How Does Relativity Affect String Mass and Vibration Frequencies?

[Mike2]

I have two questions about how the mass of the string might change due to relativistic effects. As I understand it, the mass of fermions is determined by the amplitude and frequency of vibrations of strings. The greater the frequency, the greater the mass. Also in special relativity, time slows down as you approach the speed of light. So frequencies slow near c. Clock run slower. Also in general relativity, again, time slows down near heavy objects, or in other words, frequencies get faster as you move away from heavy objects.

If this is so, then question one is: Wouldn't the vibration frequency of strings slow down as a string approaches the speed of light. And wouldn't this mean that mass (string frequency) approach zero near c? And question two: Wouldn't the frequency of strings (and thus the mass of objects) tend to increase as it moves out of a gravitational well? This latter question might be the explanation for effects attributed to dark matter and dark energy. But I will save that discussion for after my premises are confirmed.

I've looked in Zwiebach's new book and in Hatfield's introduction to QFT of points and string. Neither book seems to address this question, though I may not have looked carefully enough. Yet this does seem to be a fundamental question that should be asked. So I do appreciate any insight you might have in this area. Thanks.

Mike

 

[Mike2]

I have two questions about how the mass of the string might change due to relativistic effects. As I understand it, the mass of fermions is determined by the amplitude and frequency of vibrations of strings. The greater the frequency, the greater the mass. Also in special relativity, time slows down as you approach the speed of light. So frequencies slow near c. Clock run slower. Also in general relativity, again, time slows down near heavy objects, or in other words, frequencies get faster as you move away from heavy objects.

If this is so, then question one is: Wouldn't the vibration frequency of strings slow down as a string approaches the speed of light. And wouldn't this mean that mass (string frequency) approach zero near c? And question two: Wouldn't the frequency of strings (and thus the mass of objects) tend to increase as it moves out of a gravitational well? This latter question might be the explanation for effects attributed to dark matter and dark energy. But I will save that discussion for after my premises are confirmed.

I've looked in Zwiebach's new book and in Hatfield's introduction to QFT of points and string. Neither book seems to address this question, though I may not have looked carefully enough. Yet this does seem to be a fundamental question that should be asked. So I do appreciate any insight you might have in this area. Thanks.

Mike

Some have suggested that the mass of a string, like the energy of particles in a well, will depend not on the frequency but on the mode of vibration - on the eigenvalue derived from the diff eqs involved. If that is the case, then eigenvalues, or mode number, or number of nodes would not change with a Lorentz transformation. So the question is whether the mass of a superstring depend on frequency or mode number.

 

[R0man]

Thank you for your interesting question, Mike.

Regarding the mass of a string and its relation to relativity, there are a few important points to consider. Firstly, it is important to note that the concept of a string is a theoretical construct in string theory, and thus its properties, including its mass, are not directly observable. Therefore, any discussion about the mass of a string must be understood within the framework of string theory.

In string theory, the mass of a string is determined by its energy, which is related to the amplitude and frequency of its vibrations. However, this relationship is not as straightforward as in classical mechanics. In string theory, the energy of a string is given by the sum of its kinetic energy and potential energy, where the potential energy is related to the string's tension. This tension is a fundamental property of the string and is not affected by its speed or its location in a gravitational field.

In special relativity, the concept of mass is not well-defined, as it can change depending on the observer's frame of reference. However, the energy of a string is a relativistic invariant, meaning it is the same for all observers regardless of their frame of reference. This is because the energy of a string is determined by the string's tension, which is a fundamental property that does not change with speed.

Therefore, to answer your first question, the vibration frequency of a string does not change as it approaches the speed of light. The energy of the string may increase, but its tension and thus its mass remain the same.

Regarding your second question, it is important to note that in general relativity, the concept of mass is also not well-defined. Instead, we use the concept of energy density to describe the effects of gravity on an object. In this context, it is true that the energy density of a string would increase as it moves away from a heavy object, but this does not necessarily mean that its frequency would increase. The relationship between the energy and frequency of a string is complex and not directly affected by gravity.

In conclusion, the mass of a string is a complex concept in the context of string theory and is not directly related to the effects of relativity or gravity. However, the energy of a string, which is related to its mass, is a fundamental property that remains constant regardless of the observer's frame of reference or the presence of a gravitational field. I hope this helps clarify your questions and provides some insight into this topic.