UNIVERSAL RESONANCE AND QUANTUM GRAVITY
The universal laws of nature are explained in terms of symmetry. The completed
infinities, mathematician Georg Cantor's infinite sets, could be explained as cardinal identities, akin to "qualia" from which finite subsets, and elements of subsets, can be derived.
Completed infinities, called "alephs" are distributive in nature, similar to the way that a set of red objects has the distributive property of redness. Linguistic predicates like red, are numbers in the sense that they interact algebraically according to the laws of Boolean algebra. Take one object away from the set of red objects and the distributive identity "red" still describes the set. The distributive identity "natural number" or "real number" describes an entire collection of individual objects.
These alephs can be set into a one to one correspondence with a proper subset of
themselves. The "infinite" Cantorian alephs are really distributive.
Yet, if we have a finite set of 7 objects, the cardinal number 7 does not really distribute over its individual subsets. Take an element away from the set and the number 7 no longer describes it.
Symmetry is analogous to a self-evident truth and is distributive via the laws of nature, being distributed over the entire set called universe. A stratification of Cantorian alephs with varying degrees of freedom. More freedom = greater symmetry = higher infinity-alephs. So the highest aleph, the "absolute-infinity" distributes over the entire set called universe and gives it "identity".
The highest symmetry is a distributive mathematical identity. This fact is reflected in part, by the conservation laws. So if an unbound-infinite-potential and a constrained-finite-bound-potential are somehow different yet the same. The difference and sameness relation is a duality. Freedom(higher symmetry) and constraint(lesser symmetry) forms a relation that can be described by an invariance principle.
On a flat Euclidean surface, the three angles of a triangle sum to 180 degrees. On the curved surface of a sphere, the three angles add up to more than 180 degrees. The two types of surfaces are not equivalent.
There is a rotational invariance for an equilateral triangle, that seems to hold for both types of surface though.
ABC = BCA = CAB = CBA = BAC = ACB
Does this rotational invariance hold for all geometries? I say yes, but I am not 100% sure yet. 99.999% It seems to point towards a type of duality for quantum mechanics and general relativity.
An interesting idea for a new "theory-conjecture" which is, that symmetry, not logic,
forms the basis of mathematical truth.
Truth = Invariance principle.
Symmetry = invariance = identity
Aristotle's law of excluded middle is really an invariance principle. Symmetry forms the basis of logic.
A V A
T|F = F|T = T
Theoretical physicist Richard Feynman derived the "sum over histories" interpretation of quantum mechanics, where a system does not have a single history, but it has every
possible history, and each history has its own probability amplitude. For example, an
electron travels from point A to point B by every possible route at once. Each possible route or "path" corresponds to a history.
The amplitude for each history defines the probability of that particular path being
followed. The number involves the "action" associated with the history-path, which
seems to determine that the path taken, will be the history closest to the "classical" trajectory, in accordance with the law of conservation of energy.
StephenHawking explains that when we apply the Feynman sum over histories to
particles moving in a background of spacetime, we must also include histories in which the particle travels faster than light and backwards in time.
I propose that these histories and worldlines are fundamental, or elementary waves-
distributions, that are ripples in a basic substrate of stochastic noise - chaos. Waves that are in phase, traveling in opposition to each other, constructively interfere with each other and are at resonance. The resonating probability waves are what we can call the "collapse of the wave function" of the Copenhagen interpretation.
The waves that are out of phase destructively interfere with each other and form the basis of the stochastic noise and quantum fluctuations, which have been empirically verified through the "Casmir effect".
A system's history or "worldline" is a resonating four-dimensional entity!
Time antisymmetry and reverse time translation of probability amplitudes is given by the equations of special relativity:
t = t'/sqrt[1-B^2]
t = -t'/sqrt[1-B^2]
(t*L) = (-L*t)
Strings and branes could actually be resonating waveforms
Since general relativity is a background independent theory, spacetime must also have its own probability density wavefunctions and sum over histories. Distributed identity. A stratification of probability density functions for relational space-time.
What we observe as an absolute spacetime expansion might not be true. The expansion is relative. From a local perspective, the universe appears to expand with radius R. From a global perspective energy density is compressed with radius 1/R. The only real constant for the universe is "h", which is Planck's constant. All other physical constants are related to this basic evolutionary parameter ...h, an energy density ratio. The singularity then becomes a limit that is approached but never reached.
If the locality principle is not going to be thrown into the trash heap, then a viable option is that space is something analogous to homogeneously distributed probability density functions(a perfect fluid?) i.e. increasing energy-density gradients, giving the observed thermodynamic arrow of time. The observed cosmic expansion is, again, a "relative" one.
A perspective effect from our local vantage point. A shrinking object gives the illusion of receding motion. Increasing *refractive* density gradients give the appearance of a Doppler-red-shift. Space increases density as matter is re-sized.
Quantum Gravity.
As a thought experiment, imagine a perfectly smooth homogenous liquid or "fluid" that
stretches out to infinity. An open universe of infinite space-time radius, is equivalent to a closed finite compression universe. There are as many fractions from zero to one as there are natural numbers from zero to infinity.
The fluid has a small distortion or vortice moving in it. How can the velocity of the
"vortice" in the fluid be measured? Its motion can only be relative to another vortice.
Total space-time energy is givenby the Einstein-Pythagorean equation:
E^2 = {mc^2}^2 + {pc}^2
Space is at right angles to time:
S
|||||---->T
The thermodynamic arrow of time, points in the direction of continually increasing
space-time density. Increasing density gradients. It is a ratio adaption:
{S/T}_n = {S/T}_n+1
S and T are reducing in tandem, such, that their ratio remains a constant c, for the
velocity of a photon of light.
S --{energy}---------- T
Energy compresses{resists} space and dilates{stretches} time.
Since potential energy equals kinetic energy, gravitational mass must equal inertial mass.
An increase in kinetic energy always causes resistance in space-time. Potential energy is at right angles to kinetic energy and gravity is at right angles to inertia. Time is at right angles to space. The duality of circle and square.
Russell E. Rierson
analog57@yahoo.com
http://ne-plus-ultra.net/pubs/rierson_resonance.pdf
String Theory Discussion Forum
[ String Theory Home ] [ Forum Index ]
Universal Resonance
[ Follow Ups ] [ Post Followup ] [ String and M Theory Duality XII ] [ FAQ ]
Posted by analog57 on July 14, 2003 at 00:54:30:
Theoretical physicist Richard Feynman derived the "sum over histories" interpretation of quantum mechanics, where a system does not have a single history, but it has every possible history, and each history has its own probability amplitude. For example, an electron travels from point A to point B by every possible route at once. Each possible route or "path" corresponds to a history.
The amplitude for each history defines the probability of that particular path being followed. The number involves the "action" associated with the history-path, which seems to determine that the path taken, will be the history closest to the "classical" trajectory, in accordance with the law of conservation of energy.
Stephen Hawking explains that when we apply the Feynman sum over histories to particles moving in a background of spacetime, we must also include histories in which the particle travels faster than light and backwards in time.
Also, the equations of relativity points towards the possibility of antisymmetric time.
I propose that these histories and worldlines are fundamental, or elementary waves-distributions, that are ripples in a basic substrate of stochastic noise - chaos. Waves that are in phase, travelling in opposition to each other, constructively interfere with each other and are at resonance. The resonating probability waves are what we can call the "collapse of the wave function" of the Copenhagen interpretation.
The waves that are out of phase destructively interfere with each other and form the basis of the stochastic noise and quantum fluctuations, which have been empirically verified through the "Casmir effect".
A system's history or "worldline" is a resonating four dimensional entity!
Time antisymmetry and reverse time translation of probability amplitudes is given by the equations of special relativity:
t = t'/sqrt[1-B^2]
t = -t'/sqrt[1-B^2]
(t*L) = (-L*t)
Strings and branes could actually be resonating waveforms
Since general relativity is a background independent theory, spacetime must also have its own probability density wavefunctions and sum over histories. Distributed identity. A stratification of probability density functions for relational space-time.
Interesting...
The Planck length, 10^(-35) meters, sqrt(G*hbar/c^3) and below, is postulated to become a boiling sea of chaos called "quantum foam". These are vacuum fluctuations, where the geometry and topology of space becomes probabilistic.
John Wheeler derived the "quantum foam" concept in 1955.
http://www.usd.edu/phys/courses/phy...rk/wheeler.html
Spin foam concept:
http://faculty.washington.edu/smcoh...rainySpace.html
http://math.ucr.edu/home/baez/foam/
A geodesic is the shortest distance between two points on a curved surface. An object in free fall traces out a geodesic. Parallel translation with tangent vectors along a curved manifold is an abstraction of course. It is difficult to imagine actual "infinitesimal tangent vectors" following imaginary paths on spacelike hypersurfaces.
Infinitesimals are mathematical objects, less than finite but greater than zero. It seems to me that symmetry groups resolve the infinitesimals paradox quite nicely!
Worldlines seem much more "realistic" than imaginary paths and tangent vectors. The coordinate independence of GR, is very appealing.
Richard Feynman's sum over histories-path integral, gives a particle's four dimensional worldline, from point A to point B. The principle of least action applies and energy is conserved. It appears that the universe has laws to maximize efficiency.
Thought experiment:
An object in "free fall" is basically equivalent to an inertial reference frame, if the object is relatively small. Two clocks are synchronized at the top of a tower. Also, there are more clocks affixed along regular intervals from the bottom, to the top OF the tower.
When the clock is dropped from the tower, it will be accelerated at 9.8 meters/sec^2. Yet, since it is in free fall it will be equivalent to a rest frame. As its velocity continues to increase in its fall, it will have a relativistic time dilation, t1:
t1/sqrt[1-(v/c)^2]
Where "v" is the instantaneous velocity at any one "instant", approximately
The clocks affixed to the tower will have the approximate gravitational time dilation, t2:
t2/sqrt[1-2GM/((c^2)*r)]
G is Newton's universal gravitational constant. M is mass of the perfectly spherical planet that the tower is standing on. r is the radius of the perfectly spherical planet and c is the speed of light in vacuum.
As the clock falls next to the tower, at each instant that the falling clock passes a clock affixed to the tower, a third observer would observe the two clocks to be ticking at the same rate.
The clock at the bottom of the tower will be the slowest, since it is in the stronger part of the gravitational field. When the falling clock reaches this bottom level, the two clocks should have the "same" time dilation?, if the falling clock was dropped from rest, with no additional accelerating forces.
Energy is conserved.
t1/sqrt[1-(v/c)^2] = t2/sqrt[1-2GM/((c^2)*r)] ?
Russell E. Rierson
analog57@yahoo.com
http://superstringtheory.com/forum/dualboard/messages12/409.html
Follow Ups: (Reload page to see most recent)
* Re: Universal Resonance -- dr_syed_ameen2000 7/14/03 (0)
* Re: Universal Resonance -- sol 7/14/03 (1)
o Re: Universal Resonance -- analog57 7/17/03 (0)
5 комментариев:
Re: Is the universe a quantum computer?
posted on 11/03/2003 12:26 AM by analog57
[Top]
[Mind·X]
[Reply to this post]
It could be that the universe is a logic circuit that is a closed feedback loop. The infinite tower of turtles would no longer be necessary.
There is a duality of physics for a circle of radius R and 1/R . Objects and the interstellar space within the galaxies shrink in tandem, while the intergalactic space shrinks at a slower rate, which gives the local perception of expanding intergalactic spacetime. It would really be a self contained "logic loop".
[<-[->[<-[->[U]<-]->]<-]->]
So the boundary for the universe is that it has no boundary. Universal resonance.
Very similar to the transactional interpretation of quantum mechanics, but also different.
Why not describe Einstein's equation as a rule that tells the geometry of space how to evolve as function of time? Lorentzian manifolds M, diffeomorphic to R x S, where the manifold S represents space, and t, an element of R, represents time. So spacetime is sliced into instants of time as an arbitrary choice, or possibly units of Planck's constant.
F: M---> R x S
Spacetime becomes quantized or "sliced up" but that could be what nature really does. According to relativity, an objects position and momentum can only be defined with respect to a another object. Yet the universe as a whole has no frame of reference outside of itself, so how can its momentum be defined? It can only be defined with reference to itself. Worldlines fill up spacetime and the criss crossing of world lines mark events beyond the need for coordinate systems or coordinates. Points in spacetime are given the name "events" so there is a coordinate independence.
The geometric view of physics means that the laws of physics are the same in every Lorentz reference system. Local Lorentz invariance. But since the universe has no exterior reference frame, and it must refer to itself, its world line intersects with itself. This quantized-evolution of spacetime dictated by GR and QM, means that the world line of the past intersects with the world lines of the present, for the universe. A geometric stacking of space like slices, parameterized by t, The universe is a function of itself. Spacetime becomes compressed. As the time evolution proceeds in the thermodynamic direction of t, the space like sheets continually increase in density. The information storage of space time.
Is it possible to also derive Einstein's field equation strictly in terms of quantum mechanical operators? using n-dimensional cross sections of cotangent vector spaces? Near a massive object M, the *isobar* cross sections increase in density, as wavefunction density gradients?
Two compression waves, in phase, with the same amplitude and wavelength moving in opposite directions, become resonating "standing waves":
As the entropy continues to increase in the universe, and if the universe is a closed system, the entropy may be considered to be the interpretation of a "damping force". This damping force may also be one possible solution to the dark matter enigma.
Solve the Schwarzschild solution for the entire universe, since the universe can be postulated to be a closed system with nothing outside itself. The condition of "nothingness" leads one to ask "What are the properties of nothingness?" Of course there are no measurable properties, but nothingness in itself must be a type of massless solid. A condition that has no distance - metric scales. In other words, there is no outside to the universe, no measurable border between something and nothing.
Re: Is the universe a quantum computer?
posted on 11/03/2003 10:07 PM by claireatcthisspace
[Top]
[Mind·X]
[Reply to this post]
yup, it had to happen, he follwed me here aswell (Russell)--~.> Why don't you fly over to my house and post your text on my fridge?
(in humour)(UK humour)
Claire
http://www.kurzweilai.net/meme/frame.html?main=/articles/art0386.html?m%3D1
name = Russell E. Rierson
REALITY = MIND The Universal Mind creates itself - self referentially - retroactively. Retroactive teleological causation can be described by the transactional interpretation of quantum mechanics, where wave distributions of probability originate in the past, present, and future - giving a super Copernicanative juxtapositional - teleological basis FOR our perceptual reality... There is no preferred frame of reference. The perceptual Universe emerges from the fundamenmtal essence that is the unspoken - undefinable - undifferentiated TAO. Events become actualized when waves from the past and the future interfere with each other, converging to the ever- present NOW on the Euclidean plane of a holographic n-1 dimensional hypersurface. This is manifested by the time invariance of energy conservation, such, that time itself is actually a perceptual illusion. The wave patterns[probability distributions] also create what we perceive as spacetime[gravitons], mass, and "energy". Gravity is also virtual. Since the Universe has no exterior reference frame, and it must refer to itself, such, that its overlapping Lorentz invariant geometry is a computational self configuration. The evolution of spacetime, as dictated by GR and QM, means that the past history of the Universe is carried along with the present, FOR the Universe. A densification of the Universal space-like Euclidean hypersurface. The Universe is a function of itself. Space becomes relativistically "contracted", "virtual" time becomes relativistically dilated. As the time evolution proceeds in the thermodynamic direction of "virtual" time, the n-dimensional Euclidean hyper-plane continually increases in information density. The information storage of perceptual space-time. A metric field can be defined by the primary substratum of events. Thus the intrinsic geometrical structure of spacetime is predicated on the pseudo-Riemannian spaces via the affine relationships — all physical events are fully reducible to manifestations of the substratum i. e. the event density generating a metric field. Stochastically speaking, gravity must be taken beyond the limits of classical reality, where the mean value of the stress energy tensor of quantum fields also has fluctuations as a source of stochastic Einsteinian vacuum equations. Such is the necessary foundation for neo-classical gravity and the viability of inflationary cosmology based on the vacuum energy dominated phase. Metric fluctuations and spacetime gravitons form an elementary substrate. Yes, the shortest distance between two points is a straight line; energy is conserved. The uncertainty principle and gravity are related to the same mathematical properties. The proof of the
In Reply to: Universal Resonance posted by analog57 on July 14, 2003 at 00:54:30:
july,14.2003
analog57:
But the Feynman's probability(Sum over Histories) approach seems wrong when one studies the "Nature Of Chemical Bond"and the "electron transfer processes"in all kinds of reactions as well as the Hydrogen bond and Electronegativity and electron affinity problems.One can hardly argue about these and also about electron tunnelling phenomenon.
Posted by sol on July 14, 2003 at 15:39:30:
In Reply to: Universal Resonance posted by analog57 on July 14, 2003 at 00:54:30:
Russell,
I am glad you came to this board. There will no doubt be some adjusts on my side and familiarity with who Russel is, and for Russel will get the feel of this board:).
So to the post.
The elliptical orbit has to be considered, as well as oscillations. These represent something in terms of mass identificatin(energy) and mass loss?
So how are Em and gravitational waves intertwined?
What is a light Cone? I need more familiarization, and here we have light(em wave that is longitudal) that travels a great distance, and if we consider the essence of the boson, what is a graviton(transverse wave undertanding) too?
So we see the some interesting dynamics of the loop.
Mass consideration and dualism(oscillations), finds itself rotating back and forth(like a pendulum), and all paths, a probability distribution as you point out(between longitudal and transverse wave production).
What is the measure of the total energy of that consideration(mass and we are left to consider the energy) and the gravitational waves speak to us.
Ligo and Lisa will bcome very helpful here in the new language developement.
Welcome to the board. I hope you will continue to share your points of view:)
Sol
Posted by analog57 on July 17, 2003 at 01:45:42:
In Reply to: Re: Universal Resonance posted by sol on July 14, 2003 at 15:39:30:
Thought Experiment:
A clock is dropped from a high tower. Along the length of the tower, at fixed intervals, are more clocks. As the clock continues its downward descent, it is accelerated at one "g", ~ 9.8 m/sec^2 .
tower......free fall
[Ct0]<--->[Cf0]
|
|
|
[Ct1]<--->[Cf1]
|
|
|
[Ct2]<--->[Cf2]
|
|
|
[Ctn]<--->[Cfn]
|
|...
At the top of the tower, at the "instant" of release, both clocks t0 and f0 are ticking at the same "rate".
During the fall, the free falling clock wil pass a clock on the tower at one "instant". Does the rate of the two clocks correspond at the insant? Does the rate of [Ct1] = [Cf1] ? Does the rate of [Ctn] = [Cfn] ? Approximately?
Does T/sqrt[1-(v/c)^2] = T/sqrt[1-2GM/(c^2)*r] ?
I posted my clock-tower thought experiment to different places on the internet. Someone who wishes to remain anonymous sent the answer below:
Answer:
quote:
------------------------------------------------------------
On Tue, 15 Jul 2003, Russell E. Rierson wrote:
> A clock is dropped from a high tower. Along the
length of the tower,
> at fixed intervals, are more clocks. As the clock
continues its
> downward descent, it is accelerated at one "g", ~
9.8 m/sec^2 .
[snip]
> At the top of the tower, at the "instant" of
release, both clocks t0
> and f0 are ticking at the same "rate".
If you are asking about weak-field gtr, this is true
automatically if all
the clocks are "ideal clocks".
(An ideal clock is just one which is not subject to
instabilities or
affected by acceleration, temperature, etc., as any
real clock would be.)
> During the fall, the free falling clock wil pass a
clock on the tower
> at one "instant". Does the rate of the two clocks
correspond at the
> insant?
For a moment forget all but two clocks, one falling
and the other held
motionless in a uniform gravitational field. You are
apparently asking
about "the relative rates of these clocks at the
instant when the falling
clock passes the static one". When you pose the
question in this way,
perhaps it is easier to see that the answer depends
upon precisely how you
are comparing the "rates" of the two clocks!
Here is a suggestion for refining your question.
Instead of a falling
clock and a stationary clock, assume you have two
labs, each equipped with
an ideal clock. The first lab is at the origin.
There is a uniform
gravitational field in the z direction (this only
makes sense in the
weak-field approximation to gtr, incidentally). The
second lab is
initially at the origin (the second clock is initially
synchronized with
the first clock, for example by the usual "Einstein
synchronization
procedure", which is valid in any static spacetime)
and at time t = 0 is
dropped and begins to fall in the -z direction. An
observer in the second
lab keeps a laser beam aimed at an observer in the
first lab throughout
the experiment. Question: how does the frequency of
the laser as observed
by the observer in the first lab change over time (by
his own clock)?
Anon.
------------------------------------------------------------
end quote.
Is gravity a statistical probability distribution?
Yes, the force called gravity is actually geometry, non-Euclidean geometry, where spacetime becomes anisotropic and inhomogeneous in the presence of mass-energy.
Then the question becomes "what is space?" "What is time?"
Space is relational. Time is a process.
Heisenberg Uncertainty:
DxDp >= hbar/2
The relation becomes totally "chaotic" below the Planck length. So, space could be described as a self similar relation which is generated by the quantum foam, and forms Penrose's "spin networks".
The curvature of spacetime could be represented as a Gaussian distribution? If mathematics only is an approximation of reality, then the mathematics of probability corresponds "exactly" with reality.
The Riemann tensor explains how a tangent vector, parallel translated around a tiny parallellogram is changed. So, to say that spacetime is "curved" means how much a tangent vector changes during parallel transport around a loop. Parallel transport is the translation of an infinitesimal tangent vector along a geodesic.
The probability distribution should agree exactly with the Riemann tensor of Einstein's relativity.
Is the universe a closed system? The million dollar question.
Stephen Hawking explains closed loop histories of quantum theory, where particles travelling forward, then backwards in time, annihilate one another. Hawking explains that these closed loop histories are confirmed by one interpretation of the Casmir effect.
This is allowed by the Heisenberg uncertainty principle for brief periods smaller than the Planck time. 10^(-43) sec.
http://clinton4.nara.gov/Initiatives/Millennium/shawking.html
quote:
------------------------------------------------------------
The possible particle histories have to include paths that travel faster than light and even paths that go back in time. Before anyone rushes out to patent a time machine let me say that in normal circumstances at least, one can not use this for time travel. However paths that go back in time are not just like angels dancing on a pin. They have real observational consequences. Even what we think of as empty space is full of particles moving in closed loops in space and time. That is they move forward in time on one side of the loop and backwards in time on the other side. These closed loops are said to be virtual particles because they can not be measured directly with a particle detector. However their effects can be measured indirectly. One way is to have a pair of metal plates close together. The effect of the plates is to reduce slightly the number of closed loops in the region between the plates relative to the number outside. There are thus more closed loops hitting the outside edges of the plates and bouncing off than there are hitting the inside edges. One would therefore expect there to be a small force pushing the plates together. This force, which was first predicted by the Turkish physicist Hendrick Casimir, has been observed experimentally. So we can be confident that closed particle loops really exist.
------------------------------------------------------------end quote.
Why not solve the Swcharzchild solution for the entire universe? Solve for the imaginary time value of the Schwarzchild solution using something called analytic continuation, which becomes periodic in the imaginary time direction. Quantum field theory calculations where imaginary time is periodic, with period 1/T are equivalent to statistical mechanics calculations where the temperature is T.
http://math.ucr.edu/home/baez/week138.html
...
The periodic waveforms that are opposed yet "in phase" would be at standing wave resonance,which would be equivalent to the observed statistics of the thermodynamic arrow of time?
Russell E. Rierson
analog57@yahoo.com
Отправить комментарий