# Speed of Light and Relativity of simultaneity!

1. Oct 23, 2011

### darktangent1

Here is a question which can seem stupid to a lot but it has stuck it my mind and i can not move forward.

There are two points to it.

1 - The speed of light is same in all inertial frame of references. So if an observer is moving with a relative velocity 'v' withrespect to another stationary observer and a light bulb is switched on both of them will see the bulb light at the same time.

2 - The simultaneity is always relative. If some one states that two events are relative then the same events can not be relative to another person. To prove this i have the following example in the book

Two events happen, sally is moving with a relative velocity 'v' to sam. So sam measures both of the events to be simultaneous and sally measure the event Red to happen first.

My Problem.

Now the problem in my mind is if the speed of light is same in all inertial frame of references, THEN the speed of light and in result event measurement for sam and sally should be same irrespective of the Relative velocity between them. So why does sally measures event Red to happen first if Light is traveling at the same speed.

Last edited: Oct 23, 2011
2. Oct 23, 2011

### ghwellsjr

Here's the problem. Neither Sam nor Sally have any way of knowing if the distant light bulbs actually come on simultaneously, they can only know if the light propagating through space arrives at their own locations simultaneously, correct? That's because we cannot track the progress of light through space, we just don't know where it is at any given point in time.

So to solve this problem, Einstein creates the concept of a Frame of Reference in which he defines, not measures, the propagation of light to be c. This means that if you see two distant lights that are an equal distance from you come on simultaneously, then those two remote events are simultaneous, by definition in that FoR, not by measurement.

Another FoR, moving with respect to the first one, because it uses its own definition for the propagation of light, will determine that events that are simultaneous in the first FoR are not simultaneous in the second FoR, simply because it has defined the propagation of light to be c in its FoR.

The images for your scenario are all from the point of view of a FoR in which Sam is at rest. So in image (b), when Sam actually sees the light from the two equidistant bulbs arrive simultaneously at his location, then this FoR defines, not measures, the two events of the light bulbs as happening simultaneously as depicted in image (a). Note that in all your images, the two bulbs are depicted as being equidistant and stationary with respect to Sam at all times.

So it's because the problem is stated from the point of view of a FoR in which Sam is at rest and the facts that he sees the two flashes simultaneously and the bulbs are equidistant from him, that we can say the two flashes occurred simultaneously, by definition in that FoR which means that Sally will neither see the flashes simultaneously nor conclude that they occurred simultaneously in a FoR in which she is at rest.

3. Oct 24, 2011

### darktangent1

Great! What an explanation. Thanks a lot.

The Define and Measure thing really solved the issue in my mind.

Last edited: Oct 24, 2011
4. Oct 25, 2011

### Dimosthenis S

Hi Darktangent1.... This is my first, so ...hi in general :) Well, I must say that I did not follow your example fully, but the answer might well be that when you are talking about the speed of light being the same in all inertial frames, what that basically means is that the light has its own speed in a specific space.... this is not at all curious, it is as simple as the speed of sound, which is the same in given conditions, regardless if e.g. you are in a airplane or walking in the street.... Light travelling is just another phsycial phenomenon, no magic here.....

5. Oct 25, 2011

### Dimosthenis S

....And something else, please let me clarify one thing: When I am saying that the speed of sound is the same, no matter if you are inside an airplane or walking, I am just referring to the speed of those two; the air, as a medium, is supposed being homogeneous and not moving.... And then, that means also, that if the airplane has a sealed cabin, the environment inside the airplane is moving in a different speed than the -stand still- air of the outside enviroment, and so the speed of sound inside the cabin is in a world on its own; that brings of course the question: are there sealed environments inside our enviroment, where electgromagnetism behaves independetly? And if so, what are the physical constraints that make the said enviroment sealed, like e.g. the body of the airplane? Similarly, are there any other outer enviroments, where electromagnetism behaves differently (the same as we are talking about atmospheres - that reads mediums for the sounf to propagate - existing in planets other than earth)?.... Frankly, I am not sure if I can answer, right now ( :) ), since we must have first to find out a way, if there is any of course, to measure such things......
greets

Last edited: Oct 25, 2011
6. Oct 25, 2011

### nitsuj

I came across this "game" called Universe Sandbox. I think it crudely simulates gravity and stuff.

One cool thing that can be done is to have objects moving at what ever speed, say 0.9c and then have that object flash a pulse of light. With other objects present it helps understanding the concept of simutaneous events.
Fun to play with and learn from too.

7. Oct 25, 2011

### ghwellsjr

Well, no, the speed of light in all inertial frames is defined to be the same, not measured. But the speed of sound can be measured in any situation, it doesn't have to be defined in order to make a meaningful Frame of Reference.
No, there are no sealed environments that cause light to behave differently than it would in an unsealed environment. And this shows a difference between light and sound. In order to get sound to travel at the same speed in a moving environment (like an airplane) as it would outside on the ground with no wind blowing, you have to seal the air inside from the air outside so the air inside will seem like it is stationary with respect to the airplane. With light, you don't have to do that. Even out in the open, as long as the airplane, or spaceship, or whatever, is traveling at a constant velocity (and we are ignoring the effects of gravity), it will appear to have exactly the same characteristics as any other similar situation.

8. Oct 25, 2011

### Dimosthenis S

I have considered both of the understandings of this definition, and I have come to the conclusion that the meaning is that light has a constant velocity in a given medium, thus the example I gave with the sound

In my mind, there are not any theoritical constraints, for e.g. different universes to carry their own light, to tell it simply, just as different planets can have atmosphere and as such, sound. One could also consider any medium that slows down light, like glass, to be a sealed environment on its own - no need for sealed environments to only offer greater speed

9. Oct 25, 2011

### ghwellsjr

"Both"? I only gave one definition which I thought had only one way to understand it. What's the other one?

Even if there were a medium in which light exclusively had a constant speed (this is the idea behind the Lorentz Ether Theory), it's pointless to defend that concept because it is impossible to identify the state of that medium, unless you know something that none of the rest of us are privileged to know, in which case, I beg you to share it with us.
You better be careful. Crackpots tend to get themselves banned on this forum. We're here to teach and learn about relativity in this universe, not speculating about some other universe. I think it can safely be said that you may have a lot to learn, but if not, you cannot teach something that is contrary to the accepted theory of relativity. Please take this with the right attitude and if you are not familiar with the rules of this forum, please read them before proceeding. I hate to see another person get banned.

Last edited: Oct 25, 2011
10. Oct 25, 2011

### yoron

Dimosthenis, it's a little trickier than that.

There's one famous scientist that has created this universe where 'light pours like honey', and I expect most of us to know his name :) But lights property of being 'c' is one grounded on experiments, not theory. Why it is 'c', as in a defined 'speed' relative some ruler in 'time', we don't know. Light seems to be in too much of a hurry to stay and explain it to us, but we have to go by what experiments tell us. And if you do so you will need to define the universe from those.

'Frames of reference' is how we define that invariant 'c', relative different observers. It is not a sealed cabin, instead becoming a unique definition for each object/observer, relative all other 'objects/observers', inside SpaceTime. There is two ways of defining a speed. Either relative something else, like Earth, and so defining that as being 'still', or by using a 'black box scenario' in where you are enclosed, not knowing any other 'frames of reference' to define as being still.

Einstein used 'Black boxes' to define 'motion' and doing so he found two types of 'motion'. He called one uniform motion and the other accelerations. Light follows a geodesic, an easiest path defined by gravity, and when that path increase in gravitational potential, as when light falls into Earths atmosphere it doesn't speed up. Instead we will observe it, being 'at rest' relative Earth, as getting a higher 'energy' (blue shift). That's also a experimental definition, not theoretical.

And in a 'black box scenario' measuring a light ray to 'blue shift/raise its 'energy'' inside that box (from light bulb to detector), it will mean one of two things, either you and your box are on a planet, or you are accelerating. Turning the arrangement (source - sink) around inside a accelerating rocket, finding the light to 'red shift/lose 'energy', is the equivalence to measuring a light ray sent from Earths surface into space, instead of measuring it from the surface. And that is accelerations (and decelerations).

Doing the same experiment inside a uniformly moving ship (light bulb - detector) will have no effect on that light rays 'energy/blue-red shift'. And it won't matter if you accelerate that space ship, and then stop, to move uniformly again. The experiment can only show you the exact same. So, either that 'relative motion', as relative Earth, or a 'black box scenario' is what exist for defining a motion, and in a 'black box scenario' Earth can be defined to uniformly accelerate, at one constant Gravity.

What makes a 'time dilation' and 'Lorentz contraction' is the way light never change that 'speed'. It doesn't matter what you define yourself as moving at, relative Earth. It will still have the same invariant speed when a observer/detector gets your light signal, no matter if he finds himself moving from you, or towards you. And that's also a experimental fact, not theoretical.

So the night sky is both 'time dilated' and 'Lorentz contracted' relative you watching it, but you won't notice that, because the light that reach your eyes is of one invariant speed and will fill your brain with one coherent image, of SpaceTime.

11. Oct 25, 2011

### DaveC426913

dark, you've gotten several very good in-depths answer.

The very short version of the answer is this:

'relativity' is short for 'relativity of simultaneity'. The very crux of relativity is simply that observers in different reference frames will disagree on whether two events separated by space are simultaneous.

Once you accept that, you'll see that the paradoxen vanish.