Re: strings near the speed of light
From: Mark Palenik (markpalenik_at_wideopenwest.com)
Date: 08/31/04
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Date: Mon, 30 Aug 2004 20:22:24 -0500
"Mike" <no..spam@please.com> wrote in message
news:XSOYc.628$Pd2.259173@monger.newsread.com...
> They consider the quanta of the gravity of general relativity to be the
> graviton. But I am not aware of any quanta used for Special relativity. It
> would seem that there would be no avoiding consideration of no preference
in
> inertial reference frames of SR. Still, I've not seen how they take into
> account even special relativity in string theory. How can they possibly
> avoid it? If the frequency of vibration is subject to special relativistic
> effects, it would seem this offers a method of proving the vibrational
> characteristics of what could only be some sort of extended object of
string
> theory or M-theory. This is too easy. What's going on here???? I can't
> believe they're that blind. I must be missing something. But I can't
imagine
> what.
I'm an undergrad in physics, so I haven't studied string theory yet, but I
think I can help you out anyway, since you seem to have quite a few
misconceptions.
First of all, the graviton isn't a "quanta of general relativity". The
graviton is the quantization of the gravitational field, specifically, of
gravitational waves, like the photon is the quantization of electromagnetic
waves. Just as a classical theory of Electromagnetism was devised by
Maxwell before it was described by quantum mechanics, a classical theory of
gravity, called General Relativity, was devised by Einstein before it was
made into a quantum field theory. In both cases, the classical theories
aren't wrong, but are what the quantum theories reduce to on large scales.
Creating a QFT that describes gravity is proving to be difficult, however,
since renormalization doesn't remove the infinities that pop up.
As for Special Relativity, SR doesn't describe fields, it describes the
behavior of moving bodies. There's nothing to quantize. I could, however,
mention that quantum mechanics does reduce to classical mechanics on large
scales, so if you were to use a relativistic Hammiltonian when you write
your Schroedinger wave equation, it should reduce to SR. As I said before,
I'm just an undergrad, so I don't really know how you would go about getting
that to work.
Quantum Field Theories, on the other hand, like those that describe E&M and
gravity are relativistic. They use 3+1 dimensions with a time dimension
that has the opposite metric of the spacial dimensions.
Now, as for string theory, I don't really know what in string theory is
supposed to be analogous to mass, but I would guess that it's not actually
frequency. If anything, I would assume that vibrational modes are more
important than frequency in string theory, although the two are related.
Any string can only vibrate at particular eigen values, since real strings
have end points, and the end points are either fixed, or have some sort of
boundary value that applies to them. So, the strings can vibrate in their
first excited state, second, third, etc. The vibrational mode is the number
of half wave lengths present along the string, and is an example of
something that would be invariant under SR.
Speaking of which, mass is also invariant under SR, as it is defined as
sqrt(E^2 - P^2), when C is set to 1, or sqrt(E^2 - P^2C^2)/C if you don't
set C to 1. This is sometimes caleld m_naut, but usually just m. The
quantity E^2/C^2, however, which is what appears in momentum, does change
with velocity. There is no reason to call this value "m", however, since it
is not the m that appears in force, and both it and m_naut appear in the
formula for kinetic energy.
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