The relativity of the distance.



.THE BEHAVIOUR OF MEASURING-RODES AND CLOCKS IN MOTION

In page 37 0f his Relativity Einstein writes about the relativity of
the distance. There is very strange conclusion that the distance
becomes smaller when the speed v tends to the light speed c.
He takes as a base the relation of the Lorentz transformation:
x'=( x-v.t)/R which gives the distance x' in K' (train) when we
know the x and t in K (embankment). Here is what Einstein says in his
book:
"I place a metre-rod in the x'-axis of K' in such manure that
one end (the beginning) coincides with the point x'=0, whilst the
other end (the end of the rod coincides with the point x'=1. What is
the length of the metre-rod relative to the system K? In order to learn
this, we need only ask where the beginning of the rod and the end of
the rod lie with respect to K at a particular time t of the system K.
By means of the first of the Lorentz transformation the values of these
two points at the time t=0 can be shown to be:
x(beginning of the rod)=0.R
x(end of rod)=1.R
R being the squares root of the Lorentz transformation"..
In this way he finds that the distance between the points is
D=R=(1-v^2/c^2)^0.5.
When v=c, the distance D=0.
For me is very strange that nobody observed that the rod gets in this
case an infinite mass and a volume zero!!!
On the other hand the above relation is wrongly used. The real
relation which is valid for this case and allows us to resolve this
problem, is the following:
x=(x'+v.t')/R.
So the distance D becomes bigger and for v=c distance should have an
infinite value. That means that if the train travels with speed c the
two ends of the rode should be one in the infinite and one still here
near us.
This could be a real possibility, isn't it?

.

Relevant Pages

  • Re: The relativity of the distance.
    ... .THE BEHAVIOUR OF MEASURING-RODES AND CLOCKS IN MOTION ... In page 37 0f his Relativity Einstein writes about the relativity of ... There is very strange conclusion that the distance ... Not strange at all - confirmed by over 100 years of experiment. ...
    (sci.physics.relativity)
  • Re: THE LENGTH IS NOT SHORTENING IN EINSTEIN RELATIVITY
    ... attached to a train then for a distance of 1m in the K2 we should ... I have a rod in K2 system in motion". ... is that a rod at rest in the K1-system or in the K2-system? ...
    (sci.physics.relativity)
  • Re: Newbie questions -- after my 1st season of fishing
    ... other DT line, up to 45 feet, (well over fifty feet, including leader ... considerable range of applications, without stressing the rod. ... distance casting. ... Assuming proper design and adherence to AFTMA standards, a 6 weight rod ...
    (rec.outdoors.fishing.fly)
  • Re: THE LENGTH IS NOT SHORTENING IN EINSTEIN RELATIVITY
    ... attached to a train then for a distance of 1m in the K2 we should ... I have a rod in K2 system in motion". ... is that a rod at rest in the K1-system or in the K2-system? ...
    (sci.physics.relativity)
  • Re: what length contraction in only one direction?
    ... no see that the distance gets infinite length when v=c. ... Here is why if a rod ... of 1m gets infinite mass it must get and an infinite lenght, ... He takes as a base the relation of the Lorentz transformation: ...
    (sci.physics.relativity)
Quantcast