## Friday, December 20, 2013

### 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.