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Speed of light constant

  1. Oct 4, 2012 #1
    Am a bit confused about the speed of light being constant, does this mean that whatever speed I am going at, up to and including the speed of light, I will always measure it as going 300000000 mts/sec faster than myself?
     
  2. jcsd
  3. Oct 4, 2012 #2

    Doc Al

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    Yes, you will always measure the speed of light to be c with respect to you, regardless of your motion with respect to anything else.
     
  4. Oct 4, 2012 #3
    Welcome to PF! :smile:

    Not necessarily so; and note that you can never reach the speed of light.

    If you set up a standard inertial reference system* in the lab, then you will next measure the speed of light in vacuum to be nearly 3E8 m/s wrt that reference system. That is a constant: it is the same in all directions, and independent of the motion of the source. Moreover, you don't need to be at rest in your reference system, and neither has the light detector to be at rest in that system.

    Many people (even teachers) confound that "constant" with a different kind of constancy, which is that the speed of light is invariant. With that is meant that if you measure light - even coming from the same source - with another standard reference system that is in uniform motion relative to the first, you will again find the same speed.

    Now, if you do what you seem to suggest - take your physical system out of your lab and in your car, and measure the one-way speed of entering light rays while you are driving - then you may not find the same value. However, after you re-synchronize your on-board clocks at that velocity, then you'll have again a standard reference system if you keep approximately an inertial course. Subsequently you'll find again the standard value.

    * For a simple explanation see section 1 of http://www.fourmilab.ch/etexts/einstein/specrel/www/
     
    Last edited: Oct 4, 2012
  5. Oct 4, 2012 #4

    Erland

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    Are you here talking about the car as an accelerated frame of reference?

    For if the car is moving with a constant velocity wrt the lab system, then, certainly, the speed of light will be measured to c inside the car.
     
  6. Oct 4, 2012 #5
    Not necessarily so: "clock synchronization" is for each velocity different, so that it isn't a standard reference system anymore (it is not auto-correcting). Therefore I stressed the importance of synchronization at that velocity.

    For others who perhaps not understand this, see: http://www.bartleby.com/173/9.html
     
    Last edited: Oct 4, 2012
  7. Oct 4, 2012 #6

    Erland

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    Do you mean that if we put two synchronized clocks at different places in a car at rest, and then accelerate the car up to a constant velocity, then, after the acceleration, the clocks are no longer synchronized, wrt an observer inside the car?
     
  8. Oct 4, 2012 #7

    Erland

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    Do you mean that if we put two synchronized clocks at different places in a car at rest, say one clock in the front seat and one in the back seat, and then accelerate the car up to a constant velocity, then, after the acceleration, the clocks are no longer synchronized, wrt an observer inside the car?
     
  9. Oct 4, 2012 #8
    Exactly.

    Edit: I doubt however that this can be detected with current technology; a car is too slow and too small.
     
    Last edited: Oct 4, 2012
  10. Oct 5, 2012 #9
    So does this mean if I am emitting the light it will always leave me at c whatever speed I am doing? If I am moving at say 1/2 c and measure the light to be leaving me at c how can someone who is not moving still measure that light at c?
    You mention clocks and I think I read somewhere that einstein said something about time changing how does that work?
     
  11. Oct 6, 2012 #10
    Yes, just like sound: the speed of the emitter does not affect the speed of propagation.
    (that is called in the first paper that I linked for you the "second postulate").
    I think that the question should be phrased the other way round (often a misunderstanding already exists in the question). Someone who is not moving will still measure that light at c, independent of the motion of the source; that is the second postulate, based on a well established theory of electromagnetism and radiation.
    So, the question to ask is: how can you, when you are moving, also measure that light at c? And that was indeed the question around 1900. In the introduction of the paper that I linked for you this was said to be "apparently irreconcilable" with the first. How much of it did you read?
    Probably you mean "time dilation". However, for one-way light speed, the first (and main!) change is a man-made change, as explained in the first section of the paper to which I gave you a link. He explains clock synchronisation. Did you understand it?

    And did you read my last remark about what happens when you accelerate with such a reference system to a new constant velocity (post #3)? Assuming that you use perfect clocks and that you can measure precisely enough: then without doing a new synchronisation you will not measure light leaving you at c, but at approximately* c-v for light that leaves you straight ahead. And that result is probably just what you would expect. :smile:


    *"approximately": still good approximation at 1% of c, but poor at 0.5 c. I now prepared a numeric example if someone is interested
     
    Last edited: Oct 6, 2012
  12. Oct 8, 2012 #11
    Have tried to read the link but it seems long winded and difficult to follow.
    I assume that inertial means moving at a constant speed.
    I am having problems with the fact that the speed of light is not dependant on the speed of the source, whereas normally the speed of something is dependant on its source i.e. if I fire a gun the speed of the bullet depends on the speed and direction of the gun although the speed is always the same relative to the gun. Someone standing still will measure the bullets speed as being different to that of the moving person holding the gun. With light I get the impression that both would measure it as moving at c, is this the case?
    As you keep talking about synchronising clocks does time change somehow relative to the person doing the measurement so changing their perception of speed.
     
  13. Oct 8, 2012 #12

    Doc Al

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    Yes, exactly.

    You might find the following discussion of special relativity easier to follow: Special Relativity. That's the first lecture in a series that covers all the usual relativistic effects, such as time dilation, length contraction, and the relativity of simultaneity.
     
  14. Oct 8, 2012 #13

    Erland

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    Suppose we have two inertial systems S1 and S2 and that S2 moves with velocity u wrt S1, -c<u<c. Also assume that an object O moves with a constant velocity v wrt S2, in a direction parallell to the direction of the motion between S1 och S2. Here -c<=v<=c, so O might be a photon, but it doesn't have to.

    Now what is the velocity w of O wrt S1?

    In classical physics, we have w= u+v. But this simple addition formula is invalid in SR, where we have the more complicated velocity addition formula:

    w=(u+v)/(1+uv/c^2).

    If u and v are small compared to c, then the denominator is close to 1, and then this almost reduces to the classical case. For small mundane velocities, the error in the classical formula is not detectable without very advanced instruments.

    It can be shown from this SR-formula that w<=c, with equality if and only if v=c or v=-c (we assumed that -c<u<c). So the relative velocity of a light source does not matter, light speed will be measured to c in all inertial systems (yeah yeah Harrylin, the clocks must be synchronized). And a velocity greater than c will never be measured.
     
  15. Oct 8, 2012 #14
    The speed of sound waves in the air, or water waves on the ocean don't have anything to do with the source. Generally, waves travel at a speed in the medium that depends on the characteristics of that medium, not on anything having to do with the source of the waves.

    The difference is that light waves have no medium except space, and space is the same regardless of your frame of reference.
     
  16. Oct 8, 2012 #15
    At first sight, that's a nice introduction of the basics. :smile:

    Regretfully some of it is misleading, partly because the author postpones the introduction of what it means to set up a reference system (incl. what "speed of light" here means) to after discussing the results of measurements with such a system.
    For example, compare "Light travels at c relative to the observer" just before giving a one-way light speed example (as if it's a True Measurement, see also the word "Truth" in the header!), with the Wikipedia article on that same topic:
    http://en.wikipedia.org/wiki/One-way_speed_of_light
     
  17. Oct 8, 2012 #16

    Doc Al

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    Sorry, harrylin, but I believe you are making things even more confusing for a beginner by focusing (as you often do) on one-way speed of light issues.
     
  18. Oct 8, 2012 #17
    One-way speed is the focus of the OP and I usually try to answer the question of the OP. But I fully agree that for a complete beginner it may be better to explain two-way speed of light measurements first (Fowler's lecture mixes them up however).

    Note: on top of that, that lecture spreads misinformation in the introduction concerning MMX, which only in the best case causes threads like https://www.physicsforums.com/showthread.php?t=631954.

    It may be a good idea to start a wiki kind of page with links to good web lectures for beginners. Make it a topic on the forum feedback? :smile:
     
    Last edited: Oct 8, 2012
  19. Oct 8, 2012 #18

    ghwellsjr

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    Einstein focused on the one-way speed of light issue in his 1905 paper introducing Special Relativity. His second postulate focuses on the one-way speed of light.

    Beginners need to understand that when we are talking about measuring the speed of light being equal to c, we are always talking measuring the round-trip speed of light. When we are talking about the one-way speed of light, we are not talking about a measurement but rather an arbitrary assignment, an arbitrary definition, an arbitrary stipulation, an arbitrary assumption, an arbitrary postulate, an arbitrary axiom, according to Einstein.

    Look at the OP's question:
    He's asking about measuring the one-way speed of light. We have to assume that he's asking about the speed of light in the direction that he is moving, not in the direction from where he is coming from, otherwise, he would have wondered if the light would be going slower than himself.

    If we point out to him that if he measures the round-trip speed of light by putting a mirror in front of him (like Einstein discussed in his 1905 paper), he will get the same answer that he will get if he does the same measurement in the opposite direction by putting the mirror behind him. This usually surprises beginners until they realize that it's the same measurement, the only difference being the two directions of light travel happen in the opposite order.

    Then they have to realize that it is impossible to know if it takes the same time for the light to traverse the distance to the mirror as it takes for the reflection to get back to the observer and this is where Einstein's arbitrary assignment of those two times being equal comes in. This is where we get the unmeasurable one-way speed of light being equal to the same value as the measured two-way speed of light--it's by assignment.

    This is the foundational basis of Einstein's argument for Special Relativity, both in his 1905 paper and in his 1920 book. I don't understand why we should hide this from beginners. It's how the theory began. I support harrylin's focus and if he hadn't been here prior to now, I would have been.
     
  20. Oct 8, 2012 #19
    wait so the speed of the light going to the mirror is not the same as the speed of the light being reflected from the mirror? Only that the total distance over the total time is the same? That kinda makes sense since some energy is lost due to reflecting but I always thought that the amplitude was the lost energy not the velocity
     
  21. Oct 8, 2012 #20

    Erland

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    No, no. Light speed is constant and the same in all directions. What the other posters talk about is just the difficulties in defining and measuring it.
     
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