Re: SRian method 'proving' classical EM invariance; ROFFLMAO!


"Bilge" <dubious@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote in message
news:slrne51uc7.a1.dubious@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
eleaticus:
>Obviously, each of x2-x1, y2-y1, z2-z1 are scalars under translation.
They
>change neither absolute value, nor sign. (Schwartz)

Are really so stupid as to not know the difference between a number
and a spatial distance? x2 - x1 is a number. A spatial translation in
the x direction is the vector (x2-x1, 0, 0).

You are confusing (terribly confusing) a coordinate translation with some,
say, particle's translation. As you know but ... hmmm, you do understand
the diference, do you?

Coordinates x2 and x1 could be the locations of an object's locus over time,
but that is a special case of the general and has nothing to do with the
question of coordinate transformation, and would be about, as said above,
perhaps an object's movement, which is not relevant to the question of
coordinate transormation.

Also, in such a case both x1 and x2 would be in the original formulation of
the equation and have nothing to do with the requirement that one must use
the difference formula to enable the obvious invariance of distance under
classical translation.(And, btw, being in the equation as a difference would
not need supplemention to show the invariance.)

The subject is and has been for years, coordinate
transformations/translations, and certainly only coordinate translations.

>Obviously, too, there is no specification of distance and direction
required
>to use the difference form.

Then don't try to use it as a distance in a particular direction.

As you quoted above, x2-x1 does NOT change sign under the classical
transforms, and thus implies a direction in those cases where direction is
intended, in which case it might be x1-x2 that should be used. But that
usage (or x2-x1 as implying direction) would be in the original equatin and
is not basic to coordinate translation/transformation, which "doesn't give a
***" about what coordinates imply. The coordinates are there and each gets
transformed.

>Just what translation direction or distance do I have to specify to say,
>instead of the simple(ton) x, (x2-x1)?

To use that as a distance or direction you have to specify what that
means in terms of distance and direction.

In curved space you might have a point about distance but in a discussion of
the classical transformations rather than the SR-crap that says there is
curved space, flat space is the assumption.

And YOU are the one that brings up direction for a distance based on your
idiocy that x2-x1 is a vector (just because the form has a sign?).

Strange, that you insisted herein that x2-x1 is a vector and then say it is
a number (scalar, not implying invariance).

>You are being so weird in this post of yours. You have no idea what the
>subject is?

>> >as is any scalar function of it,

>> Ovbiously not, since the gradient generates translations.

>Hmmm. A scalar function of a scalar is not a scalar? Hunh?

The gradient of a scalar function of a scalar is a vector.

F = -\grad_r (k/r) = (k/r^2) \hat{r}

In which case the gradient of a scalar function is neither a scalar nor a
scalar function of a scalar.

What'sa matter, you?

>> You can't represent a distance by anything until you first specify
the
>> metric for the geometry you assume so that you can define an inner
>> product. The reason the metric is called the metric is because it
>> defines the measure of a distance.
>
>The subject is the classical transformation in classical, flat space.

In which case you assume a galilean metric.

Of course, and do so implicitly unless you assume ignorance or other forms
of corruption on the part of your audience.

Hmmm. That means, perhaps, I should have specified the obvious. You, for
instance, are corrupt or you wouldn't have brought up all this metric stuff
in arguing against the galilean/classical translations.

>How many metrics are in use when you don't imagine there is a time term
>involved in the 'prime invariant', nor curved space?

However many you can specify for the numer of dimensions you want
to use.

lol. ok, the metric isn't the set, it is the individual elements of a metric
vector.

>> No, the distance is given by the scalar product of the vector (x2 -
x1)
>> with itself. You can't define a scalar product without specifying a
metric
>> (unless you simply don't realize what you have assumed).

>I do leave unsaid 'signed' distance because I talk about equations in
which
>the coordinates are used to represent distances.

Coordinates are not distances. Coordinates are n-tuples of numbers
which label points. Nothing about the lengths or orthogonality of any
lines in the coordinate system is implied until you specify a metric.

Coordinates ARE distances, although, as I have said many times, the distance
they name before usage is only the distance from the origin, and then, in
use, only directly useful distances when the origin is ideally located. Yet,
indirectly useful when put in the difference form I specify: x2-x1.

>Innyhoo, again, the difference forms are invariant under the classical
>xforms being discussed.

What's your point? Everything I said was completely general.

Perhaps YOU would sometimes make your point explicit. Your history suggests
you consider yourself to be arguing and putting me down.

You KNOW I am posting about the basics: the LET versus the classical, and
when it is the classical in particular all this metric stuff (and your
confounding of coordinate and locus translations) is not valid as an
argument against me.

However, it is very interesting and I am glad you have posted it.

Perhaps, if you could/would make it clear with an explicit point about your
agenda, some of our verbiage might be unnecessary.

>You perhaps came in in the middle, so to speak. TheSRian method of the
title
>was the use of gamma and beta and NOT the coordinate transformations.

What's your point?

See the immediate above.

thank you,

eleaticus
ee-lee-AT-i-cus





.

Loading