Sunday, August 23, 2015

PQ-QP=H/2IPI Equation under Avatar Explained

UPDATE: this post primarily discussed my old twitter avatar. I might re-upload my old avatar in the future - depending on my blood sugar level.

In case you ever wondered what the equation under my old avatar meant:

(PQ-QP)=H/2IPI . First off, the program that created the Obama like campaign poster only printed text in all capital letters, which might create minor typographical confusion. Equation should read:  PQ-QP=h/2iπ

The numerator, top part of the fraction, of the right hand side of the equation is "h bar" = ℏ = the reduced Planck's constant = h/2 π  = H/2PI of the above equation since  π = pi ≅ 3.14159265359. FYI, you can get the html code for h-bar from "Musings: Partly collected thoughts" Friday, December 18, 2009 post "h-bar in HTML" and more math symbols from "HTML Entities for symbols, mathematical symbols, and Greek letters"

A few pages from the basic introduction to physics book, Giancoli, Douglas C. Physics: Principles with Applications. 5th ed. Upper Saddle River, N.J.: Prentice Hall, 1998. Print.,  describes what Planck's constant is and how it's used to calculate quantized energy levels:

 Serway, Raymond A., Robert J. Beichner, and John W. Jewett, Jr. Physics For Scientists and Engineers. Fifth ed. New York: Saunders College, 2000. also points out that Planck's constant is used to calculate angular momentum:

And talks about linear momentum = p = mv

The left hand part of the equation is the commutator of [PQ] = PQ - QP . From WolframAlpha article on the "Commutator":

Let A^~B^~, ... be operators. Then the commutator of A^~ and B^~ is defined as

If  a commutator equals zero, the equation commutes. Obviously, this equation doesn't commute, because the difference on the right hand hand side of the equation does not equal zero. In fact, the difference represents the Heisenberg Uncertainty, as discussed in Swanson, D. G. Quantum Mechanics: Foundations and Applications. New York: Taylor and Francis, 2007. Print.

The above highlighted equation, with slight rearrangement, represents the equation under my avatar:

i[P, Q] = hbar = PQ-QP=h/(2ipi)=h/2iπ

Giancoli prosaically describes what the Heisenberg Uncertainty principle means: that in Quantum Mechanics subatomic microscale,  observers can only identify either a point's location, or its momentum exactly, but not both simultaneously:

Giancoli's exercise points out Heisenberg UP only is of practical concern on QM scale, but, plugging in numbers representative of the macroscale validates that Newtonian Mechanics simplified equations are still valid on the macroscale of general human experience.

So, if you're a batter you can still precisely identify a baseball's exact position and velocity using old school Newtonian Classic Mechanics. However, if you conclude that Heisenberg's equation only applies to electrons flying around in their orbits, Giancoli seeks to disabuse you of this notion with a philosophical dissertation:

I suspect most engineers, and possibly many scientists, don't think about the philosophic underpinnings of equations they use. In fact, Brian Greene's "Elegant Universe" implies that Classic Mechanics, and Einstein's tweak of Newton in his General Relativity, with their underlying assumptions of complete mechanistic determinism, only governs in the macro world and that it is only on the micro scale when Quantum Mechanics kicks in.

 From "The Elegant Universe Part 2 - String's the Thing" starting at 8:45

"To understand the universe on extremely small scales, we have to use our other set of laws, quantum mechanics. And as we'll see, QM paints a picture of the universe so drastically different from General Relativity, that you'd think they were describing two completely separate universes. To see the conflict between General Relativity and QM, we need to shrink way, way, way down in size. And as we leave the world of large objects behind and approach the microscope realm the familiar picture of space in which everything behaves predictably begins to be replaced by a world with a structure that is far less certain.  And if we keep shrinking getting billions and billions of times smaller than even the tiniest bits of matter atoms and the tiny particles inside of them the laws of the very small QM say that the fabric of space becomes bumpy and chaotic."

 Giancoli points out that although the effects from QM are numerically negligible and can for practical purposes be ignored when calculating the arc of a baseball pitch in Greene's "world of large objects", the underlying philosophical implications cannot. Complete determinism is dead and the Copenhagen interpretation rules on both large and small scales.

So, Giancoli would disagree with the snarky cartoon in Claes Johnson on Mathematics and Science:

Finally, you may very well ask yourself: "Self, why on earth does 'p' stand for linear momentum?"

My undergraduate Physics book asserts that "p" in the equation for linear momentum p = mv stands for the Latin word for movement, but doesn't volunteer what that word may be.

Prompted by my old physics book, I decided to skim the pages of the glossary of my old Latin grammar book: Horn, Annabel, and John Flagg Gummere. Using Latin III. Chicago, Ill.: Scott, Foresman, 1954. Print. and came across a few possible candidates.

FYI, the "Language, literature, and life" subtitle on title page:

sounds almost like Michael Savage Borders, Language, Culture:

but back to what I at first thought were the pertinent glossary pages:

"p" could stand for the Latin word "petitio" = blow or attack.

which might come as a hat tip to the fact that momentum is conserved during a collision, from Doug Giancoli "e-Study Guide for: Physics for Scientists and Engineers":

"p" could also stand for either for "pondus" for "mass" or else "pomum" which might be a hat tip to Newton with his probably apocryphal apple story:

"p" could also stand for "possum" or "potens" = power influence which I might say is an homage to possums, but since possums just look like overgrown mangy rats, nobody in their right mind would wish to pay homage to them.

However, the website gives their explanation in the post "Why is p used to stand for momentum in physics equations?"

"Impetus comes from the Latin in- + petere to go to, seek -- from Greek petesthai to fly, piptein to fall, pteron wing.  Also, push and pull derive from the Latin pellere."

2000clicks references post "What does the p in momentum stand for and what does it mean?" but corrects their incorrect description of momentum as a quotient p=m/v and correctly described p=mv as a product.

Rielcasinillo on to the question: "In momentum calculations why does p stand for momentum?" reiterates the above theory, and adds the observation that p's just naturally go with q's:

"Taken from the answer of Horsin' Around. p is used because the word "impetus" formally in place of "momentum" comes from the latin, "petere," to go towards or rush therefore we get "p" another way to look at it is q is used for the reaction and p is the mirror image of q so therefore since "to every action, there is an equal and opposite reaction," we choose p to go with q"

From article on "Momentum"

"The origin of the use of p for momentum is unclear. It has been suggested that, since m had already been used for "mass," the p may be derived from the Latin petere ("to go") or from "progress" (a term used by Leibniz)."

Finally from "Physics for Kids: Momentum and Collisions"

"No one is quite sure why "p" is used for momentum. It likely came from the Latin word "petere" which means "go towards". They couldn't use 'm' because that was already used for mass."
Hence, trying to nail down the exact time and place of the adoption of the nomenclature of p = linear momentum offers a graphic analogy to Heisenberg's Uncertainty Principle. From EUREKA! PHYSICS

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