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12:00 PM
idk how much longer I can go without seeing these EHT images
I've been a good boy I want to see them now :(
 
#Metoo
 
"One first cute improvement appears in the list of authors. Aside from Aharonov, Cohen, and Elitzur – who have produced lots of garbage about "weak measurements" over the years – another stellar co-author has been added, the crackpot-in-chief Lee Smolin."
 
where is that from?
 
hey guys, there's one thing I'm confused about. normally when we deal with a wave function, we can use/solve Schrödinger's equation to determine its evolvement with time, but our $\psi$ is not always a wave function, for instance when we talk about spin. so what confuses me is, why don't we have a "Schrödinger equation" for such $\psi$?
 
It is still a wavefunction
ie an element of a Hilbert space
It's just not $L^2(\mathbb{R}^3)$
But instead the Hilbert space of square integrable spinor functions
 
12:12 PM
right, but Schrodinger's equation is only for $L^2(\mathbb R^3)$ right?
 
No
Or at least it depends what you mean by that
 
well, can we use the S equation for spin, eg?
 
$$\hat{H}\psi(t) = -i\hbar \partial_t \psi(t)$$
is valid for all Hilbert spaces
The form of $\hat{H}$ will vary depending on the space used
 
oh right
@Slereah I think this is what got me confused
 
The form for spinors will give you the Pauli equation
 
12:15 PM
Lee Smolin (; born June 6, 1955) is an American theoretical physicist, a faculty member at the Perimeter Institute for Theoretical Physics, an adjunct professor of physics at the University of Waterloo and a member of the graduate faculty of the philosophy department at the University of Toronto. Smolin's 2006 book The Trouble with Physics criticized string theory as a viable scientific theory. He has made contributions to quantum gravity theory, in particular the approach known as loop quantum gravity. He advocates that the two primary approaches to quantum gravity, loop quantum gravity and string...
 
but we don't use the Schrodinger equation to derive the Pauli matrices
we just use the commutation relations
 
looks nothing like a crackpot. Who is writing that commentary
 
but you want to say that $\hat H$ for spin are the pauli matrices?
 
The Pauli matrices are involved, yes
Although $\hat H$ is a bit more complicated
The form of $\hat{H}$ is given by the problem you're studying
it's not derived from the Schrödinger equation
 
no sure, but when dealing with $L_2(\mathbb R^3)$, we use the Schrodinger equation after having determined $\hat H$, $V$
but in the case of spin, we don't even do that
so could the theory of spin have been developed without the schrodinger equation?
 
12:22 PM
there's goes one of the bins
19 mins ago, by Slereah
"One first cute improvement appears in the list of authors. Aside from Aharonov, Cohen, and Elitzur – who have produced lots of garbage about "weak measurements" over the years – another stellar co-author has been added, the crackpot-in-chief Lee Smolin."
@vzn
 
I wonder, what happens if the stern gerlac experiment is done before the double slit
I think we will see two bright spots, but then we won't be using the languages of hamitonians to describe it or even a wavefunction
how would quantum mechanics evolved if history had took that path otherwise
 
'The only correct sentence in the paper is a sentence in which the authors refer to themselves,
"all cretins are liars",
but even this sentence isn't quite right. It's misspelled.'
 
12:40 PM
Hi, everybody.
 
long time no see
 
Why is zeroth even an ordinal number
 
Well, gentlemen.
 
because the empty set is technically, an ordering
It's the ordering of no things
 
I think I am going with the original design and having the other version as a separate species that becomes extinct for some reason.
 
12:43 PM
In fact, the 0 ordinal is quite special in that it is not a successor nor a limit
 
All I know is that "zeroth" bugs me. I mean, a zeroth law of thermodynamics, for example
 
Zeroth indicates something where all else based on
 
Anyway, back to physics 101. How much would it cost to build an Orion nuclear star ark with 2018 technology?
For example: say that for some reason tomorrow, some cataclysmic event is about to happen. How much money would it take to build a colonisation ark capable of sustaining at least 500 - 2,000 people for generations until they find a new planet to live in?
With current technology?
Aka: Orion nuclear spacecraft are the only viable option, meaning: "SCREW YOU, PARTIAL TEST BAN TREATY! WE NEED TO GET OFF THIS ROCK!"
 
uh
Money would't really be a good measure.
 
Step 1, we need to have idea on how far later that cataclysm happened
 
12:45 PM
Look. I just want to know how much it would cost to build this thing with 2018 money.
 
And I'm giving my opinion that the question is nonsense.
 
@Secret. The cataclysm has not happened yet.
But it will happen soon, and it is probably going to end up with RIP Sol System.
Just for the sake of this scenario.
 
Right, you aren't going to "buy" something like that.
 
not knowing the time we will not be prepared in time and we will all die
 
You can try to guess how many people and how much time it would take, and then multiply that by $100/hour if you want.
But I still think that's nonsense.
 
12:47 PM
If we funneled an international effort to build an Orion nuclear bomb-propelled interstellar ark, how much money would the price tag be for initial construction, R&D, maintenance of the already assembled parts in orbit, launch of the personnel and colonists, plus equipment, etc.?
 
If you have to get off the earth because earth is going to end, the money cost of things will change a lot.
Money might not even make sense any more.
For example, you might realize you need all of the aluminum available.
 
What kind of economics will take over when doomsday is impeding?
snipped
 
So then suddenly providing aluminum becomes a big deal.
 
So, what if I told you in 2020, RIP Sol System?
 
So now suppose you're an aluminum mine. Are you really going to sell aluminum to fund an ark that you aren't going to get to ride on?
@FutureHistorian Then the economy would immediately cease to exist as we know it.
 
12:49 PM
Two years to build a colonisation ark before the entire system is gone.
O_O
 
@FutureHistorian Yeah, again, no economy... or at least it would be completely different from what we're used to.
 
Alright, now I get it.
 
I like how you choose 2020...
 
Alright, so...cataclysm aside.
 
...The Promised Year
 
12:50 PM
How much would it cost if we just throw the cataclysm scenario out the window?
As in: assuming we start construction for whatever reason, how much would it cost?
 
@FutureHistorian So like, Elon Musk decides to build your ark thingy?
 
Either that or Elon Musk + Jeff Bezos.
Oh and never forget to count other national space programs on this one.
 
How many people?
How long?
 
Since it is an interstellar mission.
Project Orion was a study of a spacecraft intended to be directly propelled by a series of explosions of atomic bombs behind the craft (nuclear pulse propulsion). Early versions of this vehicle were proposed to take off from the ground with significant associated nuclear fallout; later versions were presented for use only in space. Six tests were launched. The idea of rocket propulsion by combustion of explosive substance was first proposed by Russian explosives expert Nikolai Kibalchich in 1881, and in 1891 similar ideas were developed independently by German engineer Hermann Ganswindt. General...
Here are the specifications.
Problem?
 
I wonder if time is a better measure, even if you assume all the materials available, the assembling rate will be limited by the technology
 
12:51 PM
The price tag is in 1968 USD.
So, how much would it cost given some updates to the concept + adjusting for inflation in today's money?
Here is the detailed paper by Freeman Dyson himself.
 
So why are you asking us? Multiply the 1968 cost by inflation.
Beh, the tech changes probably don't matter that much.
 
What???
 
::shrugs::
 
Because I want to know if any single nation or company could even afford such a monster of a spacecraft project.
 
Company, no.
Where do you think a company is going to get that much money if not from the government?
You can't sell a space ark.
 
12:54 PM
^
 
Suppose the thing carries 100 people.
Suppose the cost is 3 trillion.
 
Well, can any single government make such a monster?
Because......
 
That means each participant needs to pay 30 billion.
 
Found your price tag for the Momentum-limited Orion.
In 2018, that would be 2,631,790,747,126.44 USD.
 
Where are you going to get 100 people with 30 billion each willing to fund your ark-producing-company?
 
12:55 PM
I am not paying 30 billion
 
...and that 30 bn was for 1968 USD.
 
By comparison, the energy-limited variant would be.....
Wait for it.
26,317,907,471,264.37 USD!
In 2018 money.
suspenseful music plays in the background
So, 3 to 30 trillion 2018 USD.
Take one version.
 
that's even worse, none of us will have that amount of money even enmass
 
So.....not even an international effort for the 3 trillion USD version will do?
 
@FutureHistorian @DanielSank do we ever have multnational projects that goes to trillions?
 
12:57 PM
This is the "Momentum-limited" version Freeman Dyson proposed.
 
the worst I heard only reach 3 digit billions
 
Well, that the momentum-limited one is smaller, less heavy and faster.
Oh and...less costly.
100 metres in diameter, with a dry mass of 100,00 tonnes, 300,000 1 Mt nukes, a departure mass of 400,000 tonnes, capable of 1 Earth gee of acceleration to 0.033 c, and is 3 trillion USD in terms of price tag.
Oh and...they are capable of a one-way, no slow down 133 year journey to Alpha Centauri (which Proxima b is part of anyway).
@Secret? Too much still?
 
I don't know, I never heard of any multnational project that reached trillions, thus I don't know if it is possible with 2018 levels
Also Daniel is not responding
 
By comparison, the energy-limited one is....20 km in diameter, has a mass of 10,000,000 tonnes, with 30,000,000 1 Mt nukes, a departure mass of 40,000,000 tonnes, capable of 0.0033 c, and 0.00003 Earth gees of acceleration, which means an estimated mission time of 1,330 years and a price tag of 30 trillion USD in today's money.
So, the Momentum-limited one is both faster and cheaper.
So, we are going to assume the momentum-limited version is the one being chosen for construction.
 
@Secret Dunno. How much does CERN cost?
 
1:02 PM
eh... (wikipeding...)
 
1 billion USD annually to operate.
 
@Secret Eh?
 
9 billion USD in construction costs.
 
Online chat is an asynchronous communication protocol.
 
oops, I am too impatient, apologies
Forbes said $13.25 billion just to discover the higgs
still nowhere near trillion
 
1:04 PM
So, question: does this mean a resurrected Orion program is basically the most expensive project in human history?
And (hopefully) it is worth those 3 trillion USD to achieve an interstellar mission.
 
hmm... 1 digit trillions might be not that far fetched...
 
It is a long-term investment, though.
 
It seems China is trying to do some trillion dollar investment on trade
 
And the Orion project I propose to resurrect (in spite of international law violations, due to the whole..."no testing nukes in space thing") would be a similar long-term investment.
@Secret? So, that being said...if we started R&D and construction NOW....
How long to finish the momentum-limited monster of an interstellar ark?
I am assuming that private companies and space programs both cooperate on this one.
 
I don't know, but I will put a budget on 10-20 years, it's a huge shape after all
 
1:08 PM
So...2018 is initial R&D and construction.
 
LEt me check how long it takes to build the LHC...
 
Now...what do we do about 300,000 1 Mt nukes?
 
because ANYTHING is going to be less complicated than the LHC
 
10 years.
 
@FutureHistorian I’d speculate instead that the most expensive project in human history will simply be to survive and grow long enough for a project like Orion to be necessary and feasible
 
1:09 PM
Hmmmm. Could make sense.
Still, assuming we somehow begin construction tomorrow, we could finish (assuming a 10 - 20 year investment and no funding cuts or delays)....between 2028 - 2038.
Hmmmm. Not bad for an interstellar mission.
Now, ETA to Proxima b would be HOW LONG if you account for deceleration?
Key phrase: if you account for deceleration.
 
it's quite realistic, and the orion might finish a bit earlier because it is much less complicated than the LHC IMO
 
The 133 year time period is NOT including slowing down.
@Secret. Then again, you are building 300,000 1 Mt nuclear warheads.
Got to invest on high-end security to keep those warheads from falling into the wrong hands.
 
I’d say it’s wildly unrealistic, insofar as it only incorporates the costs of building a ship that can escape Sol
 
You also need to account for R&D costs, paying people to keep those 300,000 nukes safe, the cost of the equipment to get all that U-235 + the launch costs to get the stuff into orbit, you get the point.
Right?
 
It doesn’t take into account the cost of making a ship that humans can inhabit during that time
 
1:13 PM
Actually..... @Semiclassical. Question: how many personnel can the momentum-limited Orion host?
As in: personnel such as crew and colonists?
 
guys, I need to be afk a bit, carry on the discussion when I am absent
 
No idea.
There’s also the opportunity costs, insofar as humanity would be choosing to devote its resources to this project vs other routes
 
If a Sol-level catastrophe was scheduled to hit in the next ten years, I think you’d be much more likely to see people working in archives which would preserve the memory of himsnity
 
That is kind of what I proposed.
So...2028.
We have 10 years to either bail or be extinct.
And then after we leave, ETA to Proxima b?
 
1:18 PM
@FutureHistorian Were I awake enough to read that, maybe
 
Including slowing down.
Then again, I originally proposed 2 years.
So..... :(
Anyway, how long to reach Proxima b at 0.033 c, including deceleration?
 
How many light years away is that?
 
4.25 light years?
It is literally next to the Sol System.
Well, that is until it got sterilised or destroyed or whatever for this scenario.
It is still next to Sol.
If it is not destroyed, but is instead sterilised for whatever reason.
 
Wiki quotes 4.2 light years
 
I know.
4.25 is more specific.
 
1:24 PM
Yeah, well, I didn’t. Hence why I asked
 
It is fine.
So....133 years to reach that system + the rest of the Alpha Centauri trinary star system (Proxima Centauri is part of Alpha Centauri).
 
Assuming you can reach that speed, yes
 
And.....wait.
10 days to slow down, right?
Hmmmmm.
So...133 year mission it is, then.
Well, we reach Proxima b in 2161.
And we colonise the planet.
There we go. Earth 2.0.
Sort of.
 
1:47 PM
I just thought of a potentially fun problem:
If the "naive" period of a mechanical oscillator is $T$, what is its period taking special relativity into account?
 
I dunno, I guess you'd have to find out the effect of relativity on rigidity and elastic deformations
Or more abstractly, find a relativistic-invariant version of the harmonic oscillator
 
I was thinking that just the speed of the oscillator would lead to time dilation effects.
 
I guess you can consider an abstract harmonic oscillator as two timelike curve with a potential between them
 
Isn't the oscillator doing the twin paradox thingy?
 
Of the form... $k x^\mu x_\mu$?
 
1:50 PM
hi
I have some doubts
 
that's probably the simplest version
 
@Akash.B ok
By the way, a lot of people say they have 'doubts', but to be honest, that sounds really weird to a native English speaker.
 
so can I?
 
@Slereah Cool.
@Akash.B Can you what?
You can ask whatever you want.
 
1:54 PM
The apparently original paper for it : aapt.scitation.org/doi/10.1119/1.17513
Apparently they don't use a relativistic invariant Lagrangian
The Lagrangian term is $$- \frac{k}{2} x^2 \frac{t}{c}$$
 
In double slit experiment ,how electrons will move if there are no slits?
 
They will crash in the screen
 
@Akash.B If there are no slits, the electrons will hit the barrier and stop.
@Slereah Careful, "screen" could refer to the detector thingy.
 
Wall?
Apparently Synge wrote about the relativistic oscillator
Although I think that was in his other book
The SR one
 
@DanielSank then how did electrons manage to move through barrier in double slit experiment ?it should only pass through slit isn't it?
 
2:01 PM
@Akash.B I don't understand what you're asking.
 
5 hours ago, by Akash. B
In modern physics, the double-slit experiment is a demonstration that light and matter can display characteristics of both classically defined waves and particles; moreover, it displays the fundamentally probabilistic nature of quantum mechanical phenomena. The original experiment was performed by Davisson and Germer in 1927. The double-slit experiment was first performed by Thomas Young in 1801. His experiment was part of classical physics, well before quantum mechanics and the concept of wave-particle duality. He believed it demonstrated that the wave theory of light was correct, and his experiment...
@DanielSank see that figure ^^
 
ok
The electrons go through the slits, but they are waves so they have diffraction.
 
understood what I meant?
 
Diffraction refers to various phenomena that occur when a wave encounters an obstacle or a slit. It is defined as the bending of light around the corners of an obstacle or aperture into the region of geometrical shadow of the obstacle. In classical physics, the diffraction phenomenon is described as the interference of waves according to the Huygens–Fresnel principle. These characteristic behaviors are exhibited when a wave encounters an obstacle or a slit that is comparable in size to its wavelength. Similar effects occur when a light wave travels through a medium with a varying refractive index...
@Akash.B No, I do not understand what you mean. If there are no slits, the electrons do not go through.
You can imagine that the electrons sort of change direction as they go through the slits.
Electrons are not little solid balls of charge.
They are waves.
 
@DanielSank then how did they appear behind that barrier where there is no slit?
 
2:09 PM
They do not.
Why do you think the electrons appear behind the barrier if there is no slit?
 
@DanielSank aren't they like waves?
 
@Akash.B yes
 
"Intuitively, Cartan geometry studies the geometry of a manifold by ‘rolling without sliding’ the ‘model geometry’ G/H along it. "
That's not intuitive at all >:|
@Akash.B what do you mean by "no slit"
Do you mean no slit in the barrier, or no barrier at all
 
hey @DanielSank how do you gauge the relationship between the English and Russian versions of this paper?
written in Russian and translated to English?
how good is the translation?
I'm weirded out by the lack of a translator credit
JETP usually has one
 
@EmilioPisanty uh
How much do you care about this?
My Russian is not particularly good.
 
2:25 PM
@DanielSank not much =P
but this is interesting
0
A: Reference request: Susskind-Glogower original paper

Emilio PisantySome excellent news: fifty years after its demise, the journal Physics ─ as it appears on citations, but perhaps better referred to as Physics Physique физика as its title appears on its cover, or Physics Physique Fizika as its latin-alphabet transcription ─ has now been made available online, fr...

 
@EmilioPisanty cool
 
2:47 PM
@EmilioPisanty I may need to bug you about split-step Fourier at some point
Not immediately, but I do have it as a mini-goal to implement it in Mathematica
 
3:03 PM
@EmilioPisanty my Russian colleague said the Russian version of the title is "sloppy".
 
always nice to be able to speak French
 
@Slereah for a certain definition of 'intuitive' :P
as a slogan / mental image, it's intuitive enough
in terms of the relevant details...not so much
 
3:30 PM
@DanielSank lolz
@Semiclassical sure
 
the main obstacle has been that, for all I know about the continuous FT, I haven't had to deal with the DFT much
and it's the DFT that the FFT applies to
 
@Semiclassical it's a pain in Mathematica because there's no clean analog to matlab's fftshift
 
Right.
 
so doing functions in $k$ space is kinda awkward
 
yeeeah
 
3:38 PM
but I made this one in MM using split-step Fourier
 
there's a nice discussion of how to implement split-step Fourier in python here: jakevdp.github.io/blog/2012/09/05/quantum-python
 
donkeys ages ago
 
nice
what's the initial condition & potential?
 
I'm reasonably certain that the notebook used for that is here dropbox.com/s/8jad0cbd63peoww/SpectralMethods6.nb?dl=0
@Semiclassical it's not Schrödinger if that's what you're thinking
it's a Kelvin wake with a point-source boat
 
ahh
so some other wave equation
 
3:40 PM
hence the overall Kelvin-wake look =P
 
@Semiclassical well
not really
so Kelvin wakes are essentially defined by their dispersion relation $\omega = \sqrt{gk}$
there we go
so if you wanted to make a formal wave equation with an explicit local laplacian you'd need to square that twice to $\omega^4 = g^2 k^2$
 
... which is all sorts of trouble because that fourth time derivative allows for decaying and growing exponentials on top of your oscillatory solutions
 
3:44 PM
and you know which one is going to win in the presence of numerical noise
so yeah
the explicit wave equation didn't work
 
how does the split-step Fourier method work there, then?
 
@Semiclassical you have the dispersion relation
that's all you need
 
Really?
 
really
 
huuuh
 
3:45 PM
think about it
 
You mean, dispersion relation is all you need for split-step Fourier?
 
no, I'm saying more than that
I'm saying that split-step Fourier is the embodiment, in code, of the dispersion relation
the dispersion relation is just telling you that any mode with wavenumber $k$ advances a phase $\omega \,\Delta t$ in time $\Delta t$ where $\omega=\omega(k)$ is an explicit, known function
so
you just separate out into modes, and you impose an explicit phase on them
 
hmm
that's an interesting way to look at it
 
evolve a bit in real space, then in momentum space, and then again ad infinitum
 
3:49 PM
yep
I mean, the dispersion relation doesn't know anything about any potential or anything, so you also need that
as well as handling of the boundary conditions
 
right
 
which in that notebook is an absorbing mask, implemented as the dampingFunction
or you'll get reflections off of the boundary, which you probably don't want
 
the potential is what'll dictate the evolution in real space
for boundary conditions...hmm
 
or maybe you do? who knows
 
probably not, no
 
3:52 PM
what is it you actually want to do?
 
1D scattering of quantum waveforms off of barriers
but in time, so not just plane waves
most obvious example being a gaussian wavepacket bouncing off a barrier
 
my prof said that was a hard problem
 
it is
 
but that plane wave solutions were a good approximation
 
3:59 PM
@Semiclassical that's actually something I'm meant to implement at some point
 
I'd actually like to see the wavepacket bouncing off in time
plane wave approximation won't give you that
 

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