Thanks for this! So if I understand correctly, an “orthogonal” collision in which a particle is moving near light speed along, say, the x-axis, and a particle moving along the y-axis, the y-dimension mass of the fast (x-velocity) particle would still be what used to be called its ‘rest mass’, while it’s x-direction mass would be much greater! That does make sense, and I guess I already knew that, but had never given much thought to how that complicates the collision (which would not really be orthogonal in any case since all motion is relative).
Edited to add: so when I teach my highschool students that mass is a scalar quantity, is that technically wrong? As in …is mass then a vector too in the relativistic world?
Mass is an invariant scalar, yes. It is not wrong. Mass is not a vector in the world of special relativity. Momentum (p) is the vector component that takes care of those other effects.
I never thought that much about it either but the video nicely describes the effects of applying force along different vectors and how the vectors eventually align with Newtonian physics as the velocities drop below ‘relativistic’ speeds. Overall, it was a timely rabbit hole to spend some time reviewing, because I recently reread my old university physics textbooks and class notes before finally tossing them out for a big Spring cleaning effort.
Special relativity hasn’t changed – the predictions of the theory remain exactly as they were. How we express the theory has changed. You can, if you insist and know the math, map the current mathematical description of SR to the older description, but (as has been pointed out) the newer description is a lot easier to apply broadly, something Einstein himself recognized.
Even if you move the goal post e=mc^2 says mass increase is real.
Under the contemporary definition of ‘m’, that equation is only valid in the rest frame of the thing moving. Did you watch the video?
Put another way, we no longer express the way that the behavior of something changes with velocity in term’s of the thing’s mass. But the changes in behavior are the same whether you’re formulating relativity in terms of rest mass or in terms of relativistic mass. And those predicted changes in behavior are very easy to test, e.g. in a particle accelerator.
As in … let’s have a standardized “velocity unit” where speed of light = 1 just like the A.U. (or I suppose the lightyear) are standardized distance units? Leave it to physicists to decide on that scale! Sorta like astronomers saying the entire universe is Hydrogen, Helium, and the trace amounts of everything else are all metals.
Not exactly – in this system, c is a unit-less number with value 1. You just have to re-insert the appropriate powers of c where needed if you want to tidy things up when you’re done.
I guess this is why I rarely reach this unit in my high school physics classroom. I’ll let the university profs take it on from Newton and from what I’m able to parrot from Einstein.
This is Begging the Question of what Falsification means.
We do not falsify measurements, we falsify hypotheses and predictions. The requirement is that it should be possible, at least in theory, to make a measurement which would contradict the hypothesis or prediction. Relativity does not predict that all sorts of measurements are possible in all circumstances.