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, and then sychronize all clocks in each frame to the value of its respective juxtaposed clock, there is no reason to think that the clock rates would change and differ when the frames are compared. You argue that the clock rates would appear different as one frame views the other, but what's your reason for this assumption? AG 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/cac06e4a-175f-4dc4-b85d-6a7847e588ben%40googlegroups.com.
