## What Quantum Mechanics and Chaos Theory Teach us about PEMF and Energy Medicine.

1) In the world of the quantum FREQUENCY matters, not intensity. Intensities are complex amplitudes that squared give a probability of measuring an observable.

You do not need higher intensity, the key is frequency resonance

2) In a quantum and chaotic system, small inputs can be amplified and have large effects.

Again finesse over force

3) The human body is holographic and fractal in space and also in time.

Branching of arteries, bronchioles, nerves are fractal branches.

Body fractal in time when looking at the bodies many rhythms like heartrate, breathing rate, electrical activity in the brain and more.

It turns out in many cases, chaos is healthy where order is unhealthy (heart rhythms and brain waves for example).

4) Butterfly effect in Chaos, small changes can produce big differences. If there is a strange attractor relating to overall health of the body, only gentle nudges would be needed to bring it back into balance.

Related to PEMF, low intensity, earth frequency devices are based on modern quantum and chaos theory, work with the body and assist the body in its ability to heal itself.

You do not need higher intensity, the key is frequency resonance

2) In a quantum and chaotic system, small inputs can be amplified and have large effects.

Again finesse over force

3) The human body is holographic and fractal in space and also in time.

Branching of arteries, bronchioles, nerves are fractal branches.

Body fractal in time when looking at the bodies many rhythms like heartrate, breathing rate, electrical activity in the brain and more.

It turns out in many cases, chaos is healthy where order is unhealthy (heart rhythms and brain waves for example).

4) Butterfly effect in Chaos, small changes can produce big differences. If there is a strange attractor relating to overall health of the body, only gentle nudges would be needed to bring it back into balance.

Related to PEMF, low intensity, earth frequency devices are based on modern quantum and chaos theory, work with the body and assist the body in its ability to heal itself.

## Quantum Chaos

Universe to solar system to everyday scale to microscopic realm

Amazing scientific stew of QM and Chaos

Don't mix that easily.

electronic devices, art, greatest mystery in math.

Why are they not kindred spirits

They both highlight the unpredictibility of nature and the limits of human knowledge.

In that way they seem like bedfellows.

The frenzied motion of atoms

At a deeper level their are

1) Chaos is founded by a deterministic worldview, where the future is determined by the present.

Only one thing can happen. Given current conditions of the universe, there is one unique future.

Quantum theory sees the world as probability, there is no certainty, there is only probability.

Nothing is certain to happen. Probability of finding an electron at a certain place at a certain time.

2) Chaos is forbidden in quantum mechanics.

Differential equation at the heart of quantum theory which describes everything as a blurr of probability waves.

Their are waves that control these probabilities (find electron at a certain place with a certain speed, energy, etc.

The waves themselves change and evolve, deterministically it turns out. Interesting paradox.

Although the interpretation of these waves is in terms of probability, their evolution the waves evolve is deterministic.

Because Schrodinger equation is linear, it cannot in itself give rise to chaos.

3) Uncertainty principle... Making simultaneous measurements of a certain type.

Cannot measure both position and velocity simultaneous.

You can push one uncertainty down but the other one goes up...

No way around it, it is built into the fabric of mathematics and the universe.

Cannot measure position and velocity.

It destroys our whole concept of state space...

What is state space?

It is the amount of information you need to predict the future of a deterministic system.

State of pendulum, initial angle and initial velocity... Need both.

Heisenberg will NOT PERMIT THIS!!

It's true in ALL of classical theory that we cannot have the two things we need to predict the future.

We are not allowed to have the 2 things we need.

States and trajectories in QM become blurry and ill defined once we get to the atomic scale where quantum structure.

The fine structure we need for chaos gets smoothed out and washed away by quantum mechanics.

For all these reasons Quantum Chaos should not exist

Amazing scientific stew of QM and Chaos

Don't mix that easily.

electronic devices, art, greatest mystery in math.

Why are they not kindred spirits

They both highlight the unpredictibility of nature and the limits of human knowledge.

In that way they seem like bedfellows.

The frenzied motion of atoms

At a deeper level their are

1) Chaos is founded by a deterministic worldview, where the future is determined by the present.

Only one thing can happen. Given current conditions of the universe, there is one unique future.

Quantum theory sees the world as probability, there is no certainty, there is only probability.

Nothing is certain to happen. Probability of finding an electron at a certain place at a certain time.

2) Chaos is forbidden in quantum mechanics.

Differential equation at the heart of quantum theory which describes everything as a blurr of probability waves.

Their are waves that control these probabilities (find electron at a certain place with a certain speed, energy, etc.

The waves themselves change and evolve, deterministically it turns out. Interesting paradox.

Although the interpretation of these waves is in terms of probability, their evolution the waves evolve is deterministic.

Because Schrodinger equation is linear, it cannot in itself give rise to chaos.

3) Uncertainty principle... Making simultaneous measurements of a certain type.

Cannot measure both position and velocity simultaneous.

You can push one uncertainty down but the other one goes up...

No way around it, it is built into the fabric of mathematics and the universe.

Cannot measure position and velocity.

It destroys our whole concept of state space...

What is state space?

It is the amount of information you need to predict the future of a deterministic system.

State of pendulum, initial angle and initial velocity... Need both.

Heisenberg will NOT PERMIT THIS!!

It's true in ALL of classical theory that we cannot have the two things we need to predict the future.

We are not allowed to have the 2 things we need.

States and trajectories in QM become blurry and ill defined once we get to the atomic scale where quantum structure.

The fine structure we need for chaos gets smoothed out and washed away by quantum mechanics.

For all these reasons Quantum Chaos should not exist

Links the realm of reality... Atoms berock of reality

Imagination - pure number theory. Prime numbers are the "atoms" or building blocks of numbers.

Number theory - An old question is, can we find a formula for prime numbers.

Divisble by one and itself.

Formula for the next prime number.

Can we understand statistics of prime... Sometimes big space... Rules governing spacing.

How many prime numbers are between 1 and 100... = 25

Primes become rarer...

Staircase structure.. Counts always goes up by one.

Gauss - Trend Line

Number of Prime numbers less than N = N/logN

Imagination - pure number theory. Prime numbers are the "atoms" or building blocks of numbers.

Number theory - An old question is, can we find a formula for prime numbers.

Divisble by one and itself.

Formula for the next prime number.

Can we understand statistics of prime... Sometimes big space... Rules governing spacing.

How many prime numbers are between 1 and 100... = 25

Primes become rarer...

Staircase structure.. Counts always goes up by one.

Gauss - Trend Line

Number of Prime numbers less than N = N/logN

## Riemann - Improved Formula

Can we improve over the trend line.

Riemann - Found a stunning formula for the staircase part.

The wave = "the music of the primes"

If added enough if it would exactly match the prime.

Riemann Hypothesis -

Music is made of waves

Proving Riemanns Hypothesis is greatest unsolved problem in math. Which frequencies.

Prime numbers encoded in a discrete set of frequencies.

Zeros of the Riemann Zeta function are the magic frequencies.

The frequencies of the Riemann waves look uncannily like the frequencies of a quantum chaotic system.

That is the BIG POINT.

There is some chaotic system whose quantum counterpart would hold the secret to the music of the primes.

Riemann - Found a stunning formula for the staircase part.

The wave = "the music of the primes"

If added enough if it would exactly match the prime.

Riemann Hypothesis -

Music is made of waves

Proving Riemanns Hypothesis is greatest unsolved problem in math. Which frequencies.

Prime numbers encoded in a discrete set of frequencies.

Zeros of the Riemann Zeta function are the magic frequencies.

The frequencies of the Riemann waves look uncannily like the frequencies of a quantum chaotic system.

That is the BIG POINT.

There is some chaotic system whose quantum counterpart would hold the secret to the music of the primes.

**The atoms of arithmetic , prime numbers are connected to the atoms of reality.**

And the link between them is CHAOS.And the link between them is CHAOS.

## So what is quantum chaos?

What we

Quantum signatures of deterministic chaos.

Classical system that is chaotic.

Now we shrink the chaotic system down to the atomic size...

Is there any vestige or signature of chaos in the quantum realm.

billiards...

Particle moving in straight lines on a frictionless pool table.

Bounces of cushions... Perfectly elastic... So bounces off forever.

What are the trajectories in the long run.

Simple shape... Motion stays regular... Two balls start close together... Stay together very long time.

Ball in stadium shape... Rapidly exponentially diverge.

Sensitive dependence on initial conditions. Trademark of chaos.

Think of a trajectory as a blurry probability wave, a kind of fuzz around what was once a classical trajectory.

Where the wave is most likely to be found... Expected values.

You can think of a wave...

In circlular pool table... You have waves and its like

Nodes of vibration is where there is no vibration... that is where sand collects.

Very regular looking.

Do same experiement with stadium shape.

Thought there would be random wave patterns... speckled

The speckle effect is a result of the interference of many waves of the same frequency, having different phases and amplitudes, which add together to give a resultant wave whose amplitude, and therefore intensity, varies randomly.

Chaos is poised between randomness and regularity

Perfectly repeating trajectory... They are rare and unstable trajectories, but they leave their mark,

because they leave scars (Heller).

Classical particle

Quantum signatures of deterministic chaos.

Classical system that is chaotic.

Now we shrink the chaotic system down to the atomic size...

Is there any vestige or signature of chaos in the quantum realm.

billiards...

Particle moving in straight lines on a frictionless pool table.

Bounces of cushions... Perfectly elastic... So bounces off forever.

What are the trajectories in the long run.

Simple shape... Motion stays regular... Two balls start close together... Stay together very long time.

Ball in stadium shape... Rapidly exponentially diverge.

Sensitive dependence on initial conditions. Trademark of chaos.

Think of a trajectory as a blurry probability wave, a kind of fuzz around what was once a classical trajectory.

Where the wave is most likely to be found... Expected values.

You can think of a wave...

In circlular pool table... You have waves and its like

Nodes of vibration is where there is no vibration... that is where sand collects.

Very regular looking.

Do same experiement with stadium shape.

Thought there would be random wave patterns... speckled

The speckle effect is a result of the interference of many waves of the same frequency, having different phases and amplitudes, which add together to give a resultant wave whose amplitude, and therefore intensity, varies randomly.

Chaos is poised between randomness and regularity

Perfectly repeating trajectory... They are rare and unstable trajectories, but they leave their mark,

because they leave scars (Heller).

Classical particle

## Three Types of Chaos

Three types of chaos. Computer models of (from top to bottom) a random wave, spinning rotators, and electron flow. The random wave is the random addition of waves, an example of quantum chaos. A simple rotator is three or more rods connected at their ends to allow them to rotate independently about these connection points. This independent rotation is an example of classical chaos. The branching lines are the tracks of electrons moving chaotically under classical laws. The colours show the angles at which they were launched. Chaos is observed when patterns emerge from complex dynamic systems with unpredictable behaviour. These models form an artwork by Professor Eric Heller.

## Scarred Quantum Wave

Scarred quantum wave. Computer model showing the paths taken by a wave trapped inside a stadium- shaped cavity. The paths show the movement of a particle which is behaving like a wave (showing wave-particle duality), as it bounces around the cavity. The pattern has features characteristic of classical and quantum mechanics. It is similar to a random quantum wave, formed by randomly adding together waves travelling in all directions. However, it is known as a scarred quantum wave, because it features classical periodic orbits (repeating paths) which give it symmetry, forming a double diamond". Modelled by Professor Eric Heller at Harvard University, USA."

## Classical and Quantum Chaos - Eric Heller

Computer models of two types of chaos. The sphere (upper left) is a random wave, an example of quantum chaos. It is formed by the random addition of quantum waves. At lower right, the branching lines are the tracks of electrons spreading out under the influence of a random electrical landscape. The different colours show the angles at which electrons were launched from the starting point. Chaos is observed when patterns emerge from complex dynamic systems with unpredictable behaviour. The models were produced as artworks by Professor Eric Heller.

## Classical and Quantum Physics

Classical to quantum physics. Sequence of computer models showing the progression from classical to quantum physics. At top left, the movement of a classical particle, such as an electron, is shown. In classical physics, the position and trajectory of the particle can be precisely described, along with its energy. In quantum physics, the position and energy cannot be known at the same time. The particle is considered to be spread over a volume (progressively shown towards bottom right), with its position described by probabilities. It will also have wave properties the colours show the varying phase of the wave. This model was created as an artwork by Professor Eric Heller.

Trajectory threads like crochet..

Visualize how classical

Rosetta

Correspondance.

Minature quantum dots.

Electrons act as pure waves at low temperature.

Trajectory threads like crochet..

Visualize how classical

Rosetta

Correspondance.

Minature quantum dots.

Electrons act as pure waves at low temperature.

## Quantum Waves 1

Quantum waves. Computer model showing many wave paths superimposed onto the surface of a sphere. The paths simulate the motion of a particle which is behaving like a wave (wave-particle duality). Quantum theory states that as the particle moves it creates many wave trains", which can collide to produce one random quantum wave, an example of quantum chaos. Chaos in classical mechanics would result in waves travelling in all possible directions randomly, whereas in quantum mechanics, chaos is approached when the waves are added together randomly. The waves were modelled by Professor Eric Heller, Harvard University, USA."

## Quantum Waves 2

Quantum waves. Computer model showing the movement of many waves (wave paths, intersecting blue and purple lines). The paths represent the motion of particles which are behaving like waves (wave-particle duality). Quantum theory states that the waves associated with the moving particles can collide to produce one random quantum wave, made up of waves moving in all directions. The particles travel from the top of the image downwards, stopping when they reach the pink line in the lower frame. The waves were modelled by Professor Eric Heller, Harvard University, Cambridge, Massachusetts, USA.

## Electron Flow

Electron flow. Computer model representing the flow of electron particles through a two- dimensional electron gas (2DEG). The 'gas' is composed of many free electrons, which can move around in only one plane. The 2DEG possesses an electric potential. Irregularities in this potential produce a 'bumpy' surface. The model shows the paths taken by electrons released one at a time into the gas. The negatively-charged electrons were deflected by the bumps in the gas, producing an intricate branching pattern. The electron flow was modelled by Professor Eric Heller, Harvard University, Cambridge, Massachusetts, USA.

## Quantum Resonance

Quantum resonance. Computer model showing quantum resonance. A quantum wavefunction is seen as the parallel waves moving up from bottom. They hit a barrier (black, lower centre). The wavefunction, which describes a particle such as an electron, diffracts through the central hole in the barrier. The waves then reflect from the next, semicircular barrier, and bounce around in the cavity. Usually, only small amounts of waves go through the hole, but if the wavelength matches the size of the cavity, then electrons of that wavelength (energy) accumulate (resonate) in the cavity. Some waves (green) diffract past the barriers. This model was created as an artwork by Professor Eric Heller.

Heisenberg Uncertainty also illustrated..

Below slit definite momentum, uncertain position

At slit, definite position, uncertain momentum

Heisenberg Uncertainty also illustrated..

Below slit definite momentum, uncertain position

At slit, definite position, uncertain momentum

## Quasicrystal

Quasicrystal. Computer model of a quasicrystal generated by the addition of nine equally-spaced particles behaving like waves (showing wave- particle duality). The waves met at the centre of the yellow sun", producing a quasicrystal. Within the sun the pattern approximates to a mathematical Bessel function; there is regular repetition, concentric circles forming about the centre. As the pattern moves outwards from the sun, this order is lost, with similar structures appearing at irregular intervals. The yellow "slice" is one repeating unit of the pattern. The quasicrystal was modelled by Professor Eric Heller, Harvard University, USA."

## Wave Energy

Wave energy. Computer simulation showing ray trajectories traveling at different speeds through a random, weakly deflecting medium in a three-dimensional plane. The rays are analogous to ocean waves and the deflecting medium act in a similar way to ocean eddies. The eddies act as an optic lens and cause refraction of the waves resulting in areas of concentrated energy. This is visible as a pattern of twisting and branching known as caustics. It is believed that caustics resulting from strong ocean eddies interacting with wave action may be the cause of giant ocean waves known as freak, or rogue waves. Such waves have been reported to reach as high as 30 meters and have been blamed for the disappearance of some ships. Simulation created by Eric Heller, Professor of Physics at Harvard University, Massachusetts, USA.

Caustics can give rise to cusp singularities.

Caustics can give rise to cusp singularities.