The dark-matter rumour mill

Any WIMPs in here?

You shouldn’t believe everything you read in the blogs (except this one of course).

Yesterday, the rumour mill was in overdrive as the Resonaances blog said a paper was due to be released a week on Friday in the journal Nature about a possible detection of dark matter.

What constitutes dark matter, which is thought to make up around 90% of the material in the universe, is a hot topic of research these days with researchers vying to be the first to provide direct evidence of it. If true, it would perhaps be the discovery of the year.

The new rumours are based on the latest results from the Cryogenic Dark Matter Search (CDMS) located in the Soudan Underground Laboratory in Minnesota, which is searching for weakly interacting massive particles or WIMPs — a prime candidate for dark matter.

We were a little suspicious of the rumours as Nature is published on Thursday with embargos for news items about its papers on Wednesday evening at 6pm GMT. However, the paper could have been an advanced online publication in Nature or perhaps was due to be published in Science, which is published every Friday.

The rumours were also backed by a series of talks being given by various members of the CDMSteam at labs such as CERN on 18 December - the same date as the paper would be published.

However, Leslie Sage, a senior editor at Nature, wrote to Resonaances saying there was no suchNature paper and the rumours were unfounded.

I contacted Priscilla Cushman from the CDMS collaboration and based at the University of Minnesota, who confirmed to me that indeed they have not submitted a paper to Nature.

So why are they presenting the results at different labs on the same day? “Since there is no major conference at this time in which to present them we are coordinating our talks,” Cushman toldphysicsworld.com.

CDMS researchers will, however, be publishing an arXiv paper on the morning of Friday 18 December about their latest results, so we will have to wait until then.

Cushman says the group were quite taken aback by the rumours going around. “It is certainly an interesting social phenomena [sic],” says Cushman. But ultimately it was “lots of smoke and not much fire”.

Taking an author’s ‘literary fingerprint’

Billy S A king of infinite space

Imagine this: a much-celebrated author locks himself away to begin work on his masterpiece, a novel called The Meta Book that will comprise an infinite number of words all strung together in the writer’s unique literary style. While this may sound like the plotline to a short-story by one of the great magical realist authors of Latin America, it is actually the idea of a trio of physicists in Sweden.

Sebastian Bernhardsson and his colleagues at Umeå University are interested in the unique “literary fingerprint” left by famous authors. They conceptualize a writer’s use of language as a complex system in the same way that scientists model the climate, the economy or ant colonies.

By feeding an author’s entire oeuvre into their calculations, they find that each writer creates a unique curve on a graph representing the number of different words used as a function of the total number of words. What’s more, this signature curve can be detected in every single work of a particular author regardless of what they are writing about.

Publishing their findings in New Journal of Physics the authors create curves for the works of Thomas Hardy, DH Lawrence and Herman Melville. “It is like everything an author can think of writing is processed by a mental pipeline which imposes a unique fingerprint on an authors’ infinite meta-book,” says Bernhardsson. I think, what he means by this is that (statistically speaking) there is a common thread running through everything these authors wrote — as if they were plucking extracts from their infinite corpus.

Now, the literary purists out there may be reading this and seething at yet another example of uncouth physicists trying to impose rigid mathematical frameworks onto works of unquantifiable beauty, or of “unweaving the rainbow” as Keats famously accused Newton. If anything, however, the results of this research reveal the opposite. For 75 years, language analysts have assumed that all literature, regardless of author, follows the same statistical pattern when viewed as a whole. This was based on the law proposed by American linguist George Kingsley Zipf stating that the frequency of a word is inversely proportional to its occurrence.

In this new view of fiction, however, each author defines their own unique law based on non-trivial mathematics. “It shows that, even statistically speaking, our personality is not drowned by the general rules, and structure of the language itself,” says Bernhardsson.

The researchers intend to develop their work by testing their meta book concept for more authors and languages other than English. So who knows — maybe the magical literary worlds of Borges and Márquez will be next in line to have their curves exposed.

On Her Majesty’s Space Service

Agency men: Drayson and Scolese

The UK’s science minister Paul Drayson was licensed to thrill yesterday when he turned up at the Rutherford Appleton Laboratory to announce that the UK will set up its own executive space agency. Lord Drayson hinted that it might be called “Her Majesty’s Space Service”, and said it would provide “a unified approach to ensure the UK gains a bigger share of the global space market”.

Drayson was speaking to researchers at the 5th Appleton Space Science Conference, and the announcement was met with warm applause. Not surprising, because space scientists have been waiting at least 20 years for the news!

Space science funding is currently done by six government departments and two research councils — and it is not clear whether the new agency will coordinate these activities, or take over funding altogether.

However, Drayson was very clear that the overall spend on space science research will not change. And he was also adamant that the UK space community has long been at a disadvantage for not having an executive agency to negotiate its participation in international projects.

Although the UK is a leader in space science and technology, the government had not been particularly keen on space. The country has shunned manned space missions and the 1986 Space Act makes it very difficult for a private company to launch anything into space from British soil. The reason, believe it or not, is that firms cannot afford adequate insurance to comply with the indemnity requirements of the act.

But then Gordon Brown came to power in 2007 — and apparently Brown loves space science, or so I was told by a leading space scientist at the post-conference drinks reception. It seems that when Brown was Chancellor of the Exchequer he asked his minions to identify up-and-coming industry sectors and guess what was at the top of the list?

Indeed, in his speech Drayson said that 20,000 Britons are employed directly by the space industry, which is worth £6.8bn per year.

“It’s a recession proof industry” he claimed, citing 9% growth every year for the last decade. And the good news is set to continue, with 5% growth forecast for the next decade.

Drayson’s speech was followed by the Appleton Lecture by Chris Scolese, who is associate administrator of NASA. I wonder if the second in command of the world’s most famous space agency gave Drayson any tips on setting up an agency?

The A to Z of the AB effect

Electrons (blue) passing either side of a current-carrying solenoid shows the Aharonov-Bohm effect in action.

The Aharonov-Bohm effect is one of those weird, counter-intuitive consequences of quantum mechanics that makes physics the fascinating subject it is.

Discovered 50 years ago by Yakir Aharonov and the late David Bohm at the University of Bristol in the UK, the AB effect, as it is known to insiders, is being celebrated today at a special conferenceat Bristol.

In case you weren’t aware, the AB effect describes the fact that an electrically charged particle passing through a region where both the magnetic and electric fields are zero is nevertheless affected by the electromagnetic potential in that region.

It can best be understood by considering a beam of electrons passing through two slits and then around either side of a current-carrying solenoid, as shown by the blue lines in the picture above.

Although there is no magnetic field outside the solenoid, the potential is different on the two sides, which means that the wavefunction of the electrons travelling past one side of the solenoid are phase-shifted by a different amount compared with the electrons travelling past the other.

The AB effect can be verified by allowing the electron beams to interfere: the resulting fringe patterns shift depending on whether the solenoid is on or off.

The conference, which also marks the 25th anniversary of Michael Berry’s discovery of the related “Berry phase”, has attracted a crowd of specialists from around the world, including Aharonov himself.

I went to the conference dinner at the university’s Georgian-period Goldney Hall, where guests were treated to a marvellous menu of roast asparagus with goat’s cheese mousse and Serrano ham crisps, slow-cooked rump of lamb with quince sauce, and confit of raspberries.

Spotted among the guests were Bob Chambers, who confirmed the AB effect experimentally back in 1960, former Brookhaven chairman Michael Hart and independent physicist Julian Barbour, author of The End of Time.

Today’s first lecture session back at the university’s physics department was chaired by Murray Peshkin from Argonne National Laboratory in the US, who introduced Sir Michael by saying “he is a man of few words but many syllables — so listen carefully”.

Berry’s lecture was entitled “Semifluxon degeneracy choreography” and he duly proceded to use a fair few long-syllabled words, including “Gaussian random simulation”, “traceless real symmetric 2×2 matrices” and “rearrangements of nodal domains”.

The talk was a bit over my head, but on such occasions I take comfort in Richard Feynman’s famous phrase that “nobody really understands quantum mechanics”.

Closing in on dark matter

The physics blogosphere has been wild with rumour in recent days that researchers in the Cryogenic Dark Matter Search (CDMS) in the US may have obtained the first direct evidence for dark matter in the form of Weakly Interacting Massive Particles.

The CDMS group gave simultaneous lectures at SLAC and Fermilab late on Thursday evening UK time that would, or would not, announce major new findings, depending on whose blog you read

My colleague Michael Banks has been listening in to the webcasts and emailed me to say that “the outcome is that it is not conclusive evidence of dark matter, but they did have two events on a background of 0.5… so some signal, but not the five events needed for a discovery”.

An arxiv paper on the new results should be there by early morning.

It appears, Michael tells me, that the first event was detected on 27 October 2007, with a recoil energy of roughly 12 keV, and the second was seen earlier that year at roughly 15 keV. A third event lies just outside their box with recoil of 12 keV. Apparently this gives the lower bound on theWIMP mass for these recoil energies as roughly 0.5 GeV.

CDMS has a neat summary here. This is the key sentence: “We estimate that there is about a one in four chance to have seen two backgrounds events, so we can make no claim to have discovered WIMPs.”

We’ll have more on this later in our news channel so stay tuned. In the meantime,
Cosmic Variance have been doing a live blog which has lots of as-it-happens stuff to get stuck into to.

RELATIVITY -VII

Odds and Ends

Well you've more or less seen it all. But a couple of things still remain . . .

1: Loading Other Objects!

By now you'll be totally bored with the teapot. Luckily, Warp supports other objects. First you'll need to visit the Download page to download some models. Once you've unzipped these onto your computer, simply click on the big yellow button in the middle of the console. This will bring up a box that will allow you to load the new objects. May I recommend the lattices, as they make visualising special relativity a lot easier. Most of the objects are great fun, for example I bet you've never seen the Eiffel tower like this:

2: Keyboard short cuts.

You might be overawed with all the keyboard shortcuts used by Warp, but don't worry! Simply press F1 to bring up a little help box to remind yourself of all the keys! Hurrah! Or you can look at the next lesson for a quick summary.

RELATIVITY -VI

Bright Lights - The Headlight Effect

We now turn our attention to one of the stranger effects of special relativity, the headlight effect. The best way to explain this is to imagine a torch that, in its own frame, emits a beam of light in the shape of a cone. This cone's sides make an angle of phi with respect to the x-axis (i.e. the torch is pointing along the x-axis). This is shown in the following diagram.

Now imagine that the torch moves along the x-axis with some velocity, v. Contrary to what you might expect, the angle phi will become narrower! This contraction is known as the Headlight effect. The amount that phi narrows is given by the following equation:

So what does this mean in relation to Warp? Well, the important thing to note is that the torch isn't giving off any less light. The same amount of light is being focused into a smaller area. Therefore, an approaching torch will seem brighter than a stationary torch. Likewise, a receding torch will appear darker. This doesn't just apply to torches. It also applies to any object traveling towards an observer. The change in light intensity, I, is given by the following relationship:

.

You can see the headlight effect in Warp by trying the following:

1. Arrange the object as you like it.
2. Press 'd' to turn off the Doppler effect.
3. Increase the speed to some arbitrary value.
4. Guess what? Use 'space' and 'return' to alter the time and hence view of the object. Boy, I get tired of saying that!

If you arranged the object so that it is speeding towards you then you should see something like this:

Notice how bright the teapot is. However, if the object is traveling away from you then you should see something more like this:

Here the headlight effect has darkened everything to such an extent that you can't see much of the original colour! Of course this can be a bit of a pain so you can turn the headlight effect off:

• Press 'h' to toggle the headlight effect on / off.

Okay, you should now understand all of the relativity effects that Warp simulates. The best way to learn about these things is to have a play around with Warp, and see what you can do. However, by now you are probably bored with the teapot and want to try other things. Well, that's the subject of the next lesson.

RELATIVITY - V

All the Colours of the Rainbow - The Doppler Effect

Okay, those of you with good memories will recall that the teapot in Lesson 1 changed colour as we increased the speed. This is all down to the good ol' Doppler Effect. For those of you who don't know what that is, let me explain . . .

Remember the last time you heard an ambulance go by? Remember how the pitch of the siren changed as the ambulance went past? That's the Doppler effect. The sound waves emitted by the siren get squashed up as the ambulance comes towards you, and hence the siren seems high pitched. Likewise, when the ambulance has passed, the sound waves are stretched out and hence you hear a low-pitched siren.

Light also behaves like a wave (except in Quantum Mechanics, but Einstein didn't like Quantum Mechanics so we'll pretend it doesn't exist (!)). Therefore, it is subject to exactly the same effect. Light emitted from an object rushing towards us will have its waves squashed up. Hence, the colours will be shifted towards the blue end of the spectrum. Conversely, light waves from an object rushing away from us will appear redder. These changes are called blue shift and red shift respectively. At very high speeds visible light emitted by the object can be shifted out of the visible spectrum, and hence the object would not be visible to the human eye!

The original wavelength is shifted according to the following formula:

Here, lambda is the wavelength, v is the speed, and theta is the angle that the vector to the point on the object makes with the direction of motion (for those who are interested).

Warp simulates the Doppler effect on fast moving objects. In order to see this, try the following:

1. Set the speed to zero and arrange the object to your preference.
2. Press 'h'. This turns off the Headlight effect, which we are not interested at the moment, but we will come back to later.
3. Now hold down 'a' to increase the speed slowly.
4. As ever, use 'space' and 'return' to get the object back on the screen.

You will notice that the colour of the object slowly changes. You may even end up seeing bands of colour. This is due to the angle term in the pervious equation. You may end up seeing something like this:

As you can see the object suddenly turns white (like the left hand side of the teapot above). This means that the colour has been shifted out of the optical spectrum. In reality it would no longer be visible, but Warp shows this as white to aid visibility.

The Doppler effect is the reason that Warp draws everything in green to start with. Green is in the middle of the optical spectrum, so you are able to get a good range for both red and blue shifting. However, if you are only interested in, say, blue shift (objects coming towards you), then you can change the original colour of the objects. To do this you need to use the '+' and '-' keys, which will slowly change the hue of an object until you are happy. So if you are interested in blue shifting you might want to start of with a red teapot to give yourself the largest possible colour range to play with.

• Use '+' and '-' to change the hue of the object.

However, sometimes you won't want to see the Doppler effect. After all, those colours can be a bit hard on the eyes. So . . .

• Press 'd' to turn off the Doppler effect. Press 'd' again to turn it back on.

You now know all about the Doppler effect and how colour is used in Warp. However, you might remember that I mentioned the 'headlight effect'. Well, this is another interesting phenomena of special relativity and is the subject of the next lesson.

RELATIVITY - IV

Lorentz Transforms Explained

Ergh! What a nasty sounding title. But it's not that bad. No really! First, think of an experiment . . .

Two spaceships, A and B, are driving towards each other. A spaceman, who is sitting still in space, sees both spaceships going at 1,000,000 m/s (one million metres per second). The pilot in spaceship A wants to know how fast spaceship B is approaching him. In pre-Einstein physics (i.e. before special relativity) he would assume that spaceship B approaching him at 2,000,000 m/s.

Spaceship B then slows to a halt. The pilot decides to do an experiment and measure the speed of light. He measures the speed of a ray of light heading towards him. He gets a result of 300,000,000 m/s (that's three-hundred million metres per second).

Meanwhile, spaceship A is still going at 1,000,000 m/s. The pilot also decides to measure the speed of a ray of light coming towards him. What result does he get?

1. 301,000,000 m/s (three-hundred and one million metres per second)?
2. 299,000,000 m/s (two-hundred and ninety nine million metres per second)?
3. 300,000,000 m/s (three-hundred million metres per second)?
4. Eh?

If you said '2' or '4' then go back and reread this lesson from the beginning. If you said '1' then nearly every physicist in the world would agree with you . . . up until 1905 and Einstein that is. The correct answer is '3' because the speed of light is the same for all observers. This is what special relativity is all about. It doesn't matter if you are traveling at 200,000,000 m/s or standing still, you will always get the same result for the speed of light. A Dutchman named Hendrik Antoon Lorentz realized that this could be explained if objects in motion undergo transformations called the Lorentz Transformations.

In these equations x, y, z and t set the coordinates of space and time respectively from an observers point of view. Also, x', y', z' and t' set the coordinates according to the subject. The velocity, v, is in the direction of the x-axis and c is the speed of light. So what does this mean? Well, it means that funny thing happen to the way things look. For example, the first image shows a stationary lattice. The second image shows the same lattice traveling towards us at close to the speed of light! Notice how you can see the back of some of the lattice members despite the fact that they are in front of you! Very strange.

v = 0 m/s

v -> c

Warp simulates the Lorentz Transformations, and it is worth pointing out that if you try moving around a warped object you might find it a bit strange. First of all, as you increase the speed, the object will generally shoot off into the distance. Why? Well, look at the first equation given in this lesson. You see that if we increase the velocity, v, but hold the time, t, constant then x' will diverge from x. Of course in real life it's impossible to increase your speed instantaneously but this is exactly what happens in Warp. Warp holds time still until you tell it otherwise. Remember in the RELATIVITY-II when the teapot went shooting off as you increased the speed? Well you are now in a position to understand what was going on. The speed was increased, the time wasn't, so x' became large and hence the teapot shot off into the distance. Simple.

The result of all this waffle is that when you change you speed in Warp, you will also have to change the time. As outlined earlier, you do this using 'space' and 'return'. If you forget to do this, your object will disappear off the edge of the Warp universe, and you'll be terribly upset.

Anyway, the object may behave in unpredictable ways because of the way that the twisting at high speeds. If you don't want to get thoroughly confused when moving around objects I recommend reducing the speed before moving. I also find that it is easier to work with the camera fixed on the axes of the Warp universe as outlined in RELATIVITY-I. If you recall, this involved pressing 'r' to toggle the 'camera relative' mode.

That said, if you do want to be completely perplexed, please try moving / rotating the teapot around at high speed and see what happens!

Moving on, the observant among you will have noticed that the colour of objects in Warp also changes. This is due to Doppler Shifting

RELATIVITY - III

Experiments at High Speed!

Having mastered the control of the camera, you are now ready to see Warp do what it was designed to do. That is showing you what things would look like at (very) high speeds. To change the speed you need to use the Speed Bar on the left hand side of the Console Bar, as shown below.

The green line indicates your current speed in the direction of the z-axis of the Warp universe. The z-axis is directly into the screen when you start Warp, and the camera's velocity is always along this axis. By clicking with the left mouse button on the Speed Bar and dragging the mouse, you can change your speed. The line will change size to indicate the speed. Furthermore, its colour will gradually change to yellow as you get close to the speed of light. The scale of the Speed Bar is logarithmic. This means that the Speed Bar is clearer at higher speeds. For example, leftmost tick mark (the one above the '0') indicates a speed of 0 m/s. The rightmost tick mark (the one above the 'c') indicates the speed of light (exactly 299,792,458 m/s !). The marks in-between from left to right indicate 20%, 40%, 60% and 80% of the speed of light respectively. This logarithmic scale allows you to vary your speed more sensitively as you approach the speed of light. Instead of using the mouse, it is possible to change your speed using the keyboard, which can be more sensitive than the mouse.

• Press 'a' to increase your speed.
• Press 'z' to decrease your speed.

This is all well and good, but the exciting stuff happens in the main window. Try this . . .

1. Rearrange the camera and teapot so that it is off centre.
2. Increase the speed gradually from 0 m/s to about 90% of the speed of light.
3. You should see the teapot shoot of into the distance. Don't worry! This is meant to happen! More about this in Lesson 3, but for now bring back the teapot by holding down the space bar. The teapot will come rushing towards you. Let go of the space bar when the teapot is nearby. If the teapot went too far, hold down return to bring it back.

You'll probably see something a bit like below . . .

Wooahh! What's going on here? Our teapot has been hideously deformed. And it changed colour. And, is it just me, or did it get brighter too? Well, I'm sure the physicists among you will tell us that this is all down to Einstein's Theory of Special Relativity. In fact there are three different effects going on here.

• Lorentz Transformations
• Doppler Effect
• Headlight Effect

We will explain these one at a time in later lessons. But first, try holding down the 'space bar' again. You should see the teapot shoot of past you. What you are doing is setting time in motion. Whereas before time was frozen and you were seeing a snapshot of the teapot, by pressing the 'space bar' you increase time by a small amount. The teapot there for starts moving because of it's velocity relative to the camera. You can reverse time by pressing 'Return'. And if things get completely out of hand, you can set the time back to zero by pressing 't'. So just for completeness . . .

• Press the 'space bar' to increment the time in the Warp universe.
• Press 'Return' to reverse increment the time.
• Press 't' to reset the time.

RELATIVITY - II

Changing the View

Warp consists of a three-dimensional environment that may be navigated using the mouse or the keyboard. When Warp starts, the you should be presented with the following screen:

In this case the object is a teapot viewed from above. This isn't obvious at first, so we need to change our point of view. The viewpoint can be changed by using the arrow buttons on the Console Bar. It is also possible to use the keypad to achieve the same effect.

• Keys '4' and '6' move the camera horizontally left and right respectively.
• Keys '8' and '2' move the camera vertically up and down respectively.
• Keys '5' and '0' move the camera into and out of the screen respectively.

That said, you might prefer to use fixed movement axes. This means that the arrows on the Console will always move the camera along the axes of the Warp universe. If this sounds like a good idea then press 'r' to change into this fixed axis system. While this may not seem like a good idea at first, it becomes more useful later, so keep it in mind.

• Press 'r' to toggle 'camera relative' mode on / off.

Note that if you go inside the teapot you will see the teapot as a wireframe. This is because Warp tries to save computing time by not drawing the inside (or in some cases the back) of objects. Normally this isn't a problem, but if it ever does bother you, just press 'b'. This will force Warp to draw everything properly. The downside it that Warp may run slower.

• Pressing 'b' will force Warp to draw the inside (or back) of objects. Pressing 'b' again will return Warp to normal.

The wireframe inside of the teapot is shown below.

It is also possible to rotate the camera by clicking and dragging with the left mouse button within the Main Window. This can be a little confusing but the blue grid beneath the object should allow you to keep your bearings. I recommend that whenever you want to move around the object, you should align the camera in the direction of the z-axis. This is shown by a red line on the Grid. At the end of the line there is a red '+' so you will know which direction the camera is facing. Camera rotation can also be done using the keyboard.

• Keys '[' and ']' rotate the camera up and down respectively.
• Keys ',' and '.' rotate the camera left and right respectively.

The object orientation can also be changed. Clicking and hold the right mouse button. The blue grid will appear again. Then drag the mouse. The object will rotate about its centre point until you are happy with its orientation, as shown below.

Alternatively, you can use the arrow keys to rotate the object to its desired position. Changing the view might be slow and jerky on slower computers. You might be able marginally improve performance by using the following options:

• Pressing 'w' will make Warp switch to 'wireframe' mode. Pressing 'w' again will change back to 'solid' mode.
• Pressing 'c' will make the Console Bar disappear. This is also useful for revealing parts of the object that may be hidden behind the Console. You can still rotate the camera and object using the mouse, but you will need to use the keyboard to change the position of the camera. Pressing 'c' again will bring back the Console.
• Pressing 'g' will toggle the Grid on / off. However, this can make moving around the object confusing.

A screen showing a wireframe teapot with no console is shown below.

Now you can move about the camera, you are ready to do some experiments with special relativity!

RELATIVITY - I

An introduction to special relativity

Albert Einstein developed the special theory of relativity (or special relativity) in 1905. Before special relativity, there were a number of problems with the classical explanations of electromagnetism which in Einstein's view contradicted the principle of relativity.

Special relativity is based on two simple postulates:

1. The special principle of relativity: The laws of physics are the same for all observers, regardless of their velocity.

2. The speed of light in a vacuum (c) is constant: That is, everyone will always measure the speed of light as being the same (i.e. c = 299,798,458 m/s), regardless of their own velocity.

The important point here is that the speed of light is the same for all observers. Suppose you measure the speed of a beam of light travelling towards you and record it's speed as c. According to Newtonian (or classical) physics, if someone else travelling at 1 m/s (relative to you) were then to measure the speed of a beam of light travelling towards them, then they would measure the speed of light to be c + 1 m/s. However, this does not prove to be the case in practice - everyone records the same speed of light regardless of their velocity relative to each other. Einstein explained this by proposing that the way you view space and time to be different from the way the other person views space and time. The mathematical description of this became the special theory of relativity.

Special relativity remained controversial for many years after it's first publication. However, as experiments became more accurate, special relativity was accepted by the scientific community. Despite this, Einstein did not recieve a Nobel prize for this work - he was granted that honour for his work on the photo-electric effect.

The special relativity simulator, Warp, is an attempt to explain some of the strange consequences of special realativity. What does it mean that my view of space and time is different to your view? Well, if you follow the next few lessons and have a play with Warpthen hopefully you will understand...

How does relativity theory resolve the Twin Paradox?

Time must never be thought of as pre-existing in any sense; it is a manufactured quantity. --Hermann Bondi

Paul Davies's recent article "How to Build a Time Machine" has rekindled interest in the Twin Paradox, arguably the most famous thought experiment in relativity theory. In this supposed paradox, one of two twins travels at near the speed of light to a distant star and returns to the earth. Relativity dictates that when he comes back, he is younger than his identical twin brother.

The paradox lies in the question "Why is the traveling brother younger?" Special relativity tells us that an observed clock, traveling at a high speed past an observer, appears to run more slowly. (Many of us solved this problem in sophomore physics, to demonstrate one effect of the absolute nature of the speed of light.) Since relativity says that there is no absolute motion, wouldn?t the brother traveling to the star also see his brother?s clock on the earth move more slowly? If this were the case, wouldn?t they both be the same age? This paradox is discussed in many books but solved in very few. When the paradox is addressed, it is usually done so only briefly, by saying that the one who feels the acceleration is the one who is younger at the end of the trip. Hence, the brother who travels to the star is younger. While the result is correct, the explanation is misleading. Because of these types of incomplete explanations, to many partially informed people, the accelerations appear to be the issue. Therefore, it is believed that the general theory of relativity is required to explain the paradox. Of course, this conclusion is based on yet another mistake, since we don't need general relativity to handle accelerations. The paradox can be unraveled by special relativity alone, and the accelerations incurred by the traveler are incidental. An explanation follows.

Let us assume that the two brothers, nicknamed the traveler and the homebody, live in Hanover, N.H. They differ in their wanderlust but share a common desire to build a spacecraftthat can achieve 0.6 times the speed of light (0.6c). After working on the spacecraft for years, they are ready to launch it, manned by the traveler, toward a star six light-years away. His craft will quickly accelerate to 0.6c. For those who are interested, it would take a little more than 100 days to reach 0.6c at an acceleration of 2g's. Two g's is two times the acceleration of gravity, about what one experiences on a sharp loop on roller coaster. However, if the traveler were an electron, he could be accelerated to 0.6c in a tiny fraction of a second. Hence, the time to reach 0.6c is not central to the argument. The traveler uses the length-contraction equation of special relativity to measure distance. So the star six light-years away to the homebody appears to be only 4.8 light-years away to the traveler at a speed of 0.6c. Therefore, to the traveler, the trip to the star takes only eight years (4.8/0.6), whereas the homebody calculates it taking 10 years (6.0/0.6). It is instructive to discuss how each would view his and the other?s clocks during the trip. Let?s assume that each has a very powerful telescope that enables such observation. Surprisingly, with careful use of the time it takes light to travel between the two we can explain the paradox.

Both the traveler and homebody set their clocks at zero when the traveler leaves the earth for the star (event 1). When the traveler reaches the star (event 2) his clock reads eight years. However, when the homebody sees the traveler reach the star, the homebody?s clock reads 16 years. Why 16 years? Because, to the homebody, the craft takes 10 years to make it to the star and the light six additional years to come back to the earth showing the traveler at the star. So to the homebody, the traveler?s clock appears to be running at half the speed of his clock (8/16.)?

As the traveler reaches the star he reads his clock at eight years as mentioned, but he sees the homebody?s clock as it was six years ago (the amount of time it takes for the light from the earth to reach him), or at four years (10-6). So the traveler also views the homebody?s clock as running half the speed of his clock (4/8).

On the trip back, the homebody views the traveler?s clock going from eight years to 16 years in only four years' time, since his clock was at 16 years when he saw the traveler leave the star and will be at 20 years when the traveler arrives back home (event 3). So the homebody now sees the traveler's clock advance eight years in four years of his time; it is now twice as fast as his clock. On the trip back, the traveler sees the homebody?s clock advance from four to 20 years in eight years of his time. Therefore, he also sees his brother?s clock advancing at twice the speed of his. They both agree, however, that at the end of the trip the traveler?s clock reads 16 years and the homebody?s 20 years. So the traveler is four years younger. The asymmetry in the paradox is that the traveler leaves the earth?s reference frame and comes back, whereas the homebody never leaves the earth. It is also an asymmetry that the traveler and the homebody agree with the reading on the traveler?s clock at each event, but not vice versa. The traveler?s actions define the events.

The Doppler effect and relativity together explain this effect mathematically at any instant. The interested reader will find the combination of these effects discussed in The Fundamentals of Physics, by David Halliday et al. (John Wiley and Sons, 1996). Paul Davies also does a nice job explaining the Twin Paradox in his book About Time (Touchstone 1995, ppf 59.) My explanation follows Davies?s closely; I hope my graph adds further clarity. The reader should also note that the speed that an observed clock appears to run depends on whether it is traveling away from or toward the observer. The sophomore physics problem, mentioned earlier, is a special case as it applies only when the motion of the traveler passes the observer?s reference frame with no separating distance in the direction of motion.

For those with a little more formal physics background, a spacetime diagram also explains the paradox nicely. It is shown with the supporting calculations for the Doppler effect on the observed time. Proper time is time in the frame of the observer.?

Relativity and the Cosmos

In November of 1919, at the age of 40, Albert Einstein became an overnight celebrity, thanks to a solar eclipse. An experiment had confirmed that light rays from distant stars were deflected by the gravity of the sun in just the amount he had predicted in his theory of gravity, general relativity. General relativity was the first major new theory of gravity since Isaac Newton's more than 250 years earlier.

Einstein became a hero, and the myth-building began. Headlines appeared in newspapers all over the world. On November 8, 1919, for example, the London Times had an article headlined: "The Revolution In Science/Einstein Versus Newton." Two days later, The New York Times' headlines read: "Lights All Askew In The Heavens/Men Of Science More Or Less Agog Over Results Of Eclipse Observations/Einstein Theory Triumphs." The planet was exhausted from World War I, eager for some sign of humankind's nobility, and suddenly here was a modest scientific genius, seemingly interested only in pure intellectual pursuits.

THE ESSENCE OF GRAVITY

What was general relativity? Einstein's earlier theory of time and space, special relativity, proposed that distance and time are not absolute. The ticking rate of a clock depends on the motion of the observer of that clock; likewise for the length of a "yardstick." Published in 1915, general relativity proposed that gravity, as well as motion, can affect the intervals of time and of space. The key idea of general relativity, called the equivalence principle, is that gravity pulling in one direction is completely equivalent to an acceleration in the opposite direction. A car accelerating forwards feels just like sideways gravity pushing you back against your seat. An elevator accelerating upwards feels just like gravity pushing you into the floor.

If gravity is equivalent to acceleration, and if motion affects measurements of time and space (as shown in special relativity), then it follows that gravity does so as well. In particular, the gravity of any mass, such as our sun, has the effect of warping the space and time around it. For example, the angles of a triangle no longer add up to 180 degrees, and clocks tick more slowly the closer they are to a gravitational mass like the sun.

Many of the predictions of general relativity, such as the bending of starlight by gravity and a tiny shift in the orbit of the planet Mercury, have been quantitatively confirmed by experiment. Two of the strangest predictions, impossible ever to completely confirm, are the existence of black holes and the effect of gravity on the universe as a whole (cosmology).

COLLAPSED STARS

A black hole is a region of space whose attractive gravitational force is so intense that no matter, light, or communication of any kind can escape. A black hole would thus appear black from the outside. (However, gas around a black hole can be very bright.) It is believed that black holes form from the collapse of stars. As long as they are emitting heat and light into space, stars are able to support themselves against their own inward gravity with the outward pressure generated by heat from nuclear reactions in their deep interiors.

Every star, however, must eventually exhaust its nuclear fuel. When it does so, its unbalanced self-gravitational attraction causes it to collapse. According to theory, if a burned-out star has a mass larger than about three times the mass of our sun, no amount of additional pressure can stave off total gravitational collapse. The star collapses to form a black hole. For a nonrotating collapsed star, the size of the resulting black hole is proportional to the mass of the parent star; a black hole with a mass three times that of our sun would have a diameter of about 10 miles.

General relativity may be the biggest leap of the scientific imagination in history.

The possibility that stars could collapse to form black holes was first theoretically "discovered" in 1939 by J. Robert Oppenheimer and Hartland Snyder, who were manipulating the equations of Einstein's general relativity. The first black hole believed to be discovered in the physical world, as opposed to the mathematical world of pencil and paper, was Cygnus X-1, about 7,000 light-years from Earth. (A light-year, the distance light travels in a year, is about six trillion miles.) Cygnus X-1 was found in 1970. Since then, a dozen excellent black hole candidates have been identified. Many astronomers and astrophysicists believe that massive black holes, with sizes up to 10 million times that of our sun, inhabit the centers of energetic galaxies and quasars and are responsible for their enormous energy release. Ironically, Einstein himself did not believe in the existence of black holes, even though they were predicted by his theory.

THE START OF EVERYTHING

Beginning in 1917, Einstein and others applied general relativity to the structure and evolution of the universe as a whole. The leading cosmological theory, called the big bang theory, was formulated in 1922 by the Russian mathematician and meteorologist Alexander Friedmann. Friedmann began with Einstein's equations of general relativity and found a solution to those equations in which the universe began in a state of extremely high density and temperature (the so-called big bang) and then expanded in time, thinning out and cooling as it did so. One of the most stunning successes of the big bang theory is the prediction that the universe is approximately 10 billion years old, a result obtained from the rate at which distant galaxies are flying away from each other. This prediction accords with the age of the universe as obtained from very local methods, such as the dating of radioactive rocks on Earth.

According to the big bang theory, the universe may keep expanding forever, if its inward gravity is not sufficiently strong to counterbalance the outward motion of galaxies, or it may reach a maximum point of expansion and then start collapsing, growing denser and denser, gradually disrupting galaxies, stars, planets, people, and eventually even individual atoms. Which of these two fates awaits our universe can be determined by measuring the density of matter versus the rate of expansion. Much of modern cosmology, including the construction of giant new telescopes such as the new Keck telescope in Hawaii, has been an attempt to measure these two numbers with better and better accuracy. With the present accuracy of measurement, the numbers suggest that our universe will keep expanding forever, growing colder and colder, thinner and thinner.

General relativity may be the biggest leap of the scientific imagination in history. Unlike many previous scientific breakthroughs, such as the principle of natural selection, or the discovery of the physical existence of atoms, general relativity had little foundation upon the theories or experiments of the time. No one except Einstein was thinking of gravity as equivalent to acceleration, as a geometrical phenomenon, as a bending of time and space. Although it is impossible to know, many physicists believe that without Einstein, it could have been another few decades or more before another physicist worked out the concepts and mathematics of general relativity.

Solar Energy

Tran 1 Solar Energy About 47 percent of the energy that the sun releases to the earth actually reaches the ground. About a third is reflected directly back into space by the atmosphere. The time in which solar energy is available, is also the time we least need it least - daytime. Because the sun's energy cannot be stored for use another time, we need to convert the suns energy into an energy that can be stored. One possible method of storing solar energy is by heating water that can be insulated. The water is heated by passing it through hollow panels. Black-coated steal plates are used because dark colors absorb heat more efficiently. However, this method only supplies enough energy for activities such as washing and bathing. The solar panels generate low grade heat, that is, they generate low temperatures for the amount of heat needed in a day. In order to generate high grade heat, intense enough to convert water into high-pressure steam which can then be used to turn electric generators there must be another method. The concentrated beams of sunlight are collected in a device called a solar furnace, which acts on the same principles as a large magnifying glass. The solar furnace takes the sunlight from a large area and by the use of lenses and mirrors can focus the light into a very small area. Very elaborate solar furnaces have machines that angle the mirrors and lenses to the sun all day. This system can provide sizable amounts of electricity and create extremely high temperatures of over 6000 degrees Fahrenheit. Solar energy generators are very clean, little waste is emitted from the generators into the environment. The use of coal, oil and gasoline is a constant drain, economically and environmentally. Will solar energy be the wave of the future? Could the worlds Tran 2 requirement of energy be fulfilled by the powerhouse of our galaxy - the sun? Automobiles in the future will probably run on solar energy, and houses will have solar heaters. Solar cells today are mostly made of silicon, one of the most common elements on Earth. The crystalline silicon solar cell was one of the first types to be developed and it is still the most common type in use today. They do not pollute the atmosphere and they leave behind no harmful waste products. Photovoltaic cells work effectively even in cloudy weather and unlike solar heaters, are more efficient at low temperatures. They do their job silently and there are no moving parts to wear out. It is no wonder that one marvels on how such a device would function. To understand how a solar cell works, it is necessary to go back to some basic atomic concepts. In the simplest model of the atom, electrons orbit a central nucleus, composed of protons and neutrons. Each electron carries one negative charge and each proton one positive charge. Neutrons carry no charge. Every atom has the same number of electrons as there are protons, so, on the whole, it is electrically neutral. The electrons have discrete kinetic energy levels, which increase with the orbital radius. When atoms bond together to form a solid, the electron energy levels merge into bands. In electrical conductors, these bands are continuous but in insulators and semiconductors there is an energy gap, in which no electron orbits can exist, between the inner valence band and outer conduction band [Book 1]. Valence electrons help to bind together the atoms in a solid by orbiting 2 adjacent nuclei, while conduction electrons, being less closely bound to the nuclei, are free to move in response to an applied voltage or electric field. The fewer conduction electrons there are, the higher the electrical resistively of the material. Tran 3 In semiconductors, the materials from which solar sells are made, the energy gap E.g. is fairly small. Because of this, electrons in the valence band can easily be made to jump to the conduction band by the injection of energy, either in the form of heat or light [Book 4]. This explains why the high resistively of semiconductors decreases as the temperature is raised or the material illuminated. The excitation of valence electrons to the conduction band is best accomplished when the semiconductor is in the crystalline state, i.e. when the atoms are arranged in a precise geometrical formation or “lattice.” At room temperature and low illumination, pure or so-called intrinsic semiconductors have a high resistively. But the resistively can be greatly reduced by doping,” i.e. introducing a very small amount of impurity, of the order of one in a million atoms. There are 2 kinds of doping. Those which have more valence electrons that the semiconductor itself are called donors and those which have fewer are termed acceptors [Book 2]. In a silicon crystal, each atom has 4 valence electrons, which are shared with a neighboring atom to form a stable tetrahedral structure. Phosphorus, which has 5 valence electrons, is a donor and causes extra electrons to appear in the conduction band. Silicon so doped is called n-type [Book 5]. On the other hand, boron, with a valence of 3, is an acceptor, leaving so-called holes in the lattice, which act like positive charges and render the silicon p-type[Book 5]. Holes, like electrons, will remove under the influence of an applied voltage but, as the mechanism of their movement is valence electron substitution from atom to atom, they are less mobile than the free conduction electrons [Book 2]. In a n-on-p crystalline silicon Tran 4 solar cell, a shadow junction is formed by diffusing phosphorus into a boron-based base. At the junction, conduction electrons from donor atoms in the n-region diffuse into the p-region and combine with holes in acceptor atoms, producing a layer of negatively-charged impurity atoms. The opposite action also takes place, holes from acceptor atoms in the p-region crossing into the n-region, combining with electrons and producing positively-charged impurity atoms [Book 4]. The net result of these movements is the disappearance of conduction electrons and holes from the vicinity of the junction and the establishment there of a reverse electric field, which is positive on the n-side and negative on the p-side. This reverse field plays a vital part in the functioning of the device. The area in which it is set up is called the depletion area or barrier layer[Book 4]. When light falls on the front surface, photons with energy in excess of the energy gap interact with valence electrons and lift them to the conduction band. This movement leaves behind holes, so each photon is said to generate an electron-hole pair [Book 2]. In the crystalline silicon, electron-hole generation takes place throughout the thickness of the cell, in concentrations depending on the irradiance and the spectral composition of the light. Photon energy is inversely proportional to wavelength. The highly energetic photons in the ultra-violet and blue part of the spectrum are absorbed very near the surface, while the less energetic longer wave photons in the red and infrared are absorbed deeper in the crystal and further from the junction [Book 4]. Most are absorbed within a thickness of 100 æm. The electrons and holes diffuse through the crystal in an effort to produce an even distribution. Some recombine after a lifetime of the order of one millisecond, neutralizing their charges and giving up energy in the form of heat. Others reach the junction before their lifetime has expired. There they are separated Tran 5 by the reverse field, the electrons being accelerated towards the negative contact and the holes towards the positive [Book 5]. If the cell is connected to a load, electrons will be pushed from the negative contact through the load to the positive contact, where they will recombine with holes. This constitutes an electric current. In crystalline silicon cells, the current generated by radiation of a particular spectral composition is directly proportional to the irradiance [Book 2]. Some types of solar cell, however, do not exhibit this linear relationship. The silicon solar cell has many advantages such as high reliability, photovoltaic power plants can be put up easily and quickly, photovoltaic power plants are quite modular and can respond to sudden changes in solar input which occur when clouds pass by. However there are still some major problems with them. They still cost too much for mass use and are relatively inefficient with conversion efficiencies of 20% to 30%. With time, both of these problems will be solved through mass production and new technological advances in semiconductors.

Bibliography

Tran 6

Bibliography

1) Green, Martin Solar Cells, Operating Principles, Technology and System Applications. New Jersey, Prentice-Hall, 1989. pg 104-106 2) Hovel, Howard Solar Cells, Semiconductors and Semimetals. New York, Academic Press, 1990. pg 334-339 3) Newham, Michael ,Photovoltaics, The Sunrise Industry, Solar Energy, October 1, 1989, pp 253-256 4) Pulfrey, Donald Photovoltaic Power Generation. Oxford, Van Norstrand Co., 1988. pg 56-61 5) Treble, Fredrick Generating Electricity from the Sun. New York, Pergamon Press, 1991. pg 192-195