Phasing out small shampoo bottles

Those tiny bottles of shampoo and conditioner that hotels provide would last me about two weeks but I usually stay just one or two days and I suspect that the rest will be thrown away, which seems awfully wasteful of both shampoo and plastic. Do hotels expect you to leave the remnants behind or are you doing them a favor by taking the partially used bottles with you, saving them the trouble of throwing them away? It seems vaguely wrong to take them home with me without being given explicit permission and I have personally vacillated between taking them and leaving them. It would be nice if hotels left a little note telling guests like me who worry about such trivialities what to do.

But now apparently some hotels are going to be providing full-size bottles that are refillable, so that the ambiguity is removed.
That’s a welcome development. Now if they could do something about the waste of the remnants of those little bars of soap …

Relativity-2: The CERN-Gran Sasso experiment

(For previous posts in this series, see here.)

The nice feature about the experiments involved in the recent reports of faster than light neutrinos is that the basic ideas are so simple that anyone can understand them. It involved producing neutrinos at the CERN laboratory in Switzerland and detecting them at the Gran Sasso laboratory in Italy. By measuring the distance between the two locations and the time taken for the trip, one could calculate the speed of the neutrinos by dividing the distance by the time.

The measured distance was about 730 km so if we take that as the exact value, and if the neutrinos were traveling at exactly the speed of light (299,792 km/s), the time taken would be 2.435022 milliseconds (where a millisecond is one-thousandth of a second) or equivalently 2,435,022 nanoseconds (where a nanosecond is one-billionth of a second). What the experimenters found was that the actual time taken was 60 nanoseconds less than this time, which seemed to require the neutrinos to be traveling slightly faster than the speed of light. Since the existence of faster than light particles has never been confirmed before, this would be a major discovery and so the search is now underway to see if this conclusion holds up under close scrutiny.

If the experimental results are at fault and the effect is spurious, this must arise from errors in the distance measurement and/or the time measurement. Although the time difference that produced the effect is very small (60 nanoseconds out of a total travel time of over 2 million nanoseconds constitutes only about 0.0025% of the total time), the experimenters say their time measurements are accurate up to 10 nanoseconds, much less than the size of the error needed to resolve the discrepancy, thus ruling that out as the source of error. Similarly, if the actual distance were less than the measured distance by just 18 meters, the effect would again go away. The experimenters used GPS technology to measure the space and time coordinates of the events and say that their experiment can measure distances up to an accuracy of just 0.2 meters, making that too an unlikely source of any error. As for the possibility of some kind of random statistical fluctuations causing the effect, the number of neutrino measurements they have taken over the past two years exceed 16,000, which makes that highly unlikely as the source of error.

So why is there still skepticism? It is because the very feature of neutrinos that makes this experiment so conceptually simple is also what makes it so difficult to rule out what are called systematic errors. These are artifices of the experimental setup that can bias the results consistently in one particular direction, unlike random errors that can go either way and can be reduced by repeating the experiment a large number of times, as was done in this case. Unearthing systematic errors is difficult and time consuming because it depends on the esoteric details of the experimental set-up. What some other groups will now try and do is identify possible sources of systematic errors that the original experimenters did not consider, while others will repeat the experiment with different experimental set-ups, measuring the time and distance using different techniques so that the likelihood of systematic biases pushing the results in the same direction is reduced. Yet other groups will examine if any of the side effects that would automatically accompany faster than light travel are also seen. It is this kind of investigation for replicability and consistency that characterizes science.

But getting back to the original experiment, the reason that neutrinos are good for measuring velocities that may exceed the speed of light is that they usually travel at speeds close to or at the speed of light. If a particle has zero mass (as is the case with ‘photons’, the name given to particles of light), then according to Einstein’s theory of relativity, it must travel exactly at the speed of light. If it has a mass, however small, it can approach the speed of light but never attain it because to do so would require an infinite amount of energy. But it takes less energy to accelerate lighter particles to high speeds than it does heavier particles.

In the case of neutrinos, we have not been able to directly detect them having any non-zero mass as yet. All we have been able to do so far is put a small upper limit on the amount of mass it can have, which is 2 eV/c2 which is about 3.5×10-33 kg. (By comparison, the particle with the smallest mass we know, the electron, has a relatively huge mass of 511,000 eV/c2.) It had long been assumed that the mass of the neutrino was exactly zero. But it turns out that there are three kinds of neutrinos and that they may oscillate from one kind to another as they travel through space, and the postulated mechanism for such oscillations require that they have non-zero mass. The purpose of the CERN-Gran Sasso experiment was to actually look for such oscillations, and it just so happened that it turned up the evidence that neutrinos may be traveling faster than light, completely shifting the focus of attention. Such accidental discoveries when looking for something else are not uncommon in science, the discovery of X-rays being one of the more famous examples.

Next: The elusive neutrino

The oligarchy exposed

Critics of the Occupy Wall Street movement have asserted that their goals are not clear and they don’t have solutions, although it is pretty obvious (as this Tom Tomorrow cartoon says) that economic injustice is their main grievance. But Paul Krugman points out that the hysterical response to the Occupy Wall Street movement is a telling indicator of the fact that the protestors have achieved one major goal: they have put the role of the financial oligarchy in causing the nation’s problems in the spotlight and they are squirming and want to shut down the discussion. They much prefer to do their work in the shadows.

The answer, surely, is that Wall Street’s Masters of the Universe realize, deep down, how morally indefensible their position is. They’re not John Galt; they’re not even Steve Jobs. They’re people who got rich by peddling complex financial schemes that, far from delivering clear benefits to the American people, helped push us into a crisis whose aftereffects continue to blight the lives of tens of millions of their fellow citizens.

Yet they have paid no price. Their institutions were bailed out by taxpayers, with few strings attached. They continue to benefit from explicit and implicit federal guarantees — basically, they’re still in a game of heads they win, tails taxpayers lose. And they benefit from tax loopholes that in many cases have people with multimillion-dollar incomes paying lower rates than middle-class families.

This special treatment can’t bear close scrutiny — and therefore, as they see it, there must be no close scrutiny.

Peter Singer’s review of Steven Pinker’s new book

The always readable Steven Pinker has a new book out titled THE BETTER ANGELS OF OUR NATURE: Why Violence Has Declined arguing that there has been a steady drop in violence over time. The equally readable Peter Singer has a very positive review of the book, of which the following is an excerpt.

Against the background of Europe’s relatively peaceful period after 1815, the first half of the 20th century seems like a sharp drop into an unprecedented moral abyss. But in the 13th century, the brutal Mongol conquests caused the deaths of an estimated 40 million people — not so far from the 55 million who died in the Second World War — in a world with only one-seventh the population of the mid-20th century. The Mongols rounded up and massacred their victims in cold blood, just as the Nazis did, though they had only battle-axes instead of guns and gas chambers. A longer perspective enables us to see that the crimes of Hitler and Stalin were, sadly, less novel than we thought.

Since 1945, we have seen a new phenomenon known as the “long peace”: for 66 years now, the great powers, and developed nations in general, have not fought wars against one another. More recently, since the end of the cold war, a broader “new peace” appears to have taken hold. It is not, of course, an absolute peace, but there has been a decline in all kinds of organized conflicts, including civil wars, genocides, repression and terrorism. Pinker admits that followers of our news media will have particular difficulty in believing this, but as always, he produces statistics to back up his assertions.

The final trend Pinker discusses is the “rights revolution,” the revulsion against violence inflicted on ethnic minorities, women, children, homosexuals and animals that has developed over the past half-century. Pinker is not, of course, arguing that these movements have achieved their goals, but he reminds us how far we have come in a relatively short time from the days when lynchings were commonplace in the South; domestic violence was tolerated to such a degree that a 1950s ad could show a husband with his wife over his knees, spanking her for failing to buy the right brand of coffee; and Pinker, then a young research assistant working under the direction of a professor in an animal behavior lab, tortured a rat to death. (Pinker now considers this “the worst thing I have ever done.” In 1975 it wasn’t uncommon.)

Relativity-1: Going backwards in time

Part of the reason that recent reports of the detection of neutrinos traveling faster than the speed of light aroused such excitement is because of claims that such a discovery would overthrow Einstein’s venerable theory of relativity and that if you could send a signal faster than the speed of light, you could go backwards in time. Are these claims true or simply overheated? If true, what exactly was overthrown? And what does it mean to ‘go backwards in time’ anyway?

My initial reaction to the faster-than-light neutrino report was one of skepticism, saying that I would wait and see if the result held up but was not hopeful that it would. I did not give my reasons for this pessimism and reflecting later, I thought I should because understanding what was claimed (and why) serves as a good vehicle to understand the elements of the theory of special relativity as well as how science works., so the next series of posts will deal with these questions. (I was overdue for a series of posts on a single topic anyway.)

Let’s look first at the ‘backwards in time’ claim. There is a simple (but wrong) way of interpreting this and a more subtle (but correct) way.

To see the simple way in which something traveling faster than the speed of light can cause things to appear to go backwards in time, think of a situation in which a man fires a gun at another man but with the bullet traveling faster than the speed of light. Nothing requires the shooting of people to understand this phenomenon but this is the customary example that is used, perhaps because a bullet is the fastest object that most people can think of (although it is still much slower than the speed of light) combined with the fact shooting someone is so dramatic and final that reversing the process seems impossible, kind of like Jesus rising from the dead.

Suppose the shooter is at point A and the person hit is at point B 10 meters away. Suppose you are standing right next to the person at B. If the bullet travels faster than the speed of light, what will you see? Remember that we ‘see’ something only when the light from that event enters our eyes. Since the speed of light (at 299,792 km/s) is beyond anything we are familiar with from our everyday experiences, let’s greatly slow things down by assuming that it travels at (say) 1 m/s and that the bullet travels at (say) 2 m/s.

You will see the gun at A firing 10 seconds after it fires because the light from that instant will take that much time to travel the 10 meters to reach you. But one second after the gun is fired, the bullet will have traveled two meters towards B (and you), and light emitted by the bullet at that point will take only 8 more seconds to reach you. In other words, you will see the bullet at the 2 meter point 9 seconds after the gun is fired, which is one second before you see the gun firing. Similarly you will see the bullet at the 4 meter mark 8 seconds after the gun fires, at the 6 meter mark 7 seconds after the gun fires, at the 8 meter mark 6 seconds after the gun fires, and the bullet entering the person at B 5 seconds after the gun fires. Put it all together and what you see first is the person at B being hit (five seconds after the gun fires) and then in the next five seconds will see the bullet emerging from the victim and traveling back and entering the gun.

This no doubt looks like is going backwards in time. But this example is not what is meant by going backwards in time according to the theory of reelativity. After all, the victim was in fact hit five seconds after the gun was fired so there is no actual reversal of the ordering of the events. What you saw is more like watching a film run backwards, which is not really going backwards in time. This effect is an illusion, an artifice caused by the fact that light takes time to travel and your special location next to the victim. Had you observed the whole sequence of events while standing next to the shooter at A, you would not have noticed anything unusual because you would have seen the gun fire right at the beginning, the bullet at the 2 meter mark after 3 seconds, at the 4 meter mark after 6 seconds, at the 6 meter mark after 9 seconds, at the 8 meter mark after 12 seconds and hitting the person at B after 15 seconds. Everything would have seemed normal.

What this example does illustrate is that specifying the time at which an event occurs by the time noted by an observer is not satisfactory because it depends on where the observer is situated relative to the events. (For example, the bullet was observed at the 2 meter mark at 3 or 9 seconds after the gun was fired depending on where you were standing.) We will also see later that in addition to the location, the state of motion of the observer (if you were observing the events from a moving train, for example) also affects the time at which they see events.

It is in trying to unambiguously pin down exactly when something happens that we arrive at a deeper understanding of Einstein’s theory of relativity and what we really mean by going backwards in time.

Next: The CERN-Gran Sasso experiment