SERVING THE QUANTITATIVE FINANCE COMMUNITY

 
User avatar
FaridMoussaoui
Posts: 400
Joined: June 20th, 2008, 10:05 am
Location: Genève, Genf, Ginevra, Geneva

Re: "Unified Revolution" new book by Espen Haug

January 28th, 2019, 4:56 pm

I never said there is a connection. All what I said is that Minkowski formula is as mysterious as Ramanujan divergent series (for me).

Wick rotation: https://en.wikipedia.org/wiki/Wick_rotation
 
User avatar
Collector
Posts: 4205
Joined: August 21st, 2001, 12:37 pm

Re: "Unified Revolution" new book by Espen Haug

January 28th, 2019, 5:03 pm

I never said there is a connection. All what I said is that Minkowski formula is as mysterious as Ramanujan divergent series (for me).

Wick rotation: https://en.wikipedia.org/wiki/Wick_rotation
 thanks!,my Wicked comment was just a statement about the  universe and the quantum world. 

Interesting that Poincare introduced Wick rotation, I have to read more off his work and see if I understand any of it.
 
User avatar
katastrofa
Posts: 7935
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri

Re: "Unified Revolution" new book by Espen Haug

January 28th, 2019, 11:37 pm

I never said there is a connection. All what I said is that Minkowski formula is as mysterious as Ramanujan divergent series (for me).

Wick rotation: https://en.wikipedia.org/wiki/Wick_rotation
I didn't I write that you said/wrote that there was such a connection. You just mentioned Wick rotation, about which I also though at that point after reading previous posts. I listed the connections between distinct theories of physics, because physical theories can be transformed between one another - with or without extra assumptions. I don't see anything mysterious about Minkowski's construction of space, though. It's a postulate Minkowski made about spacetime. Maybe that makes it a bit mysterious.
 
User avatar
tw
Posts: 1053
Joined: May 10th, 2002, 3:30 pm

Re: "Unified Revolution" new book by Espen Haug

January 29th, 2019, 8:35 pm

I never said there is a connection. All what I said is that Minkowski formula is as mysterious as Ramanujan divergent series (for me).

Wick rotation: https://en.wikipedia.org/wiki/Wick_rotation
I didn't I write that you said/wrote that there was such a connection. You just mentioned Wick rotation, about which I also though at that point after reading previous posts. I listed the connections between distinct theories of physics, because physical theories can be transformed between one another - with or without extra assumptions. I don't see anything mysterious about Minkowski's construction of space, though. It's a postulate Minkowski made about spacetime. Maybe that makes it a bit mysterious.
All this talk of quantum theory and the Riemann zeta function reminds me of the work of Michael Berry (and coworkers) in observing connections between
random matrix theory and the distribution of the Riemann zeta zeros. I think the gist was that the Gutzwiller trace formula semiclassically gives the eigenvalue distributions of classically chaotic systems and the form is very suggestive of the zeta function.
IIRC they were searching for the hamiltonian whose quantized form had 
eigenvalues which matched the zeros of the zeta function to somehow come up with a novel way to make progress with the Riemann hypothesis and came up  some really simple form ...H=x p I think.

His papers are here
 
User avatar
katastrofa
Posts: 7935
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri

Re: "Unified Revolution" new book by Espen Haug

February 1st, 2019, 1:19 am

Oh, Riemannium - a fictional element, whose energy levels correspond to zeta's zeroes, and in the classical limit are chaotic :-) Some people indeed try to prove Riemann hypothesis in that way.

Berry phase has a sentimental meaning for me - a part of my PhD thesis was related it, and in such a (discovery) way that I had to read about this, erm, anholonomy of the connection in a fibre bundle in virtually every discipline and field. I even read  Stephenson's Cryptonomicon, because I confused Berries! I got obsessed with the Michael one (not as much as with Stewart Parkin though, but more than with Duncan Haldane). I kept telling people that Berry phases were everywhere like some loony - until I met a colleague of Michael Berry at one conference, who told me that Michael liked to say that himself. So I stopped, because I didn't like being unoriginal... Why are you doing this again, tw? Making me talk about myself ;-) Thanks for bringing back the memories of good times, though :-)

Anyway, AFAIR, for some class of physical systems, the sign of the curvature generally determines whether the evolution of the system is stable or not (chaotic).
For noncognoscenti, to understand the structures imagine a field of vectors, each pointing in any direction - this is the so-called Berry connection, a sort of a vector potential. The rotation of that potential is called Berry curvature and it can be imagined as a field produced by those vectors (many magnetic phenomena in physics are described by that). If you transport a vector along some closed trajectory in this vector space (horizontal transport), you may start and end with the vector pointing in a different direction - the change is the Berry phase, a sort of an irreproducibility of a vector over the horizontal transport. Disclaimer: I may not be completely precise as I forgot the formalism, but the constructions are intuitive and easy to imagine.

Berry phase is actually one of the reasons why I don't like Minkowsky's spacetime - its flatness. I'm not learnt in cosmology, but I've always naively suspected that many quirky results (e.g. black holes with their incredible properties) would disappear if the true spacetime curvature was considered or equivalently the Berry phase introduced. Because of the curvature one cannot simply apply the "ergodicity" assumption as I described in the previous crazy post: when one drags the system (Universe) though the manifold of different states, it acquires some geometric phase, so it will never come back the same to the starting point (like our life doesn't reset when we visit the place we were born). This breaks the ergodicity assumption, which underlies the Wick rotation trick... But such matters require more elucidation and oughtn't be discussed without kush.

Anyway,+Basta! Physics is for escapists. The world has more urging unsolved problems.
Last edited by katastrofa on February 1st, 2019, 10:53 am, edited 1 time in total.
 
User avatar
Cuchulainn
Topic Author
Posts: 59386
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
Contact:

Re: "Unified Revolution" new book by Espen Haug

February 1st, 2019, 10:52 am

Minkowsky's

Dot the i?
 
User avatar
Collector
Posts: 4205
Joined: August 21st, 2001, 12:37 pm

Re: "Unified Revolution" new book by Espen Haug

February 1st, 2019, 10:56 am

Minkowsky's

Dot the i?
Minkowski or Minkowsky? I see both used,  and yes Dot ?
 
User avatar
tw
Posts: 1053
Joined: May 10th, 2002, 3:30 pm

Re: "Unified Revolution" new book by Espen Haug

February 1st, 2019, 2:27 pm

Oh, Riemannium - a fictional element, whose energy levels correspond to zeta's zeroes, and in the classical limit are chaotic :-) Some people indeed try to prove Riemann hypothesis in that way.

Berry phase has a sentimental meaning for me - a part of my PhD thesis was related it, and in such a (discovery) way that I had to read about this, erm, anholonomy of the connection in a fibre bundle in virtually every discipline and field. I even read  Stephenson's Cryptonomicon, because I confused Berries! I got obsessed with the Michael one (not as much as with Stewart Parkin though, but more than with Duncan Haldane). I kept telling people that Berry phases were everywhere like some loony - until I met a colleague of Michael Berry at one conference, who told me that Michael liked to say that himself. So I stopped, because I didn't like being unoriginal... Why are you doing this again, tw? Making me talk about myself ;-) Thanks for bringing back the memories of good times, though :-)

Anyway, AFAIR, for some class of physical systems, the sign of the curvature generally determines whether the evolution of the system is stable or not (chaotic).
For noncognoscenti, to understand the structures imagine a field of vectors, each pointing in any direction - this is the so-called Berry connection, a sort of a vector potential. The rotation of that potential is called Berry curvature and it can be imagined as a field produced by those vectors (many magnetic phenomena in physics are described by that). If you transport a vector along some closed trajectory in this vector space (horizontal transport), you may start and end with the vector pointing in a different direction - the change is the Berry phase, a sort of an irreproducibility of a vector over the horizontal transport. Disclaimer: I may not be completely precise as I forgot the formalism, but the constructions are intuitive and easy to imagine.

Berry phase is actually one of the reasons why I don't like Minkowsky's spacetime - its flatness. I'm not learnt in cosmology, but I've always naively suspected that many quirky results (e.g. black holes with their incredible properties) would disappear if the true spacetime curvature was considered or equivalently the Berry phase introduced. Because of the curvature one cannot simply apply the "ergodicity" assumption as I described in the previous crazy post: when one drags the system (Universe) though the manifold of different states, it acquires some geometric phase, so it will never come back the same to the starting point (like our life doesn't reset when we visit the place we were born). This breaks the ergodicity assumption, which underlies the Wick rotation trick... But such matters require more elucidation and oughtn't be discussed without kush.

Anyway,+Basta! Physics is for escapists. The world has more urging unsolved problems.
"anholonomy of the connection in a fibre bundle" ? Wow. You were doing the fancy stuff.

I spent significant chunks of my research career trying to see if partial summations of Gutzwiller could help to 
understand molecules with enough energy to fall apart but where the dynamics were surprisingly resistant to ergodicity.
Happy days.

Favourite Michael Berry anecdote.  (proper academic bullying!)
Nervous grad. student giving talk on something quantum ish.( can't remember what it was).
Berry stands up and says something like.. "I see what you are trying to do but it is completely wrong and mistaken"
Grad student, very shaken, "ermmm ermmmm why do you say that?"
Berry says,  "sorry I don't have time to explain".
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       
 
User avatar
Cuchulainn
Topic Author
Posts: 59386
Joined: July 16th, 2004, 7:38 am
Location: Amsterdam
Contact:

Re: "Unified Revolution" new book by Espen Haug

February 1st, 2019, 6:02 pm

Minkowsky's

Dot the i?
Minkowski or Minkowsky? I see both used,  and yes Dot ?
Mathematicians use i. For he rest of you, y is fine
https://en.wikipedia.org/wiki/Minkowski_inequality
 
User avatar
katastrofa
Posts: 7935
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri

Re: "Unified Revolution" new book by Espen Haug

February 1st, 2019, 6:47 pm

Minkowsky's

Dot the i?
Minkowski or Minkowsky? I see both used,  and yes Dot ?
From "local" history: he was born during January Uprising in the Kingdom of Poland (the part of Poland, which was under the occupation of Russian Empire after the partition). Wikipedia says that some time later his family fled to Germany from pogroms (they were the habit in those times and region: with or without Russians siccing everybody on everybody, mostly Jews were being killed in dozens of religious, political and social conflicts). So he probably had a Polish name at birth, but Lithuanians would call him Minkovskis, Ukrainians Мінковський (Minkowskij), so why not Minkowsky in English? :-)
 
User avatar
katastrofa
Posts: 7935
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri

Re: "Unified Revolution" new book by Espen Haug

February 3rd, 2019, 12:22 am

Oh, Riemannium - a fictional element, whose energy levels correspond to zeta's zeroes, and in the classical limit are chaotic :-) Some people indeed try to prove Riemann hypothesis in that way.

Berry phase has a sentimental meaning for me - a part of my PhD thesis was related it, and in such a (discovery) way that I had to read about this, erm, anholonomy of the connection in a fibre bundle in virtually every discipline and field. I even read  Stephenson's Cryptonomicon, because I confused Berries! I got obsessed with the Michael one (not as much as with Stewart Parkin though, but more than with Duncan Haldane). I kept telling people that Berry phases were everywhere like some loony - until I met a colleague of Michael Berry at one conference, who told me that Michael liked to say that himself. So I stopped, because I didn't like being unoriginal... Why are you doing this again, tw? Making me talk about myself ;-) Thanks for bringing back the memories of good times, though :-)

Anyway, AFAIR, for some class of physical systems, the sign of the curvature generally determines whether the evolution of the system is stable or not (chaotic).
For noncognoscenti, to understand the structures imagine a field of vectors, each pointing in any direction - this is the so-called Berry connection, a sort of a vector potential. The rotation of that potential is called Berry curvature and it can be imagined as a field produced by those vectors (many magnetic phenomena in physics are described by that). If you transport a vector along some closed trajectory in this vector space (horizontal transport), you may start and end with the vector pointing in a different direction - the change is the Berry phase, a sort of an irreproducibility of a vector over the horizontal transport. Disclaimer: I may not be completely precise as I forgot the formalism, but the constructions are intuitive and easy to imagine.

Berry phase is actually one of the reasons why I don't like Minkowsky's spacetime - its flatness. I'm not learnt in cosmology, but I've always naively suspected that many quirky results (e.g. black holes with their incredible properties) would disappear if the true spacetime curvature was considered or equivalently the Berry phase introduced. Because of the curvature one cannot simply apply the "ergodicity" assumption as I described in the previous crazy post: when one drags the system (Universe) though the manifold of different states, it acquires some geometric phase, so it will never come back the same to the starting point (like our life doesn't reset when we visit the place we were born). This breaks the ergodicity assumption, which underlies the Wick rotation trick... But such matters require more elucidation and oughtn't be discussed without kush.

Anyway,+Basta! Physics is for escapists. The world has more urging unsolved problems.
"anholonomy of the connection in a fibre bundle" ? Wow. You were doing the fancy stuff.

I spent significant chunks of my research career trying to see if partial summations of Gutzwiller could help to 
understand molecules with enough energy to fall apart but where the dynamics were surprisingly resistant to ergodicity.
Happy days.

Favourite Michael Berry anecdote.  (proper academic bullying!)
Nervous grad. student giving talk on something quantum ish.( can't remember what it was).
Berry stands up and says something like.. "I see what you are trying to do but it is completely wrong and mistaken"
Grad student, very shaken, "ermmm ermmmm why do you say that?"
Berry says,  "sorry I don't have time to explain".
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       
Well, my fascinations with those assholes (and "science" altogether) ended when I came to believe that the vast majority of Western scientists were mediocre bullies or their pre-stage, sneaky no-talent toadies. Your anecdote doesn't shock me.

Would it be possible to have a look at your old works or could you recommend some related materials? It's something completely new to me and sounds intriguing.
 
User avatar
tw
Posts: 1053
Joined: May 10th, 2002, 3:30 pm

Re: "Unified Revolution" new book by Espen Haug

February 5th, 2019, 11:19 am

Oh, Riemannium - a fictional element, whose energy levels correspond to zeta's zeroes, and in the classical limit are chaotic :-) Some people indeed try to prove Riemann hypothesis in that way.

Berry phase has a sentimental meaning for me - a part of my PhD thesis was related it, and in such a (discovery) way that I had to read about this, erm, anholonomy of the connection in a fibre bundle in virtually every discipline and field. I even read  Stephenson's Cryptonomicon, because I confused Berries! I got obsessed with the Michael one (not as much as with Stewart Parkin though, but more than with Duncan Haldane). I kept telling people that Berry phases were everywhere like some loony - until I met a colleague of Michael Berry at one conference, who told me that Michael liked to say that himself. So I stopped, because I didn't like being unoriginal... Why are you doing this again, tw? Making me talk about myself ;-) Thanks for bringing back the memories of good times, though :-)

Anyway, AFAIR, for some class of physical systems, the sign of the curvature generally determines whether the evolution of the system is stable or not (chaotic).
For noncognoscenti, to understand the structures imagine a field of vectors, each pointing in any direction - this is the so-called Berry connection, a sort of a vector potential. The rotation of that potential is called Berry curvature and it can be imagined as a field produced by those vectors (many magnetic phenomena in physics are described by that). If you transport a vector along some closed trajectory in this vector space (horizontal transport), you may start and end with the vector pointing in a different direction - the change is the Berry phase, a sort of an irreproducibility of a vector over the horizontal transport. Disclaimer: I may not be completely precise as I forgot the formalism, but the constructions are intuitive and easy to imagine.

Berry phase is actually one of the reasons why I don't like Minkowsky's spacetime - its flatness. I'm not learnt in cosmology, but I've always naively suspected that many quirky results (e.g. black holes with their incredible properties) would disappear if the true spacetime curvature was considered or equivalently the Berry phase introduced. Because of the curvature one cannot simply apply the "ergodicity" assumption as I described in the previous crazy post: when one drags the system (Universe) though the manifold of different states, it acquires some geometric phase, so it will never come back the same to the starting point (like our life doesn't reset when we visit the place we were born). This breaks the ergodicity assumption, which underlies the Wick rotation trick... But such matters require more elucidation and oughtn't be discussed without kush.

Anyway,+Basta! Physics is for escapists. The world has more urging unsolved problems.
"anholonomy of the connection in a fibre bundle" ? Wow. You were doing the fancy stuff.

I spent significant chunks of my research career trying to see if partial summations of Gutzwiller could help to 
understand molecules with enough energy to fall apart but where the dynamics were surprisingly resistant to ergodicity.
Happy days.

Favourite Michael Berry anecdote.  (proper academic bullying!)
Nervous grad. student giving talk on something quantum ish.( can't remember what it was).
Berry stands up and says something like.. "I see what you are trying to do but it is completely wrong and mistaken"
Grad student, very shaken, "ermmm ermmmm why do you say that?"
Berry says,  "sorry I don't have time to explain".
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       
Well, my fascinations with those assholes (and "science" altogether) ended when I came to believe that the vast majority of Western scientists were mediocre bullies or their pre-stage, sneaky no-talent toadies. Your anecdote doesn't shock me.

Would it be possible to have a look at your old works or could you recommend some related materials? It's something completely new to me and sounds intriguing.
I am flattered! 

It has been a while (i.e. decades) but Brack and Bhaduri's "semiclassical physics" or even Gutzwillers' book ("Chaos in Classical and quantum mechanics" but I found his writing style a little too loose) we both useful to me. For all his personal quirks I found Berry to be an excellent writer.

If you really wanted to look at the unsophisticated end of the literature: T. Weston, M. S. Child & J. Tennyson “Quantum monodromy in the spectrum of H2O and other systems”, Molecular Physics Vol. 96 Pp.371 (1999) or T. Weston & M. S. Child “Spectral consequences of periodic orbit bifurcations of AB2 stretching vibrational modes”, Chemical Physics Letters Vol. 106 Pp.250-270 (1996)

All of this was briefly in fashion in the 90s and was beautiful but hopeless impractical.
Everyone was fascinated by how the tension between linear quantum theory applied to nonlinear chaotic underlying systems
(or molecular systems cascading into chaos) and how the quantum localisation effects were very close to  the dimensions of modern molecular spectroscopy.
A common question used to be what happens if we create a wavepacket that fits in a loop of the homoclinic tangle (the common route to chaos in conservative systems)? 
 
User avatar
katastrofa
Posts: 7935
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri

Re: "Unified Revolution" new book by Espen Haug

February 5th, 2019, 11:35 am

Thanks! Champagne bottle model? I will sip at it with pleasure at the weekend ;-)
 
User avatar
Collector
Posts: 4205
Joined: August 21st, 2001, 12:37 pm

Re: "Unified Revolution" new book by Espen Haug

February 5th, 2019, 4:35 pm

just google "Champagne model"  and go for the top three bottles or so...

but dont forget you are dealing with "chaotic underlying systems"
 
User avatar
Collector
Posts: 4205
Joined: August 21st, 2001, 12:37 pm

Re: "Unified Revolution" new book by Espen Haug

April 20th, 2019, 4:07 pm

I know u are tired of fysiks, but the Schwarzschild radius is at the center of the world and is normally given as 

 \begin{equation}
r_s=\frac{2GM}{c^2}
\end{equation}
in other words it looks like we need to know the mass size to find it, plus the Newton gravitational constant (that Newton himself never mentioned or used (?), but that has become a holy cow), and we need to know the speed of light. 

But no, we can find the Schwarzschild radius of a gravitational object just by observing any electromagnetic wave passing by, the  Schwarzschild radius  is given by

 \begin{equation}
r_s = \frac{2RR_h(\lambda_h-\lambda)}{\lambda_{h}R_h-\lambda R} 
\end{equation}
where \(\lambda\) and \(\lambda_h\) is the wavelength at two altitudes(radii, R and R_h) of a single electromagnetic beam.

No need for G, no need for the mass size, no need for knowing the speed of light. The Schwarzschild radius is hidden in a beam of light coming or moving towards the gravity object). While holy cow G and even M are quite mystical, the wavelength of light is more logical, and it is all that is needed to know the Schwarzschild radius of any mass.

this can be very useful when wanting to know the Schwarzschild radius of an object, just look at a beam of electromagnetic radiation coming out from, or moving towards the object, and one know its Schwarzschild radius.

All major gravity phenomena can be predicted accurately from a single beam of electromagnetic radiation. Has anyone mention this before? 

If one could measure the wavelength of light with an iPhone one could know the Schwarzschild radius of any object of interest, it could be a hit, at least i would find it very useful (one drawback, it only works on spherical objects, well more and more of them in our time )

The world of gravity is hidden in a single beam of light (even the Schwarzs child)
ABOUT WILMOTT

PW by JB

Wilmott.com has been "Serving the Quantitative Finance Community" since 2001. Continued...


Twitter LinkedIn Instagram

JOBS BOARD

JOBS BOARD

Looking for a quant job, risk, algo trading,...? Browse jobs here...


GZIP: On