@Slereah I guess if you mean a primary electron from lightyears away that one would be more delocalized - until you observe it when it interacts with the earth's atmosphere :P
there aren't a lot of ways to interact with electrons that don't localize or destroy them :P
could you say that such an electron would have been travelling towards all directions for 10000 light years, and then when it touched earth's atmosphere, those other directions all vanished into thin air?
@LeakyNun You could say that but then you would start one of those pointless discussions about quantum interpretations :P
@Slereah I feel this is a weird question: A measurement apparatus is some device that sits locally in some lab, and we human observers exist locally at a point. How do you expect us to make "delocalized measurements"?
in the bosonic case you just can put all of them into the same state and then the particle nature "dissolves" because you just have millions in the same state
@Slereah isn't what actually happens in conduction this horrible rabbit hole where you flip between "the electrons move very fast", "the electrons move very slowly" and "what does 'moving' even mean" at every step? :P
@Slereah i tried to calculate it (i hope i haven't made any mistakes), assuming a copper wire of length 1 m and width 1 mm, and a current of 1 A
density of copper = 8.96e6 g/m^3 copper wire width 1e-3 m, length 1 m volume = 3.14e-6 m^3 mass = 28.1 g molar mass of copper = 63.546 g/mol number of electrons = 0.442 mol = 2.66e23
assume current is 1 A, so 6.24e18 electron charges per second
if electrons travel at velocity v then 2.66e23 * v = 1 m * 6.24e18/s v = 2.35e-5 m/s
@qwerty yeah i'm referring to the model that we all learnt in high school
@ACuriousMind so i tried to do that, i assumed the electrons have initial velocity u and final velocity v, and the photon emitted has frequency f, this gives us 2 equations with 3 unknowns, and i ended up with f = 2(1 - v/c)mc^2/h and u = 2c-v; is the contradiction that 2c-v would be faster than light?
@LeakyNun I mean that's certainly a contradiction. The specific contradiction you get doesn't matter, you can also get stuff like $c=0$, see physics.stackexchange.com/a/225538/50583
I'm not sure why it's an "issue", but it's certainly the case that all electrons have the same mass - otherwise you wouldn't call them all electrons, the rest mass is one of the defining characteristics of a particle species
The relevant distinction is that the atom is a composite system with internal states of different energies. The electron is a fundamental particle without internal structure, so it has no "excited states" when it's on its own.
not really, QM/QED courses usually never discuss emission in terms of this mass, because as Slereah said the mass difference is practically completely negligible
perhaps a better analogy is: "where" is the energy something gains when you lift it up in the Earth's gravitational field? (hint: it's not "in the atmosphere" between the object and the Earth, gravity doesn't care about vacuum or not)
the traditional answer is that the energy is "in the electromagnetic/gravitational field", which is correct in the sense that you can write down an expression that integrates over the field and returns the energy "in it" but otherwise has very little concrete meaning
When a photon of light hits a mirror does the exact same photon of light bounce back or is it absorbed then one with the same properties emitted? If the same one is bounced back does it's velocity take all values on $[-c,c]$ or does it just jump from $c$ to $-c$ when it hits the mirror?
Or, is t...
In response to your earlier question, energy is stored in the electric field around the hydrogen atom. When you excite the atom the field changes and the change in that energy is responsible for the change in mass.
of course you can look at the case $m=0$, but purely classically, there really isn't anything with $m=0$
the photon is very much a quantum notion, and probably overused in such semi-classical explanations because people find it easier to reason about small billiard balls than waves
Gf course, if we accept that photons exist, then they have $E=pc$. But that's not a purely classical statement because photons are not classical objects.
@LeakyNun It's certainly true that you need to be rather careful about this as if the electron was a classical point mass there energy stored in its field, and hence the mass, would be infinite.
But changes in the energy stored in the field still make sense.
The level of his stuff on YouTube is a bit too low for most of us here in this chat, but I think he does an excellent job of explaining without over simplifying.
i've seen it claimed somewhere that FTL (faster than light) leads to travelling backwards in time and hence paradoxes, and then Sabine said that "travelling backwards in time" makes no sense because a particle going left back in time is the exact same as a particle going right forward in time
"Back in time" is a meaningless phrase. The more accurate way to describe travelling backwards in time in your Delorean is to say there is a closed timelike curve.
Travelling faster than light allows the observer to travel along a closed timelike curve, though the process for doing this is a little involved. It involves acc eleration as well as travelling faster than light.
I will try to be as explanatory as possible with my question. Please also note that I have done my share of googling and I am looking for simple language preferable with some example so that I can get some insight in this subject.
My question is what is so special about $c$? Why only $c$. Its li...
@Slereah ACM's answer is correct (local detectors) but should be augmented: for extracting maximum precision in the measuring, we tend to want the detectors to be tiny. In the end, the detectors are always some entity localised in space (but amusingly, someone recently claimed to have detected stuff delocalised in time over the detector's spacetime region), but that does not mean that the quantum particle is localised; the detection could imply that the particle was delocalised
over part of the apparatus before arriving at the tiny detector.
@LeakyNun Chad Orzel in "How to teach Relativity to your Dog" covers the FTL -> BTT in quite the detail using spacetime diagrams. It is very very good.
@Slereah although Bloch states are maximally delocalised, you are always mathematically allowed to work purely in terms of localised states e.g. Wannier, and so your argument fails for the strict mathematical proving standards.
@Slereah If your detector is large to the point of imprecision, that does not mean that it isn't localised. It would much more often just be that a localised part of the detector is doing the detecting and you are losing that information in the mundane, classical, manner
@LeakyNun no, you are just being sloppy in your argumentation. You should just check out the wonderful treatments
@ACuriousMind my objection here is that it seems like your answer is that FTL is just undefined already in SR so we shouldn't consider them at all, so we shouldn't even use a spacetime diagram
so yes, the things with the spacetime diagrams show...something, but it's not really clear what statement they prove: The existence of that "tachyon" is inconsistent with numerous other parts of physics, that it would lead to weird time paradoxes is perhaps the least of our worries
@LeakyNun I'm just explaining why I don't think the stuff with the spacetime diagrams really shows anything: They're just postulating something that contradicts numerous aspects of physics (a particle that can travel faster than light in the naive sense in Minkowski space) and derive another contradiction.
It's not wrong, but we're not really showing anything but that garbage assumptions yield garbage results :P
@ACuriousMind ok but when we're doing "naive" SR with clocks and twins and whatnot, nobody is asking "but what happens to the current in my electric circuit", right
@ACuriousMind @Slereah If by "electrons moving" in the Drude model you mean the drift velocity (the non-zero "average" motion) then there is a dependence on the strength of the applied electric field and some phenomenological time constant $\tau$; $v_{dr} \approx -\frac{e\vec{E}\tau}{m_e}$. For aluminum, $\tau = 8 \times 10^{-15}$ s at room temperature.
at a more course grain level, i suppose electrons in the drude model must move slow because the drude model is non-relativistic :-)
Or, I guess you could talk about the expected value of the speed of an electron in the Drude model, which is $\langle v \rangle$ taken w.r.t. the Maxwell speed distribution, which is of order $T^{1/2}$ (temperature).
@SillyGoose The true reason is that Drude model is still mostly classical and is still too wrong to obtain the correct semi-classical limit; quite a big chunk of the book is interested in getting you to learn the actually correct semi-classical picture.
