Physics Discussion Thread

[Amber G.]

Meanwhile: If it is confirmed, this would be the smallest black hole on record, heralding a new class of black holes we never even knew how to look for...From MIT's tech review:
Scientists have spotted a tiny black hole that may be just 12 miles across

[Amber G.]

Another important news item about proton size - Precise measurement affirms that the particle’s radius is smaller than physicists once thought


How Big Is the Proton? Particle-Size Puzzle Leaps Closer to Resolution

[Mort Walker]

Meanwhile: If it is confirmed, this would be the smallest black hole on record, heralding a new class of black holes we never even knew how to look for...From MIT's tech review:
Scientists have spotted a tiny black hole that may be just 12 miles across

Can you resolve something that is 19 Km wide when the wavelength of X-rays are 0.01-10 nm and the distance is some 100 trillion Km away? It seems you would be pushing the limits of spectroscopy at this point.

[Amber G.]

Meanwhile: If it is confirmed, this would be the smallest black hole on record, heralding a new class of black holes we never even knew how to look for...From MIT's tech review:
Scientists have spotted a tiny black hole that may be just 12 miles across

Can you resolve something that is 19 Km wide when the wavelength of X-rays are 0.01-10 nm and the distance is some 100 trillion Km away? It seems you would be pushing the limits of spectroscopy at this point.

Good question! Yes those number seem unbelievable ..But a few points:
- The blackhole is discovered, in this case by its "accretion disk" - gas, dust, plasma, what have you — swirling around the black hole and is much bigger. The size of the black hole is derived by it's mass/ gravitational effect (see physics dhaga --

"Bol, bol, bol mister golmatol
just how massive is a big black hole?
half the radius divide by G
and multiply by square of c."

- The accretion disk - can be seen, because the spinning particles are accelerated to tremendous speeds by the huge gravity of the black hole, releasing heat and powerful x-rays and gamma rays out into the universe as they smash into each other. Also because they are near the black hole velocities are *very* high and there is dilation/gravitational effect --particles going in one direction has tremendous doppler shift etc..

In this case they say:

To find this one, the team scanned a catalogue of 100,000 stars within the Apache Point Observatory Galactic Evolution Experiment (APOGEE), an infrared survey of the stars in the inner galaxy. They found a few hundred stellar candidates that seemed to be wobbling because of gravitational effects induced by other nearby objects. The team narrowed their search down to a binary star system called J05215658. They realized that what looked like a binary star was probably a black hole orbiting another star every 83 days.

..

More details at :https://science.sciencemag.org/content/ ... 37/tab-pdf

- BTW the first "direct" detection of the black hole was by gravitational waves. (see earlier posts here).. and then we have seen one in optical/em spectrum much later.

****
Yet the resolving power is almost unbelievable. As I mentioned in chandrayaan dhaga - NASA's deep space network was able to "see" CY-1 a few meters wide at the distance of the moon. And that old/recent picture of the first black hole .. resolving power equivalent to reading an iPhone screen held at New York from California.
***
The formula Resolving power = diameter (or objective)/ wave_length gives upper bound but now we have learned to use distributed telescopes (held at large distances - with extremely accurate clocks, GPS locations , and computers) to increase the effective diameter to almost the size of the earth. Hence such high resolving power..10^9 or more.. == size of an apple at the distance from the moon in micro-waves and much more in smaller wavelengths).
Truly amazing.

[Mort Walker]

^^^Thanks AmberG!

I figured it had something to do with the Schwarzchild Radius calculation using the accretion disk.

With radio telescopes you use multiple antennas to configure a very large effective aperture, so the gain increases many times. As you said, synchronization is the key here using accurate timing.

[Amber G.]

^^^ You are welcome.
BTW, Prof Sahdev's lecture which I posted above is very nice and you will like it. It is about black-holes and SYK model etc.. Hope he gets a Nobel.

[Vayutuvan]

AmberG ji, I searched for

Bol, bol, bol mister gol matol physics on Google.

BRF figures quite prominently in the search results.

[Amber G.]

^^^:)
(I have seen our physics and math dhaga has been mentioned and some of my posts found their way in some serious places )
Things like Banana Equivalent Dose (I heard it before but it became popular again after it was used in brf) and some other stuff which I will not mention here to protect some privacy).

[Amber G.]

Posting a good reference for those who are interested in Hindu/Indian Calendars.
History Of Calendar-Panchanga Committee Report"
History of the Calendar
in Different Countries Through the Ages

M.N. Saha and N.C. Lahiri

[ArjunPandit]

AmberG ji, I searched for

Bol, bol, bol mister gol matol physics on Google.

BRF figures quite prominently in the search results.

i can take quite a bit of credit for directing the pigeon through the holes..
my 4 year old son knows a variant of this ..although i have not taught him the formula yet...

[Amber G.]

Xpost: For those who are interested in Hindu Calendars.. (Two posts of mine for easy reference):

Just to put accurate information - Few items.

- Vikram Samvat which many/most (but not all) follow in India epoch is 56 BC. It is a luni/solar calendar. (Months are lunar and years are solar (sidereal year and not tropical year).

- GOI follows (officially) Shak (or Shake) samvat which is based on epoch around 72 AD . This is purely a solar (based on tropical year) calendar. - No "khsay" or "adhik" tithi/month etc - dates/months do not skip/repeat as in other Indian/Hindu calendar). (I don't know anyone except GOI - who follows this. Ordinary folks who use shak epoch used month/tithi based on gatkali/vikram etc... there are some other, less commonly, used epochs too.

- Most/all astronomers and panchangs use "gatkali" epoch - start of Kaliyug - (-) 3101==> (Epoch = 18 February 3102 BC. 3102BC = year -3101 by the way.) The month/tithis follows as Vikram samvat.

- With minor exceptions all hindu calendars months/tithis are based on gatkali calculations. Some Indian states like Rajasthan start month at the beginning of full moon (purnimant) while others (like Bengal etc) start at the new-moon.
(length of the year here is based on sidereal year (about 365 days 6 hours 9 minutes 10 seconds).

- GOI and most in India also follow Gregorian Calendar (Purely Solar Calendar based on tropical year = 365 days, 5 Hours, 48 Minutes and 45 seconds - about 20 minutes shorter than sidereal year). The epoch is 3000 years after Kaliyug officially started.

Today it is Sunday, Mrig Krishna 5 , 2076 Vikram Samvat, (In some states the month is Kartika), Kartika Krishna 5 , 5120 Gatkali, Kartik 27, 1940 Shake (per official GOI), November 17, 2019 (Gregorian), 15/3/1440 ( Muslim) and of course JDN = 2458802 ..(JDN=0 == November 24, 4714 BC, Gregorian proleptic.)

(Note I used purnimant month as common in Rajasthan. Here a new month starts about 15 days before some of other states )

And of course the UNIX (or techie time) = 1573759195 (Seconds after January 1, 1970, Thursday) Now by my clock


(Disclaimer: As I have no other calendar except Gregorian with me, all above is derived by my calculations and is *not* checked by any actual calendar (I live in US and at present do not have any other calendar or a panchangs and too lazy to check with wiki - I am depending mainly on my memory - learned the method to do calculations decades ago so if dates are wrong please let me know .. TIA - Dates/tithis may be off by a day or two.. as position of moon/sun calculated in USA lat/longitude are different than those use to calculate these in other places. I do have a computer so Unix time and JDN are, I think, correct.)

*****

Let me just point something out - because this is important and many/most people do not fully understand.
Just few points - Best is to look it up, unfortunately there are many sources which are not accurate and are confusing.

This technical information is necessary if one is looking at any historic document to draw accurate conclusions.

==> The Indian Calendar Reform Committee, appointed in 1952, identified more than thirty well-developed calendars. (So there are *many* variants , and one has to be very careful examining historic documents)

-- All variants of the Surya Siddhanta calendar and were/are in use across different parts of India.

--The two calendars most widely used today are the Vikrama calendar (I am most familiar with) which is followed in Nepal as national calendar and also in the Indian regions like western and northern India and the Shalivahana or Saka calendar which is followed in Andhra Pradesh, Karnataka, Maharashtra and Goa.

- In 56 BC, Vikrama Samvat era was founded by the emperor Vikramaditya of Ujjain following his victory over the Sakas. Later, in a similar fashion, Satavahana king Gautamiputra Satakarni initiated the Saka era to celebrate his victory against the Sakas in the year AD 78.

Some popular calendars:

( Hindu calendars in India)

Vikram Samvat: - lunar months, solar sidereal years
Shaka Samvat (traditional): - lunar months, solar sidereal years
Shaka Samvat (modern/GOI ): solar tropical
Bangla calendar: solar tropical years
Tamil Nadu/Kerala: solar tropical years such as Tamil calendar
Nepali calendar with Bikram Sambat: solar tropical years
Gatkali - lunar months, solar sidereal years - used in Panchangs ..old indian texts s surya/sidhhant etc..Basis of all..(My father's hand copied calendars collected over hundreds of year - he put the gatkali year for clarity)

Most holidays in India are based on the first two calendars. A few are based on the solar cycle, (Sankranti (solar sidereal) and Baisakhi (solar tropical))

Hope this is helpful and make things a little clearer.

[SriKumar]

Question about the above post- was there a documented reference to designate 3102 BC as the beginning of Kali yug per gatkali calendar? When and where was that documented? Are there any documents pre-dating 3102 BC saying that Kali yug would begin [x] years hence.

[Amber G.]

Question about the above post- was there a documented reference to designate 3102 BC as the beginning of Kali yug per gatkali calendar? When and where was that documented? Are there any documents pre-dating 3102 BC saying that Kali yug would begin [x] years hence.

The first I I read about this was from SuryaSidhanta (I had a sanskrit copy - learned enough sanskrit/math to read it. I do have an english translation too. (And some others in astronomy books dealing with Indian Astronomy by other authors.
According to the Surya Siddhanta, Kali Yuga began at midnight (00:00) on 18 February 3102 BCE.

This is based much more on math (defining the yuga's etc ..and then back-calculating when the position of all planets at the starting point etc) and having data about star positions available to to author *then* from earlier dates.

But the same date is taken by virtually all other Indian astronomers like Aryabhata etc who lived even earlier. The reference is in RigVeda .. references can be found in any reputable book or Encyclopedia. (the Induand the Rg-Veda, Page 16, By Egbert Richter-Ushanas). This is also documented in many purans etc.

My interest was purely mathematical. One of the best reference I have is a "HIndi Visva Kosh" - about 20 Volumes dealing with many subjects written/edited by really great scholars.

***
I don't know any documents prior to or around 3000 BC - But I am *not* a historian and my knowledge here is very limited. Earliest mathematics I personally have seen is old Jain texts but they are only 1000-2000 years old.

According to KD Abhyankar, the starting point of Kali Yuga is an extremely rare planetary alignment, (depicted in the Mohenjo-Daro seals) ... And there are various references.. Since this is considered the date when Krishna returned to Vekuntha there is a shila at a temple in Bhalka
(Did google here is one image: https://upload.wikimedia.org/wikipedia/ ... LKA-07.jpg

****
Mathematically what is important are some values of precession and planet movements given by people like Bhaskara makes it certain that those astronomers did have access to some well kept records dating hundreds of years from some of their gurus. Otherwise they would *not* have been able to calculate some values with that accurately.

****
The reference I gave (MN Shaha's report) is quite good. Articles in Encyclopedia Britanica etc are not that bad. Some of my father's writings .. hundreds of pages of tables constructed by old calendars etc is quite good.

[SriKumar]

Thanks. Seems to be the only case of all calendars listed, including Gregorian, where start of an epoch is not related to a human event- birth/defeat/conquest, rather it is related to a planetary position. Puzzled to read it is mentioned in Mirnjo Daro seals, but then it should not be surprising since both Rig Veda writing and Indus VC happened in close proximity (Punjab/Sindh area). It is quite possible that Rig Veda itself might be older than 3000 BC, maybe a lot more.

[ArjunPandit]

^^not sure where else to post, but many UK tabloids reporting that there has been evidence of life on mars in the form of insects

https://www.express.co.uk/news/science/ ... ity-images

personally, I am dismissive of such claims unless they come officially (either through denials), but lets keep our minds open

[Amber G.]

^^^ Case of pareidolia (the human tendency to "see" recognizable shapes in random patterns) I think. Not for the first time, not this for the last time.
( Although Entomologist William Romoser, is a Ohio University professor, and this is from a "research poster" and OU has a press release etc.. OTOH poster presentations are less formal than peer-reviewed papers published in science journals)

[ArjunPandit]

^^^ Case of pareidolia (the human tendency to "see" recognizable shapes in random patterns) I think. Not for the first time, not this for the last time.
( Although Entomologist William Romoser, is a Ohio University professor, and this is from a "research poster" and OU has a press release etc.. OTOH poster presentations are less formal than peer-reviewed papers published in science journals)

didnt know there was a term for it..in the skies of bundi rajasthan my cousins and used to watch clouds (a rarity). The clarity of night sky used to be even more tempting..we used to hear roars of IAF jets in 90s .. i was being told that they are mig 21s and 23s..that got me attracted to migs ...

[Amber G.]

Thanks. Seems to be the only case of all calendars listed, including Gregorian, where start of an epoch is not related to a human event- birth/defeat/conquest, rather it is related to a planetary position. Puzzled to read it is mentioned in Mirnjo Daro seals, but then it should not be surprising since both Rig Veda writing and Indus VC happened in close proximity (Punjab/Sindh area). It is quite possible that Rig Veda itself might be older than 3000 BC, maybe a lot more.

Interesting observation.

(My favorite "start" would be "Big Bang" but that is too much in past!)

But to be fair, many such calendars (epoch based) are mathematical in nature. More used in scientific literature (so that people have a standard and clarity) than in actual use. Similar epochs are JDN (based on noon on Monday, 1 January 4713 BC in the Julian calendar), of modern era Newcomb's (Jan 0, 1900 or Jan 2000) etc used for US Ephemeris.). Many computer clocks, and atomic clocks have their own well defined epochs.

But these epochs are not that popular in real life and real life there is quite a bit of non-standard and sometime even confusion exist. As said there are/were at least 30 different epochs were in practice in Hindu calendars alone. Even "Shaka" (Official GOI, and popularly used in Bengal and south) has another version used by Jains which started about a 1000 years ago before the other!

Julian/Gregorian are somewhat standard today but they were real mess just a few hundred years ago. Change to Gregorian officially happened in India (and UK, USA) in 1752 but most of the Europe (and French colonies in India) happened much earlier (1582).. while in some parts of the world (eg Russia) much later (1918). So even in recent historical records one has to be *very* careful dating them. ( Date like "Jan 1 1700" will be different in different nations)

Earlier things were even much more messier ...Julius and Augusts brought reforms but still things in different parts of the world was different.

[SriKumar]

Thanks. An un-related question...
Is it true that Aryabhatta's model of the solar system was earth-centric (as opposed to heliocentric)? I read this somewhere and it was not clear to me how one could predict the planet paths (and sun's position in a constellation) correctly with a wrong model of the universe (visible to naked eye). Sounds unture but still curious. Since you've read the original Surya Sidhanta I thought I'd ask.

[UlanBatori]

We venture into this Hall of Pure Science with great tredpidation, but have a simple question:
Is it true that one can calculate the amount of mass converted to light in this big event, from the equation e (Joules) = m(kilograms)*{c(m/s)}^2? Seems like the "light" is confined in a narrow beam out of each side of the explosion center. With the e calculated by integrating over the observed beam diameter with a Gaussian distribution. Wonder where one can get the centerline intensity though.

Any gyan on why a spherically symmetric explosion generates two collimated beams? This is something that has bothered me for a long time about pulsars, quasars etc etc.

[sudarshan]

Any gyan on why a spherically symmetric explosion generates two collimated beams? This is something that has bothered me for a long time about pulsars, quasars etc etc.

Magnetic field due to spin/ rotation, maybe? The beams are also probably only part of the energy output, there would be other components of the explosion which may not be charged or magnetized, and which would be spherically symmetric in their outward propagation (pure guess-work on my part, not sure about any of this).

[UlanBatori]

Seems to be a very common occurrence, perhaps because all the Artists' Conceptions show the same thing. The beams go spinning round and round like a polis car beacon too. But only in one plane. I don't know why a spherically symmetric gravity field/ compression would develop into rotation about one axis*. I mean in reality, not computer graphics artists' conceptions. Why should magnetic field be so concentrated too ( never made any sense to me).

*BTW, this beautiful fact is used in another gentle application: Underwater explosions. An explosion outside the hull of a submarine can be designed to send a jet directly pointed at the hull, piercing it. Finis for the sub. But that takes some sort of shaped charge.

I assume that the cited Gamma Ray source must have been a Black Hole that got "too big for its britches". So is there a limit to gravity where it turns into a repulsive force, or where it is unable to resist the pressure due to the heating that it generates? Perhaps a limit where only something as energetic as Gamma Rays can escape? But if Gamma Rays also travel at speed of light, how are they escaping the Event Horizon, unless the Event Horizon is breached somewhere?

Thinking aloud at great risk, I wonder whether Pulsars are Black Holes?

Oh wait!! There is rotation about TWO axes: One is the disc-like galaxy plane, the other is the axis perpendicular to the galaxy axis, so that the jet axis revolves.

Now if it is shown that the beams rotate about two axes like the flashing swords of the Jedi, we are back to 3 discrete, coherent rotations replacing a spherically symmetric gravitational attraction. Maybe the Artists Conceptualizers (99% of them can be traced to one NASA artist, I have met him once) have not caught on to this, or maybe I just haven't watched enough videos.

Isn't this a spontaneous reduction of Entropy I wonder?

Also, the "Diameter" of Black Hole to my little mind, is like the Rotational Core of a vortex. Except for one thing: the rotational core of a vortex can be extremely strong and have a very small radius. So vortex core diameter is not a unique indicator of strength. But the diameter of a Black Hole must be the Event Horizon, i.e. given by the radius where the radial speed exceeds speed of light, so that "no information can escape".

It is easily shown that the suction into a vortex pulls small unbalances in tangential velocity closer into the core, and thus magnifies the tangential speed (conservation of angular momentum, though I don't quite understand why it should be conserved). So I can see why galaxies have rotation. But WHY in just one plane, when the "suction" is spherically symmetric?
And no wonder the final jet ejection occurs apparently along the axis of rotation. So once the ejection jet starts, is this a steady-state system? Stuff gets pulled in along one plane, and ejected normal to it?

There must be some simple Physics/Math law that dictates why there is such a limting value for gravity inside a Black Hole.
I wonder if the same can be set up in ordinary (not by relatives) fluid dynamics: a cylindrical spinning core where stuff is ejected along the axis in Both Directions. IOW, Black holes are not spherical at all, but long cylindrical pakistans/anti-pakistans?
In this case, maybe the ejection/explosion event is simply a Vortex Burst. The tube bends somehow and becomes unstable?

(Back to more important things such as Impeachment Hearings..)

[Amber G.]

Magnetic field due to spin/ rotation, maybe? The beams are also probably only part of the energy output, there would be other components of the explosion which may not be charged or magnetized, and which would be spherically symmetric in their outward propagation (pure guess-work on my part, not sure about any of this).

Huge magnetic filed exist but to add - No mystery here ; simple physics. A gamma ray burst (high energy photon) depends on all the factors, not only the energy which produced it. Gamma rays (or other wavelength radiation for that matter) from sun, or a typical atomic explosion, or radiation from a radioactive isotope, or light from a candle is generally spherically symmetric. .. Laser light pointer, radiation from particle accelerator etc are highly directional. Radiation from super nova, from merging (binary rotating at very high speed )neutron stars, black-holes are quite pointed - specially high energy (short wavelength - gamma rays) photon. Even other cosmic ray particles, electrons/protons/etc.. are focused ... some lower wavelength (x-rays) coming from outer side ( some call it "after-glow") is more spherically symmetric. Apart from magnetic field (which affects the direction of charged particles) the high rotational speed, and huge gravitational field near those massive objects (gravitational lensing) bend the space-time; and photons just follow the physics and get directed in the direction. Let me know if i could add some more understanding - it needs some math/physics and understanding of basic physics of black-holes, neutron starts and photons etc.

[Amber G.]

Thanks. An un-related question...
Is it true that Aryabhatta's model of the solar system was earth-centric (as opposed to heliocentric)? I read this somewhere and it was not clear to me how one could predict the planet paths (and sun's position in a constellation) correctly with a wrong model of the universe (visible to naked eye). Sounds unture but still curious. Since you've read the original Surya Sidhanta I thought I'd ask.

You are welcome.
My basic interest when I read Suryasidhanth (I was quite young) was math / astronomy not so much history or Sanskrit. Learned the language to understand the math as there was no good translation I could find. Learned how they did trigonometry, algebra, continued- fractions, number-theory etc.

Later on when I was a grad student in US, there was one prof who was interested in historical astronomy. Wish I had more time then and did some work then. May be after I retire go back.

Few points/tidbits:

- Earth/centric vs heliocentric model does not make much difference in math for moon and sun's orbits. But for planets heliocentric model makes math a little easier. Interesting that Writers of Suryasidhanta - even Aryabhata knew (or suspected) to add "sun" related term - basically math as if heliocentric method for planets.

- For outer planets they certainly knew (and noticed in math) that orbits calculation are more exact if one think that orbits are elliptical vs circular. (Here the correction terms added followed similar pattern if the orbit was an ellipse) (No they did not, like Kepler said it but noticed the some math terms looked similar).

- They certainly knew the sidereal motion of earth. The earth spins (and not the sky with fixed stars) in about 23 hours and 56 minutes etc.. (The value was exact up to fraction of second).
-They emphasized the *importance* to do measurement instead of believing in old values. (Some how this is lost in many later Indian astronomers - they believed in old "shastras" in stead of doing better measurements and find better parameters.
- Their value for sidereal year, synodic lunar month was quite accurate. (This means that they had access to at least few hundred year records).

[UlanBatori]

Right on cue: Another article in ScAm written as if in Santa Barbara, CA, they know all about what goes on inside and outside a Black Hole. Wonder if a Black Hole can travel at the speed of light, so that it's on you b4 u ever realize that it's coming: after all u cannot see it.
So as I point out above there is a small problem. Apparently stars above a certain mass will collapse to a Black Hole, unlike say our Sun which will only become a shrivelled little White Dwarf or neutron star. So something as massive as the thing that generated all those Gamma Rays, must have been a monster black hole that had eaten millions of Suns. So there is clearly a way that mass and energy can shoot out of a Black Hole. The whole flaw in the physics models appears to be the silly stuff about the speed of light posing a barrier.

Does gravity travel at the speed of light? Or infinitely faster?

[Amber G.]

This could go both in Physics and Math dhaga .. An exciting discovery in finding elegant proof in Math,, inspired by results from physicists. Wow!

Three physicists wanted to calculate how neutrinos change. They ended up discovering an unexpected relationship between some of the most ubiquitous objects in math. Basic Math.

A nice article here below but there will be quite bit more in popular/general journals.

Neutrinos Lead to Unexpected Discovery in Basic Math

Terence Tao opened an email from three physicists he didn’t know. The trio explained that they’d stumbled across a simple formula that, if true, established an unexpected relationship between some of the most basic and important objects in linear algebra.

The formula “looked too good to be true,” said Tao, who is a professor at the University of California, Los Angeles, a Fields medalist, and one of the world’s leading mathematicians. “Something this short and simple — it should have been in textbooks already,” he said. “So my first thought was, no, this can’t be true.”

Then he thought about it some more.

The physicists — Stephen Parke of Fermi National Accelerator Laboratory, Xining Zhang of the University of Chicago and Peter Denton of Brookhaven National Laboratory — had arrived at the mathematical identity about two months earlier while grappling with the strange behavior of particles called neutrinos.

They’d noticed that hard-to-compute terms called “eigenvectors,” describing, in this case, the ways that neutrinos propagate through matter, were equal to combinations of terms called “eigenvalues,” which are far easier to compute. Moreover, they realized that the relationship between eigenvectors and eigenvalues — ubiquitous objects in math, physics and engineering that have been studied since the 18th century — seemed to hold more generally.

Although the physicists could hardly believe they’d discovered a new fact about such bedrock math, they couldn’t find the relationship in any books or papers. So they took a chance and contacted Tao, despite a note on his website warning against such entreaties.

“To our surprise, he replied in under two hours saying he’d never seen this before,” Parke said. Tao’s reply also included three independent proofs of the identity.

A week and a half later, the physicists and Tao, whom Parke called “a fire hose of mathematics,” posted a paper online reporting the new formula.
..
Pure mathematicians feel similarly. “This is certainly both surprising and interesting,” said Van Vu, a mathematician at Yale University. “I did not suspect that one can compute eigenvectors using only information about eigenvalues.”

Vu and Tao proved a somewhat related identity together in 2009 (which is why Denton, Parke and Zhang thought to contact Tao to begin with),

Terrence Tao a few years ago gave a proof to Mehta-Dyson conjecture in related field. This related to eigenvalues of random matrices a field quite interesting to physicists like us.

[tandav]

This could go both in Physics and Math dhaga .. An exciting discovery in finding elegant proof in Math,, inspired by results from physicists. Wow!

Three physicists wanted to calculate how neutrinos change. They ended up discovering an unexpected relationship between some of the most ubiquitous objects in math. Basic Math.

A nice article here below but there will be quite bit more in popular/general journals.

Neutrinos Lead to Unexpected Discovery in Basic Math

Terence Tao opened an email from three physicists he didn’t know. The trio explained that they’d stumbled across a simple formula that, if true, established an unexpected relationship between some of the most basic and important objects in linear algebra.

The formula “looked too good to be true,” said Tao, who is a professor at the University of California, Los Angeles, a Fields medalist, and one of the world’s leading mathematicians. “Something this short and simple — it should have been in textbooks already,” he said. “So my first thought was, no, this can’t be true.”

Then he thought about it some more.

The physicists — Stephen Parke of Fermi National Accelerator Laboratory, Xining Zhang of the University of Chicago and Peter Denton of Brookhaven National Laboratory — had arrived at the mathematical identity about two months earlier while grappling with the strange behavior of particles called neutrinos.

They’d noticed that hard-to-compute terms called “eigenvectors,” describing, in this case, the ways that neutrinos propagate through matter, were equal to combinations of terms called “eigenvalues,” which are far easier to compute. Moreover, they realized that the relationship between eigenvectors and eigenvalues — ubiquitous objects in math, physics and engineering that have been studied since the 18th century — seemed to hold more generally.

Although the physicists could hardly believe they’d discovered a new fact about such bedrock math, they couldn’t find the relationship in any books or papers. So they took a chance and contacted Tao, despite a note on his website warning against such entreaties.

“To our surprise, he replied in under two hours saying he’d never seen this before,” Parke said. Tao’s reply also included three independent proofs of the identity.

A week and a half later, the physicists and Tao, whom Parke called “a fire hose of mathematics,” posted a paper online reporting the new formula.
..
Pure mathematicians feel similarly. “This is certainly both surprising and interesting,” said Van Vu, a mathematician at Yale University. “I did not suspect that one can compute eigenvectors using only information about eigenvalues.”

Vu and Tao proved a somewhat related identity together in 2009 (which is why Denton, Parke and Zhang thought to contact Tao to begin with),

Terrence Tao a few years ago gave a proof to Mehta-Dyson conjecture in related field. This related to eigenvalues of random matrices a field quite interesting to physicists like us.

Link to paper?

[Amber G.]

This could go both in Physics and Math dhaga ....

Link to paper?

The physics paper is at https://arxiv.org/abs/1907.02534
The mathematics paper (currently in the process) will be published in "Communications in Mathematical Physics.".
Online arXiv is at https://arxiv.org/pdf/1908.03795.pdf
(The proof of the result (which the physicists "discovered" a few months ago - but which was not known before) was done Tao.

[Vayutuvan]

Terrence Tao a few years ago gave a proof to Mehta-Dyson conjecture in related field. This related to eigenvalues of random matrices a field quite interesting to physicists like us.

Amber G. ji,

Could you please give a short summary of the significance of eigenvalues of random matrices to physicists? My guess is that it has some thing to do with QM/particle interactions/Special Unitary Groups.

[Amber G.]

Terrence Tao a few years ago gave a proof to Mehta-Dyson conjecture in related field. This related to eigenvalues of random matrices a field quite interesting to physicists like us.

Amber G. ji,

Could you please give a short summary of the significance of eigenvalues of random matrices to physicists? My guess is that it has some thing to do with QM/particle interactions/Special Unitary Groups.

There are some good write-ups by Terrence Tao (For general public) and Freeman Dyson. Quite a few review articles are there since the techniques originally developed to understand nuclear spectra / energy spectra of of nucleus of heavier atom found use in many other physics and other (like biology) fields.

Here is some you and others may like to listen .... (These are from oral History of Princeton - Web stories by Freeman Dyson - looking at that work in present perspective)
Energy levels of complex systems: background By Freeman Dyson
Inviting Mehta to Princeton - and How this work is important
My work with Mehta is now more relevant

****
Historically - Understanding energy levels of nucleus like Uranium (Remember around and Post WWII atomic research was very important) was very important. This is because unlike Hydrogen or Helium you are dealing with *many* particles and many body problems are hard. What Wigner (He got Nobel for nuclear shell structure), Dyson and others found that things actually become easier when there are many many particles and one can study statistical properties rather than solving it old fashioned way. The energy levels behave very much like eigen values of certain random matrices. And these further are like lot of work done by Ramanujan on the statistical properties of zeta functions.

Dyson and Mehta, though physicists, were good in Math so they developed many pioneering techniques. Mehta was relatively unknown - though he won all sorts of gold medals in school and college before Bhaha sort of found him (he was one of his star student).. Mehta's work as a graduate student impressed Wigner and he asked if Mehta will like to join Princeton after his PhD which became very good for Physics. (Mehta later on went on to join TIFR, U of Delhi, IITs and was visiting prof at many Indian, US, France, China, USSR etc - Sadly he left India due to some political reasons, gave up his Indian Citizenship and spent decades outside India but returned to India later on where he died.

Mehta's books on Matrix theory and (Math book) and Random Matrices are classic. (He wrote many popular articles in Hindi scientific magazines - quite a few in French, English. He also wrote extensively about his travels and visits in France, Europe, US, USSR, China, Tibet, Japan, Brazil etc - most of it in Hindi and/or French, few are translated in English.

(Tidbit - I did know these guys quite well both, as profs and mentors and they were *very* generous and like a father figure to me. I was actually with Prof Mehta when Nobel for Wigner was announced attending a summer school in Bangalore where Mehta was teaching and I accompanied him to a shopping trip to buy a gift - a tie made by locals. )

Just a side remark - Apart from a world class physicist - Mehta spoke (*fluently*!!) and wrote in *many* languages. Hindi (and virtually all Indian languages), French, German, Russian, Spanish (and understood Italian, and some other European Languages), Japanese, Mandarin Chinese. That was really impressive. (And when I say "spoke" == he could read/write and almost spoke like a native!).

[Amber G.]

Meanwhile this is becoming routine.. but still very exciting.

From LIGO (Tweeter): .
Signal in LIGO/Virgo data. Most likely gravitationalwaves from a source with one component in NS-BH mass gap. Observed 24 minutes ago. Find out more at: https://gracedb.ligo.org/superevents/S191216ap/

[ArjunPandit]

Please see this post from 2009 in this dhaga: viewtopic.php?p=594446#p594446

"Bol bol bol... ..
Mister Gol Matol
Just how massive is a big black hole?

Half the radius
Divide by G
and Multiply by the
square of C ...."

.

Inspired by this legendary poem ...
arz kia hai..

Magnetar Magnetar, You're a rare neutron star
Only 23 of you are found so far
your magnetic field goes afar
Is stronger than anything known so far
Magnetar Magnetar, rarer than a pulsar

Magnetar Magnetar, You're a rare neutron star
You are smaller in size than island of Manhanttan
but you weigh thrice our sun
You're small but you are dense
your one teaspoon weighs hundred million tonnes
Magnetar Magnetar, rarer than a pulsar

Magnetar Magnetar, You're a rare neutron star
You rotate very fast,
and you dont long last
On you the time goes slow
you have gamma and X ray glow
Magnetar Magnetar, rarer than a pulsar

Magnetar Magnetar, You're a rare neutron star
Your field warps time and space
Much so that I can see my own face
Magnetar Magnetar, rarer than a pulsar

Magnetar Magnetar, You're a rare neutron star
I can't come close to you
Might be sphagettified if I do
Out of curiousity I'll still do
I like you for what you are
Magnetar Magnetar, rarer than a pulsar

Magnetar Magnetar, You're a rare neutron star
you're born out of a supernova
or may be a pulsar
we know few of you
we know little of you
Indigo will find more of you
we will know more of you
Magnetar Magnetar, rarer than a pulsar

Arjun Pandit©
Dec 22, 2019
Heavily Influenced by 'Spiderman Spiderman Tune Churaya Mere Dil Ka Chain',\
Idea came while fixing my son's magnetic toys and day-dreaming about magnetism
O karlo copy, jaise main bada famous poet hoon

[Amber G.]

^^^Nice!

[Amber G.]

Start of the new decade with an announcement of a gravitational wave discovery! GW190425. The heaviest neutron star binary seen till date!


GW190425 is remarkable. The total mass of the two stars is about 3.4 times that of our sun. That’s huge for these astronomical sources!

This discovery is a powerful testimony of the invisible universe we are discovering with gravitational-wave astronomy.

No electromagnetic counterpart was reported for GW190425, so unlike the last 2017 discovery, location of the galaxy or the star is unknown. (This is also the first ever gravitational wave detection with single detector - LIGO Livingston)

More at: https://dcc.ligo.org/LIGO-P190425/public
(Soon other newspapers and tv station will also be coming out with big stories

[vsunder]

There is a 65 year old conjecture supported by numerical simulations and experiments in the laboratory in Fluid Mechanics, more precisely in Rayleigh-Benard convection.

https://en.wikipedia.org/wiki/Rayleigh% ... convection

One can see these band patterns or hexagonal patterns in cloud formations as well as in these beautiful pictures:

https://www.flickr.com/photos/brian_tom ... 9296346997

https://hexnet.org/content/hexagonal-cl ... ntic-ocean

In the subject two numbers are very important, the Nusselt number that is a measure of the average heat transport naively speaking and the Rayleigh number which is again a measure of the ratio of the buoyancy force/viscosity. The conjecture now fully proved mathematically rigorously is:

Nusselt number < C (Rayleigh number)^{1/3}

C is a universal constant.

I am pleased to have proved this result above joint with an old friend and previous collaborator and especially as the proof is not long but involved very tricky cancellations and estimates. Here is the Arxiv post as it appeared yesterday:

https://arxiv.org/pdf/2001.01662.pdf

At very low Rayleigh numbers heat flows in the fluid via conduction. As the Rayleigh number increases, the fluid forms cells of the type pictured above bands, hexagons etc. There is a lot of work on stability etc by the astronomer S. Chandrasekhar on such stability investigations in his book and also by others. Chandrasekhar was mainly interested in heat transport in stellar atmospheres.

https://www.amazon.in/Hydrodynamic-Hydr ... B00C59C7ZA

As the Rayleigh number increases further > 1800 instability sets in and turbulence starts in the bulk of the fluid though there is a thin boundary layer in the fluid in contact with the heat source where conduction is still the process for heat transfer. This attached article has some details of this aspect of Rayleigh-Benard flows:

http://www.diva-portal.org/smash/get/di ... FULLTEXT01

Some precise definitions are

Nusselt number

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

Rayleigh number:

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

Engineers tell me that in their discipline, the Rayleigh numbers they encounter is in the regime 10^6 to 10^8.

[Vayutuvan]

Inspired by this legendary poem ...
arz kia hai..

Magnetar Magnetar, You're a rare neutron star ...

Nice. I had to look up what is Magnetar is on Wikipedia.

[Vayutuvan]

The conjecture now fully proved mathematically rigorously is:

Nusselt number < C (Rayleigh number)^{1/3}

C is a universal constant.

I am pleased to have proved this result above joint with an old friend and previous collaborator and especially as the proof is not long but involved very tricky cancellations and estimates. Here is the Arxiv post as it appeared yesterday:

https://arxiv.org/pdf/2001.01662.pdf

Thanks, downloaded. Here is hoping I can understand the main thrust of the argument if not all the technical details.

Did you move to a different place?

[vsunder]

^^ I did not move anywhere. A nice left over problem is to find the sharp value of the universal constant rigorously. The proof we give just proves there is a universal constant. We are looking at the Rayleigh number regime going to infinity so very large. The engineering and Physics literature
as for example in wiki

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

indicates that experimentally one has C=0.15, see the section on experimental correlation in the wiki link(by the way the statement with 1/3 power in the wiki link is now rigorous by our work). Also there is a reference by Iersley et al ( Journal of Fluid Mechanics, 2006, p. 159) that says 0.139 for C by numerical evidence. There is no rigorous proof and I have no idea how to get this theorem. There must be an extremal situation that must give the best constant but I do not know what it is. I suppose some young person may find a way.

[Amber G.]

As I and many others predicted, this is becoming routine..

"Signal in LIGO/Virgo data. Most likely a GravitationalWaves from a source with one component in NS-BH mass gap. Observed [recently] ."

More at:

https://gracedb.ligo.org/superevents/S200115j/

[Amber G.]

Meanwhile sharing an article from MIT alum magazine .. for those interested in fluid (of really sticky kind) flow may be interested --- On this date in 1919 - about a century ago -
Boston's Great Molasses Flood killed 21 and injured 150 others...

Here's how an MIT professor determined the disaster's cause..

"Solving the Great Molasses Flood Mystery"

Lot of interesting physics there...


Link: https://alum.mit.edu/slice/solving-grea ... od-mystery

....many MIT professors and alumni have served as expert witnesses or on fact-finding commissions. Almost a hundred years ago, Civil Engineering Department head Charles Spofford investigated and identified the cause of one of Boston’s most sensational disasters, the Great Molasses Flood.

On January 15, 1919, a 50-foot-high steel tank holding 2.3 million gallons of molasses suddenly ruptured in Boston’s North End. Flowing at the unexpected speed of 35 miles an hour, it formed a 15-foot high tsunami of 14,000 tons of viscous goop. Strong enough to knock houses off their foundations and sweep a train off its tracks, the wave killed 21 and injured 150 in the densely populated area.

Professor Charles Spofford solved the 1919 molasses mystery...
(Litigation swiftly followed and lasted for years. Three theories arose to explain the catastrophe: the tank exploded due to fermentation of the molasses; anarchists or Bolsheviks set off a bomb, or a structural failure led to disaster. US Industrial Alcohol, the company owning the tank, steadfastly blamed anarchists.)

Among the litigants was the Boston Elevated train line, since the flood had severely damaged its overhead rail infrastructure in the North End. The company hired civil engineering professor Charles Spofford (Class of 1893), an authority on structural engineering and bridge design, to prove that USIA was at fault. Spofford examined and tested pieces of the tank at MIT labs.

According to Dark Tide: The Great Boston Molasses Flood of 1919 by Stephen Puleo, Spofford reported that the steel plates were thinner than the original plans had called for and could not withstand the pressure of so much molasses. In addition, the tank lacked enough rivets to properly fasten the plates. In fact, during the initial explosion, witnesses described rivets shooting out everywhere like machine gun bullets. With its weak walls and shortage of rivets, he concluded, “In my judgment, the tank was improperly designed and its failure was due entirely to structural weakness.”

Spofford calculated, “A stress as great as 18,000 pounds per square inch is as high as should have been permitted under any circumstances.” However, the fatal load of 2.3 million gallons exerted pressure of 31,000 pounds per square inch on the tank walls, “a figure nearly double that which should have been allowed.” He noted, “The factor of safety is but 1.8, while ordinary practice would have called for from 3 to 4.”

<skip ... read the article>
.

..Spofford continued a distinguished career of teaching and research at MIT until retiring ..