Truth is the highest energy state of a system, it is also the foundation or unity.

Innocence is the ability to see things for what they are.

Intelligence is the ability to make great conceptual leaps.

Knowledge is the physical manifestation of consciousness.

Wisdom is the ability to project into the future and see the consequences of every choice.

As we continue our journey through life we built up layers of filters (in our minds) until innocence is buried.

These filters can be beneficial or harmful and affect our perception of the world around us.

They have an effect on the degrees of freedom in a fractal sense.

The resolution of a system defines the limits of any value assigned to it.

Infinity could be the changing value inside of a cycle.

Love only has value if it is given away.

Freewill is the material expression of love.

If reality contains both infinity and unity then it is either is a multifaceted jewel or the singularity dancing.

There is a fractal and holographic aspect to our reality. There is at one level a material expression of the information stored holographically that we perceive. At a deeper level we connect to this information through our consciousness and every choice we make is branching out in a fractal pattern.

The tree of knowledge of good and evil.

The tree of life.

The tree is a fractal representation of the heavens and the earth.

It is inside of the time domain.

It is consciousness.

Choices bifurcating there way to somewhere or some-when else.

There are only so many choices that can be made in one lifetime but every choice branches out into infinity.

Notice that in the lower half of the tree (the root system) which represents the earth, most of the paths lead to the abyss, only one path leads to the light.

Every choice has a fractal quality to it and you have to figure out which way leads to the light.

Love and freewill are connected.

Stay on the path of love.

This path leads to the light.

All of the other paths lead to the abyss/chaos. ]]>

From Wikipedia, the free encyclopedia

List of unsolved problems in physics Why doesn't the zero-point energy of vacuum cause a large cosmological constant? What cancels it out?

In cosmology the vacuum catastrophe refers to the disagreement of 107 orders of magnitude between the upper bound upon the vacuum energy density as inferred from data obtained from the Voyager spacecraft of less than 1014 GeV/m3 and the zero-point energy of 10121 GeV/m3 suggested by a naïve application of quantum field theory.[1] This discrepancy has been termed "the worst theoretical prediction in the history of physics."[2]

The magnitude of this discrepancy is entirely beyond the descriptive power of any kind of commonplace comparison. It has been observed that the statement "the universe consists of exactly one elementary particle" is closer to being true, by at least ten orders of magnitude, than the incorrect vacuum-catastrophe prediction.

It should be stressed that quantum field theory in itself gives no prediction for any measurable vacuum energy unless several assumptions are made that have no grounds in observation or established theory. These include the assumption that quantum field theory acts as a natural and effective field theory down to the Planck scale and the assumption that vacuum energy gravitates.[3] The nature of vacuum energy continues to be of great theoretical interest because of the ambiguities in what our best theories appear to suggest for it.

The problem was identified at an early stage by Walther Nernst,[4] who raised the question of the consequences of such a huge energy of vacuum on gravitational effects.[5] A recent philosophical and historical assessment is provided by Rugh and Zinkernagel. ]]>

From Wikipedia, the free encyclopedia

This article is about the probability theoretic principle. For the classifier in machine learning, see maximum entropy classifier. For other uses, see maximum entropy (disambiguation).

This article includes a list of references, but its sources remain unclear because it has insufficient inline citations. Please help to improve this article by introducing more precise citations. (September 2008)

Bayesian statistics

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Theory

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Probability interpretations

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Bayes' rule

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Prior

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The principle of maximum entropy states that, subject to precisely stated prior data (such as a proposition that expresses testable information), the probability distribution which best represents the current state of knowledge is the one with largest entropy.

Another way of stating this: Take precisely stated prior data or testable information about a probability distribution function. Consider the set of all trial probability distributions that would encode the prior data. Of those, one with maximal information entropy is the proper distribution, according to this principle.

Contents

1 History

2 Overview

3 Testable information

4 Applications

4.1 Prior probabilities

4.2 Maximum entropy models

5 General solution for the maximum entropy distribution with linear constraints

5.1 Discrete case

5.2 Continuous case

5.3 Examples

6 Justifications for the principle of maximum entropy

6.1 Information entropy as a measure of 'uninformativeness'

6.2 The Wallis derivation

6.3 Compatibility with Bayes' theorem

7 See also

8 Notes

9 References

10 Further reading

11 External links

History

The principle was first expounded by E. T. Jaynes in two papers in 1957[1][2] where he emphasized a natural correspondence between statistical mechanics and information theory. In particular, Jaynes offered a new and very general rationale why the Gibbsian method of statistical mechanics works. He argued that the entropy of statistical mechanics and the information entropy of information theory are principally the same thing. Consequently, statistical mechanics should be seen just as a particular application of a general tool of logical inference and information theory.

Overview

In most practical cases, the stated prior data or testable information is given by a set of conserved quantities (average values of some moment functions), associated with the probability distribution in question. This is the way the maximum entropy principle is most often used in statistical thermodynamics. Another possibility is to prescribe some symmetries of the probability distribution. An equivalence between the conserved quantities and corresponding symmetry groups implies the same level of equivalence for both these two ways of specifying the testable information in the maximum entropy method.

The maximum entropy principle is also needed to guarantee the uniqueness and consistency of probability assignments obtained by different methods, statistical mechanics and logical inference in particular.

The maximum entropy principle makes explicit our freedom in using different forms of prior data. As a special case, a uniform prior probability density (Laplace's principle of indifference, sometimes called the principle of insufficient reason), may be adopted. Thus, the maximum entropy principle is not just an alternative to the methods of inference of classical statistics, but it is an important conceptual generalization of those methods. It means that, thermodynamics systems need not be shown to be ergodic to justify treatment as a statistical ensemble.

In ordinary language, the principle of maximum entropy can be said to express a claim of epistemic modesty, or of maximum ignorance. The selected distribution is the one that makes the least claim to being informed beyond the stated prior data, that is to say the one that admits the most ignorance beyond the stated prior data.

Testable information

The principle of maximum entropy is useful explicitly only when applied to testable information. A piece of information is testable if it can be determined whether a given distribution is consistent with it. For example, the statements

The expectation of the variable x is 2.87

and

p2 + p3 > 0.6

are statements of testable information.

Given testable information, the maximum entropy procedure consists of seeking the probability distribution which maximizes information entropy, subject to the constraints of the information. This constrained optimization problem is typically solved using the method of Lagrange multipliers.

Entropy maximization with no testable information takes place under a single constraint: the sum of the probabilities must be one. Under this constraint, the maximum entropy discrete probability distribution is the uniform distribution,

p_i=\frac{1}{n}\ {\rm for\ all}\ i\in\{\,1,\dots,n\,\}.

Applications

The principle of maximum entropy is commonly applied in two ways to inferential problems:

Prior probabilities

The principle of maximum entropy is often used to obtain prior probability distributions for Bayesian inference. Jaynes was a strong advocate of this approach, claiming the maximum entropy distribution represented the least informative distribution.[3] A large amount of literature is now dedicated to the elicitation of maximum entropy priors and links with channel coding.[4][5][6]

Maximum entropy models

Alternatively, the principle is often invoked for model specification: in this case the observed data itself is assumed to be the testable information. Such models are widely used in natural language processing. An example of such a model is logistic regression, which corresponds to the maximum entropy classifier for independent observations.

General solution for the maximum entropy distribution with linear constraints

Main article: maximum entropy probability distribution

Discrete case

We have some testable information I about a quantity x taking values in {x1, x2,..., xn}. We express this information as m constraints on the expectations of the functions fk; that is, we require our probability distribution to satisfy

\sum_{i=1}^n \Pr(x_i\mid I)f_k(x_i) = F_k \qquad k = 1, \ldots,m.

Furthermore, the probabilities must sum to one, giving the constraint

\sum_{i=1}^n \Pr(x_i\mid I) = 1.

The probability distribution with maximum information entropy subject to these constraints is

\Pr(x_i\mid I) = \frac{1}{Z(\lambda_1,\ldots, \lambda_m)} \exp\left[\lambda_1 f_1(x_i) + \cdots + \lambda_m f_m(x_i)\right].

It is sometimes called the Gibbs distribution. The normalization constant is determined by

Z(\lambda_1,\ldots, \lambda_m) = \sum_{i=1}^n \exp\left[\lambda_1 f_1(x_i) + \cdots + \lambda_m f_m(x_i)\right],

and is conventionally called the partition function. (Interestingly, the Pitman–Koopman theorem states that the necessary and sufficient condition for a sampling distribution to admit sufficient statistics of bounded dimension is that it have the general form of a maximum entropy distribution.)

The λk parameters are Lagrange multipliers whose particular values are determined by the constraints according to

F_k = \frac{\partial}{\partial \lambda_k} \log Z(\lambda_1,\ldots, \lambda_m).

These m simultaneous equations do not generally possess a closed form solution, and are usually solved by numerical methods.

Continuous case

For continuous distributions, the simple definition of Shannon entropy ceases to be so useful (see differential entropy). Instead Edwin Jaynes (1963, 1968, 2003) gave the following formula, which is closely related to the relative entropy.

H_c=-\int p(x)\log\frac{p(x)}{m(x)}\,dx

where m(x), which Jaynes called the "invariant measure", is proportional to the limiting density of discrete points. For now, we shall assume that it is known; we will discuss it further after the solution equations are given.

A closely related quantity, the relative entropy, is usually defined as the Kullback–Leibler divergence of m from p (although it is sometimes, confusingly, defined as the negative of this). The inference principle of minimizing this, due to Kullback, is known as the Principle of Minimum Discrimination Information.

We have some testable information I about a quantity x which takes values in some interval of the real numbers (all integrals below are over this interval). We express this information as m constraints on the expectations of the functions fk, i.e. we require our probability density function to satisfy

\int p(x\mid I)f_k(x)dx = F_k \qquad k = 1, \dotsc,m.

And of course, the probability density must integrate to one, giving the constraint

\int p(x\mid I)dx = 1.

The probability density function with maximum Hc subject to these constraints is

p(x\mid I) = \frac{1}{Z(\lambda_1,\dotsc, \lambda_m)} m(x)\exp\left[\lambda_1 f_1(x) + \dotsb + \lambda_m f_m(x)\right]

with the partition function determined by

Z(\lambda_1,\dotsc, \lambda_m) = \int m(x)\exp\left[\lambda_1 f_1(x) + \dotsb + \lambda_m f_m(x)\right]dx.

As in the discrete case, the values of the \lambda_k parameters are determined by the constraints according to

F_k = \frac{\partial}{\partial \lambda_k} \log Z(\lambda_1,\dotsc, \lambda_m).

The invariant measure function m(x) can be best understood by supposing that x is known to take values only in the bounded interval (a, b), and that no other information is given. Then the maximum entropy probability density function is

p(x\mid I) = A \cdot m(x), \qquad a < x < b

where A is a normalization constant. The invariant measure function is actually the prior density function encoding 'lack of relevant information'. It cannot be determined by the principle of maximum entropy, and must be determined by some other logical method, such as the principle of transformation groups or marginalization theory.

Examples

For several examples of maximum entropy distributions, see the article on maximum entropy probability distributions.

Justifications for the principle of maximum entropy

Proponents of the principle of maximum entropy justify its use in assigning probabilities in several ways, including the following two arguments. These arguments take the use of Bayesian probability as given, and are thus subject to the same postulates.

Information entropy as a measure of 'uninformativeness'

Consider a discrete probability distribution among m mutually exclusive propositions. The most informative distribution would occur when one of the propositions was known to be true. In that case, the information entropy would be equal to zero. The least informative distribution would occur when there is no reason to favor any one of the propositions over the others. In that case, the only reasonable probability distribution would be uniform, and then the information entropy would be equal to its maximum possible value, log m. The information entropy can therefore be seen as a numerical measure which describes how uninformative a particular probability distribution is, ranging from zero (completely informative) to log m (completely uninformative).

By choosing to use the distribution with the maximum entropy allowed by our information, the argument goes, we are choosing the most uninformative distribution possible. To choose a distribution with lower entropy would be to assume information we do not possess; to choose one with a higher entropy would violate the constraints of the information we do possess. Thus the maximum entropy distribution is the only reasonable distribution.

The Wallis derivation

The following argument is the result of a suggestion made by Graham Wallis to E. T. Jaynes in 1962.[7] It is essentially the same mathematical argument used for the Maxwell–Boltzmann statistics in statistical mechanics, although the conceptual emphasis is quite different. It has the advantage of being strictly combinatorial in nature, making no reference to information entropy as a measure of 'uncertainty', 'uninformativeness', or any other imprecisely defined concept. The information entropy function is not assumed a priori, but rather is found in the course of the argument; and the argument leads naturally to the procedure of maximizing the information entropy, rather than treating it in some other way.

Suppose an individual wishes to make a probability assignment among m mutually exclusive propositions. She has some testable information, but is not sure how to go about including this information in her probability assessment. She therefore conceives of the following random experiment. She will distribute N quanta of probability (each worth 1/N) at random among the m possibilities. (One might imagine that she will throw N balls into m buckets while blindfolded. In order to be as fair as possible, each throw is to be independent of any other, and every bucket is to be the same size.) Once the experiment is done, she will check if the probability assignment thus obtained is consistent with her information. If not, she will reject it and try again. Otherwise, her assessment will be

p_i = \frac{n_i}{N}

where pi is the probability of the ith proposition, while ni is the number of quanta that were assigned to the ith proposition (if the individual in our experiment carries out the ball throwing experiment, then ni is the number of balls that ended up in bucket i).

Now, in order to reduce the 'graininess' of the probability assignment, it will be necessary to use quite a large number of quanta of probability. Rather than actually carry out, and possibly have to repeat, the rather long random experiment, the protagonist decides to simply calculate and use the most probable result. The probability of any particular result is the multinomial distribution,

Pr(\mathbf{p}) = W \cdot m^{-N}

where

W = \frac{N!}{n_1! \, n_2! \, \dotsb \, n_m!}

is sometimes known as the multiplicity of the outcome.

The most probable result is the one which maximizes the multiplicity W. Rather than maximizing W directly, the protagonist could equivalently maximize any monotonic increasing function of W. She decides to maximize

\begin{array}{rcl} \frac{1}{N}\log W &=& \frac{1}{N}\log \frac{N!}{n_1! \, n_2! \, \dotsb \, n_m!} \\ \\ &=& \frac{1}{N}\log \frac{N!}{(Np_1)! \, (Np_2)! \, \dotsb \, (Np_m)!} \\ \\ &=& \frac{1}{N}\left( \log N! - \sum_{i=1}^m \log ((Np_i)!) \right). \end{array}

At this point, in order to simplify the expression, the protagonist takes the limit as N\to\infty, i.e. as the probability levels go from grainy discrete values to smooth continuous values. Using Stirling's approximation, she finds

\begin{array}{rcl} \lim_{N \to \infty}\left(\frac{1}{N}\log W\right) &=& \frac{1}{N}\left( N\log N - \sum_{i=1}^m Np_i\log (Np_i) \right) \\ \\ &=& \log N - \sum_{i=1}^m p_i\log (Np_i) \\ \\ &=& \log N - \log N \sum_{i=1}^m p_i - \sum_{i=1}^m p_i\log p_i \\ \\ &=& \left(1 - \sum_{i=1}^m p_i \right)\log N - \sum_{i=1}^m p_i\log p_i \\ \\ &=& - \sum_{i=1}^m p_i\log p_i \\ \\ &=& H(\mathbf{p}). \end{array}

All that remains for the protagonist to do is to maximize entropy under the constraints of her testable information. She has found that the maximum entropy distribution is the most probable of all "fair" random distributions, in the limit as the probability levels go from discrete to continuous.

Compatibility with Bayes' theorem

Giffin et al. (2007) state that Bayes' theorem and the Principle of Maximum Entropy (MaxEnt) are completely compatible and can be seen as special cases of the Method of Maximum (relative) Entropy. They state that this method reproduces every aspect of orthodox Bayesian inference methods. In addition this new method opens the door to tackling problems that could not be addressed by either the MaxEnt or orthodox Bayesian methods individually. Moreover, recent contributions (Lazar 2003, and Schennach 2005) show that frequentist relative-entropy-based inference approaches (such as empirical likelihood and exponentially tilted empirical likelihood - see e.g. Owen 2001 and Kitamura 2006) can be combined with prior information to perform Bayesian posterior analysis.

Jaynes stated Bayes' theorem was a way to calculate a probability, while maximum entropy was a way to assign a prior probability distribution.[8]

It is however, possible in concept to solve for a posterior distribution directly from a stated prior distribution using the Principle of Minimum Cross Entropy (or the Principle of Maximum Entropy being a special case of using a uniform distribution as the given prior), independently of any Bayesian considerations by treating the problem formally as a constrained optimisation problem, the Entropy functional being the objective function. For the case of given average values as testable information (averaged over the sought after probability distribution), the sought after distribution is formally the Gibbs (or Boltzmann) distribution the parameters of which must be solved for in order to achieve minimum cross entropy and satisfy the given testable information. ]]>

From Wikipedia, the free encyclopedia

This article may be confusing or unclear to readers. Please help us clarify the article; suggestions may be found on the talk page. (February 2009)

Digital philosophy is a direction in philosophy and cosmology advocated by certain mathematicians and theoretical physicists, e.g., Gregory Chaitin, Seth Lloyd, Edward Fredkin, Stephen Wolfram, and Konrad Zuse (see his Calculating Space).

Contents

1 Overview

2 Digital philosophers

3 Fredkin's ideas on physics

4 Fredkin's "Five big questions with pretty simple answers"

5 Compatibility between Fredkin's ideas and M-theory

6 See also

7 References

8 External links

Overview

Digital philosophy is a modern re-interpretation of Gottfried Leibniz's monist metaphysics, one that replaces Leibniz's monads with aspects of the theory of cellular automata. Since, following Leibniz, the mind can be given a computational treatment, digital philosophy attempts to consider some main issues in the philosophy of mind. The digital approach also try to deal with the non-deterministic quantum theory; digital philosophy assumes that all information must have finite and discrete means of its representation and it assumes that the evolution of a (physical) state is governed by local, deterministic rules.[1] In a digital universe, existence and thought would consist of only computation. (However, not all computation would be thought.) Thus computation is the single substance of a monist metaphysics, while subjectivity arises from computational universality. There are many variants of digital philosophy, but most of them are digital theories that view all of physical realities and cognitive science and so on, in framework of Information theory.[1]

Digital philosophers

Rudy Rucker. In his book "Mind Tools" (1987),[2] mathematician/philosopher Rudy Rucker articulated this concept with the following conclusions about the relationship between Math and the universe. Rucker's second conclusion uses the jargon term 'fact-space' ; this is Rucker's model of reality based on the notion that all that exists is the perceptions of various observers. An entity of any kind is a glob in fact-space. The world - the collection of all thoughts and objects - is a pattern spread out through fact-space. The following conclusions describe the digital philosophy that relates the world to fact-space.

The world can be resolved into digital bits, with each bit made of smaller bits.

These bits form a fractal pattern in fact-space.

The pattern behaves like a cellular automaton.

The pattern is inconceivably large in size and dimensions.

Although the world started simply, its computation is irreducibly complex.

Edward Fredkin. In his paper "Finite Nature" (1992),[3] computer pioneer Edward Fredkin stated two fundamental laws of physical information. In terms of unsolved problems in physics these two fundamental laws have two fundamental consequences.

All information must have a digital means of its representation.

An informational process transforms the digital representation of the state of the system into its future state.

If Fredkin's first fundamental law of information is correct then Einstein's theory of general relativity theory is not entirely correct, because the theory does not rely upon digital information.

If Fredkin's second fundamental law is correct then the Copenhagen interpretation of quantum mechanics is not entirely correct, because quantum randomness lacks a digitally deterministic explanation.

Stephen Wolfram. In Chapter 9 of [4] A New Kind of Science, Stephen Wolfram presents an outline of a multiverse automaton.

Below the Planck scale, there is an informational substrate that allows the build-up of time, space, and energy by means of an updating parameter.

The updating parameter for the multiverse is analogous to time via a mathematical isomorphism, but the updating parameter involves a decomposition across alternate universes.

The informational substrate consists of network nodes that can simulate random network models and Feynman path integrals.

In physical reality, both energy and spacetime are secondary features. The most fundamental feature of reality is signal propagation caused by an updating parameter acting upon network nodes.

The multiverse automaton has a model consisting of informational substrate, an updating parameter, a few simple rules, and a method for deriving all of quantum field theory and general relativity theory,

The totally finite nature of the model implies the existence of weird, alternate-universe forces that might, or might not, be too small for empirical detection.

Fredkin's ideas on physics

Fredkin takes a radical approach to explaining the EPR paradox and the double-slit experiment in quantum mechanics. While admitting that quantum mechanics yields accurate predictions, Fredkin sides with Einstein in the Bohr-Einstein debates. In "The Meaning of Relativity", Einstein writes, "One can give good reasons why reality cannot at all be represented by a continuous field. From the quantum phenomena it appears to follow with certainty that a finite system of finite energy can be completely described by a finite set of numbers (quantum numbers). This does not seem to be in accordance with a continuum theory, and must lead to attempts to find a purely algebraic theory for the description of reality. But nobody knows how to find the basis for such a description." Einstein's hope is a purely algebraic theory, but Fredkin attempts to find a purely informational theory for the description of reality. However, physicists find some vagueness, problems with Bell theorem compatibility, and lack of empirical falsifiability in Fredkin's expression of his ideas. In "Digital Philosophy (DP)", Chapter 11,[5] Fredkin raises the question, "Could physics have a strong law of conservation of information?" Fredkin answers his own question, "If so, we have to rethink particle disintegrations, inelastic collisions and Quantum Mechanics to better understand what is happening to the information. The appearance of a single truly random event is absolutely incompatible with a strong law of conservation of information. A great deal of information is obviously associated with the trajectory of every particle and that information must be conserved. This is a big issue in DP yet such issues are seldom considered in conventional physics."

Fredkin's "Five big questions with pretty simple answers"

According to Fredkin,[6] "Digital mechanics predicts that for every continuous symmetry of physics there will be some microscopic process that violates that symmetry." Therefore, according to Fredkin, at the Planck scale, ordinary matter could have spin angular momentum that violates the equivalence principle.There might be weird Fredkin forces that cause a torsion in spacetime. The Einstein-Cartan theory extends general relativity theory to deal with spin-orbit coupling when matter with spin is present. According to conventional wisdom in physics, torsion is nonpropagating, which means that torsion will appear within a massive body and nowhere else. According to Fredkin, torsion could appear outside and around massive bodies, because alternate universes have anomalous inertial effects.

Compatibility between Fredkin's ideas and M-theory

Fredkin uses many metaphors and analogies in attempting to convey his ideas. Straightforward interpretations of Fredkin's ideas seem to violate Bell's inequalities. However, careful consideration might reveal considerable merit underlying Fredkin's metaphors.

Let us imagine that our universe consists of the following 5 components:[clarification needed]

a one-dimensional antimatter clock that measures the flow of information running backward in time;

a one-dimensional matter clock that measures the flow of information running forward in time;

a six-dimensional directional-measuring device that measures the flow of information with respect to curvature and torsion of spacetime;

a three-dimensional volume-measuring device that measures the amount of information with respect to volume;

an alternate-universe engine that runs the 4 Fredkin measuring-devices with respect to information.

Let us assume that the 'alternate-universe engine' is basically similar to the model described in Wolfram's "A New Kind of Science", Chapter 9. How might the remainder of the "Digital Mechanics" philosophy described in (1)-(4) possess a meaning in terms of M-theory?

Matrix string theory formulates M-theory as a random matrix model. M-theory might have a good approximation by a theory that has a gauge group consisting of U(N) for some large N. If such an approximation is valid, then the group U(N) might describe the 4 Fredkin measuring devices. The 6-phase clock described in Fredkin's "Digital Mechanics" might be a counting mechanism for the 6-dimensional directional-measuring device that measures the curvature and torsion of information flow. Note that all 4 of these hypothetical Fredkin measuring devices assume a notion of absolute space, time, and information that would depend upon the 'alternate-universe engine' for any empirical validity.

Fredkin's concept of the multiverse as a finite automaton with absolute space, time, and information might be isomorphic to a sheaf uniformization axiom. Such an axiom might establish a sheaf structure that supports uniform mapping of Einstein–Hilbert actions and Feynman actions across alternate universes. ]]>

Shared publicly - Yesterday 7:18 AM

Maybe It Wasn’t The Higgs Particle After All http://b4in.org/iBMm

Last year CERN announced the finding of a new elementary particle, the Higgs particle. But maybe it wasn’t the Higgs particle, maybe it just looks like it. And maybe it is not alone.

Many calculations indicate that the particle discovered last year in the CERN particle accelerator was indeed the famous Higgs particle. Physicists agree that the CERN experiments did find a new particle that had never been seen before, but according to an international research team, there is no conclusive evidence that the particle was indeed the Higgs particle.

The research team has scrutinized the existing scientific data from CERN about the newfound particle and published their analysis in the journal Physical Review D. A member of this team is Mads Toudal Frandsen, associate professor at the Center for Cosmology and Particle Physics Phenomenology, Department of Physics, Chemistry and Pharmacy at the University of Southern Denmark.

“The CERN data is generally taken as evidence that the particle is the Higgs particle. It is true that the Higgs particle can explain the data but there can be other explanations, we would also get this data from other particles”, Mads Toudal Frandsen explains.

The researchers’ analysis does not debunk the possibility that CERN has discovered the Higgs particle. That is still possible – but it is equally possible that it is a different kind of particle.

“The current data is not precise enough to determine exactly what the particle is. It could be a number of other known particles”, says Mads Toudal Frandsen.

What was it then?

But if it wasn’t the Higgs particle, that was found in CERN’s particle accelerator, then what was it?

“We believe that it may be a so-called techni-higgs particle. This particle is in some ways similar to the Higgs particle – hence half of the name”, says Mads Toudal Frandsen.

Although the techni-higgs particle and Higgs particle can easily be confused in experiments, they are two very different particles belonging to two very different theories of how the universe was created.

The Higgs particle is the missing piece in the theory called the Standard Model. This theory describes three of the four forces of nature. But it does not explain what dark matter is – the substance that makes up most of the universe. A techni-higgs particle, if it exists, is a completely different thing:

“A techni-higgs particle is not an elementary particle. Instead, it consists of so-called techni-quarks, which we believe are elementary. Techni-quarks may bind together in various ways to form for instance techni-higgs particles, while other combinations may form dark matter. We therefore expect to find several different particles at the LHC, all built by techni-quarks”, says Mads Toudal Frandsen.

New force needed for new particles

If techni-quarks exist, there must be a force to bind them together so that they can form particles. None of the four known forces of nature (gravity, the electromagnetic force, the weak nuclear force and the strong nuclear force) are any good at binding techni-quarks together. There must therefore be a yet undiscovered force of nature. This force is called the the technicolor force.

What was found last year in CERN’s accelerator could thus be either the Higgs particle of the Standard Model or a light techni-higgs particle, composed of two techni-quarks.

More http://b4in.org/iBMm ]]>

https://www.youtube.com/watch?v=TiKYvUtpJXA

Aug 07, 2009

Fundamental assumptions have an overwhelming influence on how we interpret and discuss new observations.

One such assumption that shapes our accepted view of the Universe is that gravity dominates the motion of galaxies.

It is difficult to change these types of fundamental belief systems. For example, in the time of the Hellenic astronomer Claudius Ptolemaeus, it was a widely held fundamental assumption that the Earth was the center of the cosmos. In fact, there were many good reasons to believe it. The stars, the sun, and the planets visibly move across the sky and the Earth obviously feels very solid and fixed.

According to the best thinkers at the time, the heavenly bodies were positioned on invisible spheres with as many as five spheres per planet. By allowing for spheres within spheres, one could explain the retrograde movement of the planets. To its credit, much was explained with this world-view. With Ptolemy’s sophisticated use of epicycles, deferents, and the innovative introduction of the equant, the Ptolemaic system was very successful at predicting such things as the precession of equinoxes as well as planetary motion (more so than the Copernican system when it was first developed).

However, by the sixteenth century, Galileo’s observations of the phases of Venus were completely incompatible with the Ptolemaic system. Subsequently, Kepler’s prediction of the transit of Venus in 1631 was a great success for the heliocentric, Copernican view of the solar system.

Not to be unnecessarily provocative, but there are interesting similarities between the Ptolemaic paradigm and the current theories surrounding Dark Matter and galaxies. Just as there were good reasons to believe in invisible celestial spheres driving a Geocentric Model, there are reasons to believe in invisible spheres (called “haloes”) of dark matter surrounding galaxies.

It all has to do with how the mass of a galaxy is measured. One popular approach to compute galactic mass is the orbital method. In the orbital method, the rotational velocity of stars (the red shift of radio waves from hydrogen gas around the stars) is used to infer the mass of the galaxy. The math is relatively straightforward: once the stellar orbital velocity (or “velocity dispersion” for the galaxy) and the distance from the center of the galaxy that contains the mass in question are measured, then it is easy to solve for mass. However, the math only includes gravity as the potential energy source for the system.

The problem that begets dark matter is as follows. When the mass of a galaxy with this gravity-only approach is derived, there is more computed mass than visible matter. That is, the sum of the mass of all the stars and visible dust in the galaxy is far less than the mass derived with the Orbital Method. If gravity drives the rotational velocity of the stars in the galaxy, then there must be hidden mass in the form of invisible dark matter. What if gravity is not the dominant force driving the rotational velocity of galaxies?

Today, asking this question is like asking a learned astronomer in 1550, “What if the Earth is not at the center of the cosmos?” Asserting that gravity is not a dominant dynamical force in the motion of galaxies is just as shocking to astronomers of our current time. However, there is good evidence that supports the notion that electromagnetic forces in plasma act on the cosmological scale.

Hannes Alfven (Nobel Laureate for his work in plasma physics), proposed that galaxies reside in immense, gyrating, Birkeland currents that convert large-scale electromagnetic forces into rotational energy in a galactic system. In turn, leakage currents in the galaxy are converted into rotational energy in star systems. Seminal work by Anthony Peratt (e.g. see Snell and Peratt, 1995) has shown that the flat rotational curve of galaxies is well modeled by plasma simulations without the need for dark matter. All the observations of the galactic core, the intense X-rays, gamma rays and rotational energies could be explained with sufficient current densities driving the galactic system (Peratt, 1986).

The typical flat rotational velocity curve of a galaxy does not indicate hidden dark matter mass, it indicates that another force is at work. This is why deriving the mass of a galaxy using equations that only include gravity as the source of potential energy leads to problems. Additional electromagnetic forces are at work that drive the galaxy like an electric homopolar motor (see a summary in Donald Scott’s book “The Electric Sky”). ]]>

http://luth2.obspm.fr/~luthier/nottale/arEDU08.pdf

Scale relativity and fractal space-time: theory and

applications

Laurent Nottale

CNRS, LUTH, Paris Observatory and Paris-Diderot University

92190 Meudon, France

laurent.nottale@obspm.fr

May 29, 2009

Abstract

In the first part of this contribution, we review the development of the theory of

scale relativity and its geometric framework constructed in terms of a fractal and

nondifferentiable continuous space-time. This theory leads (i) to a generalization

of possible physically relevant fractal laws, written as partial differential equation

acting in the space of scales, and (ii) to a new geometric foundation of quantum

mechanics and gauge field theories and their possible generalisations.

In the second part, we discuss some examples of application of the theory to

various sciences, in particular in cases when the theoretical predictions have been

validated by new or updated observational and experimental data. This includes

predictions in physics and cosmology (value of the QCD coupling and of the cosmological

constant), to astrophysics and gravitational structure formation (distances of

extrasolar planets to their stars, of Kuiper belt objects, value of solar and solar-like

star cycles), to sciences of life (log-periodic law for species punctuated evolution,

human development and society evolution), to Earth sciences (log-periodic deceleration

of the rate of California earthquakes and of Sichuan earthquake replicas, critical

law for the arctic sea ice extent) and tentative applications to systems biology.

1 Introduction

One of the main concern of the theory of scale relativity is about the foundation of

quantum mechanics. As it is now well known, the principle of relativity (of motion)

underlies the foundation of most of classical physics. Now, quantum mechanics, though it

is harmoniously combined with special relativity in the framework of relativistic quantum

mechanics and quantum field theories, seems, up to now, to be founded on different

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grounds. Actually, its present foundation is mainly axiomatic, i.e., it is based on postulates

and rules which are not derived from any underlying more fundamental principle.

The theory of scale relativity [67, 68, 69, 72, 79, 95] suggests an original solution to

this fundamental problem. Namely, in its framework, quantum mechanics may indeed be

founded on the principle of relativity itself, provided this principle (applied up to now to

position, orientation and motion) be extended to scales. One generalizes the definition of

reference systems by including variables characterizing their scale, then one generalizes the

possible transformations of these reference systems by adding, to the relative transformations

already accounted for (translation, velocity and acceleration of the origin, rotation

of the axes), the transformations of these scale variables, namely, their relative dilations

and contractions. In the framework of such a newly generalized relativity theory, the laws

of physics may be given a general form that transcends and includes both the classical and

the quantum laws, allowing in particular to study in a renewed way the poorly understood

nature of the classical to quantum transition.

A related important concern of the theory is the question of the geometry of space-time

at all scales. In analogy with Einstein’s construction of general relativity of motion, which

is based on the generalization of flat space-times to curved Riemannian geometry, it is

suggested, in the framework of scale relativity, that a new generalization of the description

of space-time is now needed, toward a still continuous but now nondifferentiable and fractal

geometry (i.e., explicitly dependent on the scale of observation or measurement). New

mathematical and physical tools are therefore developed in order to implement such a generalized

description, which goes far beyond the standard view of differentiable manifolds.

One writes the equations of motion in such a space-time as geodesics equations, under the

constraint of the principle of relativity of all scales in nature. To this purpose, covariant

derivatives are constructed that implement the various effects of the nondifferentiable and

fractal geometry.

As a first theoretical step, the laws of scale transformation that describe the new

dependence on resolutions of physical quantities are obtained as solutions of differential

equations acting in the space of scales. This leads to several possible levels of description

for these laws, from the simplest scale invariant laws to generalized laws with variable

fractal dimensions, including log-periodic laws and log-Lorentz laws of “special scalerelativity”,

in which the Planck scale is identified with a minimal, unreachable scale,

invariant under scale transformations (in analogy with the special relativity of motion in

which the velocity c is invariant under motion transformations).

The second theoretical step amounts to describe the effects induced by the internal

fractal structures of geodesics on motion in standard space (of positions and instants).

Their main consequence is the transformation of classical dynamics into a generalized,

quantum-like self-organized dynamics. The theory allows one to define and derive from

relativistic first principles both the mathematical and physical quantum tools (complex,

spinor, bispinor, then multiplet wave functions) and the equations of which these wave

functions are solutions: a Schrodinger-type equation (more generally a Pauli equation

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for spinors) is derived as an integral of the geodesic equation in a fractal space, then

Klein-Gordon and Dirac equations in the case of a full fractal space-time. We then briefly

recall that gauge fields and gauge charges can also be constructed from a geometric reinterpretation

of gauge transformations as scale transformations in fractal space-time.

In a second part of this review, we consider some applications of the theory to various

sciences, particularly relevant to the questions of evolution and development. In the

realm of physics and cosmology, we compare the various theoretical predictions obtained

at the beginning of the 90’s for the QCD coupling constant and for the cosmological

constant to their present experimental and observational measurements. In astrophysics,

we discuss applications to the formation of gravitational structures over many scales, with

a special emphasis on the formation of planetary systems and on the validations, on the

new extrasolar planetary systems and on Solar System Kuiper belt bodies discovered since

15 years, of the theoretical predictions of scale relativity (made before their discovery).

This is completed by a validation of the theoretical prediction obtained some years ago

for the solar cycle of 11 yrs on other solar-like stars whose cycles are now measured. In

the realm of life sciences, we discuss possible applications of this extended framework to

the processes of morphogenesis and the emergence of prokaryotic and eukaryotic cellular

structures, then to the study of species evolution, society evolution, embryogenesis and

cell confinement. This is completed by applications in Earth sciences, in particular to

a prediction of the Arctic ice rate of melting and to possible predictivity in earthquake

statistical studies.

2 Theory

2.1 Foundations of scale relativity theory

The theory of scale relativity is based on the giving up of the hypothesis of manifold

differentiability. In this framework, the coordinate transformations are continuous but

can be nondifferentiable. This implies several consequences [69], leading to the following

steps of construction of the theory:

(1) One can prove the following theorem [69, 72, 7, 22, 23]: a continuous and nondifferentiable

curve is fractal in a general meaning, namely, its length is explicitly dependent

on a scale variable ε, i.e., L = L(ε), and it diverges, L → ∞, when ε → 0. This theorem

can be readily extended to a continuous and nondifferentiable manifold, which is therefore

fractal, not as an hypothesis, but as a consequence of the giving up of an hypothesis (that

of differentiability).

(2) The fractality of space-time [69, 105, 66, 67] involves the scale dependence of

the reference frames. One therefore adds to the usual variables defining the coordinate

system, new variables ε characterizing its ‘state of scale’. In particular, the coordinates

themselves become functions of these scale variables, i.e., X = X(ε).

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(3) The scale variables ε can never be defined in an absolute way, but only in a relative

way. Namely, only their ratio ρ = ε′/ε does have a physical meaning. In experimental

situations, these scales variables amount to the resolution of the measurement apparatus

(it may be defined as standard errors, intervals, pixel size, etc...). In a theoretical analysis,

they are the space and time differential elements themselves. This universal behavior leads

to extend the principle of relativity in such a way that it applies also to the transformations

(dilations and contractions) of these resolution variables [67, 68, 69]. ]]>