3.1 General Relativity
In , three-dimensional space and then time are woven together into a space-time fabric, explaining the effects of gravitation with instead of a force. The starting point for general relativity is the , which equates free fall with inertial motion. A person in a ing elevator will experience weightlessness; objects will either float alongside them, or drift at constant speed. Since everything in the elevator is falling together, no gravitational effect can be observed. Thus, the experiences of an observer in free fall will be similar to those of an observer in deep space, far from any source of gravity. The person cannot feel any acceleration and cannot tell they are in free-fall. The issue that this creates is that free-falling objects can accelerate with respect to each other. In , no such acceleration can occur unless at least one of the objects is being operated on by a force (and therefore is not moving inertially). 5,9
Newton’s universe is like a box - an arena containing empty space with stars and galaxies affecting each other. Einstein doesn’t need a box – everything that happens affects space-time, everything that happens in space-time affects the universe. This internal fabric contains embedded celestial bodies which interact, warp, bend, and distort the space-time according to their mass. 2
Newton and Einstein’s equations make essentially identical predictions as long as the strength of the gravitational field is weak, which is the usual experience. However, there are crucial predictions where the two theories diverge which can be tested experimentally.6
3.2 Examples as to Where the Theories Diverge
3.2.1 Gravitational Lensing
In 1979 at Kitt Peak National Observatory, a piece of sky 7.8 billion light years away gave a glimpse into the workings of gravity. Two quasars only 6 seconds of arc apart (one arc-second being 1/3600 of an angular degree) were discovered and they were found to have identical redshifts and spectra. The probability of this happening coincidentally is exceedingly small, and it was postulated that this pair actually correspond to the same quasar - space-time, including light, had been bent so strongly by massive clusters of stars and galaxies that the light curves around the intervening mass resulting in multiple images viewed from Earth. This corresponds exactly to Einstein’s theory – the bending of space-time explains the existence of gravity - and the bigger the mass or nearer the object, the more curvature and stronger gravitational force.2, 6
This gravitational lensing has since been observed many more times in different locations of the universe.
3.2.2 Precession of the Perihelion of Mercury
A long-standing problem in the study of the Solar System was that the orbit of Mercury did not behave as required by Newton's equations. As Mercury orbits the Sun, the planet follows an ellipse - but only approximately: it is found that the point of closest approach of Mercury to the sun (the perihelion) does not always occur in the same place. This rotation of the orbit is called a precession.
The precession of the orbit is not peculiar to Mercury, all the planetary orbits precess. In fact, Newton's theory predicts these effects, as being produced by the pull of the planets on one another. The question is whether Newton's predictions agree with the magnitude of orbital precession. The precession of the orbits of all planets except for Mercury's can, in fact, be understood using Newton’s equations. But Mercury seemed to be an exception.
As seen from Earth, the precession of Mercury's orbit is measured to be 5600 seconds of arc per century. Newton's equations, taking into account all the effects from the other planets (as well as a very slight deformation of the sun due to its rotation) and the fact that the Earth is not an inertial frame of reference, predicts a precession of 5557 seconds of arc per century. There is a discrepancy of 43 seconds of arc per century. This discrepancy cannot be accounted for using Newton's formalism. In contrast, Einstein was able to predict, without any adjustments whatsoever, that the orbit of Mercury should precess by an extra 43 seconds of arc per century should the General Theory of Relativity be correct.6
3.2.3 Gravitational Waves and their Detection
A stationary object in a pool of water will not make waves. But an object spinning and splashing will create waves rippling away from it. Someone who observes them reaching the other end of the pool could deduce that a disturbance had occurred in the water, and might even be able to tell what produced the waves.
In much the same way, the movement of massive bodies in the cosmos is thought to generate ripples in the fabric of space-time, which are called gravitational waves. Detecting those waves will enable physicists to infer information about the phenomena that caused them.
Pairs of incredibly dense neutron stars (with a mass 2 or 3 times that of the sun compressed into a 10km diameter) swinging around each other 100 or even 1000 times a second “churn up” space-time. This is also the case with stars swirling down into black holes and the formation or collision of black holes. They are all thought to generate gravitational waves, propagating outward across space-time at the speed of light. As of yet no gravitational waves have been detected as the focus has been upon making the machine sufficiently sensitive. The Big Bang should have produced the hugest of all gravitational waves, and with the right instrument, physicists ought to be able to detect them. 2, 6
See appendix for methods of detection.
4. Quantum Mechanics
Despite above factors proving the theory of general relativity to be correct, it still falls apart at the heart of a black hole, or indeed in the Big Bang – when all matter was condensed into an infinitely small space.
Quantum mechanics was formulated by Heinsenberg, Dirac and Schrödinger in the 1920s to reformulate Newton’s approach. It takes away the idea of deterministic distinct positions and velocities replacing it with a quantum state that takes into account the uncertainty in measurements, based upon Heisenberg’s uncertainty principal.
4.1 Heisenberg’s Uncertainty Principal
In order to predict the future position and velocity of a particle, its present position and velocity must be measured accurately. The obvious way to do this is to shine light on the particle – some of the light waves being scattered by the particle which can be detected by the observer -indicating its position. However, light has limited sensitivity depending upon its wavelength – the accuracy with which the position of a particle can be measured is determined by the distance between wave crests. Thus, for precise measurements it is necessary to use high frequency (short wavelength) light.
According to Planck‘s theories, the smallest “unit” of light is one quantum – whose energy is higher at higher frequencies. But even one quantum of light will disturb the particle – changing its velocity unpredictably. And the more energetic the quantum – the greater this effect will be. The more accurately you try to measure the position of a particle, the less accurately you can measure its velocity – and vice versa. Heisenberg showed that this value of uncertainty (the product of position uncertainty and velocity uncertainty) can never fall below a certain fixed quantity – Planck’s constant.9
This firmly puts an end to the classical clockwork nature of the universe – prediction is impossible if the present cannot even be accurately mapped. It is clear to see how “wave-particle duality” exists, as particles do not have a definite position but are “smeared out” with a certain probability distribution. And light can only be emitted or absorbed in packets, or quanta.9
A successful unified theory must incorporate this uncertainty principal – Einstein’s theory general relativity leaves no room for quantum mechanics, Einstein famously stating himself that “God does not play dice”. 2
5. Steps towards Unification
5.1 The Standard Model
In quantum mechanics, the forces or interactions between matter are all supposed to be carried by particles. A matter particle, such as an electron or quark, emits a force carrying particle. The recoil from this emission changes the velocity of the matter particle, for the same reason that a soldier feels the recoil of the gun when it is fired - every force has an equal and opposite reaction force – Newton’s third law of motion. The force carrying particle then collides with another matter particle and is absorbed, changing the momentum of that particle. The net result of this process of emission and absorption is the same as if there had been a force between the two particles of matter. Each force is transmitted by its own force-carrying particle - or gauge boson. A gauge boson with a high mass is indicative of a short range force as it would be difficult to produce and exchange them over a large distance and vice versa.9
The fundamental particles fall into two “families” – leptons and quarks, each with three “generations” of successively heavier members.
Spin is the intrinsic angular momentum of particles, given in units of ħ, which is the quantum unit of angular momentum where ħ=h/2Π = 6.58x10-25 GeV = 1.05x10-34 Js. Electric charges are given in units of the proton’s charge. In SI units the electric charge of the proton is 1.6x10-19 coulombs. The energy unit is the electronvolt (eV) which is the energy gained by one electron crossing a potential difference of one volt. Masses are given in GeV/c2 (a rearrangement of E=mc2), where 1 GeV = 1.60x10-10 joules. The mass of the proton is 0.938GeV/c2 = 1.67x10-27 kg.
The Standard Model incorporates the quarks and leptons as well as their interactions through the strong, weak and electromagnetic forces. Gravity alone remains outside this model. Each force is associated with a gauge boson. Photons carry the electromagnetic force, gluons carry the strong force, and charged W± and neutral Z0 particles carry the weak force. The fundamental forces appear to behave very differently in ordinary matter but the Standard Model indicates that they are very similar in a high enough energy environment. The consistent way to treat the weak force is to unite it with the electromagnetic force - forming the electroweak force. This discovery is akin to the bringing together of electricity and magnetism as electromagnetism by James Clark Maxwell in the mid 19th century.1
5.2 Unifying Gravity with the Standard Model – the need for Quantum Gravity
The 3 main forces incorporated into the Standard Model all have associated bosons - gravity should probably follow in the same way. A massless spin two particle called the graviton is believed to be the mediating particle in the gravitational force. But it has not yet been possible to build a fully self-consistent theory that contains the graviton. As previously stated, the main difficulty in finding a theory that unifies gravity with the other forces is that the theory of gravity – general relativity – is not a quantum theory: it does not take into account the uncertainty principle. As the other forces depend on quantum mechanics in essential ways, unifying gravity would require the uncertainty principle to be incorporated into general relativity.
In terms of particles, as in the Standard Model, the uncertainty principle means that even “empty” space is filled with pairs of both non-detectable virtual particles and antiparticles. If “empty” was a literal description of space, all fields such as the gravitational and electromagnetic fields would have to be exactly zero – but the value of a field and its rate of change through time is similar to the position and velocity (i.e. change in position) of a particle – the uncertainty principal applies and overall accuracy is dependent upon the balance between the accuracy of different measurements - never dropping below Planck’s constant.. If a field in empty space was zero and the rate of change was also zero, which are precise values, this violates the principle by removing quantum fluctuations.
The fluctuations can be though of as pairs of virtual and non-detectable particles which appear together at some time, move apart, and then come together and annihilate each other. Their indirect effects, such as small changes in the energy of electron orbits, can be measured. But these virtual particles (corresponding to those gauge bosons associated with the forces) have energy, and an infinite number of virtual particles means an infinite amount of energy. From Einstein’s equation E=mc2, this requires an infinite amount of mass, which according to the theory of general relativity means the universe would be curved to an infinitely small size.
Other such absurd infinities, known as singularities, occur in the particle theories of the other three forces – but these can be removed through a nifty mathematical process called renormalisation. The drawback with this is that it doesn’t allow prediction – measured values have to be chosen to fit the observations. Attempts to renormalise quantum infinities from general relativity have proved futile – the only adjustments to be made are the strength of gravity and Einstein’s cosmological constant – still leaving singularities in the curvature of space-time, for example.9
6. Towards a Theory of Everything - The Rise(s) and Fall(s) of String Theory
6.1 String Theory - The Basics
In String Theory, in its various forms, all fundamental objects in the universe are made out of tiny loops or strands of vibrating energy known as strings. They are 1018 times smaller than a proton – so small that their shape cannot be resolved and vibrations along it behave, experimentally, just as particles. It was originally formed in the late 1960s as a failed description of the strong force but was rekindled when it was hypothesised that it could be used to explain the gravitational force and indeed unify all theories as everything comes from fundamental strings.2
These strings are thought of a closed loops or open strands in different models. It can be imagined that forces are transmitted by breaking and juggling strings. If we start with a single string that splits into two - when it splits it has effectively juggled the second string, which may split itself. Other strings are doing the same thing at the exact same time and once in a while a string gets mixed up and exchanged back and forth. 2
6.1 Initial Development
There were lots of problems to overcome throughout the early development of String Theory – it predicted a particle which travels faster than the speed of light, for example, which is impossible. Scientists began to lose faith in a model which kept unlocking such complexities and by 1973 barely anyone was continuing to work on it. On the verge of scrapping the theory completely, it was noticed that, by re-thinking the size of these strings, there was a possibility of applying it to gravity – revealing an anomalous massless particle which was currently rather in the way – to be a graviton. 10
In 1984 the complexities and mathematical anomalies were removed and the theory had the mathematical depth to encompass all four forces of the Standard Model, nicely merging the quantum mechanics with general relativity. However, String theory has a major problem in that everything is so tiny and irresolvable by machine- if it cannot be observed or tested in the way that normal theories are tested, is it philosophy or science?
String theory also requires the existence of extra dimensions, but due to what we know of a 4- dimensional universe (including time) these extra dimensions must be hidden - otherwise planetary orbits or electron orbits would be unstable and things generally wouldn’t be the way they are. They are therefore said to be curled up with strings in different orientations – unlike the four dimensions we are used to which are fairly big and flat. The dimensions are said to determine the fixed fundamental constants of nature such as particle mass and force strength. By the mid 1980s the theory seemed unstoppable.
However, behind the scenes the theory was tangled. There were 5 different, but apparently equally valid, versions of the theory which shared the basis of strings and extra dimensions, but differed over whether the strings were loops or open ended strands, or how many extra dimensions were required. String theory was being abandoned again due to lack of progress and a theory which seemed to be unravelling into nothing.10
6.3 The Breakthrough - the arrival of “M” Theory
In 1995 there was a boost in the field of unification via String Theory, Edward Witten (an and at the ) constructed a spectacular new way of looking at String Theory in which there weren’t really 5 different theories, just 5 different ways of looking at the same thing – unifying the theory into “M” Theory. However, there was a price to pay for this unification, yet another, and indeed the 11th dimension, was needed. But this extra dimension allows strings to stretch into a membranous structure, or “brane” which can have 3 or more dimensions and grow to enormous sizes. The idea is that our universe as we know it could be a brane amongst higher dimensional space, possibly opening up the idea of parallel universes existing in the other dimensions.
The “M” theory could also suggest that, contrary to gravity being the weakest of the four forces by some margin, it could be just as strong, but appears to be weaker it moves freely away from the brane on which we are held onto. “M” theory uses the idea of strings which are open ended strands, each end tied down to branes of our normal 3 dimensions, alongside loop strings which exist as gravitons – not tied down they are able to move freely into other dimensions.9, 10
The problem of experimental evidence is still a stumbling block, but with the new generation particle accelerator in CERN, the Large Hadron Collider, it may be possible to observe the graviton as it exists for a snapshot moment before disappearing into another dimension – revealing itself through missing energy. The LHC also has a chance of detecting a key prediction of String Theory which is the existence of supersymmetric particles or “sparticles” – which are like heavier equivalents of all the known particles. Whether or not these elements of the theory can be detected experimentally is key to its future.1
7. Conclusion
Physics and cosmology are leaning to a universe of many possibilities, of which we are only one. The concept of gravity has moved on from Newton’s classical mapping - to explanations of its workings large and small - and finally to a possible solution linking them all to the other forces. String Theory is elegant, providing a sound structure for a unified theory, bridging the gap between Quantum Mechanics and General relativity by effectively smoothing out the fluctuations present in the quantum world enough to allow combination. But without evidence it could simply result in being a time-consuming path which physicists have been following for 30 years that leads to a dead end.
Ultimately, the current situation is a waiting game for the discovery, or indeed lack of discovery, of predicted particles. Only then can be proven whether String Theory is real, or just a piece of mathematical artwork. Further inabilities to make experimental prediction could also mean the theory is not falsifiable whether it’s actually physically true or not. So, the argument that it represents a philosophical question remains. Critics, one of the most prominent being Lee Smolin of the Perimeter Institute in Canada claim that the features of string theory that are at least potentially testable, such as the existence of supersymmetry and cosmic strings, are not even specific to string theory. 11, 12
The emphasis upon experimental evidence is known as a positivistic approach but it is generally thought of as being unduly restrictive. The question then becomes how progressive is the theory, is it answering questions we already had? Some say the answer to this is no where String Theory is concerned, as it seems to open such a can of worms in order to solve existing problems. Without confirmation that the mathematical theory based on strings explains ideas that were not understood before, String Theory may never be fully accepted as a scientifically valid concept.12
8. References
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Particle Physics and Astronomy Research Council, (no date), Big Bang Science.
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Horizon. 2008. What on Earth is wrong with Gravity? BBC 2. January 19.
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Dept. Physics & Astronomy University of Tennessee. Sir Isaac Newton: The
Universal Law of Gravitation. [Online] http://csep10.phys.utk.edu/astr161/lect/history/newtongrav.html [Accessed March 2008]
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Ogborn J. & Whitehouse M, 2001.Advancing Physics A2. Institute of Physics. Institute of Physics Publishing.
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Wikipedia, Introduction to General Relativity, [Online] http://en.wikipedia.org/wiki/Introduction_to_general_relativity [Accessed Marc 2008]
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Dept. Physics & Astronomy University of Tennessee. Albert Einstein and the Theory of Relativity. [Online] http://csep10.phys.utk.edu/astr161/lect/history/einstein.html [Accessed March 2008]
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LIGO – Laser Interferometer Gravitational Wave Observatory. Science of LIGO. [Online] http://www.ligo.caltech.edu/ [Accessed March 2008]
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NASA – Jet Propulsion Laboratory. Gravitational Waves – LISA. [Online] http://funphysics.jpl.nasa.gov/physics/exploring-the-universe/lisa.html [Accessed March 2008]
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Hawking. S & Mlodinow L. 2005. A Briefer History of Time. Transworld Publishers.
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Greene. B, 1999. The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory. Vintage Publishers.
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Wikipedia, Positivism, [Online] http://en.wikipedia.org/wiki/Positivistic [Accessed March 2008]
-
Cartwright N. & Frigg R. 2007. String Theory Under Scrutiny. Physics World. September 2007. pp 14-15
9. Evaluation of Sources
9.1 Reliability
Reference 5 was particularly cross referenced with 9 as Wikipedia is a publicly maintained resource and can contain incorrect information. Some related articles were also highlighted as “requiring attention from an expert in the field” and were consequently avoided as sources.
A lot of starting points, for further elaboration, were taken from reference 2. Being a BBC documentary this is likely to be highly reliable information, despite being “watered down” a little and therefore requiring further investigation into concepts using other sources.
Reference 12 is also likely to be reliable coming from a scientific journal which has extensive proof reading before allowing articles to be published, as are references 9 and 10 being “popular science” books and reference 1, being a booklet produced in collaboration with CERN.
Any online information holds the possibility of containing factual errors, but most websites used came from large organisations which hold expertise in the particular field and it can therefore be presumed the information is correct.
9.2 Potential for bias
The nature the topic means that members of the scientific community are likely to hold different views on current theories. Reference 10, for example, is a book written by a famous string theorist and advocator of the theory - holding a potential for bias, but the shortcomings of the theory are also discussed. Reference 12 ends on a more sceptical note regarding String Theory, but is largely an objective discussion. It can therefore be concluded that sources were free from bias.
It should also be noted that other theories do exist but that String theory, being most developed and dominant, was investigated in this report.
10. Appendix
Gravitational Wave Detection
LIGO
In order to try and detect gravitational waves the Laser Inferometer Gravitational wave Observatory (LIGO) was established. LIGO will detect the ripples in space-time by using a device called a laser interferometer, in which the time it takes light to travel between suspended mirrors is measured with high precision using controlled laser light. Two mirrors hang far apart, forming one "arm" of the interferometer, and two more mirrors make a second arm perpendicular to the first. Viewed from above, the two arms form an L shape. Laser light enters the arms through a beam splitter located at the corner of the L, dividing the light between the arms. The light is allowed to bounce between the mirrors repeatedly before it returns to the beam splitter. If the two arms have identical lengths, then interference between the light beams returning to the beam splitter will direct all of the light back toward the laser. But if there is any difference between the lengths of the two arms, some light will travel to where it can be recorded by a photo detector. The high sensitivity to small differential displacement is achieved by suspending the mirrors at the end of each arm as pendulums using wire slings. 2, 7
Based on current models of astronomical events, and the predictions of the , gravitational waves that originate tens of millions of light years from Earth are expected to distort the 4 kilometre mirror spacing by about 10−18 m, less than one-thousandth the diameter of a .7
LISA
To complement the ground based inferometer LIGO, the Laser Interferometer Space Antenna (LISA) will be launched in 2012. LISA will be the first space-based gravitational wave observatory – its “arms” will be five million km long, a size impossible for a ground-based instrument. It is therefore sensitive to much longer wavelengths and lower frequencies than the LIGO. The interferometer will be created by linking three spacecraft which are 5 million km apart, by lasers in a equilateral triangle An interference pattern will be caused at detectors on each spacecraft from the two lasers it receives – changes in this interference pattern would be a sign of gravitational waves disrupting the alignment of the spacecraft. LISA will be able to measure changes in the laser separation down to as little as 10 picometers, which is about 1/10 the diameter of an atom. 8
