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The comment is accurate, and electricity should not be considered as having mass.

In a direct current (DC) setup, electrons will be moving continuously though the wires in a big loop. But the displacement of the electrons is not the electrical energy we are interested in.

It is instructive to think about alternating current (AC). In this case, electrons will be moving a bit forward, and then a bit back. So, basically wiggling more or less in place. There is still a lot of energy transferred.

A metaphor is a chain, like in a bicycle. You can use the chain to transfer energy, but it is not the chain links that are the energy. The movement is the energy. This is similar to electricity; it is not the electrons that move that is the electrical energy, instead the electrical energy is the movement itself.

(Due to Einstein's theory of relativity, we know that E=mc^2, which can be summarized as "all forms of energy are also mass". Considering this, all transfer of energy is transfer of mass. But it is miniscule. A small nuclear power plant could produce 4450 GWh in one year. The relativistic mass of this is 180g. All the energy produced in one full year of this plant has a total mass of 180g. So you should not consider electricity to be transfer of mass, even though it technically is :P )

(Also, since you asked for a physicist: I am not a physicist)

No worries, I'm using a loose definition of 'physicist' - anyone knowing about physics is fine :)

Thanks for your contribution; as I mentioned below, I've gotten some different answers, e.g. on http://physics.stackexchange.com/questions/2188/does-electri... where I asked the first time. Essentially, are you saying that with DC current, there is transfer of 'mass', but with AC, there isn't? In the case such as I've explained it elsewhere in this thread, this might mean that it matters how a computer is build to decide on whether the virtual sword can be stolen or not... (maybe, I haven't really looked hard at it in a few years, so I'm probably forgetting some details of it).

[Similar disclaimers about not being a physicist go here]

Something that's going to be a bit tricky here is that electrons are really, really slow when we're talking about electricity through a wire. The electrons will bounce around very quickly at random, but the average flow caused by a current is slow. Really, really slow.

https://en.wikipedia.org/wiki/Drift_velocity

For a specific but not unreasonable example:

> Therefore in this wire the electrons are flowing at the rate of −0.000023 m/s. At 60 Hz alternating current, this means that within half a cycle the electrons drift less than 0.2 μm. In other words, electrons flowing across the contact point in a switch will never actually leave the switch.

That kind of speed means that any messages sent over a copper wire are not going to be sending electrons all the way for that message. The electrons that 'carry' the message "I AM A VIRTUAL SWORD" will not go from my machine to yours as a rushing block. Instead all I'll be doing is tapping the end of a very long pole connecting our two properties, so you can read the message by the patterns of the end of the pole in your house moving ever-so-slightly.

So, I guess I am transferring mass, but nothing that comes from me goes to you.

This also assumes a very particular direction. There's nothing, as far as I'd understand, that requires me to be pushing electrons at you. I could be pulling on the pole slightly rather than pushing.

I'd love any corrections or additions to this, purely my lay understanding of the topic.

Even ignoring the speed of the electrons, this ignores that several steps of that route will almost certainly be done over fibre anyway, and at that point there is clearly no transfer or electrons from the "seller" to the "buyer". Although I have no idea whether or not this is relevant to the legal question at hand…

https://en.wikipedia.org/wiki/Effective_mass_(solid-state_ph...

Water is another good analogy. When you turn on a tap/faucet, the water that comes out is the water that was just sitting there in that last few inches of pipe, it didn't come all the way from the city's dam in that time.

Also with waves in water; put a ball floating at the beach and it'll mostly stay put bobbing up and down. (It's only when the waves actually break that there is substantial movement of actual "bits" of water.)

Ah, I apologize, but I have to join the unhelpful choir ;)

It seems to me that the question of whether or not electricity has mass is a proxy for whether or not information is tangible. This is the same interpretation that "Greg Graviton" at stackexchange has. And it is hard to meaningfully answer by yes or no; information needs material in order to exist, but by itself it is not tangible. Both yes and no are misleading.

My advice, which is completely ignorant of how law is practiced, is to find another way to settle the original question of whether or not the coerced obtaining of the virtual sword could be named "stealing". When taking intuitive notions such as "is this a _thing_ or not?" to the fundamental levels, the questions often stop making sense, as it has in this case, because the intuition is dependent on another level of abstraction. At this point it is no longer constructive to attempt obtaining answers to the questions as posed, and maybe this is why you have struggled to find a good answer. That's probably not helpful to you, but it is my best attempt at resolving this question :)

(About DC: It is more accurate to say that there is an exchange of mass. The same count of electrons go down the wire as up the other wire. There is no net transfer of mass. See also https://news.ycombinator.com/item?id=14087221 )

The "big loop" concept is fundamental: the power lines we use to move energy around are all closed loops, so, even with DC, the mass of electrons that flow in one direction is the same as the mass that flows in the opposite direction. There is no transfer of mass.

This is different from ectrostatic generators: there, AFAIK, there should be an actual transfer of mass. https://en.wikipedia.org/wiki/Van_de_Graaff_generator

This question, or variants of it, comes up on electronics.stackexchange a LOT. It's rather hard to explain in a compact way. You can either start with metaphors (which collapse under examination) or the maths (which most readers find impenetrable).

Current is measured in amperes, which have two definitions:

"a unit of electric current equal to a flow of one coulomb per second"

"that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 x 10-7 newton per meter of length"

Right away one of those definitions mentions charge (coulombs) and the other one doesn't. This is actually a better approach because while charge is usually carried by electrons, this is not always the case. Charge in semiconductors may be carried by "holes". Charge in batteries is carried by ions. Capacitors are usually considered to have a "displacement current" flow between the plates that has no carrier at all.

HOWEVER! For the purposes of the question here, we can skip all that and focus on the electrons in your appliances. Specifically, we can see that there's a complete loop between them and the substation/pole transformer feeding your house. You have no direct connection to the HV lines.

Perhaps you could say "the power company causes a magnetic force which moves the electrons in their transformer back and forth, which by electrostatics pushes the full loop of electrons in their and your wiring back and forth, which does useful work in your house".

Simple.

Disclaimer: I am not a physicist.

> the consumption of electrical energy requiring the transfer of mass, however small

Does precedent talk about transferring mass of electrons? Otherwise the transferred energy also has mass, via mass-energy equivalence.

> but in this particular argument (on ownership of virtual goods, like a sword in World of Warcraft), the issue of the mass was even more pertinent.

This on the other hand is on a bit more tenuous grounds. In theory you don't actually have to move energy (and thus mass) around to move information if you use physically reversible operations. But all practical computers use irreversible operations, which means information is sent by expending some energy, this is obvious in sending photons down a fiber or radio waves being able to power a lightbulb.

https://en.wikipedia.org/wiki/Landauer%27s_principle

See https://en.m.wikipedia.org/wiki/Electric_current#Drift_speed

I think a decent analogy is a pneumatic air power distribution system. Air particles move randomly in the pipe, but if the air is flowing, they tend to pass through the customer in a given direction and get work done. Alternating current is akin to switching the direction of air pressure twice a day, from (say) 1.5 atm to 0.5 atm.

Well, when I asked before, people said that hydraulic or pneumatic systems are not apt analogies; because there is water, oil or water actually flowing. Now it's not the water that is the energy, it's the movement thereof, or the pressure. That's where the analogy starts to break down.

For reference, the first time I asked was here: http://physics.stackexchange.com/questions/2188/does-electri... (7 years ago - time does fly). There is a bunch of discussion there (also going into at what point a water analogy breaks down), and I'm not sure they agree with each other. I mean, another way of looking at it: you can encode n bits by charging (or not charging) capacitors. Does a series of capacitors encoding '0' have a lower mass than a series encoding '255'?

So yeah I don't really understand, still not after all those years. It's probably (in part) because I have not formulated one single yes/no question that is unambiguous or does not need any interpretation to be answered. Or maybe I'm just stupid.

There is also electrons actually flowing. As far as movement of mass goes, the pneumatic system analogy is a good one. It is not a mathematically identical system.

Look, you can just look at how this stuff works. Electrons move randomly, and when there's a current they move on average in a certain direction because the electric field leans that way. That's it. See my link I pasted above, it describes what happens when a current is flowing.

A capacitor encoding '0' will have the same number of electrons as when it encodes '1' because that's the way capacitors work. You can read about it at https://en.m.wikipedia.org/wiki/Capacitor

Can you elaborate on the legal details of that 1930s case in The Netherlands please and how electricity being massless would change it.

First, note that that wouldn't change with electricity being massless; the argument in the paper I mentioned would.

Turns out it was in 1921, but either way: there was a dentist who blocked his electricity meter by putting a pen in it (it was one of those that turned to take the measurement). The question was: did this qualify as 'theft', because, according to Dutch penal code, theft requires the 'appropriation of any good'. The argument was that electricity is not a 'good' (Dutch civil law has a particular concept of a 'good', and being physical is one of the criteria. Note also that I'm not writing a paper here, and that I'm using loose translations for terms that are well-known concepts, so I'm probably making several technical mistakes here). The Supreme Court however decided that electricity was still a 'good' because it represented economic value (that was one line of reasoning, they didn't actually say 'electricity has mass, hence it's physical, hence it's a good'). The paper I mentioned then concluded from this that the Supreme Court had decided that electricity has mass (because it was considered a 'good', and 'goods' need to be physical - which is why e.g. what we now call intellectual property is not a 'good'. This has far-reaching consequences.)

So the paper went on to qualify virtual swords as goods, and then proceeded from there. There are more criteria for being a 'good', like something has to be uniquely identifiable; so the author couldn't make a straight analogy to the electricity case to make his case for virtual swords being 'goods'; I don't recall the details exactly but in the end, his qualification of virtual swords as 'goods' came down to electricity having mass. He said, essentially, that the 'sword' is the movement of electrons through systems, and that therefore it could be qualified as 'theft'. There was a separate argument about intellectual property as well of course, I don't recall either, but there was a reason that wasn't material in the precise question being asked. The whole point was of looking at the case of some people (physically) forcing a boy to transfer his virtual sword to them in some online game, and whether that constituted 'theft' or 'robbery' (which requires some aspects of the 'theft' aspect).

(Edit: also, the paper was written by an engineer who also had a law degree (maybe this paper was part of his degree, I forgot.) This is not some case of 'haha idiot lawyer'.)