# Why speed of light is measured same regardless of their speed?

1. Apr 20, 2013

### adjacent

Can someone please explain me why speed of light is measured same regardless of their speed?
Will not a person moving with 0.6c measure speed of light as 0.4c?

2. Apr 20, 2013

### Staff: Mentor

It is "just" an experimental result that the speed of light is the same for all.
No. You cannot use the everyday experience of time and space for those velocities, they are not right there any more. You have to work with relativistic mechanics. The result is that the speed of light is indeed constant for all observers. There are tons of books and webpages, explaining the details.

3. Apr 20, 2013

### Staff: Mentor

Space and time conspire to ensure that the speed of light is the same in every frame. That's one of the basic premises of special relativity.

No.

4. Apr 20, 2013

### adjacent

Thanks once again

5. Apr 20, 2013

### ghwellsjr

No one has ever measured anything that would violate the Principle of Relativity. If what you ask were true, then we would live in a different world where no one would have come up with such a Principle. So there really is no answer to your "why" question except to say that that is the way our world behaves.

6. Apr 20, 2013

### Boy@n

Couldn't the answer to 'why' be: because that's maximal speed 'fabric' of vacuum (empty space with quantum fluctuations) 'allows' photons (electromagnetical waves) to propagate?

7. Apr 20, 2013

### Staff: Mentor

The speed limit is more fundamental than light - you don't even need light to determine it, and it applies to gravity as well.
In addition, words cannot give some fundamental reason - you can just ask "why" again for any statement in words.

8. Apr 20, 2013

### rbj

no, it's more than that. Einstein's thought "experiments" made no use of results of Michaelson-Morley. in fact, i don't think that those results would have surprized him at all.

something like that.

$0.6 \ c$ relative to what?? the whole point of Relativity is that any observer that is not accelerated has an equal claim to being "at rest" as any other inertial observer. so while one observer might view this person you refer to as "moving [at] $0.6 \ c$" (implicitly relative to that observer), the person this first observer thinks is moving at $0.6 \ c$ is also an observer and is also an inertial observer with just as much reason to believe she is at rest and thinks that this first observer is moving in the opposite direction at $0.6 \ c$.

who is right? the first observer watching the second or the second observer watching the first?

the theory of Special Relativity says that they are both equally correct. they both have equal claim to being at rest. and if that is the case, there is no reason for why the laws of nature should be different for one of the observers than for the other. both observers have the very same set of Maxwell's equations apply to electromagnetic phenomena that they observe. both observers have, in their Maxwell's equations, the very same $\epsilon_0$ and $\mu_0$. and since

$$c = \frac{1}{\sqrt{\epsilon_0 \mu_0}}$$

then both observers, in their own frame of reference, must have the same $c$.

the kinda unintuitive phenomena regarding time dilation and length contraction and such come about when you consider both observes (each moving relative to the other) are examining the very same ray of light that they both observe to be moving at the same invariant speed $c$.

how is it that when one observer says "this beam of light is moving at 299792458 m/s" and the other observer says (regarding the same ray of light) that "this beam of light is moving at 299792458 m/s"? how can that be true when they are moving 179875474.8 m/s relative to each other? the only possible way for that to happen is that when they observe the other's clock, both observers see that the other's clock is ticking at a slower rate than their own clock (which, to them, is ticking away just fine at the rate it's supposed to).

does this make sense, adjacent?

Last edited: Apr 20, 2013
9. Apr 20, 2013

### Staff: Mentor

That's a dangerously misleading way of thinking about it, because once you introduce that word "fabric" (and in this context it's a metaphor, not a real thing) it is almost impossible not to fall into the error of thinking of things moving or at rest relative to that "fabric".

But even if it weren't dangerously misleading, it would still be subject to mfb's criticism: It just leads to another "why" question.

10. Apr 20, 2013

### Staff: Mentor

That is also my favorite argument for the constancy of the speed of light, although it's more compelling in hindsight. Maxwell's equations were discovered in 1861, but an entire generation of physicists spent the next 40-odd years considering (quite reasonably, given the historical context) ether theories instead of recognizing a hint from nature that the speed of light should be constant for all inertial observers.

Einstein himself chose to present the constant speed of light as a postulate ("Hey, look what happens what if we assume the speed of light is constant for all inertial observers! We don't need no stinkin' ether!") in part because in 1905 no one would be convinced by the argument that it follows directly from the principle of relativity plus Maxwell's electrodynamics. More than a century later, it's still not by no means cut-and-dried; there have been a number of threads here on exactly this topic.

11. Apr 20, 2013

### Boy@n

Sure, but not all 'why' questions make sense.

12. Apr 20, 2013

### ghwellsjr

Relative to the light.
You're missing the whole point of the Principle of Relativity. It's not that each observer is at rest and so his measurements come out the same--it's that even when an observer is not at rest but traveling at some high rate of speed, his measurements still come out the same.
But now you're talking about a different subject than the one the OP asked about. He asked about measuring the speed of light (always a two-way round-trip measurement) and it is not possible to measure or observe the propagation of a ray of light which is one-way. So if you're going to bring up this new subject, you should say that according to the second postulate of Einstein's theory of Special Relativity, each inertial observer assigns the speed of the beam of light to be c and then you can proceed to discuss the implication of the Time Dilation of the other ones clock but you still should not say that they can actually see the other ones clock ticking at the slower Time Dilated rate because they cannot.

13. Apr 20, 2013

### Boy@n

And what would happen if there were no upper limit for motion? How would nature 'behave'?

We still have that exception of spacetime expanding, where expansion itself can go faster than the speed of light/gravitation... So, if there is a star 'riding' such expansion wave, would that star go backwards in time to another star which is left behind? (Say that expansion stopped after some time, so light from that star moving faster than c would catch that other star staying behind.)

14. Apr 20, 2013

### ghwellsjr

Maxwell himself was the one who believed that his equations supported the notion of a medium in which light propagated and suggested a way to determine the absolute rest state of that medium.
As I just pointed out in my previous post, the constant measured speed of light, c, was already experimentally accepted and follows from Maxwell's equations but that is not the significance of Einstein's second postulate. Maxwell's equations are just as much at home with an absolute ether theory. It takes Einstein's second postulate (or something equivalent) to render the concept of an ether as pointless.

15. Apr 20, 2013

### Boy@n

(I hope me question will make sense.)

Right at the time spaceship travelling at 0.99C passes Sun, going towards Earth, the pilot starts measuring how much time it takes for light from Sun to reach Earth.

Observers on Earth measure about 8 minutes and 19 seconds, does the pilot measure the same amount of time since speed of light is constant for all observers, no matter of their speed?

If different time it seems strange, since distance from Sun to Earth is (for this thought experiment) constant (except if distance is shorter for the pilot, maybe due to space 'contraction'?).

If same time it also seems strange if light is moving away from spaceship toward the Earth at speed C relative to spaceship.

Last edited: Apr 20, 2013
16. Apr 20, 2013

### Staff: Mentor

Yes, as a result of expanding spacetime it's perfectly possible for sufficiently distant stars to be doing something that could be kinda sorta described as "moving away faster than the speed of light" although that certainly does not imply going backwards in time or anything like that.

I deliberately specified inertial observers to avoid the complexites of expanding and non-flat spacetime, and because I didn't want to get into the math that's needed to move beyond the "kinda sorta described as" language in the previous paragraph. You really have to thoroughly understand the simpler case of flat and non-expanding spacetime completely before you move on to the more general case. You aren't even giving anything up by making this simplification, because in the general case spacetime is still locally flat so the area around any observer so behaves as descried by special relativity.

17. Apr 20, 2013

### Staff: Mentor

Yep, that's pretty much it.

Look in the FAQ on experimental support for relativity at the top of this forum, find the references to time dilation and the relativistic muon experiment for an example of how time dilation and length contraction play together to give a consistent physics for all observers.

Basically, fast moving muons with a very short lifetime are created when cosmic rays hit the top of the earth's atmosphere. Naively, we'd expect them to decay before they reach the surface of the earth, but they don't. There are two equivalent and equally valid explanations: From the muons' point of view the distance to the surface of the earth is contracted enough for the muon to cross it in a normal undilated lifetime; from the earth's point of view the muon's lifetime is dilated enough for it to live long enough to cross the uncontracted distance.

Last edited: Apr 20, 2013
18. Apr 20, 2013

### Staff: Mentor

Yep - that's an important piece of the historical context that I mentioned.

Indeed it does, which is why (with tongue in cheek) I sometimes paraphrase the second postulate as "We don't need no steenkin' ether!".

19. Apr 20, 2013

### Boy@n

The average distance from the Earth to the Sun is 150 million km, so, what is it for that spaceship travelling at 0.99 C?

Is it simply 0.01 of that distance?

And for light (photon viewpoint) it is 0? (Since time for photon is 'frozen'.)

20. Apr 20, 2013

### Michamus

.99C relative to what? The Earth? It's always irked me when people use a percentage of lightspeed as a velocity, when it's totally relative.

For your experiment though, let's suppose a space craft is orbiting the sun at 1 million km/s at a distance roughly 150 million km. It would take light about 8 1/3 minutes to reach this space craft.

Now, let's imagine that same space ship is orbiting the sun at 300,000 km/s at a distance of roughly 150 million km. It would take light about 8 1/3 minutes to reach that space craft.

You see, SR explains that Lightspeed is Constant in the Universe. No matter your velocity, light will always propagate at light speed, even if you are the source of that light. This occurs because SR explains that from your FOR, everything else is moving and you're sitting still.

As another example: Imagine that same 1 million km/s space craft has head lights. While travelling at that speed, it decides to turn on it's headlights. The photons would emit from those head lights at C and would propagate ahead of the space craft at C. So if the space craft had a pole with an attached sensor 1km ahead of it, that sensor would register that the light reached it at C.

You see, the "AH HAH" moment for me on SR/GR was the realization that there isn't a Universal Frame of Reference. In fact, the whole point of SR/GR was to get rid of that myth of a Universal FOR and replace with a model where everything is relative to the observer.

I hope that added some clarity.

21. Apr 20, 2013

### Boy@n

The most interesting thing to me is that spacetime (distances) physically/really contract/shorten the more the faster you move...

So in my example above, what is the distance from Sun to Earth for a spaceship travelling that path at speed 0.99 of C?

22. Apr 20, 2013

### ghwellsjr

As I just pointed out in a previous post, you cannot measure the one-way speed of light. In Special Relativity, we define it to be c. So even if the pilot were stationary at the Sun, he still cannot measure how long it takes for light to get to the Earth. In the same way, we cannot measure how long it takes for the light to get from the Sun to the Earth. There is no possible measurement that allows us to start a stopwatch when some light leaves the Sun and stop it when the light arrives at Earth and yields a measurement of 8 minutes and 19 seconds. What we can do instead is figure out how far away the Sun is by whatever means we have available to us, and convert that to a distance in terms of light-seconds and then we say that the light took that same number of seconds to reach us. And according to SR, this is only true in the frame in which both the Sun and Earth are at rest. Alternately, we could use the radar method to measure how long it takes for a signal to go from us to the remote object and back to us. We assume the signal takes the same amount of time going as it does coming back so we divide our measurement by two and that gives us the assumed (and defined by SR) one-way speed of light.

Now to answer your question about the pilot, in his rest frame moving at 0.99c with respect to the Earth-Sun rest frame, he can make a radar measurement of the round-trip time it takes for light to go from the Sun to Earth and back to him and he will get a time that is about 1/14 of the time he would get if he were stationary with respect to the Earth-Sun. In the stationary case, he would measure 16 minutes and 38 seconds and then he would divide that by 2 to get 8 minutes and 19 seconds. In his moving case, he will get about 71 seconds. If he divides that by 2 he will get about 35.5 seconds but he will know that this is not correct because the Earth has moved during the time of the measurement so he needs to take that into account. And the way he does that is to assume that his measurement applies at the half-way point of his measurement, in other words, when he had traveled for 35.5 seconds. So he says that at his time of 35.5 seconds, the Earth was 35.5 light-seconds away. Now he needs to figure out how far away it was when he started from the Sun's position. He can measure the speed of the Earth coming towards him using several Radar measurements and he will determine that it is traveling at 0.99c. Therefore, in 35.5 seconds, it has traveled towards him by a distance of 35.5 seconds time 0.99c or 35.1 light seconds away. So he adds the two numbers, 35.5 and 35.1 and he concludes that the Earth was 70.6 light-seconds away from him when he left the Sun and so therefore it takes 70.6 seconds for the light to get from the Sun to the Earth. (This number is only approximately correct, since I have been doing a lot of "abouts".)

So the distance between the Sun and the Earth is different in the rest frame of a traveler than it is in the rest frame of the Sun-Earth. In fact it is Length Contracted by the factor of 1/gamma which in this case is about 1/7 and we can see that our answer of 70.6 seconds is about 1/7 of 6 minutes and 19 seconds.

23. Apr 20, 2013

### Staff: Mentor

Your speed relative to light depends on the reference frame.

- the target (earth) is moving
- the distance between both is subject to length contraction (with a factor of $\gamma=\frac{1}{\sqrt{1-0.99^2}} \approx 7.1$).
- in general, the pilot will measure a different time. The speed of light is constant, but distances and velocities (apart from light) are not.

24. Apr 20, 2013

### rbj

missed the point.

it's precisely the point.

relative to their own inertial frame of reference they certainly are.

high rate of speed implies motion. motion relative to what??

his or her measurements come out the same because his or her physics are the same because each, being in their own inertial frame of reference, are in indistinguishable situations. they are, in their own unaccelerated position, operationally at rest and it's the other observer who is moving.

the motion is relative. all inertial motion is relative. without a universal frame of reference (that is what the aether was hypothesized to be) to refer to, there is no way for any inertial observer to claim being in absolute motion or to be at absolute rest.

start with a light clock. then move on.

25. Apr 20, 2013

### ghwellsjr

This is only true if you have previously set the clock on the remote sensor so that the measurement of the speed of light will come out to be c. And after you do that, lo and behold, the measurement comes out to be c. But if the space craft changes its speed, you will have to re-calibrate (re-synchronize) the remote clock to the space craft clock so that you continue to make the same "measurement". You cannot measure the one-way speed of light apart from setting the clock to make the measurement come out to be c. All you can do is set your remote clock so that the "measurement" will come out to be c.

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