I am new, and I don't have a physics background, so please excuse the question if it is incredibly easy... Does the Heisenberg Uncertainty Principle mean that we just can't measure the location of an electron to perfect accuracy, but such a location does exit (we just can't know what it is)? Or does it mean that we can know the general location of the electron, but beyond that, the electron can not be said to exist in any particular location? So basically, does an exact location of an electron exist, even if we can't know what it is?
The Heisenberg uncertainty principle (in the case of momentum and position) says that we can measure the position and momentum exactly, but we can't predict beforehand what that position will be. Basically, the HUP for momentum and position says that the spread of the probability of what the position and momentum will be must be greater than hbar/2. So if you know momentum exactly, then the electron is equally likely to be anywhere.
I should probably explain it more simply, the electron only has a definite position when we measure that position. Before we make the position measurement, it is useless to ask "where is the electron".
And adding: there is no intrinsic limitation on measuring a single particle attribute. That is NOT what the Uncertainty Principle is about. It is about the limitation on (non-commuting) pairs of attributes. Measuring one more precisely makes the other less precise. Or you might say that knowing one reduces the constraints on the other.
The true meaning of HUP is that position and momentum are not two separate entities, but two views of the same thing, and that thing is a wavefunction.
A wonderful description. Especially when considering "particles" without rest mass (photon). (Reply #5)
That bit about measuring the position and momentum is not "THE" Uncertainty Principle, but rather an example of it. In the case of measuring a electron it is problematic because if we use a low energy photon (so as not to disturb the electron when we measure it)then the electron's position changes over a long time of the photons period. If we use a photon with a shorter period, then it has more energy and will cause the electron to react and be in a different place from where it would be if we had not disturb it. So in a way the Uncertainty Principle tells us that at the small quantum level, we can not measure (some like to say observe, but that term is often used to mislead people) particles without effecting it. Also, the Uncertainty Principle also affects the Macroscopic world as well. It's just that it's affect is so small in the macroscopic world that the effect is considered negligible.
So if an electron is a wavefunction, then saying that it can't be predicted to be found in an exact position is stating the obvious? I don't really understand what a wave function is. I've read the article on wikipedia, but there are too many things I don't know, like what a function is...among other things.
We can measure the position of an electron to any accuracy allowed by the measuring apparatus. If we had perfect instruments we would have perfect accuracy, but experimental accuracy has nothing to do with quantum uncertainty. In quantum mechanics, uncertainty in position means that the position is indeterminant; we get different values for the position when we repeat the same measurement. That is the quantum way! Generally, it is impossible for us to predict the result of a position measurement. For example, there is no answer to the question, "What is the position of an electron on a detection screen after passing through a double slit?" There are an infinite number of possibilities! Quantum mechanics will tell us all the possible results and the probability of getting each possible result. Does the quantum electron have an exact location, but we just don't know what it is? No! There are classical experiments where electrons do behave like classical particles. Classical particles do have a position at every instant; they have trajectories. But, quantum particles, including electrons in quantum experiments, do not have trajectories. The quantum particle, as others have said, has a position only at the instant it is measured.
In classical physics, there is a principle that if you know everything about a system, you can predict what will happen in the next second or the next hour, and you can rewind to predict what has happened. ie, if you're given the speed, direction, and mass of a ball, and information about a wall, then you can predict how the ball will bounce off of the wall. You can also predict where the ball was a second ago. People had thought that if you could somehow know the speed and position of every particle in the universe, and you know all the laws, then with a big enough computer you can calculate all of the events in the universe. But it was discovered that in quantum mechanics, you can only predict the probability of something happening. You could know the speed and direction of every particle in a system, but there is no way to know 100% where they will all be the next second, or where they were a second ago.