On Tuesday, December 31, 2024 at 3:31:33 PM UTC-7 Jesse Mazer wrote: On Tue, Dec 31, 2024 at 12:57 AM Alan Grayson <[email protected]> wrote:
On Monday, December 30, 2024 at 1:03:20 PM UTC-7 Jesse Mazer wrote: On Sat, Dec 28, 2024 at 1:51 AM Alan Grayson <[email protected]> wrote: On Friday, December 27, 2024 at 10:05:51 PM UTC-7 Jesse Mazer wrote: On Friday, December 27, 2024, Alan Grayson <[email protected]> wrote: 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 * The Webster’s dictionary comment was sarcastic, but ‘What could be the meaning of “rest frame” associated with “garage”?’ didn’t seem to be a sarcastic question, especially since it echoed your confusion in the other comments I quoted. 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.* I don’t know what you mean by “its initial condition.” Do you just mean its length its own rest frame? Or do you think it’s essential to the problem that we imagine some initial condition where both are at rest relative to each other, and then the car is accelerated? If so I would definitely object to that, the term “car’s rest frame” has no such implications, it would have exactly the same meaning if we assumed the car and garage have had a fixed relative velocity for an infinite time prior to the car passing through the garage. * 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. * I didn’t use any word like “because” or talk about the best conceptual explanation, I just said that the question of whether the car fits in some frame is *equivalent* to the question of the order of the events A and B in that frame. It is of course also equivalent to the question of whether the length of the car is shorter, greater, or equal to the length of the garage in that frame. Equivalent here just means logical equivalence, ie the truth value of the statement “the car doesn’t fit in this frame” is guaranteed to be the same as the truth-value of “B happens before A in this frame” and *also* the same as the truth-value of “the car is longer than the garage in this frame”; it’s impossible in either relativity or classical physics for one of these statements to be true while another one is false, or vice versa. Do you agree they are equivalent in that sense? Could you address my question here about whether you agree that, given the clarification that I am talking about logical equivalence in the sense I discussed above, the question of whether the car fits is completely equivalent to question of the order of the events A="back of car passes front of garage" and B="front of car reaches back of garage"? *I apologize for being so dumb, but whereas I'm comfortable using relative lengths of car and garage to determine fitting or not, I don't really understand that the reversal of time order, of event B preceding event A, is equivalent to car not fitting in garage.* OK, but are you making an effort to understand? In general do you actually want to understand what relativity says about these matters, or do you just want to score a rhetorical "win" for your own arguments? If you're interested in understanding rather than winning then you can't just stick by whatever way of thinking is most comfortable for you, or most conducive to your argument. *Concerning those videos, two which were reviewed on this MB, one by Brent and one by you, they falsely claim to show that from the car frame, the car really does fit in the garage.* I watched the video and I never saw him make the false claim that the pole (which takes the place of a car in that video) fits in the garage in the pole's own frame. If you disagree, can you point to a time index in the video where he says this, or a time index in the first video where he says the car fits in the garage in the car's frame? * This is what one expect to show if the disagreement of the frames is the cause of the paradox, but apparently it isn't, and the disagreement about simultaneity alone is sufficient to resolve the paradox. This is what I am trying now to understand. AG* *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 * No, I wasn’t talking about the best way to understand or explain why the car doesn’t fit, I was just talking about logical equivalence. But as I have said elsewhere, an analysis of relativity of simultaneity is needed conceptually if you want to answer the *separate* question “given that different frames disagree about whether the car fits, how can we avoid the conclusion that they must disagree in their predictions about local physical facts?” 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?" *I'm not sure. I have to think about this some more. Why can't we just stick to lengths? AG * You could at least ask some questions about whatever is puzzling you rather than just avoiding the subject by switching to exclusive talk about length. Remember, this is a purely classical scenario, no tricky issues of length contraction or simultaneity. Classically, if we have an 18-foot long limousine driving through a covered bridge that's only 6 feet wide, and you're watching from the side with the limousine moving left to right, are you genuinely unsure about whether you'll see the front of the limousine poke out of the right side of the covered bridge BEFORE or AFTER the back of the limousine first disappears behind the left side of the covered bridge? If the front didn't poke out from behind the right side of the covered bridge until AFTER the back disappeared behind the left side, that would mean there was some period of time where the 18-foot limousine was wholly obscured from view behind the 6-foot covered bridge, which doesn't make a lot of sense geometrically. *I see front of car emerging from right side of bridge first, BEFORE back of car crosses entry of bridge on left side, so the car never completely fits. I can't account for your interpretation and I didn't think it worthwhile to argue about it. Mine seems simple enough and correct. AG* *As for the videos, some of them CLAIM in their subject line, to provide a resolution of the paradox, but fail to do so. This initial claim is what I was referring to as false. And Brent posted the numbers the author calculated and IIUC they contradicted that the car could fit, even that's what was alleged. AG* *Didn't Brent's plots establish the car doesn't fit from the pov of the car frame? If so, wasn't this the origin of the paradox? If so, I fail to see how this resolves the issue. It just seems to repeat the situation which caused the idea of a paradox to arise in the first place. TY, 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/225f9316-883b-4440-a0f1-0f57318345d8n%40googlegroups.com.
