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I have never learned string theory, so please forgive me if my question sounds naive or obvious, but I would like to know and I am most likely wrong.

As far as I know, strings vibrate in different modes and different modes correspond to different fields (electrons, photons etc) which is a fascinating idea. And to the best of my knowledge, these strings never stop vibrating as to continue being the fields that we know and love, i.e. my tasty fermionic coffee.

However, does that mean that these strings are perpetually in motion? I thought that violates the law of conservation of energy?

Taken from another perspective, since strings vibrate, i.e. fluctuate, would the Fluctuation-dissipation theorem apply here and eventually stop the vibration?

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    $\begingroup$ Why would this "oscillation" disturb you in string theory if the analogous picture of a particle as "excitation of a field" in QFT doesn't? See physics.stackexchange.com/q/355487/50583, physics.stackexchange.com/q/127141/50583 for discussion of the "oscillators" in QFT, physics.stackexchange.com/q/305760/50583 for the relation between "vibrating strings" and particles, physics.stackexchange.com/q/458329/50583 for general ontology of strings and spacetime $\endgroup$
    – ACuriousMind ♦
    Commented Apr 28 at 18:40
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    $\begingroup$ @ACuriousMind You make a good point, thank you for sharing those links. I guess the "oscillation" is not what it says it is, but it is a mathematical artifact that the physics seems to match the oscillatory equations but the physical nature of the system is not oscillatory. $\endgroup$
    – Tachyon
    Commented Apr 28 at 18:55
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    $\begingroup$ What makes you believe that "the oscillation is not what it says it is"? Also, the fluctuation-dissipation theorem is completely irrelevant here as that is a theorem in statistical physics. $\endgroup$
    – Prahar
    Commented Apr 28 at 19:06
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    $\begingroup$ You might as well ask whether Newton's first law violates conservation of energy. $\endgroup$
    – Connor Behan
    Commented Apr 28 at 19:15
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    $\begingroup$ The comment says, "There is a famous theorem called the fluctuation-dissipation theorem that links random phenomena in systems to observable dissipative behavior." The keyword here is random. The FD theorem is a statement about statistical phenomena. The stringy oscillations you are referring to here are NOT random in any way. It may lead to observations that are statistical in nature (which is the case for all quantum systems), but that is not what your question is about. $\endgroup$
    – Prahar
    Commented Apr 28 at 19:29

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Regarding the dissipation, in string theory, different vibrational modes of a fundamental string are interpreted as different types of particles. The ground state refers to the lowest energy vibrational mode of the string. This would correspond to the most stable configuration of the particle.

For a particle to decay, it must transition to a lower energy state by releasing some energy (e.g., in the form of other particles). If the particle is at its ground state, there are no lower-energy states available. Hence, there's nothing it can decay into, making it stable. If the particle is isolated, then it cannot decay nor dissipate energy.

I don't understand though, why you think a vibration that keeps its energy violates energy conservation.

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  • $\begingroup$ Yes, thank you for answering. As @James pointed out in the comments under my question that I was confusing perpetual motion with "Perpetual Motion Machine" as they are 2 different concepts. And as others have pointed out, there are things that can be in perpetual motion but do not violate energy conservation. And thank for you teaching me why Muons and other heavy particles decay from a string theory point of view, very insightful. $\endgroup$
    – Tachyon
    Commented Apr 29 at 16:51
  • $\begingroup$ Do not forget also, that there are perpetual motion machines of the second kind that do not violate conservation of energy, but only the second law. $\endgroup$
    – Pato Galmarini
    Commented Apr 29 at 17:14

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