01-27-2007, 02:23 PM
by Saul-Paul Sirag
Albert Einstein in 1915 introduced the idea that gravity is to be explained as the warping of four-dimensional (4-d) spacetime. Whatever doubts physicists had - and there were many - about the reality of the 4-dimensionality of spacetime (as a unified geometrical whole which could be warped) were erased by the dramatic verification of Einstein's gravity theory (called the General Theory of Relativity) in 1919, when a group of British astronomers led by Arthur Eddington measured the bending of starlight grazing the sun during a solar eclipse. That same year, Theodore Kaluza, a Polish physicist, came up with the idea that not only the Einstein gravity theory but also electromagnetism, including the electromagnetic theory of light due to James Clerk Maxwell (1831-1979), could be derived from the assumption that spacetime is actually a warped 5-dimensional geometric structure. With Einstein's help, Kaluza's 5-d theory was published in 1921.
The decade of the 1920s was the most revolutionary decade in physics and astronomy. I will mention only the highlights. In quantum physics: deBroglie's wave-particle duality; Heisenberg's matrix mechanics, and the uncertainty principle; Bohr's complementarity principle; Pauli's exclusion principle; Schroedinger's wave function equation; Dirac's antimatter equation (which unified quantum theory and Einstein's special relativity). In astronomy: Eddington's theory of the internal constitution stars (including the sun); the discovery of galaxies beyond the Milky Way galaxy; Friedmann & Lemaitre's theory of the expansion of the universe; Hubble's observations verifying the expansion of the universe.
In the midst of this revolution, Einstein contributed seminal papers on the statistics of quantum theory and the stimulated emission of photons from atoms. These papers led to many later developments including the laser. But Einstein was primarily interested in what he called "Unified field theory," which meant the unification of gravity with electromagnetism. Kaluza's 5-dimensional version of such a unified theory was an amazing achievement, but it had the major flaw that it could not explain why we don't see the 5th dimension (which is supposed to be spatial). Another flaw was that it said nothing about the new quantum mechanics which was exploding throughout the 1920s.
The Swedish physicist Oscar Klein in 1926 spoke to both these questions by publishing his version of the 5-d theory, in which the 5th dimension is not visible to us because it is an extremely small compact dimension; in other words, each point of 4-d spacetime is replaced by a tiny circle whose radius is around 10-33 cm. This is the Planck length, which is named for Max Planck who defined this size as the basic unit of size in the quantum world. The Planck length is 20 orders of magnitude smaller than a proton (10-13 cm): so if the 5th dimension is. a Planck length circle, it is no wonder we can't walk around in it; not even a proton could do that!
Klein's Planck-length circle, as a candidate for the 5th dimension, entailed both Einstein's general relativity (applied to 5-d spacetime) and quantum theory to provide the smallness of the extra dimension. As a bonus, the theory provides a geometric explanation for the quantization of electric charge; that is why every electron carries the same charge.
This 5-d theory called Kaluza-Klein theory was forgotten in the world of physics for several decades during which the frontier of physics became the exploration of the nucleus of the atom, where two new forces were discovered: the strong and weak nuclear forces. The strong force holds the nucleus together against the electrical repulsion of the constituent protons, all carrying an identical positive charge (remember: like charges repel). The weak force causes the most common type of nuclear decay - changing one type of atom into another in a kind of 20th century alchemy. These forces were exciting things to explore, and it was obvious that any proposed "unified field theory" would be incomplete without taking them into account. In his last two decades, Einstein (1879-1955) was a revered grandfather figure, who was widely believed to be out of touch with the frontiers of physics - persisting in his doubts about the fundamental nature of quantum mechanics, and his fervent pursuit of the holy-grail of physics "the unified field theory."
It was quite a surprise to physics that by the 100th anniversary celebrations of Einstein's birth, a truly unified theory had arisen: superstring theory. Discovered in 1971 (by Raymond, Neveu and Schwarz), it required 10-dimensions of spacetime! Physicists suddenly began to read the old 5-d Kaluza-Klein theory papers (and translated them into English). In 1975, Sherk and Schwarz showed that superstring theory unifies both Einstein's theory of gravity and quantum mechanics, and also provides for the unification of all the forces: gravity, electromagnetism, and the strong and weak nuclear forces. During the Einstein celebration-year 1979, John Schwarz teamed up with Michael Green - the black and green team! - and together (over several years,) they proved that superstring theory is a self-consistent theory of quantum gravity, which includes General Relativity and Quantum Mechanics as sub-theories. This was published in 1984 and created a sensation in the world of physics. Many (especially younger) physicists immediately jumped on this "bandwagon," so that today unified field theory - the gleam in Einstein's eye - is a vast industry in physics. This is why physicists take the notion of hyperspace (10 dimensions of spacetime) seriously.
Of course, the idea of hyperspace goes way back to Plato (427-347 B.C.), who suggested in his Cave allegory, that we are like prisoners of the 3-d world, identifying ourselves with our 3-d shadows, rather than the hyper-dimensional creatures we really are. Plato never used the word hyper-dimensional, but the idea is clearly in his story of the projection of the prisoner's shadows (a 2-d projection) on the cave wall. The prisoners because they are so securely chained, come to identify themselves with their shadows cast by a fire behind them; and they believe they, as shadows, are interacting with the shadows cast by people walking behind them. One of the prisoners breaks free of his chains and escapes to the world outside the cave, where he sees the full 3-d world. He can now really interact with the other 3-d people and objects. However, he goes back to try to rescue his former fellow prisoners. They mock him and challenge him to tell them what he thinks he sees in their shadow world. Because he has been in the bright sunlight outside the cave, his eyes- are not as keenly. adjusted to the dark shadow-world in which his fellow prisoners live. They can make out the details of the shadows better than he can. This proves to them that he is merely mad.
It is worth considering that the bizarreness of the Ted Owens story is a modern-day version of Plato's Cave allegory.
Even though Plato had said of his Academy: "Let no one enter here without geometry," it took many centuries for geometry to extend to the 4th dimension. It was the 4th dimension as a doorway to the spiritual realm that inspired this geometric foray. The philosopher who attempted to geometrize the Platonic realm was Henry More (1614-1687), an influential colleague of Isaac Newton at Cambridge University. He taught that the spiritual realm extended into a 4th dimension, which he called "spissitude." But this sort of thinking caught on only when mathematicians began exploring the geometry of higher dimensional spaces.
August Moebius (1790-1868) is most famous for his discovery of the Moebius strip, a surface that has only one side. But in 1827 he described how a 3-d object (such as a right handed glove) could be turned into its mirror image (a left-handed glove) by rotating it through 4-dimensional space. Such a rotation could also be used to tie or untie a knot (whose ends are connected as in the mathematical definition of a knot); and link or unlink a chain.
Johann Carl Friedrick Zoellner (1834-1882), an astronomer at the University of Leipzig (where Moebius taught), tried to prove that the spiritual realm was 4-dimensional by having mediums such as Henry Slade link two wooden rings (one of oak and one of alder). Slade never did this, but succeeded in convincing Zoellner that he could move things through the 4th dimension by (among other things) tying four trefoil knots in a loop of string whose ends were sealed together. Zoellner wrote about these ideas in the book, Trancendental Physics, which made the notion of the 4th dimension abhorrent among scientists.
Mathematicians, largely unconcerned with the application of their discoveries, continued to explore geometries well beyond the 4th dimension. They were interested in the most general case - any number of dimensions.
Hyperspace as a word meaning a space of more than three dimensions was coined in the 1890s by mathematicians, who were exploring the geometries defined by Bernhard Riemann (1826-1866) which were not only non-Euclidean (with any degree of warping--called "curvature"), but also were spaces of any number of dimensions. Riemann, himself, even proposed that curved (non-Euclidean) 3-d space might account for gravity. He was almost right. Einstein in 1915 showed that gravity could be accounted for by a curved 4-d spacetime.
Now physics is in the (embarrassing) situation of having 10-dimensional spacetime forced on it (at least in theory) if we wish to unify general relativity with quantum theory. The major experimental test of this theory is the search for supersymmetry partners for all of the ordinary fundamental particles. Ironically, this seems to be a replay of Dirac's 1929 unification of quantum theory and special relativity, which required the introduction of anti-particle partners for all the ordinary particles. The anti-electron (the positron) was quickly discovered in 1932; but the next antiparticle, the anti-proton, was not discovered until 1955. Only then did physicists agree that the anti-matter idea must be true for all particles.
Since general relativity and quantum theory are gigantic worlds unto themselves (and hardly on speaking terms with each other), it is not surprising that in order to unify these two theories as sub-theories of a larger theory physicists have envisaged many new consequences, chief among them being the hyperdimensional (10-d) spacetime.
http://www.williamjames.com/sirag.htm
Albert Einstein in 1915 introduced the idea that gravity is to be explained as the warping of four-dimensional (4-d) spacetime. Whatever doubts physicists had - and there were many - about the reality of the 4-dimensionality of spacetime (as a unified geometrical whole which could be warped) were erased by the dramatic verification of Einstein's gravity theory (called the General Theory of Relativity) in 1919, when a group of British astronomers led by Arthur Eddington measured the bending of starlight grazing the sun during a solar eclipse. That same year, Theodore Kaluza, a Polish physicist, came up with the idea that not only the Einstein gravity theory but also electromagnetism, including the electromagnetic theory of light due to James Clerk Maxwell (1831-1979), could be derived from the assumption that spacetime is actually a warped 5-dimensional geometric structure. With Einstein's help, Kaluza's 5-d theory was published in 1921.
The decade of the 1920s was the most revolutionary decade in physics and astronomy. I will mention only the highlights. In quantum physics: deBroglie's wave-particle duality; Heisenberg's matrix mechanics, and the uncertainty principle; Bohr's complementarity principle; Pauli's exclusion principle; Schroedinger's wave function equation; Dirac's antimatter equation (which unified quantum theory and Einstein's special relativity). In astronomy: Eddington's theory of the internal constitution stars (including the sun); the discovery of galaxies beyond the Milky Way galaxy; Friedmann & Lemaitre's theory of the expansion of the universe; Hubble's observations verifying the expansion of the universe.
In the midst of this revolution, Einstein contributed seminal papers on the statistics of quantum theory and the stimulated emission of photons from atoms. These papers led to many later developments including the laser. But Einstein was primarily interested in what he called "Unified field theory," which meant the unification of gravity with electromagnetism. Kaluza's 5-dimensional version of such a unified theory was an amazing achievement, but it had the major flaw that it could not explain why we don't see the 5th dimension (which is supposed to be spatial). Another flaw was that it said nothing about the new quantum mechanics which was exploding throughout the 1920s.
The Swedish physicist Oscar Klein in 1926 spoke to both these questions by publishing his version of the 5-d theory, in which the 5th dimension is not visible to us because it is an extremely small compact dimension; in other words, each point of 4-d spacetime is replaced by a tiny circle whose radius is around 10-33 cm. This is the Planck length, which is named for Max Planck who defined this size as the basic unit of size in the quantum world. The Planck length is 20 orders of magnitude smaller than a proton (10-13 cm): so if the 5th dimension is. a Planck length circle, it is no wonder we can't walk around in it; not even a proton could do that!
Klein's Planck-length circle, as a candidate for the 5th dimension, entailed both Einstein's general relativity (applied to 5-d spacetime) and quantum theory to provide the smallness of the extra dimension. As a bonus, the theory provides a geometric explanation for the quantization of electric charge; that is why every electron carries the same charge.
This 5-d theory called Kaluza-Klein theory was forgotten in the world of physics for several decades during which the frontier of physics became the exploration of the nucleus of the atom, where two new forces were discovered: the strong and weak nuclear forces. The strong force holds the nucleus together against the electrical repulsion of the constituent protons, all carrying an identical positive charge (remember: like charges repel). The weak force causes the most common type of nuclear decay - changing one type of atom into another in a kind of 20th century alchemy. These forces were exciting things to explore, and it was obvious that any proposed "unified field theory" would be incomplete without taking them into account. In his last two decades, Einstein (1879-1955) was a revered grandfather figure, who was widely believed to be out of touch with the frontiers of physics - persisting in his doubts about the fundamental nature of quantum mechanics, and his fervent pursuit of the holy-grail of physics "the unified field theory."
It was quite a surprise to physics that by the 100th anniversary celebrations of Einstein's birth, a truly unified theory had arisen: superstring theory. Discovered in 1971 (by Raymond, Neveu and Schwarz), it required 10-dimensions of spacetime! Physicists suddenly began to read the old 5-d Kaluza-Klein theory papers (and translated them into English). In 1975, Sherk and Schwarz showed that superstring theory unifies both Einstein's theory of gravity and quantum mechanics, and also provides for the unification of all the forces: gravity, electromagnetism, and the strong and weak nuclear forces. During the Einstein celebration-year 1979, John Schwarz teamed up with Michael Green - the black and green team! - and together (over several years,) they proved that superstring theory is a self-consistent theory of quantum gravity, which includes General Relativity and Quantum Mechanics as sub-theories. This was published in 1984 and created a sensation in the world of physics. Many (especially younger) physicists immediately jumped on this "bandwagon," so that today unified field theory - the gleam in Einstein's eye - is a vast industry in physics. This is why physicists take the notion of hyperspace (10 dimensions of spacetime) seriously.
Of course, the idea of hyperspace goes way back to Plato (427-347 B.C.), who suggested in his Cave allegory, that we are like prisoners of the 3-d world, identifying ourselves with our 3-d shadows, rather than the hyper-dimensional creatures we really are. Plato never used the word hyper-dimensional, but the idea is clearly in his story of the projection of the prisoner's shadows (a 2-d projection) on the cave wall. The prisoners because they are so securely chained, come to identify themselves with their shadows cast by a fire behind them; and they believe they, as shadows, are interacting with the shadows cast by people walking behind them. One of the prisoners breaks free of his chains and escapes to the world outside the cave, where he sees the full 3-d world. He can now really interact with the other 3-d people and objects. However, he goes back to try to rescue his former fellow prisoners. They mock him and challenge him to tell them what he thinks he sees in their shadow world. Because he has been in the bright sunlight outside the cave, his eyes- are not as keenly. adjusted to the dark shadow-world in which his fellow prisoners live. They can make out the details of the shadows better than he can. This proves to them that he is merely mad.
It is worth considering that the bizarreness of the Ted Owens story is a modern-day version of Plato's Cave allegory.
Even though Plato had said of his Academy: "Let no one enter here without geometry," it took many centuries for geometry to extend to the 4th dimension. It was the 4th dimension as a doorway to the spiritual realm that inspired this geometric foray. The philosopher who attempted to geometrize the Platonic realm was Henry More (1614-1687), an influential colleague of Isaac Newton at Cambridge University. He taught that the spiritual realm extended into a 4th dimension, which he called "spissitude." But this sort of thinking caught on only when mathematicians began exploring the geometry of higher dimensional spaces.
August Moebius (1790-1868) is most famous for his discovery of the Moebius strip, a surface that has only one side. But in 1827 he described how a 3-d object (such as a right handed glove) could be turned into its mirror image (a left-handed glove) by rotating it through 4-dimensional space. Such a rotation could also be used to tie or untie a knot (whose ends are connected as in the mathematical definition of a knot); and link or unlink a chain.
Johann Carl Friedrick Zoellner (1834-1882), an astronomer at the University of Leipzig (where Moebius taught), tried to prove that the spiritual realm was 4-dimensional by having mediums such as Henry Slade link two wooden rings (one of oak and one of alder). Slade never did this, but succeeded in convincing Zoellner that he could move things through the 4th dimension by (among other things) tying four trefoil knots in a loop of string whose ends were sealed together. Zoellner wrote about these ideas in the book, Trancendental Physics, which made the notion of the 4th dimension abhorrent among scientists.
Mathematicians, largely unconcerned with the application of their discoveries, continued to explore geometries well beyond the 4th dimension. They were interested in the most general case - any number of dimensions.
Hyperspace as a word meaning a space of more than three dimensions was coined in the 1890s by mathematicians, who were exploring the geometries defined by Bernhard Riemann (1826-1866) which were not only non-Euclidean (with any degree of warping--called "curvature"), but also were spaces of any number of dimensions. Riemann, himself, even proposed that curved (non-Euclidean) 3-d space might account for gravity. He was almost right. Einstein in 1915 showed that gravity could be accounted for by a curved 4-d spacetime.
Now physics is in the (embarrassing) situation of having 10-dimensional spacetime forced on it (at least in theory) if we wish to unify general relativity with quantum theory. The major experimental test of this theory is the search for supersymmetry partners for all of the ordinary fundamental particles. Ironically, this seems to be a replay of Dirac's 1929 unification of quantum theory and special relativity, which required the introduction of anti-particle partners for all the ordinary particles. The anti-electron (the positron) was quickly discovered in 1932; but the next antiparticle, the anti-proton, was not discovered until 1955. Only then did physicists agree that the anti-matter idea must be true for all particles.
Since general relativity and quantum theory are gigantic worlds unto themselves (and hardly on speaking terms with each other), it is not surprising that in order to unify these two theories as sub-theories of a larger theory physicists have envisaged many new consequences, chief among them being the hyperdimensional (10-d) spacetime.
http://www.williamjames.com/sirag.htm
