Does Heisenberg’s principle state that it is impossible to know all about subatomic particles at the same time, or that we just can’t know about them when our tools for observing them are crashing other subatomic particles into them?
I think it is inherent. The mere act of observing something means that thing has been affected in some way. The ONLY way you (or an instrument) can gain information from an object is for that object to transmit information to you. To do that it either needs to emit that information or you need to throw something at it and then read the reflection of what you threw. In both cases the object has been changed from the state it was in prior to your observation.
Certainly, we can use more refined tools to minimize the uncertainty but it will always be there. For instance…you have a car that I want info about. 100 years ago I might have thrown rocks at it and from the way they bounced back to me I’d try and determine what the size and shape of the car was but my information is going to be pretty poor because the rocks will deform the car. Today I might use plastic pellets. My information about the car will be better than 100 years ago but it still won’t be perfect (what color is the car?).
It’s inherent. Regardless of your tools, it’s simply impossible to know both the momentum and the position of anything. This becomes clear if you consider it as a wave superposition problem, then accept that momentum is proportional to frequency. Mathematically, you can’t simultaneously be exact in both position and frequency.
The other Heisenberg relationships hold, as well – you can’t know energy and time, or total angular momentum and all projections. Again, all of this comes out in the math – pairs of items that cannot be observed simultaneously do not commute, while those that can be known will commute. All of this is inherent in Schroedinger’s equation and the associated mathm, and is totally independent of the measuring mechanism.
See any good Intro to Quantum Mechanics book.
Cal,
do you mean velocity (and position) or momentum because the mass changes with speed?
It’s always made sense to me - If you fix the position then it no longer has a velocity to measure. And the only way to measure velocity is to fix two postions over time. But doesn’t some aspect of this depend on whether the universe is discrete or continuous?
Nope – this isn’t a relativity issue, if that’s what you mean.
This is more like it, and the way it’s usually explained. But if you view the particle as a mathematical function that you can build up from a superposition of, say, sine waves, then you’ll find that in order to define the position to a very small location you need a very large range of frequencies. So small position uncertainty = large frequency uncertainty. And momentum id proportional to frequency, so a high certainty of position requires that you have a very poor idea of the momentum (and vice-versa). As I say, see a book on Quantum for details.
And this, mind you, is without even considering a possible quantization of space.
My question here is, are electrons fundamentally different than cars? Or, is the reason that electons behave in non-Newtonian ways merely a function of the fact that we cannot “see” them?
The heisenberg uncertainty would apply to measuring the speed/position of a car as well. If you attempt to fix the position of a car to get an exact measurement you must fix time. If you want to measure the speed of the car you inherently have more than one position because speed is distance/time.
A car also has much more mass than an electron, which is relevant, IIRC.
Listen to CalMeacham. The Heisenberg uncertainty principle is only valid for quantum mechanical observations. What is says is that two non-commuting operators cannot be independently applied to the same wavefunction.
Any attempt to apply it to real-world phenomena is at best hand-waving analogies, and at worst missleading.
It is for example possibe to measure position and energy independently, as they are represented by commuting operators[sup]1[/sup].
If you don’t understand what commuting operators are, then you are not ready to understand how the Heisenbergs uncertainty principle works! Take Cals advice and get a book!
[sup]1[/sup][sub[Or am I getting into a mess here? At least that’s what I remember from studying the phenomena, and my degree was in theoretical physics[/sub]
Quantum Mechanics - The dreams that Stuff are made of.
Ooops!
Please replace all pccurances of commute with commutate in my post above…
: hangs head in shame: (and hopes that it shouldn’t be 'anti-commutating operators…)
It’s a tad ridiculous to say the Uncertainty Principle applies to any macroscopic object. The corresponding de Broglie wave for a large object is so very attenuated as to be practically non-existent. The automobile’s position-space and momentum-space wavefunctions are constrained in the same manner as an electron, but the effects are unnoticeable because of its larger scale.
Electrons do behave fundementally different than cars. As an object gets smaller it behaves less and less in ways that we understand from experience with the macro world.
A very strange thought, but it might illuminate this for you. The size of an electron’s orbit around a hydrogen nucleus is the same size as its positional uncertainty. It certainly appears that the uncertainty principal is what give atoms the size that they have.
Scientists wondered for a long time why an electron didn’t simply fall in on the nucleus. But, if the electron sat on the nucleus, then we would no exactly where it was and how fast it was going. Running the idea backwards yields the result that the minimum orbit for an electron is the smallest size that would not break the uncertainty principal.
I mangled the language on that a bit, but you should get the general idea until chronos or princeton come by.