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Philosophy of Science

 


facool
I am currently reading Einstein's book "Relativity: The Special and the General Theory--A Clear Explanation that Anyone Can Understand" (I do not possess the required knowledge to read his original works). I have just come across his explanation for why 'c' is the limiting velocity. According to Einstein, the length of a rod in motion, when observed from a stationary reference frame, is the sq.root of (1 - V*2/C*2) times the length of the rod at rest. We can clearly see that as the velocity of the rod approaches c, its length approaches zero. Therefore c is the limiting velocity of the rod, or any other body in motion.

The problem with this explanation is that his equation does not actually give the length of the rod. It only gives the length of the rod as it appears to an observer in a stationary frame of reference. Therefore, there should be no problem with that value approaching, or even becoming zero as we are not saying that the actual length of the rod is becoming zero, we are merely saying that the length of the rod will appear to be zero to an observer in a stationary frame of reference.
HereticMonkey
You're sweating details that don't matter; the rod could be any size...So it's size doesn't matter...

HM
Bikerman
facool wrote:
I am currently reading Einstein's book "Relativity: The Special and the General Theory--A Clear Explanation that Anyone Can Understand" (I do not possess the required knowledge to read his original works). I have just come across his explanation for why 'c' is the limiting velocity. According to Einstein, the length of a rod in motion, when observed from a stationary reference frame, is the sq.root of (1 - V*2/C*2) times the length of the rod at rest. We can clearly see that as the velocity of the rod approaches c, its length approaches zero. Therefore c is the limiting velocity of the rod, or any other body in motion.
OK...the term you quote - sq.root of (1 - V*2/C*2) - is known as the Lorentz factor (it also applied to time and mass, as well as length). It is used to convert measurements in one frame into another.
The first point to note is that nothing with mass can reach c, so the case of 0 length cannot arise. The second point is that c is not a limit because of the equation, it is the other way around. The third point is that Einstein was careful to say more than simply stationary reference frame - stationary INERTIAL frame is key - ie the object is neither accelerating, decelerating or rotating with respect to the observer. Galilean and Lorentzian transformations only apply in inertial frames....
Quote:
The problem with this explanation is that his equation does not actually give the length of the rod. It only gives the length of the rod as it appears to an observer in a stationary frame of reference. Therefore, there should be no problem with that value approaching, or even becoming zero as we are not saying that the actual length of the rod is becoming zero, we are merely saying that the length of the rod will appear to be zero to an observer in a stationary frame of reference.

The length is immaterial since this is largely a thought experiment rather than a practical one...the point is to understand what *would* happen if such and such were possible in order to understand the global picture. There are other factors in relativity which you will probably read about in later chapters - at the moment you are in the Special Relativity bits which is his early work and is based on trying to fit Maxwell's wave equations into Galileo's system of Relativity (yes, it was Galileo, not Einstein, who 'discovered' the concept - in fact it is arguably older than that).
The fundamental thing you need to get about Special Relativity can be summed up in two statements :
1) The laws of physics apply the same in all inertial frames (ie Newtonian/Galilean physics works fine)
2) The speed of light is universal in all inertial frames (ie no matter how fast you are moving, everyone will see light travelling at the same speed).

Those two statements are the heart of the theory (in fact they ARE the theory) and it is not too difficult to start from those statements and derive the Lorentz factor and other equations of Special Relativity.
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