# A Can strings increase length without changing their energy?

Tags:
1. Jan 9, 2017

### Nickyv2423

For a string in string theory,
Energy = string tension * length
So I'm wondering if it can increase its length with increasing its energy.

2. Jan 10, 2017

### jambaugh

Short Answer: Yes, Solve and you get Tension = 0.

But since string theory is not yet a physical theory there is not yet a physical "can it happen that-a-way" answer. Whether the premises of the theory allow it will depend on what premises have been adopted (beyond my knowledge here) but I suspect zero tension strings would be considered "un-physical".

3. Jan 10, 2017

### haushofer

No, I don''t think so. In this respect strings and branes differ. Brane surface/volumes/... can develop spikes without changing its energy.

4. Jan 10, 2017

### Staff: Mentor

I would be surprised if a classical approach works here.

5. Jan 10, 2017

### jambaugh

To clarify my answer. In the example of special relativity, a physical theory, the answer to "can an object travel faster than c" is a definitive "no". It is physically impossible. In the example of say, "geometry" which is a mathematical theory not a physical one, if you ask "can two lines intersect at more than one point?" then the answer is "it depends on which geometry you consider". String/brane theories are still in the "mathematical theory" category though they are aimed at constructing a physical theory at some point. They rather represent classes or possible physical theories.

6. Jan 12, 2017

### haushofer

I don''t understand. I regard this as a mathematical question which should be answered by looking at the Nambu-Goto action. String theory would be ill-defined if the answer to the OP would be "yes", because nothing would prevent the string from becoming arbitrarily long. How would you obtain a discrete particle spectrum then, for instance ?

7. Jan 17, 2017

### jambaugh

Right, the empirical evidence of discrete particle spectra rules out theories which contradict this. As to nothing preventing the string from becoming arbitrarily long, that's an aesthetic preference until you link it to some empirical predictions. But as it stands currently there's not a full physical string/brane theory with testable quantitative predictions, there are a few qualitative predictions. Until a reasonably complete *physical* theory is hashed out (as in "here's the string-theory equation of a propagating electron" etc) one cannot be certain such qualitative predictions are consistent. Consider for example charge quantization predicted by Dirac if monopoles exist.

I am asserting that (physics) string theory must first be *defined* before the question of whether it is ill-defined can come up. Mathematical string theory might perfectly well allow the "yes" answer and consistently represent a non-physical toy model (or apply in a totally different domain. Consider a dynamical equation for e.g. rivers evolving over geological time. Mightn't someone consider modeling it via a 2-D string theory? possibly with 0 tension?? and thence we see length growing without restraint until an overlap occurs???