Source of the post
I don't find it hard to wrap my mind around that our everyday concept of simultaneity breaks down with relativity, but more specifically, the isotropy of the speed of light, what's the problem with proving it by observing the orbits within our solar system?
I totally agree here. How is it possible that all observable evidence would agree both with a non-isotropic speed of light and one that is isotropic? Is not easy to believe for me that this would result in the same universe we see? I might need Watsisname explanation here ;(
Also, let's imagine an experimental device where you place two mirrors around a light source and at the same distance to it, so the light bounces on both and goes to the observer's eyes (located far away in the normal to the line passing through both mirrors). The distance can be measured with a ruler, and the length of the optical path for a photon that goes to mirror A and then to the observer is the same as the one that goes to the mirror B and then to the observer since the observer is at the same distance to both mirrors and the light source is the same distance to both mirrors also. The only difference would be that light would have to travel in different directions to reach the observer, so that a non-isotropic speed of light could be detected with a sufficiently precise measurement on a clock (or just by making both rays to interfere and watching the interference pattern). Why wouldn't some experimental setup like this reveal this anisotropy?
Okay, let me try; the total displacement in the y direction is zero for both paths (just like in a round trip). So looking to the y-component of the displacement: the first part of the trip (from source to mirror), any real speed that light might have in that direction might be counteracted by the complementary speed in the opposite direction. And this is true for both paths, regardless of which balance of speeds they might have (which might be different for each path since they go in different directions). Now for the x-components of the total path, here they in both cases we don't perform a round trip and in both cases the distance travelled is the same so we can't expect any difference. Is this correct? I've assumed the speed of light is always counteracted by the speed in the opposite direction so it looks like half the round-trip speed is [math]
just like in the examples of the video, and I've also assumed that the the velocity vector can be decomposed in the x and y direction. Ahhhggg maybe it is true that there is no way around this thing in the end.
Another issue I have getting to understand this is; okay we have to at least impose that the speed of light is homogeneous so that in my experimental setup we can counteract the different speeds of light due to anistropies by the different paths taken to the observer. So, the speed of light is homogeneous but could be non-isotropic, wouldn't the break in the symmetry imply the non-conservation of some quantity that Noether's theorem points to in an isotropic-speed-of-light universe? Couldn't we observe this quantity not being conserved as evidence of a non-isotropic-speed-of-light universe? Why this test would also fail to recognize the difference between both scenarios?
As a final comment. If this is true (that the one-way speed of light can't be experimentally confirmed and thus could be anything that allows for a round trip speed of [math]
) the main point here will be: How awesome is relativity (and the entirety of physics) that it really doesn't care about what the actual speed of light is!!!? How awesome is that the speed of light might not be a physically determined thing at all and just a part of a conventionalism that can be modified without any change in the material world?
This makes the speed of light seem more and more like the thing relativity claims it is, not just the speed at which light propagates, but something more fundamental of the geometry of space-time (that goes beyond light and other particular phenomena of nature). A metaphor that I always liked is the one that says that the speed of light is like the poles on Earth, you can't go farther north at the north pole (because of the geometry of a sphere and not because of the technical difficulty of performing such a feat), just as you can't go faster than the speed of light because of the geometry of space-time and not because of the difficulty of breaking that speed barrier. And now I can see that we could add some more meaning to this metaphor by saying that the north pole is also, in fact, just a convention. That you can define the poles on a spherical grid at any position on the sphere you want. We chose to use the convention that defines the poles on Earth as the points where the rotational axis intersects the surface of Earth, because it was easier to talk about climatic zones but not because they were special in any geometrical aspect to any other antipodal points on the surface. Just like we took the speed of light to be half the round-trip average speed of [math]
because it was simpler to convene that the speed of light was isotropic, while in reality it doesn't matter at all. Any speed of light in a non-isotropic world (that allows for round-trips that make an average speed of [math]
) would yield the exact same results. You can't go faster than light in any case (as you can't go to the north of the north pole) because speed is relative to convention and frames of reference (just like the north direction is relative to the coordinate system you are using or what pole you consider is the northern one by convention).