On Friday, December 27, 2024 at 6:48:56 PM UTC-7 Jesse Mazer wrote:
On Fri, Dec 27, 2024 at 4:58 PM Alan Grayson <[email protected]> wrote: 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* You objected multiple times in the last few days to my terminology where "car's rest frame" refers to the frame where the car is at rest (i.e. it has position coordinates that don't change with time) and the garage is moving (so the garage is Lorentz-contracted in the car's rest frame), while "garage's rest frame" symmetrically refers to the frame where the garage is at rest and the car is moving (so the car is Lorentz-contracted in the garage's rest frame). For example in the post at https://groups.google.com/g/everything-list/c/vcrAzg4HSSc/m/XZrHB-IdAwAJ I said: "In garage rest frame, garage has length 20 and car has length 25/1.25 = 20. In the car rest frame, the garage has length 20/1.25 = 16 and the car has length 25.” And you responded: "OK, assuming car is moving, but I wouldn't call that "in the car rest frame" since you have garage length as contracted. AG" Then at https://groups.google.com/g/everything-list/c/vcrAzg4HSSc/m/mFVsDGUtAwAJ you responded by imagining “the rest frame” referred to some imaginary initial conditions that were never part of the problem I described, conditions where both the car and garage were at rest relative to each other: “IMO, the rest frame is defined as the initial conditions in this problem when the car isn't moving, and is longer than the garage. When the car is moving, we have been calling the other two frames, simply the car frame and the garage frame.” Then at https://groups.google.com/g/everything-list/c/vcrAzg4HSSc/m/1AWAOHA4AwAJ you again objected to the standard terminology in which “car’s rest frame” just refers to the frame where the car is at rest in the sense of having a fixed position coordinate, even if it is moving relative to the garage: “No one uses "rest frame" when describing the results in either frame when the car is moving. You introduced that terminology recently, claiming it is standard. AG” Then just yesterday at https://groups.google.com/g/everything-list/c/vcrAzg4HSSc/m/O12FCXvmAwAJ you again objected to this standard terminology: “What could be the meaning of "rest frame" associated with "garage"? I don't have a clue. Shall we consult Webster's Dictionary?” *I was being sarcastic. Not to be taken at face value. AG * So it would be helpful to know if you're willing to accept that my use of "car's rest frame" and "garage's rest frame" is the standard way of talking among physicists, or if you still object. *Instead of haggling over this issue, and possibly taking some of my comments out of context, we agree that when using the LT from either frame, the car or garage length in that frame has not changed from its initial condition, 12' or 10', respectively. At that point it was agreed that car cannot fit in garage because of length considerations. Consequently, following that agreement, I calculated using the LT, that the car fits or not -- fits in garage frame, doesn't fit in **car frame -- based solely on length considerations. **If the car can't fit from its frame when v = 0, it can't fit for any v > 0, since the garage gets even shorter. I think you and Brent believe it can't fit in car frame due to disagreement about simultaneity, whereas I use length contraction to reach the same conclusion. And we agree it can fit from the pov of the garage frame, since the car's length contracts. So what are we arguing about is this; does the disagreement about fit constitute an objective fact and thus a paradox? 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. * Yes you did! See our discussion at https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/B15IG50SAQAJ where I was responding to your previous comment at "I haven't thought about ordering", and I said the following: "You haven't thought about it?? Disagreement about the ordering of these two specific events (due to differences in simultaneity) is what Brent and I have both been emphasizing as the fundamental resolution of the paradox, have you not even understood that this is central to what we are arguing, and considered in an open-minded way whether or not it makes sense? *As I think I posted, I don't understand the argument that disagreement about simultaneity resolves the paradox. This is surely the standard alleged solution, but using the LT and length contraction, I seem to get a paradox if we assume disagreement about fitting is the cause of the paradox. You claim time-ordering shows the car can't fit. This is my conclusion using length contraction, whiich seems simpler. So, our disagreement of the resolution apparently has nothing to do with whether the car fits from its frame, since we're in agreement that it does not. AG * If you don't see why the ordering of these two events is considered equivalent to the question of fitting, consider a simpler classical scenario where everyone agrees about simultaneity and length. A car is passing through a covered bridge, and we are observing it in a side view with the car driving from left to right, so the front of the car begins to disappear from view under the bridge as soon as it passes the left end of the bridge, and begins to re-emerge into view as soon as it passes the right end of the bridge. Would you agree in *this* scenario, if the back of the car disappears from view on the left end before the front of the car emerges into view on the right end, that means for some time the car was fully hidden under the covered bridge, meaning it "fit" inside? And would you likewise agree that if the front of the car starts to emerge from view on the right end before the back of the car has disappeared from view on the left end (say it's a very short covered bridge and the car is a stretch limo), so there was never a time when the car was fully obscured from view by the covered bridge, that means the car did *not* fit inside?" Then at https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/KmDqElIUAQAJ you quoted my statement above "If you don't see why the ordering of these two events is considered equivalent to the question of fitting," and you responded by saying "It obviously is. Sorry about the confusion. AG" In another followup comment at https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/gi9RERcVAQAJ you quoted more of the classical covered bridge scenario I had written, and then you replied "I think I agree with your criteria for fit and not fit. What bothers me is the disagreement between frames about fitness or not, and why the alledged lack of simultaneity resolves the apparent contradiction. AG" *If time ordering establishes the car cannot fit in the garage from car's frame, won't the reverse also be true; that the car cannot fit in garage from garage frame for the same reason due to symmetric use of the LT, and that the frames are equivalent in SR. This why I haven't considered disagreement about simultaneity the resolution of the paradox. AG* *Which frame are you referring to? Presumably the car frame where you claim the car cannot fit.* Read the statement about A and B again, it's an if-then conditional that covers any frame. If we're talking about a frame where B happens before A, then the car does not fit in that frame; if we're talking about a frame where A occurs before B, or simultaneously with it, then the car does fit in that frame. * 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* Yes, the garage can be made arbitrarily short in the car's frame by picking a high relative velocity, why do you think this is at odds with the idea that the car won't fit? *I think that was a typo. Sorry about that! The car couldn't fit initially, so it can't fit when the garage is shorten from the pov of car frame. AG * Obviously if the length of the garage is shorter than the car, the car will not fit, exactly as would be true in a classical scenario with a garage shorter than a car. And in such a frame, the event B="front of car passes back of garage" happens before the event A="back of car passes front of garage", just as you'd expect in the classical covered bridge scenario I wrote about previously. *As I commented somewhere here in BLUE, won't the reverse also be true due to frame equivalence in SR and permissible symmetric use of LT; namely, that from pov of garage frame, the car won't fit due to disagreement about simultaneity? 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,* Neither classical mechanics nor relativity would agree "the garage isn't moving" is an objective fact, if by "objective" you mean something different frames can agree on. Are you saying that you think classical mechanics is indeed fatally flawed because it makes movement vs. rest entirely frame-dependent? *Well, in this case everyone with common sense knows the garage isn't moving, and what we have is relative motion, which allows us to calculate AS IF the garage is moving. AG * *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* Neither classical mechanics nor relativity would say past accelerations are relevant to any frame's definition of who is "moving" and who is "at rest". *That's one way. There could be others. Best IMO is not to confuse actual motion with the situation at hand, namely relative motion. Relative motion means that from the pov of any frame, entities in other frames appear to be moving. 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* If you're talking about visual seeing, it would depend which point in spacetime you are asking about, from some points both ends of the car will appear to be inside the garage visually, and from other points at least one end will appear outside the garage. But this only depends on which point in spacetime you choose, it makes no difference whether an observer passing through that point is at rest relative to the garage or at rest relative to the car. *I would put car observer at front of car, and garage observer at end of garage. So in case of car fitting, both see the same thing, whereas in car not fitting, their observation would be different. In this scenario, we might need a second sychronized garage observer at front of garage. In any case, let's focus on length contraction. AG * Jesse -- 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/ba01a73f-e405-4f5f-83e7-8e48aa6d83e6n%40googlegroups.com.
