How do the detectors work? In my mind they don't make physical sense. They're saying the distance between the mirrors changes, but I don't understand how that's possible in this context.
Let's say a gravitational wave compresses space. To someone inside that compressed space, there should be no noticeable difference. Light will still flow the same way through the compressed space at the same speed relative to the compression. Matter will behave identically, because both light and matter are part of the fabric of that space. As I understand it, the only way the mirror lengths could change is if space is created or destroyed.
If that doesn't make sense, consider the 2d analogy of drawings living on paper. Assume also that light moves only along the surface of the paper. If you bend the paper, the light will bend with it. But when you bend the paper, the creatures living on the paper can't know it's bent. The fabric of the paper is still identical. Even if some of the paper gets compressed in one direction, it will still have the same amount of particles, so any light travelling through there will hit the same amount of resistance. And stretching the paper, even if you're a drawing on the part being stretched, would have no effect. A 2d creature looking at something 1 foot away, even if the paper is stretched to 10 feet, won't see any difference, because the fabric light travels through is also stretched.
The only way I can see this making sense is if light travels independent of the fabric of space, but it's my understanding that light travels through it, not independent of it?
I think the crucial detail you are missing from the article is this:
"According to the equations physicists have settled on, gravitational waves would compress space in one direction and stretch it in another as they traveled outward."
LIGO is two sets of 2 L-shaped antennas spread far apart on the globe, so that we can compare the compression of space in orthogonal directions and measure the very short delay between the gravitational wave hitting the first detector followed by the second. In this case, that difference was 7 milliseconds, which is also consistent with the speed of gravitational waves (also the speed of light)
I still don't understand. It doesn't matter where the compression happens, because it should be undetectable to any light/matter that's fundamentally a part of that space? If one of the arms gets compressed - the matter will be compressed too, so light still has the same density and amount of space to travel through?
Check the comic posted by AdrianN, it explains what you're missing. Basically light takes longer to travel stretched space (but matter does not, as you correctly said).
I see. If that's true, then light travels through a higher dimension, and this is definitive proof of at least a fourth spatial dimension. Otherwise there would be nothing for the 3d space to ripple through, or for light to travel through.
I'm surprised I haven't heard that light travels independent of 3d space compression before. That would also imply that if you enter a black hole with your feet at the bottom, you would see them visibly stretched far away from you (noticeably? I'm not sure) because light would take longer in the distortion to reach your eyes.
Doubts about higher dimensions and general relativity is common and a crucial point, so I dont think you should get downvoted.
Some points which might be helpful. We have a way, using the concept of a manifold, for ants on a surface like a sphere or a dougnut to figure this out without appealing to a third dimension. One could imagining say ant geographers making maps of portions of the surface, and noting how common regions covered in two different maps have different labels/coordinates. One can then figure out a definition of when two collections of maps(called an atlas) are equivalent and then show that an atlas for a plane, sphere, doughnut are mutually nonequivalent.
But all this is topology and involves global considerations. What is relevant here is local curvature. We can also do this appealing to an extra dimensions. Now, you used the example of a folded paper and you are correct that for an ant on the surface, the curvature is indetectable. The curvature of the paper is extrinsic and not intrinsic. We say that is isometric to flat space, and its curvature tensor is 0.
On the other hand, if the ant was on the surface of a ball, it could figure out this curvature intrinsically, for instance, by measuring sum of the angles of a triangle or the distance between parallel lines keeps shrinking. Not only is this intrinsic, but it is locally measurable. One cant have maps, even for a small area of the earth's surface, without some kind of distortion because of this intrinsic curvature.
An additional complexity - in GR, spacetime is curved rather that just space. Also, dont take 'curvature' too literally, it is just a way of measuring deviation from numbers that you would get in the flat scenario.
For more read up on manifolds, riemann curvature. John Baez had some essays on the geometric meaning of the curvature tensor in terms of the volume of a ball relative to the usual flat Euclidean case.
Thanks - still not sure I get it. The "fabric" is stretched in x, squeezed in y, sure. Is it that the wavelength of the light is -not- stretched? Guess I need to go back and study physics again :/
Still not explaining it. If spacetime is stretched why doesn't light "speed up" to accommodate for it is what he's asking. I'm assuming it's because the speed of light is invariant to that.
Exactly. The speed of light in a vacuum is constant no matter how quickly/slowly your frame of reference is (Special Relativity). You can think of it as the space "stretching/shrinking" because of the gravitational wave, as that is how it looks from the point of view outside the experiment.
Another way to look at it is to change your reference to be internal to the experiment. You can imagine the experiment moving through space-time at a constant rate of speed. When the gravitational wave hits the experiment its movement through space-time changes an infinitesimal amount (faster than slower as the wave passes, or vice-versa). Since the speed of the light passing through space-time has not changed (due to special relativity), the difference between its start and end points can be used to measure the amount of change caused by the gravitational wave, essentially in the same way you can use a laser to measure the speed of a moving object relative to a stationary object. Only you are basically "bouncing" the laser off of the experiment itself to determine the change.
Here's my re-statement of this confusion, isn't everything we can experience embedded in time-space, including the LIGO experiment itself? So how is there any relative shift allowed to be detected when everything we know is fundamentally intrinsic to time-space? That is, I too would appreciate having this mis-conceptualizing, of mine, cleared away.
Another re-phrase: how can we detect that space has stretched out if all of our rulers also get stretched by exactly the same amount?
The answer is that we have a ruler that doesn't get stretched in this way: light. The speed of light is a constant dictated by the laws of physics; stretching out our flashlight to twice its normal size wouldn't make the light it emits go twice as fast. So if you just measure the time it takes for a light ray to go from one point to another, you can compute the distance that it must have traveled, and if that distance changes, then you know that the space in between must have been stretched.
Thank you. i think that settles my confusion. (it's somewhat like we witnessed a length/Lorentz–FitzGerald contraction in a situation where there was apparently no reason to witness one). Now i can go back to being simply amazed by it all.
Thanks for the nice explanation! But another question: since the expansion rate of the universe has been different at different times, does this mean that the measured speed of light would be different at different times as well?
Because if the ruler you are using to measure is expanding at rate x, the measured speed of light would be different than when the ruler is expanding at rate y?
So, during the deflationary period of the universe, the speed of light would be significantly smaller, correct? In fact, would it be "negative" due to the universe expanding faster than light?
Does this mean that in earth's gravity well, there is an absolute difference in the time light takes to travel compared with light travelling in the void of space?
Can we compute the strength of a static gravity field we are inside, by measuring the time that light takes to propagate through it?
The light is constant, which means it moves at the same speed in both cases (assuming the light is in a vacuum). It won't move faster or slower based on the gravity field (other than in the case of black hole where it can't escape at all).
What happens instead is that the speed that an object moves through space-time changes dependent upon gravity. Using an atomic clock, we've actually measured the effect of gravity to show that time moves more slowly down on earth than it does in an orbiting satellite.
Let's say a gravitational wave compresses space. To someone inside that compressed space, there should be no noticeable difference. Light will still flow the same way through the compressed space at the same speed relative to the compression. Matter will behave identically, because both light and matter are part of the fabric of that space. As I understand it, the only way the mirror lengths could change is if space is created or destroyed.
If that doesn't make sense, consider the 2d analogy of drawings living on paper. Assume also that light moves only along the surface of the paper. If you bend the paper, the light will bend with it. But when you bend the paper, the creatures living on the paper can't know it's bent. The fabric of the paper is still identical. Even if some of the paper gets compressed in one direction, it will still have the same amount of particles, so any light travelling through there will hit the same amount of resistance. And stretching the paper, even if you're a drawing on the part being stretched, would have no effect. A 2d creature looking at something 1 foot away, even if the paper is stretched to 10 feet, won't see any difference, because the fabric light travels through is also stretched.
The only way I can see this making sense is if light travels independent of the fabric of space, but it's my understanding that light travels through it, not independent of it?