One of the VERY BIG RULES of science is quantum mechanics’ Uncertainty Principle, which states it is impossible to know with complete accuracy both the position AND momentum of a particle.
Is that because the very act of measuring one destroys information about the other?
Or is it because at the microscopic level both measurements DO NOT EXIST?
My high school science teacher touched on physics one week and described the principle thusly:
Taking a ping-pong ball painted black on exactly one hemisphere, held it up to the class and said how no matter how you held the ball, you can never see all of both sides of the ball at the same side…the more you saw one side, the less you saw the other.
Well, it’s complicated. There are various interpretations of quantum mechanics which range from complicated theories of ontology and epistemology (which answer the second question in various ways) down to the “Shut Up And Calculate” interpretation, which says that none of that really matters as long as you can crank out numbers that predict the results of experiments. The following is roughly my take as a mathematician with a strong interest in foundational physics:
The explanation usually has the flavor of your first question because that provides a nice explanation for why things go wrong, but it depends heavily on a specific set-up of a specific experiment to measure a specific property, and doesn’t really support the universal truth of the HUP. Instead, it seems that what “really exists” is a certain function that describes the likelihood for a particle to be observed doing various things. And it’s when we mathematically study such functions that we find some really interesting things happening.
A rough analogy which gets at most of the relevant bits is to think of a sound wave. The usual wave we see on an oscilloscope measures the density of air at a given time. As the sound wave travels, the air is compressed and expanded according to the function.
The simplest sound wave would be a nice sine wave at a given frequency. You hear a steady tone, and your trusty oscilloscope shows a nice, even wave. As you turn a dial, the frequency goes up (the wave gets tighter and more crests show up on the screen) and down (fewer crests). If you flip a switch for your oscilloscope to display frequencies, you see a single mark on the screen, which moves right and left as the frequency moves up and down. These waves are localized in frequency-space, where any one sine wave just looks like a single point. But they’re very much not localized in density-space, where they keep waving up and down all the way out to infinity.
But we can have more complicated sounds, layering more than one sine wave on top of each other. Playing two sine waves gives various more complicated wave forms in density-space, but in momentum-space we just see two points, and their intensity measures the relative loudnesses of the two tones.
More complicated still, we could play a piano chord into the oscilloscope. The density-space display now looks complicated and jumbled, with many complex harmonics showing up. If you open up a .wav file in a basic sound-recording program, the wave form should look sort of like this. The frequency-space display, is also very complicated, with a lot of points showing up each of the different frequencies making up the whole sound.
Moving further to the other extreme, a sharp shock (like a clap) shows up as only a single point in the density-space picture. There’s a burst of pressure, and then it’s gone. It’s very localized in time. But when we plot the frequencies, they’re all over the place! In order to make up a sound like that, you need frequencies from all across the spectrum.
So it seems that no matter what sound you try to make, the more localized the sound is in time, the more spread out its frequency spectrum is. And the more localized it is in frequencies, the more spread out it is in time. The more definite a sound’s time is, the less definite its frequency is, and vice versa.
The weird part is: position and momentum of a quantum particle behave just like time and frequency do for the sound wave. The more the wave is shaped so that the result of measuring its position is predictable, the less it’s shaped so that the momentum is predictable, and vice versa, with a very definite lower bound in the accuracy of taking both measurements at once.
When I took QM, the prof spent a fair amount of classroom time demonstrating that you cannot design an experiment wherein complementary properties are arbitrarily measurable. If you measure momentum, you will affect the position, and vice versa.
Nonetheless, I am inclined to view the uncertainty principle as a property of space itself; that’s how it’s historically been viewed, and that’s how the math presents it. The observer principle might be inevitable due to the uncertainty principle, but it definitely isn’t the other way around.
A little Wiki
The only kind of wave with a definite position is concentrated at one point, and such a wave has an indefinite wavelength. Conversely, the only kind of wave with a definite wavelength is an infinite regular periodic oscillation over all space, which has no definite position. So in quantum mechanics, there are no states that describe a particle with both a definite position and a definite momentum. The more precise the position, the less precise the momentum
I use the same sound analogy as Mathochist. In my interperetation, this means that the two properties literaly do not exist simultaneously as precisely definable quantities. Luckily, chemist are rarely ever interested in (delta)T, so computations that give a precise (delta)E are just fine.
In fact, the Uncertainty Principle applies to all kinds of waves whatsoever. The big revelation in quantum mechanics was not the realization that the Uncertainty Principle applies, but the realization that matter is waves. About 90% of the weirdness you’ll encounter in quantum mechanics is ultimately due to wave-particle duality, and once you come to grips with that, it’s mostly smooth sailing.
I used to have a Heisenbergmobile, but every time I looked at the speedometer, I got lost.
Forgetting all the philosophical issues, it always struck me as being very simple:
In order to measure an object’s position, it needs to be motionless at a point in time. But if it’s motionless, then you can’t tell its speed.
Similarly in order to measure speed, it has to be moving. But if it’s moving, you can’t stop time to measure its position at the moment.
Of course, it can be done with general precision in the macro world, but once you’re dealing with subatomic particles the two measurements become impossible.
This may miss some nuances, but it’s a good conceptual basis.
Not really. You can’t measure the momentum at all if you know the position-- You can’t even tell that the thing is standing still, since that’s a measurement of momentum, too.
You’ve phrased these as two opposing questions, but my understanding is the answers to these two questions are “yes” and “yes.”
The very act of measuring one destroys information about the other; therefore, at the quantum level, those properties DO NOT EXIST to arbitrary precision. Since every possible thing you can observe is a “measurement,” then every aspect of their behavior that can be observed is subject to the rule. And if something can’t in principle be observed, then it can’t be said to exist.
The only knowledge we have of a quantum particle when it is not being observed is via a wave (the wavefunction.)
In order to know the exact position of the particle the wave would have to be a spike (a delta function.)
A wave spike requires an infinite number of different frequency component waves over an infinite range of frequencies.
So since momentum is proportional to frequency, and the number and range of frequencies is infinite, then if we can predict exactly where the particle is we inherently, intrinsically and absolutely can know nothing whatsoever about the momentum.
