Question on Greene's explanation

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In summary, the two shaky points are: 1) the justification for the last sentence in the summary; 2) whether the distinctions he makes in the section "A Minimum Size" are limited to dimensions smaller than the Planck dimension.The justification for the last sentence in the summary is that the metrics are switched for objects which are, in the first metric, smaller than the Planck dimension.
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nomadreid

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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.
 
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nomadreid said:
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"
 
  • #3
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
 

1. What is Greene's explanation?

Greene's explanation refers to the theory proposed by physicist and string theorist Brian Greene, which attempts to explain the fundamental laws of the universe through the concept of string theory.

2. How does Greene's explanation differ from other theories of the universe?

Greene's explanation differs from other theories in that it posits that the universe is made up of tiny vibrating strings, rather than point-like particles, and that there are more than four dimensions.

3. Is Greene's explanation widely accepted in the scientific community?

Greene's explanation is still a highly debated topic in the scientific community, with some physicists supporting it and others questioning its validity. However, it has gained significant recognition and has been a subject of ongoing research and experimentation.

4. Can Greene's explanation be proven?

Currently, there is no conclusive evidence that proves or disproves Greene's explanation. As with any scientific theory, it is constantly being tested and refined through experiments and observations.

5. What potential implications does Greene's explanation have for our understanding of the universe?

If Greene's explanation is proven to be true, it would greatly impact our understanding of the universe and could potentially lead to a unified theory of everything, which would explain all the fundamental forces and particles in the universe.

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