Why Can’t You Reach the Speed of Light?

A friend from high school had a good question that I wanted to share:
I have a science question!!! Why can’t we travel the speed of light? We know what it is, and that its constant. We’ve even seen footage of it moving along a path (it was a video clip I saw somewhere [Edit to add: there are now two different experiments that have done this. One that requires multiple repeats of the light pulse and a newer technique that can work with just one). So, what is keeping us from moving at that speed? Is it simply an issue of materials not being able to withstand those speeds, or is it that we can’t even propel ourselves or any object fast enough to reach those speeds? And if its the latter, is it an issue of available space/distance required is unattainable, or is it an issue of the payload needed to propel us is simply too high to calculate/unfeasable (is that even a word?) for the project? Does my question even make sense? I got a strange look when I asked someone else…
 This question makes a lot of sense actually, because when we talk about space travel, people often use light-years to discuss vast distances involved and point out how slow our own methods are in comparison. But it actually turns out the road block is fundamental, not just practical. We can’t reach the speed of light, at least in our current understanding of physics, because relativity says this is impossible.

To put it simply, anything with mass can’t reach the speed of light. This is because E=mc2 works in both directions. This equation means that the energy of something is its mass times the speed of light squared. In chemistry (or a more advanced physics class), you may have talked about the mass defect of some radioactive compounds. The mass defect is the difference in mass before and after certain nuclear reactions, which was actually converted into energy. (This energy is what is exploited in nuclear power and nuclear weapons. Multiplying by the speed of light square means even a little mass equals a lot of energy. The Little Boy bomb dropped on Hiroshima had 140 pounds of uranium, and no more than two pounds of that are believed to have undergone fission to produce the nearly 16 kiloton blast.)

But it also turns out that as something with mass goes faster, its kinetic energy also turns into extra mass. This “relativistic mass” greatly increases as you approach the speed of light. So the faster something gets, the heavier it becomes and the more energy you need to accelerate it. It’s worth pointing out that the accelerating object hasn’t actually gained material – if your spaceship was initially say 20 moles of unobtanium, it is still 20 moles of material even at 99% the speed of light. Instead, the increase in “mass” is due to the geometry of spacetime as the object moves through it. In fact, this is why some physicists don’t like using the term “relativistic mass” and would prefer to focus on the relativistic descriptions of energy and momentum. What’s also really interesting is that the math underlying this in special relativity also implies that anything that doesn’t have mass HAS to travel at the speed of light.

A graph with X-axis showing speed relative to light and Y-axis showing energy. A line representing the kinetic energy the object expoentially increases it approach light speed.

The kinetic energy of a 1 kg object at various fractions of the speed of light. For reference, 10^18 J is about a tenth of United States’ annual electrical energy consumption.

The graph above represents  the (relativistically corrected) kinetic energy of an 1 kilogram (2.2 pound) object at different speeds. You can basically think of it as representing how much energy you need to impart into the object to reach that speed. In the graph, I started at one ten thousandth the speed of light, which is about twice the speed the New Horizons probe was launched at. I ended it at 99.99% of the speed of light. Just to get to 99.999% of the speed of light would have brought the maximum up another order of magnitude.
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