# The Uncertainty Principle

1. Jun 27, 2008

### epkid08

I'm trying to figure out why exactly we have it. It's just a simple question.

Do we have this principle because human error is far to great to ever measure a particle's momentum and its location at the same time, or we just can't measure them accurately because they're without our dimension of time?

2. Jun 27, 2008

### HallsofIvy

Staff Emeritus
No, the uncertainty principle is a fact of nature. It has nothing to do with "human error" in measurements. I have no idea what you mean by "our dimension of time".

Imagine trying to determine the position and momentum of an electron. Let's say you shine a light on it and look at it through a microscope- I'll let you assume as much accuracy for the microscope as you like. But no matter how good your microscope is, you can't get the accuracy in the position better than one wavelength of light.

That in itself is not a problem- just use light with a very very small wave lenght- there is nothing at all preventing you (theoretically) from determining the position of that electron as accurately as you please (and the "uncertainty principle doesn't say you can't).

But the smaller the wavelength of the light, greater the energy: The more accurately you try to determime the positition, the harder the light hits that electron and the more the its momentum is changed.

The "uncertainty principle" says you can't improve the accuracy of a position measurement without making the accuracy of a momentum measurement worse, and vice-versa.

3. Jun 27, 2008

### epkid08

Yes, but you could say that about objects in any size, couldn't you? I mean light might affect small particles more than say it affects an elephant, but it doesn't mean the elephant doesn't experience a normal sized change.

4. Jun 27, 2008

### ZapperZ

Staff Emeritus
That is true, but that has nothing to do with the HUP at all. The HUP is more intrinsic than that. The simplest example that I've often mention is the single-slit experiment, which really is the clearest demonstration of the HUP. You ability to know the position very well (i.e. make the slit small) corresponds to your decrease in ability to predict the momentum of the photon (or electron, etc) that passed through the slit. That's why the diffraction pattern grows wider the smaller you make the slit.

Zz.

5. Jun 27, 2008

### epkid08

There's something I still don't get. When you make the slit small, let's say one unit wide, you know that the particle passed through that one unit space, but how does this affect, or tarnish your ability to measure its momentum? Or my question is, how does making a bigger slit, let you measure the particle's momentum more accurately?

6. Jun 27, 2008

### Troponin

Calculate it when measuring an elephant and see how your measurements change. The math still works, it just creates a much more profound effect at the smaller level.

If the circumstances were such that to view the position of an elephant you had to hit it with light so powerful that it completely changed the position of the elephant, you'd have to understand that you couldn't make an accurate prediction as to where it was before you viewed it.

7. Jun 27, 2008

### ZapperZ

Staff Emeritus
Let's say the slit is at location x1, and it has a width w. It will acquire an x-component of momentum, px. The smaller you make w, the larger the RANGE of px it can acquire, because, as you've noticed, as you accumulate more and more of the signal, the places where the particle hit the screen becomes wider and wider. It gives a larger statistical spread of px.

Zz.

8. Jun 27, 2008

### peter0302

It does indeed, though that change is extremely small, and so, in practice, you can't get any information from that (analogous to an electron and a very large wavelength). But try learning the position of elephants using other elephants, and now imagine how much uncertainty there'd be (analogous to an electron and a very small wavelength).

As soon as your measuring apparatus is on the same scale as the object you're trying to observe, you will inherently run into uncertainty problems, in any context. QM is special though because there is a specific, inverse relation between scale and energy (E=hf), and so the greater your accuracy, the more energetic, by definition, your measuring device, and therefore the more uncertain is your result.

9. Jun 28, 2008

### pmb_phy

This seems to be a common misunderstanding of the uncertainty principle. Uncertainty does not refer to the precision of the meaurements of observables. Even if we could measure observables exactly that would not change the intrinsic uncertainty that is a property of a system.

For exampe; I know the value on the number of dots on face of a die with infinite precision. But there is a non-zero value of the uncertainty of the number on the face. I.e. when a die is rolled I know its exact value. But that value is not known until the die is rolled. Think of uncertainty in the exact same way that you'd think of standard deviation because they are the same thing.

Pete

10. Jun 30, 2008

### Domenicaccio

I am trying to see it in the following way...

It's a fact of nature, not related to humans. Talking about "measuring" is perhaps not the happiest choice because it very often confuses people, leading them to think that the principle manifests itself only when a human tries to investigate reality, instead it happens all the time.

Instead of an external person measuring the properties of a particles, it might be better to just think that "properties" are what define how a particle interacts with the rest of the universe and its other particles/objects.

By establishing that there is a minimum uncertainty, the Heisenberg principle is actually telling us that interactions happen in terms of discrete quantities (quanta), the dimension of each of which in fact always depends somewhat on the constant "h".

It's like saying, the minimum uncertainty of a phenomenon (i.e. interaction between for instance radiation and matter) corresponds with the face that the phenomenon needs at least 1 quantum (e.g. photon) to take place. Either it takes place with 1 photon, N photons, or it doesn't take place. You cannot have it take place with half a photon. The uncertainty's "delta" is the difference (e.g. energy difference) between zero photons and 1 photon.