Physics noob tries to get better (ft.John rennie)

satan 29

5:38 AM

@JohnRennie hi sir

John Rennie

@satan29 hi :-)

satan 29

sir, how does current flow work in the quantum picture?

John Rennie

@satan29 you mean current flowing in a conductor?

satan 29

yes

John Rennie

The electrons in the conduction band of a conductor behave almost like free particles. Inside the metal they can move freely and the only restriction is when they hit the edge of the wire.

So the wavefunctions of the individual electrons are like momentum eigenstates i.e. each electron behaves as a wave with a certain momentum. OK so far?

satan 29

5:45 AM

ok

@JohnRennie is momentum something better associated with a particle...

John Rennie

The free particle solutions $e^{i(kx-\omega t)}$ are momentum eigenstates. The momentum is $\hbar \mathbf k$.

satan 29

ok

John Rennie

Which makes sense. A free particle will move at constant speed in a straight line i.e. it has a constant and well defined momentum. So you'd expect it to be a momentum eigenstate.

(as well as an eigenstate of the Hamiltonian)

satan 29

@JohnRennie sir its coming out to be $-\hbar k$

John Rennie

$\hat p = -i\hbar\frac{d}{dx}$

$$\frac{d}{dx} e^{i(kx-\omega t)} = ik e^{i(kx-\omega t)}$$

satan 29

5:51 AM

oops yes, i forgot the - sign in the operator.

carry on, sorry

John Rennie

:-)

The physical interpretation of this is that if you look at the electrons in the conduction band of a metal they are all whizzing around at different speeds (i.e. different momenta) like the molecules in a gas, but because the velocities are symmetrically distributed the net motion averaged over the electrons is zero.

i.e. on average no current flows. OK so far?

satan 29

ok so far

John Rennie

When you apply an electric field this changes the eigenstates because now the Hamiltonian has a potential energy term from the field.

satan 29

ah

John Rennie

The eigenstates are still approximately momentum eigenstates, but their energy gets shifted. The momentum states that travel in the opposite direction to the field have their energy lowered while the states that travel in the same direction of the field have their energy raised.

satan 29

5:56 AM

why are they still momentum eigenstates?

John Rennie

So what happens now is that the electrons have a net momentum i.e. when you add up the total momentum of all the electrons in all the states you find there is a net momentum in the opposite direction to the field.

@satan29 I don't remember the details, just the basic principles.

satan 29

ok

John Rennie

The point is that now there is a net momentum i.e. a net motion of the electrons, and that is just what we call a current.

satan 29

got it

sor can QM reproduce the maxwells equations entirely?

John Rennie

That's a complicated question ...

QM cannot reproduce Maxwell's equations. Do do that we need quantum field theory i.e. quantum electrodynamics.

satan 29

6:04 AM

hmm

John Rennie

But for that we start with the vector four-potential from Maxwell's equations and quantise it. So QED reproduces Maxwell's equations because it starts from Maxwell's equations.

satan 29

oh, bummer :/

John Rennie

Or I guess it's fairer to say that both QED and Maxwell's equations are derived from the same Lagrangian.

A classical treatment of the Lagrangian gives ME and a quantum treatment gives QED.

satan 29

@JohnRennie wait, so in a sense the maxwells equations are more fundamental than QFT !?

John Rennie

See above. Both derive from the same Lagrangian.

satan 29

6:07 AM

what do i type to get more details about this "lagrangian"?

John Rennie

You probably need to ask in the hbar. You're now pushing at the limits of my knowledge of QM :-)

satan 29

:-)

John Rennie

I need to work for a bit. I'll be back in about an hour.

satan 29

11:04 AM

@JohnRennie hi sir

John Rennie

@satan29 hi :-)

satan 29

sir are you here till 5 pm?

i.e 30 mins more

John Rennie

Yes ...

satan 29

can I share a google doc

John Rennie

Yes

satan 29

11:05 AM

docs.google.com/document/d/…

sir just keep it for now, Ill need it tomorrow

John Rennie

OK

satan 29

societyofrobots.com/actuators_dcmotors.shtml

sir can you explain the para "power spikes"

John Rennie

Motors also act as generators. When you first apply an EMF to a motor it draws a large current, then as the motor starts rotating it generates a back EMF that opposes the applied EMF. If you had a perfect motor (no friction) then the motor would speed up until the EMF it generated was equal to the applied EMF and at this point it would run at constant speed drawing no current.

satan 29

hmm

yes, that meks sense

John Rennie

A real motor has friction, so it accelerates until the difference between the applied EMF and generated EMF decreases to the level needed to overcome the frictional losses.

satan 29

11:11 AM

right

John Rennie

Anyhow, if you suddenly remove the applied EMF then the back EMF is unopposed and will be trying to pump a reverse current back through your PSU.

PSU?

Power Supply Unit

Ah

And if you reverse the EMF then you'll get an extra large current

satan 29

11:12 AM

hmm

John Rennie

Because now the motor acting as a generator and the reversed EMF are both pushing a current back through the PSU in the reverse direction.

satan 29

that makes sense

what was x-x eariler is now x+x

John Rennie

Yes. So you'll get a transient extra large current.

satan 29

got it.

John Rennie

The current decreases as the motor's rotation slows to a halt then reverses.

satan 29

11:18 AM

sir do you kniw what a servo motor is>

John Rennie

Vaguely ...

satan 29

from my experience, your "vaguely" is good enough :-)

John Rennie

A normal motor just spins, and it spins faster the more voltage you apply.

satan 29

yes

John Rennie

A servo motor is design to rotate by some specified angle then stop.

satan 29

11:20 AM

oh

John Rennie

They are used for controlling machinery e.g. in a remote control vehicle you could use a servomotor to control the steering.

satan 29

hmm

John Rennie

i.e. you can get it to turn the steering wheel by x degrees where x is any value you want.

There is a very similar type of motor called a stepper motor

satan 29

ok

John Rennie

This works by rotating in fixed steps, and you determine the angle by how many steps you make the motor move.

However you are limited to a resolution of one step i.e. you can't turn the motor by half a step.

satan 29

11:23 AM

right

John Rennie

A servo motor moves smoothly an the resolution is only limited by the sensitivity of the mechanism you used to build the motor.

I don't know a vast amount about this. I have used these types of motors for building RC stuff, but that was decades ago.

I imagine the technology has moved on since then :-)

satan 29

sir final question

I know the physics behind gyroscope and gyroscopic precession

John Rennie

Yes ... ?

satan 29

but

Gyroscope: A gyroscope is a device used for measuring or maintaining orientation and angular velocity.[1][2] It is a spinning wheel or disc in which the axis of rotation is free to assume any orientation by itself. When rotating, the orientation of this axis is unaffected by tilting or rotation of the mounting, according to the conservation of angular momentum.

I dont understand how it used practically?

John Rennie

I guess it depends what you are using the gyroscope for. Are you thinking of its use in navigation systems?

satan 29

11:30 AM

yes

John Rennie

In a navigation system you need to know what direction you are moving in. A compass gives you some idea but it isn't so good for measuring the up and down directions, and it can be used at all in some circumstances e.g. on a fighter plane that is screened against EM.

So you use a gyroscope mounted inside a gimbal that allows near frictionless motion about any axis.

satan 29

@JohnRennie EM?

John Rennie

Electromagnetic pulse

An electromagnetic pulse (EMP), also sometimes called a transient electromagnetic disturbance, is a short burst of electromagnetic energy. Such a pulse's origin may be a natural occurrence or human-made and can occur as a radiated, electric, or magnetic field or a conducted electric current, depending on the source. EMP interference is generally disruptive or damaging to electronic equipment, and at higher energy levels a powerful EMP event such as a lightning strike can damage physical objects such as buildings and aircraft structures. The management of EMP effects is an important branch o...

satan 29

ok

@JohnRennie alright, but how does it detect directin?

John Rennie

If your superfighter can be knocked offline by an EM pulse you're not going to survive very long :-)

satan 29

11:33 AM

yes XD

John Rennie

@satan29 Once you spin up the gyroscope it will always point in the same direction i.e. its angular momentum vector remains constant.

satan 29

and that helps how?

John Rennie

So you just have a sensor that measures the direction of the plane relative to the direction of the gyroscope. Then you have an absolute measurement of the direction the plane is going.

satan 29

ohh

John Rennie

You need to read more science fiction. If you did you'd know all this stuff. I've long thought the educational system doesn't place enough emphasis on reading science fiction :-)

satan 29

11:37 AM

:-)

thanks for today sir.

John Rennie

Admittedly you'd also believe that transdimensional warp drives exist ...

I was devastated when I learned GR and discovered that they didn't.

satan 29

well yes, Ill be trubling you with an entirely different set of qns

John Rennie

OK. I'm off now to score some lunch.

satan 29