Heisenberg
In order to have some geeky fun (and largely to test out LaTeX support for my posts), I'm going to talk a
little bit about physics today.
I've most often heard people define Heisenberg's uncertainty principle as the notion that you cannot observe something without affecting it. By looking, you disrupt, so to speak. This is actually called the observer effect. While he was still alive, it drove Heisenberg crazy that people got these confused.
Here is Heisenberg's uncertainty relation expressed mathematically: $$ \sigma_x \sigma_p \ge \frac{\hbar}{2} $$ Imagine that you have a particle, like an electron, traveling along a straight line (e.g. one dimension). In this equation, $ x $ represents the position of the electron and $ p $ represents the electron's momentum.
$ \sigma $ represents the standard deviation, as it applies to the standard bell curve in statistics. The higher the standard deviation, the more "spread out" the bell curve is along the bottom axis. A very small standard deviation would be represented by an extremely skinny bell curve that spikes sharply in the middle, with very little spread.
Think of it this way: a shotgun has a large standard deviation (large spread) and a pistol has a small one (small spread).
$ \hbar $ is simply a constant, known as Planck's constant (strictly speaking, it's Plank's reduced constant, but never mind that small detail.) It's a very small value. What the equation tells us is that there is always some uncertainty in the measurement of both the electron's position and its momentum. This is why we have a $ \sigma $ value for each: we can't measure either with 100% accuracy, only probabilistically.
More importantly, the product of $ \sigma_x $ and $ \sigma_p $ must be greater than (or equal to) a constant value that is larger than zero. Simply put: if you reduce the $ \sigma $ of one of them, the other must increase. The more certain you are of $ x $, the less certain you can be about $ p $, and vice versa.
So what does it actually mean? Let's consider the simple example of a hydrogen atom, in which we have a nucleus composed of a single proton that has a single electron lurking around in a cloud in its lowest orbital. The two particles have equivalent, but opposite, charges.
Anyone who plays with magnets understands that postive and negative charges attract one another. So why doesn't the electron spiral in and stick to the proton?
Because of Heisenberg's uncertainty relation! If the electron were to succumb to its attraction and sit alongside the proton, then we would know its position definitively. There would be almost no uncertainly about where it existed. If this were to happen, the self-correcting laws of nature would increase the uncertainty in the particle's momentum, which would give it a massive spike of kinetic energy and send it reeling away from proton.
Naturally, this tells us that we understand, quantitatively, the mechanisn by which all matter in the universe doesn't collapse on itself, but it doesn't answer the real question of why things are that way. We know the electron doesn't stick the proton, but why? Saying "because of Heisenberg's uncertainly principle" is just a way of expressing that observable reality matches Heisenberg's equation. It doesn't tell us why the laws of nature are the way they are. Don't ask me that, because I have no idea why nature is the way it is.
I've most often heard people define Heisenberg's uncertainty principle as the notion that you cannot observe something without affecting it. By looking, you disrupt, so to speak. This is actually called the observer effect. While he was still alive, it drove Heisenberg crazy that people got these confused.
Here is Heisenberg's uncertainty relation expressed mathematically: $$ \sigma_x \sigma_p \ge \frac{\hbar}{2} $$ Imagine that you have a particle, like an electron, traveling along a straight line (e.g. one dimension). In this equation, $ x $ represents the position of the electron and $ p $ represents the electron's momentum.
$ \sigma $ represents the standard deviation, as it applies to the standard bell curve in statistics. The higher the standard deviation, the more "spread out" the bell curve is along the bottom axis. A very small standard deviation would be represented by an extremely skinny bell curve that spikes sharply in the middle, with very little spread.
Think of it this way: a shotgun has a large standard deviation (large spread) and a pistol has a small one (small spread).
$ \hbar $ is simply a constant, known as Planck's constant (strictly speaking, it's Plank's reduced constant, but never mind that small detail.) It's a very small value. What the equation tells us is that there is always some uncertainty in the measurement of both the electron's position and its momentum. This is why we have a $ \sigma $ value for each: we can't measure either with 100% accuracy, only probabilistically.
More importantly, the product of $ \sigma_x $ and $ \sigma_p $ must be greater than (or equal to) a constant value that is larger than zero. Simply put: if you reduce the $ \sigma $ of one of them, the other must increase. The more certain you are of $ x $, the less certain you can be about $ p $, and vice versa.
So what does it actually mean? Let's consider the simple example of a hydrogen atom, in which we have a nucleus composed of a single proton that has a single electron lurking around in a cloud in its lowest orbital. The two particles have equivalent, but opposite, charges.
Anyone who plays with magnets understands that postive and negative charges attract one another. So why doesn't the electron spiral in and stick to the proton?
Because of Heisenberg's uncertainty relation! If the electron were to succumb to its attraction and sit alongside the proton, then we would know its position definitively. There would be almost no uncertainly about where it existed. If this were to happen, the self-correcting laws of nature would increase the uncertainty in the particle's momentum, which would give it a massive spike of kinetic energy and send it reeling away from proton.
Naturally, this tells us that we understand, quantitatively, the mechanisn by which all matter in the universe doesn't collapse on itself, but it doesn't answer the real question of why things are that way. We know the electron doesn't stick the proton, but why? Saying "because of Heisenberg's uncertainly principle" is just a way of expressing that observable reality matches Heisenberg's equation. It doesn't tell us why the laws of nature are the way they are. Don't ask me that, because I have no idea why nature is the way it is.