Does any time dilation take place within an electrical conductor when electricity is flowing through it?

Question

I am curious to know if any time dilation takes place within an electrical conductor when electricity is flowing through it.

It is my understanding that an electrical current (electromagnetic waves) moving inside of an electrical conductor, such as a copper wire, typically travels at about 1/100th of the speed of light.

This makes me wonder, when taking the Theory of Special Relativity into consideration, if the electromagnetic waves traveling through the copper wire at 1/100th of the speed of light would have any effect on the rate of Time taking place within or around the copper atoms of the wire.

Say for example that a length of copper wire at an electrical power plant continuously conducts electricity for 100 years. This copper wire is then removed from the power plant and is carbon dated. Next, say that you then take a piece of copper wire that did not conduct any electricity during those 100 years and that is carbon dated. I would like to know if there would be an age difference between the two copper wires.

I would like to point out that I am not a physicist and I am asking this question simply out of scientific curiosity.

Does any time dilation take place within an electrical conductor when electricity is flowing through it?

Answer 1

Copper at room temperature is a lattice of positive copper ions whose positions are relatively fixed, superimposed with a gas of conduction electrons. The conduction electrons have motion in random directions, with typical kinetic energy

\begin{align} \frac12 mv^2 &\approx kT \approx 25\,\mathrm{meV} \text{ (at room temperature)} \\ \frac{v^2}{c^2} &\approx \frac{2kT}{mc^2} = \frac{2\times 25\,\rm meV}{500\,\rm keV} = 10^{-7} \\ v &\approx 10^{-3.5} c \approx 10^5\rm\,m/s \end{align}

This is fast, but not relativistic. The time dilation factor for this thermal motion is

$$ \gamma = \frac{1}{\sqrt{1-v^2/c^2}} \approx 1 + \frac{10^{-7}}{2} $$

In an electrical current, the conduction electrons acquire a collective drift velocity, whose magnitude is typically $10^{-2}\rm\,m/s$ or slower. The motion of any particular electron at any instant is totally dominated by its thermal motion. Compare to the water in a reservoir, which may be “perfectly still” even while the dam downstream is vigorously draining the lake.

Say for example that a length of copper wire at an electrical power plant continuously conducts electricity for 100 years. This copper wire is then removed from the power plant and is carbon dated.

Radioactive dating analyzes the nuclei, which don’t move when the current is on. And carbon dating looks at the ratio of carbon-14 to carbon-12, so you’d be looking at contaminants in your copper. But there wouldn’t be any difference here between your continuously-used wire and your idle wire, because the nuclei which form the crystal lattice don’t move in response to the current.

You can’t tell the difference between a “new” electron and an “old” electron, because all electrons are identical.

In a beam of unstable charged particles, time dilation is definitely observable. For example in the muon $g-2$ experiment, the muon beam has $\gamma \approx 30$, so the muons have a half-life of about 60 microseconds instead of about 2 microseconds.

Answer 2

It is my understanding that an electrical current (electromagnetic waves) moving inside of an electrical conductor, such as a copper wire, typically travels at about 1/100th of the speed of light.

Your understanding is incorrect.

First, an electric current is not an electromagnetic wave. Electric currents are movements of charged particles. Electric current may be produced when an electromagnetic wave impinges on a conductive material. But the electric current and the electromagnetic wave are separate concepts.

Second, the charged particles involved in a electric current typically move at much less than 1 m/s, which is much, much less than 0.01c. This has been addressed in several earlier questions here, for example, How fast does an electron move?.

Third, the electromagnetic waves that may be causing the current (for example in a transmission line or waveguide) typically propagate at a reasonably high fraction of c, say 0.85c or so, depending on the dielectric permittivity (and magnetic permeability, but this doesn't vary much between commonly encountered materials) of the material surrounding the wire.

Does any time dilation take place within an electrical conductor when electricity is flowing through it?

The moving charge carriers (electrons) in the wire will be time-dilated (to a minute degree due to their very small velocity) from the perspective of an observer at rest relative to the wire.

The non-moving parts of the wire (the atomic nuclei of the copper atoms) don't experience time dilation because they are not moving.