Re: A question re measure
On Wed, Oct 05, 2005 at 10:45:28AM -0400, Hal Ruhl wrote: I am not a mathematician and so ask the following: In my model the ensemble of descriptions [kernels in my All] gets populated by divisions of my list of fragments of descriptions into two sub lists via the process of definition. The list is assumed to be countably infinite. The cardinality of the resulting descriptions is c [a power set of a countably infinite set] Small descriptions describe simple worlds and large ones describe complex worlds. To me there should be far more highly asymmetric sized divisions [finite vs countably infinite] of the list than symmetric or nearly symmetric [countably infinite vs countably infinite] ones. However, for each small [finite] description there is a large [countably infinite] description. The result seems to be that there are more large descriptions than small ones. If the above is correct then mathematically what are the measures of the two types of descriptions? Hal Ruhl A measure is a function m(x) on your set obeying additivity: m(\empty)=0 m(A u B) = m(A) + m(B) - m(A^B) where u and ^ are the usual union and intersection operations. The range of m(x) is also often taken to be a positive real number. Does this answer your question? Measure is generally speaking unrelated to cardinality, which is what you're referring to with finite, countable and uncountable sets. Cheers -- *PS: A number of people ask me about the attachment to my email, which is of type application/pgp-signature. Don't worry, it is not a virus. It is an electronic signature, that may be used to verify this email came from me if you have PGP or GPG installed. Otherwise, you may safely ignore this attachment. A/Prof Russell Standish Phone 8308 3119 (mobile) Mathematics0425 253119 () UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 pgpJg5TPHgKkc.pgp Description: PGP signature
Neutrino shield idea
Howdy! I friend of mine has worked on a related idea that might help this inverstigation. Please see: http://davidwoolsey.com/physics/ideas/neutrinoscope/index.html Kindest regards, Stephen - Original Message - From: John Ross [EMAIL PROTECTED] To: [EMAIL PROTECTED] Cc: everything-list@eskimo.com Sent: Friday, October 07, 2005 11:57 AM Subject: RE: ROSS MODEL OF THE UNIVERSE - The Simplest Yet Theory of Everything Yes. But building a neutrino shield would be difficult.
RE: Neutrino shield idea
Thanks for the paper relating to detection of low energy neutrinos. However, according to my model, neutrinos are very, very high energy photons (off everybody's chart, except mine). Therefore, if my model is correct, then low energy neutrinos would merely be the photons we are familiar with and would be very easy to detect. -Original Message- From: Stephen Paul King [mailto:[EMAIL PROTECTED] Sent: Friday, October 07, 2005 12:54 PM To: everything-list@eskimo.com Subject: Neutrino shield idea Howdy! I friend of mine has worked on a related idea that might help this inverstigation. Please see: http://davidwoolsey.com/physics/ideas/neutrinoscope/index.html Kindest regards, Stephen - Original Message - From: John Ross [EMAIL PROTECTED] To: [EMAIL PROTECTED] Cc: everything-list@eskimo.com Sent: Friday, October 07, 2005 11:57 AM Subject: RE: ROSS MODEL OF THE UNIVERSE - The Simplest Yet Theory of Everything Yes. But building a neutrino shield would be difficult.
Re: Neutrino shield idea
This means that beta decay proves your model wrong. - Original Message - From: John Ross [EMAIL PROTECTED] To: 'Stephen Paul King' [EMAIL PROTECTED]; everything-list@eskimo.com Sent: Saturday, October 08, 2005 12:35 AM Subject: RE: Neutrino shield idea Thanks for the paper relating to detection of low energy neutrinos. However, according to my model, neutrinos are very, very high energy photons (off everybody's chart, except mine). Therefore, if my model is correct, then low energy neutrinos would merely be the photons we are familiar with and would be very easy to detect. -Original Message- From: Stephen Paul King [mailto:[EMAIL PROTECTED] Sent: Friday, October 07, 2005 12:54 PM To: everything-list@eskimo.com Subject: Neutrino shield idea Howdy! I friend of mine has worked on a related idea that might help this inverstigation. Please see: http://davidwoolsey.com/physics/ideas/neutrinoscope/index.html Kindest regards, Stephen - Original Message - From: John Ross [EMAIL PROTECTED] To: [EMAIL PROTECTED] Cc: everything-list@eskimo.com Sent: Friday, October 07, 2005 11:57 AM Subject: RE: ROSS MODEL OF THE UNIVERSE - The Simplest Yet Theory of Everything Yes. But building a neutrino shield would be difficult.
Re: Neutrino shield idea
Dear Russell, I hope you meant to write that photons are bosons with spin1. Otherwise we would have a hard time explaining Maxwell's Field equations. ;-) About the differences between neutrinos and photons, we could also point out that photons have a null extension in the time direction and neutrinos, having a small but non-zero mass have an extension in the time direction - I am thinking here in terms of how we would embed our particles in a Minkowski or equivalent space-time diagrams. Kindest regards, Stephen - Original Message - From: Russell Standish [EMAIL PROTECTED] To: John Ross [EMAIL PROTECTED] Cc: 'Stephen Paul King' [EMAIL PROTECTED]; everything-list@eskimo.com Sent: Friday, October 07, 2005 6:12 PM Subject: Re: Neutrino shield idea Neutrinos are fermions with spin 1/2. Photons are bosons with spin 0. This is about as chalk and cheese as you can get. The difference is not energy.
What is the 'Unruh Effect'?
Hi Russell and Friends,
I just ran across the following post and
thought that you might find it interesting. Any comments?
Onward!
Stephen
On Thu, 11 Aug 2005 10:32:00 + (UTC), in
sci.physics.research[EMAIL PROTECTED] wrote:
The "Minkowski" or "inertial" vacuum state seen in an
"acceleratingframe" is a thermal state at a temperature proportional to
the"acceleration"; i.e., an heat bath containing an infinite number
ofparticles (finite density) distributed in a fashion consistent with
agas at a particular temperature.
The words in quotes are very misleading however, and require a
largeamount of clarification, because the effect has little or nothing
perse to do with acceleration or being inertial; but rather with
theoccurrrence of a causal horizon.
A quantum field theory requires you first to define a "frame",
the wordwhich -- unlike in Relativity -- does NOT a coordinate system; but
a"flow of time". Quantum theory, is you recall, treats time as
aprocess, not a dimension.
The flow of time is represented by a vector field which is
timelike.
The Minkowski or inertial frame has associated with it a
constanttime-like field which (by suitable Lorentz transformation) can
berepresented as T = d/dt -- i.e. the 4-vector T = T^{mu} d/dx^{mu}
whoseonly non-zero component is T^0 (with x^0 = t).
The Unruh frame uses a time-like field which does NOT cover
all ofspace. The flow lines are all hyperbolic, each naturally
associatedwith an observer at a given acceleration. The hyperbolas all
have, asasymptotes, the 2+1 boundary given by an equation of the form x =
c|t|;the region associated with the field being x c|t|.
The "acceleration" a is normally defined as that associated
with one ofthe worldlines in the Unruh frame. Different worldlines
have differentaccelerations associated with them.
At this boundary, the timelike field T becomes null. A
second, mirrorregion, x -c|t| has the boundary x = -c|t|. Both
boundaries meet att = 0. In this region, the field T "flows" in the
opposite direction.
The boundary x = c|t| is the causal horizon mentioned
before.
A field is uniquely determined by its values at t = 0, and the
space ofall states of a system is generally always associated with the
initialvalues of whatever system is in question. Here, that means,
there is anatural split of the underlying state space H into H1 + H2, with
H1being the state space associated with the region x c|t|, and H2
beingthat associated with the region x -c|t|.
(Solving the field equation by taking its initial values (and
theinitial values of its time derivative) comprises what's called a
Cauchyproblem. For the Klein-Gordon field, the initial values play
theanalogous role of coordinates, the initial time derivative
thecongugate momenta. The state space is then a Hilbert space in
whichthese quantities act as operators satisfying the usual
Heisenbergrelations).
H1, here, is the only one of physical relevance. But a
fulldescription of the Minkowski frame requires both H1 and H2.
Inparticular, the vacuum state |0 of a Klein Gordon field -- as seen
inthe Minkowski frame -- when expressed in terms of the H1 H2
states--becomes:
|0 = sum |n_1 |n_2 exp(-pi a).
This is readily identifiable in the language of
finite-temperaturequantum field theory. The states |n_1 can be
thought of as particlestates, those |n_2 can be thought of as states
associated with vacuumfluctuations of the corresponding heat bath (i.e.
"holes"). So, thesuperposition |n_1 |n_2 has total
energy 0, since |n_2 reflects|n_1. All the states |n_2 are
negative energy since the time flow inregion 2, x -c|t|, goes the other
way.
Since only region 1, x c|t|, is physically relevant (you
can't seepast the boundary, the causal horizon), then the actual quantum
stateassociated with it is arrived at by phase-averaging over the states
ofregion 2. This turns the Minkowski state into the region 1
state:
|00| -- Trace_2(|00|) =
V_1with |00| = sum
|n_1 n|_1 |n_2 n|_2 exp(-2 pi a)which, after
being traced over give you
Trace_2(|00|) = sum |n_1 n|_1 exp(-2 pi a)which is a MIXED
(and thermal) state, no longer a pure state,associated with a temperature
proportional to a.
Having a mixed state means you've lost information -- this
loss beingrepresented by the coefficients of the
mixture
exp(-2 pi a)which represent (up to proportion) probabilities ... and
probabilitiesalways mean you lost information somewhere.
In fact, this general process of tracing over a causal horizon
of somesort is GENERALLY how you get probabilities out of quantum
theory.Everything is a pure state, until you do a partial
tracephase-averaging cut-off on a horizon somewhere, and the
horizon,itself, can be thought of as nothing less than a way of quantifying
theword "observer".
The loss of information is readily identified with the loss
ofinformation of what's going on in the other parts of spacetime
outsidethe region x c|t|.
The
RE: Neutrino shield idea
John Ross wrote: Thanks for the paper relating to detection of low energy neutrinos. However, according to my model, neutrinos are very, very high energy photons (off everybody's chart, except mine). Therefore, if my model is correct, then low energy neutrinos would merely be the photons we are familiar with and would be very easy to detect. John, does your theory involve a set of mathematical equations which can be used to make detailed quantitative predictions about all the same situations that mainstream physics makes predictions about, or do your ideas not go beyond intuitive word-pictures? Also, do you have any response to the criticisms of pushing gravity theories made in the wikipedia article I linked to and in the excerpt from Feynman's book I quoted? Jesse
Re: Neutrino shield idea
On Fri, Oct 07, 2005 at 09:02:17PM -0400, Stephen Paul King wrote: Dear Russell, I hope you meant to write that photons are bosons with spin1. Otherwise Yes, you are right. Mea culpa! Put it down to the couple of decades since I studied this stuff... we would have a hard time explaining Maxwell's Field equations. ;-) About the differences between neutrinos and photons, we could also point out that photons have a null extension in the time direction and neutrinos, having a small but non-zero mass have an extension in the time direction - I am thinking here in terms of how we would embed our particles in a Minkowski or equivalent space-time diagrams. Indeed - I thought about raising this difference also. Neutrinos are now accepted as having nonzero mass, although that wasn't the case when I was studying physics. Also, this guy would probably come back with photons having nonzero rest mass! After all, he reckons Einstein goofed, and that relativity is a load of old cobblers, so having nonzero restmass particles traveling at the speed of light wouldn't be a problem for him! Kindest regards, Stephen - Original Message - From: Russell Standish [EMAIL PROTECTED] To: John Ross [EMAIL PROTECTED] Cc: 'Stephen Paul King' [EMAIL PROTECTED]; everything-list@eskimo.com Sent: Friday, October 07, 2005 6:12 PM Subject: Re: Neutrino shield idea Neutrinos are fermions with spin 1/2. Photons are bosons with spin 0. This is about as chalk and cheese as you can get. The difference is not energy. -- *PS: A number of people ask me about the attachment to my email, which is of type application/pgp-signature. Don't worry, it is not a virus. It is an electronic signature, that may be used to verify this email came from me if you have PGP or GPG installed. Otherwise, you may safely ignore this attachment. A/Prof Russell Standish Phone 8308 3119 (mobile) Mathematics0425 253119 () UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 pgpKEahVLEFpw.pgp Description: PGP signature
