Le lun. 6 janv. 2025, 23:28, Alan Grayson <[email protected]> a écrit :
> > > 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* > AG, your argument overlooks a key point: the very definition of "fits" depends on simultaneity. Without simultaneity, "fits" becomes meaningless because it requires a comparison of events that are spatially separated. Let me break this down: 1. In the garage frame, the car fits >From the garage’s point of view, the car’s length is contracted due to its high speed. At a given instant (according to the garage’s clock), the back of the car is past the entrance, and the front is at or before the exit. This simultaneity of events defines what "fits" means in the garage frame. 2. In the car frame, the garage is too short >From the car’s perspective, the garage is the object that is Lorentz-contracted. Here, simultaneity is different: the back of the car passes the entrance at a different time than when the front of the car is at the exit. According to this frame, the car never fits because there’s no single moment when both conditions (back in, front out) are true. 3. Why simultaneity is critical The core of the disagreement between the two frames lies in when the comparison is made. In the garage frame, "fits" means that at a single moment (according to the garage’s clock), the car is fully inside. In the car frame, "fits" would mean that at a single moment (according to the car’s clock), the garage is long enough to contain the car. These "single moments" don’t match because simultaneity is relative. 4. The flaw in ignoring simultaneity You’re asserting that "we don’t care when it fits, only that it does." But that’s equivalent to saying simultaneity doesn’t matter, which directly contradicts the principles of relativity. The notion of "fits" can only exist within a specific frame because it depends on the observer’s simultaneity. 5. Conclusion If you refuse to account for simultaneity, you’re treating "fits" as an absolute concept, an approach incompatible with special relativity. Relativity explicitly shows that spatial relationships depend on the observer’s frame, and simultaneity is fundamental to this dependence. To dismiss it is to misinterpret the problem entirely. In short: The disagreement about whether the car fits is not about length contraction alone, it’s about the relative timing of events that define "fits." Without addressing simultaneity, you’re missing the heart of the issue > 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? 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/a369e743-8f0e-48aa-a3a8-d848f2fb6815n%40googlegroups.com > <https://groups.google.com/d/msgid/everything-list/a369e743-8f0e-48aa-a3a8-d848f2fb6815n%40googlegroups.com?utm_medium=email&utm_source=footer> > . > -- 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]. 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