I am sure a cold wet flannel applied to your cranium will avert a catastrophe. Otherwise we shall miss you, Galu. 🤣
What I want to know is where you got this image:
A reference in other words. It is common enough to place a piece of clear plastic between two polarisers at right angles.
It should all look dark. But it doesn't.
But on deforming the plastic, coloured fringes often appear and show the stess patterns due to optical activity. I think we did this at "A" Level optics.
Experiments with electrons would be a different thing. Never mind all the stuff about shutters and quarter wave plates.
The experiment above is not quite the same thing as the one I quoted. I have misgivings about the one I quoted, but don't think it encourages some of the more bizarre ideas people have about entanglement.
Poor weather tonight, but I could see the new moon in a clearish sky both in the BBC coverage of the football from Germany, and on my way home from watching it. Thus:
I also found time to read Chapter 14 of "A History of the Universe in 100 Stars" by Florian Freistetter, who must be a crazy Swedish Astronomer from his name.
You recognise Cygnus, of course. Bottom left is a little triangle of stars. The uppermost slightly orange one is a double dwarf star called 61 Cygni.
Even by 1838, astronomers had noticed it moved quickly against the background sky and thought it might be close.
As telescopes improved they could measure its parallax against the Earth's orbit and estimated it close to 11 LY, though I expect they used kilometers.
This was the first measurement of the distance of a star. 😎
What I want to know is where you got this image:
A reference in other words. It is common enough to place a piece of clear plastic between two polarisers at right angles.
It should all look dark. But it doesn't.
But on deforming the plastic, coloured fringes often appear and show the stess patterns due to optical activity. I think we did this at "A" Level optics.
Experiments with electrons would be a different thing. Never mind all the stuff about shutters and quarter wave plates.
The experiment above is not quite the same thing as the one I quoted. I have misgivings about the one I quoted, but don't think it encourages some of the more bizarre ideas people have about entanglement.
Poor weather tonight, but I could see the new moon in a clearish sky both in the BBC coverage of the football from Germany, and on my way home from watching it. Thus:
I also found time to read Chapter 14 of "A History of the Universe in 100 Stars" by Florian Freistetter, who must be a crazy Swedish Astronomer from his name.
You recognise Cygnus, of course. Bottom left is a little triangle of stars. The uppermost slightly orange one is a double dwarf star called 61 Cygni.
Even by 1838, astronomers had noticed it moved quickly against the background sky and thought it might be close.
As telescopes improved they could measure its parallax against the Earth's orbit and estimated it close to 11 LY, though I expect they used kilometers.
This was the first measurement of the distance of a star. 😎
I would say its nigh on identical in its setup.
P.S. I obtained the diagram by googling "quantum eraser images". Unfortunately it did not carry a reference.
An additional search revealed the "three most common types of quantum eraser":
https://your-physicist.com/3-most-c...ents prevent a quantum system from evolving.
The third type is the "Quantum Zeno Effect" (QZE). Now what the heck is that?
Zeno of Elea was a Greek philosopher and mathematician who came up with paradoxes regarding motion, including the "Flying Arrow".
Apparently, Zeno considered that motion is an illusion.
You'll find his mathematical argument here, Steve: https://mathshistory.st-andrews.ac.uk/Biographies/Zeno_of_Elea/
I think I shall simply leave it at that! 🤓
I have resolved the matter! 🙂
To their utter shame, libretexts do not fully describe what is happening with the input light. Naturally, I spotted a discrepancy in the mathematics.
Your above diagram is the right one.
This can be done at home using a pen laser:
Downloadable PDF for the very keen Quantum Mechanicist:
https://physlab.org/wp-content/uploads/2016/07/diy-quantum-eraser.pdf
What those bounders, scallywags and scoundrels at libretexts omitted to mention is the polarised laser light source must be aligned at 45 degrees, or equivalently with an unpolarised one, another polaroid filter must be placed in front of the experiment.
Then it does what we expect, and I abbreviate the various results to the germane one:
We can leave the Quantum Zeno Effect to another day. I have done enough.
To their utter shame, libretexts do not fully describe what is happening with the input light. Naturally, I spotted a discrepancy in the mathematics.
Your above diagram is the right one.
This can be done at home using a pen laser:
Downloadable PDF for the very keen Quantum Mechanicist:
https://physlab.org/wp-content/uploads/2016/07/diy-quantum-eraser.pdf
What those bounders, scallywags and scoundrels at libretexts omitted to mention is the polarised laser light source must be aligned at 45 degrees, or equivalently with an unpolarised one, another polaroid filter must be placed in front of the experiment.
Then it does what we expect, and I abbreviate the various results to the germane one:
We can leave the Quantum Zeno Effect to another day. I have done enough.
I had noticed that a + 45° filter was not placed in front of the double slits shown in the libretext diagrams.
By looking at a couple of research abstracts I have cobbled together this brief description of a simple quantum eraser:
That'll do for me! 🤓
P.S. It would appear that in the pen laser experiment the fringes and anti-fringes shown in the libretext article are viewed simultaneously on the screen.
I did think it was an interesting experimental confirmation of what I have always thought about The Quantum:
You can measure the momentum (Fringes) or the position (Envelope), but not simultaneosly without Planck's Constant cropping up.
The same goes for Energy and Time. It can also be looked at as a matter of information. And half h(Bar) is the minimum unit.
For sure the experiment doesn't work without both the D and A polarisers.
I am also encountering The Quantum in my camera efforts. Here is Nu Bootis as I incidentally snapped it last night as part of my relentless ongoing T CrB Nova project:
These colourful stars are 0.17' apart, so we can guess that snaps of The Moon at 0.5' will be underwhelming. But I think that 8s (400 / 50) looks optimal to minimise blurring due to the Earth's rotation.
This may not make you popular at an Aussie bar if you mention it, but I have discovered that the Aussie Flag makes ABSOLUTELY NO SENSE!
Whatever is it supposed to mean? Vague notions that the big star represents The Commonwealth or maybe World Peace or something.
It certainly isn't Alpha Centauri and Crux. And Beta Centauri is a dull star IMO.
Just sayin'. 🙂
You can measure the momentum (Fringes) or the position (Envelope), but not simultaneosly without Planck's Constant cropping up.
The same goes for Energy and Time. It can also be looked at as a matter of information. And half h(Bar) is the minimum unit.
For sure the experiment doesn't work without both the D and A polarisers.
I am also encountering The Quantum in my camera efforts. Here is Nu Bootis as I incidentally snapped it last night as part of my relentless ongoing T CrB Nova project:
These colourful stars are 0.17' apart, so we can guess that snaps of The Moon at 0.5' will be underwhelming. But I think that 8s (400 / 50) looks optimal to minimise blurring due to the Earth's rotation.
This may not make you popular at an Aussie bar if you mention it, but I have discovered that the Aussie Flag makes ABSOLUTELY NO SENSE!
Whatever is it supposed to mean? Vague notions that the big star represents The Commonwealth or maybe World Peace or something.
It certainly isn't Alpha Centauri and Crux. And Beta Centauri is a dull star IMO.
Just sayin'. 🙂
The Australian flag is said to represent the Southern Cross (Crux) and the Commonwealth Star.
Six of the seven points of the Commonwealth Star represent the six states of Australia and the other represents the territories.
Unless Wikipedia has got it wrong that is! https://en.wikipedia.org/wiki/Flag_of_Australia#Construction
I admit to not being overly excited at the prospect of the imminent nova.
It is now estimated that about four dozen nova explosions occur each year in our Milky Way galaxy. https://arxiv.org/abs/2101.04045
Galactic dust has obscured many nova explosions in the past, but now the ability to observe in the infrared has allowed astronomers to penetrate the dust and get a better estimate of the nova rate, currently standing at 46, give or take 13, a year.
It is now estimated that about four dozen nova explosions occur each year in our Milky Way galaxy. https://arxiv.org/abs/2101.04045
Galactic dust has obscured many nova explosions in the past, but now the ability to observe in the infrared has allowed astronomers to penetrate the dust and get a better estimate of the nova rate, currently standing at 46, give or take 13, a year.
I enjoyed the podcast. Very interesting and well informed explanation from a man who works at the Flagstaff Arizona Lowell Observatory.
THE HOME OF PLUTO!!! Wasn't Percival Lowell the man who also saw the Canals on Barsoom, er, Mars? 😆
I checked out some of the light pollution measures taken in Flagstaff which is proud of its Observatory and has 10% of the usual light impact of a city, such that he can see the Milky Way in his back garden:
Special LED bulbs mimicking Low Pressure Sodium besides being pointed down.... so that's how it is done.
What you have neglected @Galu, is that this Nova is a mere 2,300 LY away in the Milky Way Galaxy that is 100,000 LY across. And its regular nature makes it one of about a 15 known ones, which are all dimmer.
I have realised that even my puny Nikon Coolpix A100 4.6-23mm f3.2-6.5 camera has an ISO setting that I can boost in fireworks 5s mode. A Tripod is however essential, but these are not hard to find in second hand shops for £20-30.
We await with interest, even if tonight's skies look hopeless in Portsmouth. As I have mentioned, Corona Borealis is 3/4 along the line between blue Vega and orange Arcturus which are South at midnight right now.
He advised familiarising yourself with the area in advance, and binos will help. Should be as bright as Alpha in CrB, but who knows?
Dr. Van Belle said the Nova will take about a day to get to maximum from commencement, then fade away in a week. I couldn't find any pictures from 1946 which is odd.
My effort two nights ago:
Clear Skies, as Astronomers say! 🙂
THE HOME OF PLUTO!!! Wasn't Percival Lowell the man who also saw the Canals on Barsoom, er, Mars? 😆
I checked out some of the light pollution measures taken in Flagstaff which is proud of its Observatory and has 10% of the usual light impact of a city, such that he can see the Milky Way in his back garden:
Special LED bulbs mimicking Low Pressure Sodium besides being pointed down.... so that's how it is done.
What you have neglected @Galu, is that this Nova is a mere 2,300 LY away in the Milky Way Galaxy that is 100,000 LY across. And its regular nature makes it one of about a 15 known ones, which are all dimmer.
I have realised that even my puny Nikon Coolpix A100 4.6-23mm f3.2-6.5 camera has an ISO setting that I can boost in fireworks 5s mode. A Tripod is however essential, but these are not hard to find in second hand shops for £20-30.
We await with interest, even if tonight's skies look hopeless in Portsmouth. As I have mentioned, Corona Borealis is 3/4 along the line between blue Vega and orange Arcturus which are South at midnight right now.
He advised familiarising yourself with the area in advance, and binos will help. Should be as bright as Alpha in CrB, but who knows?
Dr. Van Belle said the Nova will take about a day to get to maximum from commencement, then fade away in a week. I couldn't find any pictures from 1946 which is odd.
My effort two nights ago:
Clear Skies, as Astronomers say! 🙂
I was today investigating whether the predicted T Coronae Borealis Nova is worth getting out in the UK night for. Indeed I think it is. Somewhere between Magnitude 2 and 3 if history repeats.
Bright Novae are a rarity as this list makes clear:
https://en.wikipedia.org/wiki/List_of_novae_in_the_Milky_Way_galaxy
You have to go back to August 1975 to find a brighter one, V1500 Cygni at Magnitude 1.7. By some quirk, most of the other previous bright ones have been in the Southern Hemisphere
Supernovae are even rarer. 1987A at Magnitude 2.9 in February was about as good as it got in our lifetime.
https://en.wikipedia.org/wiki/List_of_supernovae
I missed seeing both since I had largely forgotten what stars looked like living in London.
Eta Carinae is not a Nova, but an extremely huge blue star, around 7,000 LY away, that periodically erupts. In 1845 it reached Magnitude -1.0 which made it the second brightest star in the sky, surpassing Canopus.
https://en.wikipedia.org/wiki/Eta_Carinae
Even today at Magnitude 4 it might claim to be the furthest star we can see with our eyes. It is the n-looking eta symbol here, marked with a green square:
This is how it currently looks in a telescope:
Humungous stars like this are actually very young and extremely unstable, 3 million years old. And is located in a huge gas cloud, bigger than the Orion Nebula, which is still forming stars called the Carina Nebula.
I have also discovered that Alphecca (Alpha) aka Gemma (The Jewel) in Coronae Borealis at Magnitude 2.24 has great historical significance in star classification. It is as close to pure White (A0) in the UBV classification system as stars get.
https://en.wikipedia.org/wiki/Alpha_Coronae_Borealis
We can therefore easily compare the Nova with it. A strange coincidence indeed. 😵
Bright Novae are a rarity as this list makes clear:
https://en.wikipedia.org/wiki/List_of_novae_in_the_Milky_Way_galaxy
You have to go back to August 1975 to find a brighter one, V1500 Cygni at Magnitude 1.7. By some quirk, most of the other previous bright ones have been in the Southern Hemisphere
Supernovae are even rarer. 1987A at Magnitude 2.9 in February was about as good as it got in our lifetime.
https://en.wikipedia.org/wiki/List_of_supernovae
I missed seeing both since I had largely forgotten what stars looked like living in London.
Eta Carinae is not a Nova, but an extremely huge blue star, around 7,000 LY away, that periodically erupts. In 1845 it reached Magnitude -1.0 which made it the second brightest star in the sky, surpassing Canopus.
https://en.wikipedia.org/wiki/Eta_Carinae
Even today at Magnitude 4 it might claim to be the furthest star we can see with our eyes. It is the n-looking eta symbol here, marked with a green square:
This is how it currently looks in a telescope:
Humungous stars like this are actually very young and extremely unstable, 3 million years old. And is located in a huge gas cloud, bigger than the Orion Nebula, which is still forming stars called the Carina Nebula.
I have also discovered that Alphecca (Alpha) aka Gemma (The Jewel) in Coronae Borealis at Magnitude 2.24 has great historical significance in star classification. It is as close to pure White (A0) in the UBV classification system as stars get.
https://en.wikipedia.org/wiki/Alpha_Coronae_Borealis
We can therefore easily compare the Nova with it. A strange coincidence indeed. 😵
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It may be worth stating that the brighter an object appears, the lower the value of its magnitude, with the brightest objects reaching negative values.
The brightest star visible from Earth - and often the brightest object of all - is Sirius with a magnitude of -1.46.
https://www.space.com/brightest-stars-in-the-sky
The brightest star visible from Earth - and often the brightest object of all - is Sirius with a magnitude of -1.46.
https://www.space.com/brightest-stars-in-the-sky
Didn't John McEnroe have one of his periodic tennis tantrums and famously say to the umpire at Wimbledon: "You can not be Sirius! The ball was OUT!" 🤣
I am on a mission tomorrow, maybe even tonight, if I have not lost the will to live after watching the hopeless England footballers lose again.
I must go down to the sea again, the lonely sea and the sky. Specifically Southsea Castle overlooking the Solent.
Why? To see if I can spot and photograph planet Uranus for your delight and amazement. July 15 sees it close to Barsoom, er, Mars and the famous Pleiades.
By my calculations the Moon will be absent, which is good. Hopeless Portsmouth Council have however installed new lighting at this previously relatively dark spot, so we shall see what the Sky glow score is.
I have discovered that even the pleasant local councillor, Graham Healey, in St. Jude's ward has no understanding of light pollution whatever. New LED lamps have actually made the problem worse:
Where everybody goes wrong is in neglecting the blue component of regular white LED streetlights.
This is why LED lights tend to be more harsh on the eye than good old tungsten lights, which did mystify me. In fact my sister still insists on 12V Halogen in her beautiful house.
It is also important to point them down:
This is not rocket science, nor expensive:
Hope may lie in new Amber lights, both 1700-1800K and 590nm turtle friendly lights. But notice that 2200K lights start to get ugly:
https://www.moon-leds.com/news-what-is-amber-led-pc-amber-1800k-2200k-monochromatic-amber.html
I have been researching the relevant Portsmouth City ordinance and my powers of action may be limited:
The scallywags have largely protected themselves from criticism. But I think I may be able to sort out nearby glaring blue white forecourt illumination on a Council-maintained block which hinder my street sky snaps.
Sorry to rant.
I am on a mission tomorrow, maybe even tonight, if I have not lost the will to live after watching the hopeless England footballers lose again.
I must go down to the sea again, the lonely sea and the sky. Specifically Southsea Castle overlooking the Solent.
Why? To see if I can spot and photograph planet Uranus for your delight and amazement. July 15 sees it close to Barsoom, er, Mars and the famous Pleiades.
By my calculations the Moon will be absent, which is good. Hopeless Portsmouth Council have however installed new lighting at this previously relatively dark spot, so we shall see what the Sky glow score is.
I have discovered that even the pleasant local councillor, Graham Healey, in St. Jude's ward has no understanding of light pollution whatever. New LED lamps have actually made the problem worse:
Where everybody goes wrong is in neglecting the blue component of regular white LED streetlights.
This is why LED lights tend to be more harsh on the eye than good old tungsten lights, which did mystify me. In fact my sister still insists on 12V Halogen in her beautiful house.
It is also important to point them down:
This is not rocket science, nor expensive:
Hope may lie in new Amber lights, both 1700-1800K and 590nm turtle friendly lights. But notice that 2200K lights start to get ugly:
https://www.moon-leds.com/news-what-is-amber-led-pc-amber-1800k-2200k-monochromatic-amber.html
I have been researching the relevant Portsmouth City ordinance and my powers of action may be limited:
The scallywags have largely protected themselves from criticism. But I think I may be able to sort out nearby glaring blue white forecourt illumination on a Council-maintained block which hinder my street sky snaps.
Sorry to rant.
I read the link with interest. Permit me to extract from, and expand on, your link.
PC Amber (1700K) LED lights are dark-sky friendly. Illumination wise, they give greater visibility than narrow spectrum low-pressure sodium lamps.
https://www.accessfixtures.com/pc-amber-led-lighting/
590 nm Amber LED lights cannot be seen by turtles and many other types of wildlife, making this lighting ideal for areas where it is essential to avoid disturbing natural habitats.
https://www.accessfixtures.com/590-nm-led-lighting/
The weather destroyed my hoped for spotting Uranus and Mars conjunct on July 15. And checking out the new lighting. A damp and murky cloud layer meant the photo would have been poor, so I stayed home.
But I did get a very poor shot of the expected T CrB Nova location last night through the clouds. About 11.30 PM. Again nothing.
Being bored and frustrated, I somehow got back to my favourite rainy day Maths problem, the Euler Zeta function.
The related Riemann Hypothesis about the non-trivial zeroes all being on the x=1/2 line for all values of exponent s is one of the more famous unsolved Maths problems in number theory. It's worth $1M to anyone who can crack it.
It was the genius of Leonard Euler to evaluate this infinite series known as "The Basel Problem" or Euler Zeta(2) and to consider it important:
But being Euler, he took it further, into the realm of the Prime Numbers:
This is extraordinary. It gives an infinite relation between the Prime Numbers and the Integers.
If just one prime number was different from what they are, the neat product would break!
Euler and Dirichlet also knew all about this alternating one, known as the Dirichlet Eta Function:
This gives a way of further subdividing the series quite straightforwardly.
The sums of these series converge on 1 generally, this being the Zeta:
Zeta(-1) is that interesting sum of all the integers, 1,2,3,4... which you may have met.
The odd values are not analytic, but here they are:
And for the (alternating) Dirichlet Eta Function:
What does this have to do with the real world? Quite a lot I think. I always try to visualise a probllem in a Physical way:
Here is Zeta(2) as the sum of forces from regularly spaced masses, and it takes little imagination to move the even ones to the left of the red origin for the alternating series
And here is the Prime Number related product as the particular values of Spectrum of the Hydrogen Atom:
Which leads to this:
The mind is boggled! Euler was a man ahead of his time! 😎
But I did get a very poor shot of the expected T CrB Nova location last night through the clouds. About 11.30 PM. Again nothing.
Being bored and frustrated, I somehow got back to my favourite rainy day Maths problem, the Euler Zeta function.
The related Riemann Hypothesis about the non-trivial zeroes all being on the x=1/2 line for all values of exponent s is one of the more famous unsolved Maths problems in number theory. It's worth $1M to anyone who can crack it.
It was the genius of Leonard Euler to evaluate this infinite series known as "The Basel Problem" or Euler Zeta(2) and to consider it important:
But being Euler, he took it further, into the realm of the Prime Numbers:
This is extraordinary. It gives an infinite relation between the Prime Numbers and the Integers.
If just one prime number was different from what they are, the neat product would break!
Euler and Dirichlet also knew all about this alternating one, known as the Dirichlet Eta Function:
This gives a way of further subdividing the series quite straightforwardly.
The sums of these series converge on 1 generally, this being the Zeta:
Zeta(-1) is that interesting sum of all the integers, 1,2,3,4... which you may have met.
The odd values are not analytic, but here they are:
And for the (alternating) Dirichlet Eta Function:
What does this have to do with the real world? Quite a lot I think. I always try to visualise a probllem in a Physical way:
Here is Zeta(2) as the sum of forces from regularly spaced masses, and it takes little imagination to move the even ones to the left of the red origin for the alternating series
And here is the Prime Number related product as the particular values of Spectrum of the Hydrogen Atom:
Which leads to this:
The mind is boggled! Euler was a man ahead of his time! 😎
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Euler's pi prime product sounds really tasty!
P.S. I'm praying for the skies to clear over Southsea Castle so that you can get out more! 😉
