« on: 12/11/2019 12:56:47 »
Really not intuitive... "So in the current inertial frame of either twin, the other twin is aging slower".That is basic time dilation. Time 'runs' at full speed if you're stationary, and all objects are stationary in their own frames. This is consistent with Galilean relativity: "Physics is the same in any frame". Time dilation means that time slows down for moving things, and in any frame, it is everything not stationary in that frame that is moving. So relative to the twin in the ship, the Earth twin is the one moving. Earth is just another ship after all, just a larger one than usual.
What I just can't get past is this idea that time appears to be slowing down for both twins, it just depends on whether you are measuring from one twin's position or the other's...Be careful about 'appears to be'. Time is computed to be slower in these other frames. The twins are not in each other's presence, and hence neither has a direct way to measure the other. In fact, if a clock is approaching you fast, it will 'appear' to be running faster, but that's mostly due to Doppler effect, and is why light from approaching galaxies is blue shifted despite being dilated a bit slower.
Say there are twins X and Y moving apart moving fast enough for 2x dilation.
In the frame of one twin X, his clock reads 5 and the clock of the other twin simultaneously (in X's frame) reads say 8. These are arbitrary numbers, let's just say the value of the minute hand.
Two minutes later (in X's frame), X's clock reads 7 and Y's clock simultaneously (in X's frame) reads 9.
Note that I put 'in X's frame' next to each mention of simultaneous since simultaneity is relative, and two events simultaneous in one frame are not simultaneous in another. The word is ambiguous without this reference. This (relativity of simultaneity) is the most important part because this explains why one twin comes home objectively younger than the other.
Perhaps, if it's not too much of a bother, and you understand my confusion, do you happen to know of any links to explanations that might help me...just idle curiosity as I don't NEED to know this.https://en.wikipedia.org/wiki/Relativity_of_simultaneity
That is probably one of the best places to start. They have some nice diagrams/gifs, and there's a description of the classic train thought experiment from which RoS is demonstrated from the postulate of frame independent light speed. Wiki is great for this kind of thing since it is full of hyperlinks you can click on for detail on any part that into which you want to go deeper.
The trouble I've had is that everything I've read/watched on Youtube that describes, for e.g., the twin thought experiment, always takes as a given that the "reference point" is the twin/you "here on earth"OK, I know that. For that very reason, I always choose the frame of the guy in the ship or the guy in the train, which really helps one discard a lot of the assumptions about absolute motion. With a westbound train it is pretty much true. A really fast train going west is actually more stationary (accelerates less) and has Earth rotating underneath it. Few trains move at fast enough speeds to actually cancel rotation, but jets sometimes do.
But if I assume that "I" am the other twin, the one zooming off in the space ship how can I demonstrate/reason that it is "I" that am moving and not the twin on earth that is zooming away from me at an equal and opposite velocity??Colin's answer to this is correct. There is no way to detect absolute motion, or more precisely, no local test. The two twins moving apart at high speed is entirely symmetrical, and thus each ages slower in the frame of the other. But one of them significantly changes reference frames, and does so a long distance from the other. That's what makes the difference when they are reunited. Remember RoS?
Say the rocket takes 5 years (ship time) each way, with 2x time dilation. At the turnaround point in the outgoing frame, the clock on the stationary ship reads 5 and simultaneous (in that outgoing frame), the clock of the distant (moving away) twin reads 2.5 years. Now the first twin turns around and is now stationary in a very different inbound frame. In that frame, his clock still reads 5 (he hasn't gone anywhere yet), but the clock of the distant (moving towards us) twin reads 17.5 years. During the remaining part of the exercise which the stationary twin waits for Earth to come to him, he ages 5 more years (10 total), and the traveling guy ages 2.5 more (20 total). The Earth guy has aged twice that of the 'stationary' twin.
RoS is illustrated there. Relative to two different frames (inbound and outbound), the turnaround event is simultaneous with two very different events (times 2.5 and 17.5) back on Earth.
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