Brian Greene: The Elegant Universe.
(1) Super-strings.

Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory.

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Finite strings remove infinities.

Greene's award-winning science book ( published in 1999 ) introduces us to relativity and quantum mechanics by imagining familiar comparisons with their basic ideas. String theory makes general relativity and quantum theory compatible, if it is correct. We dont know this yet because the supposed strings, that replace point elementary particles, are on far too small a scale ( the Planck scale ) to be reached by experiment, requiring the kind of energies to be found soon after the emergence of the universe in the big bang.

As Greene puts it, physicists will have to make the big bang itself do, as a cosmic accelerator experiment, and measure its results, in the laboratory of the universe.

In such extreme scenarios, as the big bang, or black holes, the conditions for the large scale physics of general relativity and small scales of quantum mechanics come together. General relativity predicted a singularity or infinitely dense point and infinite curvature at the origin of the universe, or within a black hole. This breaks down the law of space-time being geometrically curved with gravitational mass.

Quantum theory appeared to offer a way out of this impasse with Heisenberg's uncertainty principle. A photon that throws light on an electron needs a short wave-length to determine its position accurately. But shorter wave-lengths have higher energy and give the electron a kick that creates an uncertainty in its momentum. A longer wave-length disturbs less its momentum but is a less precise observation of position. It's not just a question of disturbing the momentum of a particle the more accurately it is measured for position, and vice versa.

Empty space is really a seething mass of energy eruptions, viewed on a sufficiently small scale. Tho, over-all, a vacuum has zero energy. The uncertainty relation allows energy to be borrowed in inverse proportion to the time taken. The more energetic a particle and anti-particle creation, the quicker they must annihilate each other, thus preserving the spirit of the conservation law of mass-energy, within Heisenberg's terms.

At the incredibly small Planck length, to confine a particle, in so narrow a region, is to create ( literally ) massive uncertainty. Consequently, the curvature of the space and time dimensions will lose their continuity and become too grotesquely distorted to be meaningful as left or right etc. General relativity is inapplicable to the so-called 'quantum foam'. A combined theory of quantum gravity is thus frustrated.

According to the string theorists, the cause of this difficulty is the treatment of elementary particles as infinitely small points of no dimension. Such points would be small enough to probe the quantum foam, below the Planck length. Suppose that elementary particles are one dimensional 'strings', so to speak, of about Planck length. Then they will be too 'big' to probe the quantum foam, just as one's finger is too insensitive to feel the irregularities of a granite surface.

More exactly, a Feynmann diagram, of particle interactions, has a new interpretation, owing to special relativity, if re-drawn in terms of looped strings, rather than point particles. Whoever observed the infinitessimal point particles would agree on their positions at a point of interaction. But for the finite-sized loops, coming together to form a different loop and therefore a different particle, described by a different vibration pattern, different observers would disagree when and where the interaction took place. For, in special relativity, observers in relative motion use space and time co-ordinate systems that disagree when 'now' is.

The interaction location is smeared out along the observational indefiniteness, so the force of the particle need no longer be treated as of infinite strength at an infinitessimal point. Finite strings produce well-behaved finite answers due to the blurring over of the sub-Planck scale with its quantum foam.
Nor would it avail one to pump more energy, and therefore frequency, into a string, to give it a shorter wavelength, more probing of an object's position, as is done with photons. The string is merely magnified in size, rather than becoming a magnifier.

A combined theory of quantum gravity becomes possible, after all.

String resonances as 'elementary' particles.

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A basic value of string theory is that all the supposedly elementary particles may be taken as various vibrational patterns, or resonances, of a single loop of Planck length 'string'. ( To give an idea of this measure, if an atom was expanded to the size of the known universe, the Planck length would scarcely reach the height of an average tree. )

Matter is made up of over a hundred or so atoms, depending on how many protons and neutrons they contain in their nuclei, until their number makes them too unstable to hold together. Their electric charges are neutralised by a cloud of electrons, with opposite electric charges. This accounts for the fact that the electro-magnetic force does not normally prevail over the extremely feeble, but purely attractive, gravitational force, that holds the galaxies together, the planets to the sun and things to the planets.

The electrons are elementary particles. They are mysteriously associated, in inter-actions, with neutrinos, a scarcely inter-acting particle, too light for any mass, it may possess, to be measured as yet. ( After-note, 2002: the neutrino has been found to possess a small mass. ) The protons and neutrons are made of combinations of three sub-atomic particles called quarks. ( They can also pair to form 'mesons'. ) Quarks are held together by eight possible gluons, as the name suggests.

For some presently unknown reason, the electron, neutrino and a pair of quarks come in two further sets of more massive and ephemeral versions of themselves.

Particles classify into force particles and matter particles. There are four known forces of nature. The gluons are the interactive or force particles for the 'strong force' that holds the nucleus of an atom together but does not extend beyond it.

A relatively 'weak force' is responsible for radio-active decay of the nucleus. It has its own three inter-active particles, which have been compared to 'heavy' photons, in the electro-weak theory that unites the electro-magnetic force with the weak force. The photons are the carriers or inter-active or 'messenger' particles of the electro-magnetic force.
All the particles have anti-particles, which are the same but of opposite charge. Neutral particles, like the photon, are their own anti-particle.

If matter particles are hit with higher energies, they produce more massive versions of themselves, which quickly decay into their basic versions. These are called resonance particles, hundreds of which have been found. The name is by analogy with plucking a string to put more energy into it, producing higher resonances.
In fact string theory, due to the extreme tension of strings, predicts an infinite number of higher resonances, just as there can be an infinite number of wave-lengths and correspondingly higher frequencies and the higher energies that go with them.

A vibrating string has more energy with more and, therefore, shorter wave-lengths like choppy seas instead of gentle rollers. Also, there's more energy if the 'seas' are higher, that is if their crests and troffs mark higher amplitudes. Special relativity translates energy into mass. So, the mass of an elementary particle can be understood in terms of the vibration pattern of a string.

There is a hypothesised force-carrying particle for gravitational mass, called the graviton. General relativity predicted gravitational waves, too feeble to detect by present devices.
An early success of string theory of particles as resonances was to predict the properties of the graviton. It was also calculated that 'the strength of the force transmitted by the proposed graviton pattern of string vibration is inversely proportional to the string's tension.' Since gravity is so feeble, the tension worked out at 10, to the power of 39, tons ( the Planck tension : enough perhaps to work the universe up into a light sweat )!

Not surprisingly, this tension contracts a string loop down to the afore-mentioned Planck length. The energy, for such stiff strings, must be extremely high for them to vibrate at all: on the Planck mass scale.

Greene says, suppose different people were only entrusted with one discrete monetary denomination, corresponding to energy being quantised or permitted only at certain discrete levels ( as, in the Bohr atom, electron orbits are quantised ). These people are only allowed to pay in whole number multiples of these denominations, as nearly as possible, up to the cost of a purchase ( being let off, in so far as their denomination may not fully add up to the full price ).

Likewise, strings have a minimum energy denomination proportional to the string's tension, itself proportional to the number of crests and troffs in a vibration pattern, whose energy is a whole number multiple, determined by its amplitude, of this quantised energy minimum. The typical mass-equivalent of some vibrating loop is 1, 2, 3,... times the Planck mass.

This is about the mass of a grain of dust, massively beyond the masses of elementary particles. Despite the tension of strings, quantum uncertainty ensures some vibration, which is associated with a negative energy that can cancel out the string's Planck energy, manifested in the lowest, or one times Planck energy, vibration levels. This can produce the tiny masses of elementary particles, tho not typically.
These cancellations worked perfectly for the vibration pattern hypothesised as the graviton, which is just as well, because the graviton, akin to the photon, as a force carrier, is reckoned to have zero mass.
( String pattern theory can also be related to nature's other three force-carrying particles. )


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String theory is expected to incorporate the principle of super-symmetry. For the laws of nature to be truly general, they must apply in all manner of circumstances. It should not matter when or where an event happens, from what angle, or in what motion. The law should still be observed to hold.
Laws that respect these conditions are said to exhibit certain symmetries, such as thru translations in space and time.

Special relativity is symmetric with respect to observers in relative motion, who can all equally claim they are at rest, relative to any motion between themselves and other observers. General relativity goes further, as accelerating observers are, in effect, at rest in a gravitational field. This enforces a symmetry that ensures equality of all points of view.

The other three forces are also required to enforce other more abstract 'gauge' symmetries. However, there was one further symmetry to do with space, time and motion, namely spin. This is rather as the earth rotates, as well as revolves. Elementary point particles would not seem to have a meaningful spin. But the magnetic properties of electrons, for instance, showed that in a quantum sense they had. Only, this spin did not vary like the skater pulling in her arms to spin faster.

The particle spin is a fixed quantity that goes to define its nature. Its quantum mechanical rate is spin one-half for all matter particles and spin one for three of the force carriers. The graviton would have spin two. String theory actually demands a vibration pattern that corresponds to a massless spin-two particle.

It turns out that spin invokes another symmetry principle of nature: 'super-symmetry'. Brian Greene says no more about it than: 'supersymmetry can be associated with a change in observational vantage point in a "quantum-mechanical extension of space and time".'

Whatever that means, it implied that particles must come in pairs with spins differing by one half. This would naturally partner the matter and force particles. Unfortunately, the standard model, that unifies three of the four forces ( leaving out gravity ), matched none of the existing particles. Instead of effectively halving the number of particles, super-symmetry doubled them, by positing a complete new set of partners.

However, super-symmetry pairings of bosons ( with whole number spins ) and fermions ( with half-number spins ) give cancelling contributions to particle interactions that the standard model can other-wise only make add-up by extreme fine tuning of its calculations.

The three non-gravitational forces, tho of greatly disparate strength, apparently diverged at an early stage of the big bang's evolution. The quantum flux of virtual particles were found to weaken the intrinsic force of an electrically charged particle they surrounded, until approach at very close distance. The opposite situation held for the strong force and to a lesser extent the weak force, so that at very short distance not greatly above the Planck length, the three forces' strengths converge.
But, it was found that extra quantum fluctuations provided by super-symmetric particles would make the convergence perfect.

In the super-symmetric version of string theory, it emerged that the boson and fermion patterns of vibration came in pairs.

Richard Lung.

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Hidden dimensions: part two.

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