Thursday, February 5, 2009

Standing on the Whale, Fishing for Minnows

Explorations in the theory which is known as quantum mechanics
has yielded spectacular successes and insights into the nature of the universe ,
among which is describing properties of atomic structures.

Where relativity deals with the largest objects in the universe,
quantum mechanics deals with understanding the very smallest particles
of which all objects are composed.
Quantum physics has shattered the traditional ideas of the physical universe.
Yet it's elegant equations present us not simply with scientific knowledge,
but also with philosophical challenges regarding its interpretation.
It's implications are
vast, mysterious, revolutionary, and wondrous.
After all,
What is a quantum particle?
The dreams that stuff is made of!

Quantum Mechanics has been described
as the crowning achievement of the 20th Century,
a theory that has been validated with great precision.
The quanta - the idea that at the smallest of scales,
everything is discrete; has devastated classical physics and forced us
to perceive reality in a most unreasonable fashion by conventional standards.
Yet at it's very core, the stuff upon which the physical universe is hung,
is more real than the physical universe itself.
How did we arrive here?

Hop aboard the old "wayback machine"
with Mr.Peabody and Sherman!
(which incidentally, exists courtesy of relativity ...
and/or Jay Ward!
Of course this begs the question,
in a quantum universe,
is Bullwinkle still a moose?)

In the 19th century much of the scientific community was absorbed in the study of heat properties of various objects. An abstract model that was considered was the Black Body, which was an object which absorbs all incidents of radiation and then re-emited the energy again. We can think of the radiating energy as standing waves inside our blackbody cavity. The energy of these radiating waves at a given frequency ½, should be proportional to the number of modes at this frequency. Classical physics states that all these modes have the same energy k T (a result derived from classical thermodynamics) and as the number of modes is proportional to ½ 2 :

E \propto \nu^2 kT

We would expect most of the energy at higher frequency, and this energy to diverge with frequency. When we sum the energies at each frequency we find that there is an infinite energy in this system!

This paradox was called the ULTRAVIOLET CATASTROPHE.

Physicist Max Planck resolved this untidy paradox.
He postulated that the energy of the modes
could only come in discrete packets - quanta - of energy:
E = h\nu, 2h\nu, 3h\nu, \ldots \qquad \Delta E = h\nu

Using statistical mechanics Planck found that the modes at higher frequency were less likely excited so the average energy of these modes would decrease with the frequency. The exact expression for the average energy of each mode is given by the Planck distribution:

\langle E \rangle = \frac{h\nu}{\exp(\frac{h\nu}{KT}) - 1}

You can see that if the frequency is low then the average energy tends towards the classical result, and as frequency goes to infinity we get that the average energy goes to zero as expected.

We might say this was the birth of quantum mechanical thinking.

The Clot Thickens...

Atomic Line Spectra
There was a further breakdown in classical physics regarding the observed discrete line spectra specific to each atom.
It was widely accepted that this must be due to transitions between atomic energy levels.
But this presented a considerable problem to classical physics as it predicted that accelerating charges emitted radiation.
It would thus seem that the energy orbital would be unstable as the electron slowly spiraled towards the nuclei as it emitted radiation.
There was absolutely no classical model which could explain a stable electron orbital.
In other words:
How could the electrons orbit the nucleus and not lose energy?
Why was this configuration stable?

Niels Bohr

Bohr was able to crack this puzzle by invoking the idea developed by Planck.
This quantization could not be proven on classical grounds or even justified,
but Bohr showed that when he made these assumptions,
he could predict the spectrum of hydrogen
with unprecedented accuracy.
This magical conjuring act
was able to accurately describe the energy levels
giving the exact energies of the lines actually observed in the atomic spectra.
This is the resultant equation.
E = \frac{2 \pi^2 m e^4}{h^4}-\frac{1}{n^2}

Look here for a brief presentation of the derivation of his theory.

Bohr's success was indisputable.

Unfortunately it only worked on Hydrogen.

HeisenbergThe Uncertainty Principle

"The more precisely
POSITION is determined,
less precisely the MOMENTUM is known"
This seemingly harmless sounding statement
of the "uncertainty relation" between the position
and the momentum (mass times velocity) of a subatomic particle,
such as an electron sent reverberations
through the hallowed halls of science and philosophy.
The implications are unfathomably infinite.
This relationship has profound effects
on such fundamental notions as causality
and the determination of the future behavior of an atomic particle.
But as we discussed in Anarchs Of The New Paradigm,
the implications in Art, Music, Philosophy,
and essentially all man's endeavors are fundamentally of equal significance.

Consider a particle,
say an electron, moving through space.
We describe the electron's motion in terms
of its position and momentum.
Classically speaking,
we can measure both quantities to infinite precision.
However in Quantum Mechanics,
we can never know both quantities absolutely precisely.
This is because by taking a measurement
we inadvertently have disturbed the system.

"I believe that the existence of the classical 'path'
can be pregnantly formulated as follows:

The "path" comes into existence only when we observe it.
--Heisenberg, in the uncertainty principle paper

If every concept has a meaning only in terms of the experiments used to measure it, we must agree that things that cannot be measured really have no meaning in physics. So for instance, the path of a particle has no meaning beyond the precision with which it is observed. But a basic assumption of physics since Newton has been that a "real world" exists independently of us, regardless of whether or not we observe it. (This assumption did not go unchallenged, however, by some alchemists and philosophers.)
Heisenberg now argued that such concepts as orbits of electrons do not exist in nature unless and until we observe them.
Does this perhaps suggest that all knowledge is unknowable?
There simply are no certainties.
Only probabilities.
Tumblin' Dice...
Quantum theory...
"If we know the present exactly, we can calculate the future"
-it is not the conclusion that is wrong but the premise."
--Heisenberg, in the uncertainty principle paper


So we can not be certain Bullwinkle is a moose,
in fact, merely making the inquiry
affects whether Bullwinkle is a moose or not.

Light can be both wave and particle
Some experiments show that light is a particle:
Einstein's Nobel Prize was actually for the photoelectric effect, where he showed that light carries energy in discrete amounts, a certain amount per particle. Yet other experiments also show that light is definitely a wave:
It exhibits interference patterns, which is something that only waves do.
There is however, no experiment which can show both results.
Whether light is a wave or a particle depends on how you're looking with it.
This may seem odd, but there are many examples of this sort of duality, even outside of physics. The same person could be perceived as a father, son, brother, nephew, or uncle, depending on who's perception we are dealing with.

Bullwinkle is a moose and squirrel.

Matter (us and everything else) is of a dual nature.
As discussed in the explanation of the nature of light.
The idea of duality is rooted in the debates over the nature of light and matter dating back to the 1600s, when competing theories of light were proposed by Christiaan Huygens and Isaac Newton. Through the work of Albert Einstein, Louis de Broglie, and many others, current scientific theory holds that all particles also have a wave nature. This phenomenon has been verified not only for elementary particles, but also for compound particles like atoms and even molecules. In fact, wave–particle duality applies to all objects, even macroscopic ones.

We exist as both particles and wave functions.
The wave function of an object represents the probability of finding it in a particular location or with a particular physical property (ie. it's reality) - when the probability of finding an object in a particular location or with a particular property goes to 100%, the wave function collapses and the object assumes physical properties. At this point it becomes "real".

Objects do not have any physical properties until they are observed.
Quantum physics contradicts the belief in an objective world existing independent of observation.
Our observations influence reality by collapsing the wave function of an object.
The point at which the wave collapses is consciousness itself.
An astounding yet mathematically supported reality.
Renee Descartes walks into a bar,
the bartender says 'sir can I get you a martini
'Descartes says
'I don't think...'
and he disappears.

The Tragic End Of Schrödinger's Cat
After a stint in the physics limelight, Schrödinger's cat fell on hard times.
The constant stress of never knowing from one moment to the next whether he was alive or dead took its toll on the cat's psyche. Schrödinger's cat began to drink, and drink heavily!
Often drinking himself into a catatonic stupor. Alcohol abuse began to affect his work.
This was especially evident in his last paper published shortly before his death, "Der Maus Eigenfunctionen im Unendlich-dimensional Hilbertraum", in which he published the following rather cryptic equation for analyzing the momentum of electrically-charged particles:

p[[p[p[p = <~~fafafaf | 35eeeeeeeeee >

It has been speculated that if properly understood, this strange-looking equation may have profound implications for our understanding of the interactions of particles in an electromagnetic field. Unfortunately, the original manuscript was covered with coughed up fur balls and a green-colored stain that resembled cat vomit.
One by one, Due to his drinking, his sources of funding dried up.
Soon, he found that he was no longer being invited to give seminars.
His scientific colleagues and students expressed uncertainty about whether or not he would even show up at his lectures. Some people even debated whether he was even still alive!
His last work was in telecommunications.
His invention of Cat-5 cable at Bell Laboratories laid the foundations for the Internet.
In his last days he also spent more and more of his time playing with string theory.

R.I.P. Schrödinger's cat

Physical reality is not "real"
It is the minnow we seek to catch
while standing on the whale

The title of this article is a Polynesian saying.
I first encountered it while reading a book by Joseph Campbell
Joseph Campell suggested that man's mythology was a powerful tool.
That perhaps we need a modern mythology to help us make sense of the universe
as we experience it in this time.
He postulated that the story of "Star Wars"
could actually be used to this effect in his celebrated interviews with Bill Moyers.
Though he could not not literally subscribe to any particular brand of mythology,
he recognized the importance and indeed the beauty of the stories.
And in his book, "the Hero With A Thousand Faces";
he observed that man's various mythologies were essentially all the same story.

Duct tape is metaphysical.
Duct tape is a metaphor for "the Force".
It has a light side, a dark side, and it holds the universe together.

But what is it ultimately that one seeks?
Campbell suggested "People say that what we're all seeking is a meaning for life. I don't think that's what we're really seeking. I think that what we're seeking is an experience of being alive, so that our life experiences on the purely physical plane will have resonances within our own innermost being and reality, so that we actually feel the rapture of being alive. That's what it's all finally about, and that's what these clues help us to find within ourselves."

. Evidence from man's research into subatomic physics
informs us that there is actually no such thing as physical matter.
That literally everything is energy.
Our greatest physicists
have told us that energy is controlled by consciousness.
What consciousness is, where it is,
and how it functions is the question.
(Please see Anarchs Of The New Paradigm for details.)

Universal consciousness
(the source of everything? God? Zappa's "crux of the biscuit?)
is the holy grail of the human quest for meaning.
Now of course we sentient human beings
each have consciousness,
of one sort or another ,
but how does human consciousness relate to cosmic consciousness?
this is a matter of speculation, conjecture, and controversy.
There is certainly a degree of scientific physical evidence
and indeed plenty of religio-philisophic writing that reflects on just this.
That perhaps what we allude to as "God" is not some hairy thunderer
but rather the sum of consciousness.
That each of us is a piece of God
or the cosmic consciousness.
The Hindu truth
that "I am the mystery of the Universe " comes to mind.
In the New Testament the author known as "John"
says that Jesus claimed " I am in the God, and God is in me"
paraphrased numerous times.
How about in Psalms "the kingdom of God is within you"?
Or the phrase "What you do onto the least of your brothers, you do onto me."
Lao Tzu said "at the center of your being you have the answer"
(what is at the center of your being other than consciousness itself?
The point of the wave collapse?)
Lao Tzu also said “Music in the soul can be heard by the universe.”
Might this all imply an attempt
at cosmic awareness of the nature of the universe
rather than some dogmatic mumbo jumbo
completely misinterpreted, mistranslated,
or misrepresented for centuries?
Man's quest for meaning did not begin in the 20th century.

Is it at least possible
that true seekers may have glimpsed the implications
of the quantum universe without actually doing the math?
Is there more than 1 path to ultimate knowledge?
And is man, with his hat on, taller than a taxi cab?

The physical universe is a function of "something"
in the non-physical part of reality.
(A something or a no-thing that we call consciousness.)
The source of creation
is in the non-physical consciousness.
The physical experience is the result.

No electrons were harmed in the creation of this article. In an alternate universe, Bullwinkle is the governor of Alaska and has the disembodied head of Sarah Palin hanging on his mantel.

1 comment:

Frederick Milton said...

Great Article about quantum physics and how this is a great tool to explain the universe.
I only watched like two episodes of Mr.Peabody and Sherman. they really are a funny pair.

Do you think that with can explain easy enough General Viagra with quantum physics?

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