S03E05:The Creepy Candy Coating Corollary

In Catch-22, Airman Dunbar spends all his free time with people he doesn’t like.  That makes time go by slower so he can enjoy life longer.

Physicists have their own way of slowing time.    Moving clocks tick slower than ones at rest.  Not because something goes wrong with the mechanism of a moving clock, but rather the passage of time itself slows down.  This effect, called “time dilation” is sufficiently familiar that the writers used it in joke by Leonard about a double-date that couldn’t end soon enough:  “Approaching the speed of light doesn’t slow down time. Approaching them does.”

It is tempting to use this as a launching point to discuss how a little-known patent clerk in Switzerland spent all his free time in 1905 thinking about physics problems (there was no internet or video games) and predicted all this.   That was Einstein and this was his special theory of relativity.  Normally, I love teaching special relativity.   I especially love teaching it to freshmen since so little math is required: just  distance equals rate times time and how a right-triangle works.  Yet,  I won’t do it here because it really isn’t because of the theory of relativity that we believe time goes slower for moving objects.  True, the theory of relativity is beautiful and Einstein was a one of the smartest guys ever.  But physics departments’ trash cans are full of beautiful theories and many brilliant people are long forgotten.  The real reason we believe in time dilation  is because experiments say it is so.  It is better to delve into one of them.

Particle accelerators (a.k.a. atom smashers) are great places to find things moving near the speed of light.     In the 1990’s I worked at the world’s largest particle accelerator, an international scientific laboratory called CERN, as a “post-doc”.  (A post-doc is the few years in a physicist’s life just after receiving a doctorate but before taking on a permanent post.  Although it has never been stated in the show, I think Leonard, Sheldon and Raj are all post-docs.)   While I was working at CERN,  my friends and I needed particles to test and align our detector.  The accelerator division kindly  sent us a beam of particles called muons.  Muons are just like electrons but they are heavy and undergo radioactive decay quickly, living on average for only 2.2 millionths of a second (0.0000022 seconds).  Even though these muons moved at nearly the speed of light, even light traverses only 2200 feet in 2.2 millionths of a second.  You might think that when being sent from one side of the (large) lab to the other,  you would lose most of them to decay before they arrived.  Yet,  “time dilation” came to our rescue.  The muons we needed to calibrate our detector moved at 99.9999% the speed of light and we saw their internal clocks slow down by a factor of 1000, meaning they lived 1000 times longer.   It was no problem to bring them a safe, long distance from the accelerator, down to our experiment, where we made good use of them.

CERN. The world’s largest and most powerful particle accelerator. Its longest beampipe crosses between two countries, France and Switzerland

If you could ask them, what would the muons say happened?  They likely would say that they were are at rest the whole time and rather it was me, my friends,and the whole lab moving towards them at 99.9999% the speed of light.  They are not moving so they would still measure their own average life as 2.2 millionths of a second; so how did they get across the lab to our detector without decaying?  If asked, the muons would report the distance across the lab to our experiment was 1000 times shorter than we would.  Moving near light speeds, moving objects become much shorter.  Such “length contraction” is an experimental fact.   While the muons and I may have disagreed why they reached my experiment without decaying, we both agree on the important part:  They did.

Could speed be the secret to Dunbar’s quest for longevity?  Can physicists make fountain of youth by the slowing down time with speed?  Yes…but there’s a catch.  Even if we put you on a fast rocket ship, since time slows down, your metabolic rate slows as well.  Everything around you undergoes the same slower passage of time as witnessed by the rest of us.  So Leonard has it exactly right.   He would experience time unfolding just as if he were at rest.  In fact, Leonard could well say that he really is the one at rest and it is everyone else that is moving.

That’s some catch, that Catch-0.0000022 .

S03E04: The Pirate Solution

In tonight’s episode Raj works alongside Sheldon on “The Dark Matter Problem”.   In my opinion this is the biggest problem in physics today that we have a hope of solving.

Vera Rubin discovers galactic dark matter.

Physicists love it when theories have problems. Like pulling a stray thread on a sweater, it might give you just a tuft of yarn, or it might unravel the whole thing.  The best thing that can happen to a scientist is to ruin somebody’s sweater.

One of the biggest problems of the 19th century was the age of the Earth appeared much larger than the age of the Sun.  Geologists argued (correctly) that the Earth’s age was measured in billions of years based on sedimentation rates.  Meanwhile physicists calculated that for any known energy source, the Sun would have burned out after at most 20 million years.  The physicists’ arguments were convincing and screwed up geology for a century.  Ultimately the problem was resolved by a major change in the way we understand energy.   The advent of nuclear physics in the 1930’s explained that sunshine is powered by nuclear reactions.  By converting mass into energy, a previously unknown energy source, nuclear reactions are nearly a million times more powerful than chemical reactions.  They allow us a 4.5 billion-year old sun.

Maybe that is a bad example to encourage pursuing problems.  Although the Sun-versus-Earth’s age problem signaled a misunderstanding of utmost importance, it was solved only because of work in a completely different subject than astronomy and geology.  This story is typical.

Often physicists just find things out by having a lucky break while toiling away on some other problem.  This happened to physicists in Japan working underground with a big tank of water they called “Kamiokande”.  I remember as a kid reading an essay by Isaac Asimov about their experiment: “After Many a Summer Dies the Proton”, describing their search for a decaying proton.  The theorists said they should find it, since it would solve some of their theoretical problems. Asimov’s title was premature—now, more than twenty-five years later, neither the Japanese nor any other experiment has ever seen a single proton decay.  Meanwhile, the Kamiokande physicists had to study particles called neutrinos crossing their detector since they were a source of noise.  They found while studying this noise an amazing effect called “neutrino oscillations”, which revealed essential properties of neutrinos.  The Japanese physicists had made the biggest scientific discovery in particle physics in decades.  (During that time I was in  Geneva also looking for “neutrino oscillations” with parameters the theorists said were more likely.  We found nothing.)  Had the Kamiokande experiment not been built to chase down this wrong proton-decay prediction by theorists, we wouldn’t have this important discovery.

(Asimov’s essay was just  one of many he wrote about science for the monthly “Fantasy and Science Fiction Magazine”. While I was in junior high school, Asimov’s science article was always the first thing I read when the magazine arrived, not the science fiction stories.  Perhaps that foretold why I am now only a science consultant instead of a writer.)

Our century’s problem, the dark matter problem, has many facets, but the most glaring is the speed of our solar system.  Just as Earth and other planets in our solar system revolve around the Sun, our whole Solar system orbits  the center of the Milky Way galaxy.  While every year the Earth goes around the Sun, every “galactic year” (250,000,000  Earth years, or  nearly 2 billion dog years) the whole solar system makes a full galactic orbit.   Every planet that goes around the Sun does so as described by Newton’s laws of mechanics.  The farther out a planet is from the Sun, the slower it should move, given fairly precisely by the square root of the distance.    For example, Saturn is about 9.5 times farther from Sun than the Earth is from the Sun, and so moves square-root(9.5)=3.1  times as slowly as Earth.    This works because the gravitational pull of the Sun keeps the planets moving in near-circles.   By adding up all the objects that astronomers see, the core of the galaxy should cause the stars in the rest of the galaxy to undergo orbits analogous to the planets’ motion around the Sun.  However, when astrophysicist Vera Rubin made the measurements,  she measured no drop in speed at all. Since astronomers can only count what they can see, what is light, we suspect there is dark matter filling the galaxy that pulls stronger on our solar system and other stars.   So 250,000,000 years may be a long time, but without dark matter it would be much longer.

Speed of stars vs distance from the center of the Milky Way. The Earth and Sun are located at about 8 on the x-axis.

The discovery of dark matter has told us that we don’t even know what 90% of the matter is in the universe.  While we may all be hoping Sheldon gets a Nobel Prize, let’s hope Dr. Rubin is honored as well.

Physicists would love other proof of dark matter, but we don’t even know what it is.  That is what Sheldon and Raj were working on.  Some physicists try to find it in space.  If the dark matter is made of particles that can collide and annihilate, they will give up very energetic light called gamma-rays.  This light is more powerful than even X-rays.  Gamma-ray telescopes around the world are looking for evidence of these dark matter collisions. If you look carefully at the white board, you will see the name of one gamma-ray telescope friends of mine built called “VERITAS”.  You’ll also see a sketch of how it works:  gamma rays hit the upper atmosphere and produce small amounts of light detected by big curved mirrors on the ground.   Meanwhile other physicists are competing to be the first to find the dark matter by observing directly the extremely small amount of energy a dark matter particle might deposit in a detector as they pass through Earth.   Some experiments use Sodium (which has an atomic mass 23) and other use Xenon (with atomic mass 131).  Now you know why Raj crosses out 131 and changes it to 23.  Sheldon was calculating the rate for the wrong target material, xenon not sodium.

Tune in next week in two weeks to watch  the apartment’s whiteboards for Sheldon catching up by studying sodium.

S03E03:The Gothowitz Deviation

In tonight’s episode of The Big Bang Theory, the writers dared to go where most physicists will not,  to the philosophical underpinnings of quantum mechanics.  When Penny asks Sheldon to dance with her, he replies:

To tackle a description of the Many Worlds Theory of quantum mechanics (more often called an “Interpretation” rather than “Theory”), we first need to delve into quantum mechanics itself.

Before physicists realized that quantum mechanics was necessary, their view of the world held that the outcome of any event could be completely determined–as long as you had precise enough measurements beforehand.    If you dropped a rose petal into a hurricane, all you needed was the positions and velocities of every molecule of air at just one moment and then you could calculate the final location of the rose petal with certainty.   (OK, you would also need to know all about all the birds and pieces of vinyl siding flying around too.)  As a practical matter, you could never really do this, but at least in principle it would have been possible.

This view changed forever with the discovery of quantum mechanics in the 1920’s and its experimental tests over the following decades.  The outcome of  many situations can never be predicted with certainty.  Take for example carbon-11, a radioactive atom used in life-saving medical imagers called PET scanners.   That carbon atom’s “half-life” is 2 minutes, meaning that half the carbon-11 atoms you possess at any one time will decay and disappear in 2 minutes.  But what if you had only one atom of carbon-11?  No physicist can ever say when it will decay with certainty.  The best we can do is say  that it has a 50% chance of still being around 2 minutes from now; a 25% chance 4 minutes from now; and 1 in a billion chance of being around an hour from now.   To know the exact fate of any one atom  is not a matter of not being able to see well enough inside the atom.  There is no way of ever knowing.

This fundamentally probabilistic description of nature bothered some physicists.   Even Albert Einstein objected famously:  “I am convinced that He [God] does not play dice”.   Convinced as he may have been, and as brilliant as he may have been, experiment trumps genius.    Clever experiments have shown that there is no room for what Einstein was sure of:  hidden deterministic variables that underlie the probabilistic laws of quantum mechanics.

Philosophical questions arise when you put the atom in a box for say 2 minutes and let no one check on it.  Meanwhile the condition of the atom during that time can still affect other measurements, so descriptions of the atom during this time turn out to be both important and open to interpretation.   The founders of quantum mechanics, working largely in Copenhagen, believed that the best way to view the situation was that the atom was simultaneously in a decayed and un-decayed state.   They said that only after some observer comes along and looks in the box would the atom be forced into one state or another.   In the Copenhagen Interpretation, the act of observation changes the universe.  Such is the typical training that physicists such as myself received as undergraduates.

The Copenhagen Interpretation raises difficult, perhaps unanswerable questions:  How large does something have to be to constitute an observer?  If the atom bounces into  another atom that detects its presence, is that other atom an observer?  Is a large, complicated detector a valid observer?  Must the observer possess consciousness?  Must it be human consciousness or can it be a cat’s?  Does another observer that does not know the outcome possess a different “reality”?  The most likely answer to such question is “Shut up and calculate!”.

Thus things stood for decades.  An alternative, the so-called “Many Worlds Interpretation”, emerged from the 1957 Ph.D. thesis of Hugh Everett at Princeton.  Everett never labeled his interpretation “Many Worlds” but rather originally titled his paper   “Wave Mechanics without Probability” ( “wave mechanics” meant “quantum mechanics”)  He later changed the title to something more abstruse to placate his Ph.D. committee.

In Everett’s interpretation, the probabilities were only a consequence, not an elemental part of the theory.   Not only is the state of the atom described by the equations of quantum mechanics, so are all the detectors and observers in the world.   When an object and observer meet, the two affect each other according to the usual rules of quantum mechanics.  No new process happens at the moment of observation.    Of course when an experimentalist observes the atom he or she perceives it as decayed or not; but the experimenter is now part of the system including the atom, experiencing only an “inside” view.  Meanwhile someone else, with an “outside” view, still entertains all outcomes.  The interpretation does not rest on dice.

The persistence of both outcomes in Everett’s interpretation is often described as two different worlds that propagate forward and independently in time:   one where the atom decayed and one where it did not.   Had the life of a cat  hinged on outcome of the decay,  it is often said that our world branches into two worlds, one with a live cat and one with a dead cat.  (Here we are adopting  Schrodinger’s cat, described in the season-one finale, S01E16.  These are hypothetical experiments only—no cats were harmed.)  The critical question of why we experience the world as 100% live or dead cats, never as a mixture,  was left by Everett as an exercise for the reader.

Soon after completing his Ph.D. thesis, Everett ventured to Copenhagen to explain his ideas to Niels  Bohr.  He failed miserably.  Everett left academia, never to return. The world took little notice of his work.

But times have changed.  At a recent meeting of quantum physicists, the Many Worlds Interpretation received more votes than the old Copenhagen interpretation as the picture closest to the participants’ own views.  Still, physics is not a popularity contest.   These were personal opinions, much like Einstein’s unsubstantiated claim about dice.   For the debate to be meaningful there needs to exist some prediction for which the two differ.   Hope exists in some quarters to find such tests, but I can find no specific experiment put forward.   It remains that no matter how opposed the views of two physicists on the topic, they will all calculate exactly the same outcomes of experiments.  Without an experimental prediction that differs, the fight is just a war of words not physics.  A distinction without a difference.

Except for one.  Science fiction writers and physicists alike have entertained one intrepid experiment.   The means of distinction rely on an experimenter having no fear of  approaching quantum suicide–by playing a game of quantum  Russian Roulette.  The observer  shoots a gun at his or her own head with a 50% chance of having a bullet vs. a blank.  After many trials the physicist will know if Many-Worlds is favored, since there is no experiencing a world where you are dead.  Many Worlds predicts that the observer will eventually live in a world having survived the game 100 times or more.  Unfortunately, we can never can never know what result our brave physicist friend found.  There is no way for the survivor(s), if any, to tell us.

I’ve done some stupid things for physics…

but I won’t be volunteering for the quantum suicide experiment.  It violates my university’s ethics protocols for experiments involving human subjects.

In the Many Worlds Interpretation, some measurements can encompass an infinite number of final states, or as Sheldon characterizes it:  an infinite number Sheldons in an infinite number of universes.   Luckily for us, the number of Sheldons is not just an ordinary infinity, but an even larger one called  uncountably infinite number of Sheldons.