- #106
SlowThinker
- 474
- 65
Nope, no such button. It seems Apple and Google don't quite cooperate.m4r35n357 said:See the bit where it says "more"? It's bedtime in the UK so I'll let you get on with it for now . . .
Edit: Same on Android.
Nope, no such button. It seems Apple and Google don't quite cooperate.m4r35n357 said:See the bit where it says "more"? It's bedtime in the UK so I'll let you get on with it for now . . .
m4r35n357 said:Now, if I have understood the Lorentz transform correctly, the "moving frame" length needs to be measured at different times,
and the "moving frame" time at different positions.
This is perhaps the root of my feeling that they are both unobservable, and rather contrived.
PeterDonis said:I don't know that it's "cheating", but it might be confusing, since, as I said in a previous post, the term "time dilation" has two possible meanings. One is the invariant thing you describe. The other is something that is not invariant; it's frame-dependent (the fact that a moving clock "appears to run slow", which depends on your choice of frame).
Mister T said:It seems to me, then, that differential aging is just a difference between two proper times, something that will therefore always be invariant.
Mister T said:would it be better to say that during the first half of the traveling twin's journey a proper time ##\Delta \tau## elapses on his ship and the stay-at-home twin measures this to be the dilated time ##\gamma \Delta \tau##? Likewise for the return trip.
PeterDonis said:Everything else is calculated, and using the word "measurement" for something that's calculated seems like a bad idea to me.
Mister T said:usually the word "observe" is used.
Mister T said:Say the traveling twin agrees to send a signal back home when he arrives. The stay-at-home twin gets the signal, subtracts off the travel time of the signal, and arrives at a result. That is the result of a calculation.
Mister T said:But isn't it the case that most measurements are the result of calculations?
OK, Here's the text (I intend to revisit this in the near future to tighten it up a bit):SlowThinker said:Nope, no such button. It seems Apple and Google don't quite cooperate.
View attachment 91990
View attachment 91991
Edit: Same on Android.
PeterDonis said:Yes, and it has the same problems. Unfortunately, there isn't really a good word to describe this; I often try to say "calculate", but that's cumbersome. Sometimes I've tried "judge", but that doesn't seem to help much.
Now contrast this with the stay-at-home twin's calculation of the time of emission of the signal the traveling twin sends when he turns around. He directly measures the time of arrival of the signal. He subtracts off the travel time--but how does he know the travel time? He can't measure it directly, and it's not a previously known constant like the emission frequency of the light signal. He has to calculate it. How does he calculate it? Well, he knows the traveling twin's speed--or at least he knows what speed the traveling twin said he was going to use, and how long the traveling twin intended to travel, by his own clock, before he turned around.
Back in Einstein's day and the early years of GR, that was a common way to look at it. In modern terms GR is usually only considered to be involved when spacetime is significantly curved (I.E. when tidal gravity is important). Simply using tensors and non inertial coordinates in flat spacetime is not considered GR except insofar as flat spacetime is a trivial solution of the Einstein field equations.valentin mano said:We have two synchronized clocks and one of them is acceleratated near the speed of light.The GR approach is neaded here,because SR is symmetric by the Lorenz Transforms.
valentin mano said:I was just trying to say,that the twin paradox has nothig to do with the Special Relativity.
valentin mano said:The principle of equivalence(no tidal forces)is implied here.
valentin mano said:Flat Spacetime does not mean "inertial frame of reference",which is the initial frame of Special Relativity.
PeterDonis said:Third, why is the lack of tidal forces important in analyzing the twin paradox?
valentin mano said:The same way EPR paradox is not solved in SR.