Re: Androcles, one more try

From: Randy Poe (poespam-trap_at_yahoo.com)
Date: 12/29/04 

Date: 29 Dec 2004 12:38:14 -0800

Oh goody, you did respond.

Now we can move forward.

Androcles wrote:
> "Randy Poe" <poespam-trap@yahoo.com> wrote in message
> news:1104338617.032514.210040@z14g2000cwz.googlegroups.com...
> >
> > Randy Poe wrote:
> >
> > OK, let's move forward. Let me generalize the very key
> > statement I made above, because that's where I'm moving
> > forward from.
> >
> > "I, in the S frame, can observe x at a given time t,
> > can calculate x-vt, and I will get a constant value
> > no matter what time I take that observation and do that
> > calculation."
>
> Fucking whoop-de-do. How absolutely amazing.
> Your brilliance astounds me.

We'll just see if you continue to agree with this
as we use this principle.

> > Since it distressed you to talk about a general x which
> > can be applied to different things, I'll now assign everything
> > a specific name.
> >
> > x_orig will be the x position of the origin of M (the
> > paint spot on the truck). You agree this paint spot
> > moves, and so x_orig changes in time.
>
>
> Yeah, yeah...(fixed font req.)
> ________________
> [Poe's Trucking Inc.] [ \_
> [___________________] [__^|
> oo oo o
> ^x-orig goes here.
>
>
> > x_orig' will be the value x_orig - vt. You agree that
> > I can measure x_orig at any time, subtract the corresponding
> > value of vt, and get a constant. That is, even though
> > x_orig changes with time, x_orig' does not.
>
> ________________
> [Poe's Trucking Inc.] [ \_
> [___________________] [__^|
> oo oo o
> ^x-orig' goes here.

Excellent.

> x_orig-vt is a constant in S. Got it.

More importantly x(t)-vt is a constant in S where x(t)
is the position of ANYTHING fixed with respect to the
truck.

> > You agree that I'm still measuring and calculating in
> > the S frame, right?
>
> Yeah, let's keep it that way.

Well, the important stuff happens when I want to define
variables in the M frame, so we can't keep it that way
forever.

> > Now I'll track another spot on the truck. It's going to be
> > in the cargo area of the truck, where a scientist is going
> > to be conducting light-reflection experiments. The position
> > of the light reflector AS MEASURED IN THE S FRAME will be
> > called x1.
>
>
> _____________________ _
> [Poe's Trucking Inc.] [ \_
> [___________________] [__^|
> oo oo o
> <-------vt------>
> ^x goes here ^ x1 goes here.

We're getting close. x1' will show up in the
light-reflection thingy. It isn't necessarily
where you drew it. Our traveling trucker/scientist
is going to move it to different positions.

I'm snipping a bunch of stuff that basically shows
we're finally on the same page.

Drum roll please, because this is the point that
took a week to get to:

> > Do you see that I can give you four parameters
> > (x_orig', y_orig, z_orig, t) and
> >
> > - The first three are constants (I gave you x_orig', not
> > x_orig)
>
> Yeah.
>
>
> > - You can easily calculate x_orig from x_orig' and t
>
> Yeah.
>
> > - So these three constants plus one variable (t) tell you
> > everything you need to know (position and time) about the
> > paint spot at any time in the future?
>
> Yeah.

> > The very next post will define tau, I promise, so long
> > as we agree on these simple but very important things.
>
> This is like pulling fucking teeth.

Yet this is the first time we agreed on what was constant
and what was variable. The very first time. It was
worth it. I would use the analogy "running a marathon
through glue" but anyway, we're both here.

OK. Now we have our people on the truck. They assign
spatial coordinates xi, eta, zeta to things they observe,
and time tau. The timer for tau=0 started when the truck
origin was over the road origin. xi, eta, and zeta are
measured from the truck's paint spot.

There are some functions which give me these coordinates
xi, eta, zeta, tau in the M frame, given x, y, z, t
for some event in the S frame.

But now look at this:
> > - So these three constants plus one variable (t) tell you
> > everything you need to know (position and time) about the
> > paint spot at any time in the future?
>
> Yeah.

So actually I don't need x, I can derive anything
I want to know given (x-vt), y, z, t.

In particular, there's some function that tells the
value of tau given (x-vt), y, z, t.

I'll write this as tau(x', y, z, t) where the first
variable represents the value of x-vt, the second
represents the y coordinate, the third is the z coordinate,
and the fourth the time at which I make the observation.

x', y, z and t are all measured in the S frame. This
function tells me what value of tau, in the M frame,
corresponds to those observations in the S frame.

Still bored? OK, let's cut to the chase:

When I write tau(0,0,0,t1) I mean the value of tau
corresponding to some observation at
x-vt = 0
y = 0
z = 0
t = t1

The fact that the first argument is 0 doesn't mean
x is 0. The first argument isn't x. It's x-vt.
The way I've defined things, it means that
x-vt is 0. Which means that x = 0+vt = v*t1.

As always, x, y, z, t1 are things measured in the
S frame.

             - Randy

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