I was reading a post on the Stone philosophy blog at the NY Times website, finding that the vast majority of commenters seemed smarter than the philosophy professor who wrote the post. But that is just background for my question. One commenter stated the following to illustrate their point:
Is that really true, that this is now “understood to be false”? Why *can’t *you just add the speeds together? I mean, presumably the person on the train is walking in the same direction as the train is moving, we are discounting wobbles from side to side, and of course there is no issue in terms of approaching the speed of light. So am I failing to grasp something, or is this person way off despite giving the impression of intelligence?
Possibly a clumsy reference to relativistic speeds? If you’re on a starship traveling 1 mph short of the speed of light and you trot down a corridor at 5 mph, you don’t go past the speed of light. So it’s not true that speeds always add up arithmetically like that, it only seems that way under the conditions people normally live in
Without further information, the expression “until the turn of the century (or so)” seems to nod towards relativity. At the actual speeds being talked about, of course you can add the two.
I can only imagine the writer is trying (and failing) to make some point about relativistic speeds.
Okay, so I’m not insane, stupid, or both. Whew! I even thought of that issue of approaching light speed, but discarded it immediately given that the speeds used in the example were so infinitesimal by comparison.
Just for grins one can work out the discrepancy. at 20mph the Lorentz contraction is sqrt(1 - v[sup]2[/sup]/c[sup]2[/sup]) which is 0.9999999999999995 So your 5mph is actually 4.999999999999998 mph from the reference point of the ground, and thus you are travelling at 24.999999999999998 mph.
I think the author is using relativity to give an example of something that was once thought to be necessarily true and is now known not to be. The principle holds and the example stands even if the difference happens to be small.
So you’re saying the speeds cannot simply be added even at speeds nowhere approaching the speed of light–that there is some very slight degree to which the whole is less than the sum of the parts? I was not aware of that.
This is what I find very funny: the poster you cite–or perhaps in the spirit of things I should say Dr. Gutting’s interlocutor–rites good but is blithely oblivious to the dings in his puzzler.
Granted, he is talking physics to someone who publishes on post-1960s French philosophy, who surely is aware of the l’affaire Sokal.
I think the author was trying to make the point that we wouldn’t normally say that a person walking through a train car was walking at 25 mph just as we wouldn’t say that a person walking on a plane was walking at 805 mph. Because we would normally think of our walking speed in terms of the environment we’re walking in - the train or the plane.
But the writer screws up his point by explicitly adding “relative to the ground”. When you add the specific detail, then you are walking at 25 mph in a train and the writer is wrong.
A better example would have been that when you’re driving your car down the highway, you’re moving at 65,000 mph relative to the sun. But you probably won’t get ticketed.
In fact, you probably have equipment in your house that can detect relativistic effects from speeds far lower than that train. The electrons in a current-carrying wire, under reasonable conditions, have average velocities of only centimeters per second or less, and yet a simple compass will detect the magnetic field, which is a purely relativistic effect.
Well, yes. If you board the train in the back, and during the journey you walk to the front of the train, then you can get off the train at the front when it arrives at the station, and not have to walk there along the platform. So you have actually arrived earlier at your destination turnstile than if you had deboarded the train at the back, where you got on. I.e , you “went faster” for the duration of the journey.
You could argue that (if we keep things 1-D, i.e. all velocities parallel) then the quantity we should be adding is V = c*arctanh(v/c) and if v<<c then V≈v
Honestly, at that speed, the relativistic differences are smaller than the Newtonian differences; that is, as you walk forward on the train, you push it backwards. If the train weighs ten million times more than you do, you still slow it more than the relativistic effects do.