A Revised Planck Scale?

wrote:
wrote:
Parenthetically, the revised Schwarschild radius for the proton is
about 0.8 x 10^-13 cm, which is about equal to the charge radius of the
proton and the revised Planck length.

In that case, the model is pretty much dead. High energy experiments
probe the substructure of the proton down to about three orders of
magnitude smaller than that, and there is absolutely no indication of
anything remotely resembling a horizon.

(The 1990 Nobel Prize in Physics was awarded for the first experiments
in this area. For more recent results, look up, for example, experiments
at HERA, which has a resolution on the order of 10^{-16} cm.)

A Schwarzschild black hole is a very crude approximation to the
fundamental particles that dominate each cosmological scale.
Kerr-Newman black holes are a much better approximation, but I would
not be surprised if major refinements to the K-N models are also
required. People like Paul Wesson have spent decades advocating even
more exotic candidates, such as 5-dimensional soliton-like ultracompact
objects that lack a conventional horizon.

The Discrete Fractal paradigm ( www.amherst.edu/~rloldershaw ) predicts
the approximate size, charge, angular momentum and radii of these
objects. It predicts their mass spectrum quantitatively and uniquely.
I leave it to you astrophysicists to figure out the subtle physics of
these objects, except to emphatically predict that when you come up
with a really good model for these fundamental particles, it will
rigorously and equally apply to the stellar-mass dark matter objects
and protons.

Robert L. Oldershaw

wrote:
Publish your replacement for the Schwarzchild metric
and then it can be tested.


Let's have some fun and learn something while we are doing it.

I propose the following gedanken experiment as a way to make the
concept of Discrete Scale Relativity more clearcut and readily
understandable.

Assume, for the sake of argument, that nature is a discrete fractal
hierarchy, and further that the number of cosmological scales is
infinite, and the cosmological scales are exactly self-similar to each
other. Lengths and times on neighboring scales differ by a factor of
5.2 x 10^17 and masses differ by a factor of 1.7 x 10^56. We ask
imaginary observers from the atomic and stellar scales to compare their
"universes".

The two observers are amazed to find that the other's description of
the fundamental properties of their observable universes are virtually
identical to their own, in spite of their separate studies which
appeared to indicate that the other's observable universe *should* look
radically different. They both find their scales dominated by the same
types of objects and the equations that describe these objects are,
except for arbitrary differences in notation and conventions, are also
virtually identical. They both measure their G values as = 6.67 x 10^-8
cgs.

Then the stellar scale observer asks the atomic scale observer to show
him his centimeter. The atomic scale observer holds up his centimeter,
and the stellar scale observer says, "That is NOT a centimeter; that is
1cm/5.2 x 10^17. When the atomic scale observer angrily asks to see
the stellar scale observer's cm, he laughs and says, "You are way off;
that thing is 5.2 x 10^17 cm long.

After much back and forth, the light dawns and they say in unison, "So
there are an infinite number of "centimeters" in nature, one for each
cosmological scale". Each has an equal claim to being "the centimeter".
The same is true for seconds and grams. That is Discrete Scale
Relativity in a nutshell.

Robert L. Oldershaw

"The next great awakening of human intellect may well produce a method
of understanding the qualitative content of equations." Richard Feynman

Roger Bagula wrote:
Richard Saam wrote:





Gentlemen:

Given:

Planck's constant hb 1.054572675E-27 g cm^2 sec^-1
gravitational constant G 6.6725985E-8 cm^3 sec^-2 g^-1
speed of light c 2.997924580E10 cm sec^-1

The following is list of some of the Planck scale parameters:

Planck length (hb G/c^3)^(1/2) 1.61605E-35 cm
Planck time (hb G/c^5)^(1/2) 5.39056E-44 sec
Planck mass (hb c/G)^(1/2) 2.17671E-08 g
Planck energy (hb c^5/G)^(1/2) 1.95610E-16 g cm^2 sec^-2
Planck momentum (hb c^3/G)^(1/2) 6.52483E+05 g cm sec^-1
Planck force (c^4/G) 1.21027E+49 g cm sec^-2
Planck density (c^5/(hb G^2) 5.15500E+93 g/cm^3
Planck acceleration (c^6/(hb G)) 1.03145E+97 cm/sec^2
Planck kinematic viscosity (c^7/(hb G))^(1/2) 5.56077E+53 cm^2/sec
Planck absolute viscosity (c^9/(hb G^3))^(1/2) 2.49779E+71 g cm^-1 sec^-1

It is difficult to say which has a 'physical meaning'.

Using dimensional units of mass, length & time
the constants hb, G, c can be arranged in an infinite number of possibilities.

Richard



hb = 1.054572675*10^(-27)
1.054572675`*^-27
G = 6.6725985*10^(-8 )
6.672598500000001`*^-8
c = 2.997924580*10^10
2.99792458`*^10
(hb G/c^3)^(1/2)
1.6160496497524128`*^-33
(hb G/c^5)^(1/2)
5.390561392149541`*^-44
(hb c/G)^(1/2)
0.000021767127031707378`
Two out of three wrong isn't bad?

Roger:
Thank you for the obvious corrections
Updated list as follows:

The following is list of some of the Planck scale parameters:

Planck length (hb G/c3)^(1/2) 1.61624E-33 cm
Planck time (hb G/c5)^(1/2) 5.39121E-44 sec
Planck mass (hb c/G)^(1/2) 2.17645E-05 g
Planck energy (hb c5/G)^(1/2) 1.95610E+16 g cm2 sec^-2
Planck momentum (hb c3/G)^(1/2) 6.52483E+05 g cm sec^-1
Planck force (c4/G) 1.21027E+49 g cm sec^-2
Planck density (c5/(hb G2) 5.15500E+93 g/cm3
Planck acceleration (c6/(hb G)) 1.03145E+97 cm/sec2
Planck kinematic viscosity (c7/(hb G))^(1/2) 5.56077E+53 cm2/sec
Planck absolute viscosity (c9/(hb G3))^(1/2) 2.49779E+71 g cm^-1 sec^-1


Richard

wrote in message
...
wrote:
Publish your replacement for the Schwarzchild metric
and then it can be tested.


Let's have some fun and learn something while we are doing it.

I propose the following gedanken experiment as a way to make the
concept of Discrete Scale Relativity more clearcut and readily
understandable.

It is perfectly understandable already Rob, the Schwarzschild
metric applies out to infinite distance. If you keep it as
you said, your proposal for the Schwarzschild radius of a
proton requires an increase of gravitational effects of 38
orders of magnitude at _all_ scales. Your theory is disproven
by the fact that I can stand up.

George

wrote:
wrote:
wrote:
Parenthetically, the revised Schwarschild radius for the proton is
about 0.8 x 10^-13 cm, which is about equal to the charge radius of the
proton and the revised Planck length.

In that case, the model is pretty much dead. High energy experiments
probe the substructure of the proton down to about three orders of
magnitude smaller than that, and there is absolutely no indication of
anything remotely resembling a horizon.

(The 1990 Nobel Prize in Physics was awarded for the first experiments
in this area. For more recent results, look up, for example, experiments
at HERA, which has a resolution on the order of 10^{-16} cm.)

A Schwarzschild black hole is a very crude approximation to the
fundamental particles that dominate each cosmological scale.
Kerr-Newman black holes are a much better approximation,

Nope. The ratio of angular momentum to mass of a proton is not
compatible with a Kerr-Newman solution.

but I would
not be surprised if major refinements to the K-N models are also
required. People like Paul Wesson have spent decades advocating even
more exotic candidates, such as 5-dimensional soliton-like ultracompact
objects that lack a conventional horizon.

Candidates for *protons*? I doubt it very much -- Wesson knows that
protons are made of quarks.

The Discrete Fractal paradigm ( www.amherst.edu/~rloldershaw ) predicts
the approximate size, charge, angular momentum and radii of these
objects. It predicts their mass spectrum quantitatively and uniquely.

OK. What is your prediction for the mass of the Higgs? How about the
lowest mass neutrino? Both of these are not yet known experimentally,
but should be in the next few years.

I leave it to you astrophysicists to figure out the subtle physics of
these objects,

The internal structure of the proton is quite thoroughly observed. In
particular, we know that it is mostly empty, with much smaller constituents,
and that the interactions among these constituents become weak at high
energies and short distances. If your model cannot reproduce this behavior,
with at least as much quantitative agreement with observation as QCD, then
it's dead.

Steve Carlip

wrote:

Then the stellar scale observer asks the atomic scale observer to show
him his centimeter. The atomic scale observer holds up his centimeter,
and the stellar scale observer says, "That is NOT a centimeter; that is
1cm/5.2 x 10^17. When the atomic scale observer angrily asks to see
the stellar scale observer's cm, he laughs and says, "You are way off;
that thing is 5.2 x 10^17 cm long.

After much back and forth, the light dawns and they say in unison, "So
there are an infinite number of "centimeters" in nature, one for each
cosmological scale". Each has an equal claim to being "the centimeter".
The same is true for seconds and grams. That is Discrete Scale
Relativity in a nutshell.


George Dishman wrote:
.... Your theory is disproven
by the fact that I can stand up.

Let me clarify that point, it doesn't matter what units your observers
use, if you say the physical Schwarzschild radius of a proton, then
the surface gravity of the Earth will increase too and it doesn't
matter
whether that is expressed in m/s^2 or furlongs/fortnight^2, a factor of

10^38 increase will reduce me to a monatomic layer.

George

George Dishman wrote:
It is perfectly understandable already Rob, the Schwarzschild
metric applies out to infinite distance. If you keep it as
you said, your proposal for the Schwarzschild radius of a
proton requires an increase of gravitational effects of 38
orders of magnitude at _all_ scales. Your theory is disproven
by the fact that I can stand up.

Do you live within an atomic scale system? Do you have a lifespan of
approximately 4 x 10^-9 sec? Probably not. So you are a denizen of the
Stellar Scale. I applaud your ability to stand up, but I still think
your understanding of the Discrete Fractal paradigm (
www.amherst.edu/~rloldershaw ) is in need of considerable work. It is
not really that complex, but it does require that one entertain the
possibility that nature might work in a way that in some areas is
radically different from current assumptions.

As you have kindly noted before, the places where the DF paradigm
radically differs from the standard paradigms of cosmology and high
energy physics are precisely those areas where we were forced to
extrapolate well beyond previous observation capabilities. The DF is
not in conflict with most well-tested phenomena.

Robert L. Oldershaw

wrote:

George Dishman wrote:
.... Your theory is disproven
by the fact that I can stand up.

Let me clarify that point, it doesn't matter what units your observers
use, if you say the physical Schwarzschild radius of a proton, then
the surface gravity of the Earth will increase too and it doesn't
matter
whether that is expressed in m/s^2 or furlongs/fortnight^2, a factor of

10^38 increase will reduce me to a monatomic layer.


Sigh. Consider one hydrogen that is separated as far as possible from
any object or interaction. Inside that atomic scale system G(n-1)
applies. Outside of that system G applies, so long as you remain within
a stellar scale system. That is what the Discrete Fractal paradigm
says. Are you in or out?

Rob

wrote:

George Dishman wrote:
It is perfectly understandable already Rob, the Schwarzschild
metric applies out to infinite distance. If you keep it as
you said, your proposal for the Schwarzschild radius of a
proton requires an increase of gravitational effects of 38
orders of magnitude at _all_ scales. Your theory is disproven
by the fact that I can stand up.

Do you live within an atomic scale system? Do you have a lifespan of
approximately 4 x 10^-9 sec? Probably not. So you are a denizen of the
Stellar Scale. I applaud your ability to stand up, but I still think
your understanding of the Discrete Fractal paradigm (
www.amherst.edu/~rloldershaw ) is in need of considerable work.

I think your grasp of the difference between physical
differences and values expressed in different units
needs some work.

It is
not really that complex, but it does require that one entertain the
possibility that nature might work in a way that in some areas is
radically different from current assumptions.

So far all you have said is that a denizen of an atomic
scale system would be likely to use different base units
for measurements but that the formula would still be
valid. The consequence your proposed change of the
Schwarzschild radius of a proton would be a 10^38
increase in Earth's surface gravity regardless of what
units you express it in. Sure, an atomic scale denizen
might still call it 9.81 m/s if he was defining different
physical quantities as the metre and the second but
it would still flatten me.

As you have kindly noted before, the places where the DF paradigm
radically differs from the standard paradigms of cosmology and high
energy physics are precisely those areas where we were forced to
extrapolate well beyond previous observation capabilities. The DF is
not in conflict with most well-tested phenomena.

No, it is in conflict with the fact that I can stand up if
what you say of the proton is true.

George

wrote:

wrote:

George Dishman wrote:
.... Your theory is disproven
by the fact that I can stand up.

Let me clarify that point, it doesn't matter what units your observers
use, if you say the physical Schwarzschild radius of a proton, then
the surface gravity of the Earth will increase too and it doesn't
matter
whether that is expressed in m/s^2 or furlongs/fortnight^2, a factor of

10^38 increase will reduce me to a monatomic layer.


Sigh. Consider one hydrogen that is separated as far as possible from
any object or interaction. Inside that atomic scale system G(n-1)
applies. Outside of that system G applies, so long as you remain within
a stellar scale system.

Then contrary to what you said, you are discarding
the Schwarzschild metric which determines how the
effects change with scale.

That is what the Discrete Fractal paradigm
says. Are you in or out?

Since Steve Carlip has pointed out that we can already
measure the proton at scales three orders of magnitude
smalller than your values for its event horizon, your
suggestion is already proven wrong. Count me out of
your ideas.

George