# When Electricity Takes the Shortest Path, is that Due to Quantum Mechanics?

## Main Question or Discussion Point

Hello all!

I was recently watching a documentary which delved into the theory (is it a theory?) that quantum particles can be in two places at once; indeed, millions of places at once. I've heard this all before, but the one thing that I picked up on this time was that when a particle is "observed" by its environment, it effectively has a fixed position in space.

I've often wondered exactly how electricity knows which path offers the least resistance, and then decided to take that path. I mean surely it can't just happen like that? However, having learnt that subatomic particles can be in virtually limitless places at once, is this what happens with electricity? Do electrons take every possible pathway, and the one that happens to be the shortest and most efficient is the one that is observed by the environment, and therefore is responsible for the phenomenon the we see and measure?

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Bill_K
See this interesting video of electricity (lightning) finding the path of least resistance.

DrChinese
Gold Member
Do electrons take every possible pathway, and the one that happens to be the shortest and most efficient is the one that is observed by the environment, and therefore is responsible for the phenomenon the we see and measure?
Welcome to PhysicsForums, Smedlington!

Individual particles of light (for instance) do take multiple pathways when going from point A to point B. These can interfere with each other. The *net* effect ends up most accurately describing what is observed. And that ends up being, in the case you describe, the shortest path. But keep in mind that in the usual case, you cannot select B as the final destination. There are usually many places that the particle can end up.

Electricity is the flow of electrons. And electrons do not necessarily take the shortest path in the conductor. They can flow anyway they like bounded and limited by the attraction of nucleus and lattice arrangements.

Electricity is the flow of electrons. And electrons do not necessarily take the shortest path in the conductor. They can flow anyway they like bounded and limited by the attraction of nucleus and lattice arrangements.
Obviously they don't take the physical shortest path, but the common (and generally true) phrase is that they take the "path of least resistance".

I'm pretty sure that can be explained classically, though. If electrons have two paths to get from the source to sink and one has a much higher resistance than the other, the one with the higher resistance must build up some sort of repelling force that causes electrons to take the 'easier' path. I don't think Feynman path integrals apply here, really...

Maybe this will explain something? http://en.wikipedia.org/wiki/Classical_and_quantum_conductivity

I'm still trying to get my head around why higher resistance actually slows down electron flow through that medium. Is it because higher resistance -> more frequent and incoherent collisions with ions -> smaller drift velocity of electrons -> electrons are limited in that area, so fewer end up going through it?

Obviously they don't take the physical shortest path, but the common (and generally true) phrase is that they take the "path of least resistance".

I'm pretty sure that can be explained classically, though. If electrons have two paths to get from the source to sink and one has a much higher resistance than the other, the one with the higher resistance must build up some sort of repelling force that causes electrons to take the 'easier' path. I don't think Feynman path integrals apply here, really...
That's not how resistance works. Electrons can go any way they want to. But their average movement will be guided by the electric field. No repelling force works here.
en.wikipedia.org/wiki/Electron_mobility

I'm still trying to get my head around why higher resistance actually slows down electron flow through that medium. Is it because higher resistance -> more frequent and incoherent collisions with ions -> smaller drift velocity of electrons -> electrons are limited in that area, so fewer end up going through it?
You got it almost correct except that electrons are not limited in any way in higher resistance area.

See this interesting video of electricity (lightning) finding the path of least resistance.

I'm pretty sure that can be explained classically, though. If electrons have two paths to get from the source to sink and one has a much higher resistance than the other, the one with the higher resistance must build up some sort of repelling force that causes electrons to take the 'easier' path.

Classically you would expect to find current flowing through the higher resistence as well, though at a much lesser rate. I don't think there is a classical analogy that can be applied adequately.

Classically you would expect to find current flowing through the higher resistence as well, though at a much lesser rate. I don't think there is a classical analogy that can be applied adequately.
That is exactly what you would observe in practice.

http://en.wikipedia.org/wiki/Current_divider

Current takes "the path of least resistance" because in a lot of situations the difference in resistance between paths is many, many orders of magnitude. For example, that is why a current flows down a copper wire and not into the insulation.

russ_watters
Mentor
Obviously they don't take the physical shortest path, but the common (and generally true) phrase is that they take the "path of least resistance".

I'm pretty sure that can be explained classically, though. If electrons have two paths to get from the source to sink and one has a much higher resistance than the other, the one with the higher resistance must build up some sort of repelling force that causes electrons to take the 'easier' path.
Just to be clear here: that common phrase is wrong. Electricity does not take [only](implied) the path of least resistance, it takes all available paths simultaneously, in proportion to their respective resistances.

Drakkith
Staff Emeritus
Just to be clear here: that common phrase is wrong. Electricity does not take [only](implied) the path of least resistance, it takes all available paths simultaneously, in proportion to their respective resistances.
That is what I was thinking Russ. If you have two conductors in parallel, one with twice the resistance, both conductors will have current flowing through them, so obviously it can't just be the path of lease resistance.

russ_watters
Mentor
That is what I was thinking Russ. If you have two conductors in parallel, one with twice the resistance, both conductors will have current flowing through them, so obviously it can't just be the path of lease resistance.
...and this can lead to difficulties in convincing people of the dangers of electricity. We do, occasionally, get the question asked:

'If electricity follows the path of least resistance, why would I get shocked when touching a live circuit? Shouldn't the electricity stay in the wire, since its resistance is less than mine?'

Just to be clear here: that common phrase is wrong. Electricity does not take [only](implied) the path of least resistance, it takes all available paths simultaneously, in proportion to their respective resistances.
Hahah, I know that. But I also assumed that the saying had an implied "mostly". Obviously it takes every path at once, but some are basically negligible (like the insulator mentioned previously).

This is exactly how confusion around some concepts arise. You have to just remember V=IR. It can't be made any simpler. Any effort will lead to the misinterpretation like "When Electricity Takes the Shortest Path".