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### Relative Light Speed

Posted: Mon May 07, 2018 7:57 am UTC
So recently I was having your average family discussion at the dinner table, and light speed came up. You see, we were wondering what would happen to the light inside a room that was travelling at an appreciable fraction of the speed of light.

Say you have a room 20m long, with two perfectly reflective mirrors facing each other. Now say that this room is travelling at 50% of c down it's long axis. Then the question is, how fast is a photon bouncing between the mirrors? Is it travelling at c relative to the room, or is it travelling at c relative to the same point as the room itself?

Then we ran into this question: say you removed one of the mirrors so that the light inside could travel out the window, what would happen to the velocity of said light?

This is far above my abilities as a very amateur physicist, so if someone knows the answer to my dilemma, that would be helpful.

### Re: Relative Light Speed

Posted: Mon May 07, 2018 8:24 am UTC
the light would travel at the speed of light. always. that's kind of the point of it. you would observe it at c, an observer travelling 0.5c relative to you would see it at c, and an observer travelling 0.5c in the other direction would, too. what you three wouldn't agree on would be the width of the room and when (possibly even in which order) various events took place.

### Re: Relative Light Speed

Posted: Mon May 07, 2018 11:47 am UTC
(@OP. Not responding to the above response, and certainly not arguing against it.)

Within the room the light goes at SoL relative to the room from 'back' to 'front' (with the apparent conceit that you know you're moving past something, albeit steadily). You can't see it set off, because the light you'd see the setting off by would be going the same speed and you can only see that it reached the other end because of light that has to come back from the end, which is itself only capable of getting back to you at SoL. But perhaps you stand to one side and watch as signs of the light are indicated at two points making up an isoscelese triangle (both delayed equally), if you can trust the geometry.

The same result happens when bouncing from 'front' to 'back', noting your ultimately arbitrary labelling of 'front' and 'back' upon your expectation that something that you see moving about outside your room 'must be' stationary, but is no more definitely stationary as any other constantly passing object (back to front, front to back, side to side, top to bottom, etc), and as long as you don't feel acceleration yourself then you have no better 'stationary reference' then yourself, howeverso the universe whizzes about outside your strange vanity room.

An observer outside the room (upon one or other of the objects you might improperly designate as 'stationary') will see the same symmetry of light passing in a similar isoscelean measurement (whether looking in through long picture-windows all down the side of the room or at light let escape from its mirrored-entrapment through front/back windows) but then you must realise that the unequal side of this new isosceles triangle is different from the one you use, because while you are waiting for the light to get between the point slightly to your 'forward' to the point slightly to your 'rear' (or vice-versa) the external observer sees both of your fore and aft points move in the direction they (and only they) see you moving, meaning that your observation-triangle is not (to them) isoscelean, but a skewed scalene variation. Amongst other distortions. They see 'your' light going forward take longer to go from the pursuing rear end to the fleeing front end slower than the light returning from the departing front end to the approaching rear end. Something that makes no sense to you, but then there's all kinds of things that you can't agree on, with the mutual velocity difference, including how long a full 'tick' takes (a full circuit of bounce, via both ends), the actual distance between the ends and what the wavelength of light is at any particular time (red/blue shift). The last bit includes the Doppler effect, but all has elements of Relativity. And neither you nor they will agree with the alternative 'stationary' observers you could have chosen, for whom your isosceles will be differently skewed as they pick their own way of checking that light bouncing in one direction (whatever direction that is, for them) is going the same speed as the light on the return path (whatever that opposite direction is, for them).

It's is exactly simple as that! Relatively simple, anyway, as other observers will indicate by disagreeing with my own viewpoint.

### Re: Relative Light Speed

Posted: Mon May 07, 2018 12:26 pm UTC
Teywer wrote:Say you have a room 20m long, with two perfectly reflective mirrors facing each other. Now say that this room is travelling at 50% of c down it's long axis. Then the question is, how fast is a photon bouncing between the mirrors? Is it travelling at c relative to the room, or is it travelling at c relative to the same point as the room itself?

Einstein proposed this same thought experiment. He called it the light clock. The only difference is that a clock is attacked the mirrors such that the clock ticks every time the photon hits either mirror. Here is a short article that explains light clocks much better than I even could.

### Re: Relative Light Speed

Posted: Wed May 09, 2018 12:09 pm UTC
Right. Motion in special relativity is different from classical motion in very basic ways. Velocities do not add the way you expect, for instance. The geometry of spacetime in special relativity is not Euclidean. Jewish Scientist is right to point out that your thought experiment starts to poke at the strangeness that an invariant speed of light implies and resembles Einstein's light clock very closely.

### Re: Relative Light Speed

Posted: Wed May 09, 2018 5:22 pm UTC
Teywer wrote:Is it travelling at c relative to the room, or is it travelling at c relative to the same point as the room itself?

Yes, both. Every observer measures it as traveling at c relative to themselves. The necessary conclusion to make sense of that is that observers in different states of motion measure distance and time differently, however differently is necessary to make light always seem to be covering the same distance in the same time no matter how one is moving.

### Re: Relative Light Speed

Posted: Wed May 09, 2018 7:32 pm UTC
Imagine that time is just space at an angle. (This isn't far from the truth, actually).

Now put that aside, and consider "real" space at an angle... that is, north is at 90 degrees to east, and you can lay out a grid and measure the "northness" and "eastness" of every house on the block. This works as long as we know what north is, and calculate east from it. But what if we disagree on what north is? Use the north star? Use the compass? The compass points at a (non-zero) angle to the north star. It's "in a different direction". So, all the answers come out wrong different. But they come out different in a special way. In both cases, if you square the north and east figures and then add them, the answer is identical, even though the input numbers are different. Pretty cool, huh? It's just the distance formula, or pythagorean theorem, in disguise.

When you walk in a straight line, you are walking some amount north and some amount east at the same time, and that relationship is fixed by the same formula. You can measure house positions by how much "in front" and how much "to the side" they are, and the same relationship governs the results. The angle you walk acts like a "portable north" for you.

Ok, now popj time being space at an angle. You are traveling through time but not through space (from your own point of view). You are always "right here", but "now" keeps slipping into the past. Other people may see you moving through space, but only because you are moving with respect to them.

So, now consider what happens when you snap your fingers twice, one second apart. To you, the snaps happened at the same place ("right here"), but at different times (one second by your watch). To your friend, screaming by in a blitzrocket, those two snaps happened in two different places: "right in front of me" and "way behind me".
Spoiler:
Cue Maxwell Smart: "Missed, by that much!"
But, they are the same two snaps. So, in spacetime, they have to have the same relationship to each other. They are the same "spaceetime" distance apart. (This is called the "interval")

It turns out that not only are you imagining time is space at an angle, time actually is "imaginary space" at an angle. The equivalent relationship turns out to be that you can square the time difference between the two snaps, square the space difference between the two snaps, subtract them, and the result is the same for you and for your friend. (Yes, there's a conversion factor involved between space units and time units). We say the interval is "invariant".

The conversion factor is c, the speed of light. (Hmmmmm....)

Further, if you use ic as the conversion factor (i being the square root of -1), you can use the ordinary pythagorean theorem again, and add instead of subtract. The i, when squared, becomes the requisite -1.

This needs to be visualized in four dimensional complex space, but a cartoon of it looks like this: Use the vertical axis for time, the horizontal axis for space, and that's "you, at rest", moving up the graph in time. You always see yourself that way because you are still with respect to yourself.

Somebody whizzing by will be moving through this spacetime diagram at some angle from the vertical from your point of view. It will lean towards the 45 degree diagonal that represents the speed of light. But your view of their "space axis" will also lean towards that same diagonal. As you view it, their space and their time will not be at 90 degrees, but will scrunch closer together. At the speed of light, your view of their space and your view of their time will be superimposed. And that's as far as you can go - where space and time meet.

Still, from their POV, they see their own space and time at 90 degrees, and it's your axes that seem scrunched.

For an excellent and accessible book on the subject, check out "Spacetime Physics" by Taylor and Wheeler.

Jose

### Re: Relative Light Speed

Posted: Thu May 10, 2018 10:36 am UTC
(Then, once you get your head round all that, realise that it's all totally wrong* too, and spacetime isn't really continuous like Relativity supposes but instead it's all quantized, composed of 'strings' or 'loops' that are a billionth of a billionth the size of a proton...)

*for some definitions of wrong

### Re: Relative Light Speed

Posted: Thu May 10, 2018 11:15 am UTC
I thought string theory was still "up in the air"?

And arent the loops particles rather than spacetime itself?

### Re: Relative Light Speed

Posted: Thu May 10, 2018 12:34 pm UTC
Yeah the quantization of spacetime is not something we have any evidence for, neither a compelling single theory for. Something is up at that scale, but we don't know. It's very interesting.

Special and general relativity are 100% rock solid within their realm of validity. They seem weird, but scientifically, they are not weird. It is very tempting to put all physics for which we lack intuition from our normal lives into the same sort of mental file cabinet, but it's worth being very clear that there is nothing speculative or controversial about any of the relativistic fun. (Ditto quantum mechanics.)

### Re: Relative Light Speed

Posted: Tue May 15, 2018 2:31 pm UTC
p1t1o wrote:
I thought string theory was still "up in the air"?

And arent the loops particles rather than spacetime itself?

String Theory's looking less and less plausible by the month.

In order to get fermions you need supersymmetry and that's becoming increasingly ruled out and so, because we know we do have fermions in this universe, String Theory's also becoming increasingly ruled out.

It's still a useful tool in some contexts due to the AdS/CFT correspondence that tells us that some solutions in String Theories can be converted into solutions to problems in Conformal Field Theories (which includes lots of quantum field theories of interest) and vice versa.

### Re: Relative Light Speed

Posted: Wed May 16, 2018 4:09 pm UTC
String Theory's looking less and less plausible by the month.

In order to get fermions you need supersymmetry and that's becoming increasingly ruled out and so, because we know we do have fermions in this universe, String Theory's also becoming increasingly ruled out.

I really wish people would stop saying this...
What's being ruled out "by the month" is SUSY in a particular range of energy scales, which is required by some field theoretic solutions to problems in the standard model (namely the Hierarchy problem). If we don't find SUSY within a certain range, then those proposed solutions are wrong... this whole story is within the framework of quantum field theory and doesn't care at all about strings.

String theory, on the other hand, has no requirements regarding the scale at which SUSY is broken and for all we know the SUSY breaking scale might be much higher and the Hierarchy problem gets solved some other way. The lack of prediction of the SUSY breaking scale is just a manifestation of the usual weakness of string theory in that we don't know how to construct the solution that contains the standard model. It's the same weakness that pops up in any discussion of the validity of string theory and its status is neither made better nor worse by the outcome of the current search for SUSY at the LHC.

### Re: Relative Light Speed

Posted: Wed May 16, 2018 5:11 pm UTC
But if we *had* found SUSY, string folks would say that string theory working out is now likely than we would have thought previously. So not seeing it means we get to dump on them. Boom. Suck it, strings.

### Re: Relative Light Speed

Posted: Wed May 16, 2018 5:31 pm UTC
Yeah basically... but they'd be wrong in saying that.

It would still be a good thing for string theory if we found SUSY (at any scale, really), because then it would constrain the stringy models as well. Then again, it could also be a bad thing for string theory if it turned out that those new constraints are somehow unnaturally difficult to achieve. So maybe it's actually a good thing for string theory that we're not finding SUSY at this particular energy scale

### Re: Relative Light Speed

Posted: Wed May 16, 2018 5:44 pm UTC
Eh, it's the raven paradox. It's some evidence against string theory but not definitive and, from what I've heard from the physicists here there does seem to be a general trend towards abandoning string theory as a viable model of quantum gravity (although, it is still definitely a useful thing to research).

### Re: Relative Light Speed

Posted: Wed May 16, 2018 5:59 pm UTC
There has been a trend of some sort away from string theory for quite a while (at least 20 years), because string theory has not achieved much success and it's really difficult. That doesn't make it less likely to be true, and it's not really because of the nondetection of sparticles. Supersymmetry is a feature of lots of extensions to the standard model. Maybe most?