22 January 2012
Nonsense about tension
Strings have tension, theorists say. Particles are vibrating strings, they say. But tension is a macroscopic quantity, like temperature. So is vibration. What is the meaning of a macroscopic tension in the case of strings? None. "Vibrating strings" makes as much sense as "flying toothbrushes".
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In String Theory, the string tension (T) is not a macroscopic quantity but a high-energy coupling constant having units of (length)^(-2) when hbar = c = 1. The string tension introduces a characteristic length squared in the theory, L^2. In ordinary units, this length is expressed as
ReplyDeleteL = sqrt(c x hbar/Pi x T)
Because String Theory is a theory that allegedly describes quantum gravity, the characteristic length is on the order of Planck length, Lpl = sqrt(G x hbar/c^3). The convention of units for strings is c = 1 and a dimensionless string tension, T =(1/Pi). In this convention, hbar has dimensions of (length)^2 and the gravitational constant, G= (Lpl/L)^2 is dimensionless. The claim is that a dimensionless gravitational constant makes the theory renormalizable. Since L is of order Lp, L is also the characteristic size of the string and the length scale at which interaction can no longer be localized at a well-defined point in space-time.
Ervin,
ReplyDeletethis is all correct. My point is that one reads so much about "particles being vibrating strings". This statement makes no sense - or does it?
Clara,
ReplyDeleteIn the old picture of strings, a string is given by two-dimensional world surface embedded in a D dimensional space-time. String vibrations may be interpreted as quantized oscillations of this two-dimensional world surface,following the conventional view of quantum field theory. The only string states that are observable at low energies are particles corresponding to massless string states. The conventional interpretation on observable massive string states is that the world at ordinary energies is not supersymmetric and SUSY must be broken.
That is the usual lore. But there is no evidence for that, and there is no evidence for any tension in strings...
ReplyDeleteI agree. All this stuff is a bunch of speculative ideas.
DeleteThe ordinary electromagnetic field amplitude A(t) in a given harmonic omega obeys a harmonic oscillator equation. And SHO possesses tension if out of equilibrium. It that different from strings?
ReplyDelete