Actually, you and Cosmin have much in common; both have pretentions of being mind readers. AG
On Friday, December 20, 2024 at 3:35:05 AM UTC-7 Quentin Anciaux wrote: > 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/e29e020b-bd2d-4035-8023-e55377058314n%40googlegroups.com.
