Re: A question of discrete space-time, part 3

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:
>
>> Igor Khavkine wrote:
>>
>.
>>>
>>> People have been thinking about lattices and cellular automata for a
>>> long time (think Stephen Wolfram, Ed Fredkin, etc.). There's even been a
>>> newsgroup created to discuss discrete physics models
>>> (sci.physics.discrete). If you hope to get some of your work published,
>>> you must first make sure that it is indeed original. For that, there is
>>> no substitute beside doing an extensive literature search.
>.
>> I also know of Ed Fredkin, and that he used to be a frequent newsgroup
>> contributor. However, I haven't seen any newsgroup postings by him
>> since 2003. Is he still active? I would like to have had his comments
>> on this thread.
>>
>> I also know about sci.physics.discrete and have tried to post there,
>> but that newsgroup seems to have died out in January 2005, and is no
>> longer active.
>
>i just want to add that Ed Fredkin seemed to have no use for the
>gravitational constant, G, in his theory (not sure why). his unit of
>discrete-time was many orders of magnitude larger than the Planck Time.
>
>.
>> It bears repeating that I'm not trying to convince anyone of the merits
>> of a discrete space-time over continuum physics,
>
>i am an agnostic regarding discrete vs. continuous physics, but if reality
>turned out to be discrete, i would not be surprized if the discrete units of
>time and length turned out to be the Planck units, possibly scaled by
>sqrt(4 pi) ("rationalized Planck units").
>
>i am not an agnostic about the notion of Planck units (or better yet,
>rationalized Planck units). i truly believe that nature is inherently
>scaled by them and there is no magic universal quantity defined by c or G or
>h_bar or epsilon_0 (or Boltzmann, either, for that matter). on the Planck
>scale they just don't exist as concepts of quantity which is one reason i
>think that Michael Duff is absolutely right about the "operationally
>meaninglessness" of VSL or varying G theories (or a varying h_bar theory if
>anyone puts one out). there is no way we could know the difference if they
>did vary, we would still measure them and perceive them to be the same as
>before.
>
>.
>
>> 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. Then intuition might convince yout that the whole
Planck scheme is numerology, in light of the huge value for Planck
mass. 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.

>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? 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. Newton should have used it in
his inverse square equation a = MG'/4pi r^2. Leaving 4pi off is a
slight shortcoming of his. Without the 4pi, you see amateurs
occasionally trying to explain some anomaly by guessing that maybe the
exponent is e.g. 2.0001.

>think it would be difficult to explain why this mindless mechanism of
>nature, whether operating in a continuous or discrete manner, would bother
>to be using any such seemingly contrived constants in just implementing
>physical reality.
>
>admittedly, JJ, this is more philosophy than physics. but it gets me
>wondering. sorry to pile on a little more speculation onto your thread, Ed.
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. See paper #1 on my website.
John Polasek
http://www.dualspace.net

.

Relevant Pages