On Sun, Dec 22, 2024 at 12:35 AM Alan Grayson <[email protected]> wrote:
> > > On Saturday, December 21, 2024 at 2:10:00 PM UTC-7 Jesse Mazer wrote: > > On Sat, Dec 21, 2024 at 4:12 AM Alan Grayson <[email protected]> wrote: > > On Saturday, December 21, 2024 at 12:41:56 AM UTC-7 Jesse Mazer wrote: > > On Sat, Dec 21, 2024 at 1:41 AM Alan Grayson <[email protected]> wrote: > > On Friday, December 20, 2024 at 11:20:30 PM UTC-7 Jesse Mazer wrote: > > On Fri, Dec 20, 2024 at 11:06 PM Alan Grayson <[email protected]> wrote: > > On Friday, December 20, 2024 at 8:03:38 PM UTC-7 Alan Grayson wrote: > > On Friday, December 20, 2024 at 7:47:47 PM UTC-7 Jesse Mazer wrote: > > On Fri, Dec 20, 2024 at 6:53 PM Alan Grayson <[email protected]> wrote: > > On Friday, December 20, 2024 at 3:03:36 PM UTC-7 Jesse Mazer wrote: > > On Fri, Dec 20, 2024 at 6:14 AM Alan Grayson <[email protected]> wrote: > > Please define what you mean by local events, with some examples. > > > I did that in my last two comments on the other thread, the first of which > you had said you were going to respond to in more detail. In my > second-to-last post see the two paragraphs beginning with the sentence '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?' with the example of the mini bomb and the glass of water, and in > my last post see the paragraphs beginning with '"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'--in > that comment I then went on to give examples involving endpoints of the car > and garage crossing paths with clock readings and ruler markings given at > those specific crossing points in spacetime. Can you re-read those > carefully, and if you're still unclear ask follow-up questions to either of > those comments? > > Note that in these kinds of problems we idealize things like clocks and > endpoints of the car as being like point particles that only have a single > position coordinate at a single time coordinate (likewise the bomb and the > glass of water), which I assume you won't have a problem with if you are > willing to similarly idealize the car and garage as 1-dimensional. But if > you were to treat clocks etc. as having an extension in space that was tiny > compared to the lengths of the car/garage, and passing by the ends of the > car garage at a similarly tiny distance, this would differ only negligibly > from the idealized calculation of treating them as points. > > Jesse > > > I don't have a problem with idealizations and it's clear that we're using > them in this issue. I didn't want to reply on the other thread in order not > to mess up your long post which I will eventually respond to. And I realize > that the simultaneous endpoints of a perfectly fitting car are not local > events but why does the fact that they're not simultaneous in the car frame > solve this apparent paradox? And you'll notice the author I quoted doesn't > state exactly what the paradox is. AG > > > What I'm saying is that "solving the paradox" requires understanding that > despite the disagreement over fit, there is no actual disagreement about > local events like the ones I mentioned with rulers and clocks at different > positions. But to understand conceptually how it can be possible that they > can disagree on fitting but still agree on all details about local events, > you really need to look at the way the frames have differing definitions of > simultaneity. As I pointed out on the other thread, if you imagine a > hypothetical world where there is *no* disagreement over simultaneity but > each frame still predicts that objects moving in that frame are > Lorentz-contracted, then two frames that make different claims about > whether the car fit would automatically *also* be disagreeing over clock > readings at some local events. > > As for the other author you quoted, that person is dealing with a > different version of the car/garage paradox where the car is supposed to > instantaneously accelerate to come to rest relative to the garage when the > front end reaches the back of the garage, and they're saying that this > would lead to different physical scenarios depending on whether all points > in the car accelerate simultaneously in the car frame, or if they > accelerate simultaneously in the garage frame. In the first scenario the > back end of the car will come to rest relative to the garage when it's > outside the garage (so the car never fit in either frame) and in the second > scenario the back end of the car will come to rest when it's inside the > garage (so the car did fit in both frames). This wouldn't be a mere > difference between frames as in Brent's scenario where there's no > acceleration, these would be two physically different options for how to > accelerate the car. > > > There's nothing in that scenario which models it as accelerating (actually > decelerating) to get a perfect fit. In fact, the author states that the car > fits in the garage from the garage frame, but not in the garage in the car > frame. He then states that simultaneity fails in car frame and this is the > alleged solution. At least he seems to agree with my concept of what > constitutes a paradox. AG > > > Wrong. The author does have the car stopping to get a perfect fit, but I > don't think this matters. We can assume the car is in constant motion and > get the same result re; differerence in simultaneity between frames. AG > > > There are different ways of formulating the paradox, and as you seem to > acknowledge, the author you linked at > http://insti.physics.sunysb.edu/~siegel/sr.html does talk about the car > stopping, and notes there are different possible physical scenarios for > when the back of the car stops if the front stops when it reaches the back > wall (i.e. whether the back of the car stops simultaneously with the front > according to the car frame's definition of simultaneity or the garage > frame's definition of simultaneity). Of course you can also formulate the > paradox in terms of different frames' perspective on a car moving > inertially through the garage without stopping as Brent did (that's the way > the paradox is usually formulated), but then why did you specifically ask > about a page that has a completely different version of the problem? > > > *That scenario was posted, IIRC, by Quentin, in part his demonstration of > how simple the solution, and how stupid I am. I prefer the scenario where > the car doesn't cease its motion, and IIUC, the alleged solution is the > same, which I don't understand; disagreement about simultaneity. AG * > > > I also prefer to talk about an inertial scenario with no stopping, so > let's drop the discussion of that webpage. > > > *OK. You've stated several times that events are invariant under the LT, > and you've defined "event" as a point in spacetime.* > > > No, what I've said is invariant are the local physical facts i.e. *things > that are physically happening" at a single point in spacetime, like the > reading on a physical clock there, > > > *You seem to offer ambiguous definitions of "events" which are frame > independent, like the reading of a clock.* > Just calling it ambiguous without explaining why you find it ambiguous isn't helpful. What is ambiguous about the notion of local physical facts that are about configurations of particles in a small local region of spacetime? > * I am not claiming time labels as such are frame independent. I plan to > spend some time reading your long statement below. In the meantime, since > you affirm disagreement about simultaneity is the solution to the apparent > paradox, please define exactly what paradox you are trying to solve. In my > analysis using length contraction, we have the car fitting in garage frame, > but not in car frame. Anything wrong with just accepting this result? If > not, why not? How exactly does disagreement about simultaneity solve the > paradox, whatever it is? TY, AG* > You have already asked this question about why we need to go beyond length contraction a bunch of times and I've answered a bunch of times: the paradox lies in the idea that a disagreement in predictions about whether the car fits would naively *seem* to imply genuine physical contradiciton i.e. different predictions about local physical facts as defined above, but an analysis involving simultaneity can show this isn't the case. I'll copy and paste my answer from https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/p5wwz5C5AQAJ (an answer you didn't really address in your response), and which was itself copying and pasting from some earlier posts: I have already explained the point here is pedagogical (in several other posts that you never responded to--I think it would help the discussion if you would respond to every post where I ask you a question, instead of taking a sporadic approach). Here was what I said in the first post where I made this point: 'The reason physicists bother to talk about a hypothetical scenario like this is pedagogical, they want to get students to think about situations where the perspective of different frames might *seem* to lead to real physical contradictions, and then looking at it more closely they'll understand how the "real" physical predictions in relativity are always about local events, and that by considering different definitions of simultaneity we can show the two frames do agree about all local events on rulers and clocks. 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?' 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.' > > > > or the crossing point of the worldlines of two physical objects like the > back of the car and the front of the garage. (In relativity the word > 'event' can either be used to refer to a physical point in spacetime and > all the physical things that occur there, or it can be used to refer to > some specific physical thing happening there like a clock reading) Since > you were OK with the idea of "point in spacetime" as a sort of idealized > limit of very small finite regions of spacetime, just think of > coordinate-invariant statements about the arrangement of particles (like > the atoms making up a clock or a ruler or the end of a car, or the photons > making up a light ray) that are inside a very small volume in space if you > looked at the particles in that region for a very brief moment of time (we > could think of this as an 'infinitesimal' region of spacetime). Things like > the hand of an analog clock pointing at a particular mark on the clock > within that infinitesimal spacetime region, or a set of photons passing > through the region that carry an image of some other event that's on the > past light cone of that region. > > The *coordinates* associated with a point in spacetime in some frame are > not part of what I mean by physical events at that point in spacetime, > although there may be some physical clock readings and ruler markings that > match up with those coordinates, but not all frames will take those > clock/ruler readings as "canonical" in terms of defining coordinates. > > > * So, if the moving car fits exactly, what basis you do have for claiming > the two events in the garage frame, front and back of car with same time, > fail to transform simultaneously under the LT, to the car frame?* > > > By "fail to transform simultaneously" do you just mean the idea that two > different points in spacetime which are assigned the same time coordinate > in one frame are assigned different time coordinates in another frame? > > > *Not exactly. I'm thinking of measurable time, such as the same time the > front of car reaches end of garage, and back of car reach the front of > garage. (from pov of garage frame). These events seem to satisfy your > definition of simultaneous events, and your claim that they are frame > independent under the LT. If so, since they must transform **frame-independent > using the LT, I don't see how they could yield any disagreement in > simultaneity, which seems to be required to solve the paradox, whatever it > might be. AG* > As I illustrate in my longer numerical example of local events which you say you're going to address in a future post, in the same local region of spacetime where the front of the car reaches the back of the garage you have two *different* clock readings, on clock #3 at the front of the car and clock #4 at the back of the garage, each of which had previously been synchronized with the clocks at the back of the car and the front of the garage using the Einstein synchronization procedure, used in the car rest frame to synchronize the two car clocks and used in the garage rest frame to synchronize the two garage clocks. Both the clocks at the back of the car and the front of the garage read 0 when they passed each other, but when the clock at the front of the car reaches the back of the garage, the car clock in that local region read -7.5 and the garage clock in the same local region read 3.5. So, without arbitrarily picking one set of clocks as canonical and discarding the other readings (i.e. picking which to use to define a frame-dependent notion of time), how are you supposed to get any definite statement about the "measurable time" between the local event of the back of the car passing the front of the garage and the local event of the front of the car reaching the back of the garage? Do you think the "measurable time" here would be -7.5 or 3.5 or neither? > > > If so, see above, time coordinates are not part of what I mean by > "physical events". > > > * AND, supposing they do NOT transform simultaneously, what exactly is the > apparent paradox you think you are trying to solve, and how is the alleged > failure of simultaneity in the car frame, the solution**? AG * > > > The paradox is how the two frames can disagree (in coordinate terms) about > whether the car fits, and in particular whether the event A="back of car > passes front of garage" happens before or after event B="front of car > reaches back of garage", and yet they can agree about *all* local physical > facts at the point in spacetime where A occurs and at the point in > spacetime where B occurs. > > > > In Brent's inertial version with no stopping, you need to consider > simultaneity to see how both frames can agree on all local events, > > > *But if frames agree on local events, an event being defined as a position > and time in spacetime, there can be no violation of simultaneity. AG* > > > Did you read the comment before the one you are responding to here? I > don't understand why you think agreement on local events would have > anything to do with simultaneity, I explained why it doesn't there. > > > *I don't understand it, because you keep saying events are invariant using > the LT, so if you're transforming two events with the same time labels,* > > > I don't think I used the phrase "events are invariant using the LT". > Physical events don't transform at all, only their coordinate labels do. > > > *OK, so if the time labels represent the measured time of physical events, > they will transform simultaneously under the LT.* > See above, there are no local physical facts which represent "measured time" in some way that's independent of a convention about which set of physical clocks to treat as canonical. The only local physical facts are the clock readings themselves, which can differ in the same local region of spacetime, if you're looking at clocks in motion to each other which are part of sets that have been previously synchronized by the Einstein convention in their rest frames. > * But then how can you use failure of simultaneity to solve the paradox? > Did Brent affirm or deny failure of simultaneity to "solve" the paradox? AG* > > > Also, if you don't *already know* what physical events occurred at a > particular point in spacetime (for example you don't know what a clock > reads there), but you are given a set of initial conditions in each frame > (including initial reading on that same clock at time coordinate 0 in the > frame), then you can can *derive* a prediction about the physical event in > different ways in different frames, using formulas derived from the LT like > the time dilation equation (which tells you how fast the physical clock > ticks relative to the time coordinate). In that case both frames will end > up with the same prediction about the local physical event, but arrived at > with different calculations. If you'd like a numerical example of this > using initial conditions from Brent's example, just ask and I can provide > one. > > > * I would assume the two events, which are simultaneous in the garage > frame, will remain simultaneous in the car frame. * > > > No, time labels are just that, labels, they are not actual physical events > at each point, or in my above alternative formulation, they are not > necessary consequences of any specific arrangement of particles that occurs > in a tiny region of spacetime. Please look again at what I posted at > https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/hYkasRQOAgAJ > for some of the other physical events that happen at the same point as the > event "front of car reaches back of garage" in Brent's example, and then > look at my followup question after the quote: > > "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: > > > So we have front and back of car satisfying simultaneity, as real events, > and using the LT the transformed event to the car frame, are not > simultaneous? AG > I don't understand what "So we have front and back of the car satisfying simultaneity, as real events" means. Front and back of the car describe worldlines that pass through many different events/points in spacetime, if you are talking about two specific events on the wordlines of front and back, which ones do you mean? And the statement of mine you are responding to said nothing about simultaneity so I don't know why you wrote "So" in response to what I wrote. Were you referring to the part where I talked about clocks and front and back of car and garage being synchronized by the Einstein synchronization procedure? If so, the Einstein procedure itself only "synchronizes" clocks in a frame-dependent way, you synchronize two clocks at rest relative to each other by assuming the time for light to travel from clock A to clock B must be the same as the time for the light to travel from B to A, that's true in the clocks' rest frame but other frames where the clocks are in motion say these two light travel times are *not* equal, so setting the time on the two clocks with this assumption leads them to be synchronized in the time coordinates of their rest frame but out-of-synch in the time coordinates of other frames. > > > --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." > > In the above example, do you understand that "Clock #3 at the front of the > car read t = -7.5" would be a statement not about coordinates but about the > actual configuration of particles in the infinitesimal region of the front > of the car reaching the back of the garage, i.e. there is a specific > collection of atoms we call "Clock #3" and its physical hand is pointing at > a physical painted-on marking that reads -7.5? Likewise that "Clock #4 at > the back of the garage read t' = 3.5" is a statement not about coordinates > but about a second physical clock in this region and which marking its hand > is pointing to? If so you can see why looking at these clock readings (and > at the readings in the neighborhood of the different event 'back of car > passes front of garage', where both clocks read 0) is not sufficient to > settle definitively whether this event happens BEFORE or AFTER the event of > the back of the car passing the front of the garage. As a matter of > coordinate convention, the car frame takes clock #3 as "canonical" for > defining time coordinates, while the garage frame takes clock #4 as > canonical for defining time coordinates, so they get different answers in > spite of agreeing about the physical readings of both clocks in this region. > > > > *Are you claiming that if the car doesn't stop, Brent's model, then there > is no failure of simultaneity? I've always thought failue of simultanaeity > is alleged to be the solution. If not, then what's the problem we're trying > to solve, and its solution? Sorry; I feel totally confused. AG* > > > No, in terms of the time-coordinates they assign to physical events, the > two frames always disagree about simultaneity and in some cases about the > order of pairs of events which aren't simultaneous in either frame, like > the events A and B above. > > > *Do you see how this can be confusing? You now claim the two events, with > time measured in garage frame when car fits perfectly in garage, don't > transform simultaneously, when previously you asserted they DO, under the > LT? AG* > I never asserted that they do "transform simultaneously" in terms of time coordinates (and simultaneity is a purely coordinate-dependent notion), I just said that readings on each clock in the local neighborhood of a given event are agreed by all observers. But different observers disagree on which local clocks to treat as canonical for the sake of defining a time coordinate, and since they pick different local clocks they get different conclusions about the time coordinate (like -7.5 vs. 3.5 above). Jesse > > > Do you think you can define simultaneity in a way that only refers to > facts about what's happening at a single point in space time, with no > reference to any relation between that point and any other point in > spacetime? > > > *No. Of course not. AG* > > > OK, that's why statements about simultaneity are not statements about > local physical events. > > Jesse > > > > If you think you can, tell me what specific local facts you are referring > to, given a particular choice of point in spacetime (say, the point where > the worldline of the back of the car crosses the worldline of the front of > the garage). > > Jesse > > > so it's just the same physical scenario described in different coordinate > systems; in the version on the website you need to consider simultaneity > for a very different reason, because it's specified that the car's back end > can stop simultaneously with the front end in either the car frame and the > garage frame, resulting in genuinely different physical scenarios. > > -- > 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/b072983c-712c-4338-b184-8bc37c4b02f9n%40googlegroups.com > <https://groups.google.com/d/msgid/everything-list/b072983c-712c-4338-b184-8bc37c4b02f9n%40googlegroups.com?utm_medium=email&utm_source=footer> > . > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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