I've read somewhere that if you consider a classical random walk driven by totally uncorrelated noise, then you can define position x and velocity v in some way such that [x,v]=1.

Anyone have any idea what I'm talking about?

In physics.stackexchange.com/questions/238976/… this question, guill answers by ml

In physics.stackexchange.com/questions/238976/… this question, guill answers in 3) by introducing self-induction on moving electron. Can someone please explain how come self induction was produced and effected a straight moving electron?

Howdy

What did one physicist say when he wanted to fight another physicist?

"Let me atom!"

Where does bad light end up?

In a prism.

How does it end up there?

It breaks the laws of physics.

@Slereah Apparently it's not known if $S^2\times S^2$ carries a metric of positive curvature.

@0celo7 what is an extensor?

nvm it seems like it's only used by that name in this book.

this is a bad book.

no clue

what's the best geometry/topology for physics book i can read right now?

I read danu's answer.

Do any of you live in the Los Angeles area? It will be cool to study, and compute things . . . . . let me know

@AnubhavGoel electrodynamics isn't my favourite subject, but as far as I can tell part (3) of guill's answer is complte rubbish.

@0celo7 None of us are free of \sin

→ 4 messages moved to Trash

@JohnRennie why move to trash?

@DavidZ I'm in grumpy mood this morning (lack of sleep) and on reflection I thought the tone was a bit immoderate, though that is the way I feel and I take none of it back.

uh, ok

I thought it was fine

Well the chat you linked said quite explicitly that rooms cannot dictate what users discuss in them.

So the question is

What happens to a timelike curve inside an Alcubierre bubble

I hear it is causally isolated, but what happens

Does it hit a horizon

There's a white hole type horizon in the forward direction

i.e. even a null geodesic cannot propagate in the forward direction farther than the horizon

Unfortunate

I had the idea of a little bus roundabout using warp bubbles to have CTCs with no geodesics, but that would imply leaving a warp bubble to go on another one

Because otherwise you need overlapping bubbles and I'm pretty sure those allow closed geodesics

I don't even know if overlapping bubbles would work

That is the idea thrown aroud to prove that Alcubiere allows CTC but I haven't seen any hard computations of it

I think it works fine with Krasnikov, tho

Krasnikov's metric is pretty fucked up

Thinking about it

The horizon is a pretty good proof that a single warp bubble cannot cause any CTCs

Even if you do the argument that as the thickness goes to 0 it resembles a tachyon, the inside still can't exchange information with the outside

Although

In a realistic case

Maybe you could have a bubble go back and forth

And the deformation on the bubble it may acquire through interacting with gravitational systems may inform on what is up there

not quite a CTC but you are certainly peeking outside the light cone

@Danu Yes please. Can't hurt :)

"the paper also argues that these problems are absent if the bubble velocity is subluminal, although the drive still requires exotic matter"

I wonder what would be a realistic warp bubble that we could produce

Subluminal, tiny bubble with thick walls

Probably round the Planck scale with quantum inequalities

@JohnRennie The answer is accepted and misguiding. Can anything be done for it?

Downvote it

"The interior of the bubble is causally disconnected. It's not possible for the bubble to be turned off or steered from the inside. But there is no reason it cannot be affected from an outside agency at a pre-planned points, or even simply have a finite lifetime, naturally deteriorating to stop at the intended destination."

Hm

That could work, too

Oh man

Turning off a spacetime structure

You know what that means

Sigmoid functions ahoy

Hi guys! which is the difference between parton-level and hadron-level processes? What do they mean?

Parton level is quark gluon interactions

Hadron level is meson and baryon interactions

Ok.. but, why is it important to remark the difference when one want to analyze data?

Not a clue

I know you can use effective theories to do hadron interactions without referring to partons at all

I don't mean theoretical stuffs… I have a data set of an event and I can analyze it as hadronic-level or parton-level and I would to know what is the difference

I think it might just depend on energy?

At low energy partons will not interact directly

The same way that you don't have to care about nuclei collision if you smash atoms at low speed

There's probably some energy scale where parton collision becomes relevant

Krasnikov uses the Deneb star a lot when he talks about warp drive

I think he might be an alien from Deneb

umhh ok

thanks

IIRC in effective models you use a specific energy scale for hadrons

Where below that energy you can just consider hadron interactions as particles themselves

I think it's somewhere around the binding energy

Like... a few hundred MeVs?

For light mesons, at least

@AnubhavGoel You can downvote it, and if you have the rep vote to delete it.

Although remember that per PSE rules, you can't delete it for being a dumb garbage answer

As long as it is dumb garbage that tries to answer it

Also I guess maybe parton collisions involve parton jets?

I'm lazy as hell today

(supposing hell is extremely lazy)

Well some people upvote if they don't know the answer but it sounds right

@Slereah Yo there might be an easy way to show that an odd sphere has a nonzero vector field

I know of an elementary proof that an odd sphere's antipodal map is homotopic to the identity

@MAFIA36790 hey

well, you should look for some math phys program ;-P

@MAFIA36790 and theoretical physics at least?

I probably would prefer math however

@yuggib Do you know how to prove the thing I did yesterday

My proof was probably amateurish and overkill

@yuggib I think one doesn't get an appreciation for what mathematical physics actually does when one hasn't first learned the physicists' way of thinking about things. I mean, you had a reason you began as a physicist and then drifted towards math, right? Do you really wish you had only studied math in the first place?

@ACuriousMind don't know; probably not

Does anyone know that website where you chuck in like a long decimal like "0.12412479812479" and it'll output the closest 'special' numbers like "Oh this number is pretty close to root 17, and a bit close to pi/7" and stuff so you can identify what your number probably is

however there are some parts of the standard physics program that are a huge loss of time

@JohnRennie We cannot vote to delete accepted and/or positively scored answers.

there surely is an importance in having a physical intuition/perspective

@JoshuaLin It's called the inverse symbolic calculator

@ACuriousMind thanks

however nowadays most mathematical physics researchers teach on mathematics departments; so if you are in a physics degree, you won't probably have any opportunity of being in contact with them

@ACuriousMind how do you know about that

it's tricky

@0celo7 no I don't know

@0celo7 I...think I saw it mentioned in some answer somewhere on math.SE/physics.SE/MO? I'm not sure

there's also a cool website

Where you input any series of numbers

@0celo7 it seems a reasonable statement the one about zero points of the derivative though

And it will tell you if it's a specific number series

oeis.org

It's a neat website

@yuggib Yes it's reasonable and also true :)

@yuggib as a mathematical physicist, what is the worst abuse of rigor that you have witnessed in physics

And was it me

@Slereah $1\sim\pi$.

Well they have the same order of magnitude

That is downright reasonable

@Slereah I am not sure...probably treating unbounded operators as matrices is one of the brutal ones.

@yuggib it works

and we built an atom bomb by doing it

so I really don't see why it's bad

But the atom bomb is a hoax

What about treating distributions as functions

is it awful

Or using infinitesimals

@Slereah distributions as functions, mildly awful

infinitesimals can be rigorously defined in math ;-P

Oh yeah but trust me we don't

Honestly the worst abuse I've seen is not defining the covariant derivative along a curve as the covariant derivative along the pullback bundle of the curve

it's dreadful

every GR text gets it wrong

>implying physicists doing GR even know what a pullback bundle is

the geodesic equation doesn't even make sense without it

Writing the geodesic equation rigorously is a lot of trouble for nothing tho

@Slereah to be fair many riem geo books don't either

Who cares about the atlas

@yuggib: You ninja'd me answering that Fock space question :P

Psh I answered it before :p

btw do some interacting theories have a Fock space?

Sine Gordon has a basis of sort

@ACuriousMind :-D

I fixed my car stereo

Not sure if you can get a Fock space with it though

Now I can subwoof without problems

@ACuriousMind we need a coordination in order to avoid wasted effort ;-)

The solution is to stuff a sock in the problem area

@Slereah The only-semi-relativistic theories like the Nelson model have a Fock space representation

of course they do not satisfy the Wightman axioms

What Wightman axiom fails in interacting theory btw?

Is it the vacuum state one

quadratic scalar interacting theories satisfy the Wightman axioms, need renormalization and a non-unitary change of representation, but still they have a Fock space representation

Neat

@Slereah what do you mean?

Well most of the Wightman axioms seem pretty general for a QFT

I assume only a few of them fail in interacting theories

indeed

Why do you think they fail in interaction theories?

Unique vacuum seems like one that can fail

however hidden in the poincaré group there is the hamiltonian ;-)

Because @yuggib just said that it fails

For a start Sine Gordon has $\aleph_0$ vacua

@Slereah He said that the semi-relativistic theories like the Nelson model fail the axioms

@Slereah I said that there are theories that are not fully relativistic, and therefore you don't have wightman axioms

Which is not surprising because they are, well, not relativistic

^

But is what I said true, though

Also what does the Fock space like for $\phi^4$

Is it more soliton bullshit

Or is it just a thing like "It exists"

And that's about the extent of it

@Slereah I'm not sure what you mean - you don't get a Fock space for interacting theories because you don't get the creation and annihilation operators as modes of the free fields

@Slereah I don't think that there is a Fock space for $\varphi^4$

Oh

you said quadratic

I thought you said quartic

nvm

no no, not quartic

Also @ACuriousMind I think Sine gordon has them?

Like you have creation and annihilation operators for the soliton solutions

quadratic are trivial I know...however are still interacting theories ;-)

Eeeeeh

Well I guess you could say Dirac is left handed interacting with right handed :p

What is a spinor?

It's a section of the associated bundle of the Spin bundle

What's a spin bundle

Or it's a section of the... odd part of the Clifford bundle?

I forget

Or is it even

It's the $SL(2,C)$ principal bundle thing

@ACuriousMind ?

@0celo7 What?

One thing I'm not sure about is

Is sine gordon really fully solved

Like if you use superpositions of all the soliton and breather solutions

Do you have EVERY possible solution of the equation

Apparently one of the important part of Sine Gordon is that it has infinitely many conservation laws

Which helps to reduce quite a bit the possible interations

@ACuriousMind !

spinors

It basically only allows collisions and a bound state of two

@0celo7 Something that transforms in a spinorial representation. You'll have to be more precise about what you want to know.

For a start is it the Clifford thing or the cover of the rotation group thing :p

@Slereah Irrelevant question in $d\neq 2$

(Clifford algebra seems to be the more general of the two)

Well gee what's so bad about 2 dimensions

Try to find the universal cover of the 2D Poincaré group!

(IT IS THE SAME)

the same as what?

As the Poincaré group itself

That thing is all simply connected

No, $\mathrm{SO}(2)\times\mathbb{R}^2$ is not simply connected

@ACuriousMind I know that

But what about $SO(1,1) \times R^2$

But I have no idea what that even means

The connected part is just $R^+$

@Slereah Oh, yes, indeed

@0celo7 Well, then ask a specific question. I'm not going to spew facts about spinors at you only to have you say "I know that" at the end :P

I'm okay with spewing spinor facts

But it's probably not rigorous enough for @0celo7 :p

does wavelength mean photon is waving in space?

By the way, is it possible to write the Dirac equation using only Majorana spinors?

Can I write down the dynamic of an electron with Majorana spinors

Or are they different from Weyl spinors

I would think that Majorana spinors would work for all spinors since they are part of the "real" clifford algebra

None of that fake complexified algebra

@Slereah Splitting a Dirac fermion into Majorana parts is rather pointless - the equations never decouple, unlike the Weyl case.

But it is possible, yes?

@ACuriousMind not with that attitude!

@Slereah In the dimensions where Majorana spinors exist, yes

I guess the majorana part is like

A sum of the particle and antiparticle bit of Dirac spinors

Don't they exist in all dimensions?

@AnubhavGoel I don't know what "photon is waving in space" is supposed to mean.

What happens if you try to use the regular spacetime algebra instead of the Dirac algebra in the wrong number of dimensions

@ACuriousMind two possibilities. 1) it is oscillating somehow. 2) It is very friendly

@ACuriousMind Does photon move in a straight line or does it curve sinusodialy in space?

@Slereah No

I think they exist in $1,2,3,4\text{ mod } 8$ dimensions?

Quite odd

@AnubhavGoel straight line. The magnitude and polarization of the electric and magnetic fields composing the photon are what oscillate.

@Jim I like the latter possibility

What happens in 5D

What fucks up in the Clifford algebra

Hm

Wait

Is it related to like

The link between complex sets and $R^n$

Since there is nothing between quaternions and octonions

@ACuriousMind I assume photons are friendly. I hear they are very light-hearted

but then $3$ manages to be there, by being unit quaternions

Is there no algebra of unit octonions

Does probability wave of matter like electron move in straight line or it oscillates?Like Matter moves here and there

?

@AnubhavGoel yes

Probability does not "oscillate"

That's the amplitude

@Jim Yes to what?

@AnubhavGoel I'm not sure what you're trying to ask - the wavefunction is not a point-like object (not a physical object at all), it doesn't "move" in the classical sense.

@Slereah Sure, but it's non-associative

Is it related to that bit then?

Do you need the even part of the algebra to be associative

For Majorana to exist

@AnubhavGoel your statement. You made a "a OR b" statement, which was true so I said "yes"

or is it entirely unrelated

@ACuriousMind I probably know your random facts

But I still do not know what a spinor is