leightwing:
I was just glossing through this thread, and I'm pretty sure this will fall into the category of an oft asked question but.. What the heck:
If an actual piece of string (with no elasticity) could be stretched perfectly straight from here to say 10 light years away, wouldn't pulling on its end here instantaneously move it at its other end?
Hi Leightwing,
There is a feature in your thought experiment that allows it to produce faster than light communication. You arbitrarily assigned an elasticty to the string of 0. That is ...it has an infinite modulus of elasticity. The maximum speed of force tranmission in a material is the speed of a pressure wave inside the material which is the speed of sound. The speed of sound in an infinitely stiff material is infinite but the speed of sound in any material made of matter is bounded on the high side by limits intrinsic with the structure of matter.
Any conventional material you can make a string out of is connected with molecular bonds. A force applied to the string is transmitted from molecule to molecule through these bonds. The bonds are electromagnetic in nature and the electromagnetic force is transmited through force carrier particles called bosons. The bosons are generated when there is a displacement between charges (electrons and protons) No displacement (elacticity) between the molecules means no bosons and therefore no transmitted force. So clearly the elacticity cannot be 0. But what if it is almost 0, a really really stiff string.
Well...The boson for the electromagnetic force is the photon...oops. So since the photons are being generated and absorbed along the length of the string to send the force up the line the limit of the speed in the ideal case where the process is straight as an arrow and 100% efficient is...C.
SO what if you make the string out of pure quarks and use the strong nuclear force to transmit the force. Well the boson for the strong nuclear force is the gluon and gluons are massless particles that travel at ...C. oops again.
There may be other arguments against ftl force transmission that are more general but sending a force through a massive structure is clearly not going to break the limit! Hope this helps.
PH