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String Theory: The Uncertainty Principle

Werner Heisenberg is best known in quantum physics for his discovery of the uncertainty principle, which has the consequence that to make measurements of very short distances — such as those required by string theory — very high energies are required.

The uncertainty principle states that the more precisely you measure one quantity, the less precisely you can know another associated quantity. The quantities sometimes come in set pairs that can’t both be completely measured.

What Heisenberg found was that the observation of a system in quantum mechanics disturbs the system enough that you can’t know everything about the system. The more precisely you measure the position of a particle, for example, the less it’s possible to precisely measure the particle’s momentum.

The degree of this uncertainty was related directly to Planck’s constant — the same value that Max Planck had calculated in 1900 in his original quantum calculations of thermal energy. Heisenberg found that certain complementary quantities in quantum physics were linked by this sort of uncertainty:

  • Position and momentum (momentum is mass times velocity)

  • Energy and time

This uncertainty is a very odd and unexpected result from quantum physics. Until this time, no one had ever made any sort of prediction that knowledge was somehow inaccessible on a fundamental level. Sure, there were technological limitations to how well a measurement was made, but Heisenberg’s uncertainty principle went further, saying that nature itself doesn’t allow you to make measurements of both quantities beyond a certain level of precision.

One way to think about this is to imagine that you’re trying to observe a particle’s position very precisely. To do so, you have to look at the particle. But you want to be very precise, which means you need to use a photon with a very short wavelength, and a short wavelength relates to a high energy.

If the photon with high energy hits the particle — which is exactly what you need to have happen if you want to observe the particle’s position precisely — then it’s going to give some of its energy to the particle. This means that any measurement you also try to make of the particle’s momentum will be off.

Similar explanations work if you observe the particle’s momentum precisely, so you throw off the position measurement. The relationship of energy and time has a similar uncertainty. These are mathematical results that come directly out of analyzing the wavefunction and the equations de Broglie used to describe his waves of matter.

How does this uncertainty manifest in the real world? For that, let me return to your favorite quantum experiment — the double slit. The double slit experiment has continued to grow odder over the years, yielding stranger and stranger results. For example:

  • If you send the photons (or electrons) through the slits one at a time, the interference pattern shows up over time (recorded on a film), even though each photon (or electron) has seemingly nothing to interfere with.

  • If you set up a detector near either (or both) slits to detect which slit the photon (or electron) went through, the interference pattern goes away.

  • If you set up the detector but leave it turned off, the interference pattern comes back.

  • If you set up a means of determining later what slit the photon (or electron) went through, but do nothing to impact it right now, the interference pattern goes away.

What does all of this have to do with the uncertainty principle? The common denominator among the cases where the interference pattern goes away is that a measurement was made on which slit the photons (or electrons) passed through.

When no slit measurement is made, the uncertainty in position remains high, and the wave behavior appears dominant. As soon as a measurement is made, the uncertainty in position drops significantly and the wave behavior vanishes. (There is also a case where you observe some of the photons or electrons. Predictably, in this case, you get both behaviors, in exact ratio to how many particles you’re measuring.)

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