# Speed of light hypothetical question

1. Jul 10, 2011

### anti666

Slight theoretical question that i have difficulty wrapping my head around.

Lets imagine a confined room traveling trough space at .9c on a line defined by points A and B. Lets say that in this room is a light source. If this light source is turned on than does the light inside the room still travel at c in every direction?

If so then lets assume that the direction that the room travels in is from A to B, length of the room is the same as distance between A and B and finally that the light source is at the center of the room.
Now if the light source is turned on when it is in point A, than the light would reach point B faster than c?

I'm not aiming at FTL travel, just wondering if light itself could in some cases be made travel faster than c or observed to be traveling faster than c?

2. Jul 10, 2011

### bobc2

Yes it does still travel at c in every direction.

No. A person sitting in the room would still observe the light to travel at speed c. That is an amazing mystery, isn't it? Google "Space Time Diagram" and see if you can get more insight into this. There are other posts here that shed "light" on the mystery. And others may jump in here to provide you with more insight as well.

Again, the answer is no. There are no known cases of light itself being made to travel faster than c.

3. Jul 10, 2011

### anti666

Yes i can understand how the observer in the room would 'see' the light traveling at c.

However i think that the light itself would reach point B faster than c in the given scenario. If not, than why?

If the distance between A and B was 0.9ly, than under normal circumstances light would travel from A to B in one year. However in my given scenario the light the source inside the room would reach B in less than one year?

I am aware of that, but could it be theoretically possible based on what we know today?

Last edited: Jul 10, 2011
4. Jul 10, 2011

### WannabeNewton

You are assuming classical vector addition laws apply. The velocity of the train doesn't add linearly with the velocity of the light with respect to point B. The vector addition law in SR is $s = \frac{u + v}{1 + (vu / c^{2})}$.

5. Jul 10, 2011

### bobc2

It would not, because:

X = ct

t = X/c

where X is the distance traveled to point B and t is the time taken to travel the distance. If you are sitting in the room watching, then that equation is the same whether the room is moving with respect to some outside reference or not. And the value of c does not change. Thus you get the same answer for t, either way (that is when you are just considering only what is going on from the point of view of the observer inside the room).

Now, this is a different question. You are now comparing the observations of a rest observer compared to the observer in the moving room. Clock readings and distances traveled will certainly be different for two observers in relative motion with respect to each other. The observer at rest could report a reading on his clock at the instant the light reaches point B. But the observer in the moving room will report a different time on his clock. Also, the two observers will report different distances between points A and B. But, again, both will measure the speed of light to be c.

No. There is no theory based on anything new we know today that would change this.

6. Jul 10, 2011

### bobc2

This space-time diagram attempts to indicate a 4-dimensional geometric explantion for the strange situation you're dealing with. Apologies if it just makes it more confusing. In this case we show just one of our normal 3 dimensions (X1) along with the 4th dimension (X4) of Minkowski space-time.

Here we have a red rocket and a blue rocket moving in opposite directions with respect to some black reference system. Each is moving along its own 4th dimension (world line), i.e., X4, at speed c. The strange thing that seems to happen with special relativity is that a given observer's X1 axis (one of the normal spatial directions) rotates in the 4-D universe so as to always result in photon world lines bisecting the angle between X4 and X1. Note that this is the case for the black rest system as well as the blue and red coordinate systems.

So, you see in the diagram that the blue and red guys live in two different 3-D cross-sections of the 4-D universe. Quite mysterious for sure! This of course results in different views of clocks and distances. The blue guy sees the red rocket as being shorter than his own and the red guy sees the blue rockete as being shorter than his. Red and Blue read different clock times (positions along the 4th dimension).

7. Jul 10, 2011

### anti666

It seems to me that using c as a constant would not make sense, if one would try to prove that c could be greater (in some hypothetical scenario) than what we currently believe it to be.

But light from the source inside the room would reach B before the source itself would reach B (even from rest observer standpoint), thus exceeding the speed that the room itself is traveling?

From searching a bit i have found actually something that somewhat resembles what i'm trying to get at here. Its http://www.nasa.gov/centers/glenn/technology/warp/ideachev.html#alcub" (found it by accident actually)

Last edited by a moderator: Apr 26, 2017
8. Jul 10, 2011

### Staff: Mentor

What?

Why would the source itself reach B before the light?

The key here is that in that scenario you are not moving through LOCAL SPACE at greater than c, so there is no problem. (If it does work at least, it doesn't at the moment and probably won't anytime in the forseeable future.)

Last edited by a moderator: Apr 26, 2017
9. Jul 10, 2011

### anti666

Lets say you are trying to calculate the wattage of a lightbulb. On it it says 60W. Now are you really going to use that figure of 60W as a constant for your calculations to find the real and accurate wattage of the lightbulb?

10. Jul 10, 2011

### WannabeNewton

C is a conversion factor and nothing more. I could set c = 1 and you wouldn't even see it in the equation in the natural units.

11. Jul 10, 2011

### Staff: Mentor

That's not really a good example. The 60W is what the bulb is supposed to put out. I would measure the power usage and light given off to determine how close to 60W it actually is.

In any case, the speed of light has been measured as c, and so many things work as a result of using c in calculations that if it were NOT correct we would have noticed by now. Energy conversions, power outputs, how different EM effects work, ETC.

12. Jul 10, 2011

### ctxyz

Though the above is a badly formed question , I will try to answer it. Suppose that the room moves in the direction of the +x axis at speed v with respect to a certain frame of reference, with B at the rear and C at the front. The light emitted from the midpoint (A) has the following equations:

1. In the frame of the room:

$$ct_B=d/2$$
$$ct_C=d/2$$

where d is the distance BC.

So, in this case :

$$t_B=t_C=d/(2c)$$

2. In the frame wrt which the room moves at speed v:

$$ct'_B+vt'_B=d/2$$
$$ct'_C=d/2+vt'_C$$

In this case:

$$t'_B=d/(2(c+v))$$
$$t'_C=d/(2(c-v))$$

In this case it would 'appear" that the light moves at $c+v$ and $c-v$ respectively but this is only due for the fact that you are observing the COMBINED movement of the room and of the light front. This is called "separation speed" or "closing speed" and it is the speed of two DIFFERENT entities that cover ONE common distance.

Not really, see above.

13. Jul 10, 2011

### Staff: Mentor

The invariance of c is well established by a wide variety of experiments that did not assume it's invariance.

http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

14. Jul 11, 2011

### anti666

This was not meant to be a 'good example', it was meant just to illustrate what i meant with my original comment.
I have no difficulty accepting that c (as in speed of light in vacuum) is the constant we believe it to be. But i have difficulty seeing how c is the upper limit of the speed that light can (seem to) travel at in every (theoretically) possible scenario. And it becomes even more difficult when i take into consideration that the light source and the observer are also moving independently from eachother.
However the following quote seems to be the answer i was looking for.

15. Jul 11, 2011

### Staff: Mentor

The first, the invariance of c, logically implies the second, the universal speed limit. You cannot have one without the other.

Do you understand the traditional derivation of the Lorentz transform from Einstein's two postulates?