@freemo I don't like to refer people to books online. I'm not trying to be pretentious or imply that you haven't read the book.
That said, if you check the first chapter of Landau & Lifshitz Mechanics, in the first few pages you will see his argument for the homogeneity and isotropy of space. Although I admittedly make more radical statements, this is what I have in mind when I insist on these kinds of symmetries and why I claim that we can't have science without them.
Also I have not seen this argument in any other mechanics book, that's why I like to recommend this one in particular.
@3ammo As I already said even if light is asymmetric it doesn't break the isotropy or homogeneity of space anyway necessarily. So even if we agree that that **theory** is true and extends to light symmetry (which is nothing more than an untestable hypothesis) it still doesn't show light must be symmetric.
@freemo As I said, to keep the symmetry of space with asymmetric light, you have to have some theory to *explain* the asymmetry of light, just like out current theory explains the asymmetry of sound. In THAT theory, we must have a signal of some sort, that signal must be postulated to have constant speed in all directions: a de facto "new light".
@3ammo No you dont... no matter what theory you have that explains why the light is asymmetric doesnt change the fact that symmetry of space will always be observed. Any theoretical experiment that can be verified experimentally, if you arbitrarily change light to be asymetric without any framework, it can be at random, ijust needs to preserve two-way consistency, if you do this the experimental nad theoretical results will **always** be the same as when the light is symmetric.
Therefore you do NOT need a theory to explain why the light is asymmetric in order to keep the symmetry of the observed space to be the same, the symmetry of the observed space is guaranteed to be preserved so long as the two-way speed of light is preserved. This is the very reason it is untestable in the first place.
@3ammo By the way on the wikipedia page on this topic which i already linked there is a section that shows the lorentz transformation generalized for asymetric c and should become immediately obvious why it would result in the same observed laws of physics as we would expect and see.
@3ammo Another very relevant quote from that wikipedia article which basically repeats what I keep telling you:
"Using generalizations of Lorentz transformations with anisotropic one-way speeds, Zhang and Anderson pointed out that all events and experimental results compatible with the Lorentz transformation and the isotropic one-way speed of light must also be compatible with transformations preserving two-way light speed constancy and isotropy, while allowing anisotropic one-way speeds."
@freemo Okay, this discussion is getting a little bit out of hand for me.
We have already established that we both agree we can have consistent descriptions of our measurements with anisotropic speed of light. This is not the issue.
What I am saying is that we are not allowed to make statements like "In reality, c is anistropic, but whenever we measure it it looks like everything is symmetric". That statement is not forbidden because we have an experiment that contradicts it (we already established that it's compatible with measurements), but because it's logically incompatible with the framework we already chose. Why is logically incompatible? Because it asserts that there is a fundamentally anisotropic physical effect, without a theory behind it. If we decide to put a theory behind it, then that theory will have to conform to the symmetry *because we said so*. If it does, then it will have some isotoropic signal.
If we allow arbitrary, UNDETECTABLE effects to enter the theory but have a way of canceling them out at measurement, then this more than just "making the math difficult". This is adopting a different theory, which gives us a different view of reality. Again, I am fine with that, but I wouldn't call it a mere "convention".
I think I understand your points. I don't think I can explain mine better.
What I am saying is that we are not allowed to make statements like “In reality, c is anistropic, but whenever we measure it it looks like everything is symmetric”. That statement is not forbidden because we have an experiment that contradicts it (we already established that it’s compatible with measurements), but because it’s logically incompatible with the framework we already chose. Why is logically incompatible? Because it asserts that there is a fundamentally anisotropic physical effect, without a theory behind it. If we decide to put a theory behind it, then that theory will have to conform to the symmetry because we said so. If it does, then it will have some isotropic signal.
So we somewhat agree here. I do agree that no one could ever say “in reality one-way c is anisotropic”, theory or no theory in not even testable and will not contradict existing theory if true anyway so not even theoretically testable.
What I am saying, which is more important really is that for the exact same reasons you cant say “in reality one-way c is anisotropic” you also can not say “in reality one-way c is isotropic”, for all the same reasons, there is no theoretical framework you could use to prove it.
So my point all along has been “It is fundamentally unknowable due to the physical laws” and since the theoretical laws are a description of the physical laws it is also unknowable in theory.
So to take my point back another step, not only is the isotropy of one-way c unknowable, but whatever it does in reality (be isotropic or anisotropic) you will never have a way to discern one from the other. It is inherently unfalsifiable. Which is also why the idea that it is isotropic is merely a convention, it makes our math easier and any assumption of its nature gives the same results so we pick the one that is mathematically the easiest to do.
@3ammo Yes i think most of this has been dueling definitions and perhaps a little philosophy at best.
My philosophy is that anything that is unknowable and untestable is in all possible states and once and isnt particularly worth talking about “one true reality”.. To me the unobservable nature of one-way c is of the same sort as the unknowable nature of variables in the heisenberg uncertainty principle. That is nothing and everything is true at the same time until it can be observed and since it can never be observed it exists in a state of superposition with itself where any arbitrary interpretation is equally valid and true.
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