On Friday, December 27, 2024 at 9:16:39 AM UTC-7 Jesse Mazer wrote:
On Friday, December 27, 2024, Alan Grayson <[email protected]> wrote: On Thursday, December 26, 2024 at 9:39:41 PM UTC-7 Jesse Mazer wrote: On Thursday, December 26, 2024, Alan Grayson <[email protected]> wrote: On Thursday, December 26, 2024 at 2:56:04 PM UTC-7 Jesse Mazer wrote: On Thursday, December 26, 2024, Alan Grayson <[email protected]> wrote: On Thursday, December 26, 2024 at 3:26:41 AM UTC-7 Alan Grayson wrote: On Thursday, December 26, 2024 at 12:12:43 AM UTC-7 Jesse Mazer wrote: On Wednesday, December 25, 2024, Alan Grayson <[email protected]> wrote: On Wednesday, December 25, 2024 at 5:14:21 PM UTC-7 Jesse Mazer wrote: On Wednesday, December 25, 2024, Alan Grayson <[email protected]> wrote: *Why do refer to transformations that don't preserve time ordering? IIUC, such transformations only occur when assuming motion faster than light. * No, that’s not correct. Motion faster than light would be required if there was a claim of causal influence between events with a spacelike separation; but there’s no such claim here; in both Brent’s example and mine, if we consider the event A of the back of the car passing the front of the garage and the event B of the front of the car reaching the back of the garage, there is a spacelike separation between those events, and neither event has a causal influence on the other. *I'm asking a general question. Why do you refer to failure of time ordering? What was the point you thought you were making? AG* Because as you previously agreed, the question of whether the car fits reduces to the question of whether the event A = back of car passes front of garage happens before, after, or simultaneously with the event B = front of car reaches back of garage. Since these events have a spacelike separation in both Brent’s and my numerical examples, in relativity different frames can disagree on their order, that’s the whole reason we say frames disagree on whether the car fits. *As I recall, you were writing about the failure of TIME ordering, and this would mean violation of causality, not what we're discussing on this thread. AG * You either recall incorrectly or misunderstood at the time, but disagreement about the time ordering of two events A and B does NOT imply any violation of causality; it just implies the spacetime interval between A and B is spacelike, but normally this is combined with the assumption that there are no causal influences between events with a spacelike separation. Do you understand what the spacetime interval is? If I gave you the difference in time coordinates T = tB - tA for the two events along with the difference in position coordinates X = xB - xA, would you know how to calculate the spacetime interval and judge whether it is timelike, spacelike or lightlike? *But if so, you're not within the postulates of SR, which is what this discussion is about. So what point do you think you're making? AG* *Re: paradox: Assume there's an observer located in the garage. This observer is in the garage frame. This observer sees the car easily fit in the garage. Imagine another observer riding in the car. This observer is in the car frame and observes being in the garage but never fitting in the garage. What are the observations when the two observers pass each other, in juxtaposed positions?* I’ve asked this before, but by “see” do you mean in terms of when the light from different events reaches their eyes, or something more abstract like a computer animation they create of when events occur in their frame, once they have measured the time and position coordinates of all events using local readings on rulers and clocks at rest relative to themselves? *Nothing more abstract. One observer sees the car sticking outside the back of garage, the other sees it inside, when both are juxtaposed. * You didn’t quite answer my question—you are just talking about what they see with their eyes, right? *I used the word "see". Is this not clear enough? AG* Not entirely, since it’s routine in relativity problems to use words differently from everyday speech, for example in ordinary speech when you talk about “observing” some event we are usually talking about visual sight, but in relativity talking about what someone “observes” always refers to how things happen in the coordinates of their frame, not to visual sight. If so, there is no disagreement between observers passing through the same point in spacetime about whether the car fits in a visual sense. *Really? So if the garage is 10' long in rest frame, * Do you mean 10’ in the garage’s rest frame? As I said before, just using “rest frame” without specifying a particular object is unclear. *I appreciate your thoroughness but here I just left out "its", as in "... 10' long in its rest frame", and I think you should have easily inferred my meaning. AG * Given that you had recently objected to my use of the phrases “car’s rest frame” and “garage’s rest frame” and hadn’t acknowledged my response about how this is a standard way of speaking in relativity, I didn’t think it was safe to assume that. It would help if you would acknowledge when something I’ve said has led you to revise a view, even on something minor like terminology, otherwise I don’t know when a given point needs to be re-litigated. The recent discussion about how we can talk about events that are spacelike separated without implying any faster than light causal influence is another example; do I need to keep arguing that or does the fact that you dropped that discussion mean you concede the point? Could you please address my comment above so I know if we’re in disagreement on these points? *I don't object to your terminology. As I stated, if I had included "its" in my statement, there would have been no ambiguity about terminology. And as far as I can recall, I never objected to the use of your quoted statements about rest frames. AG* *What could be the meaning of "rest frame" associated with "garage"? I don't have a clue. Shall we consult Webster's Dictionary? As for my numerical example, I suggest you do the arithmetic, and if you don't get my prediction, I will concede the argument. AG * *Yeah, use 12' and 10' for the lengths of the car and garage respectively when at rest (which means no motion of car). Then using the LT determine how fast the car must be moving to contract the car's rest length to .000001' from the pov of the garage frame. Then place the car in the center of garage, and recognize how easily it fits (by any method of your choice). Now, from the pov of the car frame, and the speed of the car previously calculated, calculate the contracted length of the garage, and place the car at the center of the garage. Does the front of the car extend beyond the rear of the garage, whereas previously it did not? No need to worry about what "seeing" means in this comparison.* It’s critical that you specify if by “see” you are talking about what light signals are reaching their eyes at that point, or if you are talking about the coordinates they assign to front and back of car and garage at simultaneous moments in their own frames; the answer will be completely different depending on what you mean. If you are just talking about visual seeing, I can do that, but just be aware that most of the usual textbook equations of relativity including length contraction are *not* intended to address visual appearances. Jesse *Let's forget about "seeing" in these scenarios since I agree it unnecessarily complicates the analyses. I will go back to your post with my question marks and try to resolve as much as possible. However, I don't think we can resolve anything in these discussions, for this reasonaaaaa. I proposed a scenario where from the garage frame the car fits with ease, whereas from the car frame it fails to fit and in fact easily extends beyond the rear end of garage. I conjecture that your response will be that different frames give different measurements, so there's nothing particularly noteworthy about this situation, and it certainly doesn't amount to a paradox. This result concerning fitting or not can easily be concluded without any arithmetic. Is my conjecture about your response correct? AG* Sure, if we are talking about local measurements in each frame rather than visual seeing, I see no paradox in the fact that they disagree on the time order of the spacelike separated events A=“back of car passes front of garage” and B=“front of car passes back of garage” and therefore disagree on fitting. *In the example I posted, the frames disagree on fitting, and AFAICT there's nothing to suggest a disagreement on the time order of events. In fact, what you claim doesn't seem physically impossible in either frame. Can you show me EXACTLY how you reached this conclusion, without referring to one of your other posts? It seems that you pulled that conclusion out of the preverbial hat. AG* You can easily just look at the times of events in either Brent’s numerical example or mine to see the two frames disagree on the order of the two events I keep bringing up, A=“back of car passes front of garage” and B=“front of car reaches back of garage”. In my example, A and B happen simultaneously at t = 0 in the garage frame, while in the car frame B happens at t’ = -15, which is before the time when A happens in the car frame at t’ = 0. And isn’t it obvious that if some frame says that B happens before A, meaning the front of the car reaches the back of the garage before the back of the car has yet entered the front of the garage, then that’s equivalent to the statement that in that frame the car doesn’t fit, whereas in a frame where A happens before B or simultaneously with it, the car does fit in that frame? This is one of the most basic aspects of analyzing the problem that we’ve talked about over and over, and you’ve previously agreed to, I don’t understand why there’s be any confusion here. *Your memory is in error. I never agreed to that. Which frame are you referring to? Presumably the car frame where you claim the car cannot fit. How can it not fit when via contraction the length of the garage can be made arbitrarily short with sufficient velocity via the LT? I didn't understand Brent's plots or your numerical example well enough to make that conclusion. I thought I indicated that with my question marks on your analysis. AG * As I’ve said, I think the basic “threat” of this problem is a disagreement over local physical facts, so once one understands they don’t disagree on any of the readings on specific physical clocks in the vicinity of A and B, that initial threat disappears. If your position is that a disagreement about fitting / time order of A and B is inherently paradoxical *even if* there is no disagreement on local physical facts (including both clock readings and visual appearances at any point in spacetime), then I would ask you to address the question I asked in this paragraph from a few posts back Why do you see disagreement about whether something "fits" as a fatal flaw, but *not* see it as a fatal flaw when we have any other quantity that differs between inertial frames, like disagreement about simultaneity in relativity, or disagreement about velocity or x-coordinate or distance intervals in both relativity and classical mechanics? You have never given any explanation of this--it seems likely it's just a matter of appealing to your personal intuitions. *Not just intuition. In this case I believe there is one objective reality, whether the car fits or not.* That’s just restating your intuition that “fitting” must be part of objective reality, it doesn’t answer my question about why you see this case as fundamentally different than the other frame-dependent issues I mentioned above. Suppose someone says “it’s a fatal flaw in both relativity and classical mechanics that two frames can disagree about which of two objects has a greater velocity, there can only be one objective reality!” Would you agree or disagree? *In this problem we can assume the garage isn't moving as an objective fact, but IIUC we can still use the LT to contract the garage's measured length from the pov of the car frame. Do you agree with this use of the LT? And the only way to justify this pov is to know the car's history, of being accelerated at some point in its past. I can only comment on particular situations. AG* If you disagree, do you have any reasoned argument for this, or is it just an intuition that fitting is part of objective reality but velocity is not? * This is why I modeled the problem as having the observers in each frame juxtaposed. In this situation, how can the observers make diametrically opposite conclusions about fitting? Consequently, I believe SR is fatally flawed. AG* By juxtaposed do you just mean both observers are at the same point in spacetime? *The labels in spacetime depend on the frame of reference since each label is arbitrary and frame dependent, so the two observers won't agree on the labels, but apparently they can be co-located. AG* But as I pointed out they won’t have a different visual opinion about whether the car fits in this case, *So, in your opinion, if the car doesn't fit in the car's frame, the observer nevertheless in this frame will see that it fits because that's what the garage observer sees? AG* and an observer’s non-visual judgments of the time and position events happen in their frame doesn’t depend on their position in that frame. Jesse Whereas the argument that it'd be unacceptable to have a theory where frames could disagree about which events locally coincide is much more straightforward, it would lead to different predictions about local interactions which leave permanent records as in my example of the bomb shattering the glass only if the clock attached to the bomb reads a certain time at the moment it passes the glass. *Since we have two observers in this scenario, one in each frame, one riding in the car who is located at the comparison point in garage, at its center, and the other at the center of garage, we can consider the observers as juxtaposed, at the same location in spacetime. AG* *and car is .00001' long in garage frame when car is moving, and car is, say, in center of garage, the observer in car frame, residing inside car, won't observe his car just won't fit in garage because of huge contraction of garage in car frame, when both observers are juxtaposed, presumably at the same point in spacetime?* You would have to specify more details, like the rest length of the car and the relative velocity of car and garage and the location of the observers, in order to determine whether both observers at that point see it fit or both observers see it not fit. But suffice to say *if* an observer at rest relative to the garage is visually seeing the car fit when the observer is passing through a given point in spacetime, then an observer at rest relative to the car who is passing through that same point in spacetime is also visually seeing the car fit (even if the car does not fit in terms of local position and time measurements in his frame), this is a straightforward consequence of all frames agreeing about local configurations of photons at a single location in spacetime. I could give a numerical example at some point to illustrate this, but if you couldn’t follow my earlier numerical example I doubt this would be clear to you either, which is why I suggest it would be a good idea to return to my last response to one of your “?” responses on that example and continue from there. Jesse -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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