On Fri, Dec 20, 2024 at 11:06 PM Alan Grayson <[email protected]> wrote:
> > > On Friday, December 20, 2024 at 8:03:38 PM UTC-7 Alan Grayson wrote: > > On Friday, December 20, 2024 at 7:47:47 PM UTC-7 Jesse Mazer wrote: > > On Fri, Dec 20, 2024 at 6:53 PM Alan Grayson <[email protected]> wrote: > > On Friday, December 20, 2024 at 3:03:36 PM UTC-7 Jesse Mazer wrote: > > On Fri, Dec 20, 2024 at 6:14 AM Alan Grayson <[email protected]> wrote: > > Please define what you mean by local events, with some examples. > > > I did that in my last two comments on the other thread, the first of which > you had said you were going to respond to in more detail. In my > second-to-last post see the two paragraphs beginning with the sentence 'But > are you asking a different question about what is the motive for demanding > that any claims about how things work in different frames needs to pass the > test of giving identical local predictions, in order to qualify as good > physics?' with the example of the mini bomb and the glass of water, and in > my last post see the paragraphs beginning with '"The car fits" or "the car > fits" are not statements about local events, i.e. statements about things > that happen at a single spacetime point in one of Brent's diagrams'--in > that comment I then went on to give examples involving endpoints of the car > and garage crossing paths with clock readings and ruler markings given at > those specific crossing points in spacetime. Can you re-read those > carefully, and if you're still unclear ask follow-up questions to either of > those comments? > > Note that in these kinds of problems we idealize things like clocks and > endpoints of the car as being like point particles that only have a single > position coordinate at a single time coordinate (likewise the bomb and the > glass of water), which I assume you won't have a problem with if you are > willing to similarly idealize the car and garage as 1-dimensional. But if > you were to treat clocks etc. as having an extension in space that was tiny > compared to the lengths of the car/garage, and passing by the ends of the > car garage at a similarly tiny distance, this would differ only negligibly > from the idealized calculation of treating them as points. > > Jesse > > > I don't have a problem with idealizations and it's clear that we're using > them in this issue. I didn't want to reply on the other thread in order not > to mess up your long post which I will eventually respond to. And I realize > that the simultaneous endpoints of a perfectly fitting car are not local > events but why does the fact that they're not simultaneous in the car frame > solve this apparent paradox? And you'll notice the author I quoted doesn't > state exactly what the paradox is. AG > > > What I'm saying is that "solving the paradox" requires understanding that > despite the disagreement over fit, there is no actual disagreement about > local events like the ones I mentioned with rulers and clocks at different > positions. But to understand conceptually how it can be possible that they > can disagree on fitting but still agree on all details about local events, > you really need to look at the way the frames have differing definitions of > simultaneity. As I pointed out on the other thread, if you imagine a > hypothetical world where there is *no* disagreement over simultaneity but > each frame still predicts that objects moving in that frame are > Lorentz-contracted, then two frames that make different claims about > whether the car fit would automatically *also* be disagreeing over clock > readings at some local events. > > As for the other author you quoted, that person is dealing with a > different version of the car/garage paradox where the car is supposed to > instantaneously accelerate to come to rest relative to the garage when the > front end reaches the back of the garage, and they're saying that this > would lead to different physical scenarios depending on whether all points > in the car accelerate simultaneously in the car frame, or if they > accelerate simultaneously in the garage frame. In the first scenario the > back end of the car will come to rest relative to the garage when it's > outside the garage (so the car never fit in either frame) and in the second > scenario the back end of the car will come to rest when it's inside the > garage (so the car did fit in both frames). This wouldn't be a mere > difference between frames as in Brent's scenario where there's no > acceleration, these would be two physically different options for how to > accelerate the car. > > > There's nothing in that scenario which models it as accelerating (actually > decelerating) to get a perfect fit. In fact, the author states that the car > fits in the garage from the garage frame, but not in the garage in the car > frame. He then states that simultaneity fails in car frame and this is the > alleged solution. At least he seems to agree with my concept of what > constitutes a paradox. AG > > > Wrong. The author does have the car stopping to get a perfect fit, but I > don't think this matters. We can assume the car is in constant motion and > get the same result re; differerence in simultaneity between frames. AG > There are different ways of formulating the paradox, and as you seem to acknowledge, the author you linked at http://insti.physics.sunysb.edu/~siegel/sr.html does talk about the car stopping, and notes there are different possible physical scenarios for when the back of the car stops if the front stops when it reaches the back wall (i.e. whether the back of the car stops simultaneously with the front according to the car frame's definition of simultaneity or the garage frame's definition of simultaneity). Of course you can also formulate the paradox in terms of different frames' perspective on a car moving inertially through the garage without stopping as Brent did (that's the way the paradox is usually formulated), but then why did you specifically ask about a page that has a completely different version of the problem? In Brent's inertial version with no stopping, you need to consider simultaneity to see how both frames can agree on all local events, so it's just the same physical scenario described in different coordinate systems; in the version on the website you need to consider simultaneity for a very different reason, because it's specified that the car's back end can stop simultaneously with the front end in either the car frame and the garage frame, resulting in genuinely different physical scenarios. Jesse -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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