On Monday, January 6, 2025 at 2:58:12 PM UTC-7 Alan Grayson wrote:
On Monday, January 6, 2025 at 2:44:56 PM UTC-7 Quentin Anciaux wrote: Last try. So as you agreed, the two observers being in different frame, they don't share the simultaneity plane. The key to understanding the situation is that the two observers (the person in the garage and the person in the car) don’t share the same idea of what events happen at the same time. This is because, in relativity, the concept of "simultaneity" depends on the observer’s motion. What does "fit into the garage" mean? For the car to "fit into" the garage, we’re asking if: The back of the car has passed the entrance of the garage and The front of the car is at, or before, the exit of the garage at the same time. Why is there disagreement? 1. For the garage’s observer: The car looks shorter because of Lorentz contraction. They can say: "At the same time, the back of the car has passed the entrance, and the front is at or before the exit." So, for them, the car fits. 2. For the car’s observer: The garage looks shorter because of Lorentz contraction. They see events differently. For them, the back of the car passes the entrance before the front reaches the exit. So, they say: "The car never fits inside the garage." Why no contradiction? The disagreement comes from the fact that the two observers don’t share the same plane of simultaneity: In the garage’s frame, the "fit" happens because the events (back passing entrance and front at exit) occur simultaneously. In the car’s frame, those events don’t happen at the same time. The car sees the garage’s doors acting at different times to avoid a crash. Conclusion: The paradox is resolved because "fitting into the garage" depends on when you decide to check if the car fits, and different observers disagree about what "at the same time" means. This is a direct result of how special relativity changes our understanding of simultaneity. Quentin *As I've previously stated, the issue, if there is one, is that the frames disagree about whether the car fits in the garage, not when it fits, or how good or bad the fit is. This is obvious from length contraction alone, that the frames disagree. This fact is unchanged by the disagreement about simultaneity. So if you or anyone want to use the disagreement on simultaneity and length contraction, to put some numbers on this problem, that's fine. But it shouldn't be concluded that the underlying enigma has been solved. AG* *Quentin, look at it this way: the speed of the car can be assumed sufficiently fast, so that its length can be assumed to be any tiny fraction of the garage's length we wish, from the pov of the garage frame. With this contracted length for the car, and noting that the garage's length remains unchanged, the car can easily fit in the garage. We don't care when it fits, only that it does fit. Now, from the pov of the car frame, the garage, which is initially assumed to be shorter than the car, becomes even shorter. So, at whatever speed has been assumed, the car can never fit in the garage.These conclusions have absolutely nothing to do with simultaneity. AG* lun. 6 janv. 2025, 22:37, Quentin Anciaux <[email protected]> a écrit : A troll feels absolutely no shame. Le lun. 6 janv. 2025, 22:25, Alan Grayson <[email protected]> a écrit : On Monday, January 6, 2025 at 11:46:52 AM UTC-7 Alan Grayson wrote: On Monday, January 6, 2025 at 3:11:47 AM UTC-7 Alan Grayson wrote: On Sunday, January 5, 2025 at 10:02:28 PM UTC-7 Alan Grayson wrote: On Sunday, January 5, 2025 at 9:43:47 PM UTC-7 Brent Meeker wrote: On 1/5/2025 7:44 PM, Alan Grayson wrote: > You claim there is no objective fact. The car fitted in the garage. > But that's only from the garage frame. If it's from only one frame and not another, that's the definition of "not objective". It's not fact. It's subjective perception. Brent You truncated my statement. You showed the car fits in one frame and not the other (the car frame). The paradox is based on the belief that this is impossible. Disproving this belief is required to resolve the paradox. AG *Here is something to consider to prove what I believe needs to be proven;* *that the two frames under consideration are not in relative motion as the* *case of two inertial frames in empty space where nothing exists other than* *these two frames. In the paradox the car is in real detectable motion if one* *views its background, whereas the garage is fixed by the same observation.* *In fact, the garage and its surroundings can be considered a rigid body from* *the pov of the car frame, entirely in motion, not just the garage. I do not say* *t**his will work in possibly eliminating the relative motion of garage from * *the pov of the car frame and thus resolving the paradox, but it's a possibility* *worth **considering. AG * *Maybe you can explain this: we started with an apparent paradox based on length* *contraction. Then, to allegedly resolve it, several MB members including yourself, * *applied both length contraction and disagreement about simultaneity to get the* *SAME result which was patently obvious with nothing more than length contraction.* *At which point victory was declared; the alleged paradox was resolved! Praise the* *Lord! Can you tell me what I'm missing? And please; don't tell me that adding doors* *on the garage was needed or necessary. Without those doors it was obvious that* *the frames would disagree about whether the car would fit at some high speed. * *Maybe Jesse and Quentin could explain this as well. TY, AG* *I'd also like to hear from Clark on this issue. He was another great advocate of putting* *doors on the garage and thinking the problem was solved. As I see it, all that's been * *accomplished is to put some numbers on the problem, to calculate how good the fit* *is or isn't, without touching on the underlying problem. As for falsifying relativity, that's* *definitely not my preference. It seems to have worked for more than a century, so it's* *highly likely to be correct. But when all the experts here give their opinions, ISTM that * *none **are in the ballpark of actually shedding light on this problem. Of course, we can* *always adopt the "shut up and calculate" pov and conclude that that's what SR says, and * *be done with it. So, Clark, what do you think? AG * > It doesn't fit from the car frame, regardless of the doors, which IMO > can be dispensed with. So, as I see it, the paradox follows from the > belief that there can't be disagreement about what the frames > conclude. Isn't this the claim that must be disproven to resolve the > paradox, and a constructive proof that the frames disagree using the > LT is insufficient? 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