Sam Woole said:
I did read your recent posts but I am sorry I could not understand them.
What about them didn't you understand? Do you understand, for example, that if I see an event through a telescope that's 25 light-minutes away, then if I assume light travels at c in my frame, that must mean the event actually happened 25 minutes before I saw it? That's just the same principle as the idea that if we spot a supernova today happening 10,000 light-years away, it must have actually happened 10,000 years ago. And that's really all you need to understand my recent posts, all I was ever doing was showing the time that Alice or Bob saw a reading on the other one's clock, then subtracting the light-signal delay to figure out when the other one's clock was "really" showing that reading. I know all the numbers may look a little intimidating, but I think you can follow them if you read carefully.
Sam Woole said:
Currently DrGreg was trying to prove that time dilation is genuine, while I was trying to show his proof was flawed.
I don't think he's really trying to prove it's genuine--he's just telling you what Sam and Alice would see if you assume the relativistic doppler shift equation is correct, but the relativistic doppler shift equation already
assumes that time dilation is real. It doesn't make any sense to accept the numbers in DrGreg's example and yet reject time dilation, because he only got those numbers using a formula that assumes time dilation is real. If you used the non-relativistic doppler shift equation, then the numbers would be different.
Do you understand how regular, non-relativistic doppler shifts work? It's pretty simple--suppose I'm traveling away from you at 20 meters per second, and every second I shoot my bb gun at a wall next to you. Also suppose each bb pellet travels at a constant speed relative to you, 100 meters per second. Despite the fact that I am shooting a new pellet every second, you will not see the pellets hit the wall every second--the reason is that after each second I am 20 meters further away, so each new bb pellet has 20 meters further to travel than the last one. Since the pellets travel at 100 meters per second, it will take them 0.2 seconds to travel 20 meters, so each new pellet takes 0.2 seconds longer than the last one to travel from my gun to the wall. So you will see the pellets hit the wall every 1.2 seconds rather than every 1 second. That's all the non-relativistic doppler shift is--it's just a consequence of the fact that the distance between two observers is changing, so each successive signal has a different distance to travel than the previous one.
But in relativity, this is only part of the doppler shift. The other part is that we assume in relativity that if I am traveling at high speed relative to you, my clock will genuinely slow down in your frame--that's time dilation. So if I'm sending a signal once every second according to my own clock, then not only is there a larger gap between signals than one second because I'm moving away from you, but the gap between signals is increased even
more because one second on my clock lasts longer than a second according to your clocks. So the relativistic doppler effect takes into account both these factors, the changing distance
and the time dilation. If you don't accept time dilation, then you shouldn't accept the relativistic doppler formula, and thus you shouldn't accept DrGreg's numbers in the first place! But it's silly to accept his numbers, which he got using the relativistic doppler equation, but then reject time dilation--it just doesn't make sense.
Same Woole said:
Flawed or not, I believe we cannot use time dilation to justify an experiment designed to prove time dilation.
Then why are you arguing as though you accept that the numbers DrGreg gave would be what Alice and Bob would see, but you just reject time dilation? Again, if you reject time dilation, it doesn't make sense to accept those numbers in the first place.
And if you think time dilation is "flawed", do you think it's logically flawed in the sense of leading to some internal contradiction, despite the fact that no mathematicians seem to agree, or do you just think that the theory isn't the correct one for describing the real world? If the first, I promise that you're wrong and that it can be proved mathematically that no contradictions arise. If the second, then we should be discussing the experimental evidence in favor of time dilation (there's a whole lot of it), not a hypothetical example which assumes time dilation is real.
Sam Woole said:
Because of your use of the time dilation, you gave more and more numbers that never appeared in DrGreg's demonstration. These numberbs complicated matters more and more, leading to more difficulties and arguments. For instance you said the distance between Bob and Alice (at Ted) was 25 light-minutes.
based on the fact that her distance when she turned around was 25 light-minutes from him
. How could I understand this 25 light-minutes? Very difficult.
Why is it hard to understand? 25 light-minutes is just the distance light travels in 25 minutes, just like a "light year" is the distance light travels in a year. I could translate this into a distance in kilometers if you'd prefer, but that'd make the calculations uglier. If the problem was that you didn't know what a "light minute" was, then you could have just asked--in general, please
ask me when you don't understand a specific thing in one of my posts, otherwise this discussion isn't going to get anywhere!
Sam Woole said:
I wish you would not give any more numbers. Whether DrGreg's demonstration is flawed or not, I believe we must justify it according to only those numbers he has given. No more new numbers.
But you keep bringing up issues which demand additional numbers, like the issue of whether there is anything "instantaneous" going on. To show that no instantaneous effects happen, I had to explain the difference between the time that Bob
sees certain things happen and the time he calculates they 'really' happened in his frame, just like we distinguish between the date we see the light from a distant supernova and the date it actually happened.
Sam Woole said:
Not only no more new numbers, we should simplifiy them. For instance, when the two clocks came together to compare, Bob's clock read 14:10 and Alice's read 17:00. The result of the comparison is: Alice's clock had worked a lot faster than Bob's, the traveled twin had become a lot older.
No, DrGreg specifically set up the problem so that the clocks were out-of-sync initially, so that you wouldn't make the mistake of thinking that if an event happened at 16:00 on Alice's clock, it must have happened "at the same time" that Bob's clock also read 16:00. Just look at the numbers, you can
see that the two clocks were set to different times at the start--when Alice and Bob started out traveling away from each other, Bob's clock read 12:00 and Alice's read 15:00. If you like you could imagine that this difference was because Alice and Bob lived in different time zones, and when they came to meet at Alice's launch pad they forgot to reset their clocks to the time zone of the launch pad. So if Bob's clock read 14:10 when they reunited, that means it must have advanced 2 hours and 10 minutes between the time Alice left (12:00 according to his clock) and the time she returned; if Alice's clock read 17:00 when they reunited, that means it must have advanced only 2 hours between the time she left (15:00 according to her clock) and the time she returned. So if they were the same age when she departed, she must have been 10 minutes younger when they reunited.