Well

I guess I need to fix that question

which is nothing but pop-science

I guess you have in mind the heuristic picture of phantom-like particles popping in and out of the vacuum

No

not really

there is nothing in the mathematics of QFT that suggest that such a picture is in any sense accurate

I guess you have in mind the heuristic picture of phantom-like particles popping in and out of the vacuum

I have more of an image of electrons getting closer

and a disturbance being made in the middle

with that being the virtual particle

thats a bit like a regular particle

but according to HUP has a few wonky properties since it's not around for long

they are a formal concept, with a very precise meaning

"virtual particles" are not to be regarded as something particle-like

Wait, they're not? I thought they're just short lived particles that borrow their energy according to HUP

with their lifetime being inversely proportional to their energies

nope

o

the HUP has nothing to do here

Oh

How do you estimate the lifetime of a virtual particle then?

particles cannot borrow energy from anywhere

@Phase again, a virtual particle is not to be regarded as something particle-like

Guess I got led astray by a wonky teacher

in technical terms, a virtual particle is a contraction of fields in the Dyson expansion of the $S$ matrix

it has nothing to do with actual particles

Tbf they probably didn't study this far

people use the words "virtual particles" because it makes communication more efficient

but it is a very misleading name

let us introduce a better name

something like "virtual contraction"

I mean

now you see all those questions are meaningless

That might work if I had any idea of any of that

I've barely gotten through Shankars Principles

I assume from that though that it's just mathematical formalism

of course, I dont expect you to understand the technical definition

rather than physical things?

exactly, just maths

it has no counterpart as far as the physical world is concerned

a lot of mathematical concepts have a corresponding reality associated, at least in principle

"virtual particles" is not one of them

@Blue $x^5/5!-x^7/7!+x^9/9!....>x^5/5!>0$, right?

bc it is decreasing and alternating

Wait so

What about the Casimir effect?

Doesn't that have a virtual particle effect?

what about it?

what do you mean by a virtual particle effect?

An old tutor said to me that Virtual particles provided the momentum for pushing the plates closer together

if you take two conductive, non charged plates and put them a short distance apart

that is the hand-wavy explanation

it doesn't stand up to inspection

@Phase The virtual particle myth is really pervasive, but the fact of the matter is that "virtual particles" only exist in the perturbative expansion into Feynman diagrams, and are absent in other approaches. Every effect you can "explain" with virtual particles you can also derive without ever mentioning them.

Oh

im just gonna stop taking what irl physics people tell me as fact

that was probably dumb of me

and, to be fair, in the typical calculation of the Casimir effect you dont even go beyond tree level, so you dont really have virtual particles

@Phase It's not your fault - as I said, the virtual particle myth is really pervasive, and even many people who should know better continue to perpetuate it, for reasons I cannot fathom

Once I finish a QM textbook like Shankar's, what path should i take so that I can eventually start actually learning QFT?

@ACuriousMind for the same reason physicists perpetuate the myth of dy/dx being a ratio

@Blue yes

Sum the series.

@0celóñe7 The problem is that the virtual particles idea creates much more confusion than it alleviates. The ratio thingy just works almost all of the time - it's wrong, but it doesn't lead you astray more often than it works.

@EnderLook $p$ is momentum.

That's a logarithm (maybe)

ups

Put it into wolfram and see what it gives

thats a cos

50/50

but $\cos(x)-1+\frac{x^2}{2}$ is positive everywhere

so is mod(cos(x))

not that that's relevant

$\cos(x)-1+\frac{x^2}{2}\ge \frac{x^4}{4!}$

?

How bout this?

Shameless method but i guess as long as its the right result

I just figured that since cos(x) can be expressed as a convergent series, I could just put cos(x) - (1 - x2/2!) into Wolfram to get what you wrote the sequence to be

and wolfram took it from there

Pretty sure you can do that sort of stuff with Convergent series

haven't studied it formally tho

oh no

i should have been in bed by now

now im hungry again

#FirstWorldProblems

It doesn't?

huh

yes it do

im off to bed anyway

buh bye

afaik for any absolutely convergent series stuff like what I did above should work

cya

@Phase that's what AFT said

o

I didnt read it

Those imaginary exponentials combine to cosine

Well yeah

but he was asking in terms of e

@ιllιlılMostafaıllııllıl not my field so I can't comment

But it looks like they're getting Javier García de Abajo's affiliation wrong, he's at icfo

@Blue what are you even trying to do?

can this be mod-deleted? it's absolutely incomprehensible: physics.stackexchange.com/questions/351864/…

(or, you know, can anyone with enough rep vote to delete?)

@Blue that's a sine function