Special Relativity
Gravitation is not responsible for people falling in love.

      Special Relativity--The Paper
The observer on the ground sees the light flash travel a
longer distance than the observer in the spaceship

The longer diagonal distance must be divided by a correspondingly longer time interval to yield an unvarying value for the speed of light.


Notice that the time does not really change
very much at low speeds.

      Special Relativity            
      General Relativity  
    General Relativity
    The ghost in the cosmos
New Scientist vol 181 issue 2433 - 07 February 2004
    Does a ghostly force haunt the universe? A new theory could simultaneously explain three of cosmology's deepest mysteries.

    THE universe is riddled with inexplicable forces. Something strange is tearing space apart. Something unknown holds spinning galaxies together. And at the beginning of time something only - guessed at - made the whole cosmos go bang.
    Cosmologists call these three somethings dark energy, dark matter and inflation. But to a large extent, these are just labels to cover their ignorance - nobody knows what caused inflation, or what dark matter and dark energy really are. Each of these phenomena is a deep mystery that could take many decades of careful observations to pin down.
    Unless, that is, all of the apparently different forces are really one and the same. A single change to the law of gravity might account for them all, if Nima Arkani-Hamed of Harvard University is right. Along with Hsin-Chia Cheng, Markus Luty and Shinji Mukohyama, he has found a new way to modify Einstein's theory of gravity, general relativity. At a stroke, it explains dark energy, dark matter and the driver of inflation. In the new theory they are all the result of the behaviour of one omnipresent fluid called a ghost condensate.
    This potential panacea for cosmology's ills came as a surprise to the physicists who invented it. All they were trying to do was explain dark energy by changing gravity's power over long distances. In 1998, astronomers had discovered that distant supernovae are dimmer and hence further away than expected, implying that the expansion of space has accelerated. What could cause such a thing? The only known force that could affect the vast scales of cosmology is gravity - but we're used to gravity pulling, not pushing.
    Indeed, Einstein's general theory of relativity says that the gravity of ordinary matter and energy is always attractive. The theory has been very successful so far. It correctly predicts the existence of black holes and gravitational lenses, and precisely calculates the orbits of planets in our solar system.
     Most cosmologists assume that there is nothing fundamentally wrong with relativity. Instead, the acceleration of the universe must be the effect of some extra and extraordinary "stuff", a dark energy that exerts a repulsive force (see "Add some energy").
    But could they be wrong? Maybe we don't need some new kind of substance after all. "It has happened before that strange gravitational phenomena were attributed to new forms of matter," says Arkani-Hamed. "In the 19th century, Urbain Leverrier noticed that the orbit of Mercury was doing weird things, and introduced a new planet called Vulcan, even closer to the sun, to explain it. Some people even found the planet." But there was no Vulcan. The oddity in Mercury's orbit was eventually explained by general relativity.
    Instead of positing a mysterious energy to fill space, why not change the nature of the gravitational force? A few physicists have tried this (see "Gravity Fixes"), but so far they have always run into the same problem. Einstein's theory fits together so tightly that changing one term in the equations can have disastrous consequences. When you open up the Swiss watch of relativity and tinker with the mechanism, it just stops working. Each attempt to alter gravity over long distances has altered the force at short range too, changing the orbits of planets in our solar system. "It seemed like it might be a closed door," says theoretical cosmologist Raman Sundrum of MIT, who has worked on theories that modify gravity.
    But Arkani-Hamed and Luty have opened that door, says Sundrum. In the past few months they have found a way to rewrite Einstein's equations, changing a term that profoundly affects the gravitational field. The new field has two components: the ordinary gravity that carries forces between matter, and a kind of fluid that fills the universe, exerting its own gravity.
    From the perspective of quantum theory, the fluid is made up of countless particles all in the same quantum state. That is like the Bose-Einstein condensates created in labs, but rather than atoms or molecules, it is made of massless "ghost" particles, each one of which is stretched out over the whole universe.
    One peculiar aspect of this fluid gives it repulsive gravity. It behaves like an elastic band, storing more and more energy as it is stretched out. In general relativity, mass and energy are not the only things to have gravity. Pressure exerts attractive gravity too, and tension, being the opposite of pressure, generates a kind of antigravity. It sounds counter-intuitive to say "tension pushes", but it means the ghost could explain the acceleration of the universe - the more it stretches, the more repulsive it gets.
    There's a certain irony here. The scientists were trying to explain acceleration without invoking some new kind of unseen stuff, yet they got a substance out of their theories after all. It's a consequence of that mathematical tidiness in Einstein's theory. Any change to the basic equations gives you an extra gravitational field that has its own energy, and so acts like a real physical substance.
    The substances that emerged from previous attempts to fix gravity turned out to be poisonous. As well as exerting their own gravity, they acted as carriers for new short-range forces between chunks of matter. But in the Harvard team's version, the stuff that comes out is a much simpler fluid. It is no more able to transmit forces than, say, air would be.
    And like air, it can be stretched and compressed. Quantum fluctuations in the big bang would have left some patches of condensate with an excess of energy. This energy would have ordinary attractive gravity, so the patches could clump together.
    Could clumps of ghost condensate perform all the roles that we need dark matter for, attracting matter to itself in the early universe, causing stars to form, and now binding galaxies together?
    The Harvard researchers are hopeful, but they cannot be sure. When the clumps of ghost condensate get dense, the maths used to describe them gets a lot harder. The team don't yet know whether the stuff could get dense enough to mimic dark matter. "We don't want to claim too much. We are careful people," says Luty. "This is question number one that we need to answer."
    The group is also cautiously optimistic about the third potential role for ghost condensate
: driving inflation. Most cosmologists agree that the universe experienced a sudden, ultra-fast stage in its expansion around 10-30 seconds after the big bang. This theory removes some apparent paradoxes in cosmology, such as why the cosmic microwave background has such a uniform temperature. Inflation means that the whole of our visible universe came from an exceedingly tiny patch of the big bang, a patch so small that it had an even temperature throughout.
    But what drove inflation? There are several physical models of what might have caused it, most of them involving an "inflaton field", an energy field that goes through a sudden change of character as the universe cools, becoming intensely repulsive for a split second.
Arkani-Hamed and his colleagues realised that the
ghost condensate could do the same thing. Along with Paolo Creminelli and Matias Zaldarriaga, also at Harvard, they have shown that the ghost could have given the young universe that fierce kick, and then settled down to its present gentle push.
    If so it would be a very tidy outcome: all three mysterious forces wrapped up into one. No more troublesome trinity. "That's the dream," says Arkani-Hamed.
    Preprints of the first papers were only released in December, and the idea is so new that the group hasn't even named the ghost particles that make up the condensate. But there have already been some positive reactions from fellow cosmologists.
    Sundrum describes himself as a "moderate fan" of the idea. "It's promising. In the standard view, dark energy and dark matter don't seem to be linked. Here, they are. But we don't yet know whether they are linked in a good way - whether this actually explains them. People should be attempting to shoot this down."
    The best anti-theory ammunition is, as always, observation. One effect the ghost should have is to make the gravity from ordinary matter oscillate in strength. But unfortunately the oscillation would be noticeable only after trillions of years, and we can't wait that long. It's also possible that the
ghost condensate interacts with matter via forces other than gravity. If it feels electromagnetic forces, for example, then it would carry a tiny extra force between electrons. This force would depend on the direction of the electrons' spin, like regular magnetism. It would be weak, but it would fade away with distance more slowly than the ordinary magnetic force. "You could take two huge magnets 10 kilometres apart and feel an extra force," says Arkani-Hamed. But if the ghost is a simple one, with no coupling to electromagnetism, this won't work.
    There is one test, however, that is more promising. Local variations in inflation are supposed to have created the warmer and colder patches in the cosmic microwave background mapped in great detail by NASA's Wilkinson Microwave Anisotropy Probe. The spread of temperatures of these spots should reveal whether or not the inflaton field was a
ghost condensate. "If we use our field to trigger inflation, the predictions are distinctively different, because these excitations are different," says Arkani-Hamed.
    Within a year or two, WMAP might have enough data to test this. If not, we'll have to wait for the European Space Agency's Planck satellite to go up in 2007. Most inflation theories predict a symmetrical, bell-shaped Gaussian distribution of temperatures. If either probe finds such a distribution then the ghost will have been exorcised. Only exorcised from its role in inflation, true - but the theory would lose much of its lustre.
    On the other hand, if the plot of the temperatures is a bit lopsided, deviating in just the right way from a Gaussian curve, the ghost will grow far stronger. It would be a triumph - a single kind of substance that kicked off the big bang, generates structure in the universe and binds galaxies. The story of the ghost condensate would be the story of the birth and growth of the universe.
    And of its death. The ghost might simply carry on accelerating space, tearing the universe apart, as any kind of dark energy would do. As the universe speeds apart, each galaxy would become cut off from the others, everything gradually fading to black. "If you take the long time limit of anything, it's depressing," says Luty.
    Or the ghost could kill our universe in an even more grisly manner. Sundrum points out that in the present model, the condensate isn't quite stable - there is a small chance that it could spontaneously break down, turning into who-knows-what. If that happened, it could blow ordinary matter to bits, obliterating any trace of life.
    The Harvard researchers think that instability will be removed in a later, more complete version of the theory. "It is still very early days," says Arkani-Hamed. Still too early to say whether the ghost condensate can really explain inflation, dark matter and dark energy. Sundrum agrees. "To me these problems are absolutely immense. We're just beginning to address them."
    But even if it does get shot down, the fact that one theory can roll these three mysteries into one may be a strong hint that they are intimately linked. If the ghost isn't the final answer to all the mysteries of cosmology, at least it might be silently pointing the way.

Stephen Battersby  

    Quantum Mechanics

Quantum Mechanics is remarkable for two seemingly contradictory reasons. On the one hand, it is so fundamental to our understanding of the workings of our world that it lies at the very heart of most of the technological advances made in the past half century. On the other hand, no one seems to know exactly what it means!

If If only people knew how frustratingly and yet wonderfully un-mundane the quantum world really is, how our familiar and solid reality ultimately rests so tenuously on the unfathomable ghostly reality beneath. No need any longer for tales of Bermuda Triangle or poltergeist activities; quantum phenomena are much stranger.

I must make it clear from the outset that it is not the theory of Quantum Mechanics that is weird or illogical. On the contrary, it is a beautifully accurate and logical mathematical construction that describes Nature superbly well. In fact, without Quantum Mechanics we would not be able to understand the basics of modern chemistry, or electronics, or material science.

Jim Al-Khalili

Quantum Theory