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Lies, Damned Lies, and Quantum Statistics

samzenpus posted about a year and a half ago | from the do-the-math dept.

Math 53

quax writes "Getting a scientific paper published that goes against the grain of conventional wisdom was never easy. Especially when it seems to contain an obvious glaring mistake. Fortunately despite already being some kind of pop celebrity with no shortage of fan mail, Einstein still opened letters he received from strangers. And this is how a trivial, fateful counting mistake was able to change the course of physics forever."

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53 comments

uhuh (5, Funny)

Anonymous Coward | about a year and a half ago | (#40885869)

Dear theoretical physicists,

Admit that most of your fields have become a branch of overpriced mathematics and stop boring us with your tales of 100 years ago.

Re:uhuh (4, Interesting)

mister2au (1707664) | about a year and a half ago | (#40885981)

or are the physicists the abstract artists of the science world while the mathematicians are the boring paint suppliers?

just saying ...

Re:uhuh (0)

Anonymous Coward | about a year and a half ago | (#40886269)

Mathematical physics is a major in various math degrees, just like finance and risk is. I don't know what should be concluded about paint, however. The fields are so intertwined that they could be called the same thing. Switching polarity doesn't help.

Re:uhuh (4, Informative)

RatherBeAnonymous (1812866) | about a year and a half ago | (#40888583)

Physicists don't think that mathematics and physics are the same thing.

When I was a physics undergrad in the mid-90's I was advised against going into the Mathematical Physics program by one of my PHD physics professors. He told me, and I'm paraphrasing, that mathematical physicists rarely make groundbreaking discoveries. He claimed the field is hampered by trying to get the math right, and that there are equations that, while being technically incorrect, are useful in general even though they fall apart in edge cases, and that many mathematical physicists find using such equations distasteful. I dropped out of physics a long time ago so I don't have my own opinion on the quality of mathematical physicists as researchers.

Re:uhuh (1)

martin-boundary (547041) | about a year and a half ago | (#40892771)

Mathematical physics is a major in various math degrees, just like finance and risk is.

Except that mathematical physics is still a kind of science, whereas finance and risk is, well... pseudo.

Re:uhuh (0)

Anonymous Coward | about a year and a half ago | (#40886499)

I suppose that denying the existence of pure mathematics is one way of staging a coup ;-).

When I were a lad, everyone celebrated the Platonic model of the universe and nascent physicists were still suckling at the teat of reality.

captcha: traitor. En garde!

What is this? (1)

Anonymous Coward | about a year and a half ago | (#40885873)

Meaningless and ambiguous summary and a slashdotted server, I want those 2 minutes of my life back.

Re:What is this? (4, Interesting)

bryonak (836632) | about a year and a half ago | (#40885913)

You didn't miss much, here's the cached article [googleusercontent.com]

In my opinion it's a lousy written piece with half of the sentences being there for the sole purpose of filling white space.

Re:What is this? (1)

Anonymous Coward | about a year and a half ago | (#40886007)

This article is a waste of time and there really is no point in posting it ony Slashdots front page.

Re:What is this? (0)

Anonymous Coward | about a year and a half ago | (#40886067)

This.

I want two minutes of my life back.

Re:What is this? (1)

RandomFactor (22447) | about a year and a half ago | (#40886097)

Yes. Skip the first four paragraphs and you'll reach the point before getting too annoyed with the fluff.

But in the year 2012... (5, Funny)

Anonymous Coward | about a year and a half ago | (#40885879)

...due to a 500 internal server error and a useless summary that is written to bait and not inform, we won't learn what that mistake was and how it changed the course of physics forever.

Re:But in the year 2012... (4, Informative)

stms (1132653) | about a year and a half ago | (#40885901)

Always check Google's cache [googleusercontent.com].

Re:But in the year 2012... (5, Funny)

Anonymous Coward | about a year and a half ago | (#40885985)

Describing Einstein as the Lady Gaga of Science is probably why the article is now 403 forbidden.

Re:But in the year 2012... (5, Funny)

ColdWetDog (752185) | about a year and a half ago | (#40886179)

Describing Einstein as the Lady Gaga of Science is probably why the article is now 403 forbidden.

Dunno.

Bad hair - check
Bushy eyebrows - check
Toneless whistling - check
Incomprehensible 'lyrics' - check

You have to admit, there are certain similarities.

I would not be surprised to learn that Lady Gaga smokes a pipe.

Re:But in the year 2012... (0)

Anonymous Coward | about a year and a half ago | (#40887491)

Now all you need is someone to get relativity and e=mc^2 in the tune of pokerface...

Re:But in the year 2012... (1)

khallow (566160) | about a year and a half ago | (#40890645)

i was aware that Lady Gaga has machine guns for breasts, but a pop icon too? That's fascinating.

Re:But in the year 2012... (5, Funny)

Alkonaut (604183) | about a year and a half ago | (#40885915)

I think slashdotters observing the state of the server has changed the state of it.

Re:But in the year 2012... (4, Informative)

Anonymous Coward | about a year and a half ago | (#40885975)

Lies, Damned Lies, and Quantum Statistics?
Posted on August 4, 2012 by Henning Dekant

Statistics has a bad reputation, and has had for a long time, as demonstrated by Mark Twain's famous quote that I paraphrased to use as the title of this blog post.

Of course physics is supposed to be above the fudging of statistical numbers to make a point. Well, on second thought, theoretical physics should be above fudging (in the experimental branch, things are not so clear cut).

Statistical physics is strictly about employing all mathematically sound methods to deal with uncertainty. This program turned out to be incredibly powerful, and gave a sound foundation to the thermodynamic laws. The latter were empirically derived previously, but only really started to make sense once statistical mechanics came into its own, and temperature was understood to be due to the Brownian motion. Incidentally, this was also the field that first attracted a young Einstein's attention. Among all his other accomplishments, his paper on the matter that finally settled the debate if atoms were for real or just a useful model is often overlooked. (It is mindboggling that within a short span 0f just 40 years ('05-'45) science went from completely accepting the reality of atoms, to splitting them and unleashing nuclear destruction).

Having early on cut his teeth on statistical mechanics, it shouldn't come as a surprise that Einstein's last great contribution to physics went back to this field. And it all started with fudging the numbers, in a far remote place, one that Einstein had probably never even heard of.

In the capital of Bangladesh, a brilliant but entirely unknown scholar named Satyendra Nath Bose made a mistake when trying to demonstrate to his students that the contemporary theory of radiation was inadequate and contradicted experimental evidence. It was a trivial mistake, simply a matter of not counting correctly. What added insult to injury, it lead to a result that was in accordance with the the correct electromagnetic radiation spectrum. A lesser person may have just erased the blackboard and dismissed the class, but Bose realized that there was some deeper truth lurking beneath the seemingly trivial oversight.

What Bose stumbled upon was a new way of counting quantum particles. Conventionally, if you have two particles that can only take on two states, you can model them as you would the probabilities for a coin toss. Lets say you toss two coins at the same time; the following table shows the possible outcomes:
                        Coin 1
                          Head Tail
  Coin 2 Head HH HT
              Tail TH TT

It is immediate obvious that if you throw to coins the combination head-head will have a likelihood of 25%. But if you have the kind of "quantum coins" that Bose stumbled upon then nature behaves rather different. Nature does not distinguish between the states tails-head and head-tails i.e. the two states marked green in the table. Rather it just treats these two states as one and the same.

In the quantum domain nature plays the ultimate shell game. If these shells were bosons the universe would not allow you to notice if they switch places.

This means, rather than four possible outcomes in the quantum world, we only have three, and the probability for them is evenly spread, i.e. assigning a one-third chance to our heads-heads quantum coin toss.

Bose found out the hard way that if you try to publish something that completely goes against the conventional wisdom, and you have to go through a peer review process, your chances of having your paper accepted are almost nil (some things never change).

That's where Einstein came into the picture. Bose penned a very respectful letter to Einstein, who at the time was already the most famous scientist of all time, and well on his way to becoming a pop icon (think Lady Gaga of Science). Yet, against all odds, Einstein read his paper and immediately recognized its merits. The rest is history.

In his subsequent paper on Quantum Theory of Ideal Monoatomic Gases, Einstein clearly delineated these new statistics, and highlighted the contrast to the classical one that produces unphysical results in the form of ultraviolet catastrophe. He then applied it to the ideal gas model, uncovering a new quantum state of matter that would only become apparent at extremely low temperatures.

His audacious work set the state for the discovery of yet another fundamental quantum statistic that governs fermions, and set experimental physics on the track to achieving ever lower temperature records in order to find the elusive Bose-Einstein condensate.

This in turn lead to the development of the Penning ion traps that were the key technology in building the first realizations of quantum computers, and are still at the heart of the NIST quantum simulator.

All because of one lousy counting mistake ...

But in the year 403... (1)

mcgrew (92797) | about a year and a half ago | (#40885983)

Forbidden

You don't have permission to access /2012/08/04/lies-damned-lies-and-quantum-statistics/ on this server.

Additionally, a 403 Forbidden error was encountered while trying to use an ErrorDocument to handle the request.

Slashdotted

Bose-Einstein Statistics (1)

Anonymous Coward | about a year and a half ago | (#40885959)

its called Bose-Einstein statistics

http://en.wikipedia.org/wiki/Bose–Einstein_statistics

not really sure why this is news

Re:Bose-Einstein Statistics (5, Funny)

mister2au (1707664) | about a year and a half ago | (#40886021)

not really sure why this is news

I blame it on relativistic time dilation ...

to an observer in travelling at Slashdot speed this appears to have just occurred, whilst to a stationary observer 87 years appear to have passed ...

this dilation seems to apply uniformly across most observed Slashdot articles (albiet with yet-to-be-explained time loops as well!)

Re:Bose-Einstein Statistics (1)

Anonymous Coward | about a year and a half ago | (#40886325)

this dilation seems to apply uniformly across most observed Slashdot articles (albiet with yet-to-be-explained time loops as well!)

Who needs LHC when Slashdot have already found the missing dimensions hidden in the loops of time. The our collective nerd energy will always produce greater energies via troll collisions than any particle accelerator can produce.

Re:Bose-Einstein Statistics (0)

Anonymous Coward | about a year and a half ago | (#40894231)

/. editors are moving backwards at a fraction of C ?

Re:Bose-Einstein Statistics (1)

quax (19371) | about a year and a half ago | (#40888161)

Not really sure why this is news.

The /. byline is: News for nerds stuff that matters.

I already interpreted this as with an OR condition. I.e. sometimes the stuff that matters doesn't have to be all new to be interesting for the /. crowd.

I think the little known fact that a major insight in physics came from an initial "mistake" is such an interesting morsel.

Especially when contemplating that nowadays physicists are constantly beset by crackpots and have subsequently being conditioned to quickly dismiss information that seems faulty. I am certainly as guilty of this as anybody. If I think I spot an obvious mistake in a paper from a dubious source I don't bother to read the rest.

If Einstein would have operated like this Bose's paper would have never been published.

Anyhow, the newsy aspect of this story is that Einstein's paper on this subject [wavewatching.net] is now available in a new translation. For some reason there was no English version anywhere to be found on the Internets.

Re:Bose-Einstein Statistics (1)

silentcoder (1241496) | about a year and a half ago | (#40892575)

>I think the little known fact that a major insight in physics came from an initial "mistake" is such an interesting morsel.

Now that is not news, as far as I can tell, the vast majority of true breakthrough's happen when somebody makes a mistake and discovers that it leads somewhere interesting.
Breakthroughs by definition imply that somebody thought outside the current confines of the box - this is very difficult (despite what motivational speakers would have you believe), quite often however when a skilled person makes a trivial error in the steps, they discover that the "error" is actually just a small step outside the box that leads to a perfectly valid conclusion and open up entirely new concepts to discover.

In mathematics this is particularly common - at least in part because of how mathematicians actually do research in their own field. When somebody does come up with a new concept of mathematics (read the history of transfinite numbers for a beautifully illustrative example) nobody really bothers with the fundamentals of making it fit in well with other basic maths. No point doing all that terrible drudge work if the idea doesn't lead somewhere interesting - so for a while everybody is just expanding the idea. It's like a house build wrong way round. There are no foundations, the first floor is just bare walls, the second floor has sparse furniture and carpetting while the third floor starts looking like a suite at the hilton.
If the idea does lead somewhere interesting, if some nice possibilities arise, it eventually starts causing problems that the house lacks foundations however. Some of those new things you're exploring is problematic, you're getting contradictory proofs - and you can't figure out which one is wrong. This is when it gets INTERESTING to do the drudge work, go fill in the foundations and carpet the first floor, because in doing so you work out what is structurally WRONG up on top, and can tell the correct and the incorrect maths apart again.

Because physics is so intrinsically mathematical (and has been ever since at least Newton), this impacts on it directly. Often new ideas in physics are based on mathematical concepts which don't yet have proper foundations. Sometimes it's the physicist who through a mistake discovers where the foundation is wrong or missing.
This is a classic example - a human error (in following steps) turned out to actually be more correct than the steps were. That allowed us to see that we'd been using the wrong KIND of statistical probability for a significant part of quantum mechanics for a very long time and solved a number of unanswered questions.

Re:Bose-Einstein Statistics (1)

quax (19371) | about a year and a half ago | (#40894509)

Wouldn't expect mathematics to have this much trouble to get published though.

If Bose's work had not been picked up by Einstein it would have gone unnoticed.

Mathematics as purely logical science doesn't have the problem that it may ran afoul preconceived notions about how nature operates.

Re:Bose-Einstein Statistics (1)

silentcoder (1241496) | about a year and a half ago | (#40899027)

Oh it happens, though perhaps less rarely. Just ask George Cantor....

Re:Bose-Einstein Statistics (1)

quax (19371) | about a year and a half ago | (#40899713)

Interesting. Just read up on it [wikipedia.org].

Had no idea that transfinite numbers were such a controversy. When I first learnt about the distinction between countable and non-countable infinite sets I thought it made perfect sense.

Amazing that it was so offensive to many great mathematicians. (Not surprised about the religious objections though. After all these people seem to live for the opportunities to get their nickers in a bunch over nothing).

AGW Anyone? (-1)

Anonymous Coward | about a year and a half ago | (#40886093)

Gee I thought you were talking about all the made up evidence pointing to AGW.

Oh well.

http://scottishsceptic.wordpress.com/2011/05/25/how-is-global-warming-a-fake/

Summary of the article in a Haiku (2)

tstrunk (2562139) | about a year and a half ago | (#40886329)

Science did not know
Identical Particles
Exist. Bose did.

There's not much more content. Bose introduced the concept of identical particles. This lead to Bose and Fermi statistics and new insight in physics.
Plus: Bose had trouble publishing it.

bogus slashdot summary (3, Insightful)

bcrowell (177657) | about a year and a half ago | (#40886783)

The slashdot summary is completely garbled. It contains this sentence: "Especially when it seems to contain an obvious glaring mistake." There is nothing like this in the article. The mistake described in the article is a mistake that Bose made during a lecture, which happened to lead to a calculation that described how nature actually works. By the time Bose wrote his paper, there was not "an obvious glaring mistake." It was now presented as a scientific hypothesis, intentionally formed, about how nature actually works.

Re:bogus slashdot summary (1)

quax (19371) | about a year and a half ago | (#40887651)

Reading comprehension?

"Especially when it seems to contain an obvious glaring mistake."

Bose's paper was rejected because the mainstream opinion was that he didn't count the photons correctly. This was exactly the kind of "mistake" that he made in his lecture that miraculously lead to the correct radiation spectrum formula (Planck's law).

Einstein directly addressed this critique in his follow up paper [wavewatching.net] (paragraph 7 search for "Ehrenfest").

So, I fully stand by my summary.

Re:bogus slashdot summary (0)

Anonymous Coward | about a year and a half ago | (#40888085)

I still don't get it. Maybe you can help me out here...

1) Did he actually make a mistake in his lecture?

2) Did he realize this was a mistake? When?

3) Was there a mistake in his paper and research?

  I can't find a straight answer anywhere...

Re:bogus slashdot summary (2)

quax (19371) | about a year and a half ago | (#40888459)

1) Did he actually make a mistake in his lecture?

2) Did he realize this was a mistake? When?

3) Was there a mistake in his paper and research?

1) When he lectured on the suspect he wanted to demonstrate how the know statistical physics did not produce the Planck law but rather the ultraviolet catastrophe. Hence he wanted to demonstrate that the theory at the time was faulty. But he made a "mistake" along the way and out popped Planck's law.

The "mistake" was the way that you count the states available to a photon. I.e. as illustrated in the coin toss example nature doesn't count photons as distinguishable particles like coins. Nature counts head-tail and tail-head as only one state.

This is obviously wrong in the macroscopic domain. Bose realized that this "mistake" must actually correctly reflect how nature accounts for states in the quantum domain.

2) During or shortly after his lecture Bose must have realized that his "mistake" must actually reflect the correct statistics for photons.

3) We now know that Bose's static is entirely correct for Bosons, but at the time all particles were imagined to exhibit the same statistic as macroscopic particles. I.e. they were thought to be always properly distinguishable. But it turns out you cannot put "labels" on Bosons, not even theoretically. I.e. if you have two identical Lego pieces and you exchange them between two identical Lego projects, you may not be able to immediately tell the difference, but you know that a real change occurred and you could make this explicit by labeling and keeping track of the Lego bricks. At the quantum domain there is no equivalence to this, in a quantum "Lego" project (e.g, a Bose-Einstein condensate) nature will not make a difference, not even in principle, if you exchange two identical particles that are in the same quantum state. Actually, even the concept of such an exchange loses all meaning.

He's Lucky... (0)

Anonymous Coward | about a year and a half ago | (#40886913)

...They could have called him a Denier and not even looked at his paper.

uhh... (1)

seansobes (1691592) | about a year and a half ago | (#40887511)

This article is the biggest load of shit I've ever read. Nothing was explained. It was just rambling in a bad English dialect.

Re:uhh... (1)

quax (19371) | about a year and a half ago | (#40887557)

You can always go to the original articles that are linked on the site if you really want to understand it.

Bose's paper [wavewatching.net]
Einstein's paper [wavewatching.net]

Re:uhh... (1)

Guignol (159087) | about a year and a half ago | (#40893819)

Out of mod points, offtopic for this particular thread
Anyway, I don't understand why you are being so badly trolled against, but before you leave completely disgusted I wanted to let you know that your submission was welcome and apreciated, it was a nice article, and as someone before me pointed out, stuff that matters is not an AND relation to news for nerds, plus, there is the new translation so it is news anyway.
So thanks quax and post again ;)

Re:uhh... (1)

quax (19371) | about a year and a half ago | (#40894543)

Thanks :-)

And no worries, I've been long enough on this site to take the good with the bad.

Incorrect author for the quote (0)

Anonymous Coward | about a year and a half ago | (#40888025)

Apparently the author of the article doesn't appreciate getting his/her facts checked. Luckily someone else was able to pass the moderator and post the following.
http://en.wikipedia.org/wiki/Lies,_damned_lies,_and_statistics

-- Mark Twain popularized the quote but the originator is in question.

Re:Incorrect author for the quote (1)

quax (19371) | about a year and a half ago | (#40888663)

Actually the author of the quote was Mark Twain as he was the first to put it in print.

But he was by his own accord not the the one who originally uttered it.

(deja vu...) (0)

Anonymous Coward | about a year and a half ago | (#40901499)

(but now seems more boo than vu).

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