On Saturday, December 14, 2024 at 11:27:37 PM UTC-7 Jesse Mazer wrote:
On Sat, Dec 14, 2024 at 10:46 PM Alan Grayson <[email protected]> wrote: On Saturday, December 14, 2024 at 8:15:37 PM UTC-7 Jesse Mazer wrote: On Sat, Dec 14, 2024 at 9:46 PM Alan Grayson <[email protected]> wrote: On Saturday, December 14, 2024 at 2:16:36 PM UTC-7 Jesse Mazer wrote: On Sat, Dec 14, 2024 at 12:34 PM Alan Grayson <[email protected]> wrote: On Saturday, December 14, 2024 at 7:58:34 AM UTC-7 Jesse Mazer wrote: On Sat, Dec 14, 2024 at 5:27 AM Alan Grayson <[email protected]> wrote: On Saturday, December 14, 2024 at 1:35:54 AM UTC-7 Alan Grayson wrote: On Friday, December 13, 2024 at 8:48:39 PM UTC-7 Brent Meeker wrote: On 12/13/2024 7:02 PM, Alan Grayson wrote: On Friday, December 13, 2024 at 7:30:31 PM UTC-7 Brent Meeker wrote: On 12/13/2024 3:09 PM, Alan Grayson wrote: For some rest length frame parameters, there's a v, such that for velocities greater than v, won't the car fit in all garage frames, but in none of the car frames? If this is correct, what's the justification for saying the solution exists in one set of frames, but not in another? And what's the argument that in all of these frames, simultaneity of front and back of car is satisfied? TY, AG What could it possibly mean for the car *not to fit* in the car frame! *Have you ever tried to park a car? Use your brains and you'll figure it out. It's called the Lorentz Parking Paradox. You're trying to park a car of known rest length, in a garage of known rest length. Follow me so far? Now get the car moving and from the car's frame notice how the garage length Lorentz contracts. Follow me so far? At some v or greater, the length of the garage will be smaller than the car's rest length. When this happens most sane individuals will conclude that the car won't fit. * *OK, you meant the car will not fit in the garage, in the car's frame. * * Brent* *Maybe, just maybe, this apparent paradox cannot be resolved by solely analyzing what happens in space, but in spacetime. Tomorrow I will make an effort to fully understand your spacetime diagrams and see if they shed any light on this issue. The clue might be the fact that in relativity, ds^2 is frame invariant. And FWIW, I haven't seen any convincing arguments based solely on the frame non-invariance of simultaneity. It's often claimed this non-invariance solves the problem, but detailed proofs are woefully lacking. AG* *The reason a paradox seems to exist is because the frame observers witness contrary events; the garage observer sees the car fitting in the garage, whereas the car observer sees the car not fitting in the garage, when there's only one possible thing to observe. AG* "Events" in relativity generally refer to things that happen at a single point in spacetime, like the back end of the car passing by the front of the garage with the clocks mounted to each showing particular readings; the different frames do not disagree about any localized events in this sense. Did you understand my point about why the question "did the car fit" reduces to the question "did the event A of the back of the car passing the front of the garage happen before the event B of the front of the car reaching the back of the garage"? Jesse *Yes. In relativity measurements are generally not frame invariant, such as the E and B fields in EM. But this case seems different. Imagine two observers, one in car frame and the other in garage frame, and they're both viewing the car passing through the garage, now open on both ends. Ostensibly, the former sees the car fail to fit in the garage, the latter sees the opposite. I don't believe a rigorous definition of "fit" will resolve this contradiction. * Note that when we talk about what happens in a given frame this is not what any observer sees with their eyes, it's about when they judge various events to have happened once they factor out delays due to light transit time, or what times they assign events using local readings on synchronized clocks that were at the same position as the events when they occurred. For example, if in 2025 I see light from an event 5 light years away, and then on the same day and time in 2030 I see light from an event 10 light years away, I will say that in my frame both events happened simultaneously in 2020, even though I did not see them simultaneously in a visual sense. And if I had a set of clocks throughout space that were synchronized in my frame, when looking through my telescope I'd see that the clocks next to both events showed the same date and time in 2000 when the events happened. When you say 'I don't believe a rigorous definition of "fit" will resolve this contradiction', which of these is closer to your meaning? 1. If event A = "back of car passes through front door of garage" and B = "front of car reaches back of garage", then *even if* you grant that the question "does the car fit" is defined to be 100% equivalent to the question "does A happen before B", you still think an analysis of how simultaneity works in relativity which shows that the two frames can disagree about the order of A and B is *not* sufficient to resolve the paradox. *I just wrote a more detailed reply and it was lost. Yes, if both frames disagree about car fitting, IMO paradox is alive and well. I assume observers in each frame view the same phenomenon, so regardless of what relativity claims, they must see the same thing. This is different from the general case of different frames making different measurements, but I can't precisely explain in this case, the distinction between these two types of measurements. AG * They see exactly the same local events. As I said before, if there are a pair of clocks attached to either end of the garage which are synchronized in the garage frame, and a pair of clocks attached to either end of the car which are synchronized in the car frame, then in Brent's example they both see that when the back of the car passes the front of the garage (event A), the back car clock and front garage clock both read 0; and when the front of the car reaches the back of the garage (event B), the front car clock reads -7.5 and the back garage clock reads 3.5. The only difference is the *convention* each frame adopts about which clocks are synchronized--the car frame calls the car clocks "synchronized" and the garage clocks "out-of-sync", and the garage frame calls the garage clocks "synchronized" and the car clocks "out of sync". Thus, based on their different conventions, the car frame says the event A happened later than event B (A at time 0, B at time -7.5), and the garage frame says the event A happened earlier than event B (A at time 0, B at time 3.5). Consider an analogy with disagreements about spatial coordinates. Say there is a post on the ground, and two observers both define the x-axis of their respective coordinate systems by rulers which touch the post, but the two observers place the x=0 mark of their respective rulers 2 meters apart from one another, so that the post is next to the 3 meter mark on the ruler of observer #1, and next to the 5 meter mark on the ruler of observer #2. The only difference is that they have different *conventions* for defining the x-coordinate of objects on the ground, with each one defining x-coordinate by markings on their own ruler. There is no disagreement about the fact that the post is next to the 3 meter mark of observer #1's ruler and next to the 5 meter mark of observer #2's ruler, but because of their different conventions, this means observer #1 says "the post has position x=3 meters" and observer #2 says "the post has position x=5 meters". Do you think this is some deep physical contradiction, or would you agree it's a mere difference in the convention used about which ruler to use when assigning x-coordinates? If the latter, then why do you think the situation with the garage and car is any different? All observers agree about what all specific physical clocks read at event A and B, they merely differ on their respective conventions about which clocks to use to assign t-coordinates to events A and B. 2. You grant that there is a good explanation for why different frames can disagree about the order of A and B, but you have an argument or strong intuition that the question "does A happen before B" is *not* equivalent in meaning to "does the car fit in the garage" *Not sure how to answer your question. I haven't thought about ordering. Nonetheless, any disagreement about whether car fits means the paradox is alive and well. AG * 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? *I meant I hadn't considered the ordering you postulated as effecting simultaneity. By "fit", I always meant the ordering you described, and that the paradox is alive and well under such ordering. * By "the paradox is alive and well" do you just mean that the car rest frame and the garage rest frame disagree about the order of those events A and B? *IIRC, I never discussed order of events; just contraction of lengths from different frames. I thought it paradoxical that the frames could disagree on whether the car could fit or not (and Brent gave the conditions for a fit in a recent post). Now I am not so sure. Maybe the frames can disagree about whether the car fits, and there's no problem. That seems to be the consensus view on this MB and elsewhere. AG* If so, why is that paradoxical, given that it follows naturally from the way different inertial frames define their time coordinates? You didn't answer my question earlier about whether you think it's "paradoxical" that observers using different rulers to define position coordinates can disagree about the coordinates of a post in the ground. *As I just wrote, I never discussed coordinates. AG * *Moreover, I don't see why in the car frame we can't have the phenomenon synchronized with the garage frame, so the observers see the same thing, at the same time, which IMO implies a paradox. AG* The claim of disagreement about fit in the car/garage problem is specifically assuming we use the standard definition of synchronization that is used for inertial frames (the Einstein convention where each frame assumes that light moves at the same speed in both directions relative to the position coordinates of that frame, and this assumption is used to synchronize clocks). *Since we're discussing relativity, we can and should use Einstein's convention for synchronization. Can the clocks in the two frames be synchronized, and if so, will it persist; and if not, why? I figure that with synchronized clocks, we can directly compare events in the two frames, and determine if two events and their endpoints will give contradictory results concerning "fit" when frame results are compared. I think this is my problem; that the frames disagree on "fit", and unless I can compare them, and for this comparison I need the clocks synchronized, I can't say if there's a contradiction or not. AG* Of course the observers could choose to adopt a different convention to define simultaniety, but then they wouldn't be using the coordinates of their inertial rest frames. If you don't see why the ordering of these two events is considered equivalent to the question of fitting, *It obviously is. Sorry about the confusion. AG* OK, glad we agree about that. 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? Jesse *Car is never fully hidden. In my interpretation, as I previously stated, the car observer is riding in the car and knows whether the car fits, or not. AG* I wasn't talking about the relativistic scenario where there is disagreement over fit, I said it was a "classical scenario" where 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." In any case, it seems we are in agreement that the question of "fit" reduces to the question of whether A happens before B or B happens before A, so no need to discuss this classical scenario further since I just brought it up to try to make the reason for that reduction more clear. Jesse *OTOH, from the garage frame, the car's length is Lorentz contracted, so most sane individuals will conclude the car WILL fit in the garage. Thus, an apparent paradox, or shall we say a discrency of whether or not, the car can fit in garage, and from the pov of which frame? Final question: are you a sane individual? These questions might be totally ill-posed. If so, with your immensely superior intellect, I'm confident you'll be able to show us how; and if so, THAT WILL BE THE SOLUTION! AG* I don't even know that "the solution" means. *It means what I wrote above. Which frame, if any, can the car be fully contained within the garage? AG * What was the problem to be solved; *Read what I wrote, and better yet what other professionals write about this apparent paradox. AG* How to educate Alan? Simultaneity is a relation between EVENTS, not car parts. *I know that. Now tell me something I don't know. (Who said anything about car parts?) 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/d459f4ea-c7d5-457f-9d28-23998a24b818n%40googlegroups.com.
