The h Bar

3:25 AM

Might be of interest:

12

Similar to: What are the different types of charge analysis?, What are the types of bond orders?, and What are some recent developments in density functional theory?, I would like to ask: What are the different variations/flavors of DFT (density functional theory)? I ask users to stick to one of ...

Beliod

3:54 AM

Sorry if this isn't the place for this, but the astronomy chat room is dead. Can anyone help me setup a location to view Neowise? Absolutely nothing I've tried has worked. And I'm assuming that my area is just a complete dead spot for the comet.

John Rennie

4:18 AM

@BioPhysicist it's just terminology. Suppose you are pushing a heavy object across a rough surface then it's you doing the work i.e. you are the one supplying energy, not the friction. Personally I have no problem with saying the friction does work. Whichever way you phrase it you are just describing an energy transfer.

@ABC the battery cannot absorb or create charge. It can only move charge around. The reason we have two spheres in my example is so the battery can move charge from one sphere to the other. If we only had one sphere then the battery couldn't charge it because it would have nowhere to move the charge from.

Captain Bohemian

5:04 AM

how is quantum computing related to quantum gravity?

by invoking the likelihood of formulating the both in terms of quantum field theory?

Dunois

6:32 AM

Hmm, if I'm going to have to ask here, then let me start with this: from whatever I've gathered on this topic, a single unit of light--and of microscopic particles in general--can be modeled as either as a hard sphere, or as a "wave". This also generalizes to a collection of said "particles". Is this correct?

John Rennie

← 1 message moved from Problem Solving Strategies

@Dunois hi :-)

Dunois

Hello.

John Rennie

"particles" are much more complicated objects than you think.

This applies to photons and electrons, protons, etc

We describe particles using a theory called quantum field theory, and this describes particles as packets of energy in an object called a quantum field that fills all of spacetime.

These packets can look like particles, i.e. like little balls, or they can look like waves. It depends on what they are doing.

As a general rule if a particle is interacting with something else, e.g. if two particles are colliding with each other, then they behave like little balls.

If a particle is just travelling along and not colliding with anything then it looks like a wave.

This is the reason for the "wave particle duality" that you've probably heard of.

Dunois

What aspect of the "particle" looks like a "wave"?

What does it even mean to look like a "wave"? I presume some amplitude is oscillating about some mean value, and this amplitude itself is moving about space and time (i.e., "the particle is moving")?

John Rennie

We're all used to the everyday world where balls are ... well ... just balls. They have a position and they have a speed.

But when you get down to elementary particles they are fundamentally different. A particle like an electron does not have a position. It is more like a fuzzy cloud that is spread out over a region of space.

Likewise it doesn't have a speed. It has a range of speeds.

The difference between behaving like a particle and behaving like a wave comes down to how spread out the particle is i.e. how big the fuzzy cloud is.

Dunois

6:52 AM

@JohnRennie could you elaborate a bit on this?

John Rennie

@Dunois it's hard to say much more without diving into the maths. The problem with QM is that it's inherently a mathematical theory. When we talk in general terms, like calling particles "fuzzy clouds" this is only a metaphor.

Dunois

Okay, let's stay with the fuzzy cloud idea. What would diffraction and interference mean in this context? You also stated that particles generally behave like little balls when they collide (interact?) with one another. But wouldn't interference (I gather diffraction is a form of interference) require that the particles actually interact like waves? (I hope what I am trying to say makes sense.)

John Rennie

No, because in diffraction the particles are not colliding.

Dunois

7:10 AM

What actually happens in diffraction then?

John Rennie

The functions that describe particles have two properties, an amplitude and a phase.

When we have two particles interfering we add together the functions that describe the particles.

If particles only had an amplitude then the sum would always just be a positive number and we wouldn't get any interference. This is what classical mechanics predicts. However quantum particles also have a phase and it is the phase that causes the interference.

Now you're going to ask what a phase is, but this is going to get us into some maths.

Dunois

Oh no, I know what amplitude and phase are (at least at a simplistic level). So this I can understand.

But coming back to my question, quantum particles are always fuzzy clouds and also always "balls", right? So what governs whether they collide (like balls) or whether they interfere (like waves)?

John Rennie

OK, so if at a point in space the two particles have opposite phases they will cancel each other out. While if at some other point in space they have the same phase they will reinforce each other. This is all that interference is.

ACuriousMind

8:37 AM

@BioPhysicist I think this depends on whether you think of "work" as something "real" in the world or just the quantity computed by $\int F\mathrm{d}s$. Mostly there's no difference, but someone who thinks about work as being more than a bookkeeping device in our calculations will find applying the definition to something like friction absurd, like Charles argues there.

It's a variation on the theme of whether or not energy is "just a number" or "real" - people believing the latter often have difficulties e.g. seeing where it is "stored" in an electromagnetic field.

BioPhysicist

10:28 AM

@JohnRennie Work is not only done by forces that supply energy. Work has a precise definition, not a subjective, qualitative one. I feel like talking about work in the latter way just makes it more confusing for introductory students.

@ACuriousMind I'm not talking about whether or not you think energy is real. I just don't see how you can ignore the definition of work entirely and say that friction does not do work. That seems to me that you are saying the line integral is 0, which isn't true. Unless one is saying if work is non-positive then the force doesn't do work, which I think is extremely confusing.

Physics Meta

1

Q: Removing Deleted questions form Followed Posts list

My Followed Posts list is littered with Deleted questions, which I cannot remove off the list, as they've lost their "unfollow" option. How do I prune off these entries?

bug deleted-questions followed-posts

John Rennie

10:45 AM

@BioPhysicist I agree.

Jake Rose

12:12 PM

Wow am I not allowed to send photos anymore?

Everything I know about the summation convention is telling me this is wrong

How can you have a covariant tensor being equal to a contravariant tensor?

Qmechanic

12:40 PM

Should the bounty be revoked here? Thoughts?

JingleBells

1:47 PM

In Deep Q Networks, the output of the neural network is basically the q values for each action. My question is on what data and how do we train and do backpropagation on the neural network? I mean, the nn spits out q values but how do we get the target q values for each action?

ACuriousMind

3:14 PM

@JakeRose What the text is trying to say is that the co- and contravariant components of a tensor in default Euclidean space don't really differ because they're numerically equal

John Rennie

@Qmechanic yes, close it as homework and refund the bounty.

JingleBells

3:40 PM

I was thinking, instead of explicitly setting the rewards in a RL system, can't we make a system that figures out the rewards on it's own? For example, no one set the rewards for us humans in the real world, evolution has carved them in our brains.

JMac

@Qmechanic It does seem pretty crazy that it's at 4 close votes and now held open by a bounty. It seems like several if not all of the close votes will also expire during that time... That doesn't seem right to me.

Qmechanic

@JohnRennie & @JMac : Done.

Charlie

4:00 PM

@JakeRose $\delta_{ij}$ is the identity matrix.

oh ACM already answered

Jake Rose

Ahhh I see. In my head it feels like it’s neglecting the summation convention by not balancingnindices. Is this an abuse of notation? Or am I just not familiar enough?

Charlie

It's not abuse of notation, the metric tensor defines a 1-to-1 map (in finite dimensions spaces) between a vector space and the corresponding covector space, there's no reason the vector in $V$ and the covector in $V^*$ can't have the same components.

ACuriousMind

Notation is not that universal - some would say it's okay, some would say it's terribly wrong

Charlie

It's not a general relationship, it is only true in the specific case that you are dealing with the Euclidean metric, which is the identity matrix

Jake Rose

@Charlie I don’t disagree. The textbooks and notes I’ve used previously just often use the idea that “indices should always be balanced” as a core part of the Summation convention.

To me it feels like an equivalence relationship between a vector and it’s dual

Charlie

4:08 PM

Oh I see what notation you're talking about now

Jake Rose

god I’m rusty, I think it can be called a dual

Charlie

it can, $V^*$ is the "dual space" of $V$.

Jake Rose

@Charlie I get what it means, and I get what you’re saying. I’ve jsut been taught a more “summation principle is law” type of way

*rule not principle

Charlie

This is a very, very specific case where the rule can be broken without ambiguity

Jake Rose

but saying this, I’m not sure how I would say the same relation whilst respecting my idea

maybe by using brackets

Charlie

4:11 PM

In general $x_\mu \neq x^\mu$

Jake Rose

btw, I’m trying to do a bit of reading into geometry and physics. Any recommendations for good texrbooks?

Charlie

differential geometry?

Jake Rose

Yes

Charlie

in the context of GR?

most introductory textbooks cruise fairly quickly over the basics of differential geometry before starting the actual gr

And if your ultimate goal is to learn GR you're probably better off using an actual GR textbook than bothering yourself with a really heavy mathematics textbook on differential geometry first

but others may disagree

Jake Rose

originally I was just looking for a book that used normal geometry to show some beautiful ways of doing physics (e.g. Newton’s derivation of the orbits) but then I got to reading some of the “geometry of physics” and they had a mix of differential geometry, Lie groups, etc and went into both gr and quantum.

I’ve already done a course in GR

taking David Tong’s course next year too

feel like a more pure mathematics perspective on the physics might be interesting reading over summer

Charlie

4:16 PM

If you want pure diff geo you could ask in the maths chat chat.stackexchange.com/rooms/36/mathematics

Jake Rose

Geometry and Physics
Textbook by Jürgen Jost

Has a really interesting mix of subjects, probably the most what I’m looking for

@Charlie I might eventually, but I still want a physicists take.

Charlie

someone more mathematically knowledgeable than me will have to suggest something

JingleBells

4:52 PM

Hello agents

How is everyone doin'?

bolbteppa

@JakeRose MTW, hundreds of pages on diff geom for physicists in there

Gravitation (book)

Gravitation is a textbook on Albert Einstein's general theory of relativity, written by Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler. It was originally published by W. H. Freeman and Company in 1973 and reprinted by Princeton University Press in 2017. It is frequently abbreviated MTW after its authors' last names. The cover illustration, drawn by Kenneth Gwin, is a line drawing of an apple with cuts in the skin to show the geodesics on its surface. The book contains 10 parts and 44 chapters, each beginning with a quotation. The bibliography has a long list of original sources and...

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