On Thu, Oct 24, 2024 at 9:13 PM Alan Grayson <[email protected]> wrote:
> > > On Thursday, October 24, 2024 at 7:09:27 PM UTC-6 Alan Grayson wrote: > > On Thursday, October 24, 2024 at 6:52:30 PM UTC-6 Jesse Mazer wrote: > > On Thu, Oct 24, 2024 at 8:36 PM Alan Grayson <[email protected]> wrote: > > > > On Thursday, October 24, 2024 at 4:20:46 PM UTC-6 Jesse Mazer wrote: > > On Thu, Oct 24, 2024 at 3:02 PM Alan Grayson <[email protected]> wrote: > > > > On Thursday, October 24, 2024 at 12:03:22 PM UTC-6 Jesse Mazer wrote: > > On Thu, Oct 24, 2024 at 8:06 AM Alan Grayson <[email protected]> wrote: > > > > On Thursday, October 24, 2024 at 12:01:30 AM UTC-6 Jesse Mazer wrote: > > On Wed, Oct 23, 2024 at 9:03 PM Alan Grayson <[email protected]> wrote: > > > > On Wednesday, October 23, 2024 at 6:03:58 PM UTC-6 Jesse Mazer wrote: > > On Wed, Oct 23, 2024 at 7:10 PM Alan Grayson <[email protected]> wrote: > > > > On Wednesday, October 23, 2024 at 4:47:13 PM UTC-6 Jesse Mazer wrote: > > On Wed, Oct 23, 2024 at 6:31 PM Alan Grayson <[email protected]> wrote: > > > > On Wednesday, October 23, 2024 at 1:55:13 PM UTC-6 Brent Meeker wrote: > > The fact that you never specify whether "synchronized" means "set to the > same time" or "caused to run at the same rate" or both, makes me think you > don't understand your own question. > > Brent > > > I meant when juxtaposted, to set at the two clocks at the same time, and > then synchronized throughout each frame. Then I expect, but am not certain, > that the rates in the two frames will be the same. AG > > > "Synchronized" only has meaning relative to a particular frame's > definition of simultaneity--since the frames disagree on simulataneity, you > can momentarily set all clocks so that they read the same time at the same > moment relative to one frame, but you can't do this in both frames. And > whichever frame you pick, unless you artificially adjust the ticking rate > of the clocks moving relative to that frame to "correct" for time dilation, > the moving clocks won't stay synchronized with the clocks at rest in that > frame. > > Jesse > > > As I see it, when the clocks are juxtaposed, a comparison of any clock in > one frame, will read the same time as the corresponding clock in the other > frame, that is, corresponding with position as they pass each other. And > since the frames are moving with the same velocity wrt each other, I don't > see the role of simultaneity in changing the rate of any clock in any > frame. What I think this scenario shows, is that time dilation doesn't > exist. AG > > > But that's wrong according to relativity, and the Lorentz coordinate > transformation is mathematically/logically consistent, and the prediction > that the laws of physics work symmetrically in these different frames (so > that readings on natural physical clocks at different locations will align > with coordinate time in their rest frame, assuming they are synchronized > according to the Einstein convention at > https://en.wikipedia.org/wiki/Einstein_synchronisation ) has held up > experimentally. I once made a diagram showing two rows of clocks in motion > relative to each other, synchronized according to Einstein's convention, so > people can see how it works--see > https://physics.stackexchange.com/a/155016/59406 > > Jesse > > > Jesse; I'll check out your links, for sure. I will just say now that time > dilation can be established using a rest frame and moving frame, but in my > model there is no rest frame; both frames are moving. AG > > > In relativity "rest frame" is only used in a relative sense, there is no > objective truth about which frame is called the "rest frame" and which > frame is "moving". For example if you have two clocks A and B in relative > motion, you can calculate things from the perspective of the coordinate > system where A's coordinate position doesn't change with time which is > called "A's rest frame", but you can equally well calculate things from the > perspective of the coordinate system where B's coordinate position doesn't > change with time which is called "B's rest frame", and both calculations > should agree in their predictions about all local events eg what readings > show on both clocks at the moment they pass next to each other (I > illustrated this with a few clocks in the diagrams from my link). > > Jesse > > > TY. Yes, I am aware of what you wrote. That's why I tried to come up with > an example where there is no frame identified as the rest frame. I will > look at your diagrams today. I think Brent makes the same point with world > lines. AG > > > But when I referred to the calculations with A and B, no frame would be > identified as "the" rest frame, there are just two frames which as a matter > of verbal convention are called "A's rest frame" (you could also just call > it 'the frame where A has a velocity of 0') and "B's rest frame" (or 'the > frame where B has a velocity of 0'). You could also do the calculations > from the perspective of a frame where both A and B have nonzero velocity if > you wish, the point in special relativity is that the same equations of > physics apply in all inertial frames so you're free to use whichever one > you find convenient. But you do need to pick *some* spacetime coordinate > system to define how the coordinate position of each object you're > analyzing changes with coordinate time, since the equations for the laws of > physics are generally written in terms of such coordinates. > > Jesse > > > In my scenario for analyzing the Clock Paradox, can you identify where, > EXACTLY, I mistakenly assumed simultaneity, which presumably led to the > wrong conclusion? TY, AG > > > Your scenario just seems unclear to me, you said "multiple set of clocks > in both frames can be synchronized" without spelling out what technique you > want to use to synchronize them, I was just pointing out the ambiguity. If > you have two sets of clocks A' and B' where all the clocks in a given set > are at rest relative to one another, and all the clocks in A' are supposed > to be synchronized with one another, likewise all the clocks in B' are > supposed to be synchronized with one another, how are you proposing to do > this when each member of a given set is at a different location so they > can't be compared in a local way? If you synchronize them using the > Einstein synchronization convention involving the assumption that light > signals travel at the same speed in both directions, then the clocks in A' > cannot be synchronized with the clocks in B'. If you want some other method > of synchronizing clocks that are at rest relative to one another, you need > to spell out the method. > > Jesse > > > If the clocks in both frames are identical, and I set the readings of the > juxtaposed clocks to some identical value > > > By juxtaposed do you mean right next to each other spatially, i.e. you set > a clock from group A' to read the same thing as a clock from group B' at > the moment they pass next to each other? But that wasn't what I was asking > you, I was asking how you set different clocks from the *same* set so that > they are "synchronized" with one another according to you. Clocks from the > same set are at rest relative to one another and at different spatial > locations, so they will never be next to each other unless you moved them > around beforehand (and if you did that, you have to worry about time > dilation due to motion when you move them apart). Do you use the Einstein > clock synchronization convention, or something different? > > Jesse > > > I think I used Einstein's convention. Not sure I recall what it was. I > assumed the clocks exist everywhere in any frame and aren't moved. And they > could be set to the same time as the juxtaposed clock in that frame, > probably using a light signal. AG > > > I think I only need one clock other than the juxtaposed clock, with a > known distance between them. Knowing that distance, I can synchronize these > two clocks using a light signal. AG > So like two clocks A1 and A2 that are at rest relative to one another and synchronized by light signal (the Einstein convention), and then just one other clock B1 that's moving relative to them, so it first passes A1 and then passes A2 a bit later? In this case, if you set B1 to read the same time as A1 at the moment they pass next to each other, then because of time dilation due to motion in the rest frame of the A clocks, by the time B1 passes A2 its reading will be behind that of A2. Jesse > > > > > > > On 10/23/2024 6:00 AM, Alan Grayson wrote: > > In this scenario, is there any contradition with the principles of SR? > Suppose there exist two inertial frames, moving in opposite directions with > velocity v < c along the x-axis, where one clock of each frame is initially > located one unit, positively and negatively respectively from the origin, > and when these clocks are juxtaposed at the origin, the multiple set of > clocks in both frames can be synchronized? Does this scenario imply an > unwarranted affirmation of simultaneity? > > TY, 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/0869355a-967a-428d-8994-1b95abf355aen%40googlegroups.com > <https://groups.google.com/d/msgid/everything-list/0869355a-967a-428d-8994-1b95abf355aen%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/CAPCWU3LD3j_CX6w%2BZpXZoWGND2Ek98ew%3D5z_xQr%2BX8LL893MWw%40mail.gmail.com.
