 2015 #3

    PeterDonis

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    Only if you adopt the simultaneity convention of the station's rest frame. Otherwise the signals are not emitted "at the same time".
     
  5. Jul 23, 2015 #4

    Mentz114

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    To reinforce what PeterDonis said, here are ST diagrams of the station frame and the rocket frame. If you count up the blobs ( clock ticks ) on the segments AB, CB of
    the red and green worldlines, you will see they are the same in both frames. The elapsed times on clocks is invariant.
    Also you can see the loss of simultaneity of the A, C clock synching.
    Station-frame.png

    rocket-frame.png
     
  6. Jul 23, 2015 #5
    I think this is the part that is confusing me. I (think!) I understand what you are saying, that from the rest frame of the rocket ship clocks A and B are not in sync. So adjusting for the rocket ships frame would reverse the results as measured by the rocket ship.

    But in my thought experiment, the rocket ship never gets to see clocks A and B, he just gets the elapsed time from the space station. So the time elapsed between A and B is always being measured in the rest frame of the space station, so would always be 2 seconds. And the clock on the rocket ship is always being measured by the rest frame of the rocket ship, so it would always measure 1.6 seconds. Those are the only two pieces of information given.

    So it seemed to me that this is due to the set up of the experiment, in that measuring the elapsed time with two clocks in one frame and one clock in the other frame would always lead to single clock measuring the shorter time. (Again assuming all measurements are taken in the respective rest frames.)
     
  7. Jul 23, 2015 #6
    Ah, so the clocks A and B, and the clock in the rocket ship always measure 2 seconds? (From their respective rest frames?)
     
  8. Jul 23, 2015 #7

    PAllen

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    There are 3 clocks, A, B, and C (rocket). Per the space station, A and B are in synch and run at the same rate, while C runs slower than A/B. Per the rocket, A is set well
    Per the rocket, the 2 seconds between A, B readings is due mostly to B being set well ahead of A, while A and B are each running slower than C. Per the space station, A and B are in synch, and the time difference is due to C running slow.

    So, as you've set it up, everyone agrees on each clock's reading of each event, but there are completely different explanations. The rocket does consider both A and B clocks to be running slow, but also way out of synch.

    [edit: Ok, you are not necessarily disagreeing with any of the above, but proposing the observation that when one (home) clock sees a series of moving clocks go by such that they are synchronized in the normal way between themselves, then the sequence of times observed on them will evolve faster than the home clock's rate. That is a correct general observation. The observed simultaneity shift more than offsets the slower moving clock rates, per the home clock.]
     
    Last edited: Jul 23, 2015
  9. Jul 23, 2015 #8

    Dale

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    Yes. Note that using two clocks vs one clock is not a symmetric situation.
     
  10. Jul 24, 2015 #9
    So if we adopt the simultaneity convention of the rest frame, then we will always measure the one way speed of light to be the same in both direction wrt to the rest frame. And as the laws of physics are the same in every frame, then why can't we deduce that the speed of light is the same in all directions?
     
  11. Jul 24, 2015 #10

    Dale

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    Because you assumed it to begin with. It doesn't make a lot of sense to assume something and then claim to have deduced it.
     
  12. Jul 24, 2015 #11
    Ok, thanks. I think it may just be termonology that is confusing me, but I am struggling with just what I am assuming and what is physically happening.

    For example if I take any two separate events that emit a light pulse, (arbitrary close together in space to avoid any causality issues) then there is at least one frame that will see these two events as simultaneous. If that frame of reference is equidistant between those two events (edit: and at rest wrt to those two events) and the light is received by that frame at the same time, then I can say the light took the same time from both events to reach that frame.

    By the laws of physics, the light traveled at the same speed in two different directions. So I would conclude from this outcome that light travels at the same speed independent of direction. At least those two directions.

    That seems like quite a simple conclusion so I am struggling to understand what is wrong with that conclusion?
     
  13. Jul 24, 2015 #12

    Dale

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    OK, I will walk through this piece by piece. There are several things that you say which are wrong, and several which are assumptions.

    OK

    I am not sure what you mean by "causality issues", but there simply isn't any way to avoid causality.

    Not necessarily. This is only true if they are spacelike separated. Events can be timelike or lightlike separated also, in which case there will not be any frame that sees them as simultaneous.

    So, let's take this first part as "if I take any two spacelike separated events that emit a light pulse then there is at least one frame that will see these two events as simultaneous"

    Note, you have already assumed that the speed of light is isotropic. Any time you see the words "at the same time" or "simultaneous" referring to separate events then you have already assumed a simultaneity convention and therefore you have assumed c.

    A frame of reference is a coordinate system which goes out to infinity, so it doesn't have a distance between it and anything. It is everywhere.

    You can have a receiver which is equidistant from those two events in that frame. Or you can place the origin of the frame equidistant from those two events. Or both.

    Events do not have a velocity, so you cannot be at rest or moving with respect to them. This is for the same reason that a point does not have a slope or a direction.

    Frames are coordinate systems, so they cannot receive light. I believe that you mean that a receiver at the origin receives the light at the same time.

    Same comment applies here.

    Let's rephrase this as: "If a receiver at the origin of that frame of reference is equidistant between those two events (edit: and at rest wrt to the reference frame) and the light is received by that receiver at the same time, then I can say the light took the same time from both events to reach that receiver."



    Nothing is wrong with it, but you already assumed it back when you said that the events were simultaneous. It is a restatement of your assumption, not a deduction. Btw, it is a perfectly reasonable assumption.
     
  14. Jul 24, 2015 #13
    Thanks, that helped. Particularly with my terminology which I know is sloppy sometimes

    Forget this part, I was just thinking if two events were spacelike separated by large cosmological distances then it make thing more difficult.

    Yes, I understand this, so was referring to space like separation.

    Yes, understand all three points. Again, just my sloppy terminology sorry.

    This for me is the key issue I am struggling with. The dictionary definition of 'Assume' is to accept as true without proof. If we take my original example, using the pointer to simultaneously emit light from points A and points B, that are received at the same time by the receiver in the centre of space station, this isn't an assumption in my mind it is a fact.

    Because points A and B are exactly 180 degrees apart and the pointer perfectly straight from tip to tip, and because the mechanisms that switch on the light pulse at either end has been tested to be exactly the same and the mirrors that reflect the light exactly placed etc. then it is impossible for the light pulses not to be emitted simultaneously wrt to the receiver at the centre of the space station.

    So if the receiver in the centre receives the light pulses at the exact same time this proves isotropy, it isn't an assumption. Or am I missing something? That to me is like saying if two people stand at opposite sides of the earth and each drop an apple, we are assuming gravity is isotropic. Where as the results would prove this. Does that make sense?
     
  15. Jul 24, 2015 #14

    PeterDonis

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    The light being emitted from A and B at the same events at which the tips pass those points, and arriving at the receiver at the same event, are facts. But the light being "simultaneously" emitted from A and B is not a fact; it's an assumption (or convention). See below.

    Yes, because you defined "simultaneously wrt to the receiver at the center of the space station" to mean the rest of the stuff you said (that light pulses emitted when the two tips pass points A and B will reach the receiver at the center at the same event). But there is nothing in the laws of physics that requires you to adopt that definition of simultaneity, and in fact that definition doesn't make sense for observers moving relative to the receiver at the center of the space station. (That's the point of Einstein's thought experiment with the train and the lightning flashes; it's also the point of our earlier discussion in this thread, where we saw that the only way to explain the rocket's elapsed time between passing A and B being less than the station's elapsed time between those two events, in the rocket's frame, was to realize that in the rocket's frame, the station clocks are not synchronized.)

    In other words, "simultaneity", unlike the facts about what triggers the emission of light pulses and the pulses arriving at the receiver at the same event, is not given solely by the laws of physics and direct observations; it requires, in addition, the adoption of a particular convention about how it is defined, and that convention is dependent on your state of motion (or, more generally, on your choice of coordinates). The laws of physics do not depend on your state of motion (or your choice of coordinates), so "simultaneity" can't be something that is given solely by the laws of physics. And since there is no way to measure the one-way speed of light without adopting a convention about how "simultaneity" is defined, the isotropy of the one-way speed of light (as opposed to the two-way speed of light) can never be solely a matter of testing the laws of physics experimentally. You always have to add in an assumption (or convention, if you like) about how "simultaneity" is defined.
     
  16. Jul 25, 2015 #15
    Thanks again for the reply. Just to clarify I am not disagreeing with anything you say and I understand that different frames would get different results. I am just finding it difficult to understand why my choice of convention prevents me from concluding that the one way speed of light is isotropic. Or in other words does light travel through space time at the same speed in all directions.

    Isn't fair to say that if I replace the light pulses at A and B with bullets fired from two alike guns, if I wanted to test that the one way speed of a bullet was isotropic I would still need to assume simultaneity of the when the guns fire. But if the bullets travelled at different speeds in different directions due to some property of space time, then I would be able to test for this as they would not arrive at the centre point at the same time.

    This is all I was trying to understand about light. If in my set up the light sources do not both arrive at the centre point at the same time then I could conclude that light didn't travel at the same speed in all directions. So my choice of convention only defines how the test is done, it doesn't (as far as I can understand it) effect the result, only to say that if light does travel through space time at the same speed in all directions then I should detect the light pulses at the centre at the same time.

    I suppose another way I could do this is to do each test independently. For example A could send a light pulse to B, which starts A's Clock. When B detects the light pulse, it takes a picture of A's clock. Then B does the same. As light entering the lens of the camera is travelling in the same direction as the light pules, if the times on both clocks read the same, then I could say that the light travelled in both directions in the same duration.
     
  17. Jul 25, 2015 #16

    Nugatory

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    You could conclude that, or you could conclude that the light left the two sources at different times. The problem is eliminating that second possibility without making the hidden assumption that the speed of light is isotropic.

    "A sends a light pulse to B which takes a picture of A's clock" is equivalent to A sending a light signal to B saying "This is what my clock read at the moment this signal was sent". However, that information is useless to the receiver unless the receiver knows how the time on his clock relates to the time on the sender's clock - and now we're back to needing a simultaneity convention.

    If we run the experiment as you describe (A sends message to B, B sends message back to A) and they are separated by a distance of one light second so the round-trip time is two seconds... A will send a message and two seconds later he will receive a photograph of B's clock showing some number. That lets A calculate the two-way speed of light, but the number on B's clock tells A nothing about the time taken by either one-way leg.
     
  18. Jul 25, 2015 #17

    Dale

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    Yes. That is the definition that I am using. The assumption that the one way speed of light is c is such a strong and important assumption that we call it a postulate. A postulate or an axiom is an assumption that is so fundamental and powerful that it needs to be highlighted.

    And here is the assumption. The pointer is not perfectly straight in all reference frames. It is also not perfectly straight under alternative synchronization procedures. That you assume it is straight is a very reasonable assumption, but it contains hidden within it the assumption of c (and also a specific reference frame).
     
  19. Jul 26, 2015 #18
    Thanks for the reply. In other posts of a similar nature I could understand this point, as the clock synchronisation was done sending light signals between two clocks or used slow transportation etc. But in my thought experiment it is done in a mechanical way. I can test for the straightness of the pointer, see when they are statically located at positions A and B that they trigger the light pulses in exactly the same way, that A and B are exactly the same distance away from the receiver in the middle of the space station etc etc.

    So I would have thought that if the light pulses are received at the same time, (allowing for some small process variance) that I could conclude that it took the same time for each light pulse to reach the middle. I know someone in another FOR moving wrt to me may see this differently, but if they did the same experiment in their rest frame, then they would get the same result.


    I don't know if it matters too much but my idea was that A sends a signal to B and when B receives the signal takes a photo of A's clock. B doesn't send a signal back to A. So A sends a signal and 1 second later B takes a picture of A's clock. As it would take another second for the light from A to reach B's lens, then I assumed B's photo would show a 2 second elapsed time. (As I understand it, the light needed to take the picture is travelling from A to B in this case, so it isn't a two way speed of light.)

    Then at some point later B would send a signal to A and A would carry out the same procedure. When done we can compare A's photo with B's photo and see if the clocks had elapsed the same duration.

    But I am not sure if that is how an image gets from A to the camera at but I thought it was an interesting idea.
     
  20. Jul 26, 2015 #19
    Ah ok, interesting. I hadn't thought about that. Although takes some thinking about. How can something not be straight in all reference frames? I would have thought if I take any two coordinates in space and draw a line between them, it has to be straight? At least in SR, I know GR may be different.

    But even so, I would have thought that I could ignore other reference frames as I am conducting the experiment in my rest frame. So I am struggling to understand what assumptions I am making.

    From my point of view (In the middle of the space station) I can prove the pointer is straight. I can prove that within some small process error that when the pointer locates at point A or B, that it takes the same amount of time to trigger the light source. (Again wrt to me) I can also measure accurately that point A and point B are 180 degrees apart and the same distance away from the centre.

    Now I am guessing that what you were kindly trying to explain to me is that all those measurements are using conventions, but they are same conventions we have used to define most of the laws of physics we subscribe to. So using those conventions, I don't see why I cant equally say that if the light pulses arrive at the same time to the receiver in the middle of the space station, that the one way speed of light is isotropic. And hence anyone using those same conventions in their rest frame will get the same result.

    I think my problem may be that I am trying to understand just what is invariant and what isn't and getting it wrong. I know if I light a match everyone sees the match light. Where and when it lights is relative.

    So I suppose I see the one way speed of light as an invariant, in so much as the physics behind the electromagnetic wave is the same is every FOR, it just that each FOR will measure it differently if the test is done outside of their rest frame. But within their rest frame, everyone should get the same result. Does that make sense?
     
  21. Jul 26, 2015 #20
    I thought this was interesting posted by bcrowell here https://www.physicsforums.com/threa...time-and-proper-distance.824882/#post-5179606

    So as I understand this, I can say that the ends of the pointers which come in contact with the clocks or initiate the light source as per my thought experiment are simultaneous wrt to the clocks/receiver in the middle as they are at rest wrt to the ends of the pointer.
     
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