# How to visualize a moving probability wave?

1. Feb 23, 2015

### jimmylegss

I added a picture , please comment where I am wrong. As I understand it, if you shoot let's say a photon from A to B, it doesn't really travel in the traditional way. It travels as a probability wave, untill it interacts with another photon or atom of a wavelength that is shorter then itself?

So as time goes on, the probability of finding that photon in a certain spot moves from A to B at the speed of light? The red area represents, this probability and how likely it is to detect the photon in that place. The horizontal line represents the distance and location. And T is different snapshots as time goes on. I drew 3 snapshots, let's assume it takes T=5 to reach it's location with the speed of light.

Im sure the probability wave looks all wrong, but just a simple visualization to get the concept right.

So my question(s),

1. Is it true that this probability wave moves at the speed of light (given that we are talking about a photon here) in a linear fashion from A to B. So not the actual particle, but the probability to find it.

2. But technically, it could move slower or faster? As in it is possible to detect it near A, even though it should almost have reached B judging by the speed of light? So there is a chance that if you turn on a detector near A after time T=4 (let;s say it takes T=5 to go from A to B if you assume light speed), there is a very small chance you could still detect it near A some of the time if you repeat the experiment many times? And as it is affected by this detector, it will then move the remaining distance to B in the classical sense as a particle at the speed of light? Thus technically travelling slower then the speed of light for the total distance between A and B?

3. Could you then say that the average speed of light is 300m m/s? As in if you don't interact with the photon in between A and B, you will always measure light speed. But if you measure it in between you will get different speeds between A and B, but averaging light speed in the end?

Or does this probability wave always travel exactly the speed of light? Or am i just babbling nonsense and have I got this completly wrong? Where do I go wrong?

Any feedback would be welcome

Thanks!

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2. Feb 23, 2015

### Staff: Mentor

Its not really a probability wave - its called a wave-function and its square gives the probability of, if you measured the particles position, of finding it there.

I will limit myself to electrons because photons are more problematical without going into the details why.

Its actually a wave packet that spreads out:
http://en.wikipedia.org/wiki/Wave_packet

The speed of that spreading depends on the mass of the particle and the kinetic energy it's emitted with - and its not the speed of light.

Thanks
Bill

3. Feb 23, 2015

### jimmylegss

Alright thanks for the reply. It is more like this then?
http://en.wikipedia.org/wiki/File:Wave_function_of_a_Gaussian_state_moving_at_constant_momentum.gif [Broken]

And the area of the wave is the probability of finding it there?

So let;s say it is an electron moving through a vaccuum, and it travels 50% the speed of light.

If you would discover it early in the wave , does that mean, because it's position x is lower then where it should be on average, it's momentum is greater?

And vice versa if you discover it in a greater x?

So let's say it moves at 150k km/s. After 0.1s, the largest chance of discovering it would be at 7.5k km, in the direction you shot it too right? But there is also a chance you discover it at 9m km after 0.1s, but then that would mean it has a lower momentum because x is greater?

If this is true, is which part in the momentum changes, the speed or the mass?

Does this also mean that if you place a detector at a certain place between A and B, there is a chance you will not detect it? but it will still arrive at B? (i guess quantum tunneling?)

Thanks

Last edited by a moderator: May 7, 2017