On Wednesday, December 25, 2024 at 10:33:19 AM UTC-7 Jesse Mazer wrote:
On Wed, Dec 25, 2024 at 4:34 AM Alan Grayson <[email protected]> wrote: On Tuesday, December 24, 2024 at 9:11:35 PM UTC-7 Jesse Mazer wrote: On Tue, Dec 24, 2024 at 3:22 PM Alan Grayson <[email protected]> wrote: On Tuesday, December 24, 2024 at 10:43:55 AM UTC-7 Jesse Mazer wrote: On Tue, Dec 24, 2024 at 6:13 AM Alan Grayson <[email protected]> wrote: On Tuesday, December 24, 2024 at 3:30:15 AM UTC-7 Alan Grayson wrote: On Tuesday, December 24, 2024 at 1:30:59 AM UTC-7 Alan Grayson wrote: On Tuesday, December 24, 2024 at 1:23:44 AM UTC-7 Brent Meeker wrote: On 12/23/2024 11:48 PM, Alan Grayson wrote: On Monday, December 23, 2024 at 11:03:36 PM UTC-7 Brent Meeker wrote: On 12/23/2024 9:36 PM, Alan Grayson wrote: On Monday, December 23, 2024 at 9:38:34 PM UTC-7 Alan Grayson wrote: On Monday, December 23, 2024 at 9:33:36 PM UTC-7 Brent Meeker wrote: All you have to do is solve for the speed at which the Lorentz contraction is 10/12 so that the car is ten feet long in the garage frame. Brent I know that. What I don't know is which question you're allegedly answering. AG More important question; didn't you deny my claim that for a sufficient velocity the car either fits or doesn't fit, as an objective fact that the paradox seems to deny? AG If I was thinking clearly I did. An objective fact is not reference frame dependent. Brent Obviously, you guys can only speak in riddles, If you would ever solve one the riddles you might learn something. Telling you answer just leads to your saying you're not convinced and around it goes. so I have to assume you can't answer the underlying question; Or you might assume you just too dumb or stubborn to learn the answer. Brent You have no answer, just some plots pretending to be an answer. Just riddles upon riddles. AG Why I don't believe the gurus here have the answer; you'll note how easy it is to pose the question, and how easy it is to offer a proposed solution; namely, the disagreement about simultaneity. But that's obviously not enough. As Quentin's behavior exemplifies; the mere statement of the solution is hardly sufficient. One then needs an ARGUMENT connecting the alleged solution, to the construction of the problem; that is, the paradox. But Quentin is totally UNAWARE of this requirement, which his link fails to provide, and then he's perfectly satisfied with accusing me as a troll. You, Brent, allege the solution in your plots, which I admit I fail to see the connecting argument just alluded to. But if you really understood the solution, and pride yourself in your teaching skills of relativity, you could offer a text solution, which should be a relatively short paragraph. But that remains wanting. AG Reviewing how time transforms using the LT, it does appear that for a perfectly fitting car for which its time parameter is identical at its end points, time does NOT transform to identical time parameters of the car's end points in the car frame, since in the garage frame the spatial parameter of the end points differ in the transformation equation. I'm not entirely certain, but I think this establishes the disagreement concerning simultaneity between the frames. Now, to resolve the paradox, requires an ARGUMENT to, in effect, DECONSTRUCT the claim of a paradox depending on this disagreement. AG The argument is that both frames agree on all the local physical facts at the front of the car as it reaches the back of the garage--in my example they both agree that the physical clock at rest relative to the car there reads -15 and the physical clock at rest relative to the garage there reads 0. Their only disagreement is the *convention* they each use about which physical clock to treat as canonical for the purpose of assigning an abstract time-coordinate to that location in spacetime. *What convention are you referring to? Einstein uses the same clocks in each frame, which are synchronized at rest, and then go out of synch when motion is initiated. He never refers to different clocks.* Are you talking about the 1905 paper? He does in that paper imagine originally creating two rigid measuring systems at rest with each other and then imparting a velocity to one relative to the previous rest state (in section 3 starting at https://einsteinpapers.press.princeton.edu/vol2-trans/160 ), but this notion of them starting at rest relative to one another isn't an essential part of his argument, you could equally well imagine two rigid measuring systems that have been moving relative to each other forever (or at least for the whole duration we are considering in the problem), and he dispenses with this notion in other works where he discusses two measuring systems in relative motion (like the section of his book Relativity: The Special and General Theory at https://philosophie.ens.fr/IMG/EGS%20Einstein%20relativity%208-9.pdf ). And although both systems are equipped with the same *types* of clocks, they are not literally sharing the same individual clocks--there are some clocks at rest relative to the first rigid system, and a different set of clocks at rest relative to the second system. Finally, he doesn't imagine syncing the clocks beforehand and then seeing them "naturally" go out-of-sync when one system is imparted a velocity relative to the first, instead he talks about synchronizing each system's own clocks using his light-signal method *after* he talks about giving them a relative velocity, on the page at https://einsteinpapers.press.princeton.edu/vol2-trans/160 where he writes: "The origin of one of the two systems (k) shall now be imparted a (constant) velocity v in the direction of increasing x of the other system (K), which is at rest, and this velocity shall also be imparted to the coordinate axes, the corresponding measuring rod, and the clocks. ... Further, by means of the the clocks at rest in the system at rest and using light signals in the manner described in §1, the time t of the system at rest is determined for all its points where there is a clock; likewise, the time tau of the moving system is determined for all the points of the moving system having clocks that are at rest relative to this system, applying the method of light signals described in §1 between the points containing these clocks." * And the LT has both clocks, whatever they might be, in its transformation equations, namely t and t'. I've never seen of any choice about which physical clock is treated as canonical. * Yes, but in terms of physical clock readings, all frames agree that *both* of those readings t and t' are seen on clocks from different measuring systems that are passing through the region of the event in question, with the different measuring systems and their clocks having a relative velocity. Each frame simply *defines* the time coordinate of an event by the reading on the single clock at that location that is at rest in that frame, not by any of the other clocks that are in motion in that frame--that's all I mean by treating one clock as canonical. Trust me as someone who studied this stuff that this is the standard understanding of how inertial coordinate systems are defined physically, and that it's understood that the section of Einstein's original 1905 SR paper I quoted above is talking about this idea, whether or not you've ever seen it. *Any clock seems satisfactory. But even if your argument holds, it's not obvious how this would DECONSTRUCT the argument that the car fits in the garage in one frame, but not in the other. AG* It doesn't! It deconstructs the idea that this constitutes a paradox in the sense of contrary predictions about objective reality, once you realize that in relativity "objective reality" consists only of local physical facts, and that frames can disagree on the order of events (and thus on whether the car fits) without the slightest disagreement about any local physical facts. *FWIW, SR preserves causality, so your claim about time order of events not being preserved is incorrect.* I said frames *can* disagree on the order of events, not that they *always* disagree on the order of events. For events with a time-like separation, they always agree on the order; for events with a space-like separation, you can find frames that disagree (I have said this several times in our previous discussion). Assuming no FTL causal influences, events with a space-like separation don't causally influence one another. *And I've seen the Einstein quote and it has no impact on my position in these matters. Do you have a quote where he says that only objective facts are preserved at each event in spacetime?* Are you asking if he'd agree that all frames agree on local physical facts? Or are you asking if he'd agree that only such local physical facts are considered "objective"? If the former it'd be very obvious to any physicist that all frames must agree on such local facts, because of considerations of local *interactions* that leave permanent effects like my example in the post at https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/Fou17sn5AQAJ about the bomb blowing up near the glass of water and shattering it; I could try to look for a quote of him saying this explicitly if you doubt this, I'm sure I could at least find some physicists talking about this. If the latter, I suppose calling these facts "objective" is a bit philosophical, but the point is that it's not seen as a defect in a theory or contradiction that different frames can disagree about things that are *not* local facts, but it certainly would if they did make different predictions about local facts. BTW, even in classical mechanics two frames can disagree about the *distance* between two events, so why does disagreement about the *time* between events seem so much more problematic to you? Out of curiosity I went back and looked at what my old SR textbook had to say about these subjects--the text is "Special Relativity" by A. P. French, which I believe is pretty commonly assigned in intro SR classes. Page 90 talks about how measurements should consist of readings which coincide in space and time with the event they are measuring: "It is very important to realize, as Einstein in essence pointed out, that the role of an observer is simply to record coincidences, i.e., pairs of events which occur at the same space-time point. A clock reading at a particular point in a given frame of reference is an event in this sense; in- deed, our concern in this chapter is overwhelmingly with events of this kind. The things that we more familiarly think of as physical events—e.g., the collision between two objects, or the emission of a photon by an atom—are, for our purposes, to be regarded as happenings that coincide with events describable as readings on clocks. The incessant references to clock readings may well seem artificial and somewhat wearisome, but they do serve to emphasize an absolutely essential feature—that we are dealing with a very explicit problem of measurement." French goes on to make a point similar to my bomb/glass of water example about how when events coincide at the same point in spacetime this can have permanent effects viewable later: "Although an event is by definition represented by a single point in space-time, it may nevertheless leave an enduring record of itself. A criminal touches a glass, for example, and leaves a fingerprint. The touching of the glass is an event, occurring at a unique place and a unique time in a given frame of reference. A second later, even if the glass has not been moved, the finger- print is at a different point in space-time. But it remains as a record that a certain event took place. A still more pertinent example would be of a watch that falls onto a concrete floor and stops dead. If it is left where it fell, it represents a permanent record of the "watch-strikes-floor" event. And an observer, coming upon the scene long afterward, can note down the space and time coordinates of the event as measured in a reference frame defined by the floor (for space coordinates) and by the hands of the watch (for time coordinate)." And then he talks about how we should not be misled by the notion of an observer being "in" a given frame, that each observer can certainly observe the local clock readings of clocks used by different frames: "The last remark above should make it clear that an observer is not necessarily limited to making measurements in a reference frame to which he himself is attached. One can appeal to all kinds of familiar experience that embody this fact. For example, one is a passenger in a train that shoots through a station. On the platform is a sign with an arrow pointing in the train's direction of motion and carrying the words "New York 10 miles." Just above the sign is a station clock that reads 10:53 A.M. As an observer attached to a certain reference frame, defined by the train, one can nevertheless record the space-time coordinates of an event—"train passes through station"—as measured in the relatively moving reference frame of the station and the ground to which it is attached. Very often, however, one will see statements such as the following: "An observer A in frame S observes that an event occurs at position x and time t; the same event is observed to occur at position x' and time t' by an observer B in frame S'." What is really being said here is just that the event has space-time coordinates (x, t) in one frame and (x', t') in the other. But there is conjured up a picture of an observer, cloistered in his own particular frame of reference, unable to record anything except the measures of position and time in that frame. Our example of the passenger in a train shows how unnecessarily restrictive this is. The passenger can note not only the reading on the station clock but also the reading on his own watch." * And since coordinate systems are arbitrary, as well as what values clocks are sychronized to, what OBJECTIVE facts at events do you think are preserved? There appear to be none.* I am just talking about the facts of the physical clock readings at each event, like my example where the local event of the front of the car reaching the back of the garage coincided with the local clock in the garage system reading 0 and the local clock in the car system reading -15 (are you planning to return to that example to clarify your '?' responses?) While the choice of which inertial coordinate systems to use is arbitrary, once you have specified that the origin of two inertial coordinate systems coincides and their relative velocity (along with the fact that they are each using clocks synchronized in their own frame by the Einstein procedure), it's not arbitrary which pairs of other clock readings in each system coincide locally (these pairings are of course given by the Lorentz transformation equation for the time coordinate). * Finally, my argument that a paradox exist is about as straight-forward as one can imagine, based as it is solely on length contraction, yet you dismiss it out of hand, for an ill-defined concept of limited objective local reality at events in spacetime.* Are you saying that what is ill-defined is calling such local facts "objective" (if so see my comment above), or are you saying that the notion of local physical facts is itself ill-defined? If the latter this would be another example of you just throwing adjectives at without offering any substantive criticism or specific points you want to clarify, similarly to how you earlier called it "ambiguous" and later "not absolutely clear". * IOW, you seem to have defined the paradox out of existence by your claim that only local objective facts are preserved. Based on your extensive reading on SR, does Einstein have anything to say about the Lorentz Parking Paradox? Anything? IMO, unless proven otherwise, it indicates a fatal flaw in SR. AG* Why do you see disagreement about whether something "fits" as a fatal flaw, but *not* see it as a fatal flaw when we have any other quantity that differs between inertial frames, like disagreement about simultaneity in relativity, or disagreement about velocity or x-coordinate or distance intervals in both relativity and classical mechanics? You have never given any explanation of this--it seems likely it's just a matter of appealing to your personal intuitions. Whereas the argument that it'd be unacceptable to have a theory where frames could disagree about which events locally coincide is much more straightforward, it would lead to different predictions about local interactions which leave permanent records as in my example of the bomb shattering the glass only if the clock attached to the bomb reads a certain time at the moment it passes the glass. Jesse Once one realizes that they agree about all local physical facts at each point in spacetime, *Is measured time the same in both frames? Of course not. Does this mean measured time is NOT a physical fact which is frame dependent? AG* I referred not just to a "physical fact" but to an *objective* physical fact, i.e. one that doesn't depend on human conventions (as an analogy, if you choose a position for the origin of a spatial coordinate system and the orientation of your coordinate axes, there may then be a fact about the x-coordinate of some physical object in this system, but it depends on your conventional choice of how to position our coordinate system so it isn't an objective fact in my sense, for example if another physicist wasn't informed about our choice, we'd have no reason to expect them to independently arrive at the same coordinate system, and thus no reason to expect them to assign the same x-coordinate to that physical object). Measured time between events is not an objective fact in this sense (unless you are talking about proper time between two events along a specific timelike worldline that goes through both, but this can only make sense for events with a time-like rather than a space-like separation), it depends on which clocks you *choose* to use to assign coordinate time. Jesse *Why do refer to transformations that don't preserve time ordering? IIUC, such transformations only occur when assuming motion faster than light. But if so, you're not within the postulates of SR, which is what this discussion is about. So what point do you think you're making? AG* *Re: paradox: Assume there's an observer located in the garage. This observer is in the garage frame. This observer sees the car easily fit in the garage. Imagine another observer riding in the car. This observer is in the car frame and observes being in the garage but never fitting in the garage. What are the observations when the two observers pass each other, in juxtaposed positions? AG* -- 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/d20ed24c-51ea-4a3d-9201-0ccad77a1cd8n%40googlegroups.com.
