# Question on Greene's explanation

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My first question is whether the next paragraph is a correct summary, and then I have questions about the two shaky points mentioned in the summary.
In "The Elegant Universe", Greene presents the division of energy of strings into the winding energy, the uniform vibrational energy, and ordinary vibrational energy. The latter does not partake in the following considerations. In each dimension: the winding energy is proportional to the radius of that dimension (assuming it to be circular), the winding and uniform vibrational energies are inversely proportional to each other , hence the uniform vibrational energy is inversely proportion to that radius. Two distance metrics are defined which are functions of the dimension radius, depending on whether one observes the results of the winding energy or of the uniform vibrational energy of the probes, so that, in units of the Planck distance, the measurement of the same object (first shaky point: any object to be measured, or only the dimension to be measured?) will give two results, according to which metric is used, but these two results will be inversely proportional to one another (or, with appropriate units, simply inverses). The metrics overlap when the object to be measured is the Planck length. In general, the metrics are isomorphic to one another. We have four situations:
(1) use probes of low uniform vibrational energy probes (of energies of wavelengths greater than twice the Planck distance) and high winding energy and observe the uniform vibrational energy results ( so that we could observe objects larger than the Planck distance,) : we get our usual results.
(2) use probes of low winding energy and high uniform vibrational energy and observe the winding energy: this gives us results which are inversely proportional to those that we usually get, but since using this metric would be taken into consideration in the formulation of physical laws which are functions of distance, this would end up giving us the same physics. We could measure the same objects as in (1).
(3) use probes as in (1) but observe the winding energy.
(4) use probes as in (2) but observe the uniform vibrational energy.
These last two would be unusual, since we would normally observe the lower energies. However, if we do not, then (here's the second shaky point) the fact that we use the higher of the two energies means that the metrics are now switched for objects which are, in the first metric, smaller than the Planck distance.

Now, the first question: is he talking only about measuring the size of his Calabi-Yau space dimensions (so that they cannot get too small), or also of objects in general (and to establish a reason for the Planck distance)? Secondly, I am completely unclear as to the justification for the last sentence in my summary.

Any pointers would be appreciated.

## Answers and Replies

nrqed
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Gold Member
My first question is whether the next paragraph is a correct summary, and then I have questions about the two shaky points mentioned in the summary.
In "The Elegant Universe", Greene presents the division of energy of strings into the winding energy, the uniform vibrational energy, and ordinary vibrational energy. The latter does not partake in the following considerations. .
Could you tell us on what page he discusses this? I don't recall the concepts of "uniform vibrational energy" vs "ordinary vibrational energy"

Gold Member
Chapter 10

In the softback edition, Vintage Books 1999, the distinction is made on page 240 and beyond (he starts off using the distinctions for string vibrations, and then slides into using them for energies). My questions primarily concern the section "A Minimum Size", pp 252-4. In any edition, all this is in Chapter 10