Re: Twin paradox revisited ll

On Jul 23, 9:01 pm, bz <bz+...@xxxxxxxxxxxxxxxxxxxx> wrote:
"Sue..." <suzysewns...@xxxxxxxxxxxx> wrote innews:1185226392.317796.307770@xxxxxxxxxxxxxxxxxxxxxxxxxxxx:



On Jul 23, 3:01 pm, bz <bz+...@xxxxxxxxxxxxxxxxxxxx> wrote:
"Sue..." <suzysewns...@xxxxxxxxxxxx> wrote
innews:1185211838.607102.222450@xxxxxxxxxxxxxxxxxxxxxxxxxxxx:

....

The fact that i allows easy polar/rectangular coordinate conversions
results in something that is quite real and measurable.

What makes you think it is unreal?

Measure the current and voltage on an induction
motor at the same time and compute the power.
Is it real ?

Yes. The instantaneous voltage times the instantaneous current at any
instant of time is real.

Measure the current now and voltage at a specific
imaginary time on an induction
motor and compute the power.
Is it real ? Are both the times real?

It doesn't matter if you call the current i or I, if you multiply
instantaneous current time instantaneous voltage you get the instantaneous
power.

I decided someone with an 80 metre light-launcher in
their backyard can't be as unfamiliar with reactive
current as you seem to be. You are avioding the
term *apparent* power because it spoils your twin
myth.

You *know* we can measure the potential now
and the current later and determine the true power
delivered to an induction motor.

Now look at equation 511 where Maxwell's equations
learn how to be time dependent.

<<... if we want to work out the potentials at position r
and time t then we have to perform integrals of the
charge density and current density over all space
(just like in the steady-state situation). However,
when we calculate the contribution of charges and
currents at position r' to these integrals we do not use
the values at time t, instead we use the values at some
earlier time (equation) . What is this earlier time? It is
simply the latest time at which a light signal emitted
from position r' would be received at position r before time .t
This is called the retarded time. >> [an imaginary time]
http://farside.ph.utexas.edu/teaching/em/lectures/node50.html

This imaginary time is directly related to the imaginary
time of Minkowski space:
http://www.bartleby.com/173/17.html
....because the the Lorentz transform encodes
the orthogonal E and B components when the
speed of light is used as the basis for the transformation.

<< The hardest thing about working with complex numbers
is understanding why you might want to. >>
http://www.uncwil.edu/courses/mat111hb/Izs/complex/complex.html
http://en.wikipedia.org/wiki/Electrical_impedance
http://en.wikipedia.org/wiki/Wave_impedance

Not surprisingly... you will not find a discussion of
the twins paradox in Fitzpatrick's relativity lectures.
Rigourous mathmatics permits no paradox.

Sue...





.

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