relativity of time
- From: <paco1955@xxxxxxxxxxxxx>
- Date: Sun, 03 Sep 2006 06:46:36 GMT
the current period of time for observer A is from 11:00 pm (9/2/2006) thru
12:00 am (9/3/2006) in the reference frame RA.
let's call RA the "stationary" system
wA = the wrist watch of A
the current period of time for observer B is also from 11:00 pm (9/2/2006)
thru 12:00 am (9/3/2006) in the reference frame RB.
let's call RB a moving body (RB moves at a speed v relative to RA)
wB = the wrist watch of B.
wA and wB synchronize
we have defined a common "time" for A and B when A and B were at rest
relative to each other (we have established by definition that the "time"
required by light to travel from A to B equals the "time" it requires to
travel from B to A, The Principle of Relativity, p. 40, by A. Einstein)
D = the distance between two parallel mirrors in and at rest relative to RB
(the distance traveled by a beam of light reflected back to the first
mirror. the direction of motion of the light beam is the same as the
direction of motion of RB relative to RA)
tA = the time required by the light beam to travel D as measured by A with
wA
tB = the time trequired by the light beam to travel D as measured by B with
wB (the current period of time for A and B)
d = the distance traveled by RB in RA.
t = the time required by RB to travel the distance d as measured by A with
wA (the current period of time for A and B)
c = the velocity of the beam of light (299,792,458 m / s).
"any ray of light moves in the "stationary" system of coordinates with the
determined velocity c, whether the ray be emitted by a stationary or by a
moving body" (The Principle of Relativity, p. 41, by A. Einstein)
tB = D / c
t = d / v
tA = D / c, since c is the same for A and B
if c was not the same for A and B, then tB = D / c, and tA = D / (c + v).
t = d / v (in either case)
the result of this argument does not agree with the following:
tA = tB / sqrt(1 - v^2 / c^2)
why? thanks! (11:00 pm, 9/2/2006, thru 12:00 am, 9/3/2006)
.
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