## Sunday, April 27, 2008

Recall that the "Discover Magazine" was the first source where I learned some details about superstring theory around 1987 (the article was translated by Ms Markéta Synovcová to Czech in my favorite VTM magazine, issue 14/1987).

I am convinced that it was the kind of the articles that the experts would endorse at that time which is why I liked it. It talked about the thrilling calculations of the anomaly cancellation in type I string theory and many other things.

Despite their video contest, string theory in two minutes, the magazine is very different these days, especially when it comes to the qualification of the writers. In 2006, I wrote about Susan Kruglinski's weird interview with a grumpy critic of physics.

In February 2007, the magazine constructed a hitparade in which only 2 or so serious physicists have made it to the "top seven". And two weeks ago, we discussed the opinion of the magazine that the Einstein revolution has gone too far (wow!).

But if you still have any doubts that the magazine is overrun by ignorants or worse, you should read a new article found by Sabine Hossenfelder:
The incompatibility of magnets with physics: a new revolution is imminent.
The writer is Bruno Maddox, the author of a novel about his little blue dress and many satirical essays.

What does he say? Well, he says that the magnets are a complete mystery, the Standard Model has no explanation why the hell the magnets work, and even more seriously, physicists hide this dirty little secret. The situation is so bad, in fact, that even Steven Weinberg - who should be almost as smart as Maddox because he has won a Nobel prize :-) - denies that there is a mystery.

Now, is it a humor piece or not? What does he exactly want to say? And when we are laughing, and I certainly am, are we laughing for the same reason he was planning? Well, I don't think so. His "Blinded by Science" columns in the Discover Magazine include "Stuck in Creationism" where he argued that creationists are passionate about science.

Is it a satire? It doesn't look so because Maddox visited the newly opened Creation Museum in 2007. If you accept that the essence of that text was serious, Maddox has argued that evolution is incompatible with science (just like magnets are incompatible with science) which implies that there is no tension between science and religion.

Magnets: the history of their theoretical description

Stones with magnetic properties have been known for millenia. Isaac Newton hasn't written the exact law for the magnetic force but he clearly gave us a hope that it is possible.

Newton has (almost) completely understood the gravitational force that was, at the time, described by the action at a distance: objects can instantly influence other, distant objects. As Maddox correctly writes, Newton was dissatisfied with his description involving the action at a distance because it should be impossible to influence distant objects directly.

Even though Newton opposed some field-theoretical paradigms, for example a wave representation of light, the comment above may be viewed as Newton's correct prophecy about field theory.

During the 18th century, various experimental and theoretical achievements showed the interrelation between electricity and magnetism - for example, magnetic fields can be created by changing electric fields and vice versa. The force was no longer viewed as an action at a distance but rather as a result of a "field" in between the objects - an invisible array of "arrows" that inform magnets and other objects what they should do at a certain point.

And all this progress was ultimately incorporated into Maxwell's equations of the 19th century - a theory that unified electricity, magnetism, and also light. According to this theory, the electromagnetic force doesn't act instantly. The influence is never faster than the speed of light - a fact that was later proven to be universal by Einstein's special relativity.

At that moment, the ordinary magnets - that are attached to your fridge - were understood by the new theory of classical electrodynamics. In the 20th century, quantum electrodynamics extended the theory of classical electrodynamics by including quantum phenomena - that you are unlikely to verify on the surface of your fridge. String theory is one more level above them and refines the theory at very high energies or temperatures (or very tiny distances) that are inaccessible not only by your fridge magnets but also by the existing cutting-edge technology.

Classical fields: a picture

In all cases, the newer theories completely reproduce the successes of the older, simpler, theories. That's why the right explanation of the essence of fridge magnets lies in classical electromagnetism. According to this theory, there is an electric vector and a magnetic vector (two arrows) at each point of space and time. They are described by equations - Maxwell's equations - that also include terms proportional to the "density of magnetized metals", if you wish. And vice versa: the pieces of metals follow equations that are influenced by the two "arrows", i.e. by the electric and magnetic fields.

If one solves these equations, they fully reproduce the observed behavior of magnets. And the observed behavior of magnets is kind of everything there is from a physicist's viewpoint.

In quantum field theory, electromagnetism may be described as an exchange of virtual photons (or virtual strings in string theory). But these pictures can be demonstrated to be mathematically equivalent to the old equations with "arrows" and "densities of magnets", at least in the mundane situations such as those involving fridge magnets. You don't need to talk about virtual photons if you have psychological problems with such concepts. The classical field theory is enough.

And those who are capable to understand the mathematics of virtual photons know that their impact on the behavior of magnets is identical to the impact calculated by Maxwell's equations. However, the formulation in terms of virtual photons is more useful for the calculation of particle collisions.

Virtual particles are composed entirely of math

Let me mention one more opinion that Bruno Maddox shares with Peter Woit, Lee Smolin, and zillions of retarded but vocal laymen of the same kind:
"As far as I can tell, these virtual particles are composed entirely of math and exist solely to fill otherwise embarrassing gaps in physics, such as the attraction and repulsion between magnets."
Here we have it. Virtual particles (or strings or gravitons or whatever these folks like to attack) are composed "entirely of math". Is it true or not? Well, saying that "something is composed of math" is not exactly a well-defined physical assertion. What does it mean for an object to be "composed of math"?

But imagine that Maddox uses a better verb, for example "virtual photons are described entirely by math". Is it true? You bet. They're not described by novels about blue dresses. But note that Maddox's sentence also has a second part that is implicitly claimed to follow from the first one. He says that because the virtual particles are described entirely by math, it follows that there must exist a huge gap in physics.

Is it true? Well, it is a complete nonsense. The more rigorous math we can use to explain a certain effect, the more we understand this effect.

A majority of the vocal laymen - not only Maddox but also Smolin, Woit, and zillions of others - are just completely incapable to understand this very fundamental rule about physical sciences. A question can be vaguely understood and we can only use words to explain how it works. When it is more understood, we can use approximate equations and order-of-magnitude estimates.

But what does it mean for a physical effect to be fully understood? Well, it means that we actually have the exact equations that agree with it. Ideally, we can also solve them - at least qualitatively - using our computers or, preferrably, in our heads. But there cannot be any "deeper" understanding of the essence of a phenomenon than the exact equations that describe it.

But, as Feynman said, the ignorance about mathematics is a severe limitation that prevents one from following physics. Nevertheless, many vocal laymen try to act importantly. Their idea about the "maximum understanding" assumes that all mathematics will have to be completely eliminated from the explanation. Indeed, the Standard Model - or string theory or any other theory in science - fails to achieve such a goal. But this fact doesn't mean that physics is incomplete or that it is plagued by gaps; it only means that Maddox et al. are plagued by a lethal mental insufficiency when they try to define the goals of science.

The importance and percentage of mathematics in our explanation of physical phenomena has been increasing for some time and it is all but guaranteed that this process will continue, whether or not the insufficient people get this point.

Ignorance, mystery, and self-confidence

Stefan, Sabine's husband, talks about the Dunning-Kruger effect whose basic rule says that the average expected self-confidence of a person is an increasing function of his ignorance. Well, unfortunately, it seems to be the case. But there exists another, less provoking law: the feelings that the world is mysterious are increasing functions of the ignorance, too.

Some people think that the black holes or the Planckian collisions remain completely and qualitatively mysterious to all the physicists. It is not really true these days. But one shouldn't be surprised that other, more ignorant people will be shocked by magnets or other simple things. Paradoxically, the more elementary physics effect you consider, the more people you can find who actively view it as a mysterious one. (That's because the very ignorant - and therefore very numerous - people don't even try to ask advanced questions.)

For example:

Mirrors. Why aren't the images upside down?

Around 2002, I've heard about the most important problem in physics from a humanity friend of mine in the Society of Fellows. He argued that the most pressing problem of the cutting-edge physics was the question why mirrors reflect the images left-to-right but no upside-down.

We were in the pub and it was a lot of fun. But I did want to know whether he was joking or not because the functioning of mirrors is something that many of us understood in the kindergarten. Even at average high schools, children are taught how not only flat mirrors but even parabolic and other curved mirrors work. But at the end, it seemed pretty clear that the conclusion that "mirrors are the most profoundly mysterious puzzle of the cutting-edge science" was a consensus of all humanity and social scientists at Harvard and other top places. ;-)

Mirrors: coordinates

Just to be sure, let me also include an answer to the question about mirrors. What the mirrors actually do is to reverse the front-back direction. If the axis "x" is perpendicular to the mirror while the axes "y" and "z" are parallel with it, i.e. if the mirror is located at "x=0", then the image of a point "(x,y,z)" in the mirror will have coordinates "(-x,y,z)". Only the sign of the front-back direction "x" has flipped. One can easily draw a picture that shows that if the angles of reflected beam agrees with the angle of the incoming beam, another old law that we can also prove from Maxwell's equations, then the reflected beams will behave just like if they were directly emitted by the point "(-x,y,z)" behind the mirror.

That's why the images "look" indistinguishable from actual objects at a different place.

Note that the coordinates "y" (left-to-right) and "z" (up-to-down) are treated in the same way if you transform "(x,y,z)" to "(-x,y,z)". Neither of them changes the sign. So why do we say that the mirror switches the left and the right? Well, it is because we tend to make an additional psychological transformation in our head. We want to imagine that the person in the mirror is real and that he is standing next to us and looking in the same direction.

How do we make him stand next to us? We can't mirror him because such a transformation is discontinuous and cannot occur to real people in the real world, just in the world of mirrors. Instead, we "tell him" to rotate by 180° around the vertical "z" axis. That transforms his coordinates "(-x,y,z)" to "(x,-y,z)". At this moment, his head is up just like ours and he is looking in the same direction but his left and right sides are reversed: it is because the "y" coordinate has changed the sign.

Why did we rotate him around the vertical "z" axis and not a horizontal axis? Because of psychological reasons connected with the gravitational field. The gravitational field makes us feel uncomfortable if our head is down and legs are up. So whatever we mentally do with our images should keep the head above the legs. And because we want to make the person in the mirror as similar to us as possible, we also transform him so that he looks in the same direction.

With this rotation, the interpretation of the left side and the right side gets switched. But if you avoid any transformations, it is only the front-back direction that is reversed in the mirror and both directions parallel to the mirror are treated in the same way: in fact, neither of them is reversed!

This brings me to another situation. Sometimes the images are reflected upside-down. Just imagine that there is a mirror on the ceiling. The image of the point with coordinates "(x,y,z)" has coordinates "(x,y,-z)" in this case: the head is objectively below the legs. Because the only simple transformation we can add in our heads is a rotation of the image around the vertical "z" axis, it can't change anything about the fact that the image is upside-down.

Summary

To summarize, there exist many physics questions whose answers are well-known to the people who actually study physics. Each of them has a certain degree of complexity and was understood at some point in the past. As students learn physics, they pretty much reproduce the history of physics. They begin to learn the simpler answers that have been known for millenia and some of them end up with the contemporary cutting-edge science. For example, the position of objects in the mirrors was certainly understood in the ancient Greece if not earlier - and small kids can also learn it - while the forces between magnets have been understood for a few centuries and high school pupils are the appropriate group to start to learn what these forces are and where they come from.

The fact about the preservation of the information by the black holes has been understood for more than a decade. So it is a newer result and whenever a result is newer, the number of people who actually understand it gets lower. But these people do exist. My estimate is that 10,000 people in the world really understand why we know that the information is not lost during the Hawking evaporation. It is a small percentage of the world's population but absolutely speaking, it is not such a low number. They are just not being heard.

If you're a rather generic member of a large enough group, be almost sure that when you don't understand how something - something that demonstrably exists in reality and that is also described in a textbook at a certain level - works, it is almost certainly because of your own limitations, i.e. because your knowledge is not quite at a sufficient level, or because your formal or informal teachers haven't been good enough in explaining the mystery to you. It is not due to the incompleteness or errors in the existing science.

And that's the memo.

#### 1 comment:

1. My problem is explaining how magnets change water thus making swelling go down faster thus reducing pain. What has worked the best is to explain that water is like a bowl of spaghetti but by speeding up the electrons it changes into little spaghetti Os that move more freely in the tissue.
Hans Albert Quistorff, LMP
Antalgic Posture Pain Specialist