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Topic: Heisenberg Uncertainty Principle  (Read 4746 times)

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Offline lukeli88

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Heisenberg Uncertainty Principle
« on: June 20, 2008, 02:36:51 PM »
I was just wondering, is the Heisenberg Uncertainty principle true only because of the limitations of technology, or is it inherently true? In other words, if we have infinitely precise instruments (just assume) to measure the position or momentum of a particle, it should not have any effects on measuring the other, right? So, is it only a limitation of technology or is it just impossible to know both the momentum and position of a particle?

Offline Yggdrasil

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Re: Heisenberg Uncertainty Principle
« Reply #1 on: June 20, 2008, 03:13:46 PM »
It is an actual physical limitation, not a technological limitation.  Measurement of a system distrubs the system (changes the actual wavefunction of the system) in such a way that certain physical observables cannot be known simultaneously.

Here's the quantum mechanical explanation probably won't make too much sense if you have not had an advanced course in QM.  However, I provide it here for completeness:

In order for a system to have a defined value for a certain physical observable (e.g. position, momentum, energy), the system must be in an eigenstate of the quantum mechanical operator corresponding to that physical observable (e.g. the position operator, the momentum operator, the hamiltonian, etc.).  The position and momentum operators do not share the same eigenstates (i.e. they don't commute).  Therefore, if your system is in an eigenstate of the position operator (i.e. you know its position precisely), the momentum is not known because you are not in an eigenstate of the momentum operator.

Offline tamim83

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Re: Heisenberg Uncertainty Principle
« Reply #2 on: June 23, 2008, 10:19:34 AM »
Here is another example that may make sense. 

Suppose you wanted to take a picture of an electron in an atom.  You would need short wavelength light to do it.  Taking the picture would cause the atom to absorb the light and eject the electron.  So, you would know how fast the electron is going and thus it's momentum with a bit of certainity.  But you would have no idea where exactly it came from.  So the very act of trying to observe the atom alters it.  This set-up is a thought experiment proposed by Heissenberg himself. 

It is a physical limitation for "small systems".  No matter how "good" our technology is, we will always come up against this problem.  However, it isn't a big issue when the mass of the object is large.  This is why you can take a picture of a baseball being pitched and know where it is and how fast it is going to a high level of certainty. 

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