Ok, for a change in pace from momentum for a moment, Consider the good old light speed limit. Now I am not going to get into whether on not some tiny subatomic particle can do something weird and interesting only to physicists with nothing better to worry about, and a HUGE research budget.
Lets think about a macro example, something that at least in principle “anyone” could actually do, and see.
Suppose you have two sheets of metal plate, and arrange them like scissor blades, so the corner is just laying over each other. Like the diagram above. I don’t want to complicate this with rotating surfaces and stuff (makes my head hurt) and nothing moving so fast that we have to worry about relativity.
So lets bolt or weld one in place and we’ll move the whole other one laterally, so the “V” closes (but neither is rotating).
Now let’s think about the nip-point, the black dot in the pics, the bit where the edge of the top and bottom plate cross (one above the other). At a small angle, for even a small speed, that nip point is going to be “moving” pretty damn fast. Its not actually moving, of course, only one of the plates is moving.
How fast? Well, if we keep things well away from relativity speeds, Then
Nip Speed = Sheet Speed / tan(Angle).
So if Angle = 1°, which is pretty easy to setup with a protractor really, then
Nip Speed ≈ 60 × Sheet speed,
which is pretty interesting, but no biggie. But what if I had a pretty good X-Y stage and took a bit of time. I could easily get Angle = 0.1°, then
Nip Speed ≈ 600 × Sheet speed.
So if I give a good shove, say 40 km/hr, which you gotta admit isn’t terribly close to light speed, then Nip Speed ≈ 20,000 km/hr, which is pretty respectable.
But hey, its just a point in space, not an actual THING moving that fast.
But what if we put a piece of paper in there. That’s one FAST cut on the paper!
Alright that’s interesting, but hey, what if I was a physicist with only a small budget, but lots time to tinker with some good engineering gear. Turns out you really CAN adjust angles to 10-6 or so degrees accuracy. Let’s just suppose we can do 10-4 degrees, cos we have SOME time, but not so big a budget.
Now, what about this top steel sheet, can’t we get it a bit quicker? Say 1000 m/sec (3600 km/hr). Ok, that’s pretty respectable, and not so easy, but this isn’t much more than most bullets, in fact supersonic bullets regularly exceed this, and big guns (battle ships, etc.) regularly do a LOT more. Rockets achieve this pretty regularly, and any satellite would probably fall out of the sky that slow.
OK, so away it goes, nice steady speed, cos we really tinkered with the gear. And we have our nice clean piece of paper in the nip there. The wee bit of paper is going to get cut at
Nip Speed ≈ (6 × 108) × Sheet speed
≈ 2.4 × 109 km/hr
≈ 2 × Speed of light
Now THAT is impressive.
Cutting the paper
So our paper is being cut at twice the speed of light. Of light. You know, that thing NOTHING can happen faster than.
Really? Well, yeah.
There’s nothing here that’s impossible or anywhere close to relativistic speeds. We could probably get arbitrarily fast with a few tweaks, a bit more time to tinker (and larger budget, but not too large, or we might get frightened off and just talk about at the pub…).
These are steel plates, and while it’s a really good piece of paper, there’s nothing here to stop that cut happening. Its fast, but not all that fast, especially since the nip point means there’s no “spreading” of the effect, in the way like a bullet might, impacting on a piece of paper.
So what happens to the sheet? And if you think the bend of the sheet will cause problems, pick something really easy to cut, like (say) a gas or whatever: for sure NOTHING is getting away from the nip point!
There is an actual physical change occurring faster than light speed here. ANY change causes physical effects radiating away from the change point. This change point is, well, FAST. REALLY fast. Mind bogglingly fast. Literally faster than fast!
At the very least there’s going to be one hell of a burst of blue light! And that just might attract the attention of the auditors, so it might be best to get the drinking in before the experiment.
And what about two observers one going left to right, the other right to left? One is going to see the paper severed before it’s cut!
Is your head spinning yet? Because I think the other one might actually see the paper UN-CUTTING… Around about then, some serious drinking is in your immediate future (or past, I guess)
Anyone got a wee research fund floating around? I think I have a really cool project for you!