Yes, I saw your weather looked rotten. This eclipse doesn't often come up at a reasonable hour. But the Moon was a pain last night for my usual disappointing Nova shot.
I will try and get a better reference picture tonight at 21.30 BST, because I want a good shot of Algol at full brightness to compare.
It is hard to spot the change IMO, and things like fall-off at the edge of a frame don't help. I also found my old Nikon CCD D60 and newer CMOS D3200 cameras are wildly different on sensitivity at the same settings.
Noise reduction doesn't seem to make a scrap of difference with rogue red pixels on the D60. The D3200 has none.
This is an old shot of Perseus on the D60 at 4s, ISO 1600 and f1.8 taken higher up, and I checked that it is no eclipse. It's not too bad:
That area top right is apparently the double cluster. I think we can see that Algol is brighter than Rho in the neat little pentagon bottom left.
I have finally figured out the self-timer button on the D3200 too. So sharper pictures I hope.
I will try and get a better reference picture tonight at 21.30 BST, because I want a good shot of Algol at full brightness to compare.
It is hard to spot the change IMO, and things like fall-off at the edge of a frame don't help. I also found my old Nikon CCD D60 and newer CMOS D3200 cameras are wildly different on sensitivity at the same settings.
Noise reduction doesn't seem to make a scrap of difference with rogue red pixels on the D60. The D3200 has none.
This is an old shot of Perseus on the D60 at 4s, ISO 1600 and f1.8 taken higher up, and I checked that it is no eclipse. It's not too bad:
That area top right is apparently the double cluster. I think we can see that Algol is brighter than Rho in the neat little pentagon bottom left.
I have finally figured out the self-timer button on the D3200 too. So sharper pictures I hope.
I took a few shots of Algol tonight at magnitude 2.1, and it's still hard to spot that it's normally 3x brighter than Rho mag 3.3 just below it, and Beta Persei, so I don't know how the ancient Egyptians spotted this 2.86 day eclipse pattern. Centre, about 1/3 way up.
But they did apparently, according to recently investigated manuscripts. Otherwise it was about 1750 when this was properly documented.
https://en.wikipedia.org/wiki/Algol
It's a very interesting triple star system. 94 LY away. A new hot white star of 3 solar masses and 180 sols brightness, a 1 solar mass red giant at 6 sols brightness at 0.06 AU, which is 6 million miles, orbiting it, and another hot star of 2 solar masses orbiting them both at 3 AU, which is about the distance of Jupiter. The hot star is accreting mass from the red giant appreciably, and you might think it will go Nova or something.
You can guess that the red giant star blots out about 2/3 of the brightest one.
Apparently this system passed within 10 LY of us 7.3 million years ago, and would have been brighter than Sirius.
But they did apparently, according to recently investigated manuscripts. Otherwise it was about 1750 when this was properly documented.
https://en.wikipedia.org/wiki/Algol
It's a very interesting triple star system. 94 LY away. A new hot white star of 3 solar masses and 180 sols brightness, a 1 solar mass red giant at 6 sols brightness at 0.06 AU, which is 6 million miles, orbiting it, and another hot star of 2 solar masses orbiting them both at 3 AU, which is about the distance of Jupiter. The hot star is accreting mass from the red giant appreciably, and you might think it will go Nova or something.
You can guess that the red giant star blots out about 2/3 of the brightest one.
Apparently this system passed within 10 LY of us 7.3 million years ago, and would have been brighter than Sirius.
I am ever keen to further understand the fiercely difficult subject of Quantum Mechanics. The Cabibbo Angle in Quark mixing seems to be quite hard. But let's have a go!
https://cerncourier.com/a/the-cabibbo-angle-60-years-later/
Yes, most of it went over my head too. But the big takeaway is Nicola Cabibbo got the idea from the Polarimeter. The real Chiral stuff comes from the third generation of Quarks, but mixes in with the lower generations.
The only bit I didn't really get, was how handed molecules twist the light a particular way regardless of orientation, but on further thought, I suppose a right handed thread is always right handed whichever way you point it.
Left handed threads are used in bicycle pedals and wheel nuts IIRC. To stop them loosening.
The second video is very interesting too, if a bit harder, and I found the difference between the continuous properties of the sine waves and the gaussian envelope startup ones quite informative in signal processing problems.
Because everybody struggles with the Gaussian envelope of a sine wave. whether in electronics and loudspeakers, or Quantum Mechanics, It needs clear thinking, and even now, I am not sure I totally get it.
But both are exponential functions.
It's surprising to me that the lowly rainbow and now this sugar water thing leads to interesting mathematics.
https://cerncourier.com/a/the-cabibbo-angle-60-years-later/
Yes, most of it went over my head too. But the big takeaway is Nicola Cabibbo got the idea from the Polarimeter. The real Chiral stuff comes from the third generation of Quarks, but mixes in with the lower generations.
The only bit I didn't really get, was how handed molecules twist the light a particular way regardless of orientation, but on further thought, I suppose a right handed thread is always right handed whichever way you point it.
Left handed threads are used in bicycle pedals and wheel nuts IIRC. To stop them loosening.
The second video is very interesting too, if a bit harder, and I found the difference between the continuous properties of the sine waves and the gaussian envelope startup ones quite informative in signal processing problems.
Because everybody struggles with the Gaussian envelope of a sine wave. whether in electronics and loudspeakers, or Quantum Mechanics, It needs clear thinking, and even now, I am not sure I totally get it.
But both are exponential functions.
It's surprising to me that the lowly rainbow and now this sugar water thing leads to interesting mathematics.
Regarding the "waveform of the envelope soliton" illustrated above.
A soliton is a wave with just a single crest which can travel a long distance without spreading out, thus maintaining its shape.
Apparently, the tendency for the wave to disperse is balanced by "a self-focusing nonlinearity".
Solitons can happen in water, as first discovered by John Scott Russell in 1834 in the Union Canal near Edinburgh.
Infrared solitons can travel for thousands of kilometres through optical fibres, and are used to carry information across oceans.
Wikipedia mentions the soliton solution to the nonlinear Schrödinger equation: https://en.wikipedia.org/wiki/Soliton#:~:text=In mathematics and physics, a soliton is a,after collisions with other such localized wave packets.
Soliton solutions apply to many areas of physics, including hydrodynamics, quantum mechanics and particle physics.
A soliton is a wave with just a single crest which can travel a long distance without spreading out, thus maintaining its shape.
Apparently, the tendency for the wave to disperse is balanced by "a self-focusing nonlinearity".
Solitons can happen in water, as first discovered by John Scott Russell in 1834 in the Union Canal near Edinburgh.
Infrared solitons can travel for thousands of kilometres through optical fibres, and are used to carry information across oceans.
Wikipedia mentions the soliton solution to the nonlinear Schrödinger equation: https://en.wikipedia.org/wiki/Soliton#:~:text=In mathematics and physics, a soliton is a,after collisions with other such localized wave packets.
Soliton solutions apply to many areas of physics, including hydrodynamics, quantum mechanics and particle physics.
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I'm (once again) reminded of the late Seigfried Linkwitz and his "raised cosine" (not the same thing, I know! but not a bad approximation) sine envelope for speaker testing. He may have come up with this (he wrote an AES paper on this circa 1980s, I don't have a reference offhand) before the word wavelet was coined, and certainly before wavelets became in vogue for "the new DSP method," IIRC the mid-late 1990s.
Its under the heading "Shaped toneburst generator" near the bottom of this page:
https://www.linkwitzlab.com/sys_test.htm
I wonder if he knew about the Gaussian envelope as compared to the raised cosine. Offhand, the latter seems easier to calculate.
As Linkwitz shows, such a wave produces a short "burst" of sound yet has relatively narrow bandwidth for such a short signal. I'm surprised this kind of signal isn't used more often for audio testing, especially of loudspeakers. Maybe it's used in proprietary areas and doesn't get much exposure.
I'm not as familiar with (almost the same thing?) solitons, though I've read an article about traffic and how some highways have features that cause a slowdown of traffic at certain spots, and they call these spots solitons.
I feel a 'Gaussian burst' coming on!
A 'Gaussian burst' is a sine wave modulated by a Gaussian exponential function in the time domain (shown in red in the LH figure). The Fourier transformation of the burst is also a Gaussian exponential function in the frequency domain (shown in blue in the RH figure). By defining the Gaussian burst in the time domain it is possible to control the corresponding frequency range of interest in the frequency domain.
That's got to be useful for testing loudspeakers has it not?
If we ignore the MHz that is!
So nobody is interested in circular polarisation? Which is a phase change. All part of the repertoire to me.
I have watched another 3Blue1Brown video about the Gaussian or Natural Distribution. A thing of great beauty in 1 or 2 dimensions.
This thing is fundamental in signal processing, where it is linear. In Quantum Mechanics it is different, because you cannot know the phase angle of the wave, though you can know the group and phase velocities, and their product, which is c squared in a vacuum.
What is beautiful about the Gaussian Impulse is that it is its own transform in the time and frequency domains, whether electrically on wires, or spatially with apertures:
What does this mean? IMO, that nearly EVERYBODY gets the wrong solution in Audio... rectangular or pistonic responses are VERY BAD.
They lead to ringing or lobing.
Which is a bit like discovering that Kepler's Third Law is WRONG. The Algol star system got me thinking about this. How do they calculate the masses of the main two stars?
See it's not how it really works:
The correct Newtonian solution, which I found in an Astrophysics reference book at the library today, is another thing of beauty:
a^3 is a transformed value though. Which takes some thinking about too.
https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Supplemental_Modules_(Astronomy_and_Cosmology)/Cosmology/Astrophysics_(Richmond)/11:_Kepler's_Third_Law
I love the stuff where you do things properly, not dumbed down.
I have watched another 3Blue1Brown video about the Gaussian or Natural Distribution. A thing of great beauty in 1 or 2 dimensions.
This thing is fundamental in signal processing, where it is linear. In Quantum Mechanics it is different, because you cannot know the phase angle of the wave, though you can know the group and phase velocities, and their product, which is c squared in a vacuum.
What is beautiful about the Gaussian Impulse is that it is its own transform in the time and frequency domains, whether electrically on wires, or spatially with apertures:
What does this mean? IMO, that nearly EVERYBODY gets the wrong solution in Audio... rectangular or pistonic responses are VERY BAD.
They lead to ringing or lobing.
Which is a bit like discovering that Kepler's Third Law is WRONG. The Algol star system got me thinking about this. How do they calculate the masses of the main two stars?
See it's not how it really works:
The correct Newtonian solution, which I found in an Astrophysics reference book at the library today, is another thing of beauty:
a^3 is a transformed value though. Which takes some thinking about too.
https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Supplemental_Modules_(Astronomy_and_Cosmology)/Cosmology/Astrophysics_(Richmond)/11:_Kepler's_Third_Law
I love the stuff where you do things properly, not dumbed down.
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With docking accuracy required of < 10 cm, I imagine NASA calculates at least a 13 body problem. 8 planets, earth's and 4 jupiter moons at least.
Johannes did well considering he knew naught of the force of gravity, and his laws remain useful to our understanding of how the planets move in our Solar System.
We need Newton’s generalised version of Kepler’s third law to determine the masses of:
- binary stars
- black holes
- exoplanets
And we need Einstein to step in when planning trajectories for spacecraft!
I've been reading that the majority of stars have a binary partner*, with single stars accounting for only 15% of all stars: https://www.space.com/22509-binary-stars.html It has even been suggested that our Sun could once have had a similar-size binary partner: https://en.wikipedia.org/wiki/HD_186302 (*or are part of systems with three or more stars.)
Ah, good work,@Galu. you have the exact relationship for a. At least in Newtonian Mechanics. I can work with that.
What I want is the Quantum Mechanical or maybe just the General Relativity relationship including Lorentz Covariance, because it will precess in General Relativity, just like Mercury's elliptical orbit...
Beta Lyrae looks an easy binary star eclipse candidate:
It's high up at 3AM right now. I am after Beta Lyrae dimming every 13 days.
I will mull over how to do this as a sort of Bohr atom too, using Schrodinger's equation. This would be like a Muonium atom, where the electron is replaced by a x200 heavier Muon.
Muon research is always of great interest at CERN. It may lead to new Physics.
This is a very good video if you want a serious take on it. The actual frequency of the Photon emitted in a Hydrogen Atom is the difference in "orbital" frequency between the n=1 and n=2 states, as a superposition problem.
This works out at 1/4 x 13.6 eV with a Cos 3x factor in this case. It's not rigorous though because Schrodinger is not Lorentz Covariant nor does it include spin, for which you need the Dirac Equation. But maybe good enough.
What I want is the Quantum Mechanical or maybe just the General Relativity relationship including Lorentz Covariance, because it will precess in General Relativity, just like Mercury's elliptical orbit...
Beta Lyrae looks an easy binary star eclipse candidate:
It's high up at 3AM right now. I am after Beta Lyrae dimming every 13 days.
I will mull over how to do this as a sort of Bohr atom too, using Schrodinger's equation. This would be like a Muonium atom, where the electron is replaced by a x200 heavier Muon.
Muon research is always of great interest at CERN. It may lead to new Physics.
This is a very good video if you want a serious take on it. The actual frequency of the Photon emitted in a Hydrogen Atom is the difference in "orbital" frequency between the n=1 and n=2 states, as a superposition problem.
This works out at 1/4 x 13.6 eV with a Cos 3x factor in this case. It's not rigorous though because Schrodinger is not Lorentz Covariant nor does it include spin, for which you need the Dirac Equation. But maybe good enough.
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I just realised that we need the Time-dependent Schrodinger Equation here. Not the Time-independent one. Sorry.
This is a PROPER Physics lecture by Professor Shankar at Yale.
He is very funny too:
My lecturers weren't half as good as this guy. A collection of some of his stuff here:
https://campuspress.yale.edu/rshankar/selected-lectures-talks/
His Student Quotes are a laugh a minute for the really keen Physics student. 🤣
This is a PROPER Physics lecture by Professor Shankar at Yale.
He is very funny too:
My lecturers weren't half as good as this guy. A collection of some of his stuff here:
https://campuspress.yale.edu/rshankar/selected-lectures-talks/
His Student Quotes are a laugh a minute for the really keen Physics student. 🤣
I just wanted to peek on that video. Found myself totally absorbed for 45 minutes. Brilliant teacher. I think I understand the gist of it but cant follow all turns in the math... but at 46:55 it started to get a bit blurry as I hear it - around what goes on in vacuum... "quantum fluctuation"... I predict that the concept of fluctuations will change to something else in the future when we will understand more of the resins why an atom cant sit still in a well - its so typical human that we reach for a term to describe what we actually not know but express ourselves as if we where dead sure... "quantum fluctuations" ;-) - is it dark energy (an other one... or affiliated?), is it an electrical field potential variation, is it due to..... please cc: me the memo once you sort it...
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I think you did very well to hang on to that point. This is Lecture 6 in the series, so we are jumping in at the deep end! I have Lecture 7 on my "to do" list, but am winging it a bit because I know a lot of this stuff.
I reviewed Lecture 5 to know that his particle in a box is the infinite square well. The Psi and Psi Star product is just finding the magnitude of the complex vector, which is a complex number thing.
Nobody likes the vacuum energy, but how else do you explain what nudges a Uranium atom to disintegrate, instead of just mooching along unchanged?
It's when you consider a mixed state, here Psi 2 and Psi 3, which is a bit like the Balmer spectral emission lines in Hydrogen, all tidily added up with a Pythagorean 3,4,5 triangle to keep the maths simple, you find a system who's measureables oscillate with time, which is unlike the individual stationary energy states. This is what fires off the Photon.
But you can imagine what life would have been like at a PROPER University, where everyone wants to know the REAL stuff taught by Professors.
We stopped at the finite and infinite (Particle in a box) square well and the harmonic oscillator time-independent stuff at mine. Which was disappointing. No General Relativity either.
Some of Professor Shankar's wit, which we can all enjoy:
I have been doing some suicide Gravity calculations just to amuse myself. You know a = 32 feet/s^2 and s = !/2 a t^2.
It's alarming. After 2 seconds you are falling at 64 feet per second, which is about 45 mph. You have fallen 64 feet, which is the roof height of a 4 storey building.
I wouldn't fancy my chances of surviving this... which make me wonder why we feel safe in cars!
But as Woody Allen said: "Nobody in Brooklyn ever thought about suicide when he was growing up. They were too depressed." 🤣
I reviewed Lecture 5 to know that his particle in a box is the infinite square well. The Psi and Psi Star product is just finding the magnitude of the complex vector, which is a complex number thing.
Nobody likes the vacuum energy, but how else do you explain what nudges a Uranium atom to disintegrate, instead of just mooching along unchanged?
It's when you consider a mixed state, here Psi 2 and Psi 3, which is a bit like the Balmer spectral emission lines in Hydrogen, all tidily added up with a Pythagorean 3,4,5 triangle to keep the maths simple, you find a system who's measureables oscillate with time, which is unlike the individual stationary energy states. This is what fires off the Photon.
But you can imagine what life would have been like at a PROPER University, where everyone wants to know the REAL stuff taught by Professors.
We stopped at the finite and infinite (Particle in a box) square well and the harmonic oscillator time-independent stuff at mine. Which was disappointing. No General Relativity either.
Some of Professor Shankar's wit, which we can all enjoy:
I have been doing some suicide Gravity calculations just to amuse myself. You know a = 32 feet/s^2 and s = !/2 a t^2.
It's alarming. After 2 seconds you are falling at 64 feet per second, which is about 45 mph. You have fallen 64 feet, which is the roof height of a 4 storey building.
I wouldn't fancy my chances of surviving this... which make me wonder why we feel safe in cars!
But as Woody Allen said: "Nobody in Brooklyn ever thought about suicide when he was growing up. They were too depressed." 🤣
I checked to find that the short-lived muonium atom is formed when an antimuon captures an electron.
The result is an atom similar to hydrogen, only no proton.
An antimuon is the antiparticle of a muon, which is essentially a heavy electron.
I read that muonium could change our understanding of physics and the universe! 😎
Because muonium is such a lightweight and simple atom, exploring its fine structure provides a way of testing one of the fundamental symmetries of physics - Lorentz symmetry.
Lorentz symmetry is the suggestion that the laws of physics remain the same for all observers, no matter how they are moving. If this symmetry were to be violated it could indicate that the universe is much more complicated than we realise.
Learn more about muonium research here: https://scisimple.com/en/articles/2025-01-23-muonium-a-simple-atom-with-big-insights--a9p02n6
I see now that you were referring to the 'muonic hydrogen atom' and not 'muonium'!
Since the muon is about 200 times heavier than the electron, muonic hydrogen is about 200 times smaller (across) than ordinary hydrogen.
This is actually quite plausbible and would follow the former path of human studies and insight evolution ;-)
//
The Muon is particularly sensitive to virtual particles, which is why it's good to measure. Isn't it the anomalous magnetic moment that is not exactly 2?
I think the answer to the vacuum energy thing that TNT mentioned is that the Electric Potential Energy function also fluctuates in terms of E and B.
The Energy of the particle is the sum of kinetic and potential energy, the Haniltonian H in shorthand.
I enjoyed the final Lecture VII in a much more relaxed way. The first half can be winged a bit and is very much like Fourier Analysis with the spiky Dirac Delta function, but the second bonus part is fascinating leading to Fermions and Bosons having different sorts of wave functions, where pairs of particles are indistinguishable.
I don't think we have an eclipse tonight, for the third successive night:
I have not been able to find a current timetable for this anywhere. Looks like I have to do EVERYTHING! Weather is horrible tomorrow, but may be better in Sweden. Hint.
I think the answer to the vacuum energy thing that TNT mentioned is that the Electric Potential Energy function also fluctuates in terms of E and B.
The Energy of the particle is the sum of kinetic and potential energy, the Haniltonian H in shorthand.
I enjoyed the final Lecture VII in a much more relaxed way. The first half can be winged a bit and is very much like Fourier Analysis with the spiky Dirac Delta function, but the second bonus part is fascinating leading to Fermions and Bosons having different sorts of wave functions, where pairs of particles are indistinguishable.
I don't think we have an eclipse tonight, for the third successive night:
I have not been able to find a current timetable for this anywhere. Looks like I have to do EVERYTHING! Weather is horrible tomorrow, but may be better in Sweden. Hint.
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