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From: colp on 22 Jun 2010 14:34
On Jun 22, 11:48 am, stevendaryl3...(a)yahoo.com (Daryl McCullough)
wrote:
> colp says...
>
>
>
> >On Jun 22, 12:34=A0am, stevendaryl3...(a)yahoo.com (Daryl McCullough)
> >wrote:

> The point is that a physical theory specifies particular
> inferences that can be drawn. If you want to draw inferences
> that go beyond these, then you can certainly do so, but then
> you aren't exploring that theory, you're making up your own
> theory. If you discover something new, that's to your credit.
> If you derive a contradiction, that's your fault.
>
> If you apply the Lorentz transformations to a noninertial coordinate
> system, then it's not SR's fault if you get nonsense.

Right. The thing is that observations of time that are made in one
inertial frame can be used as the basis of of an inference which
involves a different inertial frame. For example, a twin can know
whether on not time is dilated for the other twin (with respect to his
own time) if he can measure radio pulses from that twin that are sent
each time the other twin's clock ticks and he knows his velocity
relative to the other twin. That knowledge can can then then be used
as the basis of an inference which involves knowledge of different
inertial frame.
From: colp on 22 Jun 2010 14:44
On Jun 22, 11:48 am, stevendaryl3...(a)yahoo.com (Daryl McCullough)
wrote:
> colp says...

> >At this point I'll ask a question with respect to the second premise:
> >What elapsed time will be shown by an clock traveling at constant
> >speed of 0.866c when a stationary local clock shows an elapsed time of
> >1 second?
>
> To compute the elapsed time on a clock, you have to specify the
> end points: elapsed time from what event to what other event?
> You need to specify the end points in order to compute elapsed time.

OK, how about this one?

What elapsed time will be shown by an clock traveling at constant
speed of 0.866c when a stationary local clock shows an elapsed time of
1 second, and the two clocks are at the same place at the beginning of
that second?
From: Sue... on 22 Jun 2010 15:29
On Jun 22, 2:34 pm, colp <c...(a)solder.ath.cx> wrote:
> On Jun 22, 11:48 am, stevendaryl3...(a)yahoo.com (Daryl McCullough)
> wrote:
>
> > colp says...
>
> > >On Jun 22, 12:34=A0am, stevendaryl3...(a)yahoo.com (Daryl McCullough)
> > >wrote:
> > The point is that a physical theory specifies particular
> > inferences that can be drawn. If you want to draw inferences
> > that go beyond these, then you can certainly do so, but then
> > you aren't exploring that theory, you're making up your own
> > theory. If you discover something new, that's to your credit.
> > If you derive a contradiction, that's your fault.
>
> > If you apply the Lorentz transformations to a noninertial coordinate
> > system, then it's not SR's fault if you get nonsense.
>
> Right. The thing is that observations of time that are made in one
> inertial frame can be used as the basis of of an inference which
> involves a different inertial frame. For example, a twin can know
> whether on not time is dilated for the other twin (with respect to his
> own time) if he can measure radio pulses from that twin that are sent
> each time the other twin's clock ticks and he knows his velocity
> relative to the other twin. That knowledge can can then then be used
> as the basis of an inference which involves knowledge of different
> inertial frame.

There are not any radio pulses on a coordinate system.

Daryl is unlikely to discuss anything physical so you
might as well learn what he is referring to.

http://en.wikipedia.org/wiki/Coordinate_time
http://en.wikipedia.org/wiki/Einstein_synchronisation

http://www.bartleby.com/173/17.html

Sue...


From: paparios on 22 Jun 2010 16:05
On 22 jun, 14:44, colp <c...(a)solder.ath.cx> wrote:
> On Jun 22, 11:48 am, stevendaryl3...(a)yahoo.com (Daryl McCullough)

>
> > To compute the elapsed time on a clock, you have to specify the
> > end points: elapsed time from what event to what other event?
> > You need to specify the end points in order to compute elapsed time.
>
> OK, how about this one?
>
> What elapsed time will be shown by an clock traveling at constant
> speed of 0.866c when a stationary local clock shows an elapsed time of
> 1 second, and the two clocks are at the same place at the beginning of
> that second?

The Lorentz equations are:

x=(x’+vt’)/(sqrt(1-v^2/c^2)) ; t=(t’+vx’/c^2)/(sqrt(1-v^2/c^2))

x'=(x-vt)/(sqrt(1-v^2/c^2)) ; t’=(t-vx/c^2)/(sqrt(1-v^2/c^2))

So if (x,t) are the coordinates of the stationary clock and (x',t')
are the coordinates of the traveling clock, then we have the
following:

When x=0 and t=0 both clocks are colocated and then x'=0 and t'=0
(from the second group)

When t=1 sec, x=0, so from the second equation group we have

x'=(-259980)/0.5=-519960 km
t'=1/0.5=2 sec

Miguel Rios
From: Daryl McCullough on 22 Jun 2010 17:15
colp says...

>Right. The thing is that observations of time that are made in one
>inertial frame can be used as the basis of of an inference which
>involves a different inertial frame. For example, a twin can know
>whether on not time is dilated for the other twin (with respect to his
>own time) if he can measure radio pulses from that twin that are sent
>each time the other twin's clock ticks and he knows his velocity
>relative to the other twin. That knowledge can can then then be used
>as the basis of an inference which involves knowledge of different
>inertial frame.

That certainly is true, but you have to remember that time dilation
is a relationship between a clock and a coordinate system. It is *not*
a relationship between two clocks.

That is, the fundamental quantity associated with dilation is
dT/dt, which is the rate at which T, the elapsed time on a clock,
varies with t, the coordinate time for a particular coordinate
system. The prediction of SR is that dT/dt = square-root(1-(v/c)^2),
where v is the velocity of the clock as measured in an inertial
coordinate system, and t is the time coordinate of that coordinate
system. This is *not* a comparison between two clocks, it is a
relationship between one clock and one coordinate system.

--
Daryl McCullough
Ithaca, NY

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