On Feb 25, 1:40=A0pm, thro...@[EMAIL PROTECTED]
(Wayne Throop) wrote:
> : finite guy <adamle...@[EMAIL PROTECTED]
>
> : Why is the 'most accurate' method just not used all of the time?
>
> Because it's often simpler to use newtonian expressions, and if you've
> only measured to one part in a billion, or if you're only concerned with
> modeling situations that you will only be able to verify to one part
> in a billion, the extra effort is wasted. =A0(The "one part in a
billion"
> is an arbitrary illustrative figure only.)
>
> : Certainly, Newtonian and Einsteinian ideas are regarded somewhat
> : 'differently'. =A0In what way are they really different.
>
> When you get right down to it, they differ in the coordinate transform
> wrt which the laws of physics are invariant. =A0(Phrasing it that way
lead=
s
> to wondering why the coordinates matter... they don't, really, but it's
> an easy way to see what's going on (or, it seems easy to me).) =A0This
in
> turn leads to differing formulas for kinematics and dynamics, in
particula=
r
> velocity "addition" (or actually, velocity transforms are mere
addition),
> and in expressions for momentum and kinetic energy, and other
miscelania.
> If you simplify the einsteinian expressions by taking the limit as
velocit=
y
> approaches zero, they turn into the newtonian ones.
>
> : Would you, if possible, explain why E=3Dmc^2 is a planar equation and
> : why the 'plane of time' in it is not conceptualised at all?
>
> I'm afraid I don't understand why there *should* be a "plane" of time.
> Certainly, just because a quantity is multiplied by itself doesn't
> really imply there's a "plane" of time. =A0If it did, then the newtonian
> expression for distance covered in a given time at a given acceleration
> (ie, the newtonian approximation of d=3D(1/2)at^2) would involve a
"plane
> of time", and it doesn't seem necessary.
>
> Or, just consider what acceleration is: velocity per time. =A0How much
> do you speed up in a second. =A0Since velocity is distance per time,
> acceleration has units of disance per time squared. =A0Again, this has
> nothing to do with geometry, except perhaps in a *very* abstract sense.
>
> Similarly, the d^2/t^2 units of "c^2" in E=3Dmc^2, do not imply that
there=
> are two different directions of time, or a geometrical plane. =A0Now, to
g=
et
> into "where does the c^2 come from anyways" would be a bit more complex.
> In the abstract, it's a matter of units analysis. =A0Energy has *units*
> of mass times velocity squared, for reasons similar to the reason why
> acceleratio has units of distance per time squared. =A0It doesn't have
to
> do with there being a "plane" involved, it has to do with how you use
> things with velocity terms in them to calculate the amount of energy.
> Potential energy (in the newtonian approximation) is m*d*a, and kinetic
> energy is (1/2)mv^2, for reasons that have nothing to do with "planes".
> Instead it has to do with the same reason you get time squared when you
> use time and acceleration to calculate distance.
>
> Wayne Throop =A0 thro...@[EMAIL PROTECTED]
=A0http://sheol.org/throopw
Thanks again for a lucid response.
I will reply more to your thoughts later today.
Most assuredly though, there are 2 different directions of 'time'.
Lateral Time through the spatial plane and Axial Time from spatial
plane to spatial plane.
Even neglecting time momentarily,
why is E=3Dmc^2 a purely planar equation for spatial (cubic)
reality...?
I am curious as to how this is commonly expressed?
Thanks.
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