Why bother answering a troll ? He will never admit anything, will change what he says if he's cornered. His sole purpose and pleasure is trolling. You end a troll by ignoring it. Ignoramus as him and cosmin are better dealt with plain silence, that's all these shitty human beings deserve.
Le ven. 20 déc. 2024, 11:09, Jesse Mazer <[email protected]> a écrit : > > > On Fri, Dec 20, 2024 at 2:09 AM Alan Grayson <[email protected]> > wrote: > >> *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* >> > > "The car fits" or "the car fits" are not statements about local events, > i.e. statements about things that happen at a single spacetime point in one > of Brent's diagrams. But the back of the car does pass the front of the > garage at a single point in spacetime in this problem, so if there was a > clock #1 attached to the back of the car and a clock #2 attached to the > front of the garage, all frames would have to agree in their predictions > about what each clock reads at the moment they pass through that one point > in spacetime. Likewise if a clock #3 is attached to the front of the car > and a clock #4 is attached to the back of the garage, those clocks would > cross paths at a single point in spacetime so both frames would have to > agree in their predictions about what they each read at the meeting, which > they do. > > You can also imagine there is a ruler Rg at rest relative to the garage > running along its length, and another ruler Rc at rest relative to the car > and running along the same axis, so the two rulers are moving alongside > each other at 0.8c. In this case, for any of the types of events I > mentioned above like clock #1 passing clock #2, both frames also must agree > about what marking on Rg this event coincides with in space, and what > marking on Rc it coincides with. These are all facts about things that are > happening at individual points in spacetime, not facts which require > talking about a range of positions of times, like whether the car "fits". > > In Brent's scenario, assume clocks #1 and #3 at the back and front of the > car were synchronized in the car's rest frame by the Einstein > synchronization procedure, and clocks #2 and #4 at front and back of the > garage were synchronized in the garage's rest frame using the > synchronization procedure. Also assume the localized event of the back of > the car passing the front of the garage coincided with both clock #1 and > clock #2 there reading t=0 and t'=0 respectively, and that this happened > right next to the x=0 mark on ruler Rc and the x'=0 mark on ruler Rg. All > frames agree on these facts, which are exclusively about what happened at a > single point in spacetime, namely the point where the back of the car > passed the front of the garage. > > Given these assumptions, according to relativity they will *also* agree in > all their predictions about a second event, the event of the front of the > car reaching the back of the garage. Specifically they will agree that at > the same point in spacetime as this second event, all the following are > true: > > --Clock #3 at the front of the car read t = -7.5 > --Clock #4 at the back of the garage read t' = 3.5 > --this event of the front of the car reaching the back of the garage > coincided with the x=12 mark on ruler Rc > --this event of the front of the car reaching the back of the garage > coincided with the x'=10 mark on ruler Rg > > There is no disagreement on any of these local facts. The only > disagreement is that each observer adopts a different *convention* about > which ruler and clocks to treat as canonical for the sake of assigning > coordinates--the car rest frame defines time-coordinates by the clocks at > rest in the car frame (clocks #1 and #3) and the ruler at rest in the car > frame (Rc), while the the garage frame defines time-coordinates by the > clocks at rest in the garage frame (clocks #2 and #4) and the ruler at rest > in the garage frame (Rg). Based on these conventions, the car observer says > the event of the back of the car passing the front of the garage happened > AFTER the event of the front of the car reaching the back of the garage, > therefore the car never "fit", while the garage observer says the event of > the back of the car passing the front of the garage happened BEFORE the > event of the front of the car reaching the back of the garage, therefore > the car "did" fit. But this is not a disagreement about any of the local > facts I mentioned. > > (BTW I earlier derived these numbers as the coordinates assigned to the > event in each frame at > https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/43aKXeEUAQAJ > but here I'm just emphasizing that coordinate judgments can be grounded in > local readings on physical clocks and rulers, something I also talked about > at > https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/BvxSA-b3AAAJ ) > > > >> >> 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 * >> > > See above about what I mean by localized events. > > > >> >> >> 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 * >> > > There is no frame-dependence in predictions about localized events, and > according to relativity these are the only real physical facts in the > problem, everything else is a matter of conventions about how you *label* > these events with position and time coordinates, no more problematic than a > classical physics scenario . > > >> >> >> >> 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.* >> > > OK, in a word problem if I say that in a classical problem, at t=0 seconds > a spaceship is initially at position x=7 meters away from the origin, and > it's moving in the +x direction at 12 meters/second, would you know how to > write down the equation for its position as a function of time x(t), and > plot this as a line on a graph with position in meters on the horizontal > axis and time in seconds on the vertical? If so, that's really all that a > "worldline" is. > > Likewise, if we have various such worldlines for different objects, and we > want to know the position of each object at a particular time like t=5, do > you understand why this would just be a matter of plotting a horizontal > line that goes through the t=5 mark on the vertical axis (a classical line > of simultaneity), and seeing the point it intersects each worldline? > > >> *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* >> > > He's trying to illustrate a slanted line of simultaneity that connects two > events that are simultaneous in the car's frame, as graphed in the garage > frame. But the visual length of this line in the diagram is not meant to > correspond to an elongated length in either frame, it just looks longer > because it's being translated from relativistic (Minkowski) geometry where > the length of a spacelike line segment is given by sqrt(x^2 - t^2) into a > diagram in a 2D euclidean space (your computer monitor) where if we label > the two spatial axes x and y, then the length of any slanted line segment > is given by sqrt(x^2 + y^2). In Minkowski geometry the length of a slanted > segment should be *less* than the distance along the x-axis between its > endpoints, but in Euclidean geometry it's greater because of that switch > from a minus to a plus, and we are only capable of intuitively visualizing > Euclidean geometry so that's what we use for our imperfect diagrams. That's > why the diagram has to show the car as longer here even though according to > the relativistic math the proper length of that line segment should really > be shorter. > > > >> >> >> * 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 * >> > > All they see is the sum of light from multiple events which are > individually localized in space and time. Imagine for example that they are > watching an image of the car and garage on a screen (it makes no difference > to the problem), such that every bit of light they see was emitted by a > specific pixel at a particular moment in time. In this case, even in a > classical problem where there are no disagreements about simultaneity or > distance in terms of the coordinates each observer assigns, as long as the > light takes a finite speed to get from the pixel that emitted it to an > observer's eye, different observers may visually *see* events at different > times and in different orders. Even in this purely classical scenario you > could have *visual* disagreements about whether the car fits (i.e. one > observer sees the light from the event of the back of the car passing the > front of the garage BEFORE seeing the light from the event of the front of > car reaching the back of the garage, a different observer sees it AFTER), > even though classically they won't disagree once they correct for light > transit times in order to assign time-coordinates to these events. > > >> >> 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* >> > > Do you definitely deny what I said about all observers agreeing about all > local events, now that I've clarified a little what I mean by "local > events"? Or are you saying that *even if* they agree about all local > events, you still think there must be a separate objective truth about the > question of whether the car fits, a fact of the matter that is somehow more > than the sum total of all the facts about localized events (including all > local readings on measuring-instruments)? > > > >> >> >> 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 * >> > > Do you think someone with such a God's-eye perspective would find it > baffling that different coordinate systems may disagree about which of two > events has a greater x-coordinate, and that there is no objective truth > about the matter independent of how we choose to orient our spatial x-y-z > axes for the sake of assigning position coordinates? If you're OK with > there being no objective truth about this, why are you suddenly *not* OK > with the fact that there might similarly be no objective truth about which > of two events has a greater t-coordinate, independent of our conventions > about how to define coordinate systems? > > 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/CAPCWU3LF4UVdejjmHbB7jQMQgGnbZ2N7aNAf2GMejfjy%3DQrw8g%40mail.gmail.com > <https://groups.google.com/d/msgid/everything-list/CAPCWU3LF4UVdejjmHbB7jQMQgGnbZ2N7aNAf2GMejfjy%3DQrw8g%40mail.gmail.com?utm_medium=email&utm_source=footer> > . > -- 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/CAMW2kAq%2BgQ2425iRaNpspLyj5CQ0%2BrguwVtgXj0KunqdYMo0vw%40mail.gmail.com.
