Archive for the ‘Physics’ Category

Noether-Pauli-Jung

March 29, 2018

What happens when the fourfold of Noether’s Theorem is spliced together with the fourfold of Pauli-Jung? Both have Space-Time and Matter-Energy. The former has Conservation and Symmetry, and the latter has Causality and Synchronicity.

I had to remind myself that Conservation means consistency (of matter or energy) through time (and space), and Symmetry means consistency (of form) through space (and time), so in some sense they are dualistic.

Combined, one has the three axes of dual concepts, represented above.

Further Reading:

https://equivalentexchange.wordpress.com/2012/05/04/noethers-theorem/

https://equivalentexchange.wordpress.com/2018/01/23/atom-and-archetype/

[*10.68]

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Atom and Archetype

January 23, 2018

A few weeks ago I ran across this nice review of the book Atom and Archetype: the Pauli-Jung letters 1932-1958. This is a collection of letters exchanged between psychiatrist Carl Jung and physicist Wolfgang Pauli over a course of years. Evidently, Pauli was quite the metaphysician and Jung was intrigued by Einstein’s physics of relative space and time. Together in dialectic they argued and struggled to join together the disparate notions of mind and matter.

What mainly caught my eye was a diagram that I’ve slightly altered and shown above. I’ve mainly just replaced energy with matter-energy for two reasons: first because matter and energy are inter-convertible and second because matter conditions space. This results in similarity to the fourfold diagram for Lucretius that I’ve shown before, consisting of Particles, the Void, Falling, and Swerving.

Further Reading:

https://www.brainpickings.org/2017/03/09/atom-and-archetype-pauli-jung/

Carl Jung and Wolfgang Pauli / Atom and Archetype: the Pauli-Jung letters 1932-1958, Princeton University Press; Updated edition (July 21, 2014)

https://www.amazon.com/Atom-Archetype-Pauli-Letters-1932-1958/dp/069116147X/ref=sr_1_1?s=books&ie=UTF8&qid=1516537804&sr=1-1&keywords=atom+and+archetype

https://equivalentexchange.wordpress.com/2011/10/10/lucretius-on-the-nature-of-things/

https://equivalentexchange.wordpress.com/2014/02/17/matter-energy-space-and-time/

https://equivalentexchange.wordpress.com/2015/01/16/wave-particle-duality/

https://equivalentexchange.wordpress.com/2012/05/04/noethers-theorem/

[*10.60]

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A Rosetta Stone

December 6, 2017

Abstract of Physics, Topology, Logic and Computation: A Rosetta Stone by John Baez and Michael Stay:

In physics, Feynman diagrams are used to reason about quantum processes. In the 1980s, it became clear that underlying these diagrams is a powerful analogy between quantum physics and topology: namely, a linear operator behaves very much like a “cobordism”. Similar diagrams can be used to reason about logic, where they represent proofs, and computation, where they represent programs. With the rise of interest in quantum cryptography and quantum computation, it became clear that there is extensive network of analogies between physics, topology, logic and computation. In this expository paper, we make some of these analogies precise using the concept of “closed symmetric monoidal category”. We assume no prior knowledge of category theory, proof theory or computer science.

  • Physics
  • Logic
  • Topology
  • Computation

Perhaps Category Theory is a “Fifth Essence”?

Further Reading:

http://math.ucr.edu/home/baez/rosetta/rose3.pdf

https://arxiv.org/abs/0903.0340

[*9.168, *10.50]

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The Sackur-Tetrode Equation

May 18, 2015

sq_sackur_tetrode

The Sackur-Tetrode Equation expresses the entropy of a monatomic classical ideal gas. Including quantum aspects of the system gives this formula a more detailed description than it would have otherwise. Above I’ve tried to represent the four uncertainties that constitute the equation in its information theoretic version: positional, momenta, quantum, and identity.

From Wikipedia:

In addition to using the thermodynamic perspective of entropy the tools of information theory can be used to provide an information perspective of entropy. The physical chemist Arieh Ben-Naim rederived the Sackur–Tetrode equation for entropy in terms of information theory, and in doing so he tied in well known concepts from modern physics. He showed the equation to consist of the sum of four entropies (missing information) due to positional uncertainty, momenta uncertainty, the quantum mechanical uncertainty principle and the indistinguishability of the particles.

http://en.wikipedia.org/wiki/Sackur%E2%80%93Tetrode_equation

http://en.wikipedia.org/wiki/Entropy_%28information_theory%29

[*9.4]

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Wave-Particle Duality

January 16, 2015

sq_wave_particle_dualityIs the fundamental nature of light and matter more like a wave or is it more like a particle? After hundreds of years of scientific research the answer is … Yes! Light and matter have aspects of both: sometimes one and sometimes the other. Kind of like that duck-rabbit illusion where the drawing flips back and forth between a duck or a rabbit.

Now that we have the irreconcilable duality of wave and particle, can we add to the confusion and enlarge it into a four-fold? Two additional aspects (from physics) come to mind: motions, as in the motions of particles, and fields, as in electric and magnetic fields.

We immediately can see this four-fold as a play of dimensions: (idealized) particles have 0 dimensions, motions have 1 (along a path), waves have 2 (or more), fields have 3 (or more).

sq_lucretiusWe can also see this four-fold in a weak analogy with the Four Elements: particles for earth, waves for water, motions for fire, and fields for air (or space). Also compare to the four-fold for Lucretius!

Should fields above be replaced with wave-functions? I guess a wave-function is a kind of field of probabilities of existence over space and time, so perhaps it makes no difference!

Links:

http://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality

http://en.wikipedia.org/wiki/Field_%28physics%29

http://en.wikipedia.org/wiki/Rabbit%E2%80%93duck_illusion

http://dl.acm.org/citation.cfm?id=2811288&picked=formats

Charis Anastopoulos / Particle or Wave: The Evolution of the Concept of Matter in Modern Physics

Notes:

I like Forces better than Motions.

[*7.152, *8.32]

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Maxwell’s Equations

August 17, 2014

sq_maxwell_eq2

Actually, just the left hand side of the equations, because it looks better that way. The right hand sides are just a click away.

E and B are the electric and magnetic fields, respectively. is the “del” operator.

The divergences ∇ · E and ∇ · B are the “fields emanating from the sources.”

The curls ∇ x E and ∇ x B are the “circulation of the fields.”

http://en.wikipedia.org/wiki/Maxwell%27s_equations

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Matter, Energy, Space, and Time

February 17, 2014

sq_MESTHere’s a nice little fourfold that I’ve overlooked until now, kind of like a four-leaf clover. If you search for images of matter, energy, space, and time, several websites show a diagram quite similar to this, and some have interesting things to say.

One shows free energy instead of energy in general. Free energy is energy that is able to do work, and that is an important distinction, especially if you are thinking about the Four Causes. Then the four can be considered fundamental resources.

There are some other things to consider from these references. One is that there is the familiar equivalence between matter and energy. Another is the equivalence principle between gravity and acceleration.

Also, there are obvious analogies between this fourfold and the Four Elements and the Four States of Matter. sq_Noether's TheoremI have also used the pairs space-time and matter-energy as two parts of the fourfold Noether’s Theorem, the other two parts being symmetry and conservation. There is also the fourfold Spacetime that has some similarities to this one. And let’s not forget the atomism of On the Nature of Things by Lucretius.

Be sure and watch the upcoming television series Cosmos: a Spacetime Odyssey, hosted by Neil deGrasse Tyson. I’m sure there will be much talk of Matter, Energy, Space, and Time.

Notes:

There is even a term coined for Matter-Energy-Space-Time: MEST. Of course, MEST also stands for Math, Engineering, Science, and Technology! No, sorry, that’s STEM!

http://lornaalkana.com/portfolio/graphic-design/ticket-space-time-energy-matter/

Links:

http://abyss.uoregon.edu/~js/ast123/lectures/lec09.html

http://www.zamandayolculuk.com/cetinbal/htmldosya1/ModernScience.htm

http://billmoyers.com/2014/01/10/the-new-cosmos-a-spacetime-odyssey/

[*7.90, *8.32]

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States of Matter

August 22, 2013

states_of_matterThe four most familiar states of matter are solid, liquid, gas, and plasma. Other states exist (such as Bose-Einstein condensates), but if I talk about them I couldn’t put them into a nice fourfold.

Note that the sequence of plasma, gas, liquid, and solid is arranged in the order of highest to lowest temperature (usually). Compare this to the classical Four Elements of Empedocles (Fire, Air, Water, and Earth) and to the made-up fourfold of Bright-to-Dark, based on light.

http://en.wikipedia.org/wiki/State_of_matter

http://www.chem4kids.com/files/matter_states.html

http://gizmodo.com/there-are-way-more-than-three-states-of-matter-1182677930

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Light and Dark: Matter and Energy

June 21, 2013

light_and_dark_matter_and_energy

What are dark matter and dark energy? We do not know; we just know of them by their effects.

Dark matter is thought to be present in halos around galaxies since the estimated amount of matter is too small to keep the galaxies rotating at their measured rate. Dark energy is thought to be present in the empty spaces between galaxies pushing them apart because the velocities separating them are actually increasing instead of slowing down. Nobody knows what dark matter and dark energy really are, but new theories are often being suggested. Perhaps one of these theories will be tested soon and we will have a better idea of what these mysterious materials and forces are.

Could it be that dark matter and dark energy are linked by an equation, like normal “light” matter and “light” energy? For ordinary matter and energy, which are really two aspects of the same thing, it is Einstein’s famous equation: E= m*c^2. But since we have no idea what the dark stuff is, we can only conjecture.

Why should we care what these things are that are so difficult to characterize? In any scientific investigation, if we have gaps and inconsistencies in our knowledge and our theories it just bothers us to no end. We’re just not happy until we figure out the puzzle. In this case, the universe is almost completely made up of these dark parts, so it seems pretty important.

Unfortunately in my diagram the horizontal axis is light energy-dark energy, which is separating, and the vertical axis is dark matter-light matter, which is combining. In many of my fourfolds the horizontal axis is combining or conjunctive and the vertical axis is separating or disjunctive. Is the energy-matter dual more important than the conjunctive-disjunctive dual? Perhaps this fourfold doesn’t really fit but I like it anyway.

http://en.wikipedia.org/wiki/Dark_matter

http://en.wikipedia.org/wiki/Dark_energy

http://science.nasa.gov/astrophysics/focus-areas/what-is-dark-energy/

http://science.nationalgeographic.com/science/space/dark-matter/

http://hetdex.org/dark_energy/dark_matter.php

Eric Chaisson / Epic of Evolution

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The Four Laws of Thermodynamics

May 24, 2013

four_laws_of_thermodynamics0th Law: Heat doesn’t flow between objects of the same temperature.

1st Law: Heat cannot be created or destroyed.

2nd Law: Entropy increases by the flow of heat in a closed system not in equilibrium.

3rd Law: Entropy approaches a constant minimum in a system as temperature approaches absolute zero.

References:

http://www.ridgenet.net/~do_while/sage/v7i1f.htm

http://www.physicsforidiots.com/thermodynamics.html

http://en.wikipedia.org/wiki/Laws_of_thermodynamics

Peter Atkins / Four Laws That Drive the Universe

[*3.169, *7.164]

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