The analogy is imperfect, as c is not just the speed of light, it is also the universal upper bound of the speed in general, whereas the Mach can be exceeded.
Yes, but as far as special relativity is concerned the mach number is by definition the fastest way to propagate information (a signal) as a wave through a given medium.
This is why if you squeeze a crystal the internal wavefronts interact relativistically.
Just pick up any special relativity textbook (if you don't know Special Relativity, it really only requires basic algebra to understand most of it and is pretty intuitive once you've read it). I recommend Taylor's "Spacetime Physics" which has lots of fun pictures and examples.
Anyway, you can think of special relativity is being all about information: if I look at something moving, it takes time for the light to reach me and by the time it has the thing I see isn't quite there any more. When things go really fast this becomes noticeable, as information about where something is can only travel so fast.
If you think of the deformation of a transparent crystal you could see what's going on pretty much immediately (light is slower in a dense medium, but not appreciably so in this example). But in an opaque crystal only the waveforms due to displacement (AKA "sound waves") can transmit "state" information from one place to another.
So you can draw the same Minkowski diagrams you would for interstellar space, only instead imagine them being inside the crystal. You can pretty immediately see that the maximum speed of information propagation is the speed of sound, so any deformation can only be learned about by a signal moving that fast. The same pictures that show a speeding rocket foreshortened now describe your crystal deformation when seen from various perspectives. Of course with a crystal you can squeeze from multiple sides which can make the diagrams a lot more interesting!
Things like this pretty much justify all the time spent procrastinating on HN. Thank you. (And also don't thank you, this is variable reinforcement at its purest.)
So if you can formulate "sonic relativity" like this, what happens when you trick it to provide faster-than-sound signals? Say, you emit an acoustic signal in one place, and route an electric wire with sensors and actuators that transmit it outside of the medium and re-emit as sound closer to observer. I.e. a sound-world analogue to a wormhole. Can you some (or any) of the time travel trickery that is said to be implied by any possible FTL?
Also, how is it that Minkovsky's diagrams work, apparently length contraction and time dilation can be seen as working too[0], and yet we know we can go faster than speed of sound in a medium?
Of course you can though the “time travel” is only apparent to someone who can only see as fast as Ma, not to someone who can see at, say, the speed of light. This is not really any more thrilling than the higher-dimensionality stores of “Flatland”
And such time travel isn’t as interesting as it is in the story books.
While I agree that the maths needed to understand Special Relativity are simple, SR itself not so much: we get used to things like the twins paradox, but do we really understand it?
They seem pretty mundane consequences of SR and not even paradoxical.
General relativity, on the other hand.....ok I passed some classes back in the day but looking back I’m not sure I ever understood it, except at a very shallow level.
I can't answer your question, but I had an uninformed thought.
This idea reminds me of what happens when you dangle a very long slinky and then release it. The bottom of the slinky hovers in place until the collapsing top finally reaches it. The information that the top end lost its support has to propagate through the slinky.
That's something different. There's two effects going on:
1) Each 'slice' of the slinky, whether near the bottom, middle, or top, wants to fall down under the influence of gravity.
2) Once the top is released, spring forces in the slinky want to compress it so that the top and bottom both move towards the middle.
Therefore you'll briefly have one part somewhere in the bottom half (not necessarily the "bottom"--it depends on how strong the spring is), that's being pulled up at 9.8m/s^2, which ends up matching the speed that the slinky center of mass is falling down, thereby making it appearing to hover in place for a moment.
I’ve always wondered if there was some analogous technique for drawing out parallel programming from lock acquisition to atomic variables. I always find them so much more difficult to reason about in code form due to all the ways different threads can interact, it seems drawing them on 2D might help.
you already can do this in 1d by just writing out the possible sequences of events. Feynman diagrams are used to help enumerate all possible particle interactions, including 'virtual' interactions, but there are no virtual interactions in multithreaded programming.
There are virtual interactions in multithreaded programming. Virtual in this sense basically means internal - if two threads have a secret backchannel to send messages and you don't have access to any of their internals, you can model their behavior with "virtual" messages. To be general, it would even be a mixture of all possible implementations.
Only those messages detectable from the outside are "real".
Besides, if you have threads separated by significant difference, there isn't even a canonical ordering of events due to special relativity.
Aren't they though? Also, I'm sure someone will eventually match this concept with something, probably building an esoteric language for describing parallel programs with Feynman diagrams, just for the kicks.
Yea I know, but it still leaves something to be desired. You can encode a 3D shape as a list of all possible of 2D slices too, but often it'll be easier to visualize as a 3D shape. It's not a perfect metaphor, but I'm looking for new ways to visualize concurrency.
