CERN's Shrinkage Dance

Time marches on at the usual rate in your own reference frame no matter how fast you go. It’s the other guys who have timing issues from your point of view. But it's not that their clocks run any slower or faster than yours. It's just that they have a different perception of simultaneity (because of the vx/c^2 term in the time transform) so they want to start or stop counting at the wrong time. Events in Einstein's philosophy can only be simultaneous in one reference frame so one or the other gets a head start in any other context. You're going to get a different result if you start counting before I depart for example. That's time dilation in a nutshell. There's also a scaling factor, but that's really just a calibration exercise to ensure that you're comparing apples to apples.

You're also supposed to maintain your geometry in your own reference frame at cruising speed no matter what you’re made of so the other guys have to see you shrink in order to balance the books. That's a bit tricky though because the worldline x=L+vt transforms to x’=gamma*L. CERN says material properties have to intervene while you're getting underway to undo that elongation. Otherwise it would be a dead give-away for detecting your own motion at cruising speed with the curtains closed.

You might ask how an object shrinks before our eyes while it’s getting underway. Does the front shrink towards the back or vice versa? Or is it a centre of mass thing? And what happens to the space which is vacated? Conventional wisdom says Mother Nature is just opposed to the premise of unilateral acceleration. She insists that you accelerate different parts of an object at different rates so it will have the correct length at whatever cruising speed it achieves. Born rigidity is an attempt to add some mathematical rigour to that, but it fails miserably when gravity is at play. The issue also comes up in the Ehrenfest Paradox and the solution in that case is subjective pi (aka. non-Euclidean geometry.) It’s a tangled web they weave. But it’s all based on a survey of opinion as opposed to cold, hard math so we should take it with a grain of salt until someone puts it to the test. I wouldn’t bet the farm on it because we’ve been schooled by Mother Nature before when we jumped to conclusions like that.

In the meantime, you have to learn how to do CERN’s shrinkage dance if you want to pass your exams. The trick is to follow the math in the formation flying case and do the dance if the players are tethered in any way, even if the tether is made of jello. Just to be clear, the dance starts with the proper length at cruising speed (x’=L) and you have to work backwards to get x=L/gamma+vt. Everyone agrees on that use case. If anyone asks how long it’s going to be when it lands (smoothly), the answer is L and the interview is over.

Home Page

Comments

Post a Comment

Popular posts from this blog

The Brass Tacks of the Twin Paradox

Image
The Brass Tacks of the Twin Paradox Back Story Remember Einstein’s Twin Paradox? Someone goes walkabout at near light speed and winds up younger than their twin who stayed at home. It seems like a conundrum wrapped in an enigma because the the experts insist that moving  clocks tick more slowly than one another. It's patent nonsense of course because you can't be both older and younger than your twin when you're standing face-to-face at the family reunion. So what's up with that? Are they pulling our proverbial legs? Here's the geometry in question: Conventional Wisdom You can find several explanations in the literature and on YouTube (see links below for example.) The general consensus is that  the symmetry is broken by the traveller's antics at the waypoint. The about face at that location is supposed to be the give-away. That's how we know whose clock is running slow. But naysayers with an ounce of common sense are quick to point out that we're being ...
Read more

The Brass Tacks of the Andromeda Paradox

Image
The Subjective "Now" Interpretation of Special Relativity Back Story In the Andromeda paradox (aka. Rietdijk–Putnam argument), we are given to understand that there's a certain faction of hostile actors in the Andromeda galaxy who want to invade the Earth. They have presented their case to their local council and the matter has been put to a vote. An astronomer on Earth observes the verdict through a telescope and, after correcting for the propagation delay, works out the time at which our fate was sealed. A passerby sees the same image at the same time, but having a skewed perception of simultaneity, arrives at a completely different conclusion. So when exactly did the verdict make the transition from the uncertain future to the certain past? i.e. When is "now" over there? Conventional Wisdom Conventional wisdom says the question is invalid. What you see is what you get. All perceptions of "now" over there are real because, unlike regular spacetime ev...
Read more
Derive the Lorentz Transformation The fastest way is to generalize Galilean relativity like this: X = A(x - vt) T = B(t - Cvx) where the constants A, B, and C are to be determined. The reverse transformation is: x = (X/A + vT/B) / (1 - Cv^2) t = (T/B + CvX/A) / (1 - Cv^2) These equations have to work if x is swapped with X and t is swapped with T so: A = B = 1 / sqrt(1-Cv^2) The constant C puts an upper limit on the velocity v so it should be expressed in terms of a speed limit: C = 1 / c^2 The value of ‘c’ is pretty much arbitrary because it’s really just a unit conversion factor. Any non-zero real number will do the trick. You could set it equal to one with no loss of generality. You just have to measure space and time in the same units. The last step, which was Einstein’s deep insight, is to notice that the same is true of Maxwell’s equations. i.e. The phase speed of an electromagnetic wave in the absence of any external fields is also unity if you measure space and time in the same...
Read more