Archive for the ‘Physics’ Category

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

[*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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Schrödinger’s Cat

January 11, 2013

schrodingers_catNow let’s look at another thought experiment, that of Schrödinger’s Cat. This thought experiment is supposed to confound the micro and macro worlds of quantum physics and ordinary, human-size physics. A cruel device is built consisting of a closed box which contains a sample of radioactive material, a mechanism to release poison into the box if an atom of the radioactive material decays, a living cat, and a door that must be opened to reveal the condition of the cat to an external observer.

The story of the experiment goes that if the observer waits to open the box until there is a 50% probability that an atom decays, the state of the cat (hidden in the unopened box) to the observer will be both alive and dead. The cat’s so-called wave-function will be a superposition of the wave-function of a live cat and that of a dead cat, which will collapse into one or the other only by the opening of the door and the observation of the actual condition of the cat. This is called the Copenhagen Interpretation.

Some say that the detector of the poison release mechanism will be the true observer in this experiment, and before the external observer opens the door the cat will be definitely alive or dead because of the action of the mechanism. This might be considered the objective collapse theory. Others say that the world splits in two between a world where the cat is alive and one where the cat is dead. This is called a many-worlds interpretation.

There seems to me a similarity between Maxwell’s Demon and Schrödinger’s Cat. The fourfold elements of the experiment are shown above, but now consider these elements in a system in terms of Aristotles’s Four Causes. The material causes are the discreet constituents of the experiment, everything from box to atoms to cat to observer. The efficient cause is the decay or non-decay of a radioactive atom. The final cause is action of the observer in opening the box. The formal cause is the poor cat in its ambiguous state, simultaneously both dead or alive.

It doesn’t make too much common sense to say that the opening of the box and the observing of the cat “causes” the atom to have really decayed or not, and so concretize the past and the cat into a certain way of being, but that is mostly what the Copenhagen Interpretation is saying. Indeed, Linear Logic, which has been described many times on this blog, has been used to describe aspects of quantum physics for decades.

References:

http://en.wikipedia.org/wiki/Schr%C3%B6dinger%27s_Cat

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

[*7.138]

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Maxwell’s Demon

December 17, 2012

maxwells_demonI am currently reading Tor Norretranders “The User Illusion”, and he opens the book with chapters on information theory and thermodynamics. His description of the thought experiment “Maxwell’s Demon” made me realize that this system has all the ingredients of a fourfold: the two chambers, the demon, the door between the two chambers that the demon operates, and the molecules that the demon allows to or prevents from passing through the door from one chamber to another. The only way between the two chambers is through the door. The molecules are in a gaseous state, with a distribution of velocities, so some are moving faster than others.

The major physical action that the demon can perform is to open or close the door. If the demon did this randomly, it would accomplish nothing, and the system would ultimately evolve the same as one without door or demon. Instead the demon is able to open and close the door so as to allow faster molecules to collect in one chamber and slower molecules to collect in the other. The demon doesn’t touch the molecules, but he is somehow able to tell whether a molecule is fast or slow so he can decide whether to open or close the door.

The purpose of the thought experiment is to suggest that this system could violate the second law of thermodynamics by increasing order. By letting faster molecules move to one chamber, the system would then be able to do work by, for example, powering an engine. Perhaps the temperature differential is also able to power the demon itself. We would then have a perpetual motion machine, one that could give us unlimited energy, as long as there was a surplus of energy after the needs of the demon.

However, the modern analysis of the thought experiment shows that entropy does indeed increase within this system because the demon would eventually have to forget information about the molecules, and his forgetting would increase entropy. The demon would have to be an irreversible process.

References:

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

Tor Norretranders / The User Illusion: Cutting Consciousness Down to Size

[*7.130]

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The Physical Force Carriers

July 6, 2012

The probable discovery of the Higgs Boson was announced recently. I was initially confused about the difference between the Higgs and the yet to be discovered Graviton. After some reading on the internet, I’m still confused, but they are theorized to be two different particles, since the Graviton is the quantum manifestation of the force of gravity, and the Higgs is the quantum manifestation of the field that gives certain particles mass. Since the Graviton can effect Photons, and the Higgs can’t, they must be different.

You would think that since particles have to have mass to be effected by gravity, they would have to be related. I guess there are some theories out there that do that, but none have been validated. Additionally, the Higgs Boson is part of the Standard Model, and the Graviton isn’t, even though the Higgs doesn’t seem to fit nicely into those 4 x 4 matrices.

The above fourfold is patterned after the Four Fundamental Forces of Physics.

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

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

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

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