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, 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? 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. 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: --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 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. > > > 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/841f1ec9-71b5-461b-94c2-9b3df13fd28dn%40googlegroups.com > <https://groups.google.com/d/msgid/everything-list/841f1ec9-71b5-461b-94c2-9b3df13fd28dn%40googlegroups.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/CAPCWU3%2B10KXxnYP0UkJX%2BNvXmG_kaCb_Zvn_KadX38kZyLj-Fw%40mail.gmail.com.
