Re: A question of discrete space-time, part 3
- From: robert bristow-johnson <rbj@xxxxxxxxxxxxxxxxxxxx>
- Date: Thu, 30 Jun 2005 04:53:28 +0000 (UTC)
in article d9tfc7$1umn$1@xxxxxxxxxxxxxxxxxxxxx, John C. Polasek at
jpolasek@xxxxxxxxxx wrote on 06/29/2005 02:33:
> On Sun, 26 Jun 2005 16:43:08 +0000 (UTC), robert bristow-johnson
> <rbj@xxxxxxxxxxxxxxxxxxxx> wrote:
>
>> in article d9j53b$1oe6$1@xxxxxxxxxxxxxxxxx, Ed Hanna at stq50@xxxxxxxxx
>> wrote on 06/25/2005 04:37:
>>
..
>>> This seems to provide hope of finding a basis for unifying relativity and
>>> quantum mechanics, by proposing a discrete space-time at the Planck scale.
>>
>> the Planck Time and Planck Length are so ridiculously small (from the POV of
>> our human existence) that i can't see how any meaningful accuracy is lost if
>> all of these differential equations (Schrodinger, Maxwell's, GR or GEM) were
>> expressed in discrete form (a la Euler) as one would do if trying to
>> simulate these equations on a computer. might not be the true
>> representation of reality, but i can't see how it would be measurably
>> different. well, i wouldn't want light or gravitational propagation to be
>> in the shape of an expanding cube or tetrahedron (instead of spherical
>> expansion), so somehow i think these discrete "cells" could not have some
>> absolute fixed orientation. i dunno how to model it so that no direction in
>> space appears to be preferred over another.
>>
>> so, to take advantage of an opportunity to spout off a personal theory (and
>> at risk of having a real physiker like JJ Lodder label this Platonic
>> aestheticism, not physics), i just want to repeat that it still seems
>> obvious that Nature (whoever she is) has shown us (from our anthropocentric
>> measurements of c, G, h_bar, and epsilon_0) a preference of units that are
>> defined in accord to these four definitions:
>>
>> 1. One unit of mass is equivalent to one unit of energy (or
>> equivalently, the unit velocity is the speed of light).
>> 2. A particle or photon with a wave function of one unit of radian
>> frequency shall have one unit of energy.
>> 3. The force applied to a unit mass in one unit of gravitational flux
>> density shall be one unit of force and a single unit of
>> gravitational flux density shall result from a unit mass
>> distributed over a unit area.
>> 4. The force applied to a unit charge in one unit of electrostatic
>> flux density shall be one unit of force and a single unit of
>> electrostatic flux density shall result from a unit charge
>> distributed over a unit area.
>>
>> so then, what you get for the four base units (and their relationship to the
>> Planck units):
>>
>> T = sqrt( h_bar*(4*pi*G)/c^5 ) = sqrt(4*pi) * T_P
>>
>> L = sqrt( h_bar*(4*pi*G)/c^3 ) = c*T = sqrt(4*pi) * L_P
>>
>> M = sqrt( h_bar*c/(4*pi*G) ) = 1/sqrt(4*pi) * M_P
>>
>> Q = sqrt( h_bar*c*epsilon_0 ) = 1/sqrt(4*pi) * Q_P
>>
>> = e/sqrt(4*pi*alpha)
>
> It would have been instructive to include the numerical values with
> each expression.
they're just numbers, some of which are way out of our scale of perception.
they are simply a factor of 3.545 off (high or low) from the Planck units so
the natural unit of time is still somewhere around 10^-44 second.
> Then intuition might convince yout that the whole
> Planck scheme is numerology,
it's not numerology. it's a choice of units that are more natural and less
anthropocentric. numerology is saying that the Fine-structure constant is
alpha = (cos(pi/137)/137) * tan(pi/(29*137)) / (pi/(29*137)) .
that's an example of numerology. since time and length and mass and charge
are dimensionful, we can make units that can define them with whatever scale
we want. Planck units do so so that 4 universal constants are 1.
> in light of the huge value for Planck mass.
like the speed of light, the Planck mass simply is what it is. instead,
it's the mass of atomic particles that are so small.
> This value is so out-of-scale as to invalidate the concept.
>
>> (both the speed of propagation, c, _and_ the characteristic impedance, Z_0,
>> in free space for both E&M or gravity waves turn out to be 1 in these units.
>
> The units are the heart and soul of physics. Change them to 1 and you
> have debased physics into mathematics, which cannot possibly do
> anything in physics but corroborate here and there.
i have no idea what that means.
>> this is why i just don't understand why either Planck, regarding G, and the
>> CGS system, regarding epsilon_0, did not "rationalize" the system of units.)
>> if you discretize space and time with cell size of L and T (and measure mass
>> and charge in units of M and Q), there are no scaling constants that nature
>> would be using to express or implement those difference equations taken from
>> the well known differential equations of QM, E&M, GR (or GEM). and that is
>> attractive because the alternative is saying that for some hard to explain
>> reason, nature takes this amount of, say, electric charge flux diverging
>> from some point and scales it with some number pulled out of the air like
>> 4*pi or 4*pi*alpha (if "e" is the unit charge) to get the E field, and i
>
> You don't see the function of 4pi?
it won't be in Maxwell's Equations nor the GEM counterparts.
> An electrical charge radiates
> isotropically over 4pi steradians which you know of course, but you
> can then define distributions as
> DS = q coul/4pi SR = q/sr = charge detectable in sr s.radians
> E = q/4 pi rI^2 = q/A = q/sr*r^2 = charge detectable with area A
> There is nothing arbitrary about 4pi.
it's a number that comes from geometry. it belongs naturally in Coulomb's
Law and less naturally in Maxwell's Eqs. i see no reason why nature would
naturally set the characteristic impedance of free space to 4*pi. like c,
the most natural units set Z0 to 1.
> Newton should have used it in his inverse square equation a = MG'/4pi r^2.
> Leaving 4pi off is a slight shortcoming of his.
i wouldn't blame Newton for that at all. didn't Gauss come later? not to
"blame" but i wish Planck would have chosen to normalize 4*pi*G instead of
G, and whomever physicists who defined the electrostatic CGS units had
chosen to normalize epsilon_0 instead of 4*pi*epsilon_0. that would make
more sense.
> My theory posits a discrete space time if you want to look at it that
> way. Everything originated in electron positron pairs in cells of
> specific dimension 3.541e-14m.
Planck units can be defined without considering the properties of any
particular particle or object or substance or "thing". it's a scaling that
comes from just an empty vacuum. when you enter electrons or whatever
particles into the picture, you can then measure or describe the properties
of those particles in terms of the units already naturally apparent.
--
r b-j rbj@xxxxxxxxxxxxxxxxxxxx
"Imagination is more important than knowledge."
.
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- Re: A question of discrete space-time, part 3
- From: John C. Polasek
- Re: A question of discrete space-time, part 3
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