The mean distance they move in a copper wire between collisions is about 0.00000004 meters. At 100 km/s it would take 0.4 picoseconds to travel that distance.
And yet we know it’s mostly just empty space. I’m assuming it’s more because of the electromagnic force being particularly strong at those scales rather than a straight up “collision” right?
Atoms aren't really empty. They're electron clouds with an extremely dense core of protons and neutrons, but the electron clouds are what we care about.
To add a bit of a complication, if two particles that have mass, even one as tiny as the electron, come closer together than some minimum, general relativity predicts that they would collapse into a (really really tiny) black hole. Of course, we don't know how and if general relativity really works at this level, so the relevance of this is unclear.
You can even take it up a level and say that interaction events are the only things that really exist. That's more or less what Copenhagen QM boils down to. It is not at all a given that "particles" even exist between interactions.
Intuition insists that if something happens here and something apparently related happens over there and you can move here and there around to make a line or curve, then something physical is moving between here and there.
But actually - no. Not necessarily. All you have are ghost traces of an apparent chain of causality. And you can play with those traces experimentally to make them do incredibly weird shit in very surprising ways.
I'm so tired of this. If atoms are "empty space", then there's no such thing as non-empty space, which makes the concept meaningless. Electron clouds have all the properties we want from non-empty space, mainly excluding other objects made of non-empty space, so let's just admit that's what non-empty space is and move past this pseudo-profound silliness.
https://www.youtube.com/watch?v=tMP5Pbx8I4s
And with this, there's no empty space in atoms, as the vacuum perturbations from each particle spread out to infinity, so inside the atom there's more energy in those perturbations than outside - the space is less empty inside than outside.
Either I'm going schizo or I should read some real books on the subject.
As I understand it, the idea in the video is that if vacuum can be seen as non-linear elastic medium, then with the right functions for elasticity and stress, you can create conditions where EM waves at high enough frequency will hit the "sweet spot", a local minimum, where the energy gets confined in space by those non-linear properties, and can't leave without supplying additional energy. And such confined energy seems to behave like you'd expect particles to.
Again, I am not a physicist, so I'm probably wrong in understanding what half of the words I used above mean. But I do understand the idea of multiple forces creating semi-stable states that are "energy traps". For instance, the balance between electric repulsion vs. attraction from strong nuclear force is what defines how tightly bound is the nucleus of any given atom (aka. the "nuclear binding energy"). The nucleus can't expand or split apart, nor can it contract, unless you supply additional energy. When you do - say, you hit a large atom with high-speed neutrons to break past strong force attraction, or smash two small nuclei together at high speeds to overcome electric repulsion, the other force takes over resulting in a rather spectacular release of energy[0] as matter finds new stable configuration.
So I feel the idea here is similar, but with stress and elasticity in place of strong and electric forces - if there's enough energy propagating through some space, the wave gets trapped in a spatially-confined region instead of dispersing into the medium.
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[0] - https://www.marketbusinessnews.com/wp-content/uploads/2014/0...
No, it does not. It illustrates that the portion of an atom that strongly scatters alpha particles occupies a small fraction of the atom's volume. Asserting that alpha particle scattering is the only correct definition of the threshold between emptiness and non-emptiness is an awfully strange position to take.
When interacting with other electrons at energy scales relevant to human life, i.e. maybe ten electron volts and down, an electron cloud is somewhere between solid (core electrons especially in heavy atoms) and squishy (valence electrons). Give a rock the ol' "I refute it thus!" and your toes will report that that rock's electrons are quite competently occupying their space.
Ask an alpha particle at nuclear energy scales a million times greater, and that electron cloud is like a swarm of gnats to a speeding car. The electrons only interact with the alpha electromagnetically, and it takes another object that interacts through the strong nuclear force to really bother a nucleus (most of the time).
Ask a neutrino, and it will tell you that all the nuclei in the Sun are but a wisp of fog.
This is a good example of how approximations valid in one regime fail in another but are not therefore useless. Rutherford's experiment reveals that there is more going on with matter than what can be probed by fingers and microscopes and chemical reactions, but it in no way invalidates those other observations.
https://en.wikipedia.org/wiki/Golgi_apparatus
Similarly, organelles group related process together. So for example DNA related proteins are in a nucleus not inefficiently bouncing off the cell wall.
Which helps explain why mitochondria were so beneficial. Keeping a bunch of related machinery all tightly clustered together it makes more efficient use of each individual protein and can quickly replace anything that gets damaged. ATP however can diffuse through the cell just fine because so many processes use it that extra copies isn’t a major issue.
That said, I don't remember the orders of magnitude here, the relevant question being how cold "room temperature" is with respect to the Fermi level -- a quick Google suggests quite cold, in which case the Fermi velocity should be a very good approximation.
In which case, it's interesting to realise that the motion of the electron gas comes mainly from Pauli exclusion rather than thermal noise! It's not a result I would have expected.
- Sean M Carroll's work, in particular his Biggest Ideas in the Universe books: https://www.preposterousuniverse.com/biggestideas/
- Artur Ekert, basically the father of Quantum Cryptography has an amazing course for free on youtube: https://www.youtube.com/@ArturEkert . It's a very precise and understandable explanation of quantum computing, and some of the math that is involved with quantum mechanics.
- If you have hours to spare, watch Richard Behiel's videos on Youtube. He's like the 3Blue1Brown of Quantum Physics. His latest video on superconductivity and the Higgs Field is almost 5 hours long (!!!) https://youtu.be/DkH1citHtgs?si=-yQNYDu9TlTpE1A0 . It builds on his other videos, so I'd recommend starting at the beginning.
Very not my field, but perhaps that's "all the paired electrons"? Brief ai-ing (do we have a verb yet?) suggests only some small fraction of conduction electrons form pairs, let alone all the rest.
This doesn't happen with unpaired free electrons because their energy spectrum is pretty close to continuous.
What definitely affects resistance is the vibration of the nuclei lattice, in which thermal energy is also stored. This vibration makes the electrons more likely to scatter. This means even in a non-superconducting metal, resistivity drops as you get colder.
The special thing about superconductors is that there's a temperature where the resistivity suddenly drops to zero. (If you look up "superconductivity resistance against temperature", you'll see some graphs showing what I mean.)
I don't know exactly the details of why this happens, but it has something to do with Cooper pairs. Electrons in these states are also sensitive to being knocked out and bumped up to regular conducting states by thermal noise.
This is pedantic because there's practically no difference. But just to be pedantic, it's not the speed of light and I'd argue it's not usually even close to the speed of light. In communications we are talking about anywhere from 60% to 80% the speed of light through most mediums.
I was thinking of using a high-frequency trading example, but here's a case that's a bit more normal: stadium concert audio for a live band. Stadiums are big enough that you need to deal with latency issues for audio, because the back of the venue will get its audio a bit later than the front of the venue (assuming the sound is wired so the board is in the front of the floor and no adjustments are made). That is obviously disconcerting to the audience. Adjustments usually are made to handle this problem.
Then were somehow able to turn the light bulb on and apply a charge to the that rod at the same time. While also having a detector that can sense a photon and a change in electric field some equal distance away from the bulb and rod.
Then the photon (from the bulb) would reach our detector before the detection of the change in electric field (from the rod)?
Let's suppose the medium is just plain air, and not particularly humid.
Copper is clearly a different medium than fiber optic.
That is why I stipulated a single medium for the experiment.
The complicating factor here is that when you have electricity flowing in a wire, the fields are generally mostly outside the conductor, not in it. That is, the signal propagation delay depends more in what you are using as an insulator around wire than the material of the wire. This has had practical consequences in the past; if you replace the insulating jacket of one wire in a twisted pair with a slightly different material, on long runs it will ruin your signal.
Is the only part that's not wrong in your post.
Photons only have one speed in empty space. They slow down when traveling through any medium other than vacuum.
> However, electrical conduction is the movement of electrons, not photons.
Electrons move because they influence each other through their fields, which are transmitted by photons. Electrical conduction happens at the speed of the fields, not at the speed of the electrons. When you push one more electron into one side of a conductor, an electron flows out the other side when the fields reach the other side, not when the electron does.
(As an analogy, consider a rubber hose full of steel balls. When you slowly push an additional ball in from one side, another ball starts to fall out of the other side as you push the first ball in, perceptually instantenously⁰, regardless of the speed you are pushing the new ball in.
(0): After a delay of (length of tube)/(speed of sound in steel)
It's only after the fields interact with electrical charges (atoms and their electrons for example) that a secondary field is induced as these charges begin to oscillate. This field will add over the original field, "shielding" an external observer from the original oscillation and apparently slowing down the propagation of electromagnetic waves.
There's a very good video by 3Blue1BRown that explains this kind of weird concept way better than I could: https://www.youtube.com/watch?v=KTzGBJPuJwM
It's close enough to c that you should just use c but it can be observed that it's less.
"In a vacuum, electromagnetic waves travel at the speed of light, commonly denoted c."
I would expect that in air, that the photon from the light source and the perturbance of the electric field from the charge to reach the detector at the same time.
The perturbation of the electrical field causes EM radiation (radio), which moves at the speed of light.
Overall the picture is like this:
- massless particles like photons travel at speed c in empty space, in a straight line
- massive particles like electrons travel at a speed slightly less than c even in empty space, in a straight line
- inside a medium, any particle traveling in a straight line will quickly bounce off/be absorbed and re-emitted in a new direction because of some field given off by another particle; so, the average speed at which particles actually traverse through the material is lower than c. How low depends on properties of the medium, mainly how dense it is; for copper and most metals commonly used in electronics, this varies between 60-80% of c.
- When applying a potential difference to a metal wire, the electrons which normally are moving at speeds very close to c in the empty space between atoms in random directions (amounting to an overall speed of 0 along the wire) will start collectively moving in the direction of the potential difference (towards the positive node), at a very low average speed called "drift speed"; this is caused by their normally completely random bounces now being biased in the direction of the electric field;
- However, the current in the wire (the EM radiation) moves extremely fast along the wire, at the same speed that light moves (on average) through the wire. You can think of this as being caused by photons (since EM waves are photons) moving much more easily than electrons through the wire, simply because they don't have a charge of their own and so don't get caught so easily by other atoms as electrons do.
So you have 5 speeds relevant to this: the speed of light/photons/EM waves in vacuum (c), the speed of an electron in vacuum (very close to c), the average speed of all electrons in a metal wire without any electric potential (0), the average speed of all electrons in a metal wire with an electric potential (drift velocity, very small), and the speed of EM waves in a wire (60-80% of c in typical conductors).
Edit: one more note that complicates this picture, but the EM waves in a charged wire don't really move inside the wire, or not entirely - they move mostly around the wire - which means that their actual speed depends not (just) on the material from which the wire is made, but also the insulation outside the wire. That is, the EM field will propagate a different fraction of c for a copper wire than for an aluminum wire; but also for a copper wire wrapped in plastic versus one exposed directly in the air.
This brings me to a Veritasium video of a few years back that I didn't quite understand at the time. [1]
The claim being made was that if you connected a light bulb to a switch, with 300'000 km of wire left and right, and if the switch and the light bulb were 1 m away, the light would turn on in 1/c seconds.
But this would imply that the information travel is not along the wires, but straight from the switch to the light bulb?
In theory the change in electric field will induce a small current in the other wire, and their magical science lamp turns on at any non-zero electricity. Whether the wires are connected or not at the far end doesn’t matter.
They never clarified how strong the other current would be.
Also, the phenomenon being discussed in the Veritasium video is slightly different, and that video sort of mixes up two things to make things more mysterious.
The simple explanation for what is going on in the video is that whenever you have a voltage change in a circuit, such as closing it with a switch, you get a tiny bit of radio waves being emitted radially outwards from that point out *.
In the Veritasium experiment, with a very precise measurement tool, they could detect the tiny radio pulse emitted by the switch at the moment it was closed, far before the main current reached the same point moving along the long wires.
The other thing he was mixing this up with is the Poynting vector, which is a mathematical object that represents the direction along which power (as in, worl, the thing you measure in Watts, not the actual current which you'd measure in Amperes) propagates in an electrical circuit. It's not clear at all that the Poyinting vector is a meaningful aspect of reality and not just some mathematical tool. It does happen to coincide with the direction that the radio waves propagate as described earlier, so some physicists do like to interpret it as a deeper, physically real, thing that is related, but you can just as easily ignore it.
Note that when I say that it's "not real", this is similar to how I would describe the Lagrangian and Hamiltonian of a classical mechanics system. It's an extremely useful mathematical tool and it predicts the behavior of the system perfectly well, and is mathematically equivalent to Newton's laws of motion. But while the laws of motion describe real direct aspects of reality, such as objects having mass and momentum, the Lagrangian doesn't really represent an actual thing in physical reality.
The above comes with a gigantic caveat: in QM, the Lagrangian and Hamiltonian correspond to the wave function, which is, to the best of our current understanding, the real underlying thing behind reality, with particles and waves and things localized being the artifical objects we introduce merely for convenience.
* This is normally completely negligible for DC current, but for AC current, where the current switches direction all the time, a relatively high amount of radio waves get generated radically put from the wires along their whole direction. This can lead to problems such as AC power lines causing significant radio interference. This is also normally described as "parasitic", since the power those waves carry is lost from the transmission line, which is designed to carry as much as possible of the power generated at the source towards the destination.
"Random Motion: Even without current, electrons are jiggling around at high speeds (~10⁶ m/s at room temperature) due to thermal energy. The electric field just adds a slight bias to this chaotic motion, resulting in the net drift."
no, not because it's every which way.
it doesn't create net current because if, randomly, net charge moves in some direction, the resultant electric field will put pressure on the random movement to bring it back to equilibrium, 0.
This thermal motion is essentially random, and the electrons constantly scatter off the nuclei every which way, so it cancels out and doesn't create a net current.
So, it's less than the electrons gently move under the influence of an electric field, and more that it introduced a slight bias in the existing thermal motion.
E: To clarify in case it may have been unclear, this is unrelated to the speed of propagation of the electric field, which as the article says is the speed of light.