On Monday, December 9, 2024 at 9:08:33 PM UTC-7 Jesse Mazer wrote:
On Mon, Dec 9, 2024 at 8:28 PM Alan Grayson <[email protected]> wrote: On Monday, December 9, 2024 at 4:54:34 PM UTC-7 Brent Meeker wrote: On 12/9/2024 3:24 PM, Alan Grayson wrote: On Monday, December 9, 2024 at 2:01:28 PM UTC-7 Brent Meeker wrote:> > Nothing odd about dilation and contraction when you know its cause. > But what is odd is the fact that each frame sees the result > differently -- that the car fits in one frame, but not in the other -- > and you see nothing odd about that, that there's no objective reality > despite the symmetry. AG The facts are events in spacetime. There's an event F at which the front of the car is even with the exit of the garage and there's an event R at which the rear of the car is even with the entrance to the garage. If R is before F we say the car fitted in the garage. If R is after F we say the car did not fit. But if F and R are spacelike, then there is no fact of the matter about their time order. The time order will depend on the state of motion. Brent Since the car's length can be assumed to be arbitrarily small from the pov of the garage, why worry about fitting the car in garage perfectly, and then appealing to difference in spontaneity to prove no direct contradiction between the frames? It seems like a foolish effort to avoid a contradition, when one clearly exists. AG What's the contradiction? *ISTM that the car can, or cannot fit in garage given the initial condition that in the rest frame, the car is longer than the garage; in other words there is an objective reality, but the frames differ on whether the car fits or not.* Can you define what "fits in the garage" would mean in objective terms, i.e. a definition that does not depend on simultaneity or choice of frame? If you can't even define that phrase in any objective terms, why do you believe there is any objective reality here? Is it just some kind of strong intuitive hunch that there "should" be some kind of objective reality attached to such a notion? *"Fits" means the car's length is equal to garage's length, or less. If car exactly fits, this is ambiguous from the pov of garage frame due to lack of simultaneity, and this is the consensus solution to an alleged paradox. But what happens if the car's velocity is increased, so car fits with room to spare? This is the case I have been posting about. AG * * If one avoids the issue of simultaneity, by not requiring the car to perfectly fit in the garage, we get opposite conclusions from the frames. AG* The paradox does not depend on the assumption that the car is the same length as the garage in either the car frame or the garage frame (or that they have the same rest length), *I don't make this assumption. AG* if that's what you mean by "perfectly fit in the garage". Even if the car's rest length is much shorter than the garage's rest length, so it fits easily in the garage frame, *No, this isn't the initial assumed car length. Its length is assumed larger than the garage, and the question is whether it can fit due to its motion which causes length contraction. AG* you could always pick a sufficiently large relative velocity such that the car would be longer than the garage in the car's rest frame, *No, the car's length decreases in the garage frame only due to its motion. In the car's frame, the car's length doesn't change. AG* and thus it would not fit in that frame, so the paradox remains. Not sure what "opposite conclusions from the frames" could mean if you don't have a specific way to define "fits in the garage" in a way that doesn't depend on picking some frame or another. Jesse *As I understand the problem, in the initial rest frame the car is assumed to be larger than the garage. Then the question is whether it can fit when the car is in motion due to length contraction. In the car's frame, the garage length decreases, so there is no possibility of the car fitting. OTOH, from the pov of the garage frame, the car's length shrinks, so there is some velocity where it fits perfectly. If the velocity continues to increase, the car fits with room to spare. So, I have shown that the frames differ in concluding whether the car fits, or not, and the question is whether this is a paradox. If you conclude it is not, then you deny there's an objective reality such that the car fits, or doesn't fit. And "fits" just means the car's contracted length is EQUAL TO or LESS than the garage's length. AG* -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion visit https://groups.google.com/d/msgid/everything-list/89c06dbb-6347-47e5-a5b1-52bacce7922en%40googlegroups.com.
