Relativistic Baseball

One of my favorite comics, XKCD, is now up to something new: answering interesting questions with physics!

The first question: What would happen if you tried to hit a baseball pitched at 90% the speed of light? The answer…

The constant fusion at the front of the ball pushes back on it, slowing it down, as if the ball were a rocket flying tail-first while firing its engines. Unfortunately, the ball is going so fast that even the tremendous force from this ongoing thermonuclear explosion barely slows it down at all. It does, however, start to eat away at the surface, blasting tiny particulate fragments of the ball in all directions. These fragments are going so fast that when they hit air molecules, they trigger two or three more rounds of fusion.

After about 70 nanoseconds the ball arrives at home plate. The batter hasn’t even seen the pitcher let go of the ball, since the light carrying that information arrives at about the same time the ball does. Collisions with the air have eaten the ball away almost completely, and it is now a bullet-shaped cloud of expanding plasma (mainly carbon, oxygen, hydrogen, and nitrogen) ramming into the air and triggering more fusion as it goes. The shell of x-rays hits the batter first, and a handful of nanoseconds later the debris cloud hits.

When it reaches the batter, the center of the cloud is still moving at an appreciable fraction of the speed of light. It hits the bat first, but then the batter, plate, and catcher are all scooped up and carried backward through the backstop as they disintegrate. The shell of x-rays and superheated plasma expands outward and upward, swallowing the backstop, both teams, the stands, and the surrounding neighborhood—all in the first microsecond.

Suppose you’re watching from a hilltop outside the city. The first thing you see is a blinding light, far outshining the sun. This gradually fades over the course of a few seconds, and a growing fireball rises into a mushroom cloud. Then, with a great roar, the blast wave arrives, tearing up trees and shredding houses.

Everything within roughly a mile of the park is leveled, and a firestorm engulfs the surrounding city. The baseball diamond is now a sizable crater, centered a few hundred feet behind the former location of the backstop.

This is going to be awesome.

The End of Moore’s Law

Theoretical physicist Michio Kaku argues that the end of Moore’s Law is coming sooner than later:

Years ago, we physicists predicted the end of Moore’s Law that says a computer power doubles every 18 months.  But we also, on the other hand, proposed a positive program.  Perhaps molecular computers, quantum computers can takeover when silicon power is exhausted.  But then the question is, what’s the timeframe?  What is a realistic scenario for the next coming years?  

Well, first of all, in about ten years or so, we will see the collapse of Moore’s Law.  In fact, already, already we see a slowing down of Moore’s Law.  Computer power simply cannot maintain its rapid exponential rise using standard silicon technology.  Intel Corporation has admitted this.  In fact, Intel Corporation is now going to three-dimensional chips, chips that compute not just flatly in two dimensions but in the third dimension.  But there are problems with that.  The two basic problems are heat and leakage.  That’s the reason why the age of silicon will eventually come to a close.  No one knows when, but as I mentioned we already now can see the slowing down of Moore’s Law, and in ten years it could flatten out completely.  So what is the problem?  The problem is that a Pentium chip today has a layer almost down to 20 atoms across, 20 atoms across.  When that layer gets down to about 5 atoms across, it’s all over.  You have two effects.  Heat–the heat generated will be so intense that the chip will melt.  You can literally fry an egg on top of the chip, and the chip itself begins to disintegrate  And second of all, leakage–you don’t know where the electron is anymore.  The quantum theory takes over.  The Heisenberg Uncertainty Principle says you don’t know where that electron is anymore, meaning it could be outside the wire, outside the Pentium chip, or inside the Pentium chip.  So there is an ultimate limit set by the laws of thermal dynamics and set by the laws of quantum mechanics as to how much computing power you can do with silicon.  

You can watch the video here.

Physicist Uses Math, Writes Paper, To Beat Traffic Ticket

What would you do to get out of a traffic ticket, if you were convinced you were innocent? Probably not as much as Dmitri Krioukov, a physicist based at the University of California San Diego, who was fined for (purportedly) running a stop sign. In a paper titled “Proof of Innocence,” Krioukov argues three physical phenomena combined at just the right time and misled the officer:

We show that if a car stops at a stop sign, an observer, e.g., a police ocer, located at a certain distance perpendicular to the car trajectory, must have an illusion that the car does not stop, if the following three conditions are satis ed: (1) the observer measures not the linear but angular speed of the car; (2) the car decelerates and subsequently accelerates relatively fast; and (3) there is a short-time obstruction of the observer’s view of the car by an external object, e.g., another car, at the moment when both cars are near the stop sign.

When Krioukov drove toward the stop sign the police officer was approximating Krioukov’s angular velocity instead of his linear velocity. This happens when we try to estimate the speed of a passing object, and the effect is more pronounced for faster objects. In Krioukov’s case, the police cruiser was situated about 100 feet away from a perpendicular intersection with a stop sign. Consequently, a car approaching the intersection with constant linear velocity will rapidly increase in angular velocity from the police officer’s perspective. A sneeze caused Krioukov to slam on the brakes hard as he approached the stop sign. With a potential car blocking the officer’s view for a split second, it appeared as though Krioukov never slowed down.

This mathematical description swayed the judge (or maybe he was simply impressed by Krioukov dedication in writing a paper on this personal incident), and the case was dismissed. What a way to get out of paying a traffic ticket!


(via Physics Central)

The Science of the Ponytail

In more bizarre scientific research, physicists have come up with an equation that explains and predicts the shape of a ponytail.

Professor Raymond Goldstein worked on the equation with Professor Robin Ball from the University of Warwick and Patrick Warren, from Unilever’s Research and Development Centre. According to them, this equation aims to “solve a problem that has puzzled scientists and artists ever since Leonardo da Vinci remarked on the fluid-like streamlines of hair in his notebooks 500 years ago”.

The abstract of the paper, which will appear in Physical Review Letters Journal, follows:

A general continuum theory for the distribution of hairs in a bundle is developed, treating individual fibers as elastic filaments with random intrinsic curvatures. Applying this formalism to the iconic problem of the ponytail, the combined effects of bending elasticity, gravity, and orientational disorder are recast as a differential equation for the envelope of the bundle, in which the compressibility enters through an “equation of state.” From this, we identify the balance of forces in various regions of the ponytail, extract a remarkably simple equation of state from laboratory measurements of human ponytails, and relate the pressure to the measured random curvatures of individual hairs.

The best part? The scientists have come up with a new mathematical quantity known as the Rapunzel Number. Very clever.


(via BBC News)

The World’s Longest Running Lab Experiment

The longest running lab experiment in the world is over three quarters of a century long…and is still going. From Popular Science:

The pitch-drop experiment-really more of a demonstration-began in 1927 when Thomas Parnell, a physics professor at the University of Queensland in Australia, set out to show his students that tar pitch, a derivative of coal so brittle that it can be smashed to pieces with a hammer, is in fact a highly viscous fluid. It flows at room temperature, albeit extremely slowly. Parnell melted the pitch, poured it into a glass funnel, let it cool (for three years), hung the funnel over a beaker, and waited.

Eight years later, a dollop of the pitch fell from the funnel’s stem. Nine years after that, another long black glob broke into the beaker. Parnell recorded the second drop but did not live to see the third, in 1954. By then, his experiment had been squirreled away in a dusty corner of the physics department.

The pitch-drop experiment might have fallen into obscurity (or a wastebasket) had it not been for John Mainstone, who joined the physics department at UQ in 1961. One day a colleague said, “I’ve got something weird in this cupboard here” and presented Mainstone with the funnel, beaker and pitch, all housed under a bell jar. Mainstone asked the department head to display it for the school’s science and engineering students, but he was told that nobody wanted to see it. Finally, around 1975, Mainstone persuaded the department to take the bell jar out for the world to see.

To this day, no one person has actually witnessed the moment a drop of pitch has detached and fallen. But that may change. Why? The experiment is now broadcast on a live webcam. John Mainstone is betting that the next drop will happen in 2013. Just don’t hold your breath.

Freeman Dyson on Life and Work

Freeman Dyson, a pioneer quantum physicist and mathematician, has some excellent advice for living.

At the age of 88, why does he continue working?

I continue working because I agree with Sigmund Freud’s definition of mental health. To be healthy means to love and to work. Both activities are good for the soul, and one of them also helps to pay for the groceries.

His advice would to those who have been working for (a) one year and (b) 30 years?

 Advice to people at the beginning of their careers: do not imagine that you have to know everything before you can do anything. My own best work was done when I was most ignorant. Grab every opportunity to take responsibility and do things for which you are unqualified.

Advice to people at the middle of their careers: do not be afraid to switch careers and try something new. As my friend the physicist Leo Szilard said (number nine in his list of ten commandments): “Do your work for six years; but in the seventh, go into solitude or among strangers, so that the memory of your friends does not hinder you from being what you have become.”

I highly recommend reading Dyson’s commentary and book reviews at New York Review of Books.


(via More Intelligent Life)

Top Ten Physics Breakthroughs of 2011

Physics World begins thusly:

The two physics stories that dominated the news in 2011 were questions rather than solid scientific results, namely “Do neutrinos travel faster than light?” and “Has the Higgs boson been found?”

After that disclosure, the Physics World editorial team has compiled a nice end-of-the-year list. The first place goes to Aephraim Steinberg and colleagues from the University of Toronto in Canada for their experimental work on the fundamentals of quantum mechanics:

Steinberg’s work stood out because it challenges the widely held notion that quantum mechanics forbids us any knowledge of the paths taken by individual photons as they travel through two closely spaced slits to create an interference pattern.

This interference is exactly what one would expect if we think of light as an electromagnetic wave. But quantum mechanics also allows us to think of the light as photons – although with the weird consequence that if we determine which slit individual photons travel through, then the interference pattern vanishes. By using weak measurements Steinberg and his team have been able to gain some information about the paths taken by the photons without destroying the pattern.

See the rest of the breakthroughs and links to the original articles.

Higgs Boson Explainer

The physics world is all abuzz about the potential discovery of the Higgs boson, so-called the “God particle.” Researchers at the Large Hadron Collider say that two recent experiments hint at the particle’s existence (though the data is not conclusive). But what exactly is the Higgs boson, and why is it so important?

Here is how Roger Cashmore from the University of Oxford explains it:

What determines the size of objects that we see around us or indeed even the size of ourselves? The answer is the size of the molecules and in turn the atoms that compose these molecules. But what determines the size of the atoms themselves? Quantum theory and atomic physics provide an answer. The size of the atom is determined by the paths of the electrons orbiting the nucleus. The size of those orbits, however, is determined by the mass of the electron. Were the electron’s mass smaller, the orbits (and hence all atoms) would be smaller, and consequently everything we see would be smaller. So understanding the mass of the electron is essential to understanding the size and dimensions of everything around us.

It might be hard to understand the origin of one quantity, that quantity being the mass of the electron. Fortunately nature has given us more than one elementary particle and they come with a wide variety of masses. The lightest particle is the electron and the heaviest particle is believed to be the particle called the top quark, which weighs at least 200,000 times as much as an electron. With this variety of particles and masses we should have a clue to the individual masses of the particles.

Unfortunately if you try and write down a theory of particles and their interactions then the simplest version requires all the masses of the particles to be zero. So on one hand we have a whole variety of masses and on the other a theory in which all masses should be zero. Such conundrums provide the excitement and the challenges of science.

There is, however, one very clever and very elegant solution to this problem, a solution first proposed by Peter Higgs. He proposed that the whole of space is permeated by a field, similar in some ways to the electromagnetic field. As particles move through space they travel through this field, and if they interact with it they acquire what appears to be mass. This is similar to the action of viscous forces felt by particles moving through any thick liquid. the larger the interaction of the particles with the field, the more mass they appear to have. Thus the existence of this field is essential in Higg’s hypothesis for the production of the mass of particles.

We know from quantum theory that fields have particles associated with them, the particle for the electromagnetic field being the photon. So there must be a particle associated with the Higg’s field, and this is the Higgs boson. Finding the Higgs boson is thus the key to discovering whether the Higgs field does exist and whether our best hypothesis for the origin of mass is indeed correct.

For another interesting explainer of the Higgs boson particle and the Higgs field, see this quasi-political explanation by David J. Miller from University College London.

The Mystery of the Faster than Light Neutrinos

I’ve been following this story of “faster than light neutrinos” since the news first came out in late September:

CERN says a neutrino beam fired from a particle accelerator near Geneva to a lab 454 miles (730 kilometers) away in Italy traveled 60 nanoseconds faster than the speed of light. Scientists calculated the margin of error at just 10 nanoseconds, making the difference statistically significant. 

To date, there have been more than 80 papers published trying to explain the 60-nanosecond discrepancy. But according to one physicist, Ronald van Elburg at the University of Groningen, the scientists at CERN neglected to consider nuances of the time mechanism. In particular, in order to synchronize the two locations (they are more than 700km apart, after all), the team used GPS satellites, which each broadcast an accurate time signal from orbit some 20,000km overhead. But herein lies the problem, according to van Elburg:

So what is the satellites’ motion with respect to the OPERA experiment? These probes orbit from West to East in a plane inclined at 55 degrees to the equator. Significantly, that’s roughly in line with the neutrino flight path. Their relative motion is then easy to calculate.

So from the point of view of a clock on board a GPS satellite, the positions of the neutrino source and detector are changing. “From the perspective of the clock, the detector is moving towards the source and consequently the distance travelled by the particles as observed from the clock is shorter,” says van Elburg.

By this he means shorter than the distance measured in the reference frame on the ground.

The OPERA team overlooks this because it thinks of the clocks as on the ground not in orbit.

How big is this effect? Van Elburg calculates that it should cause the neutrinos to arrive 32 nanoseconds early. But this must be doubled because the same error occurs at each end of the experiment. So the total correction is 64 nanoseconds, almost exactly what the OPERA team observes.

Here is the full paper (PDF). And the conclusion:

We showed that in the OPERA experiment the baseline time-of-flight is incorrectly identified with the Lorentz transformation corrected time-of-flight as measured from a clock in a nonstationary orbit and in fact exceeds it by at maximum 64 ns. The calculation presented contain some simplifying assumptions, a full treatment should take into account the varying angle between the GPS satellite’s velocity vector and the CERN-Gran Sasso baseline. We expect that such a full treatment will find somewhat lower value for the average correction. This is because the velocity of the GPS satellite is most of the time not fully aligned with the CERN-Gran Sasso baseline. In addition full analysis should be able to predict the correlation between the GPS satellite position(s) and the observed time-of-flight.

We know from special relativity that time is reference frame specific. This paper shows that Coordinated Universal Time (UTC) happens to be less universal than the name suggests, and that we have to take in to account where our clocks are located. Finally, making all calculations from the correct reference frame might also lead to further improvement of the accuracy of GPS systems as the errors reported here for the time-of-flight amount to a ±18 m difference in location.

I am skeptical. This is rudimentary physics, and I can’t believe that the OPERA scientists would have neglected to consider such a triviality. I’ll be paying attention to how this story unfolds…

Why Can Nothing Go Faster than the Speed of Light?

If you’re a high school or college student studying physics, certainly one of the topics you cover is speed of light. Your teacher/professor probably explained that nothing can go faster than c, that constant equivalent to 299,792,458 meters per second. However, if you still find yourself scratching your head, unable to answer the question “Why can nothing go faster than the speed of light?” I encourage you to read the explanation below, which I found on Reddit. I usually post snippets to quote, but I make exception here. The explanation below, excuse the pun, is positively enlightening.


There are a lot of simple, intuitive explanations of this to be had out there … but I kind of hate them all. You might google around a bit and find discussion of something called “relativistic mass,” and how it requires more force to accelerate an object that’s already moving at a high velocity, stuff like that. That’s a venerable way of interpreting the mathematics of special relativity, but I find it unnecessarily misleading, and confusing to the student who’s just dipping her first toe into the ocean of modern physics. It makes the universe sound like a much different, and much less wonderful, place than it really is, and for that I kind of resent it.

When I talk about this subject, I do it in terms of the geometric interpretation that’s consistent with generalrelativity. It’s less straightforward, but it doesn’t involve anything fundamentally more difficult than arrows on pieces of paper, and I think it offers a much better understanding of the universe we live in than hiding behind abstractions like “force” and outright falsehoods like “relativistic mass.” Maybe it’ll work for you, maybe it won’t, but here it is in any case.

First, let’s talk about directions, just to get ourselves oriented. “Downward” is a direction. It’s defined as the direction in which things fall when you drop them. “Upward” is also a direction; it’s the opposite of downward. If you have a compass handy, we can define additional directions: northward, southward, eastward and westward. These directions are all defined in terms of something — something that we in the business would call an “orthonormal basis” — but let’s forget that right now. Let’s pretend these six directions are absolute, because for what we’re about to do, they might as well be.

I’m going to ask you now to imagine two more directions: futureward and pastward. You can’t point in those directions, obviously, but it shouldn’t be too hard for you to understand them intuitively. Futureward is the direction in which tomorrow lies; pastward is the direction in which yesterday lies.

These eight directions together — upward, downward, northward, southward, eastward, westward, pastward, futureward — describe the fundamental geometry of the universe. Each pair of directions we can call a “dimension,” so the universe we live in is four-dimensional. Another term for this four-dimensional way of thinking about the universe is “spacetime.” I’ll try to avoid using that word whenever necessary, but if I slip up, just remember that in this context “spacetime” basically means “the universe.”

So that’s the stage. Now let’s consider the players.

You, sitting there right now, are in motion. It doesn’t feel like you’re moving. It feels like you’re at rest. But that’s only because everything around you is also in motion. No, I’m not talking about the fact that the Earth is spinning or that our sun is moving through the galaxy and dragging us along with it. Those things are true, but we’re ignoring that kind of stuff right now. The motion I’m referring to is motion in the futureward direction.

Imagine you’re in a train car, and the shades are pulled over the windows. You can’t see outside, and let’s further imagine (just for sake of argument) that the rails are so flawless and the wheels so perfect that you can’t feel it at all when the train is in motion. So just sitting there, you can’t tell whether you’re moving or not. If you looked out the window you could tell — you’d either see the landscape sitting still, or rolling past you. But with the shades drawn over the windows, that’s not an option, so you really just can’t tell whether or not you’re in motion.

But there is one way to know, conclusively, whether you’re moving. That’s just to sit there patiently and wait. If the train’s sitting at the station, nothing will happen. But if it’s moving, then sooner or later you’re going to arrive at the next station.

In this metaphor, the train car is everything that you can see around you in the universe — your house, your pet hedgehog Jeremy, the most distant stars in the sky, all of it. And the “next station” is tomorrow.

Just sitting there, it doesn’t feel like you’re moving. It feels like you’re sitting still. But if you sit there and do nothing, you will inevitably arrive at tomorrow.

That’s what it means to be in motion in the futureward direction. You, and everything around you, is currently moving in the futureward direction, toward tomorrow. You can’t feel it, but if you just sit and wait for a bit, you’ll know that it’s true.

So far, I think this has all been pretty easy to visualize. A little challenging maybe; it might not be intuitive to think of time as a direction and yourself as moving through it. But I don’t think any of this has been too difficult so far.

Well, that’s about to change. Because I’m going to have to ask you to exercise your imagination a bit from this point on.

Imagine you’re driving in your car when something terrible happens: the brakes fail. By a bizarre coincidence, at the exact same moment your throttle and gearshift lever both get stuck. You can neither speed up nor slow down. The only thing that works is the steering wheel. You can turn, changing your direction, but you can’t change your speed at all.

Of course, the first thing you do is turn toward the softest thing you can see in an effort to stop the car. But let’s ignore that right now. Let’s just focus on the peculiar characteristics of your malfunctioning car. You can change your direction, but you cannot change your speed.

That’s how it is to move through our universe. You’ve got a steering wheel, but no throttle. When you sit there at apparent rest, you’re really careening toward the future at top speed. But when you get up to put the kettle on, you change your direction of motion through spacetime, but not your speed of motion through spacetime. So as you move through space a bit more quickly, you find yourself moving through time a bit more slowly.

You can visualize this by imagining a pair of axes drawn on a sheet of paper. The axis that runs up and down is the time axis, and the upward direction points toward the future. The horizontal axis represents space. We’re only considering one dimension of space, because a piece of paper only has two dimensions total and we’re all out, but just bear in mind that the basic idea applies to all three dimensions of space.

Draw an arrow starting at the origin, where the axes cross, pointing upward along the vertical axis. It doesn’t matter how long the arrow is; just know that it can be only one length. This arrow, which right now points toward the future, represents a quantity physicists call four-velocity. It’s your velocity through spacetime. Right now, it shows you not moving in space at all, so it’s pointing straight in the futureward direction.

If you want to move through space — say, to the right along the horizontal axis — you need to change your four-velocity to include some horizontal component. That is, you need to rotate the arrow. But as you do, notice that the arrow now points less in the futureward direction — upward along the vertical axis — than it did before. You’re now moving through space, as evidenced by the fact that your four-velocity now has a space component, but you have to give up some of your motion toward the future, since the four-velocity arrow can only rotate and never stretch or shrink.

This is the origin of the famous “time dilation” effect everybody talks about when they discuss special relativity. If you’re moving through space, then you’re not moving through time as fast as you would be if you were sitting still. Your clock will tick slower than the clock of a person who isn’t moving.

This also explains why the phrase “faster than light” has no meaning in our universe. See, what happens if you want to move through space as fast as possible? Well, obviously you rotate the arrow — your four-velocity — until it points straight along the horizontal axis. But wait. The arrow cannot stretch, remember. It can only rotate. So you’ve increased your velocity through space as far as it can go. There’s no way to go faster through space. There’s no rotation you can apply to that arrow to make it point more in the horizontal direction. It’s pointing as horizontally as it can. It isn’t even really meaningful to think about something as being “more horizontal than horizontal.” Viewed in this light, the whole idea seems rather silly. Either the arrow points straight to the right or it doesn’t, and once it does, it can’t be made to point any straighter. It’s as straight as it can ever be.

That’s why nothing in our universe can go faster than light. Because the phrase “faster than light,” in our universe, is exactly equivalent to the phrase “straighter than straight,” or “more horizontal than horizontal.” It doesn’t mean anything.

Now, there are some mysteries here. Why can four-velocity vectors only rotate, and never stretch or shrink? There is an answer to that question, and it has to do with the invariance of the speed of light. But I’ve rambled on quite enough here, and so I think we’ll save that for another time. For right now, if you just believe that four-velocities can never stretch or shrink because that’s just the way it is, then you’ll only be slightly less informed on the subject than the most brilliant physicists who’ve ever lived.

Source: Reddit.

Side note: if you’re interested in learning more about space and the time continuum, I high recommend Brian Greene’s The Elegant Universe. I read it a few years ago, and it’s one of the best general (i.e., not a textbook) books on space and physics I’ve read.