It's professor Dave, let's learn about the Heisenberg uncertainty principle. Once Schrodinger and pals had sufficiently developed the brand new field of quantum mechanics, some perplexing implications arose. For one, in classical mechanics an object will have a precise value for its position and momentum at all times. In quantum mechanics, this was no longer the case. If a quantum particle were to have precise values for position and momentum it would simply be a particle, but all particles are also waves, so this kind of determinism no longer applies. Instead, as we saw with the Schrodinger equation, the quantum realm is probabilistic in nature. This brought about the issue of how to describe the position and momentum of the electron. Under the Copenhagen interpretation of quantum mechanics, an electron simply does not possess precise values for both of these parameters at the same time, so when we take a measurement, the result is randomly drawn from a probability distribution. An electron will seem to be in a particular location if and only if we measure its location. However, if we know its location we can no longer know its precise momentum, or what it's doing, and this notion is summarized in Heisenberg's uncertainty principle. This states that when looking at complementary variables like position and momentum, the more precisely one parameter is known, the less we know about the other. Here, delta x represents the uncertainty in position, while delta p is the uncertainty in momentum, and their product must be greater than h over 4 pi. If the uncertainty in one parameter decreases, the uncertainty in the other must increase, and if one becomes known with total certainty, the other becomes unknowable. The important thing to realize is that this has nothing to do with our measuring instruments. This is a fundamental quality of matter. We can't reduce an electron to particle like determinacy, as it is also a wave, as was demonstrated by the double slit experiment. Furthermore, this forces us to examine what it is to make an observation. To know the location of an object, to see it, at least one photon must hit our eyeballs. But if a quantum system interacts with even just one photon such that it can be seen, that interaction itself will alter the state of the system. So the seemingly innocent act of observation has a concrete impact on the system. When this problem of measurement emerged, the scientific community was in total confusion. This notion, and the idea that nature was not deterministic but rather probabilistic on the most fundamental level, had incredible philosophical implications and many scientists developed thought experiments to elucidate the absurdity of a probabilistic universe. The most famous of these thought experiments was developed by Schrodinger himself, as he could not accept the Copenhagen interpretation. It is called Schrodinger's cat, and it focuses on the bizarre concept of quantum superposition. The idea is that if the Copenhagen interpretation is correct, a quantum system can exist in a number of different states, and until the system is observed it exists in a superposition of all these states. Once observed, it collapses into one of the definite states according to its probability. Schrodinger did not like this, and he came up with a paradox. He supposed that there was a box containing a single radioactive atom. At any given moment this atom has the potential to decay, emitting a high-energy particle. Inside the box there is also a cat, a flask of poison, and a device with the ability to detect radiation. If the device detects that the atom has decayed, it will trigger a mechanism that breaks the flask of poison and the cat will die. If it does not detect this, it won't, and the cat will be alive. The problem arises when we isolate this system from observation. According to the Copenhagen interpretation, the atom is in a superposition of decaying and not decaying, which seems pretty abstract and harmless, but because of the mechanism in the box, that means that the cat must be in a superposition of dead and alive. Only once you open the box and look inside will you observe the cat as being one or the other. Schrodinger meant for this paradox to discredit the Copenhagen interpretation but there are many camps that believe that this dead/alive superposition is a concrete reality. This thought experiment remains a classic, and it is frequently referred to when comparing different interpretations of quantum mechanics. But enough about cats, let's finish up with Heisenberg. Thanks for watching, guys. Subscribe to my channel for more tutorials, support me on patreon so I can keep making content, and as always feel free to email me:
