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From: Inertial on 4 Aug 2010 23:56
"Tony M" wrote in message
news:131d484f-428e-45ba-9e71-d41b3ebb15e6(a)5g2000yqz.googlegroups.com...
>I guess that's still not very clear. What I mean by two distinct
>events is the same pair of distinct events for both observers, NOT
>like someone said before: event one - O passes O' and event two - O'
>passes O. That would be just one event.

The relationship between the measurements of the duration of the events (k)
will depend on BOTH the location of the events themselves, and the relative
velocities of the observers. There is no fixed 'k' for any given pair of
observers that applies to measurements of all pairs of events.

What is it you think is a twist here? Is there are point to all this?

From: kenseto on 5 Aug 2010 09:49
On Aug 4, 5:47 pm, Tony M <marc...(a)gmail.com> wrote:
> Whether right or wrong, it’s just an idea, so here it is:
>
> Let there be two observers O and O’, moving directly towards each
> other at relative velocity v (considered positive in this case,
> negative if moving away). Let delta_t and delta_t’ be the rates
> measured by O and O’ on identical clocks at rest in their respective
> frames. By convention both observers define k = delta_t/delta_t’ and
> agree on its value (where possible values for k are 1/gamma <= k <=
> gamma). It is unknown to the observers at this point whether delta_t>= delta_t’ or vice-versa and no assumption can be made (until they
>
> determine k). By their convention it can be one or the other, but not
> both. Now, the trick is to determine the value of k.
>
> One way of measuring k is by sending an EM signal from O to O’ and
> applying the formula k=f’/f/(1+v/c), where f and f’ are the
> frequencies of the EM signal as measured by O and O’ and then
> communicated to each other.
>
> The same ratio k applies to length and mass transformation. (Also, in
> this scenario the value of k has a special significance.)

Both O and O' will not know the value of k. Therefore each must
include the following possibilities when predicting the rate of each
other's clock rate as follows:
Fron O's point of view:
The t' clock is running slow:
Delta(t')=gamma*Delta(t)
The t' clock is running fast:
Delta(t')=Delta(t)/gamma

From O' point of view:
The t clock is running slow:
Delta(t)=gamma*Delta(t')
The t clock is running fast:
Delta(t)=Delta(t')/gamma

The paper in the following link gives detail description of this new
theory:
http://www.modelmechanics.org/2008irt.dtg.pdf

Ken Seto
From: kenseto on 5 Aug 2010 10:01
On Aug 4, 11:24 pm, Tony M <marc...(a)gmail.com> wrote:
> On Aug 4, 5:47 pm, Tony M <marc...(a)gmail.com> wrote:
>
> > Whether right or wrong, it’s just an idea, so here it is:
>
> > Let there be two observers O and O’, moving directly towards each
> > other at relative velocity v (considered positive in this case,
> > negative if moving away).
>
> ----------------------
> Based on Inertial's excellent observation I am re-defining delta_t and
> delta_t' as follows:
>
> Let delta_t and delta_t’ be the time intervals measured by O and
> respectively O' between two distinct events.

Don't you mean that delta _t' is the predicted value on the t' clock
for a specific interval of delta_t on the t clock????

Ken Seto

> ----------------------
>
>
>
> > By convention both observers define k = delta_t/delta_t’ and
> > agree on its value (where possible values for k are 1/gamma <= k <=
> > gamma). It is unknown to the observers at this point whether delta_t>= delta_t’ or vice-versa and no assumption can be made (until they
>
> > determine k). By their convention it can be one or the other, but not
> > both. Now, the trick is to determine the value of k.
>
> > One way of measuring k is by sending an EM signal from O to O’ and
> > applying the formula k=f’/f/(1+v/c), where f and f’ are the
> > frequencies of the EM signal as measured by O and O’ and then
> > communicated to each other.
>
> > The same ratio k applies to length and mass transformation. (Also, in
> > this scenario the value of k has a special significance.)- Hide quoted text -
>
> - Show quoted text -

From: Sue... on 5 Aug 2010 13:53
On Aug 4, 5:47 pm, Tony M <marc...(a)gmail.com> wrote:
> Whether right or wrong, it’s just an idea, so here it is:
>
> Let there be two observers O and O’, moving directly towards each
> other at relative velocity v (considered positive in this case,
> negative if moving away).

========================

> Let delta_t and delta_t’ be the rates
> measured by O and O’ on identical clocks at rest in their respective
> frames.

Two identical meter sticks taped to two identical
gun barrels would seem to be really close to
*identical* clocks. Unless you harbor notions about
perpetual motion, you can work the rest out from
this.

http://en.wikipedia.org/wiki/Noether's_theorem#Applications

See also:
<< The key to understanding special relativity
is Einstein's relativity principle, which states
that:

All inertial frames are totally equivalent
for the performance of all physical experiments.


In other words, it is impossible to perform a
physical experiment which differentiates in any fundamental sense
between different inertial
frames. By definition, Newton's laws of motion
take the same form in all inertial frames.
Einstein generalized this result in his special
theory of relativity by asserting that all laws
of physics take the same form in all inertial
frames. >>
http://farside.ph.utexas.edu/teaching/em/lectures/node108.html

Sue...



>By convention both observers define k = delta_t/delta_t’ and
> agree on its value (where possible values for k are 1/gamma <= k <=
> gamma). It is unknown to the observers at this point whether delta_t>= delta_t’ or vice-versa and no assumption can be made (until they
>
> determine k). By their convention it can be one or the other, but not
> both. Now, the trick is to determine the value of k.
>
> One way of measuring k is by sending an EM signal from O to O’ and
> applying the formula k=f’/f/(1+v/c), where f and f’ are the
> frequencies of the EM signal as measured by O and O’ and then
> communicated to each other.
>
> The same ratio k applies to length and mass transformation. (Also, in
> this scenario the value of k has a special significance.)

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