On Sunday, January 26, 2025 at 12:38:09 PM UTC-7 Jesse Mazer wrote:
On Sun, Jan 26, 2025 at 12:26 PM Alan Grayson <[email protected]> wrote: On Sunday, January 26, 2025 at 10:04:54 AM UTC-7 Alan Grayson wrote: On Sunday, January 26, 2025 at 9:13:54 AM UTC-7 Jesse Mazer wrote: On Sun, Jan 26, 2025 at 1:54 AM Alan Grayson <[email protected]> wrote: On Saturday, January 25, 2025 at 11:25:53 PM UTC-7 Brent Meeker wrote: On 1/25/2025 10:13 PM, Alan Grayson wrote: On Saturday, January 25, 2025 at 9:06:18 PM UTC-7 Brent Meeker wrote: On 1/25/2025 6:34 PM, Alan Grayson wrote: On Saturday, January 25, 2025 at 6:47:22 PM UTC-7 Jesse Mazer wrote: On Sat, Jan 25, 2025 at 8:07 PM Alan Grayson <[email protected]> wrote: On Monday, December 9, 2024 at 2:01:28 PM UTC-7 Brent Meeker wrote: > > Nothing odd about dilation and contraction when you know its cause. > But what is odd is the fact that each frame sees the result > differently -- that the car fits in one frame, but not in the other -- > and you see nothing odd about that, that there's no objective reality > despite the symmetry. AG The facts are events in spacetime. There's an event F at which the front of the car is even with the exit of the garage and there's an event R at which the rear of the car is even with the entrance to the garage. If R is before F we say the car fitted in the garage. If R is after F we say the car did not fit. But if F and R are spacelike, then there is no fact of the matter about their time order. The time order will depend on the state of motion. Brent Jesse; it's the last two of Brent's sentences that I find ambiguous. What does he mean? What about them do you find ambiguous? He's just saying that if there's a spacelike separation between the events F and R (as there was in his numerical example), then you can find a frame where R happens after F (as is true in the car frame where the car doesn't fit), and another frame where F happens after R (as is true in the garage frame where the car does fit). *What does he mean by "But if F and R are spacelike, then there is no fact of the matter about their time order."? (What you wrote above?) * Brent writes > Yes. Just what Jesse wrote above. It means the two events were so close together in time and distant in space that something would have to travel faster than light to be at both of them. *More important I just realized that in the frame of car fitting, the events F and R aren't simultaneous, so how does one apply disagreement on simultaneity when one starts with two events which are NOT simultaneous? AG* Brent writes > That's why you should talk about events being spacelike...the relativistic analogue of simultaneous. *I'd like to do that. BUT if the Parking Paradox is allegedly solved by star**ting in the garage frame where the car fits, the pair of events which define fitting are not spacelike since they occur at different times! * You didn't read the definition of "spacelike" that I wrote above. You want everything fed to you in tiny bites of knowledge which you forget eight lines later, so the questions start all over again. Brent *I read it, but didn't like it. Big difference. Maybe you should stop trying to read my intentions. You may be smart, but reading my intentions is way above your pay grade. How could two events with the same time coordinate be referred as "so close together". Moreover, in all discussions of solutions to the paradox, events that are simultaneous in one frame, are shown not simultaneous in another frame. This being the case, the two events of the car fitting in garage frame are simply NOT simultaneous! Also, Jesse seems to be referring to different events than the ones you refer to. So there's a muddle IMO. As a teacher, your preferred method is to intimidate students. Grade now D+. AG * Why do you think I am referring to different events? I referred to the same events F and R that Brent did (F is the event of the front of the car coinciding with the garage exit, R is the event of the rear of the car coinciding with the garage entrance). If you don't like Brent's verbal explanation, I also gave you a mathematical definition of "spacelike separation" in two recent posts on the "Brent on Parking Paradox" thread at https://groups.google.com/g/everything-list/c/QgVdhXi3Hdc/m/KC2lIKyrDQAJ and https://groups.google.com/g/everything-list/c/QgVdhXi3Hdc/m/FF7TpbG-DQAJ -- "If you know the distance x and time interval t between the two points/events in the coordinates of any inertial frame, to say they are spacelike separated just means that x > ct (and an equivalent definition is that neither point is in the past or future light cone of the other one)". Since I explicitly referred to a time interval t between the two events, if you had paid attention to that you would have known not to say "the pair of events which define fitting are not spacelike since they occur at different times". Jesse *Earlier I confused spacelike with timelike, but now I am clear about that. I also recall your post defining spacelike for simultaneous events. I was confused about my reference to different events referred to by you and Brent. The core issue now is that we need simultaneous events in the garage frame where the car fits, to determine a disagreement about simultaneity with the car frame. Otherwise, it make no sense to speak of any disagreement about simultaneity.* I think it does make sense to say that disagreement about order of non-simultaneous events is a consequence of the relativity of simultaneity, I explained why in the recent post at https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/zx1LFvELDgAJ -- did you read it? And it is common to include disagreement about event order in discussions of the relativity of simultaneity, as in the the second paragraph of the "description" section of the relativity of simultaneity wiki article at https://en.wikipedia.org/wiki/Relativity_of_simultaneity#Description Anyway, this is just a linguistic issue, if you want to use a separate phrase "relativity of event-order" you can, it only leads to a cosmetic change to the argument--instead of saying that disagreement about fitting is a consequence of relativity of simultaneity, one can just say disagreement about fitting is a consequence of relativity of event-order for the events F and R. On the other hand, if you want to think about fitting not in terms of events F and R but just in terms of a comparison of the length of the garage with the length of the car, then since "length" in a given is always defined in terms of the distance between front and back at a single moment in time in that frame, that does involve picking events on worldlines of the front and back that are simultaneous, so the fact that the two frames disagree on the lengths can be understood in terms of their disagreement about simultaneity. *I suppose, from you pov, I did it again; referring to difference in times for fitting to mean non-simultaneous. Did Brent ever prove the events could be non-simultaneous in time, yet be spacelike? I don't think so. AG * Yes, Brent's definition of spacelike separation at https://groups.google.com/g/everything-list/c/gbOE5B-7a6g/m/CgV9j1QQDgAJ was "the two events were so close together in time and distant in space that something would have to travel faster than light to be at both of them", which is equivalent to my definition that x > ct. For example if an event A happens on Earth today, and 2 years later another event B happens on Alpha Centauri 4 light years away (measured in the Earth/Alpha Centauri rest frame), something would have to travel twice the speed of light to be at both of them, and x > ct because x = 4 light years and ct = 2 light years. On the other hand if event B happened on Alpha Centauri 8 years after A, the two events would be timelike separated (x < ct) and something traveling at half the speed of light could be at both. And if event B happened on Alpha Centauri 4 years after A, the two events would be lightlike separated (x = ct) and something would need to travel at exactly the speed of light to be at both events. Jesse *Brent's solution is an approximation, which turns me off, but there's an exact solution of two events in garage frame with the same time coordinate; namely the front and back of the car when the back enters the garage. Now we have two simultaneous events, which happen to be spacelike, but the important fact in this problem is that they're simultaneous. Now, supposing their images in car frame are not simultaneous, how does this resolve the paradox. I don't think it does. 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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