Gardner: Relativity, making space exploration that much more difficult

Sorry for the delay on this one, folks.

Last week, I touched on some of the scientific theory driving Christopher Nolan’s new intergalactic thriller Interstellar. There will be no spoilers here, but it is helpful for moviegoers to have a basic understanding of some of the science at play.

Quick recap: Einstein’s theory of special relativity is based on two important postulates. First, the laws of physics are the same for all observers travelling in constant motion relative to one another. Second, the speed of light — roughly 186,000 miles per second — is the same for all observers, regardless of their relative motion or the motion of the light source.

Taken together, these two ideas presents us with some rather odd conclusions about how space and time are measured based on the relative motion of an outside observer.

If the speed at which a light beam barrels past a spacecraft is equal both for a vehicle at rest and a vessel travelling at a rate of even 185,999 miles per second, something must account for the fact that both observers would record the same, unchanged velocity when measuring the speed of the light beam.

Inexorably, we are led to the astounding conclusion — even to Einstein, when first proposed — that the only way we could possibly account for light remaining constant is to adjust our measurements of space and time themselves. As the spacecraft in the above example nears the speed of light, the ship would literally contract and time would indeed slow down for those inside, if measured by an outside observer.

It sounds like mystical mumbo-jumbo, but concrete physical experimentation has repeatedly supported these hypotheses.

Taking all of this into account, we can conclude that space and time are intimately connected, contracting and dilating directly with one another as an object in motion nears the speed of light. In fact, Einstein dubbed the term “spacetime” to join the two when depicting a uniform, four dimensional universe.

The ideas are lofty, but that’s only half of the equation. Einstein’s theory of special relativity explains and predicts how our measurements of space and time would be affected under very specific circumstances, but how does all of this play out outside these special scenarios?

Einstein had an answer for that question, as well, though it wouldn’t be revealed to the scientific community until he published his theory of general relativity in 1916. Taking his newfound understanding of the interconnectivity between space and time, Einstein was eventually able to apply the ideas of relativity to the entire universe by taking into account the laws of gravitation.

Before delving any deeper, let’s take a look at an important concept known as the equivalence principle.

If you were to hold a pencil and a book at equal heights and drop them at the same time, they would each accelerate toward to the ground at a rate of 9.8 meters per second squared, landing at precisely the same time. This is due to the earth’s gravitational pull. Conversely, if you were travelling in a rocket outside the earth’s gravitational field that was accelerating at exactly 9.8 meters per second squared, you would be able to conduct the same experiment, with both objects falling precisely as they would as if they had been dropped on earth.

This seems inconsequential, but it presents us with several important conclusions. First, is that the laws of nature in an accelerating frame of reference are equivalent to the laws in a gravitational field, as long as the rate of acceleration is equal to the gravitational pull. With this in mind, we can study the effects a gravitational field would have on an object by observing how that object would behave in a spacecraft travelling at the equivalent rate of acceleration.

Imagine a rocket travelling at a constant rate of motion outside the earth’s gravitational field. To an outsider observer, a beam of light shot from one side of the ship to the other would appear as a straight line. If the rocket is accelerating at 9.8 meters per second squared, that beam of light, when viewed by the outside observer, would appear as a curved line.

Using the equivalence principal, we can conclude that this same phenomena would hold true for a beam of light under the influence of a gravitational field, and it does. Experimentation conclusively confirms that light does, in fact, bend around objects — i.e. stars, galaxies — exerting large gravitational fields.

Because the speed of light is the fastest known rate of motion, we can assume that whatever path the beam of light takes is the most efficient way of getting from one point to another. Adding the notion that this path is sometimes curved due the effects of gravity led Einstein to another astounding conclusion: spacetime itself is curved.

Picture a flat, empty mattress. If we were to roll a marble across the mattress, it would travel briefly in a straight line before coming to rest. Now, picture the same mattress, but with a large bowling ball in the center. We can physically see the bowling ball’s weight creating a depression on the mattress. If we were to roll the marble near the outside of the mattress now, it would follow an elliptical or circular path around the bowling ball.

This thought experiment provides us with a useful analogy for describing spacetime. The marble doesn’t follow this new curved path because of the bowling ball itself. Rather, the marble’s path is altered due to the curvature of the mattress. Applying this idea on a universal scale, Einstein concluded that light bends around an object not because of the object itself, but due to the curvature of spacetime resulting from the object’s gravitational field.

So what does this mean in terms of relativity? Just as spacetime is affected when an object in motion nears the speed of light, it is similarly affected by the curvature resulting from a gravitational field. If a space traveller were to explore a planet closely orbiting a star possessing a gravitational pull exceeding that of earth’s, time would pass by more slowly for the explorer compared to those who chose to remain on our home planet.

After spending only a day on this unknown planet, the traveller could return to earth to conceivably find that his friends had aged more than 20 years during his 24-hour expedition. As the strength of gravitational fields increase, the effects on spacetime become more profound.

This notion, as you can imagine, presents us with some very troubling implications regarding the idea space exploration outside our solar system, which brings me back to Interstellar. You should have the tools now to grasp most of the concepts that don’t veer into the realm of pure speculation. So with that, go out, grab a bucket of popcorn, and enjoy one of the finest depictions of relativity to grace the silver screen.