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Is the speed of light infinite?

  1. Mar 20, 2013 #1
    I have been reading up on time dilation a bit this morning, and for the first time, I think it really clicked. Its raised some questions that I haven't seen answered anywhere, so I was hoping someone here could help.

    As I understand it, and please correct me if I am wrong, the only thing that affects time is our speed relative to other objects. This is why a man traveling much faster will age less from his point of view than he will to others. This is also why you can't exceed the speed of light - because if you get close to it, time slows down for you. You would appear to be traveling near the speed of light to an earthly observer, but would be traveling "slower" than you perceive yourself to be traveling.

    This is where I see tons of problems, and I assume its because I don't grasp the concept.

    If we cannot ever reach the speed of light, then isn't the speed of light faster than infinite speed? If I have the means to move some mass as fast as I wanted, time would only keep passing slower and slower, and the SOL would always be faster. This means a particle with mass can move infinitely fast, but still be outrun by light, doesn't it?


    1. How can someone 'approach the speed of light'? If a man moving 99% SOL, according to an observer on Earth, really would age more (and I know this has been proven), then less time really would pass for the traveler. This means that the traveler could, in principal, know that he is traveling slower than his observer on Earth measures. Well, if we use the traveler as the stationary frame of reference, couldn't this exact same effect happen if someone on his rocket built a new rocket, and launched off of it going the same direction, with a velocity proportional to the first rocket leaving Earth? Could this go on forever, with each new rocket observing his own speed to be the same as the first rocket observed his to be? Would any of these velocities be any closer to the speed of light than the other? If not, then how is it that we give the SOL a value at all?

      Or is the SOL that we perceive the same SOL that a person moving 100,000,000 km/h would perceive? If that's the case, then I think I get it. But, this would mean that it isn't really a constant, just a constant relative to every possible observer. Wait a minute.. is that sort of the point of relativity?
     
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  3. Mar 20, 2013 #2

    phinds

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    Infinite? No, that's just silly. The speed of light is c.

    If you are sitting on earth and a beam of light hits you from the sun, it is traveling at c.

    If you are sitting on earth and a beam of light that was emitted by a spaceship traveling away from Earth at 99% of c hits you, it will be traveling at c (and it will be red-shifted in frequency)

    If you are sitting on earth and a beam of light that was emitted by a spaceship traveling towards Earth at 99% of c hits you, it will be traveling at c (and it will be blue-shifted in frequency)

    Nothing with mass can travel at c.

    In your own time frame you age exactly the same regardless of your motion, not more, not less. If you travel along a different world-line than someone else (say you're on a spaceship moving away from Earth and then you come back) then you may age differently than someone who was on Earth the whole time, but that is NOT because your biological processes are different than his, it's just because you were on a different world-line.

    Yes, this is very weird but it is what it is. It seems weird to us only because our normal lives and senses are not in a realm where it happens to us (in a noticeable way).
     
  4. Mar 20, 2013 #3

    PeterDonis

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    Basically this is true (at least, it's true as long as gravity is not present or can be neglected, but I assume that case is what you meant to ask about). However, you have to have the proper meaning for "affects time". See below.

    This is where it becomes important to be precise. "Age less" is ambiguous as it stands. You never perceive yourself to be aging any differently; to you, other people that are moving fast relative to you appear to age more slowly, but to those other people, *you* appear to age more slowly. That often confuses people because they can't see how both of those things can be true. The key is that there is no objective way to determine which of two people is "really" aging less unless they meet up again at some point and compare their clocks.

    You might want to check out the Usenet Physics FAQ entry on the twin paradox:

    http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

    (There are *lots* of discussions of the twin paradox here on PF as well, but I would recommend reading the above FAQ first before diving into them.)

    Not really. See above.

    You never perceive yourself to be "traveling" at all; you always perceive yourself to be at rest. If you got in a rocket and set off from Earth at nearly the speed of light, relative to Earth, then the Earth and the rest of the universe would seem to you to be traveling at nearly the speed of light. You yourself would seem normal and at rest.

    I won't comment on the rest of your post because I think you need to reconsider your thinking in the light of the above, but there is one thing at the end:

    Yes, the speed of light is the same for every observer.
     
  5. Mar 20, 2013 #4
    After reading more and discussing this with a friend for a few hours, I think I understand it. The faster you travel, the slower time passes, relative to something slower than you. So light will always move at the speed of light, whether its coming from your flashlight or someone slower than you. The difference is in how time passes for you.

    I imagine it like two people shooting guns. Both guns shoot at 100m/s. Steve shoots his gun standing still, but Jack shoots his while running 90 m/s. If this really happened, then Jack's bullet would be traveling at 190 m/s relative to Steve. However, if time passed 10x slower for Jack, and his gun still shot at 100 m/s away from him, to Steve it would only be traveling 10 m/s faster than Jack, which is still 100m/s. Steve's bullet, according to jack, would be traveling at 10 m/s unless time dilation was factored in. In reality, it would also move at 100m/s.

    This means that no matter how fast you go, the change in the progression in time will always equate with the speed of light. The difference is in "how long" it takes a second to tick, for lack of better words.
     
  6. Mar 20, 2013 #5
    Thank you Peter, it clicked. Correct me if I'm wrong, but trying to exceed the speed of light is a little bit like trying to drive faster than a bullet fired from your car. In space.

    Edit: Actually, its more like everyone has a stopwatch that has a normal second hand on the front, but the second hand on the back slows down proportionally to the speed its traveling away from whoever is looking at it. You can only see the front of the watch, and other people can only see the back, and according to everybody's watch light travels at 299,792,458 m/s.

    Edit 2: The experiments done with clocks moving at different speeds verify that the passage of time varies with velocity. However, this doesn't imply that light travels at a constant speed. I don't see a reason that the two must go hand in hand really, unless c has been observed while traveling at various speeds. I've looked for some experimental proof of this, but all I'm finding is people saying that "x wouldn't work without c being constant". To me, it seems like there should be a better answer than this. A moving observer should also be able to measure the light from a stationary (relative to the Earth, or whatever other reference frame used) light source and get the same results as if he measures the light from a light source moving the same velocity as him. Has this been done? Or, we could reflect the light from objects in space which are moving away from us, and measure the speed of this light.

    tl;dr - Are there any experiments which verify that c is a constant?
     
    Last edited: Mar 20, 2013
  7. Mar 20, 2013 #6

    PeterDonis

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    "Faster" and "slower" are frame-dependent. To you, the other object is traveling faster than you are, since to you, you are always at rest.

    This is true, but I'm not sure how it follows logically from what you said before.

    This doesn't look like a good analogy to me. For one thing, I don't see how any of this matches up with how SR actually models time dilation and relative velocity mathematically. Have you looked at the actual math?

    For another thing, you have ignored the fact that in relativity, velocities don't add linearly the way you have assumed here. Suppose the guns fired bullets moving at 0.9c. Steve fires his gun "standing still" (note that this implies a choice of reference frame, in this case Steve's rest frame--it's not a frame-independent objective fact), and Jack fires his gun while moving at 0.8c relative to Steve. The relativistic velocity addition formula is

    [tex]v' = \frac{u + v}{1 + uv / c^2}[/tex]

    where [itex]u[/itex] is the relative velocity of the two observers, one who sees an object moving at [itex]v[/itex] and the other who sees that object moving at [itex]v'[/itex]. For Jack's bullet moving relative to Steve, we have [itex]u = 0.8c[/itex] and [itex]v = 0.9c[/itex], so [itex]v' = 0.99c[/itex]; Steve will see Jack's bullet moving at 0.99c relative to him, not 1.7c. For Steve's bullet moving relative to Jack, we have [itex]u = - 0.8c[/itex] and [itex]v = 0.9c[/itex], so [itex]v' = 0.36c[/itex]; Jack will see Steve's bullet moving past him at 0.36c, not 0.1c.

    I don't really see this analogy either. Again, have you looked at the actual math?

    This might be ok if you could specify, mathematically, how the reading of the second hand on the back of the watch is determined. "Slows down proportionally" isn't quite right.

    They verify a lot more than that: they verify the specific mathematical formula that SR uses to predict exactly *how* the passage of time varies with (relative) velocity.

    It does when you look at the mathematical formula that has actually been verified by these experiments, since that formula requires that light travel at a constant speed.

    It's not as simple as that, because in order to measure the speed of light the way you are describing, you would have to take measurements in various states of motion and then compare them. But how do you compare them without knowing how the rate of time flow varies with your state of motion? And how do you know how the rate of time flow varies with your state of motion, if you don't make some assumption about how the speed of light behaves? There's a chicken and egg problem here.

    The best we can do is to to test for indirect effects that we would expect to occur if the speed of light were variable. An example of such an experiment is the classical Michelson-Morley experiment:

    http://en.wikipedia.org/wiki/Michelson–Morley_experiment

    In the end, the best argument for the speed of light being constant is that we can make very accurate predictions by assuming that it is in our theory, whereas nobody has come up with an equally accurate theory that has a variable speed of light in it.
     
  8. Mar 20, 2013 #7

    phinds

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    I addition to all the good info Peter gave you, I would emphasize that this particular statement is incorrect. Time passes for you at exactly the same rate regardless of your speed relative to other things (and all speed is relative). In your frame of reference, you are not moving and time passes for you at one second per second.
     
  9. Mar 20, 2013 #8
    No, i have not looked into the math. I really just read about time dilation and how time can pass differently for different objects, and sort of figured out the rest. I didn't expect the math to line up with Einstein's, I was just trying to grasp the concept of time being dependent on relative velocities, and if the only argument against my analogy is that my numbers are wrong, then I think the analogy is a fine one.

    Why would you expect the numbers in an analogy to be correct anyway? Then it stops being an analogy and starts being an example.

    With the gun analogy, I was just assuming the field that the field they were standing on was the reference frame. This would be the same as Steve's point of view. I understand that there is no "faster" and "slower" in the absolute sense.
     
  10. Mar 20, 2013 #9
    True. The difference is in how time would seem to pass for you according to another observer, right?
     
  11. Mar 20, 2013 #10

    PeterDonis

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    This doesn't strike me as a good approach, for the reasons I give below.

    But the concept depends on the math. By "the math" I don't mean the specific numbers; I mean the equations and the terms in them and what they mean physically.

    It's not a matter of the numbers being wrong; it's a matter of the concepts you use in your analogy not mapping in any recognizable way to the terms in the equations. If you would actually look at the math you would see this.
     
  12. Mar 20, 2013 #11

    phinds

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    That is an artifact of how someone else sees you moving from their frame of reference, yes. Just don't get confused as to whether or not it has to do directly with how you measure the speed of light.

    You are moving right now as you read this, relative to SOME frame of reference, at every possible speed up to but not including c so how you measure the speed of light hitting you cannot possibly be a function of how fast you are moving relative to someone else.
     
  13. Mar 20, 2013 #12
    Right. However, only by already knowing c was constant would you understand that how you measure light couldn't be a function of how fast you are moving relative to someone else. If did not know that c was a constant regardless of relative motion, then this would definitely be something worth testing.
     
  14. Mar 20, 2013 #13
    Does it matter if I know whether or not I know how to calculate the volume of a sphere when all I want to know is if dropping the sphere in a bathtub will cause the water level to rise?

    I started today having no idea what relativity meant. I now understand that when an object moves relative to another object, the time which each one experiences is different, even though no difference is noticed by the object itself. This is why nothing can exceed the speed of light, you can only approach it from the point of view of another object which would appear to you to be approaching the speed of light as well.

    Seriously, if you have any interest in getting people interested in physics then your approach is terrible.
     
  15. Mar 20, 2013 #14
    If there was a 'space' or universe with just one electron. What would prevent the electron from traveling from one side to the other faster than c?
     
  16. Mar 20, 2013 #15
    How fast would you know how fast it was going if there was nothing to compare it to? Thinking about space and time as absolutes are what I think most people do. Your speed is always 0 to you. Compared to the universe would imply that there were two things: the electron and the bounds of the container it was inside.

    No matter how fast the electron travel led (which already doesn't make sense, because there is no reference frame), it would still see the speed of light the same way that you do.
     
  17. Mar 20, 2013 #16

    WannabeNewton

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    How does this follow as a logical consequence of what you said right before it? That there is a finite upper bound for the speeds of massive objects is a postulate of SR. Also, there is no need to go start insulting Peter Donis. He knows what he's doing and he's successfully educated many people on the forum. Getting interested in physics entails getting interested in the math behind it, otherwise you just start spouting random jargon.
     
  18. Mar 20, 2013 #17
    The reference point could be the center of the 'space'.
     
  19. Mar 20, 2013 #18

    PeterDonis

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    Yes, this is correct.

    But I don't see how this follows from it.

    Well, you started the thread because you were already interested, correct? If you weren't you wouldn't have bothered posting.

    But you also saw some issues with the way you were conceptualizing relativity. That's why you posted. So I would assume that, if I continue to see issues with the way you're conceptualizing relativity, you would want me to say so. That's what I'm doing.
     
  20. Mar 20, 2013 #19
    So only physicists can be interested in physics. I completely understand how important math is, and to fully understand anything in physics I know that it must be described mathematically.

    Yes, what I said doesn't follow logically. One could never deduce that the speed of light was the upper limit by what I know about SR so far. I don't understand why its the limit, I just understand that it is the limit that SR gives to objects.

    What would follow, however, is grasping the idea that there could be an upper limit to speed, and it exists because as our relative speed increases, our relative time slows down. Why light speed is the upper limit is another thing to learn, but understanding that time is not static is absolutely necessary first.
     
  21. Mar 20, 2013 #20

    PeterDonis

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    How do you figure that?

    That's right. The constancy of the speed of light is a *postulate* of SR. It's not something that gets deduced from other things; it's something the theory assumes at the outset.

    And this is the part I don't understand. Can you expand on this argument?
     
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