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Eric Pouhier
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More and more craters in North of Russia.
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Élégance.
 
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Of the none continuity of nature ... which makes things simpler. If everything was continuous the universe would be a complete chaos, that it obviously is not!
 
Spin and the Stern-Gerlach Experiment

The word “quantum” means a single share or portion [1]. In quantum mechanics, this means that energy comes in discrete chunks, or quanta, rather than a continuous flow. But it also means that particles have other properties that are discrete in a way that’s deeply counterintuitive. Today. for +ScienceSunday I want to tell you about one such property, called spin, and the experiment that discovered it: the Stern-Gerlach experiment.

(Those who wish to see this post in blog form can find it here:
http://www.thephysicsmill.com/2015/02/22/the-stern-gerlach-experiment/)

(The goal of the original experiment was actually to test something else. But it was revealed later, after the discovery of spin by Wolfgang Pauli, that this is in fact what Stern and Gerlach were measuring [2].)

Magnets

The Stern-Gerlach experiment involves magnetic fields. So before I tell you about the experiment itself, I need to quickly review some of the properties of magnets.

As you probably remember, the north pole of a magnet is attracted to the south pole of other magnets and repelled from their north pole, and vice versa—a south pole is attracted to north poles and repelled by other south poles. In other words, opposites attract.

Suppose we generate a very strong magnetic field (say, with a very big magnet or with a solenoid [3]) and put a small magnet in the field, as shown in Figure 2. What happens to it? The north pole of the big magnet will attract the south pole of the small magnet, and the south pole of the big magnet will attract the north pole of the small magnet. Since the north and south pole of the big magnet are are equally strong, these attractions will be equal and opposite, and they’ll cancel each other out so that the little magnet feels no net force. As a result, it doesn’t move up or down—it just hovers in place.

Now suppose we create a big magnet whose north pole is more powerful than its south pole, as shown in Figure 3. (It’s not actually possible to make a magnet with a stronger north pole than south pole. However, we can create the same effect by using multiple smaller magnets.) What happens now?

To answer this question, we must understand that the strength of a magnetic force depends on the distance between the interacting poles; the closer the poles, the stronger the force. This means that the net force the little magnet feels depends on its orientation, as shown in Figure 4. If the south pole of the little magnet is close to the north pole of the big magnet, the little magnet will be pulled upwards. If, on the other hand, the north pole of the little magnet is close to the north pole of the big magnet, the little magnet will be pushed downwards. If the poles of the little magnet are the same distance from the poles of the big magnet, the little magnet will feel no force. And of course, anything in between is possible. A little magnet whose south pole is just barely closer to the big north pole will feel a weaker pull than a little magnet whose south pole is very close to the big north pole.

The Stern-Gerlach Experiment

The Stern-Gerlach experiment, performed by Otto Stern and Walther Gerlach, tested whether subatomic particles behaved like little magnets. To do this, Stern and Gerlach created a magnet with a bigger north pole than south, just like the one described above, and shot a beam of electrons with random orientations through the resulting magnetic field. If electrons behaved like little magnets, then the beam would be spread out by the magnetic field, as shown in Figure 5. Some electrons would be pulled upwards, some would be pushed downwards, and some wouldn’t change direction, depending on the orientations of the individual electrons. But if electrons didn’t behave like magnets, then none of them would be affected by the magnetic field, so they would all just fly straight through.

Surprisingly, although the electrons were affected by the magnet, they didn’t spread out as in Figure 5. Instead, the electrons split cleanly into two beams, as shown in Figure 6.

That’s very weird! It implies that electrons behave like little magnets, but only sort of. A magnet can be oriented any way it likes. But an electron can only have two orientations: either aligned with the big magnet or aligned against it. So the electron can travel up or down, but it can’t stay in between. This is a distinctly quantum phenomenon—the electrons behave like magnets fixed into a pair of discrete orientations, or states, as opposed to a continuum of possible orientations. An electron’s spin is what describes which of those two states it’s in.

Where Does Spin Come From?

I won’t discuss it in detail here, but we can understand spin as emerging from the structure of the underlying quantum field theory that describes the behavior of a given particle. For those of you who know the lingo, it has to do with whether the underlying field is a vector or scalar field, and how large that vector is. (Among other sources, see_ Quantum Field Theory in a Nutshell_ by Anthony Zee.)

Interpretation

The Stern-Gerlach experiment reveals a dramatic difference between the quantum world and the world we’re used to. It’s not possible for a particle to have any old orientation; it must be oriented either with the external magnetic field or against it.

But what if there is no external magnetic field? How is the particle oriented? Somehow the act of measuring the system changed how it behaves, or at least how we perceive it. These are questions that physicists struggled with in the early twentieth century as quantum mechanics was being discovered. Indeed, to some extent, physicists are still struggling with them.

In the next few weeks, I’ll address some of these issues. Next time, I will talk about an extension of the Stern-Gerlach experiment that helps us explore, if not answer, some of these questions.

Related Reading

This is only the latest in a number of articles that I’ve written about quantum mechanics. For example, I wrote a three-part introduction to the field:

1. In the first part, I describe some of the experiments that first revealed particle-wave duality: 
http://www.thephysicsmill.com/2012/12/09/the-charming-doubleness-particle-wave-duality/

2. In the second part, I use the Bohr Model of the atom to explain how packets of energy emerge from the wave nature of matter:
http://www.thephysicsmill.com/2012/12/24/unreal-truths-the-bohr-model-of-the-atom/

3. In the third part, I describe how we can interpret matter waves as probability waves: 
http://www.thephysicsmill.com/2012/12/30/the-dice-are-loaded-probability-waves/

More recently, I wrote a pair of posts exploring particle-wave duality.

1. In the first post, I describe how a particle can be constructed from a wave:
http://www.thephysicsmill.com/2015/01/18/whats-particle/

2. In the second post, I show how particles sometimes can’t exist:
http://www.thephysicsmill.com/2015/01/25/sometimes-particle-isnt-possible/

I’ve also written a number of stand-alone articles on quantum mechanics:

1. Quantum mechanics uses complex numbers, so I wrote a short explanation of imaginary and complex numbers here:
http://www.thephysicsmill.com/2013/03/17/for-there-we-are-captured-the-geometry-of-spacetime/

2. I explain the Feynman path integral, which is a way of understanding quantum mechanics, here:
http://www.thephysicsmill.com/2013/07/16/reality-is-the-feynman-path-integral/

3. I use particle-wave duality and matter waves to explain quantum tunneling here:
http://www.thephysicsmill.com/2013/02/24/the-fundamental-oneness-of-nature-quantum-tunneling/

4. I use quantum mechanics to describe how atoms form covalent bonds here:
http://www.thephysicsmill.com/2013/11/02/a-moving-sea-covalent-bonding/

Further Reading

Here are some additional resources on the Stern-Gerlach experment:

1. If you’d like to learn a bit about the history of the Stern-Gerlach experiment, try “Stern and Gerlach: How a Bad Cigar Helped Reorient Atomic Physics.” See:
http://scitation.aip.org/content/aip/magazine/physicstoday/article/56/12/10.1063/1.1650229

2. One of the finest technical write-ups of the Stern-Gerlach experiment is in the opening chapter of Modern Quantum Mechanics by Sakurai. Excellent and detailed, but definitely not for the faint of heart. See:
http://www.amazon.com/Modern-Quantum-Mechanics-2nd-Sakurai/dp/0805382917/ref=sr_1_1?ie=UTF8&qid=1424639935&sr=8-1&keywords=sakurai+quantum+mechanics

3. There is a free textbook-like write-up of the Stern-Gerlach experiment by Jeremy Bernstein here:
http://arxiv.org/abs/1007.2435v1

Acknowledgements

Thanks as always to +Alexandra Fresch  for her line-editing.

Recently I’ve had a lot of discussions on G+  about the interpretation of quantum mechanics. (In particular, I’ve spent a lot of time talking to +Charles Filipponi  and +David R .) This article was partly inspired by those conversations. Thanks, guys!

The Winnower

I'm trying an experiment. I've cross-posted this post to the Winnower, which is an open-access academic journal. Recently, the Winnower reached out to me and suggested that I cross-post my blog posts there. If you're curious, please check it out and let me know what you think.  You can find the link here:
https://thewinnower.com/papers/spin-and-the-stern-gerlach-experiment

References

[1] http://www.etymonline.com/index.php?term=quantum
[2] https://en.wikipedia.org/wiki/Spin_%28physics%29
[3] https://en.wikipedia.org/wiki/Solenoid

#ScienceSunday   #Science   #Physics   #QuantumMechanics   #HistoryOfPhysics  
+Allison Sekuler +Rajini Rao +Chad Haney +Buddhini Samarasinghe +Aubrey Francisco +Carissa Braun +Buddhini Samarasinghe 
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Thanks for the reshare, +Eric Pouhier !
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Human creativity and numbers.
Real and complex number sets.
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For those who believe that speed of light is fast, this great video will help to understand the scale of cosmic distances and realize how small we are. It also should help one to understand that if light travels so slowly, there must be an explanation to it!
 
The unbearable slowness of light

"In our terrestrial view of things, the speed of light seems incredibly fast. But as soon as you view it against the vast distances of the universe, it's unfortunately very slow. This animation illustrates, in realtime, the journey of a photon of light emitted from the sun and traveling across a portion of the solar system."

via http://kottke.org/15/02/the-unbearable-slowness-of-light
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Very nice short video of Vesta.... and soon Ceres.

NASA Dawn's Virtual Flight Over Asteroid Vesta : http://youtu.be/YYxPw_T8Vlk
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This morning, I warmly recommend this masterpiece from Pergolesi. " Most of all, though, the work is beautiful, and its deeply spiritual loveliness has been realised in a fine period performance. "
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We're absolutely speechless and devastated.

The Islamic State (Isis) has published a video showing militants destroying ancient artefacts in a Mosul museum with sledgehammer and pickaxes. IS fighters are seen unveiling old statues in the Ninawa museum dating back to the Assyrian empire and then dragging them down to the ground, where they fall into pieces. http://www.ibtimes.co.uk/iraq-isis-take-sledgehammers-priceless-assyrian-artefacts-mosul-museum-video-1489616

#iraq #mosul #culturalheritage #isis #destruction #antiquities #assyrian #patrimony #middleeast  
Video shows IS militants dragging ancient Nineveh statues to the floor and smashing them with hammers.
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The secret lies in number theory, a simple and wonderful secret.
 
Towards a Grand Unified Theory of Mathematics and Physics

Abstract: "Wigner's "unreasonable effectiveness of mathematics" in physics can be understood as a reflection of a deep and unexpected unity between the fundamental structures of mathematics and of physics. Some of the history of evidence for this is reviewed, emphasizing developments since Wigners time and still poorly understood analogies between number theory and quantum field theory."

Link: http://www.math.columbia.edu/~woit/mathphys.pdf

Feedback: http://www.math.columbia.edu/~woit/wordpress/?p=7574
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Sadely a French Street artist attacked in Paris... Dark days ahead. 
Street artist Combo was attacked by four youth who objected to his Coexist, piece, an artwork which promotes tolerance among religions.
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Eric Pouhier

Introductions  - 
 
Simply one of the very finest author of interesting mathematical posts on Google+
 
Engagers Showcase Circle, February 1, 2015

If I sent you a notification, it means that you are included in my Engagers Showcase Circle. “Showcase” means that you are invited to leave a comment (on the original post) with a link to one of your own posts, which ideally should be one of your best recent posts.

This circle consists of people who have engaged with one of my recent posts in the form of +1s, comments and reshares.

Everyone mentioned below is also included in the circle.

Ramanujan's nested radical
https://plus.google.com/101584889282878921052/posts/3WmvWEHyMNB

The exceptional symmetry
https://plus.google.com/101584889282878921052/posts/ioQW2zGjwwM

The mystery of the missing area
https://plus.google.com/101584889282878921052/posts/QU8aYaTCufq

Sunrise
https://plus.google.com/101584889282878921052/posts/9QWbSALP2XU

Shakespearean Logic
https://plus.google.com/101584889282878921052/posts/MBqnMRgBiBJ

“Nines” by Eric Standley
https://plus.google.com/101584889282878921052/posts/aR5BF9uV5n8

Cherry pi (reshared from +David Richeson)
https://plus.google.com/101584889282878921052/posts/bixJ7eGk3Qm

Happy New Year!
https://plus.google.com/101584889282878921052/posts/ZJYFj1RogaS

The mathematics of card shuffling
https://plus.google.com/101584889282878921052/posts/fAS8Y3Yccfs

The sky and the fork in the path immediately preceding the arrival of the ice rinks of doom
https://plus.google.com/101584889282878921052/posts/2MiqiTJ1Feu

iPad landscape art (reshared from +Paul Haworth)
https://plus.google.com/101584889282878921052/posts/27EwU49z1g8

The fractional chromatic number of the plane
https://plus.google.com/101584889282878921052/posts/VbBk9JrLxqm

Dull (in Scotland) and Boring (in Oregon)
https://plus.google.com/101584889282878921052/posts/ZuMzApfSPR4

Partition and sum is fast
https://plus.google.com/101584889282878921052/posts/Ad1ism1vJpJ

The tautological clock
https://plus.google.com/101584889282878921052/posts/diAyvxM7Nuw

Mathematical Mr Men
https://plus.google.com/101584889282878921052/posts/MZ3yxPahUxa

As always, reshares of this circle are appreciated, and I look forward to seeing everyone's links. Thanks for reading my posts!
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Mathématiques, Photographie and Piano
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Extreme curiosity, huge imagination & unlimited courage !
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Paris, France - Cherbourg - Balikpapan - Singapour - Abu Dhabi - San Fransisco, Usa - Brest
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“Simplicity is the ultimate sophistication.” L. Da Vinci
Introduction
Bonjour,

Je suis né en 1963 à Brest, en France, depuis j'erre sur terre avec une certaine mélancolie et avec aussi une infinité de questions existentielles qui ne me laissent guère le temps de dormir. 

Fin 2008, j'ai décidé de reprendre l’étude des nombres comme Euclide le fit en son temps. De repartir de rien, de tout reprendre depuis le début, en effet, si un Grec ancien avait pu inventer la division et autres concepts avec très  peu d'outils et peu d'information. J'ai pensé qu'un homme du XXIeme siècle, habité par les maths, ayant un ordinateur, un excellent logiciel mathématique et un accès immédiat (merci Google & Wikipedia) à quasiment tout la connaissance du monde devrait pouvoir acquérir une meilleure compréhension du fabuleux monde des nombres. Après environ 9000 heures d'un travail tout aussi passionné qu'acharné, le 20 Juin 2012, j'ai finalement compris l’extraordinaire et incroyable Vérité sur la nature des entiers naturels... Lavoisier était encore plus dans le vrai qu'il ne pu l'imaginer "Rien ne se perd, rien ne se crée, tout se transforme. 

Quelques citations éclairées:

"La nature est fondamentalement mathématiquePythagore 

"Il ne faut pas craindre de se rebeller. La seule autorité quand on fait des mathématiques, c'est soi-même." Alain Connes

"La mathématique est une science dangereuse : elle dévoile des supercheries et les erreurs de calcul." Galilée

"Dieu a privilégié l'homme en mettant en son esprit les notions élémentaires des mathématiques afin de le faire participer au secret de sa création et aussi lui permettre d'améliorer sa condition."  Descartes 

"Mesure ce qui est mesurable et rends mesurable ce qui ne peut pas être mesuré." Galilée

"The Lord God is subtle, but malicious He is not." Albert Einstein

Any fool can make something complicated. It takes a genius to make it simple.” 
Woody Guthrie

 Quarante-deux ! (42) Deep Thought  (The Hitchhiker's Guide to the Galaxy)

"Tout ce qui est voilé sera dévoilé, tout ce qui est caché sera connu." Jésus the Galilean.

En dehors des mathématiques et de la musique, je m’intéresse à tout sauf à 2 domaines ou mon inculture est sans fond: la bande dessinée et le sport.

Pour finir, au fil des années, j'ai développé une certaine misanthropie et je compte sur vous pour en guérir.

Livre Préféré : The Road de Cormac McCarthy
Bragging rights
Bragging is lame.
Education
  • Autodidact
    Maths - Music, 1963 - 2014
    It is hard for me to know where all my knowledge comes from exactly. I have the chance to know many things, like forever ! I only accept as TRUE, concepts, ideas, theorems .... I have understood by myself.
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May 24, 1963
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MORFLOW (PSN), BachMan (for being a big fan of JSB)