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Looking to understand time dilation 
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#361
Jan411, 04:14 AM

P: 252

As for the clocks measuring different things; that is the whole point, they are not, they are measuring the same thing (a duration) but in different ways, from different perspectives, which is what relativity is all about! And the ratio between those two measurements is the key to relativity for that is surely how the apparent incompatibility of Einstein's two postulates is resolved. (viz: section 6) 


#362
Jan411, 04:38 AM

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#363
Jan411, 07:01 AM

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Just like all of the above examples, the ratio of two different circumferences is also a dimensionless number. It represents a geometric difference between the two different things being measured, not a conversion between units. Similarly with clocks, they are dilated because geometrically they are measuring the proper time along different world lines. 


#364
Jan511, 04:42 PM

P: 252

What we are discussing is two measurements of the same distance or the same time. Those two measurements are different; i.e. contracted or dilated depending upon the perspective of the observers who are performing the measuring. If two measurements of the same quantity give different values due to the different perspectives of the observers, or due to different ways of measuring then, are they not measuring on different scales? Anyway we are not here to discuss semantics. We are concerned with relativity, Special Relativity Now in respect of the apparent incompatability ofthis two postulates, Einstein said in sections 4 – 6 that For it seems to me that only changing the scale of a measurement achieves this. Maybe that is where I am becoming confused. 


#365
Jan511, 04:53 PM

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Relativity doesn't rule out the notion that there is some metaphysical truth about simultaneity, so that only one observer's clocks are "really" synchronized. But only God could no that truthaccording to relativity, there is no experimental way to show that the laws of physics "prefer" one frame, they are all exactly equivalent as far as empirical experiments go so there can be no experimental basis for judging one frame's definition of simultaneity to be "correct" and another's to be "incorrect". 


#366
Jan511, 10:13 PM

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#367
Jan611, 10:03 AM

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#368
Jan611, 10:11 AM

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#369
Jan611, 04:54 PM

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Do you not understand that Einstein's definition is based on the assumption that each frame defines "simultaneity" using light signals, making the assumption that all light signals travel at the same speed relative to that frame? He says this in the section you quote: But the in the very next section Einstein makes clear that if observers in different frames all assume light travels at a constant speed relative to themselves, then they will disagree about whether a given pair of events (like the lightning strikes in his example) are simultaneous, which is equivalent to my comment that if each frame synchronizes their own clocks using lightsignals, each frame will say the other frame's clocks are outofsync. Did you read this part of Einstein's text? If you have trouble following Einstein's example, you might also consider this one. According to Einstein's definition, two clocks in my frame are "synchronized" in my frame (i.e. they always show a given reading, say 3:00, simultaneously) if, whenever I set off a flash of light at the exact midpoint between the two clocks, both clocks are showing the same reading at the moment the light from the flash reaches them. But now suppose I am on a rocket (with the clocks at the front and back of the rocket) being observed by someone in a different frame who defines simultaneity by assuming light travels at the same speed in all directions relative to himself. If he sees the rocket traveling forward, then after the flash is set off at the middle of the rocket he will see the clock at the back moving towards the position (in his frame) where the flash was set off, while the clock at the front is moving away from that position, so if he assumes the light travels at the same speed in both directions, he must conclude the light reaches the back clock before it reaches the front clock. But I have set my clocks to both show the same reading (say, 3:00) at the instant the light from the flash hits them, so in the observer's frame the clock at the back shows a reading of 3:00 before the clock at the front shows a reading of 3:00, and thus in his frame my two clocks are outofsync. Of course as I said, the effect is totally symmetrical, since if he synchronizes his own clocks under the assumption that light travels at a constant speed relative to himself, then in my frame (using my definition of simultaneity) his clocks will be outofsync. So do you understand that according to Einstein's definition, each frame has their own definition of simultaneity and clock synchronization which different frames disagree about, and there is no physical basis to judge one frame's opinion as more "correct" than any other's? If so please read my comment again more carefully and tell me if you disagree with any specific part of it: How are you going to define "same time"? Each observer synchronizes their own clocks using the assumption that light signals travel at the same speed in all directions relative to themselves, and the result is that according to each observer's definition of simultaneity, the clocks of the other observer are outofsync. If I think my clocks are synchronized and I use my clocks to determine that your clocks are outofsync, but you think your clocks are synchronized and you use your clocks to determine that my clocks are outofsync, how do you propose to settle the matter? Remember that if we construct our own coordinate systems using clocks synchronized this way, the laws of physics will obey exactly the same equations in both coordinate systems, which means any experiment I do with an apparatus at rest in my frame will give the same result if you do the same experiment with the same apparatus at rest in your frame. Relativity doesn't rule out the notion that there is some metaphysical truth about simultaneity, so that only one observer's clocks are "really" synchronized. But only God could no that truthaccording to relativity, there is no experimental way to show that the laws of physics "prefer" one frame, they are all exactly equivalent as far as empirical experiments go so there can be no experimental basis for judging one frame's definition of simultaneity to be "correct" and another's to be "incorrect". 


#370
Jan711, 03:30 AM

P: 252

I will draw some diagrams. It may take me a day or two but I will be back. Thank you. 


#371
Jan1211, 08:41 AM

P: 252

Would I be right in saying that it isn't so much that light always travels at the same speed in vacuo where ever it travels, but that it is seen to travel at the same speed, in vacuo from whichever frame (perspective) it is viewed from.? PS will show my diagrams soon. 


#372
Jan1211, 11:41 AM

P: 3,188

"We [...] assume that the clocks can be adjusted in such a way that the propagation velocity of every light ray in vacuum  measured by means of these clocks  becomes everywhere equal to a universal constant c, provided that the coordinate system is not accelerated." Note that in GRT that isn't exactly valid anymore. 


#373
Feb311, 05:12 PM

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#374
Feb311, 08:29 PM

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