MadSci Network: Physics

Re: Is space/time a distraction as we try to travel at light speed?

Date: Mon Feb 26 09:19:50 2007
Posted By: Jim Guinn, Staff, Science, Georgia Perimeter College
Area of science: Physics
ID: 1170048960.Ph

Dear Dan,

I love this question!  The idea of the string really gives this old 
paradox a new twist, so to speak.

To answer this, we need to be very precise about our terms.  What do we 
mean by "the age" of something, or "how old" something is.  I hope that 
you will agree that what we mean is how much time passes according to that 
particular object.  For example, the age of the man in the ship is not 
determined by how much time passes for the man on Earth, but rather how 
much time passes as measured by the man in the ship.  Every object must 
measure its own time, that is, its own age.  This quantity is called the 
objectfs proper time.  To recap, the age of an object is the amount of 
time that passes as measured by that object, in other words, according to 
a clock that is being carried by that object.

You suggest using a string that "couldn't age".  According to our 
definition, that would mean a string that doesn't move through time.  
Let's use your second suggestion instead, let's assume the string is 
indestructible and although it does age, it doesn't show the effects of 
aging.  And may I make one more suggestion, just one letter?  Rather than 
a string, how about a spring?  Let's assume that one end of an 
indestructible, infinitely stretchable spring is attached to Earth, and 
the other end on the spaceship.  That way, as the ship flies away from 
Earth, the spring stretches out, and as the ship comes back, the spring 
compresses.  I made a diagram for this.  Please refer to the site
nn/MadSci/SpringShip.pdf .

The rocket starts out on the Earth, with the spring compressed, and 
several points on the spring shown at A, B, and C.  The rocket then flies 
off for a year, as measured in the rocket, at a high velocity; letfs say 
99% the speed of light.  Point C ends up at point C'.  The point B moves 
to point B' at a speed of 49.5% the speed of light and ends half the 
distance from Earth as point C' does.  Point A stays in place, so A' is 
the same as A.  On the way back, we have C' going to C'' at 99% the speed 
of light, B' goes to B'' at 49.5% the speed of light, and A' goes to A' 
with no motion.

What do we find now for the "ages"?  They can be determined using the 
standard time dilation equation for special relativity

                t = to / sqrt(1-v^2/c^2).

Point C in the rocket has aged 2 years, point B has aged 2.30 years, and 
Point A has aged 14.2 years.  Since different points on the spring 
traveled at different speeds, they have aged different amounts.  In the 
end, you have a spring which has aged a different amount for every point 
on it!  What does that mean?  Remember that any physical object is made of 
atoms, and each atom seems to have traveled through a different amount of 
time than the ones next to it.  The bottom line is that we don't need to 
consider quantum mechanics to get an idea about the effects of special 

Thinking about things this way might help you understand special 
relativistic length contraction, too.  Consider a moving meter stick, for 
example.  While you think of the front and back of the stick as being at 
the same time in your frame, in the stick's frame, the front end that you 
see is at a slightly earlier time than the back end you see.  This means 
that the front end has not moved ahead quite as much as the back end, and 
so you perceive the stick as being shorter than the stick is in its own 
frame.  See?

Well, Dan, I hope that answers your question.  Please let us know if you 
would like any more information.

Thank you for your interest.


Jim Guinn
Georgia Perimeter College

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