Quantum Mechanics I
Aug. 6th, 2005 05:24 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
danalwynA friend of mine threw a party to thank some of us for helping him and his roommate move. Before I got there his roommate managed to burn his arm in an oil fire and I got there just in time to watch them drive off to the Emergency Room. Fortunately everything turned out all right.
Not much happening today either, so I'm going to talk more about physics, although instead of what I promised, I will make a somewhat less amusing digression into the world of Quantum Mechanics, just for people who have never seen it before.
So, I'm going to have to back up a bit in my story because I've gone past one of the most important events in the history of science, basically the invention of Quantum Mechanics.
In 1913, a scientist named Niels Bohr decided that physics was too easy to understand, and decided to do something about it. The key to all of this was Rutherford's model of the atom, which Bohr decided to make even more complicated by requiring the electrons to exist in strange "orbits", something that at the time was so confusing that it eventually won him the 1923 Nobel Prize. The aftermath of this mess is what we call Quantum Mechanics.
Quantum is a word that refers to the phenomenon we now call Quantization. A brief explanation of quantization is as follows:
Take something like energy. If you look a standard lightbulb it probably says 60 Watt on it. This means that the lightbulb uses 60 Watts of electricity, a measure of power. In terms of energy is uses 60 Joules every second-so you use 3600 Joules a minute and so on and so on. So now you have an idea of the amount of energy that a joule is. A 75 kg person moving at 1 meter per second (fairly slow) has an energy of 37.5 Joules. If they go just a little faster though, they can have a different energy, 38 Joules, or 37.6 Joules, or 37.51 Joules. This is not true of quantized objects.
An electron in the lowest energy state of a Hydrogen atom has -13.6 eV of energy (ignore the minus sign, it's sort of pretty, but not that important for us), where an eV is an electron-Volt, a rather small amount of energy (used by particle physicists). An electron in the second-lowest state has -3.4 eV. There is nothing between that. Electrons with energies between these levels simply cannot exist within a hydrogen atom-they radiate that energy away. The spectrum of energies in this system is not continuous as it is in a human being. Rather it is discrete containing a certain number of distinct values, with gaps between different values.
But real quantization goes even farther. Properties like the momentum of a particle are quantized. Particles can only have certain values of momentum, and they all come in multiples of Plack's constant (1.0546 x 10-34 J sec). Worse, particles have a strange "intrinsic" angular momentum which we call spin (because it behaves like spin, not because the particle is actually spinning), which is fixed. Electrons, for instance, have spin 1/2, regardless of what you do with them (this actually means that you can have spin +1/2 or -1/2).
So Bohr, and several others, developed this theory, basing it around the legendary Schroedinger equation, and they showed it to a lot of physicists. And most of those physicists simply stood there, because reading Quantum for the first time is like waking up in the morning to find yourself clinging to the top of a speeding train that's roaring upside down underneath the Brooklyn Bridge. But some of them got all excited, because if they couldn't understand the damn thing, then neither would the grant committees, and they made a lot of money out of this and then they became professors and sat on their ass for the rest of their life.
One of the fundamental pieces of Quantum Mechanics is the Heisenberg Uncertainty Principal, henceforth referred to as the HUP. This is that legendary piece of science that says that you can't measure the momentum and position of an object at the same time, and that the act of observing one changes the other. The philosophers immediately took off with this one and began trumpeting it as the foundation to all sorts of philosophies. This is patently ridiculous-the HUP is simply the statement of a mathematical law so fundamentally boring that nobody in physics really comments on it anymore, but try telling that to the philosophy people.
An easy way to understand the HUP is to think of an indoor ice rink that suddenly suffers a power outage and goes pitch black. You've suddenly got all these skaters who are slowing to a stop out in the middle of the ice who are suddenly able to find their way back. This is sort of what life is like in the Quantum world; you've got a lot of particles out there and you don't really know where they are or what they're doing. So what physicists do is we shine something like light out there and see what happens-how light reacts with those particles. This sounds simple for you and me, who have billions of photons bouncing off of us each second, but it's a lot more traumatic for an atom.
To go back to our ice rink analogy, imagine that a rescue worker comes in with his tame gorilla. The gorilla immediately tries to locate the skaters stuck on the ice by hurtling twenty pound bowling balls out into the rink, and waiting for the screams as people get it. So when the rescue worker hears the scream, followed by the thunk of the bowling ball hitting ice, he now knows more or less where that particular skater was. But by measuring this (with some degree of error), he has also changed that person's speed because, let's face it, a gorilla hurling a twenty pound bowling ball is going to impart a great deal of momentum to you. This is more or less what it's like for a particle; it's floating there fat and happy when suddenly a photon comes up and whacks it on the head with a baseball bat. Suddenly it's careening off things like a superball in a bumper car arena.
Actually, QM makes things even worse. All we can predict in a Quantum world is a probability. In other words, we can get out our pencils and paper and computers and predict that if we try and measure the energy of a d-orbital electron in an atom like Iron, we're likely going to see it here, where here is a region with a rather peculiar shape:
But that's only a majority of the time. Sometimes electrons will be found outside of those shapes. It happens very rarely, but it does happen from time to time.
This is why we say that a particle is a wave and a particle at the same time. The probability function behaves like a wave. But when we measure it, it appears in a very narrow region, acting more like a particle. So a particle is really thing object that is sort of spread around; it may be here or it may be there, until someone measures it.
Quite frankly, this is all very confusing and ridiculous and it has absolutely no bearing on the rest of the universe-besides the part where it makes the rest of the universe possible. With Quantum Mechanics, physicists finally had the tools to do something with particle physics, except that they didn't have any damn particles to do physics on. Within years Chemists, who never bother with the details half the time, had taken over management of calculating the behavior of electrons on the known atoms-so atomic physics was put on hold, until the foundation fell out of the building. But more on that next time.
And no, I still haven't answered the question about why the nucleus stays together. That will have to wait for next time.
Not much happening today either, so I'm going to talk more about physics, although instead of what I promised, I will make a somewhat less amusing digression into the world of Quantum Mechanics, just for people who have never seen it before.
So, I'm going to have to back up a bit in my story because I've gone past one of the most important events in the history of science, basically the invention of Quantum Mechanics.
In 1913, a scientist named Niels Bohr decided that physics was too easy to understand, and decided to do something about it. The key to all of this was Rutherford's model of the atom, which Bohr decided to make even more complicated by requiring the electrons to exist in strange "orbits", something that at the time was so confusing that it eventually won him the 1923 Nobel Prize. The aftermath of this mess is what we call Quantum Mechanics.
Quantum is a word that refers to the phenomenon we now call Quantization. A brief explanation of quantization is as follows:
Take something like energy. If you look a standard lightbulb it probably says 60 Watt on it. This means that the lightbulb uses 60 Watts of electricity, a measure of power. In terms of energy is uses 60 Joules every second-so you use 3600 Joules a minute and so on and so on. So now you have an idea of the amount of energy that a joule is. A 75 kg person moving at 1 meter per second (fairly slow) has an energy of 37.5 Joules. If they go just a little faster though, they can have a different energy, 38 Joules, or 37.6 Joules, or 37.51 Joules. This is not true of quantized objects.
An electron in the lowest energy state of a Hydrogen atom has -13.6 eV of energy (ignore the minus sign, it's sort of pretty, but not that important for us), where an eV is an electron-Volt, a rather small amount of energy (used by particle physicists). An electron in the second-lowest state has -3.4 eV. There is nothing between that. Electrons with energies between these levels simply cannot exist within a hydrogen atom-they radiate that energy away. The spectrum of energies in this system is not continuous as it is in a human being. Rather it is discrete containing a certain number of distinct values, with gaps between different values.
But real quantization goes even farther. Properties like the momentum of a particle are quantized. Particles can only have certain values of momentum, and they all come in multiples of Plack's constant (1.0546 x 10-34 J sec). Worse, particles have a strange "intrinsic" angular momentum which we call spin (because it behaves like spin, not because the particle is actually spinning), which is fixed. Electrons, for instance, have spin 1/2, regardless of what you do with them (this actually means that you can have spin +1/2 or -1/2).
So Bohr, and several others, developed this theory, basing it around the legendary Schroedinger equation, and they showed it to a lot of physicists. And most of those physicists simply stood there, because reading Quantum for the first time is like waking up in the morning to find yourself clinging to the top of a speeding train that's roaring upside down underneath the Brooklyn Bridge. But some of them got all excited, because if they couldn't understand the damn thing, then neither would the grant committees, and they made a lot of money out of this and then they became professors and sat on their ass for the rest of their life.
One of the fundamental pieces of Quantum Mechanics is the Heisenberg Uncertainty Principal, henceforth referred to as the HUP. This is that legendary piece of science that says that you can't measure the momentum and position of an object at the same time, and that the act of observing one changes the other. The philosophers immediately took off with this one and began trumpeting it as the foundation to all sorts of philosophies. This is patently ridiculous-the HUP is simply the statement of a mathematical law so fundamentally boring that nobody in physics really comments on it anymore, but try telling that to the philosophy people.
An easy way to understand the HUP is to think of an indoor ice rink that suddenly suffers a power outage and goes pitch black. You've suddenly got all these skaters who are slowing to a stop out in the middle of the ice who are suddenly able to find their way back. This is sort of what life is like in the Quantum world; you've got a lot of particles out there and you don't really know where they are or what they're doing. So what physicists do is we shine something like light out there and see what happens-how light reacts with those particles. This sounds simple for you and me, who have billions of photons bouncing off of us each second, but it's a lot more traumatic for an atom.
To go back to our ice rink analogy, imagine that a rescue worker comes in with his tame gorilla. The gorilla immediately tries to locate the skaters stuck on the ice by hurtling twenty pound bowling balls out into the rink, and waiting for the screams as people get it. So when the rescue worker hears the scream, followed by the thunk of the bowling ball hitting ice, he now knows more or less where that particular skater was. But by measuring this (with some degree of error), he has also changed that person's speed because, let's face it, a gorilla hurling a twenty pound bowling ball is going to impart a great deal of momentum to you. This is more or less what it's like for a particle; it's floating there fat and happy when suddenly a photon comes up and whacks it on the head with a baseball bat. Suddenly it's careening off things like a superball in a bumper car arena.
Actually, QM makes things even worse. All we can predict in a Quantum world is a probability. In other words, we can get out our pencils and paper and computers and predict that if we try and measure the energy of a d-orbital electron in an atom like Iron, we're likely going to see it here, where here is a region with a rather peculiar shape:
But that's only a majority of the time. Sometimes electrons will be found outside of those shapes. It happens very rarely, but it does happen from time to time.
This is why we say that a particle is a wave and a particle at the same time. The probability function behaves like a wave. But when we measure it, it appears in a very narrow region, acting more like a particle. So a particle is really thing object that is sort of spread around; it may be here or it may be there, until someone measures it.
Quite frankly, this is all very confusing and ridiculous and it has absolutely no bearing on the rest of the universe-besides the part where it makes the rest of the universe possible. With Quantum Mechanics, physicists finally had the tools to do something with particle physics, except that they didn't have any damn particles to do physics on. Within years Chemists, who never bother with the details half the time, had taken over management of calculating the behavior of electrons on the known atoms-so atomic physics was put on hold, until the foundation fell out of the building. But more on that next time.
And no, I still haven't answered the question about why the nucleus stays together. That will have to wait for next time.