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Nov 16
2009

Grandfather Paradox

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  • the grandfather paradox deals with the impossibility of going back in time and killing your grandfather
As can be seen from the example above, there are possible fundamental problems of consistency and causality associated with time travel. The most prominent is the "grandfather paradox," in which you travel back in time and kill your grandfather before you were born, which means you could not have been born to then travel back in time to kill your grandfather.

 

 

  • an analysis of the grandfather paradox starts with a simple mechanical example of the paradox using two wormholes
The grandfather paradox as stated is difficult to analyze since it deals with human actions and free will. It is typical of a physics problems to start with a simpler scenario. For example, to understand aerodynamics we first start with understand simple motion, like a ball tossed in the air. For time travel and the grandfather paradox, a simpler scenario is consider a ball tossed through a wormhole, with an exit wormhole nearby in space. A wormhole is a hypothetical tunnel through the fabric of spacetime. Since both space and time are being tunneled, it is theoretically possible to produce a wormhole that not only moves you from some place to another instantaneously, but also can move you back in time.

 

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Nov 16
2009

Time Travel

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  • time travel, while a popular story line, violates most conservation laws
  • in addition, time travel violates most of the logic and consistence in language and math
An example of time travel in the original Star Trek series is an episode where Dr. McCoy falls through a time portal in a city "on the edge of forever," and changes the past in a way that erases the Enterprise and her crew, with the exception of Captain Kirk and Mr. Spock, who must return to the past to fix what McCoy has undone. Time travel is a well-worn staple of science fiction writers, but not only does it violate numerous physical laws, such as conservation of mass/energy. For example, if one were to send a bar of gold back in time for a year, then during that year there would exist two bars, the mass of one appearing from nowhere. At the end of the year, the first bar, of course, disappears restoring the balance.

The English language can't handle time travel. We conclude that the ancestors who made our language didn't have minds equipped to handle time travel. Naturally we don't, either; for our thinking is too dependent on our language. As far as I know, no language has tenses equipped to handle time travel. No language on Earth. Yet. But then, no language was ever equipped to handle lasers, television, or spaceflight until lasers, television, and spaceflight were developed. Then the words followed. If time travel were thrust upon us, would we develop a language to handle it? We'd need a basic past tense, an altered past tense, a potential past tense (might have been), an altered future tense, an excised future tense (for a future that can no longer happen), a home base present tense, a present-of-the-moment tense, an enclosed present tense (for use while the vehicle is moving through time), a future past tense ("I'll meet you at the bombing of Pearl Harbor in half an hour."), a past future tense ("Just a souvenir I picked up ten million years from now"), and many more. We'd need at least two directions of time flow: sequential personal time, and universal time, with a complete set of tenses for each. We'd need pronouns to distinguish (you of the past) from (you of the future) and (you of the present). After all, the three of you might all be sitting around the same table someday.

Perhaps the craziest of the time travel paradoxes was cooked up by Robert Heinlein in his classic short story "All You Zombies."

A baby girl is mysteriously dropped off at an orphanage in Cleveland in 1945. "Jane" grows up lonely and dejected, not knowing who her parents are, until one day in 1963 she is strangely attracted to a drifter. She falls in love with him. But just when things are finally looking up for Jane, a series of disasters strike. First, she becomes pregnant by the drifter, who then disappears. Second, during the complicated delivery, doctors find that Jane has both sets of sex organs, and to save her life, they are forced to surgically convert "her" to a "him." Finally, a mysterious stranger kidnaps her baby from the delivery room.

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Nov 16
2009

SpaceTime

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  • while space and time appear separate, relativity shows that space and time are linked and malleable
One of the major discoveries of relativity is that the Universe is a four dimensional construct, three of space and one of time, spacetime. It was also a surprise to find that the dimensions of space and time are connected, that changes in one can effect changes in the other. In addition, relativity plus experimental evidence demonstrate that the Newtonian concepts of Absolute Space and Time are incorrect and that spacetime is malleable, although it has an independent existence as proposed by the philosophical view of substantivalism.

 

 

  • space as a void is rejected on logical grounds, and must be filled either by an ether (Aristotle) or some other matter (Leibniz)
However, these descriptions of the fabric of spacetime go against our common sense. Space as a void was rejected for many years with the argument that a vacuum is nothing, and what is nothing does not exist (nonexistence is a property of nothing). Aristotle believed that space had to be `dressed', meaning that a continuous covering of material substances are required to make space real. For Aristotle, this dressing was the fifth element, ether.

Leibniz continued this idea of the link between space and matter by stating that this is no space where there is no matter, called relationism. For Leibniz, space has no absolute reality and, in particular, no force could act at a distance unless conveyed by a material medium. The view of philosophers up to the 17th century was a Universe filled with vortices of ether, always in contact.

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Nov 16
2009

Brane World Scenario

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  • A combination of string theory and supergravity leads to an eleven dimensional description of the Universe called the brane world scenario
  • Each brane universe is composed of 4D spacetime and 6D quantum space.
The latest compulation of string theory and supergravity that brings together a multi-dimensional world view with the Standard Model is called brane world. In the brane world scenario, the entire Universe is an eleven dimensional `bulk' composed of an infinite number of ten dimensional branes. Each brane is consists of a macroscopic 4D spacetime and a compacted, microscopic 6D quantum world (a Calabi-Yau space). The Calabi-Yau sector is twisted beyond all possible detection and houses all the symmetries of the Standard model.

 

 

  • Strong, weak and electromagnetic forces are carried by open strings, each attached to their branes
  • Gravity is carried by closed strings, free to travel between branes
The attractive aspect to the brane world scenario is that three of the four fundamental forces (strong, weak, electromagnetism and their assoicated particles) are represented by open strings. Gravity (and gravitons) are represented by closed strings (loops). Open strings are attached to their respective branes, but closed strings (gravity) are free to move between branes. This explains why gravity is so much weaker than the other forces, and gravity can be used to commiuncate between the branes (gravity phones). This also leads to a natural explanation for dark matter (see later lecture).

All the branes are embedded in a higher dimension all the `bulk', a pile of parallel universes. Thus, the total Universe is eleven dimensional, 4D spacetime + 6D quantum space + 1D bulk. An infinite number of parallel universes is literally just a millimeter away, but outside your 4D vision.
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Nov 16
2009

String Theory

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  • another example of a TOE is string theory, the explanation of quantum entities as tiny loops or membranes
Another recent attempt to form a TOE is through M (for membrane) or string theory. String theory is actually a high order theory where other models, such as supergravity and quantum gravity, appear as approximations. The basic premise to string theory is that subatomic entities, such as quarks and forces, are actually tiny loops, strings and membranes that behave as particles at high energies.
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Nov 16
2009

Supergravity

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  • a theory that brings gravity, relativity and quantum physics together is called a Theory of Everything (TOE)
  • one recent attempt is called supergravity, which explains the microscopic world as extra dimensions
Even a GUTS is incomplete because it would not include spacetime and therefore gravity. It is hypothesized that a ``Theory of Everything'' (TOE) will bring together all the fundamental forces, matter and curved spacetime under one unifying picture. For cosmology, this will be the single force that controlled the Universe at the time of formation. The current approach to the search for a TOE is to attempt to uncover some fundamental symmetry, perhaps a symmetry of symmetries. There should be predictions from a TOE, such as the existence of the Higgs particle, the origin of mass in the Universe.
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Nov 16
2009

Theory of Everything

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  • the Standard model is our current theory of the matter/energy worldview, and has had great success with particle physics
  • missing is a full formulation of gravity and particle physics, quantum gravity
Is that it? Are quarks and leptons the fundamental building blocks? Answer = maybe. We are still looking to fill some holes in what is know as the Standard Model.

The Standard Model is a way of making sense of the multiplicity of elementary particles and forces within a single scheme. The Standard Model is the combination of two schemes; the electroweak force (unification of electromagnetism and weak force) plus quantum chromodynamics. Although the Standard Model has brought a considerable amount of order to elementary particles and has led to important predictions, the model is not without some serious difficulties.

For example, the problem of quantum gravity is unresolved in the Standard Model. Also undefined are the values of the various constants of Nature (the speed of light, charge on the electron, etc). In fact, why the Universe is built the way it is (3D+1D macroscopic world) is unclear, although various other dimensional shapes can be ruled out as shown by the diagram below.

 

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Nov 16
2009

Hawking Radiation

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  • another example of quantum gravity phenomenon is Hawking radiation
  • Hawking radiation explores the behavior of particle production near the event horizon of quantum sized black holes
Hawking, an English theoretical physicist, was one of the first to consider the details of the behavior of a black hole whose Schwarzschild radius was on the level of an atom. These black holes are not necessarily low mass, for example, it requires 1 billion tons of matter to make a black hole the size of a proton. But their small size means that their behavior is a mix of quantum mechanics rather than relativity.

Before black holes were discovered it was know that the collision of two photons can cause pair production. This a direct example of converting energy into mass (unlike fission or fusion which turn mass into energy). Pair production is one of the primary methods of forming matter in the early Universe.

 

 

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Nov 16
2009

Gravitational Radiation

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  • ripples in spacetime are gravity waves
The existence of curved spacetime opens up the possibility that ripples or waves can exist in the spacetime continuum. These ripples are called gravitational waves. Gravity waves could be detected from colliding black holes, supernova explosions and the black hole at the core of our Galaxy.

 

 

  • to be generated, gravity waves require rapid motion of high density matter, like a supernova
During the core collapse of the supernova, vast amounts of matter are moved about at enormous speeds. The dense mass is surrounded by a strong gravitational field. Vigorous changes in gravity will produce `ripples' in the geometry of space, and these ripples can propagate outward at the speed of light, i.e. gravity waves.

 

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Nov 16
2009

Quantum Gravity

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  • Understanding of the fundamental forces of Nature will require a unification of quantum physics and general relativity
  • the development of a quantum theory of spacetime, or quantum gravity, will begins with the discovery of the graviton, a quantum particle of spacetime
Physicist frequently search for unifying principles that hopeful lead to deeper, more fundamental laws of Nature. The unification of the theory of electricity with the theory of magnetism led to an understanding of light as electromagnetic radiation. One obvious unification is between quantum mechanics and general relativity, the so-called theory of quantum gravity.

Quantum gravity is a type of quantum theory of elementary particles and their interactions that is based on the particle symmetry known as supersymmetry and that naturally includes gravity along with the other fundamental forces (the electromagnetic force, the weak nuclear force, and the strong nuclear force).

The electromagnetic and the weak forces are now understood to be different facets of a single underlying force that is described by the electroweak theory. Further unification of all four fundamental forces in a single quantum theory is a major goal of theoretical physics. Gravity, however, has proved difficult to treat with any quantum theory that describes the other forces in terms of messenger particles that are exchanged between interacting particles of matter. General relativity, which relates the gravitational force to the curvature of space-time, provides a respectable theory of gravity on a larger scale. To be consistent with general relativity, gravity at the quantum level must be carried by a particle, called the graviton.

 

 

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