# Electron smear

1. Feb 2, 2009

### nuby

Is there a physical meaning to the electron "smear" or probability cloud? If an object (electron) was to somehow travel faster than time, wouldn't it appear in multiple locations at once or as a "smear"?

2. Feb 2, 2009

Staff Emeritus
Traveling "faster than time" is meaningless.

3. Feb 2, 2009

### nuby

Ok, switch "faster than time" with "through time differently than regular matter".

4. Feb 2, 2009

That makes even less sense.

5. Feb 3, 2009

### nuby

C'mon.. Is my question that hard to comprehend?

6. Feb 3, 2009

Yes, it is, because it really doesn't make sense.

The probability "cloud" you speak of refers to the probability density of measuring the electron's position to be at that point, at a specific time. There is no reference to its motion.

What does "faster than time" or "through time differently than regular matter" mean? Seriously?

7. Feb 3, 2009

### Dmitry67

What do you think "regular matter" is made from? :)

8. Feb 3, 2009

### nuby

I was referring to the concept that an electron (singularity) within a atomic orbit is "everywhere at once" around the nucleus. Is this not correct?

9. Feb 3, 2009

### nuby

I guess I should have said composite particles. But those are probably just as irregular as electrons.

10. Feb 3, 2009

### Nick89

I don't know if an electron in orbit is considered "everywhere at once". I think what is meant that, if you would measure the position of the electron, you could find it anywhere (even on the moon), but the chance of finding it near the atom it's orbiting around is much much much larger. The 'electron smear' is just the probability wavefunction that tells you the chance of finding an electron at a certain position. Where it was before you measured it isn't really a sensical question, because you would have to measure it to know where it was before you measured it, so you have to measure it before you measure it before you ... etc :p

11. Feb 4, 2009

### nuby

So considering an electron in multiple locations at once isn't an accurate description of the actual electron/shell.

12. Feb 4, 2009

### msumm21

By "the electron traveling faster than light" do you mean that the expectation value of the electrons position, according to the underlying probability distribution function (PDF), is moving faster than light? Or are you thinking of the electron as really just non quantum mechanical object shaking and moving around in circles, ... at very high speeds > c and trying to use that as a way to interpret quantum mechanical (statistical) effects?

13. Feb 4, 2009

### vanesch

Staff Emeritus
I don't see why that wouldn't be a good way to look upon it ? (at least, that's how I look upon it)

14. Feb 5, 2009

### enomanus

Hi Peeps,
I'm new to this forum and self study QM. This thread raises an interesting question for me. How does science picture say an electron travelling in a straight line. The prob. amplitude wavepacket travels wth the velocity of the electron.! When we make make a measurement of its position , we have the probality of that result... psi ^2.! But how do we picture the electron smear travelling .? Do we picture an electron cloud with the ghostly electron smeared in it travelling withh velocity v and if so, how do we picture what happens when we measure it's position.?
I know the answer will probably be.. we can't!!!
BUT IT STILL PUZZLES ME ???
tHANKS!

15. Feb 5, 2009

### ZapperZ

Staff Emeritus
I work at a linear electron particle accelerator, and we model such electrons classically. All our particle tracking codes that we use to study the beam dynamics are all classical (relativistic) Maxwell equations acting on classical particles. And it WORKS!

Zz.

16. Feb 5, 2009

### per.sundqvist

It smears in time yes. But the reason why you could look on it classically for particle accelerators (as Zz mention) is that the time is so short, since particles travels close to the speed of light (Or?).

Assume you have a Gaussian package at t0 with size a0 (standard deviation) which travels with some "average" speed v. For the free particle case the evolution of this package is easy to calculate.

$$\Psi_0=\exp\left(i\hbar k_0-(\frac{x-x_0}{a_0})^2\right)$$

the "size" a will increase in time roughly as (for more exact result use the free Green propagator):

$$a(t)=\sqrt{\frac{\hbar t}{m}-a_0^2}$$

using $$m\;v_0=\hbar k_0$$ and, total time T=L/v0, and wavelength $$\lambda=2\pi\hbar/mv_0$$ you could play around with what you get after distance L, with speed v0 and with initial smearing size a0.

Also the potentials involved in accelerators are macroscopic, i.e., the typical "size" of them are much larger than the wavelength and a0 of the electrons, so you could safely look on the electron as a point particle. But things changes if the electron hits a region with interaction distance similar to its wavelength (slit, or double-slit for example).

17. Feb 5, 2009

### ZapperZ

Staff Emeritus
Correct. Or the potential a "free electron" sees in a periodic crystal lattice. In such cases, then the classical electron model can easily break down.

Zz.

18. Feb 6, 2009

### nuby

This is more relevant to what I was thinking/wonder about.