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

- FaridMoussaoui
**Posts:**414**Joined:****Location:**Genève, Genf, Ginevra, Geneva

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

Wick rotation: https://en.wikipedia.org/wiki/Wick_rotation

thanks!,my Wicked comment was just a statement about the universe and the quantum world.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

Interesting that Poincare introduced Wick rotation, I have to read more off his work and see if I understand any of it.

- katastrofa
**Posts:**8052**Joined:****Location:**Alpha Centauri

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.

Wick rotation: https://en.wikipedia.org/wiki/Wick_rotation

All this talk of quantum theory and the Riemann zeta function reminds me of the work of Michael Berry (and coworkers) in observing connections betweenI 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.

Wick rotation: https://en.wikipedia.org/wiki/Wick_rotation

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

- katastrofa
**Posts:**8052**Joined:****Location:**Alpha Centauri

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.

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.

- Cuchulainn
**Posts:**59727**Joined:****Location:**Amsterdam-
**Contact:**

Minkowsky's

Dot the i?

Dot the i?

Minkowski or Minkowsky? I see both used, and yes Dot ?Minkowsky's

Dot the i?

"anholonomy of the connection in a fibre bundle" ? Wow. You were doing the fancy stuff.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.

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".

- Cuchulainn
**Posts:**59727**Joined:****Location:**Amsterdam-
**Contact:**

Mathematicians use i. For he rest of you, y is fineMinkowski or Minkowsky? I see both used, and yes Dot ?Minkowsky's

Dot the i?

https://en.wikipedia.org/wiki/Minkowski_inequality

- katastrofa
**Posts:**8052**Joined:****Location:**Alpha Centauri

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?Minkowski or Minkowsky? I see both used, and yes Dot ?Minkowsky's

Dot the i?

- katastrofa
**Posts:**8052**Joined:****Location:**Alpha Centauri

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."anholonomy of the connection in a fibre bundle" ? Wow. You were doing the fancy stuff.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.

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".

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!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."anholonomy of the connection in a fibre bundle" ? Wow. You were doing the fancy stuff.

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.

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".

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.

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 H

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)?

- katastrofa
**Posts:**8052**Joined:****Location:**Alpha Centauri

Thanks! Champagne bottle model? I will sip at it with pleasure at the weekend

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

but dont forget you are dealing with "chaotic underlying systems"

but dont forget you are dealing with "chaotic underlying systems"

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)

\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)

GZIP: On