01:00 - 14:0014:00 - 21:00

1:11 AM
@naturallyInconsistent the cucumber struck

5 hours later…
5:50 AM
non-hermitian physics seems to be a hot topic these days
6:42 AM
what is the "right" or "proper" way to talk about eigenvalues of an operator?
I am reading an open quantum systems book, and it uses the language of resolvent operators. I.e., consider a Banach space $\cal{B}$. Then, consider a linear operator over $\cal{B}$, $T \in \cal{B}^*$. The resolvent operator of $T$ is $R_T(\lambda) = (\lambda \mathbb{I} - T)^{-1}$.
An eigenvalue is a $\lambda$ such that $R_T(\lambda)$ is undefined, i.e., a $\lambda$ such that $\lambda \mathbb{I} - T$ is non-invertible.
Then, an eigenvector is an element $x \in \ker(\lambda \mathbb{I} - T)$
also is this a correct statement of the theorem?
wikipedia seems to say something slightly different. it states that every real $\lambda > 0$ satisfies 1. and 2. as written in the screenshot.
@SillyGoose struck gold
where is @nickbros123 at when u need him. a whole lunch break on electric fields in matter!
one last question im left with is why $\rho$ here is not $\rho_b + \rho_f + \sigma_b + \sigma_f$
7:41 AM
@Relativisticcucumber how could you add the $\rho$s and the $\sigma$s? They have different dimensions.
@SillyGoose Why would there be an "improper" way?
7:54 AM
@ACuriousMind multiply dirac delta
but $-\nabla \cdot P$ contains info about the surface bound charges also
@nickbros123 I know that - but that's not the correct answer for this text, either, one just has to read the paragraph carefully: The text clearly states it's talking about the situation within the dielectric, i.e. the surface charges are outside of the bounds of consideration.
yeah thats true, but viewing the surface as a thick thing can also do the job
so the $\rho$ takes care of the $\sigma$ as well
there is some level of handwave involved in this explanation though
some might call it a work around
8:15 AM
the argument is: lets fix xyz coordinate system at a point on the dielectric surface, zoom in enough so that it is flat. and assert that (WLOG) the y coordinate of $P$ is non zero inside the surface, but 0 outside the surface (P is 0 outside the dielectric is assumed). Now, the y component is like a step function, so its derivative would be the dirac delta. Assmuing the other components dont vary as appreciably as the y component does, which is the case for macroscopic fields
Hello Everyone...
@ACuriousMind i mean that i want an "appropriately general" definition for eigenvalue of an operator
8:34 AM
@SillyGoose "appropriate" for what?
such that a mathematical physicist would never have to learn another definition
the problem is that terminology here is not fully consistent across different subfields: Everyone agrees that if there is an eigenvector $v$ of the operator $A$ with $Av = av$, then $a$ is an eigenvalue of $A$. The resolvent definition you have mentioned is usually said to define the spectrum, and there may be values in there that do not have corresponding eigenvectors in the general case.
people (especially those who are not deep into functional analysis) often say "eigenvalue" when they really mean "value from the spectrum"
whether this is "wrong", "sloppy", an "abuse of terminology" or something else is a matter of debate
hm i see
in the finite dimensional case, does eigenvalue and value from the spectrum coincide?
8:51 AM
yes
and also for bounded self-adjoint operators
i see
Consider a smooth function $\gamma(t)$. Can $\gamma(t)$ be a solution to two distinct initial value differential problems $(D_1, \gamma_1(t_0))$ and $(D_2, \gamma_2(t_0))$ where $D_i$ is a differential equation and $\gamma_i(t_0)$ is an initial value.
9:35 AM
@SillyGoose Obviously you have to have $\gamma_1(t_0) = \gamma_2(r_0)$, but in that case of course - every function fulfills infinitely many differential equations (namely $f$ is a solution to $g' = f'$, $g'' = f''$, etc.)
oh yes I mistakenly wrote the initial conditions. I meant to just write $\gamma(t_0)$ for all cases
@ACuriousMind what about for differential equations that are not consequences of each other. since $g' = f'$ implies $g'' = f''$ and etc.
9:55 AM
@SillyGoose e.g. $e^x$ is common a solution to both $f"-3f'+2f=0$ and $f"-4f' + 3f=0$
10:17 AM
this seems hard to do using first order differential equations
Hello @RyderRude
We know ether is not the medium at which light travel (Failure of michelson-morley experiment). Can we say spacetime curve is the medium of light?
i got one i think.. dy/dx=1 and dy/dx = $\frac{1}{1-\frac{y}{x}}$. these two have one common solution which is y=x
but the rhs of the second diff eqn is undefined at the origin. we can use some initial condition like (5,5)
Or spacetime curve is not considered as medium?
@123 it is not considered a medium as far as common terminology goes
@RyderRude What is considered spacetime curve? Is there any another idea
10:27 AM
a medium, as the Michelson Morley experiment was trying to detect, has a preferred rest frame of reference, allowing u to detect it
spacetime does not have anything like that
@123 it is just spacetime
@RyderRude You are saying MM experiment they used ether as rest frame of reference?
they assumed that there was an ether and it had a rest frame thru which they cud detect the motion of earth
the frame the experimenters were themselves in was the earth ofc
@RyderRude through light???
yeah. light was assumed to be the waves in the ether
so by measuring the speed of light in different directions, u cud tell if earth was moving through an ether
I think the idea comes from mechanical waves. like water waves required water, string waves etc... Am i correct?
10:33 AM
yes. if u r moving in water, waves in water wud change their speed depending on the direction of the wave
so if u r moving in ether, light shud do the same thing
but light didnt
But speed of light is already calculated accurately by many scientist.
like waves in water have a fixed speed wrt water's rest frame. so if ur boat is moving, the speed of the waves changes relative to u
@123 yes. light has a speed but it doesnt vary at all
hav u read Doppler effect in water? @123
@RyderRude Yes but still confused in doppler effect.
oh
consider a fish tank. relative to ground, the waves in the tank have a speed v
now consider a moving boat inside the tank
@RyderRude ok
The speed of boat is also constant?
10:37 AM
if the boat is going toward the wave, the speed of the wave relative to the boat becomes v-u, where u is the speed of the boat
if the boat is going away from the wave, the speed of the wave relative to the boat becomes v+u
so the speed is supposed to vary
so if light is a wave in a medium, its speed shut hav varied
frame of reference is ground?
@123 i have edited it
@RyderRude Aaaah .. i see
the boat is synonymoys with earth. earth is cruising thru everything in the solar system. the speed of light shud change
It means it is a matter of frame of reference.
10:39 AM
yea
but speed of light didnt change wrt the boat we r in. it's always the same
so we conclude there was no medium
It means the idea of speed of light is constant comes from MM experiment in the einstien mind.
maybe einstein got it from there
but Maxwell's eqns already said it theoretically
Because Einstein always used recently published ideas in his theory and experiments.
It is based on quite a variety of things
10:42 AM
In photoelectric effect he used max plank idea
everyone uses everyones ideas. thats life @123
it is accepted of physicists to use ideas and contribute a bit
spacetime idea already created by minkwoski. he was the teacher of einstein
minkowski noticed it after einsteins paper
and yes, einstein later did use minkowski's ideas and contributed his own stuff which was the gravity
there are many ideas in general relativity which was developed by david helbert. It was also debate who developed GR david or einstein
einstein started publishing his incomplete stuff in 1907. hilbert learned from him
10:45 AM
@123 I doubt Einstein used Minkowski's idea for SR since he created SR three years prior
But early SR didn't have spacetime
physicists dont keep ideas secret
It was just relations between space and time
@Slereah i think 123 meant einstein used minkowskis idea in making GR, which he did
True enough
but einstein contributed his own things
10:46 AM
Although GR is kind of a lot of different things combined together
Also einstein used idea of time from another famous physicist , i don't recall the name
Poincaré?
No.. Let me remember the name
lorentz maybe
No. The physicist who working on time with electrodynamic in 1901 century.
Aaaah.. i don't remember the name but his face in my mind.
And the idea of speed of light is constant comes from maxwell theory.
How einstein comes from the idea speed of light is ultimate?
10:55 AM
what do u mean
It is one of those logical positivism influence
Means nothing can go faster than speed of light
Late 19th and early 20th century saw a big influence of logical positivism in physics and this implied getting rid of a lot of theoretical intermediaries
Einstein's idea of the speed of light being constant was by simply looking at the consequences of EM and the Michelson-Morley result and just getting rid of the ether hypothesis
10:57 AM
Oooh.. It is a fluke of einstein?
As it was entirely superfluous
he used it as a postulate and gave a neat proof
it was simple and practical
Aaaahh.. I see
altho math people would prefer different postulates
people who have no problem with mathematical platonism
It means Einstein used this idea the make theory and mathematics compatible.
10:58 AM
he also gave e=mc2
he didnt use anyone elses ideas there
Yes there are few ideas ideas which only comes from einstein himself. but few not all
u cud say all four maxwell's eqns are other peoples' stuff
like Gauss's law
Yes i have read maxwell eqns are 20 , but people worked on it and made it to 4
its just different notation
using vector language
Yes i remember now. It was lorentz who worked on time. and einstein used his idea as well.
11:05 AM
it is how physics progresses
It means Einstein used latest researches from his time from big scientists and the idea clicked.
einstein made more contributions than lorentz in the end
and more than poincaire
Yes
in todays physics, anyone only makes tiny contributions
Is there any way we can find our local frame is inertial or non-inertial e.g. free fall
11:07 AM
and they all read each others papers
@123 free fall is not distinguishable from inertial. we hav discussed this months before
at least by local experiments
Yes i remember last discussion. It means there is no way
@SillyGoose $f = 0$ solves both $f = f'$ and $f' = 0$, but neither $f = f'$ nor $f' =0$ implies the other.
@RyderRude What kind of experiment we need to know local frame is inertial or non-inertial?
check for newton's first law @123
@123 u can also use Foccault pendulum
u can search. it is used to detect earths rotation @123
@RyderRude Yes i know focault pendulum
What about free fall. Is there any way if we are in a closed cabin in free fall
11:11 AM
u cant distinguish that from inertial. we hav discusses this
but there r some papers about quantum mechanics violating equivalence principle i guess
but it is not settled
Okay... It means locally spinning can only be detected (focault pendulum) but not linear motion?
yeah, becuz spinning involves acceleration
so earths spin can be detected
but linear motion can also be accelerating. e.g. free fall
Newton was really confused about this difference between spin and velocity. check out Newtons bucket argument @123
@123 yeah... uniform gravity is the exception
@RyderRude Yes i have read newton's bucket few years ago.
@RyderRude ok
11:15 AM
Einstein also got carried away by this spin detection idea. he was a Mach principle fan
it helped him develop GR
What if we constantly accelerating in straight line. By this way we can get speed more than speed of light after any time.
@RyderRude Why this is not the case?
@123 it just helped him develop GR, but Mach's principle is not correct
@123 it is not possible. u hav to use relativistic dynamics
Like i am in earth and earth is stationary. and rocket constantly accelerate in straight line. There should be moment where you can go beyond speed of light.
it rquires infinite energy
@RyderRude Why... But it is possible in thinking. why not in eqns
11:23 AM
it is there in the equations. the total energy is mc2/sqrt(1-v2/c2)
so to get near c, u need more and more energy which is impossible
Aaaahh.. I don't understand that idea
relativity doesnt physically allow u to maintain a constain acceleration forever
May there are 3 rockets in straight line , 1 is stationary , 2 and 3 are same but at 2 is at behind the 3.
it doesnt change anything
if 2 and 3 are constantly accelerating according to 1 both should become more than speed of light at some point in time, but according to 2 the rocket 3 will be stationary
It is possible in thinking why not in theory.
11:28 AM
this is just a hack which doesnt work mathematically
u cant just forget the motion relative to 1
It is always necessary use $c^2$ in SR eqn. Why we can't go beyond. Why we can't put speed more than $c^2$ .
It was just hypothesis of einstein
now u r asking complicated questions :P
This is how new ideas developed :D may be
eintein's theory leaves $c$ as undetermined. the experimentally determined value is 3x10^8 ms^-1
@RyderRude Aaaahh.. that's satisfactory
11:34 AM
so one cant accelerate to more than the experimentally determined speed limit
But einstein developed his theory by postulating undetermined "$c$" as constant in any frame of reference. May be we do not need to postulate "$c$" as constant
then that theory does not fit the universe
Ooooookay..
@RyderRude I have read there are few experiments where they observed speed of particle more than the speed of light
they r all doubtful
Another question is that. I was thinking about negative mass. In law of gravitation we used both masses positive. what one mass is negative.
11:38 AM
what do u mean
Like in annihilation same mass but opposite charges created. This is based on charge and experimentally proven. Why this idea not worked on mass.
oh
negative mass just hasnt been seen
so we dont talk about it too much
u can search for some questions about negative mass
if two same positive masses like electron-positron created based on charge from nothing. There should be creation of two negative masses electron-positron.
@123 these r not created from nothing.. otherwise energy conservation wud b violated
@RyderRude Means energy converted to mass. So what about negative energy
11:42 AM
negative energy hasnt been observed
It means it a mystery.
Does our mathematics support this idea?
u can search bout it. it can lead to stable wormholes if it exists
@123 On the level of classical Newtonian gravitation (or even classical SR), there is nothing that forbids negative mass, it just doesn't occur. In GR there's a bunch of discussion around it but it is most clearly forbidden in quantum mechanics (by the representation theory of the Poincaré group)
@123 yeah.. people have theories
@ACuriousMind Hello... Oooh i see.. Thanks
11:44 AM
@123 "negative energy" - relative to what zero? Remember that energy is always relative to some zero you choose, there is no such thing as "negative energy" objectively
GR fixes the size of energy
so negative has good meaning only in GR, and it is related to wormhole stiff
@RyderRude yes, but GR then unfixes the notion of mass!
it's notoriously hard to define "mass" in GR
It means we can never observe as negative mass. Which repels each other?
@ACuriousMind oh
you really need to stop presenting these half-truths from high level summaries as if you know what you're talking about
11:47 AM
@123 dont be hopeful at least becuz qm forbids it
@ACuriousMind but i was only commenting on negative energy
It means until new theory other than QM developed we can never observe negative mass.
@RyderRude yes but in the context of someone bringing up negative energy and negative mass together it is entirely unhelpful to just go "but in GR energy can be objectively negative" without following up with the qualification about the difficulty of the notion of mass
We also have string theory
if your goal is to just say technically correct things regardless of whether they make sense in context, you should re-evaluate the way you approach conversations
@ACuriousMind i was not correcting u.. just moving forward the conversation...
@ACuriousMind i apologise..
11:51 AM
@123 I don't really know what you mean here: In order to even talk about observing negative mass, we would have to have a theory that can even consistently contain the idea of "negative mass"
All of you give me you whatsapp no. So i can contact you whenever i will stuck in physics.
you can't really ask the question "What would happen if mass could be negative?" to current physics - in QM this can't happen, and in GR you get a list of various things that may or may not be what you meant by "negative" and "mass"
so there is no observation that would count really as an observation of "negative mass" without a lot of qualifiers
negative mass means masses that repel each other.
well, that's what you say :P
@123 please don't ask for people's contact information here - people who want you to be able to contact them outside of the site will have their information in their profile
@ACuriousMind at least give me your brain.
I always have hard time in understanding physics
At least it saves my time and age.
It is possible to create negative mass which repel with ordinary mass?
11:57 AM
no
Ooookay... Now forget about mass. It means we don't have theory of it yet.
@ACuriousMind What is the problem in finding another dimensions other than spacetime?
what
I have no idea what that question means
I have heard Einstein theory shows 11 dimensions
where have you heard that? what even is "Einstein theory"?
4 dimensions are 3-spatial and 1-time. What about other dimensions?
pls see this
12:03 PM
I'm not watching a youtube short
stop watching clickbait and start reading things that are designed to actually teach you information
But this is michio kaku a great phycisit
@ACuriousMind You are right.
Kaku is one of the worst public physics communicators in recent history, his quantum computing book was garbage (e.g. panned by Aaronson here), you're better off not believing a word he says
Aaaah i see...
@ACuriousMind Do you believe in string theory and theory of everything?
now, what has 11 dimensions is M-theory - a variant of 10-dimensional string theory - which has nothing to do with Einstein (Einstein died before they started); these theories are still active research and not universally accepted and the way their 11 dimensions relate to our 4 is complicated and essentially impossible to convey to someone who does not understand quantum field theory
Aaaah Ookay..
I have read in LHC they are trying to find another dimension. But still no success
12:16 PM
@123 Modern physics research doesn't work as straightforward as that. The LHC just smashes particles into each other. But some theories (like string theory) postulate extra dimensions (in a technical sense) and then predict a different behaviour for the particles smashing into each other than the current Standard Model. So the LHC smashes particles together,
and if they behave in the way the extra-dimension-theories predict than that would be an indicator that maybe there are extra dimensions
In michelson-morley experiment they failed to observe change in speed of light relative to earth. But how this experiment shows ether is not there. Today we know speed of light is universal constant. It is also possible ether is there.
but if they behave otherwise, it's just a sign that the Standard Model is good for now. It's not that someone at CERN specifically has an "extra dimension finder" or whatever, the experiment of smashing together the particles is pretty indifferent about which theories exactly you want to test
@nickbros123 This is rather bad. Atoms are a thing and so there is no "zoom in enough so that it is flat". There are a lot of pesky nuances to deal with just to define Maxwellian fields.
@123 physics does not work that way. Neither Michelson nor Morley changed their minds about the existence of the æther, and Einstein never considered Michelson-Morley as important for him to come up with relativity.
@naturallyInconsistent Hello. Ooh i see , i was thinking Einstein used there experimental failure
Many textbooks either lie to students, or are written by people who did not understand that it was a lie all the time. The proper science history texts cover this in great detail.
and so it is very dangerous when you listen to people who keep ignoring all these historical facts and just tell you nonsense
12:21 PM
You are right..
How can we solve the mystery of wave-particle duality? How it is possible particle behave both
like double slit experiment
where's the mystery?
Means how it is possible the particle behave both wave and particle.
why wouldn't it be possible?
I have seen the double slit experiment. If we don't see the particle behave as waves otherwise particle also it strike in unpredictable way. we only know the final outcome.
Another example is spin entangelment.
you are talking about things that are pretty unrelated to each other.
12:29 PM
I have asked this question. I thought may be this is related to extra dimensions.
In my opinion, the best way to look at wave-particle duality is to realise that underneath all of that, is quantum fields. You can only excite quantised waves on the quantum field, and each disturbing wave is itself one particle, the entire wave is one particle. This way, quantum field theory automatically explains wave-particle duality, at the cost of coming up with the complicated idea of quantum fields.
@123 why would you think it is related to extra dimensions?
just because there is a thing A you don't understand and a thing B you don't understand, that doesn't mean A and B are related
Because we can not predict the spin state. Maybe once we know the extra dimension we can predict it.
Also, what is "I have asked this question" supposed to mean? Yes, you've asked the question, everyone can see that. Why does this need to be stated?
@123 I'm sorry, but where is the logical connection supposed to be there?
I might as well say "We can not predict the spin state. Maybe if the sky was orange we could."
Hmm... You are right.
It means you are saying. Until we know correct answer some day. We can not create any idea about it.
But this is how new theories develop.
12:35 PM
new theories definitely don't develop by someone linking two things together without any argument for why they should be related
But Einstein also developed his SR without any prior proof. But experiment showed later he was correct.
Jan 31, 2018 at 17:05, by ACuriousMind
@vzn The main point of being like Einstein is not being regarded as kooky - it's also being right, which is much more difficult and much more rare.
Also Einstein did not work in a vacuum and a lot of SR was co-developed by other physicists and mathematicians
claiming that he came up with it out of nowhere is, once again, just denying actual history - there's a whole academic priority debate of who exactly developed what
Yes i have read this debate
And still you chose to make that claim to try to defend you just randomly sticking two things together? Okay, have fun with that, but I'm not helping you with it.
I am a learner. I am still stuck in newtonian physics. but have some ideas of QM, QFT and relativity.
Hopefully in future i will conquer these too.
12:44 PM
Thankyou
Always good to start the day with a chuckle
Now who cares to assist me with physics woe
@Kenshin any progress?
But there was a suggestion to put all in 4 vector formalism
Then later move back to three to three
Do you mind having a crack
u r already using the three components of four-momentum. i doubt u can use four force tho
12:51 PM
True
1

In special relativity, we know that, relativistic force is defined as F = dp/dt, where p = γmv. For forces perpendicular to the direction of relative motion, force transforms as F' = γF. Consider two particles approaching each other with equal speeds in an initial frame S. They collide at a singl...

i havent done the computation without fields but i think we need field dynamics to enforce the conservation of three momentum
Interesting idea but can someone weigh in to confirm
Let’s try and imfi
Fins e
find existing papers on it
*on phone making it harder to type
1:07 PM
@Kenshin it's just an inconsistent setup - if the collision is "instantaneous", then $\mathrm{d}t = 0, F = \infty$ (formally) and there is no contradiction. If the collision is not instantaneous, then there is no single "rest frame" for the particle but the frame attached to the particle is really non-inertial, and the whole computation becomes more complicated.
You can have a frame associated with the particle just before th collision
I mean this is how proper acceleration is defined is it not
You take a frame matching instantaneous velocity of the particle and from that frame observe the acceleration of the particle
So I guess technically I should reword my paradox to specify the frame is of the particle just before the collision occurs
@Kenshin Yes, but then during the collision the particle's velocity is no longer the frame's velocity, so then by your logic there comes some time-dependent factor $\gamma(t)F$ into play where $\gamma(t)$ depends on the difference between the particle's and frame's velocity - that's what I mean by "the whole computation becomes more complicated". It's not obvious this makes the problem vanish, but you need to work much harder to establish the apparent paradox
I’m sure it’s complicated
I’m hoping someone can help actually show the full calc to help me resolve it
I don’t mind seeing a complicated answer
I don’t think it’s as complicated as you’re implying though
I think the idea of instantaneous acceleration is established
And the right gamma factors are there for that
But I agree impulse includes an extra dt which may resolve the paradox
But then as per the comment if you resolve it that way you’d run into issues in the horizontal collision equivalent where F=F’
Because there is only.a gamma factor in the vertical force transformation law not horizontal
So if that gamma cancels out due to dt, you’d introduce a new gamma factor in the horizontal case that mucks things up
Hope that makes sense
1:40 PM
@RyderRude looks like you were interested in this in 2020 physics.stackexchange.com/questions/577910/…
I wasn’t profile stalking I just found it searching for my question
yeah i remembered that post as soon as u asked this
but i was only interested in the qualitative aspects. i didnt investigate forces assigned at the same point in spacetime
Does magnetic field is really a relativistic electric field ?
Yes
I don't know if that's the best way to think about it @123
Yeah it is the best way
1:51 PM
@Amit So why we don't see magnetic field when electron is stationary according to my frame of reference?
Because the relativistic effect is absent
@Amit hi !
hi @RyderRude
If i am moving according to stationary charge then i see the magnetic field why?
1:52 PM
@Amit long time
Relativity is y
@123 One can definitely transform into the other through a Lorentz transformation but the way you wrote it sounds like you can find a frame where you can nullify one at the expense of the other which isn't true
Basically knowing electric potential + relativity one can predict all electromagnetic interactions
@RyderRude Yes, I was taking a break I guess. But I still stalk this chat every while in a once
@Amit Pls explain it without the eqns in layman's word. Once i get the basic idea then it is always easy for me to understand the whole mathematics.
1:55 PM
@Amit yeah.. u commented once in a while
@123 Okay, in layman terms, what really transforms is the electromagnetic tensor.
@Amit :P
:D , i'll brb
tensor is way beyond from my understanding level.
Amit imagine two parallel currents
1:56 PM
Tensor to the people!! (and layman)
Now take the frame of electrons in bottom one
The electrons in the top one will then appear more separated and protons more condensed
By relativity creating an electric pull
Now return to the original frame and we describe that pull as magnetic field
Get it
Yes nice
01:00 - 14:0014:00 - 21:00