New America (27 page)

For instance, we don’t know what inertia “is.” It seems to be a basic property of matter; but why? Could it be an inductive effect of gravitation, as Mach’s Principle suggests? If so, could we find ways to modify it, and would we then be held back by the increase of mass with velocity?

Could we discover, or produce, negative mass? This would gravitationally repel the usual positive kind. Two equal masses, positive and negative, linked together, would make each other accelerate in a particular direction without any change in momentum or energy. Could they therefore transcend c?

A solution of Einstein’s field equations in five dimensions for charged particles gives an electron velocity of a billion trillion c. What then of a spaceship, if the continuum should turn out to have five rather than four dimensions?

Conventional physics limits the speed of mass-energy. But information is neither; from a physical standpoint, it represents negative entropy. So can information outrun light, perhaps without requiring any medium for its transmission? If you can send information, in principle you can send anything.

Magnificent and invaluable though the structure of relativity is, does it hold the entire truth? There are certain contradictions in its basic assumptions which have never been resolved and perhaps never can be. Or relativity could be just a special case, applying only to local conditions.

Once we are well and truly out into space, we may find the signs of a structure immensely more ample.

These speculations have taken us quite far beyond known science. But they help to show us how little known that science really is, even the parts which have long felt comfortingly, or confiningly, familiar. We can almost certainly reach the stars. Very possibly, we can reach them easily.

If we have the will.

Appendix

Readers who shudder at sight of an equation can skip this part, though they may like to see the promised table. For different velocities, it gives the values of the factors “tau” and “gamma.” These are simply the inverses of each other. A little explanation of them may be in order.

Suppose we have two observers, A and B, who have
constant
velocities. We can consider either one as being stationary, the other as moving at velocity v. A will measure the length of a yardstick B carries, in the direction of motion, and the interval between two readings of a clock B carries, as if these quantities were multiplied by tau. For example, if v is 0.9 c, then B’s yardstick is merely 0.44 times as long in A’s eyes as if B were motionless; and an hour, registered on B’s clock, corresponds to merely 0.44 hour on A’s. On the other hand, mass is multiplied by gamma. That is, when B moves at 0.9c, his mass according to A is 2.26 times what it was when B was motionless.

B in turn, observes himself as normal, but A and A’s environs as having suffered exactly the same changes. Both observers are right.

The formula for tau is (1 — v
²
/c
²
)
^½
. where the exponent “½” indictes a square root. Gamma equals one divided by tau, or (1 — v
²
/c
²
)
^½.

As for relativistic acceleration, if this has a constant value
a
up to midpoint, then a negative (braking) value —a to destination, the time to cover a distance S equals (2c/a) arc cos (1 — aS½2c
²
). For long distances, this reduces to (2c/a) l
n
(aS/c
²
where “l
n
” means “natural logarithm.” The maximum velocity, reached at midpoint, is c [1 — (1 + aS/2c
²
) -2]½.

Postscript

Since this essay first appeared, in 1975, much further thought and study have been going on. The likelihood of the “starbow” has been questioned; so has the practicality of the Bussard ramjet. These matters are still controversial, though. Meanwhile, the idea of a matter-antimatter rocket is looking more hopeful than it formerly did. The whole field of interstellar astronautics remains lively, exciting, and infinitely promising.

But mankind will never see that promise fulfilled unless we, today, continue pioneering in those parts of space that we can already reach.