#3 December 31st 12, 09:49 AM posted to sci.physics.relativity,sci.physics,sci.math,sci.astro
 Koobee Wublee external usenet poster Posts: 815 What is or is not a paradox?

On Dec 30, 11:31 pm, Sylvia Else wrote:
On 31/12/2012 5:04 PM, Koobee Wublee wrote:

From the Lorentz transformations, you can write down the following
equation per Minkowski spacetime. Points #1, #2, and #3 are
observers. They are observing the same target.

** c^2 dt1^2  ds1^2 = c^2 dt2^2  ds2^2 = c^2 dt3^2  ds3^2

Where

** dt1 = Time flow at Point #1
** dt2 = Time flow at Point #2
** dt3 = Time flow at Point #3

** ds1 = Observed target displacement segment by #1
** ds2 = Observed target displacement segment by #2
** ds3 = Observed target displacement segment by #3

The above spacetime equation can also be written as follows.

** dt1^2 (1  B1^2) = dt2^2 (1  B2^2) = dt3^2 (1  B3^2)

Where

** B^2 = (ds/dt)^2 / c^2

When #1 is observing #2, the following equation can be deduced from
the equation above.

** dt1^2 (1  B1^2) = dt2^2 . . . (1)

Where

** B2^2 = 0, #2 is observing itself

Similarly, when #2 is observing #1, the following equation can be
deduced.

** dt1^2 = dt2^2 (1  B2^2) . . . (2)

Where

** B1^2 = 0, #1 is observing itself

According to relativity, the following must be true.

** B1^2 = B2^2

Thus, equations (1) and (2) become the following equations.

** dt1^2 (1  B^2) = dt2^2 . . . (3)
** dt2^2 = dt2^2 (1  B^2) . . . (4)

I assume you meant to write

dt1^2 = dt2^2 (1 - B^2) . . . (4)

No, Koobee Wublee meant every letter in the equations (3) and (4).
shrug

Where

** B^2 = B1^2 = B2^2

The only time the equations (3) and (4) can co-exist is when B^2 = 0.

Which tells us nothing more than that when two observers observe each
other, the situation is symmetrical. Each will measure the same time for
equivalent displacements of the other. Or more simply, they share a
common relative velocity (save for sign).

Thus, the twins paradox is very real under the Lorentz transform.
shrug

blink Where did that come from?

Have you not been reading Koobee Wublee? Did Koobee Wublee not say
the Lorentz transform? shrug