# Why is light speed constant in all reference frames?

1. Oct 13, 2011

### catalyst0435

Hey, this is my first post. I am a biology major so I know pretty much nothing about physics, yet sometimes it interests me way more than chromosomes do.

So, given that I know nothing about physics, this is probably going to sound like a stupid question. But I've always wondered how it is possible that a person A moving at speed observes light emitted from their frame of reference at c, and then a person B sitting still (relative to person A of course) sees that same light travelling also at c. It seems like that just shouldn't happen.

So I think I'm right when I say it has something to do with space and time being perceived differently depending on how fast you are going. I guess when you are moving quickly, a meter seems shorter and/or a second seems longer than when you are moving more slowly? And since c is m/s, well, that explains it right? But I really have no idea. Someone rescue me from my misconceptions and more fully explain to me why this is happening!

2. Oct 13, 2011

### Hootenanny

Staff Emeritus
Welcome to Physics Forums.

The invariance in the speed of light was postulated by Einstein in the early 20th century. Einstein deduced (for want of a better word) this from the lack of an aether (i.e. the fact that light doesn't need a medium to propagate through). This invariance has been confirmed by countless experiments since. Indeed, now the meter is actually defined in terms of the speed of light. It is defined as the distance traveled by light in around 3x10-8 seconds.

You are quite correct that lengths and times varying according to your motion relative to the "thing" being measured (length contraction and time dilation respectively). However, these do not explain the invariance of the speed of light, rather they are a consequence of it.

It is interesting to note, that one can derive the "equations of special relativity" (i.e. the Lorentz transformations) without requiring that the speed of light is constant. The principle of causality (i.e. that an event cannot be caused by a future event), is enough to impose a maximum speed of transmission of information. It turns out that this coincides with the speed of light.

3. Oct 13, 2011

### catalyst0435

So, I can sort of grasp why it's the case, but why precisely must time and length vary as a consequence of invariant speed? Is there some thought experiment that would make this clearer to me?

Also, then, what exactly is the reason for light speed's invariance? If I understand your post correctly, it's because some complex equations impose a maximum speed of things? Is there a particular reason why it is light that has the privilege of getting to be at this maximum natural speed? And is there a way to understand why there is a natural maximum speed of transmission of information without knowing some serious mathematics, or will I just have to be content with "the equations prevent stuff from going faster"?

4. Oct 13, 2011

### Hootenanny

Staff Emeritus
First you must understand the Lorentz transformations: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/ltrans.html#c2

Then you can take a look at length contraction & time dilation: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/tdil.html
Such explanations a notoriously difficult and one has to strike a balance between under and over simplification. Take a look at this page: http://www.phys.unsw.edu.au/einsteinlight/jw/module3_weird_logic.htm and in particular the section entitled "Galileo's principle of relativity and Einstein's principle of special relativity".

5. Oct 13, 2011

### catalyst0435

This page confuses me. Under that section you've listed, it makes sense that a scientist performing an EM experiment on a stationary platform would observe light from his frame of reference to be traveling at c. It also makes sense that a scientist performing an EM experiment on a moving train would observe the light from his frame of reference to also be traveling at c. This mirrors Galilean relativity, says the article. But I'm not understanding how this explains why a scientist on a stationary platform would observe his moving colleague's light to be traveling at c, while his colleague simultaneously observes his own experiment's light to be traveling at c.

I think by the very end of the article, an explanation is attempted. It says essentially, "how can this invariance of speed of light from the same source but at different frames of reference be explained?" But it says the answer is "time dilation." Which I thought we established is actually a consequence, not an explanation, of invariance of speed.

6. Oct 13, 2011

### Joel_GMG

Time dilation is indeed a consequence. SR is the grand explanation.

I am afraid so, unless you are willing to invest a lot of time furthering your understanding.

Last edited: Oct 13, 2011
7. Oct 13, 2011

### A.T.

This might help:

As far SR is concerned, this is simply postulated based on experimental evidence.

Last edited by a moderator: Sep 25, 2014
8. Oct 13, 2011

### harrylin

Yes, that's roughly correct, but of course equations are man-made and can't do anything (no Sim Sala Bim magic in physics!).

The same thing can be "explained" in many ways, and it depends on your thinking which one you find most satisfying. Some people like a more mathematical explanation (it's because of the invariance of c that lengths and times are measured differently at different speeds) or a more physical explanation (it's because speed affects the measurements of lengths and times in the right way that c is invariant). So what one person regards to be a consequence, another person will regard as cause - it's more of an interplay of phenomena that are consistent with each other.
Another way is to say that all matter has wave properties and at very high speed everything becomes more and more wave-like (and thus more light-like). And again another way is to say that conservation of energy and momentum makes that the speed of light is invariant. And so on.

Then what is special about "light": it just happens that light, just like radio waves, propagates at the speed limit c because it has no rest mass (as far as we know).

9. Oct 13, 2011

### harrylin

If you account for the different synchronization of clocks as well as time dilation and length contraction, then you will find that according to the "stationary" scientist the "moving" colleague will measure the speed of a light ray in vacuum to be c relative to his platform, if he uses that platform as independent reference system.

A clarification is at its place, to reduce the mystery: if the "moving" colleague is for example in a space lab and he uses the reference system of his colleague on Earth as the "resting" reference system, then he will measure the speed of the same light ray relative to his moving lab, as measured with the Earth's standards, to be different from c. The basic rules of logic and mathematics apply as they should.

Perhaps it is useful to consider the example (just a simple example by way of illustration!) of a light clock.
en.wikipedia.org/wiki/Time_dilation#Simple_inference_of_time_dilation_due_to_relative_velocity
If every clock on the "moving" platform ticks slower by the same amount as the light clock, then an observer on that platform will measure that bouncing light ray to propagate at c.

Does that illustration help?

10. Oct 13, 2011

### whosapopstar?

Please regard spaceship 2 and spaceship 3.
All this question is a asked only from the POV of spaceship 2!!
Velocity x is different from velocity y.

If in some kind of transformation, spaceship 2 measures light speed detection at spaceship 3 as not being 300000kps, how come it measures by its own detectors, the speed of light as 300000kps? It is the same beam of light that spaceship 3 measures in between the detectors of spaceship 2! Shouldn't a transformation that measures anything but 300000kps for spaceship 3 as well, change the results of spaceship 2 detection itself?

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11. Oct 13, 2011

### ghwellsjr

You are having four different pairs of detectors traveling at different speeds "measure" the one-way speed of the same light beam and you're wondering why scientists say that they all come up with the same "measurement" of c? Correct? Is that your question?

The answer is that it is not possible to make a measurement of the one-way speed of light until you have previously defined the one-way speed of light. In Einstein's Special Relativity, that definition is c. So when you then make the "measurement", what do you get? Obviously, c.

12. Oct 13, 2011

### whosapopstar?

Please disregard earth and the big spaceship.
I am asking regarding posts that mentioned in some contexts that under a transformation, the speed of light is not necessarily 300000kps. Is it out of context regarding my question?

Last edited: Oct 13, 2011
13. Oct 13, 2011

### Staff: Mentor

To get back to the original question, we have an FAQ about this in the FAQ section at the top of this very forum:

https://www.physicsforums.com/showthread.php?t=534862 [Broken]

Last edited by a moderator: May 5, 2017
14. Oct 13, 2011

### ghwellsjr

OK, we'll just look at spaceship2 and spaceship3.

Neither one of those spaceships can measure the one-way speed of light until they independently define how long it takes for the light to traverse the distance from their individual detector1 to detector2. They can each individually measure the distance between their own two detectors using their own rulers, correct? Of course, the way you've drawn it, spaceship2 will measure a much greater distance than spaceship3, correct? But that won't matter because spaceship2 will measure a greater time interval and so the calculation when they each divide the distance by the time interval will come out the same, correct?

Now in order for each spaceship to measure how long it takes for the light to traverse from the first detector to the second detector, they have to send signals from both detectors to a timer that starts when the light gets to detector1 and stops when the light gets to detector2. They could place this timer anywhere and it shouldn't make any difference, correct? Well let's just say they put the timer next to detector2 and they will send a signal from detector1 to the timer to start the timer. So let's say they run a cable from detector 1 to the timer and let's say that the electrical signal travels in the cable at the speed of light. They also have a very short cable from detector2 to the timer to stop it.

Now they start the experiment. The flashlight comes on and some unknown time later the light hits detector1 which sends an electrical signal down the cable at the speed of light to the timer. But this signal is tracking right along with the light coming from the flashlight so the signal starts the timer at the exact same time that detector2 tells the timer to stop so the measured time interval is zero and they calculate the speed of light to be some distance divided by zero which is infinite.

Well that doesn't seem right so you rearrange the experiment and put the timer next to detector1 with the short cable and use the long cable from detector2 to bring the stop signal back to the timer. Now when you do the experiment, it will take however long the round-trip measurement of the speed of light would take for the measured time interval and so you get an answer that is presummably half what it should be.

Do you see the problem? Depending on how you set up your experiment you will get an answer for the measured one-way speed of light that is somewhere between c/2 and infinity.

There is no way to avoid or resolve this problem base purely on measurement. You might say that you should put the timer half way between the two detectors and make sure the cables are equal length but now you are merely claiming that the one-way speed of light is equal to the two-way speed of light but you haven't actually measured it.

So what Einstein proposed is that each spaceship puts the timer half way between their own two detectors and that will be the agreed upon definition of the one-way speed of light but separately for each spaceship.

You ask about transformation. What that boils down to is if spaceship2 uses his definition for the one-way speed of light to measure what happens on spaceship3, he will determine that spaceship3's measurement of the one-way speed of light is incorrect but rather is somewhere else between c/2 and infinity. The same is true for spaceship3 using his definition of the one-way speed of light to determine spaceship2's measurement.

There will never be any problem as long as you use one definition for all measurements on all spaceships. And it can be any consistent definition, even one where there is no spaceship. What we are really talking about here is the definition of a Frame of Reference which applies to all objects in the scenario. You can then use the Lorentz Transform to switch to a different definition (a different Frame of Reference) and apply that new definition to all the same spaceships or objects that you had in the first FoR.

15. Oct 13, 2011

### whosapopstar?

I think that I understand your explanation.
Thanks.

16. Oct 13, 2011

### bobc2

catalyst0435, there is a more fundamental reason for this. However, to grasp the reason you would have to wrap your brain around a couple of significant fundamental aspects of special relativity.

First of all, you must envision the universe as 4-dimensional, populated by 4-dimensional objects. Particles of matter are filament-like objects strung out predominently along the 4th dimension, including your bundles of neurons in your brain. Your bundle of brain fibers may be strung out along your 4th dimension for multiple billions of miles.

Next, you would have to understand that people moving at different speeds, at a given instant, live in different 3-dimensional cross-sections of the 4-dimensional universe. For a person moving at relativistic speed with respect to some "rest frame", his 4th spatial dimension coordinate (X4) rotates clockwise relative to the rest 4th dimension while his normal spatial dimension (X1) rotates counter clockwise.

A photon of light is oriented at a 45-degree angle relative to the rest frame. So, for any position along the 4-dimensional photon filament, its position along the X4 axis always has the same displacement value as its displacement position along the X1 axis. Thus, it is the orientation of the X4 axis together with the symmetric orientation of the X1 axis that results in the ratio X1/X4 = 1.0 for anyone, no matter what their speed. And all observers move along their own X4 at speed c. That means that for all observers, their displacement change along their 4th dimension can be calculated using a clock: X4 = ct. The reason clocks work is because t = X4/c. Caution: That does not mean time is the 4th dimension--no more than the path along an interstate is a time dimension just because you can keep track of your progress along the highway by watching your clock on the dashboard.

You should google spacetime diagram and also "block universe" to help with the understanding of these concepts.

So, even though the discovery that "the speed of light is constant" motivated the discovery of relativity, the constant speed of light is not the reason for special relativity. Rather, the constant speed of light is a consequence of this very strange way nature has chosen to work: A 4-dimensional universe, and 3-D cross-section views of the universe are different for observers moving at different speeds--and the views are oriented so that the 45-degree orientation of a 4-D filament (photon of light) will always bisect the angle between X4 and X1, no matter what the orientation (slope--angle, etc.) of the X4 coordinate.

See sketches below illustrating the concept of the symmetric rotation of coordinates for observers moving at different speeds. The lower right box emphasizes how this results in the constant speed of light for all observers. This is really the fundamental answer to your original question.

Another very significant aspect of the rotated coordinates is that the laws of physics are the same for all coordinates rotated in this scheme of symmetric X4 and X1.

Now, the fundamental question becomes, "How did nature manage to come up with the fabric of the universe woven in such a way as this, with weaving rules that give us physics?"

Last edited: Oct 13, 2011
17. Oct 13, 2011

### rbj

it's because the laws of nature are invariant for all inertial frames of reference. let's say that you and i are in our own separate space crafts, neither are being accelerated and we fly by each other at a relative speed that is very fast (say c/2). since we're not accelerated, our velocity is constant, both of us look at our own reference frame as being "stationary". we both think it's the other guy who's moving at a speed of c/2 and that our own space craft is not moving.

so who's right?

turns out we both are.

now if both of us have equal claim to being "at rest", there is no aether that marks a frame of "rest", then there is no reason for the laws of physics (such as Maxwell's equations) in your inertial frame of reference to be any different from the laws of physics in my inertial frame of reference. we both have the same $\epsilon_0$ and $\mu_0$, so we should have the same c.

r b-j

18. Oct 14, 2011

### TGlad

But that doesn't explain why light is privileged in being one of the laws of nature that must be invariant, whereas the speed of sound and the speed of a train aren't invariant.

I would describe it that a universe needs some maximum speed of communication for it to be causal. If it didn't have a maximum speed then you would get circular dependencies and the universe wouldn't really work, at least not anything like the one we're in.
Given that there is a maximum communication speed, the Lorentz equations in relativity are the simplest ones which provide it consistently, without requiring a frame of reference.

The reason that light happens to go at this speed-of-communication is probably just because it has 0 rest mass, and is a very very simple phenomenon, like the tiniest unit of communication.

Last question, why is c the value that it is?
I don't know, well I suppose it had to be some value.

19. Oct 14, 2011

### bobc2

Because the 4-dimensional photon filiment is oriented so as to bisect the angle between X4 and X1 for all observers, and all observers move along their 4th dimension (X4) at approximately 186,000 mi/sec.

20. Oct 14, 2011

### Staff: Mentor

From the Frequently Asked Questions section at the top of this forum:

https://www.physicsforums.com/showthread.php?t=511385 [Broken]

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