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Relative Motion and Time Dependance on Velocity of Light

  1. Sep 9, 2008 #1
    The relative motion and the relative time of any inertial system to another one is in literature available (to me) subject to multiplication by a factor lambda = (1-v^2/c^2)^-1/2. It is found in the Lorentz transformation as well as STR. Is it possible to arrive at the same result and formulae without the 2nd postulate of STR? I note that some physicists do not go with the 2nd postulate of STR, (Lorentz contraction for Michelson Morley device arm) but use the Lorentz transformation (with speed of light as a max inside these formulae) in their arguments - how can this make sense?

    Where can I find a derivation of the Lorentz transformation with the arguments that are put forward?

    Is the progression of physics not hampered by the 'maximum possible speed of information transmission' being the speed of light? I mean - if I do not see an object travelling at c via it's light reflection -it does not mean that it is not there. Or if I go faster than the speed of light - even directly into the light - why am I going 'back into time'? (Even in relation to the light wave or 'light particle's' clock)? I do not get this - please help!
     
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  3. Sep 9, 2008 #2

    JesseM

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    That last comment is a little confusing, the 2nd postulate doesn't say anything about Lorentz contraction, rather it says that the speed of light is the same in all inertial frames. From the two postulates of SR you can derive the Lorentz transformation for relating the coordinates of one frame to another, and from that you can derive Lorentz contraction and time dilation.
    "Use the Lorentz transformation" to do what, exactly? To derive the length contraction and time dilation equations? Like I said, the usual sequence is to start from the two postulates of SR (that the laws of physics are the same in all inertial frames, and that the speed of light is c in all inertial frames), use them to derive the Lorentz transformation, and use the Lorentz transformation to derive the length contraction and time dilation equations.
    What do you mean "the arguments that are put forward"? Do you want a derivation of the Lorentz transformation from the two postulates?
    The coordinates of events in a given inertial frame don't depend on when you see them, if that's what you mean. Normally inertial frames are defined in terms of a hypothetical lattice of rulers and synchronized clocks at rest in that frame, with the coordinates of each event depending on local readings on this lattice so there is no problem with light delays. For example, if I see an explosion through my telescope when my clock reads t=15 seconds, and I see it happened right next to the 10 light-second marking on my ruler, and the clock sitting at that marking read t=5 seconds at the moment it happened, then I assign the event a time-coordinate of t=5 seconds, not t=15 seconds when I actually saw it.

    The one tricky part about using local readings on rulers and synchronized clocks is defining what it means for two clocks at different locations to be "synchronized"--Einstein suggested the convention that each observer defines the meaning of "synchronization" using the assumption that light travels at the same speed in all directions in their own frame, so that if I set off a flash at the midpoint of two clocks, I define them to be synchronized if they both read exactly the same time at the moment the light from the flash hits them. It is true that this is just a synchronization convention--one could define what it means for clocks to be "synchronized" in other ways--but what Einstein postulated was that the laws of physics would have the interesting property that they would obey exactly the same equations in the coordinate systems of different inertial observers who each synchronize their own clocks in this way, a property of the laws of physics known as "Lorentz-invariance" (because the coordinate systems of different observers are related to one another by the Lorentz transformation). So far, all investigation into the fundamental laws of physics has backed up the hypothesis that the laws of nature are always Lorentz-invariant.
    Different inertial frames define simultaneity differently, so that if you could send a message that was faster than light in one frame, there would be some other frames where the message would actually be received at an earlier time than it was sent! And since the first postulate of relativity is that the laws of physics work the same in all inertial frames, if it were possible to have messages arrive before they're sent in one frame, then this would have to be possible in all frames.

    The reason different frames disagree about simultaneity has to do with the synchronization convention I mentioned earlier. Suppose I am in a ship with clocks at the front and back, so I synchronize them in the ship's rest frame by setting off a flash at the midpoint of the ship, and setting the clocks to read the same time at the moment the light from the flash reaches each one. But if in your frame you observe the ship to be moving forward, then if you assume the light moves at the same speed in both directions in your frame, naturally that means that in your frame the light must reach the back clock before the front clock, since the back clock was moving towards the point where the flash was set off while the front clock was moving away from that point, so the light will take longer to catch up to the front clock. Here is a little youtube movie which illustrates this point. And if you want to know more about the relation between FTL and time travel, see this recent thread:

    https://www.physicsforums.com/showthread.php?t=252523
     
  4. Sep 10, 2008 #3
    Hi JesseM,

    Thanks for your reply.

    My question should have been : What does the Lorentz transformation look like when the 2nd postulate of STR is not used to derive it? All my available resources only provide it in that form. Or does it revert back to the Galilean Transformation?.

    I am just curious about other possible explanations for the MM experiment before I start working with all the outcomes of the 2nd postulate.
     
  5. Sep 10, 2008 #4

    atyy

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    If the second postulate is not stated, and you require that the laws of physics be the same in all reference frames moving at constant velocity relative to each other, then you will find that there are two possibilities: the Galilean transform and the Lorentz transform. The two possibilities are distinguished by stating whether or not there is an upper "speed limit". (JesseM has probably posted the details on some other thread.)

    It means that if you see an object, it was there some time ago, but it is not necessarily still there. It means that when we see galaxies that are far away, we are actually seeing them as they were a long time ago. So we can use that to infer what the universe was like in the past! (Those statements are roughly right, and when want to be precise, we need to be careful about what we mean by "time".)
     
  6. Sep 10, 2008 #5

    JesseM

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    If the only assumption you make is the first postulate that the laws of physics are the same in all inertial frames, then this would be compatible with either the Galilei transform or the Lorentz transform, so it isn't enough to derive a unique coordinate transformation.
    Well, technically all you need to explain the results of the MM experiment is the idea that there is a frame where light travels at the same speed in all directions, and the idea that any object moving at speed v in this frame will be shrunk by a factor of [tex]\sqrt{1 - v^2/c^2}[/tex] (as measured in this frame) in their direction of motion, you don't need time dilation at all.
     
  7. Sep 11, 2008 #6
    I have know systematically worked my problem with this theory back to my basic concern. I am now starting to ask the questions I should have asked when I was at school. Please bear with me!

    When we 'measure' the speed of light - how do we know it is actually a constant? How could we distinguish between making a relative or real measurement? If we define a coordinate system with spatial dimensions then that is we have defined. But our measuring sticks do not necessarily conform to the 'true' spatial dimensions - depending on what is happening to them. For this argument, let us also work just with a time basis that is constant (the clock used for the measurement is in the same 'physical' location on earth).

    Has the speed of light been physically tested vertically (radially with respect to the earth's centre)?
     
  8. Sep 11, 2008 #7

    atyy

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    Yes, if two people do two different experiments and get the same value for the speed of light, that of course doesn't mean the speed of light is constant. How do we even know that both of them used the same definition of length? Let's suppose they made their rulers of the same material, and compared the lengths at the same location, so they know they had the same definition of length. What if one of them did his experiment at a colder temperature, and actually his rulers were all shorter. But he miraculously got the same result because he used a pendulum clock and the length of the pendulum shrunk by exactly the right amount, and all the errors cancelled out. Then, of course, I wouldn't believe that the speed of light is constant.

    So to make sure that silly things like that don't happen, we should get the result using the same apparatus, and vary that velocity of that apparatus. That is essentially what Michelson and Morley did (or so I am told) - I don't know if they ensured that the temperature of their apparatus was the same when it was moving at different velocities!

    Anyway, there are lots of details in doing a good experiment, so one should indeed be skeptical. I haven't been skeptical enough, so I can't tell you the details. One good place to start is:

    http://www.math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html
    http://www.math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/measure_c.html
    http://www.math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html
     
    Last edited: Sep 11, 2008
  9. Sep 11, 2008 #8
  10. Sep 11, 2008 #9

    atyy

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    Yes, there are two questions.

    1) How do you measure the speed of light
    2) If you measure the speed of light with your apparatus moving at different velocities, do you get different answers? If an "aether" existed, then the answer would be yes. If the answer is no, and the "aether" is not detected, then we say the speed of light is constant.

    I thought you were asking about the constancy of the speed of light?
     
  11. Sep 11, 2008 #10
    Hi Atyy,

    Let's be playful here.

    I am putting a new theory forward:

    Light travels faster in outer space than closer to earth or any other planet. I am also suggesting that the closer it gets to a planet and the more mass the planet holds, the slower it will go.

    The first consequence is then that the planets are further than what we think.

    Please prove me wrong (solid thought is fine with me)!
     
  12. Sep 11, 2008 #11
    I forgot to add that we are considering speed of light in a vacuum - planets in our thought game do not have atmosphere.
     
  13. Sep 11, 2008 #12

    atyy

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    When you drop a ball to earth, the ball goes faster the closer it gets to earth. Why do you think light is different from a ball?
     
  14. Sep 11, 2008 #13

    atyy

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    That's presumptuous! What if your theory is right?
     
  15. Sep 11, 2008 #14
    I am really wondering about this - there must be a simple logic explanation to prove me wrong (I do not even know myself but will think about it tonight).

    Or how about we turn it around and say that light moves faster as it approaches bodies and slower when further.

    The gravity equations are not going to help us here, because either G could be somewhat 'out' or the 'mass' that is calculated for the other planets could be somewhat 'out'?
     
  16. Sep 11, 2008 #15
    If my 'theory' is right, then a lot of our physics is obviously wrong. But I am sure that someone has checked this - anybody that can help or refer me to the correct site?
     
  17. Sep 11, 2008 #16

    atyy

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    Actually, no theory can prove you wrong. Only an experiment can (but those experiments have already been done).

    Anyway, why do you say light moves faster as it approaches a massive body? Are you really using the ball analogy?
     
  18. Sep 11, 2008 #17
    You are right - theory cannot be wrong - only less useful.

    I am sincerely worried that us scientists are taking some values for granted without making sure that they were actually tested. I have studied the Focault and Fizaut technique, as well as the improved Michelson version and I think the values are useful. My sources does not say if the speed was tested in all the directions (including vertical relative to earth).

    I am trying to get someone to prove to me that the speed of light was either measured or deduced in a proper way to be constant through space (also far from a body with a big mass).

    I am not putting forward a theory - I thought the 'theory' might prompt someone to refer me to proper data.
     
  19. Sep 11, 2008 #18

    JesseM

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    You can read about a large number of experiments to test various predictions of relativity, including the speed of light, on this page. And the GPS navigation system depends on receivers on Earth very precisely calculating their position by using the arrival time of time-stamped signals from the satellites to calculate their distance to each satellite (and thus 'triangulate' the position of the receiver) under the assumption that the signals traveled at the speed of light (the time stamps which the satellites transmit are based on precise clocks on board the satellites which are designed to compensate for the effects of relativistic time dilation in both SR and GR so that the clocks remain synchronized in an Earth-centered frame of reference).
     
  20. Sep 11, 2008 #19

    atyy

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    Oops, sorry - I thought you were being playful (which is good) - it's definitely worth taking all the possibilities to their logical conclusion.

    I don't know if the speed has been tested vertically directly.

    However, we do have a theory that incorporates the constancy of the speed of light into a framework called Lorentz covariance. We also have an alternative theory in which the speed of light is not constant and uses a different framework called Galilean covariance. Lorentz and Galilean covariance have consequences for all particles, not just light, and both have been tested in all directions, and are continually being tested by high energy experiments at places like CERN and Fermi Lab. All the experiments so far have been consistent with Lorentz covariance, and have shown Galilean covariance to be wrong by many orders of magnitude.
    http://www2.slac.stanford.edu/vvc/

    We also have a theory called General Relativity which incorporates the constancy of the speed of light and the force of gravity. In this theory, light has weight, and can be bent by gravity. An introduction to the experiments supporting this theory is given by Rainer Weiss (one of our finest skeptics of General Relativity):
    http://www.aapt-doorway.org/TGRUTalks/Weiss/WeissTalk1of9.htm

    Another place to look at the use of relativity is the Global Positioning System (GPS), which uses the constancy of the speed of light as a principle (and which would certainly count as a vertical test). However, I don't know what the error bounds on the constancy of the speed of light are from GPS.
    http://www.emis.de/journals/LRG/Articles/lrr-2003-1/index.html

    However, learning General Relativity is difficult, and I'd suggest you just take a quick look at the articles on General Relativity, and concentrate on learning Special Relativity.
     
    Last edited: Sep 11, 2008
  21. Sep 11, 2008 #20

    russ_watters

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    It's pretty simple: we have spacecraft out there in the outer solar system and we know how much fuel they used to get there and calculated their trajectories with exquisite precision. We'd notice anything more than a tiny (a few parts per billion perhaps?) deviation in the speed of light.
     
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