Using Averages To Bend the Uncertainty Principle

summerbreeze writes "Researchers at the University of Toronto have conducted a two-slit experiment, published in Science, that uses 'weak measurement' on photons to push back the boundaries of what can be known about them, given the Heisenberg Uncertainty Principle. Jason Palmer does a great job reporting this experiment to us mere mortals in a BBC article: 'The team allowed the photons to pass through a thin sliver of the mineral calcite which gave each photon a tiny nudge in its path, with the amount of deviation dependent on which slit it passed through. By averaging over a great many photons passing through the apparatus, and only measuring the light patterns on a camera, the team was able to infer what paths the photons had taken. While they were able to easily observe the interference pattern indicative of the wave nature of light, they were able also to see from which slits the photons had come, a sure sign of their particle nature."

Comments

Re:What I never understood about the uncertainty p

[mmell]

Um, just to ask - what particle? Oh, you mean the light wave?

You're understanding of the basic assertion of the Uncertainty Principal is correct - in order to know the exact position of a particle at an exact moment, you have to measure the particle which changes it's position. Right on.

However, when speaking of electromagnetic phenomena, it's generally understood that we're speaking of something which can be either a particle or a wave, depending upon the property being observed. Call it a 'wavicle', if you like. It's the act of measuring the behavior that "collapses the wave function" - i.e., I can demonstrate exactly where a photon struck a sensor under a certain set of conditions, but doing so collapses the wave function. OR I can demonstrate the wavelike properties of light, but only by sacrificing any clue to the position of the photons which create that wave structure (oddly enough, collapsing the wave function once again).

Now, this is only my understanding of the condition, and I'm not really that certain I've got it right . . .

Re:What I never understood about the uncertainty p

[Inquisitus]

The HUP is more fundamental than that. It doesn't just say that we can't know where a particle is because measurement disturbs it; rather it's telling you that the particle actually doesn't have a definite trajectory. In fact, it's so fundamental that it has its own mathematical formalism (commutativity of operators), upon which most of quantum mechanics is constructed.

It's important to realize that in quantum mechanics, the position of a particle is indefinite, and is specified by a diffuse/spread-out "cloud" probability, and only in special cases does this cloud collapse to a single point (which corresponds to the particle being in a definite place).

Note that it is possible (theoretically) to know the position or momentum of a particle, just not at the same time, since measuring one causes the other to become indeterminate.

Re:I don't get it

[Old Wolf]

Sorry to burst some bubbles, but I believe this analogy is not correct :( In fact it is not really possible to analogize quantum mechanics with anything classical, which is what people are getting at when they say that nobody really understands it.

In the experiment in TFA, they never found out which slit any particular photon went through. They have only collected some data about the average behaviour of the total set of photons. TFA suggests the scientists gathered a statistic somewhat like "X photons went through slit 1 and Y photons went through slit 2". Even here, I do not believe this is correct as I have worded it. I haven't read the paper at the article is based on, however if we follow the explanation of the first paragraph of your post, we will have an interference pattern that looks a bit different to the 50-50 one, where the possible paths between the two points have a greater 'density' of going through one of the particular slits. I would imagine that as you gradually change this ratio from 50-50 through to 0-100 the pattern would morph until it ended up being a one-slit diffusion pattern.

The rest of your post makes the same mistake as early efforts to explain the 'uncertainly principle', which was initially thought to be something like: "The particles have exact positions and momenta, but any attempt to measure them must disturb the system'. It was fairly quickly found that this was wrong, and the particles actually do not have well-defined positions and momenta (this is implicit in Schrodinger's equation and other such equations, the 'uncertainty principle' just describes a fact of the mathematical description of what a wavefunction is).

So photons only go through both slits in the function that describes their movement, not in reality.

  Certainly, photons behave according to the function that describes their movement. However, what is 'reality' is an open question (this is known as the interpretation of quantum mechanics). Some interpretations say that the photon travels through one slit but we cannot know which; some say that the function describing their movement *is* reality, and some say that 'reality' only consists of the photon's emission and its detection; not the stuff in between.