Do charges ‘really’ carry energy?
They may or may not, but it really helps explain voltage and power if you pretend they do, and make this pretence explicit
The Electricity Explained circuit simulation has the same status as arrows to represent forces - forces aren’t really arrows, but if you visualise them like that, then it makes it easier to see what’s going on, and it creates a connection with the mathematics.
The simulation makes no incorrect predictions, which is surely the most important way in which models should be judged. The objection that charges don’t ‘really’ carry energy is an argument about conventions, not an argument about mathematical predictions or macroscopic observations.
The simulation sometimes gets unflatteringly categorised as a ‘donation’ model - like bread vans carrying bread from a bakery (battery) and depositing them in a house (bulb) - but it isn’t really. It’s a mathematical model with a visual output. The correct circuit physics is hard-coded into it, so that it always does the right thing, and makes that easy to visualise.
The circuit simulation is not an analogy. You don’t have to predict how bread vans, or water in a pipe or a rope loop behaves, and then try and translate that into current, potential difference, resistance and power. It always does the right thing. It gets the ‘what?’ right, and isn’t too concerned about the ‘why?’.
The simulation doesn’t try and explain what resistance is, and has no opinion about why bigger resistances cause smaller currents. It simply correctly models power supplies as constant voltage providers that change the current they provide depending on the circuit resistance, and shows that any change sets up new patterns of potential and current everywhere at the same time (not at the speed of the charges).
There are legitimate criticisms of donation models, and I can see that it’s difficult to reconcile them with a stores and pathways story (a lot of which I have considerable sympathy with), but I think you need to be really careful about making statements about what ‘really’ happens in electric circuits.
Notice how each charge isn’t modeled as getting energy only at the power supply. As the power supply voltage is increased, the new potentials are set up everywhere instantly. Again, I’m not arguing that this is what really happens, but this model leads to no incorrect macroscopic predictions, whereas the rope loop leads to many.
The simulation visualises potentials because each black dot is exactly one coulomb
Imagine a parachutist floating down at her terminal velocity - in other words, at a constant speed.
You can imagine having a little bar chart that floats down alongside the parachutist showing how her gravitational energy store decreases as she falls. Most physicists would be comfortable saying that this bar chart shows the ‘gravitational potential energy’ of the parachutist, relative to the ground.
In other words, there is wide agreement within the international physics education community that it’s meaningful to talk about objects ‘having’ energy by virtue of their height, and that if you were to move the object around without changing its height that this potential energy travels with it.
If we changed the scale of the bar chart so that it showed the potential energy per kilogram then this would show the size of the ‘gravitational potential’ at different heights.
Gravitational potential is just the work done moving one kilogram from whatever point you choose to have zero potential to the point you’re interested in. For post-16 physics we tend to choose the zero of potential to be at infinity, but we can choose it to be wherever we like, so the ground is just as good for 11-16 physics.
We tend to say that gravitational potential is a property of space, whereas gravitational potential energy is a property of objects. Where the energy is stored is a matter of convention - in the sky diver, in the gravitational field, in the Earth-sky diver system, or nowhere at all (because energy is just a number - so the idea of a store is simply a convenient metaphor).
Whether we decide it’s stored somewhere or nowhere, 11-16 numerical calculations will produce the same answer. If a theory correctly predicts macroscopic behaviour then it is prima facie true.
As the parachutist’s gravitational store decreases, the thermal stores of the surroundings plus parachutist increase at exactly the same rate. There is a kinetic store due to the parachutist’s movement but this store doesn’t change, since her speed doesn’t change.
So we have a thing moving at constant velocity down a potential gradient shifting energy from a positional store to a thermal store.
If instead we deliberately used a model parachutist with a mass of one kilogram then the size of the gravitational potential energy of the parachutist at a given height would be identical in size to the gravitational potential at that height. So the little bar chart falling with the parachutist would show the size of the gravitational potential at each position.
The parachutist analogy is a good one. In a circuit, charges moves slowly at a constant velocity in a given wire - provided you imagine zooming out a little bit, so you don’t see the random thermal movement and the granular interactions with the lattice.
The charges ‘fall’ down an electrical potential gradient (which is, incidentally, identical to the size of the electric field, if you wanted to bring that concept in) at a terminal velocity. Just like with the parachutist, energy is shifted from a positional (potential) store to a thermal store without any change to the kinetic store.
If we choose the size of our charges to be one coulomb (and we do) then the little bar chart of ‘electrical potential energy’ at a given position in the circuit will be identical to the ‘electrical potential’ at that position.
The electrical potential at a point is the work done moving one coulomb of positive charge from the zero of potential to that point. For isolated charges we tend to choose infinity as our zero of potential, but for circuits we choose the negative terminal of the battery.
But with the simulation, instead of a bar chart next to the charge, we use the area of a transparent red circle around the charge.
Though this shifts the idea of potential from a point in the circuit to an individual coulomb of charge, this leads to no incorrect macroscopic predictions.
Whenever a coulomb of charge moves to a point of lower potential, a thermal store must increase by a number of joules equal to the size of the potential difference. This is mathematically identical to the charges themselves losing that much energy.
For 11-16 physics, single coulombs of charge ‘carrying’ energy like this to model potential is mathematically identical to the potential belonging to points on the circuit.
Or if you like, there are no 11-16 experiments that you could do to distinguish between the two representations.
We use this trick of using a more helpful, mathematically identical formulation all the time in physics when we talk about conventional current. We wouldn’t argue that the idea of conventional current is ‘wrong’ simply because we have to imagine replacing real negative electrons with made-up positive charges moving in the opposite direction.
If a formulation doesn’t lead to any mathematical or experimental contradictions then it is de facto correct.
Energy transfer between electrons and ions is not really a kinetic story
Another criticism you occasionally see is that if the charges have lost all their energy when they leave the bulb, then how do they get back to the battery.
This is because they believe that the energy I’m showing is a kinetic or maybe total store, not an electrical potential equivalent. I’m sure that’s my fault for not being clear enough, but it’s one of those points that only those with some existing facility with physics would ask - I need to find some way to make this obvious without being confusing.
We measure potential relative to some zero, and in this case we choose the zero of potential to be the negative terminal of the battery. Just like an apple dropped off a table at the top of a high building, we only need to consider the net energy change, not some absolute.
Most criticism is healthy because it forces you to think much harder, and this case is no exception, because it uncovers some interesting physics, that it’s worth exploring.
Classical physics has a simple model that electrons collide with the ionic lattice as they move through it, and that these collisions cause a net shift of energy from electron to the lattice. After each collision the electrons are accelerated by the field until the next collision. The IoP has a nice video of this using marbles and masses on a slope.
You can see that this model explicitly shows the marbles being the agents that shift energy to the lattice by colliding with it, even though they try their best to say that it’s the p.d., not the marbles themselves.
But there’s something subtly wrong with the idea that it’s the electron’s speed along the wire that causes the lattice to vibrate more when they collide with it. This movement along the wire makes only the tiniest difference (~0.001% typically) to the energy change for any given collision.
In a wire with no current, the electrons are already moving around randomly very fast - about 100,000 m/s - which is called their thermal speed. The electrons and lattice continually interact with each other, but there’s no net transfer of energy between electrons and lattice.
When there’s a current, the electrons make very slow progress along the wire, as well as having this much, much higher random thermal speed. It’s like a snail moving along the floor of a jet airliner - the speed of the snail is mostly due to the airliner, not its own efforts.
So the additional drift velocity has essentially zero effect on the energy of collisions. In the very narrow filament of a bulb, electrons have a much higher drift speed - of the order of a half a meter per second, compared with a fraction of a millimetre per second in the thicker leads.
This additional speed doesn’t affect the energy of collision, but it does affect how many extra lattice interactions there are each second.
The slowly-progressing electrons in the thick wires of the leads don’t travel very far in a second, so don’t come across much lattice to interact with, and energy is shifted slowly. In the narrow filament, the electrons are progressing much faster (though still slowly compared with the thermal speed), so they move a greater distance each second, come across more of the lattice, and have more interactions.
It’s the number of interactions per second that explains why heating happens in the filament (and not the leads), and not the energy of those interactions, because the energy is almost exactly the same in both cases.
Science doesn’t make statements about how the world ‘really’ is, even if many scientists (and teachers) think it does
Almost no contemporary philosopher of science would argue that science can arrive at a perfect, immutable and eternal description of the world. Neither does it necessarily get ever closer to such a description by applying the ‘scientific method’ of refining models and doing experiments.
Scientific world views, for example Newtonian mechanics, have the same character as games. You can’t ‘prove’ that a football team has eleven players a side, or that a match consists of two halves, or that a goal is implicitly worth only one point. These are just conventions developed in historical time by communities of people who for whatever reason happened to attach value to a game played by these rules.
It’s not to say that the rules are right, but once people accept them, then you can do experiments. You can predict that if the centre half ran in a particular way or if the trainer focused on these types of exercise then you should get these changes. If the predictions turn out not to be true, you don’t assume that the pitch was the wrong size or the game was too short.
The fundamental rules of football are not up for grabs (or very rarely), and when they are, for example when rugby and football diverged, you effectively opt out of the previous game altogether. There’s no way to prove that football is superior to rugby, or for that matter, close harmony singing.
In the same way, scientific theories have historical and social character, and make essentially arbitrary assumptions about what the world is made from and what laws connect these entities. They also have an intellectual and social ecosystem that defines what constitutes standards of proof, what are acceptable mathematical tools, the technical language to use, methods for education and induction into the theory, a variety of specialist journals, and so on - all of which have analogues in sport and many other social institutions.
Good theories make testable conjectures that don’t rely on an ever increasing set of ad hoc assumptions (about e.g. initial conditions or auxiliary theories about measurements and apparatus) to maintain their coherence. Most importantly, every so often they predict and discover the existence of something that has never been seen before. It is this ability that makes science both powerful and unique in human activity.
I’m quite a fan (in an extremely amateur way) of ontic structural realism (OSR) in the philosophy of science. This essentially says that there is an objective ‘out there’ but what’s real is the relationship between objects, not the objects themselves.
In other words, there are many mathematically equivalent ways of modelling the world, without having to decide what it’s ‘really’ made up of. For example, to model a pendulum’s motion you could use Newtonian, Lagrangian, Hamiltonian (or even quantum) mechanics. Each imagines a world made of different fundamental concepts, like mass, energy and action, with different relationships between them. The question about what the world is ‘really’ made from isn’t as important (or even meaningful) as ‘is this model the best lens through which to examine this problem?’.
It’s essentially an argument about which metaphor you’re most comfortable with
Even though the IoP does its best to emphasise that stores are just values and not real entities - the very choice of the word 'store' and the idea of a ‘pathway’ shows how difficult it is not to get drawn into thinking in metaphors.
Energy is just a number that's conserved 'as nature goes through her tricks' as Feynman says.
I don’t make a realist case for charges ‘carrying’ energy. What I do say is that by carefully choosing the black dots to represent single coulombs of positive charge, the red energy circles correctly represent the size of the electrical potential at different parts of the circuit.
Making the potential a property of the charges, not a property of position is a conventional sleight of hand, I admit, but no more so than the idea of conventional current, since it leads to no mathematical, observational or experimental contradictions.
The circuit simulation is designed primarily to make it easy to answer questions about what happens when you make a change to a circuit, without having to use numbers on meters. It is a tool for teaching and learning, which hints at the invisible internal life of wires without making any commitment about what ‘really’ happens.