The Heisenberg Uncertainty Principle
The Uncertainty Principle
In classical mechanics, if someone said there was some uncertainty in knowing the position and momentum of an object, then we would say that this is simply due to a poor experiment. If we found better equipment and used a better method then we could know the momentum and position of an object with unlimited precision.
Quantum mechanics tells us that this is wrong however and that there is a fundamental obstruction to measuring the position and momentum of an object to unlimited precision simultaneously.
Heisenberg wrote an equation saying that the uncertainty in the position of an object multiplied by the uncertainty in its momentum always had to be greater than ħ/2.
ħ is the reduced Planck constant and is equal to the Planck constant divided by 2π.
To understand why this is the case, we have to look at the de Broglie wavelength equation.
Through the photoelectric effect Einstein found that the energy of an individual photon is given by
E = hf
where h is the Planck constant
f is the frequency of the photon
The quantization of electromagnetic waves was surprising as it suggested that the amplitude of a light wave had nothing to do with its energy and it was all to do with its frequency. This is like suggesting 1 large baseball bat swing every second has less energy that 1 small baseball bat swing done every 0.99 seconds!
From Maxwell's theory of light we also have the equation for the energy of a photon
E = cp
We can also derive this equation using what we know about special relativity.
Deriving E = cp From Special Relativity
E = cp
Putting these two equations together gives
cp = hf
p =hf/c
And remember for a wave v = fλ
For light this is c = fλ
So p = hf/fλ
p = h/λ
This equation tells us that the momentum of a photon is inversely related to its wavelength. This is what the uncertainty principle boils down to.
If you want to measure something, the most direct way to do so is by looking at it and so you shine photons on it so that you can see it. If you shine low frequency, low energy, high wavelength light at it, you won't have a good idea of where the object is. It would be pretty hard to know where an electron was using light with wavelength 1m because all it would tell you is the location of the electron to within a meter. To get a more precise position, you have to use short wavelength light.
The problem with this is that short wavelength light has a high momentum. This is fine if you only want to know the position of the electron but what happens when you want to also know the velocity?
You would have to hit the electron with a photon, wait an amount of time, hit the electron with a photon again and then do the distance between the two points divided by the time you waited for.
The problem is that after you hit the electron with a photon the first time, you've changed its speed and so its not actually moving at speed v. Trying to improve your position measurement meant you've messed up your velocity measurement.
If you wanted to not change its speed a lot, you would have to use long wavelength light but then you wouldn't have a good idea of where the electron was. Trying to improve the velocity measurement messes up your position measurement.
The uncertainty principle turns out to be a fundamental property of the universe and is nothing to do with how good your technology is. No matter how hard you try, you will never be able to know both the speed and the position of an object.
Deterministic Systems
Classical physics is entirely deterministic. If we knew where every single particle in the world was right now and put it in a computer, we could run a simulation which would precisely predict all interactions between particles and we would actually have an exact simulation of the world. This would include precisely predicting all human behavior because ultimately, human's decisions come from particles acting in a way which conforms to the laws of physics. Quantum mechanics suggests that this is not entirely true.If there is no way to measure something then we can go as far as saying it does not exist. This means perfect knowledge of a particle's position means knowledge on its momentum can't exist and vice versa. Improving knowledge of one means information on the other is being lost. This means total information about particles does not even exist and so the universe can not be classically deterministic.
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Check Out My Other Posts On Quantum Mechanics (link to all posts)
The Birth Of Quantum Mechanics - The Ultraviolet Catastrophe
Schrödinger’s Kittens - The Boundary Between Quantum And Classical Mechanics
Did you see my previous post? Click the link below to check it out
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