Energy density of a 1D string?

In summary, the conversation discusses the problem of infinite mass/energy density in point-like particles in physics and how this is addressed in the context of String Theory. Strings, being one-dimensional objects, have no volume and therefore do not have infinite energy density. The conversation also touches on the assumptions and limitations of equations and models in understanding the behavior of particles and the potential for string theory to provide a more comprehensive explanation.
  • #1
James William
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Hello,

As I understand there is a problem in physics where point-like massive (or charged, etc.) particles would have infinite mass/energy (or charge, etc.) density.

I'm curious how in the context of String Theory how we address the same problem?

I have come to understand Strings as 1-dimenstional objects from which I conclude they have no volume.

Do they have infinite energy density because they have no volume?

Thanks!

(This question comes from a discussion which can be found here for further context. https://www.facebook.com/notes/gm-j...stent-with-classical-physics/1006863599387308)
 
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  • #2
James William said:
Do they have infinite energy density because they have no volume?
no

I skimmed the facebook discussion: generally, you can't go around 'willy nilly' plugging one equation into another and another without understanding the assumptions inherent in them. When you get infinities, say due to 1/r as r approaches zero, you might conclude :eek:oops there is an infinite result of some sort, and yet we never ever measure such infinities; hence a more rational conclusion is that the model [the equation] does not extend to zero r.

In the Standard Model of particle physics, quantum fields interact at points in a fixed background, flat space and time. So gravity which has so far been modeled in relativity as dynamic curvature in spacetime is not included. In string theory, the hypothetical is that those points of interaction are really one dimensional extended objects, strings. Elementary 'particles' are composed of tiny vibrating filaments of energy some hundred billion billion billion times smaller than an atomic nucleus, almost on the even tinir Planck scale. Different vibrational patterns produce different particles, which are in turn determined by different Calabi Yau shapes in space!. The key realization is that the detailed vibrational pattern executed by a string produces specific mass, electric charge, spin and so forth. The trick is to find these characteristics in the math, then figure out which characteristics match measurements.
Then there are theories with branes, two dimensional objects without volume. Same sorts of issues.
edit: where did that face come from? Does 'oops' create a face? cool! Almost like particles popping out of the vacuum.
 
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1. What is the definition of energy density of a 1D string?

The energy density of a 1D string is the amount of energy per unit length that is contained within the string. It is a measure of the energy stored in the string and is typically expressed in units of joules per meter (J/m).

2. How is the energy density of a 1D string calculated?

The energy density of a 1D string is calculated by dividing the total energy stored in the string by its length. This can be calculated using the formula E = 1/2 * μ * ω^2 * A^2, where μ is the mass per unit length of the string, ω is the angular frequency, and A is the amplitude of the string's vibration.

3. What factors affect the energy density of a 1D string?

The energy density of a 1D string is affected by several factors, including the mass per unit length, the tension of the string, and the frequency of vibration. Higher mass per unit length, higher tension, and higher frequencies all result in a higher energy density.

4. How does the energy density of a 1D string impact its behavior?

The energy density of a 1D string is directly related to its vibrational behavior. A higher energy density means that the string has more energy stored within it, which can result in higher amplitudes and frequencies of vibration. It also affects the propagation speed of waves along the string.

5. Can the energy density of a 1D string be changed?

Yes, the energy density of a 1D string can be changed by altering the factors that affect it, such as the mass per unit length, tension, and frequency. Additionally, the type of material the string is made of can also impact its energy density.

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