### 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
Message:
```
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.
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
http://www.gpc.edu/~jgui

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
relativity.

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?

Sincerely,

Jim Guinn
Georgia Perimeter College

```

Current Queue | Current Queue for Physics | Physics archives