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as I searched about the Strings theory I found out this explanation:

Since the strings have a finite size they can vibrate. All the known particles of nature are just different modes of vibration of the string. Thus the string is the only truly 'fundamental' particle.

So what does it exactly mean when saying a "finite size" what does size have to do with vibration?

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I think the point the article is making is that only objects with a size greater than zero can vibrate. So the term finite is being used to mean non-zero rather than not infinite. This is quite a common way to use the term finite in physics. Arguably it's abusing the meaning of the word, but I do see it being used that way quite a lot.

The reason only objects with a size greater than zero can vibrate is that an isolated object cannot change its momentum. If we have a point like object then the only way for that object to vibrate is for it to move to and fro. However that would be changing its momentum so this type of motion is not allowed. An extended object like a string can vibrate because different parts of the string can move in opposite directions to keep the net momentum unchanged.

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Finite can be in contrast with infinite, but also in contrast with a point, zero length,as John pointed out. As the standard model has point particles by postulate, making the particles of one dimension of finite length is in contrast to the zero length of the standard model of particle physics

The statement : "Thus the string is the only truly 'fundamental' particle" is a mathematical generic statement, not a physics one. In the mathematics of string theory the standard model can be embedded, elementary particles have a one to one correspondence, with particular vibrational energy levels of the string ( we are in quantum mechanics after all, or should be) .

The physics of the standard model does not stop at the mathematical description but also interaction and conservation of quantum states rules have to hold. One cannot turn a string representing an electron to represent a proton, unless strict interactions take place conserving lepton and quark numbers, by transferring them to other strings.

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