On Tuesday, October 29, 2024 at 1:47:36 AM UTC-6 Jesse Mazer wrote:
On Tue, Oct 29, 2024 at 2:26 AM Alan Grayson <[email protected]> wrote: On Monday, October 28, 2024 at 11:13:18 PM UTC-6 Jesse Mazer wrote: On Mon, Oct 28, 2024 at 9:47 PM Alan Grayson <[email protected]> wrote: On Monday, October 28, 2024 at 6:44:18 PM UTC-6 Jesse Mazer wrote: On Mon, Oct 28, 2024 at 7:26 PM Alan Grayson <[email protected]> wrote: On Monday, October 28, 2024 at 12:01:33 PM UTC-6 John Clark wrote: On Mon, Oct 28, 2024 at 9:19 AM Alan Grayson <[email protected]> wrote: *> The link just says that the apparent paradox is resolved by a breakdown in simultaneity, but doesn't specify exactly what that means. I notice that an apparent paradox can be defined for length contraction, whereas I was trying to resolve it for time dilation, but so far I cannot define the problem with clarity. Do you have any suggestion in this regard? AG* *The garage is 9 feet deep and has doors on the front and back that can be closed and locked, but the car is 10 feet long so apparently it can never fit in the garage. However from the point of view of somebody standing still next to the garage the car is moving so fast that, due to Lorentz contraction, the car is now only 8 feet long. And to prove that the contraction is real and not just an optical illusion, as soon as the back of the car has fully entered the garage the man quickly closes and locks the front of the garage, at that exact instant from the garage man's point of view, the car is in the garage AND simultaneously it is between BOTH of two closed and locked doors. The man then quickly runs to the back of the garage and unlocks and opens the back door which allows the card to continue on at nearly the speed of light. So there is no paradox.* *But how would this look from the driver of the car's point of view? He would see the car as being stationary and therefore 10 feet long, but the garage is moving so fast due to Lorentz contraction the garage is now only 8 feet deep not 9, and apparently making things even worse. However, what the car driver sees is that as soon as the front of the car enters the garage the garage man runs around to the back and opens the back door of the garage. From the car driver's point of view at NO time is the car simultaneously between BOTH of two closed and locked doors. So there is no paradox, although the car driver and the garage man do not agree what is "simultaneous" and what is not.* * <https://groups.google.com/g/extropolis>* *Two doors. Doors locked and then unlocked. Or whatever. You seem to have an inclination for overly complicated analyses. Why not just say the car driver knows the length of his car because he can simultaneously measure its endpoints, and due to contraction of the garage's length, he knows his car won't fit inside. In the garage frame, the car's length cannot be measured due to a breakdown in simultaneity. So this observer hasn't a valid opinion whether or not the car will fit inside. So, in this analysis the paradox is solved, and the car won't fit inside the garage. What do you find insufficient about this analysis? AG**ca* It's simply not true that there is a "breakdown in simultaneity" leading the car's length to be unmeasurable in the garage frame, the garage frame just has a *different* view of simultaneity than the car frame but they are both perfectly well-defined, and in relativity you can't say one is "true" and the other is wrong. John Clark's version makes things simpler by avoiding the need for the car to move non-inertially (decelerate), if both front and back doors of the garage are open at the moment the car passes through them, then the car can just sail right in one door and out the other. Then the two frames disagree about whether the car ever "fit in the garage" because they disagree about whether the event "front of car exits the open back door of the garage" happened before or after the event "back of car passes through the open front door of the garage". If the front of the car passing through the back door happened *before* the back of the car passing the front door, then the car was never fully inside the garage because the front end was starting to poke out before the back end was fully inside, whereas if the former event happened *after* the latter event, then the car was fully inside the garage for some time. So, disagreement over simultaneity is equivalent to disagreement over the answer to the question "was the car ever fully inside the garage at any moment?" Jesse Initially you claim there is no breakdown in simultaneity, but you conclude by claiming there is simultaneity and what it implies. I don't understand your language, what does "breakdown in simultaneity" mean and what does "there is simultaneity" mean? The meaning of simultaneity is fairly straight-forward. If, for example, an observer who is situated between two mirrors and sends a beam of light toward both, and receives their reflections at the same instant, knows their locations by making a simple calculation and correction for the time required for the round trip, and knows they are equidistant. Or, if the beams don't return at the same time, the observer knows they are not equidistant, but he can calculate how far away each one is. That occurs in some rest frame. But an observer in a relatively moving frame, will not see both reflections at the same time, even if they are equidistant in the rest frame, which is the definition of breakdown of simultaneity. IOW, events which are simultaneous in one frame, the rest frame, will not be simultaneous in the moving frame. AG I agree with all this, but what was confusing me was your connecting it to the notion of length being undefined in some frame--see below Neither phrase is used in the link or in any text on relativity I've ever seen, and the meaning isn't self-evident at all, I asked you to explain "breakdown" earlier but you didn't respond. All I'm saying is that each frame has their own well-defined definition of simultaneity, the two frames' definitions disagree, I doubt the definitions disagree. AG Maybe you mean something more abstract by a "definition" of simultaneity (for example, the general notion that in every frame it's defined by local readings on clocks that are at rest in the frame and synchronized by the Einstein convention), but all I mean is that for a given pair of events, if one frame defines them as simultaneous, a different frame defines them as non-simultaneous. OK. AG and neither is objectively more correct than the other (analogous to how different inertial frames have their own definitions of what the 'velocity' of different objects is and none is preferred, velocity is an inherently coordinate-dependent quantity). None is preferred, but both frames use the same coordinate system. AG They both use the same *type* of coordinate system, but if they don't assign the same position and time coordinates to each event, that means they use "different coordinate systems" in the way physicists talk. And I'm also saying that if you are using the phrase "breakdown in simultaneity" in a way that has something to do with your claim that length is undefined in some frame, IMO, length defined in a rest frame, and depends on simultaneity? AG Length is not specifically defined in the object's rest frame, no (though the 'rest length' is). Length in relativity simply refers to the distance between the front and back end of an object at a single moment in time, so it can be defined for moving objects--for example if the back end's position as a function of time in your frame is x_b = 0.8c*t and the position of the front end is x_f = 0.8c*t + 2 light years, then for any given value of t, say t=0, the distance between the front and back end is always 2 light years (for example at x=0 we have x_b = 0 and x_f = 2 light years), so the length of the object is 2 light years in this frame. Jesse I see I have been making a mistake on some of these issues. For example, many of the peculiar results of SR are due to the fact that we must use the LT in order for the SoL to be frame independent. So, the length of a rod can be measured differently in different frames, and the breakdown in simultaneity just means that events which are simultaneous in one frame, will not be simultaneous in another frame. IOW, just like the E field in the S frame will have different values in the S' frame, E', there's no inherent contradiction with different values of length say, in different frames. In the car garage problem, the car length and other variables could be frame dependent, but the only contradiction would be if the frames disagreed on whether the car could fit in the garage. BTW, the link which started this discussion does refer to simultaneous measurements and infers, but doesn't explicitly state that the resolution of the apparent paradox depends on the differing results of simultaneity between the frames, which I referred to as a breakdown in simultaneity. 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]. 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