| Science Forum Index » Physics Forum » Part 1: Time Dilation simplified Math |
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| Guest |
 Posted: Thu Feb 10, 2005 2:21 pm |
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This is Part1 of 3 small parts.
1.Initial Setting:
Earth: Ve0 = 0 , Te0 = 1 (D)
Final Distance(twin travels): Df = 1000
Twin_A: Va0 = 50, Ta0 = 1/4Te0
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2. Simulated Math of when Twin_A reaches Furthest Distance from Earth:
Unchanged: Ve1=0 & Va1=50
Te1 = 1000
Ta1 = 1/4 Te1 = 250
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3. Simulated Math of when Twin_A has returned back to Earth
Ve2 = 0
Va2 = -50
Te2 = 1000(leave) + 1000(return) = 2000
Ta2 = 1/4 Te2 = 500
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It is important to fix any calculation errors before moving to Part2:
4. Therefore are the math proportionalities above correct or where is
there an error?
5. **** Basically the dilated time for Twin_A to go distance of 1000 =
same dilated time for his return therefore 250 + 250 = 500 ****
Correct? |
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| Jesse Mazer |
| Posted: Thu Feb 10, 2005 4:39 pm |
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Guest
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guskz@hotmail.com wrote:
[quote:87522a7ca5]This is Part1 of 3 small parts.
1.Initial Setting:
Earth: Ve0 = 0 , Te0 = 1 (D)
Final Distance(twin travels): Df = 1000
Twin_A: Va0 = 50, Ta0 = 1/4Te0
[/quote:87522a7ca5]
What do Te0 and Ta0 mean? Are they just the time-coordinate on each
twin's clock at the moment Twin_A departs from his earth twin? If so,
why did you write Ta0 = 1/4Te0? The standard assumption in the twin
paradox is that both twin's clocks read the same time at the moment they
depart (Ta0 = Te0 = 0), so then when the travelling twin returns to the
same position as the earth-twin, you can compare what their clocks read
at that moment and see how much time the journey took according to each
twin's clock.
Jesse |
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| Guest |
| Posted: Fri Feb 11, 2005 9:43 am |
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Jesse Mazer wrote:
[quote:fc89165069]guskz@hotmail.com wrote:
This is Part1 of 3 small parts.
1.Initial Setting:
Earth: Ve0 = 0 , Te0 = 1 (D)
Final Distance(twin travels): Df = 1000
Twin_A: Va0 = 50, Ta0 = 1/4Te0
What do Te0 and Ta0 mean? Are they just the time-coordinate on each
twin's clock at the moment Twin_A departs from his earth twin?
Correct they're the Initial Setting[/quote:fc89165069]
[quote:fc89165069]If so,
why did you write Ta0 = 1/4Te0?
Good point (that's the time loss %)[/quote:fc89165069]
Because Va0 = 50 ...he just reached the constant speed of his Time
Travel
(Excluding acceleration time which affects the total time dilation of
travel very little if Twin_A travels very very far).
[quote:fc89165069]The standard assumption in the twin
paradox is that both twin's clocks read the same time at the moment
they
depart (Ta0 = Te0 = 0),
[/quote:fc89165069]
Excluding acceleration (In this case it's the very INITIAL instant he
reached the constant velcocity of 50).
Either way: That's why I never assigned an initial value to Ta0
So if Te0 = 0 then Ta0 = 1/4 (Te0) = 0
[quote:fc89165069]so then when the travelling twin returns to the
same position as the earth-twin, you can compare what their clocks
read
at that moment and see how much time the journey took according to
each
twin's clock.
Jesse
[/quote:fc89165069]
To keep things visualy clear/simple, I didn't give complex numbers to
time...so the only calculation that is not direct is Ta= gamma Te
But I did make a mistake , I over simplified things and I'm mixing
apples with oranges...since the length contracts and the velocity that
each sees the other as travelling at (because I was then going to
compare it to another platform in Part 2 which won't work...I over
simplified). |
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