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ScienceWeek
THEORETICAL PHYSICS: ON THE WEAKNESS OF GRAVITY
The following points are made by Jonathan L. Feng (Science 2003 302:795):
1) Of the four known fundamental forces -- gravity, electromagnetism, and the weak and strong forces -- gravity is by far the weakest. The reasons for this weakness have long remained enigmatic. Recent proposals suggest, however, that the weakness of gravity may be evidence for extra spatial dimensions. Experiments ranging from tabletop tests of Newtonian gravity to searches for microscopic black holes in kilometer-scale detectors are now putting these ideas to the test.
2) The importance of gravity in everyday life results not from its strength but from its universality: Objects cannot be gravitationally neutral, and all bodies with mass attract. Yet as an interaction between elementary particles, gravity is extremely weak. For example, the gravitational attraction between two protons is 35 orders of magnitude weaker than their electromagnetic repulsion. This holds for protons separated by any distance r, because both gravitational and electromagnetic forces are proportional to 1/r^(2).
3) The observed weakness of gravity may, however, not be an intrinsic property of gravity, but may instead be an effect of extra spatial dimensions. This possibility is based on a simple consideration. Suppose that our three-dimensional (3D) world is merely a subspace of a higher-dimensional space, and that gravity propagates freely in all dimensions, but that all other forces are confined to our three dimensions. In contrast to the familiar three dimensions, the extra dimensions are curled up in small circles of circumference (L). Hence, moving a distance L in the direction of any of the extra dimensions brings one back to one's starting place.
4) Now suppose that at some separation distance (r L, at which point the extra dimensions become less and less important and gravity recovers its 1/r^(2) behavior.
5) If this picture is correct, then gravity is not intrinsically weak: It is as strong as electromagnetism at small length scales. It appears weak at the relatively large distances of common experience only because its effects are diluted by propagation in extra dimensions. The distance at which the gravitational and electromagnetic forces might have equal strength is unknown, but a particularly interesting possibility is that it is 10^(-19) m, the distance at which the electromagnetic and weak forces are known to unify to form the electroweak force (1-5).
References (abridged):
1. N. Arkani-Hamed, S. Dimopoulos, G. R. Dvali, Phys. Lett. B 429, 263 (1998)
2. E. G. Adelberger et al, http://arXiv.org/abs/hep-ex/0202008 (2002)
3. S. Cullen, M. Perelstein, Phys. Rev. Lett. 83, 268 (1999)
4. L. J. Hall, D. R. Smith, Phys. Rev. D 60, 085008 (1999)
5. S. B. Giddings, S. Thomas, Phys. Rev. D 65, 056010 (2002)
Science http://www.sciencemag.org
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THEORETICAL PHYSICS: THE WEAKNESS OF GRAVITY
According to Newton's law of gravitation, there is a force of attraction between any two massive particles in the Universe. This force of attraction, as stated by Newton, may be expressed as a simple relationship involving the masses of the two particles and the distance between them. When the two masses are unit masses and the distance between their centers of mass is unit distance, then the force of attraction is equal to what is called the "gravitational constant", usually denoted as "G". The gravitational constant is usually regarded as a true universal constant independent of place or time, but in some cosmological models it is proposed that the gravitational constant decreases with time as the Universe expands.
The following points are made by Frank Wilczek (Physics Today 2001 June):
1) Gravity dominates the large-scale structure of the Universe, but only by default: matter arranges itself to cancel electromagnetism, and the *strong and weak forces are intrinsically short range. At a more fundamental level, gravity is extremely weak: acting between protons, gravitational attraction is approximately 10^(-36) times weaker than electrical repulsion. The author asks: "Where does this outlandish disparity come from? What does it mean?"
2) The author points out that these questions greatly disturbed Richard Feynman (1918-1988). In 1963, in Feynman's famous paper on quantizing general relativity, the paper in which he first described his discovery of the "ghost particles" that eventually played a crucial role in understanding modern *gauge field theories, Feynman noted that the correct problem is to understand what determines the size of gravitation.
3) Wilczek points out that the same question drove Paul Dirac (1902-1984) to consider, 30 years before Feynman, the radical idea that the fundamental "constants" of nature are time dependent, so that the weakness of gravity could be related to the great age of the Universe. Dirac's argument was that the expansion rate of the Universe suggests that it began with a bang approximately 10^(17) seconds ago. On the other hand, the time it takes light to cross the diameter of a proton is approximately 10^(-24) seconds, which provides a ratio, 10^(-41), which is not so far from the mysterious 10^(-36). But the age of the Universe, of course, changes with time, so if the numerological coincidence is to abide, something else -- the relative strength of gravity or the size of protons -- will have to change in proportion. Since there are powerful experimental constraints on such effects, Dirac's idea is not easy to reconcile with standard modern theories of cosmology and fundamental interactions, theories which are extremely successful.
4) Wilczek discusses the dimensionless number N = Gm^(2)/hc, where (G) is Newton's constant, (m) is the mass of the proton, (h) is Planck's constant, and (c) is the speed of light. Substituting measured values, we find N is approximately 3 x 10^(-39), and Wilczek notes: "This is what we mean when we say gravity is extravagantly feeble." But the real problem, Wilczek suggests, is to understand the smallness of (N).
5) Wilczek then proposes that an understanding of the smallness of N can be derived from an understanding of the smallness of the mass of the proton, and in particular from the constraints imposed by the *theory of quantum chromodynamics on the coupling constants between quarks, the fundamental components of the proton. Essentially, the inter-quark coupling force increases with distance between quarks, which provides a powerful constraint on the size and mass of the proton. The smallness of N, therefore, is an apparent natural consequence of the theory of quantum chromodynamics.
Physics Today http://www.physicstoday.org
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Notes:
strong and weak forces: The weak forces are the forces responsible for the change of neutrons and protons into each other in radioactive processes and in the stars. The strong forces are the forces that hold quarks together inside protons and neutrons, and that hold protons and neutrons together inside atomic nuclei.
gauge field theories: Quantum field theory is the mathematical fusion of quantum mechanics with special relativity theory, and there are essentially 2 branches: quantum electrodynamics (applicable to charged particles involved in electromagnetic interactions) and quantum chromodynamics (applicable to nuclear particles involved in strong force interactions). In this context, a "gauge theory" is any quantum field theory which has the property of "gauge symmetry", i.e., the equations describing the field do not change when some operation is applied to all particles everywhere in space. In general, fields with gauge symmetry can be remeasured (regauged) from different baselines without affecting their properties. Quantum electrodynamics and quantum chromodynamics are examples of gauge theories.
theory of quantum chromodynamics: Quantum chromodynamics (QCD) is a theory that describes the strong interaction (strong nuclear force) in terms of quarks and antiquarks and the exchange of massless "gluons" between them. The "chromo-" in chromodynamics derives from the use of designated "color" attributes of quarks, the various "colors" labels for various quark properties.
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ON QUANTUM GRAVITY
The following points are made by J.F. Hawley and K.A. Holcomb (citation below):
1) Gravity is by far the weakest force in the Universe: in the hydrogen atom, the electromagnetic force between the proton and electron is about 10^(40) times as great as the gravitational force between them. This is fairly representative of the difference in scales between the quantum and gravitational realms, and accounts for our ability [in cosmology] to separate the two theories without ambiguity. Yet they must inevitably meet. Near a singularity, the curvature of space-time must be so great that the scale of gravity becomes comparable to that of the other fundamental forces. To describe such a state, we must find a theory of quantum gravity. Moreover, quantum mechanics has already been applied to the explanation of the other three forces, the electromagnetic force and the strong and weak interactions; should not gravity be similar?
2) It might seem as though the challenge of developing quantum gravity should not be so great. After all, special relativity and quantum mechanics were united in the 1920s by the British physicist Paul A.M. Dirac. The most significant result of Dirac's theory was its requirement that antiparticles exist, a prediction that was confirmed in 1932 by the discovery of the positron (the anti-electron). The Dirac theory is now well-established as the special relativistic quantum mechanics. More than 70 years later, however, general relativity has still not been successfully incorporated into a consistent quantum formulation.
Adapted from: J.F. Hawley and K.A. Holcomb: Foundations of Modern Cosmology. Oxford University Press 1998, p.441. More information at: http://www.amazon.com/exec/obidos/ASIN/01951049768/scienceweek
ScienceWeek http://www.scienceweek.com
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