*Pedagogical" means what? *
Relating to how the subject is taught, in this case specifically which concepts any teacher would see as important for students to understand. If a student doesn't understand that different frames agree on all local events, then they basically don't understand the first thing about how relativity works. *If car fits in one frame and not in another, isn't that what we would expect, and yet in my prior post I wrote that this seems contradictory? Why do you expect the frames must agree about this kind of local event? To avoid a contradiction? AG* As long as the laws of physics are Lorentz-invariant, that guarantees that when different inertial frames apply the same equations (including length contraction) they will get locally identical predictions, assuming they both are using initial conditions which are equivalent under the Lorentz transformation. *Presumably, in this problem, the laws of physics are Lorentz-invariant, but contrary to what you claim, they don't result in the same locally identical predictions. Maybe I don't understand what you mean by "same locally identical predictions". In fact, the results are diametically opposite, about whether the car fits in garage. AG* 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? If so just consider that there are all sorts of local interactions in physics, like collisions, that cause changes that different frames couldn't disagree about without being obviously inconsistent. For example, say you have a clock that's wired to a small bomb that will cause a localized explosion, which will be triggered when it reads 100 seconds. And say you have another object in motion relative to the clock/bomb, say a glass of water, which is going in the opposite direction so they will cross paths. Imagine different frames could disagree in their prediction about whether the event of the clock/bomb crossing paths with the glass of water coincided was at the same local point in space and time as the clock reaching 100 seconds--like, one frame predicts the clock reads 90 seconds when they cross paths, a second frame predicts the clock reads 100 seconds when it crosses paths with the glass of water. In this case, the second frame would predict the glass of water was right next to the bomb when it exploded, and so predicts that the glass will be broken up after the encounter. Meanwhile the first frame would predict the glass of water has already put some distance between it and the bomb by the time the bomb exploded, so the glass would be intact after the explosion. This is a clear physical contradiction, no? They can't both be right, and you could easily falsify one frame's prediction just by looking at the glass afterwards. On the other hand, if all frames agree in all their predictions about local events as in relativity (assuming Lorentz-invariant laws of nature), then you don't get any contradictory predictions about such localized physical interactions which affect the state of objects later. You may find it counter-intuitive that they still differ in some kind of non-local bird's-eye account of what happened, but you can't point to any differences they will see on any measuring-instruments (since instrument readings are also local events), like what a clock mounted on the back of the car reads as it passes by the front of the garage. *You keep asserting that the frames agree in all their predictions, when in this problem they surely don't! So, I don't think we agree on this, if I understand what you mean. AG * Do you disagree with my point that if different frames *didn't* have differing definitions of simultaneity, it would be impossible for the two frames to disagree about whether the car or garage was shorter without this leading to conflicting predictions about local events, like what the clocks mounted to front and back of the car will read at the instant they pass clocks attached to the front and back of the garage?' *I don't see how simultaneity or not helps in this situation. It seems impossible for the car to fit when in motion. AG * It helps by showing how the car can fit in the garage's frame without leading the garage frame and the car frame to disagree in a single prediction about local events. Does your "seems impossible" just mean you find it counter-intuitive, not that you have a concrete argument about why you think it *would* lead to disagreements in predictions about local events? *Well, in this case, using length contraction, the facts speak for themselves. What could be counter-intuitive is that there's only one real car, so how can Lorentz-invariant physics give us frame dependent results? This seems to be not only a weak point in your analysis, but seriously mistaken. AG * And in a later post, I elaborated on why differences in simultaneity are critical to avoiding contradictory predictions about localized physical events: 'In an imaginary alternative physics where different frames had no disagreement about simultaneity but different observers still all believed the length contraction equation should apply in their frame, then this would be a genuine paradox/physical contradiction, because different frames would end up making different predictions about local events. Think about it this way--if there were no disagreement about simultaneity, there could be no disagreement about the *order* of any two events (this would be the case even if observers predicted moving clocks run slow like in relativity). But if observer #1 thinks the car is shorter than the garage, he will predict the event A (the back of the car passing the front of the garage) happens before event B (the front of the car reaches the back of the garage), and if observer #2 thinks the car is longer than the garage, he will predict B happens before A. If there were no disagreement about simultaneity this would lead them to different predictions about readings on synchronized clocks at the front and back of the car/garage at the moment of those events, specifically whether the clock at A would show a greater or lesser time than the clock at B.' Jesse *Jesse; in the near future I will try to address each of the issues you've raised,* OK, please prioritize answering the question about whether you understand the basics of how position vs. time plots work in classical mechanics, because that really is a crucial prerequisite if you want to hope to understand anything about spacetime diagrams in relativity. If you don't understand it I'm sure I could find a site that lays out the essentials. And as a follow-up, did you ever study the basics of algebraic geometry? Like if you had to plot a function like y = 4x + 5 on a graph with x and y axes would you know how to do it? Likewise would you know the algebra needed to figure out where that function intercepts with another one like y = 2x +10? *Sure, I have advanced degrees in math and physics. I'd solve for x, by setting 4x + 5 = 2x + 10, and then solve for y to get the point of intersection. (I sure hope I got that right!) I've seen spactime diagrams before, but I'm more comfortable with explanatory text. Tell me this if you can; in Brent's spacetime diagrams, he often has a stretched car. Since there's nothing in the problem to indicate an elogation of the car, what's Brent trying to illustrate? AG* * but for now let me just say I don't understand how to resolve this issue, and my tentative pov is that relativity just isn't correct. Listen; we start in a rest frame of a car which is longer than a garage. and have no problem asserting that it won't fit. And that's how things seem from both entities with physical observers. So far so good. Now we imagine the car in motion and apply length contraction in both frames and we get opposite results; namely, that in the car's frame, it won't fit in the garage, but in the garage frame it does fit, and the fits gets easier as the car's velocity increases. If I imagine a real car and a real garage, from one frame it doesn't fit, the car's frame, and from the other frame, the garage, it does fit. So, if intially the car doesn't fit, from the pov of both physical entities should I expect contrary results when the car is in motion? Maybe so. But I still can't wrap my head around the alleged claim, that the observed reality will be frame dependent. I mean, how can two observers in different frames, looking at a real car, disagree on what they see?* What do you mean "see"? Are you talking about what they see visually, in terms of when light from different events reaches their eyes? If so, do you understand that when we talk about "simultaneous" events in any frame, we are *not* talking about events that are seen simultaneously in a visual sense by an observer at rest in that frame, unless the observer happens to be positioned equidistant from both events? *If we imagine observers in each frame, humans seeing or instruments measuring, how do you expect them to observe the same thing, when the final results differ hugely? The car fits when observed from garage frame, but not when observed from car frame! AG * This was another point I made in an earlier post (at https://www.mail-archive.com/[email protected]/msg97741.html <https://www.mail-archive.com/[email protected]/msg97741.html> ) which you didn't respond to: '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. *It could be both. I'm just asserting there is some objective reality about whether the car fits or not, and from this I conclude a paradox exists since results using contraction give opposite results. How do you fail to reach this same conclusion? AG* 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.' * Incidentally, I just noticed that in one of Brent's recent posts with two diagrams, he says there is a disagreement about simultanaeity, but I am not sure if he's referring to comparing the two frames, and when I interpreted this as his comparison, he got angry, denying my interpretation. My bias is that the frames should agree (on what a bird's eye observer would see?), but does that require disagreement about simultaneity? AG* What does "bird's eye observer" mean, if it's supposed to be something more than just the sum total of all local events? *Not a precise scientific term, so just forget it. It could be how God sees everything, the ultimate observer so to speak, and finds your conclusion baffling. 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/629ebc7a-4d7f-4fd2-98bf-f17be85d3057n%40googlegroups.com.
