Heisenberg Uncertainty Principle Demonstrated At Macroscopic Scales

One of the most venerable principles of modern physics is the Heisenberg Uncertainty Principle. Formulated by Werner Heisenberg in 1927,  soon after the birth of the wave mechanics form of quantum mechanics (which he contributed to as well as Erwin Schrodinger),  it sought to highlight the difficulty of obtaining accuracy when two observables are measured simultaneously at the atomic level.  In other words, the principle showed there is a limit on how precisely one can measure an object's position (x)  and momentum(p ) at the same time.

The form for the Heisenberg Uncertainty Principle, say in one dimension is:

 

                        D x D p _x  »  h

Where D x is the uncertainty in position in the x-direction and Dp _x  is the uncertainty in momentum. Assume one could obtain perfect accuracy (Dx = 0) in position, then rewriting the Heisenberg relation (in 1-dimension) to find the indeterminacy in momentum:


D p _x     ³  h/ Δx  

³  h/ 0   = ¥

That is, the indeterminacy in the position is now infinite.  

 

The take away is that simultaneous measurements at the atomic level are fundamentally indeterminate. Technically, for one of the most common forms of the Heisenberg Uncertainty Principle, this may be expressed (in terms of position x, the Planck constant h and momentum p = mv):

[x, p] = -i h/ 2 p
 

In term's of Bohr's quantum (Complementarity) Principle, the variables x (position) and p (momentum) are regarded as mutually interfering observables. This is why only one can be obtained to precision, while you lose the other.

In another sense, one can think of approaching a particle in such way (or with such apparatus) that it suddenly gets 'wavy' (Fig. 2) in some defined quantal limit. At a particular stage of resolution, as the late David Bohm noted, the particle aspect vanishes and you apprehend a wave.  But during some interim threshold one can regard it as a wavicle.  Of course, if Heisenberg's principle didn't apply - meaning we could know both the position and momentum to the same degree of accuracy, then: 

[x, p] = 0

Such that x· p – p·x = 0 spells out non-interference.

The key point is that all these relations have been believed by quantum physicists to apply at the quantum limit only, by which we mean for scales defined by the Planck constant. And with good reason! To see this, consider an automobile of mass m = 1000 kg and moving at velocity v = 10 m/s. Then the momentum p = mv = (1000 kg) (10 m/s) = 10, 000 kg-m/s. Now let Δx = 0. 05 m, the uncertainty in position of the car, and compute the uncertainty in the momentum given h = 6.626 x 10^-34 J-s.


 Δ p _x     ³  h/ Δx   ³  (6.626 x 10^-34 J-s.) / 0.05 m

One can easily see the value is so absurdly low, i.e. ~10^-32  kg -m/s,   as to be essentially irrelevant to any practical concern.
 

However, it now appears that macroscopic applications of the principle may not longer be verboten. Physicist Thomas Purdy and his team at JILA (Joint Institute for Laboratory Astrophysics ) at the University of Colorado, appear to have demonstrated the uncertainty principle at the macro scale. To accomplish this, they set out to measure the effect on the position of a visible object of some 10¹⁵   atoms, from a laser shot comprised of 100 million photons.  To do this, the team created a tiny drum 0.5mm across and first cooled it to 5 K. (Note that O K or Kelvin, is absolute zero temperature). This was to eliminate any effects from heat.


They then added tiny mirrors to each face of the drum and fired a laser. As the laser light bounced between the mirrors most of the incident photons hit the drum and transferred momentum before eventually entering a detector that calculated the drum's position. It was found the drum vibrated on the order of picometers,  or 10^-12  of a meter, due to micro-kicks from the photons impinging.


While the uncertainty in location is only a couple picometers worth, it's crucial to physicists who need very precise measurements. More importantly, it makes the 'cut' into the macro-level.

We will, of course, have to wait to see if this experiment can be confirmed, but so far there is every indication to believe it might be.

Stay tuned.

The Trayvon Martin Case and the Dogs of American-Style War

Julian Assange defends Wikileaks release of documents two years ago, mainly to do with the conduct of the occupation of Afghanistan. It is doubtful that such releases can have any substantive effect on war policy or conduct until the documents NSC 10/2 and NSC-68 (which green light never ending wars and meddling) are each mothballed!

"And Caesar's spirit, raging for revenge, with Ate by his side come hot from hell, shall in these confines with a monarch's voice, Cry "Havoc!" and let slip the dogs of war, that this foul deed shall smell above the earth. " (Julius Caesar Act 3, scene 1, 270–275

"The hallmark of a great civilization is its ability to wage peace, not war."

-Gene Roddenberry

Incredibly, throughout the media blitz on the Trayvon Martin killiing, none of the pundits commenting have brought up the obvious parallels to the mode of American, pre-emptive warfare since 2003. To summarize briefly: the very least we know (before Sanford police PR began insinuating itself) is that "Neighborhood Watch" guy George Zimmerman encountered Trayvon Martin - a young black kid in a hoodie, and suddenly felt his life threatened. We don't know how many more details there are, but based on 911 calls this is the least we know. The claims that Trayvon "attacked" Zimmerman are still under investigation and as yet no hard proof has emerged to sustain them.

The point is, prior to Zimmerman's overt action of firing his weapon, the State of Florida already had in place a reckless law known as "Stand your ground" - which basically conferred the right of ultimate self protection if one felt or sensed that his life was threatened. On this basis, one can argue that Zimmerman acted "pre-emptively" to neutralize a vague threat that had become entrenched in his sense perceptions - triggering the fear circuits in his amygdala.

Now, think of laws like this all over the nation (we also have one in Colo. called "Make my Day" after the famous catch phrase in the first 'Dirty Harry' flick - where you can shoot and kill anyone entering or already inside your home if you believe he poses a threat to your life) and the inevitable results. We'd had mass bedlam and anarchy! The rule of law as it should be would be incessantly trumped by the perception of a "threat" requiring lethal force. Or "pre-emptive lethal force" if you will.

But as odious as such laws are in terms of the lethal license they give to the feeling threatened, let us admit and concede that they have precedents on the national level! I am talking of course of the "Bush doctrine" and its prescription to justify any form of "pre-emptive war" if the U.S. feels itself threatened. (Note: the Pentagon's PR mongers like to use the term "preventive war" but I am not buying into that bollocks. This again is a form of collaterial language designed to gut critical thought, reason. Please see the book: Collateral Language: A Users’ Guide to America’s New War (2002) )

Referring back to the preceding parenthetical, the alteration of the language (including use of the term "terrorist" and "war on terror") was crucial in order for the Bushies to launch their assorted 'dog and pony' shows (including with Colin Polwell at the UN) to try to show Saddam was getting ready to have a nuke and then who knew? Maybe mushroom clouds! The impetus was then to try to drive American public opinion into embracing an absurd, unjustified invasion and occupation which ultimately transmuted into an 8 ½ year long "war" (which was obviously still an occupation).

In other words, like George Zimmerman confronted with the "threatening" (in Zimmerman's mind) hoodie-clad, tall black kid, the Bushies were confronted with a lone nation (Iraq) they perceived (in their minds) as a "terrorist" (or part of the "Axis of Evil") which had all kinds of weapons and therefore this demanded a first strike. In other words, pre-emptive action, hence striking an initial lethal blow at a country before it could strike- thereby sending its economy into carnage and slaughtering over 600,000 Iraqis according to World Health Organization estimates. (Which are, of course, lowballed by the Pentagon to no more than 100,000).

Needless to say, based on what transpired from the fall of 2002 to March 15, 2003 (public support for the war went from barely 34% in December, 2002, to more than 67% in February) it is incumbent on all Americans now to be aware that when they passively comply with collateral language pushed on them like crack (as it was by the corporate media in the runup to the Iraq invasion) they become no better than useful idiots for the military-industrial complex and perpetual war state.

If Americans instead persist in a state of false consciousness and allow their brains to be PR-dumbed down, then they assist in mutating language and thought toward an ideological agenda, rather than shedding light on the issues themselves.

Nevertheless, the PR residue from 2002-03 which fueled that Iraq invasion bubble of unreality via jingoistic illusions (and inadequate security delusions) continues today with assorted similar pressures to strike Iran - despite the fact there's absolutely no hard evidence they have any nukes, see e.g.

http://brane-space.blogspot.com/2012/03/its-still-stupid-to-launch-attack-on.html

Thus, unlike with the drumbeating in 2002-03, Americans must now do all in their power to resist the flood of media sound bites, from every yammering pundit, assuming ab initio an attack or war on Iran is morally justified, correct and "preventive" (instead of pre-emptive). Let's also reiterate once more, such pre-emptive attacks, as in the case of the U.S. invasion and attack on Iraq, and Nazi Germany's pre-emptive attacks on the Sudentenland in 1938, and Poland in 1939 (based on Poles being a "terrorist threat" to Aryan females) can't be countenanced under international law. These are guided by the Nuremberg Laws which were written after the conquest of the fascists in World War Two. Most particularly we have:

PRINCIPLE VI The crimes hereinafter set out are punishable as crimes under international law: (a) Crimes against peace: (i) Planning, preparation, initiation or waging of a war of aggression or a war in violation of international treaties, agreements or assurances; (ii) Participation in a common plan or conspiracy for the accomplishment of any of the acts mentioned under (i).

Note especially (i) which most directly embodies the entire pre-emptive war concept. It means exactly what it states, so that any nation found guilty of "planning, preparation, initiation or war of aggression" is thereby violating that principle.

The fact that so few Americans are aware of the above shows how ripe we are as a people to become even more PR-deformed.

Sadly, in the old days, before the disastrous implementation of National Security Council (NSC) Directive ‘NSC 10/2’ on June 18, 1948, this nation valued honor and only initiated wars unless first attacked. Thus, Pearl Harbor paved the way for our just entry into World War Two. Because honor underscored initiation of war, it thereby became a matter of honor to also have everyone help PAY for such using higher taxes and-or rationing of foodstuffs, gas etc. Because at that time we were on the side of moral right, we had the nation and the world with us.

Not so since that NSC 10/2 was enabled! The scope of activities enumerated under the directive included: “propaganda, economic warfare, preventive direct action – including sabotage; subversion against hostile states including assistance to underground resistance movements, guerillas and refugee liberation groups and support of indigenous anti-Communist elements in threatened countries of the free world.”

Ratcheting up the effect, and consolidating the impetus to Empire building was the document NSC-68, prepared by Paul Nitze of the National Security Council – completed by 1950. The document essentially contained the blueprint for unending strife and undeclared wars, all of which would be invoked on the basis of a zero tolerance threshold for foreigners’ misbehavior. The putative basis? To enable U.S. agitation, overthrow (or assassination) of democratically-elected leaders, and large and small occupations (ranging from the few thousand troops in the Dominican Republic in 1965, to more than 200,000 in Iraq by 2006.)

Thus, we lost our way as we invaded nations (e.g. Dominican Republic, Iraq, etc.) with no reason and engaged also in the overthrow of democratically-elected governments (e.g. Iran's Mossadegh in 1953, Jacobo Arbenz in Guatemala in 1954, assassinating Salvador Allende in 1972.) Thereby we lost honor, so that "war on the cheap" or more accurately "wars of choice" became the norm, to try to justify whatever was in the NSC 10/2 directive.

The motivating force of the Nitze document was clear in this regard:

“a defeat of free institutions anywhere is a defeat everywhere”

In other words, any place for which the U.S. even remotely construes a “defeat of free institutions” gives it license to intervene at will. This critical aspect is described thusly by Morris Berman (Dark Ages America: The Final Phase of Empire, W.W. Norton, page 118, 2006)
"Nitze emphasized the importance of perception, arguing that how we were seen was as crucial as how militarily secure we actually were. This rapidly expanded the number of interests deemed relevant to national security”

In other words, it provided the pre-emptive formula for unending war even before the Bush doctrine arrived. Gore Vidal pinpoints the emergence of the American Empire when he notes (Dreaming War: Blood for Oil and the Cheney-Bush Junta, Thunders Mouth, p. 124, 2002)

"Since 1950 the United States has fought perhaps a hundred overt and covert wars. None was declared by the nominal representatives of the American people in Congress…they had meekly turned over to the executive their principal great power to wage war. That was the end of that Constitution"

One would have hoped that MSNBC pundit Rachel Maddow in her new book, 'DRIFT' would have covered more of this backstory, but evidently not. Her focus was more on how "cheaply" war has been waged over the past 4-5 decades, effectively insulating the civilian U.S. populace from any real consequences. But she did not dig into the underlying deep causes, the offensive and dishonorable documents: NSC 10/2 and NSC -68. Well, maybe in a follow-up.

In the meantime, as we puzzle over George Zimmerman's pre-emptive over-reaction to the mere appearance of a young hoodie-clad black man in his "territory" perhaps we might also contemplate the pre-emptive over-reactions of our own nation to any and all perceived threats in the larger world.

Maybe....at some juncture... one is connected with the other.

Why the Aversion to Math in Science Exposition?

Top graphic: Energy levels E1, E2, etc.quantified by wave function for a quantum mechanical "square well". Below: calculations to work out the angle between L, S vectors in L-S coupling.

For anyone who's actually read Stephen Hawking's book, A Brief History of Time, who can forget his half joking reference in the Introduction to his Bantam editors who warned him that every equation included in his book would halve his sales. Having digested that, Prof. Hawking punted and included only one single equation: E = mc^2.

Now, a new book entitled 'The Quantum Universe: Everything That Can Happen Does Happen', by Brian Cox and Jeff Forshaw, purports to reverse this anti-equation, anti-math trend by liberally sprinkling equations throughout the text and avoiding the yen to dumb down books merely to appease pointy headed editorial bean counters and anti-math wags. This is just as well, because no decent book on quantum mechanics can avoid math given that QM is perhaps the most quantitatively based theory we have.

Further, I'd argue that without at least basic algebraic forms to show QM relations, say between energy levels and principal quantum number, n, one will not appreciate the quantum basis of the theory which is quantized energy. It is one thing to be told that energy is quantized into discrete packets of a certain size, hf, where h = 6.62 x 10^-34 J-S is the Planck constant, and f is the frequency of the radiation, it is quite another to work it out in a lab from spectral and other observations using the basic Bohr energy formula.

Thus it is that I sometimes compare those who can interpret quantitative forms, equations, graphs in a physics book, thereby gaining a much deeper insight, with readers that can go through a book like Thomas Mallory's Le Morte Arthur (special illustrated version) and mine its words as well as the sketches. While someone with only minimal vocabulary will stick exclusively to the images. Images are nice and convey some of the story, but they can't convey the entirety.

The authors Cox and Forshaw, quoted in an article in The Economist (Nov. 5, p. 101) give the reason for including all the math equations:

"We included the maths mainly because it allows us to really explain why things are the way they are. Without it, we would have to resort to the physicist- guru mentality whereby we pluck profundities out of thin air and neither author would be comfortable with guru status."

This is exactly spot-on on and why the inclusion of appropriate equations and graphs enriches and enhances the material- especially in physics- as opposed to diluting it. It's also a big reason why theoretical physicist Roger Penrose tossed all caution to the wind in writing his massive, hyper -mathematical tome: The Road To Reality: A Complete Guide to the Laws of the Universe(which includes tensors and pseudo-tensors as well as complex algebra and residues), which comes in at 1099 pages.

Penrose's book is a masterpiece for anyone who wishes to really understand modern physics, from the curvature of space-time in general relativity, to quantum indeterminism, entanglement and the uncertainty principle, to the Big Bang, non-Euclidean geometry (to describe the cosmos' shape) and even the 'no-boundary' model of Hawking and Hartle. As the cover jacket puts it, in one of three objectives accomplished (and I fully concur): "evokes the extraordinary beauty that lies in the mysterious and profound relationships between these physical behaviors and the subtle mathematical ideas that explain and interpret them."

Was Penrose fearful of overdoing it equation-wise? Hell no! Not with more than 4,950! He believed, as I do, a person seriously invested in what makes the cosmos tick will expend the effort - via the underlying mathematics needed- to find out, and thereby gain a much fuller appreciation. Is he thereby writing for the "masses"? No, of course not! He is rather writing for that (not too tiny) segment that appreciate a hefty book which includes not only terrific description but the math to flesh it out.

Of course, The Economist is evidently unsatisfied with authors Cox and Forshaw in their reasons for including the equations. As the reviewer puts it (ibid.):

"That stance might comfort the authors but to many readers they will nonetheless seem to pluck equations out of thin air. Yet their decision to include some of the hard stuff leaves open the possibility that some readers might actually engage in the slog that leads to the higher pleasures."

Indeed! And that was found exactly to be the case for those who purchased Penrose's 'Road to Reality' because they wanted at least a glimpse of that road and some understanding, not just pabulum to make them think they grasped the essence of cosmic laws when they'd done nothing of the sort.

Further, if it is true that some readers might think equations are "plucked out of thin air" then that is a sign that perhaps some steps in reaching a critical equation were omitted. By contrast, Penrose excludes no such steps and for more completeness he even appends questions for readers in his footnotes to ensure they are following!

Sadly, mathophobia is all too prevalent on the planet, even when people are confronted with basic algebra. This makes me believe that the level of math education has not been all it can be. Kids then left the grade school or high school environment with a pathological fear of the slightest hint of a symbol x, y or z- almost as bad as some people harbor for spiders. Eliminating this fear probably will take much more effort than many educators can give, but one hopes that very soon it will be eliminated ....certainly in the near future.

Mathematics is too important an area, irrespective of which context one sees it in.