First, a disclaimer: I make no assertion that the information presented here is useful in any way beyond an interesting mental exercise. I am not a physicist, and have no formal scientific training. What I do have though is an intense curiosity about theoretical physics, and a recent abundance of relatively free mental time, in the form of a drive back from Des Moines, IA last weekend. At the very least, the mental rambling that follows proved to be an interesting mental diversion to fill some empty miles…and I hope it gives you an opportunity to stretch the way you normally think about the often counter-intuitive world we live in. Which is why I chose to share it.
I started thinking about the way we typically measure speed, as a distance over a period of time. Cars drive along in miles per hour…and that makes sense for everyday comparative purposes. If I’m driving along at 60mph and cut my speed in half, I say I’m now going 30mph. That’s an accurate way to express the concept, and would be understood by just about anyone. However, there is another way to look at it. It’s also accurate, albeit unusual, to say I’m now going 60 miles per 2 hours.
In fact, I realized that when considering the speed of light, it makes much more sense to think of speed in this way. It allows an interesting perspective on some of the most counter-intuitive concepts relating to the constant we call “c”.
For instance, nothing can move faster than light moves in a vacuum. This is common knowledge, but it leaves the average person asking, “why 299,792,458 meters per second?”. What it is it about that speed in particular that is special? It’s hard to overcome the mindset that limits of speed are limits in technology. If my car won’t travel 150 miles per hour, I could get a faster car that would. Yet we know that traveling faster than the speed of light is seemingly impossible, regardless of the technology.
So let’s take a detour. It makes logical sense to say you can’t travel a negative distance. I can take two steps forward, or three steps back, but either way I’ve taken a positive number of steps. The only difference is the direction. I can’t move less than 0 meters. So it’s no leap of intuition to say that the minimum speed someone can travel from point A to point B is 0 units of distance per unit of time.
Logically, the same is true of time. I can’t imagine myself moving a negative amount of time either. For example, I can’t perform a task in less than 0 seconds. So it’s no leap of intuition to say that the maximum “speed” I can travel from point A to point B is some amount of distance in 0 units of time. In other words, instantly.
In effect, that’s exactly what happens at the speed of light. Time stops. As a consequence of relativity, time moves slower at high speeds until it ultimately stops at the speed of light. We tend to imagine this as experiencing things in slow motion, where we might feel time passing more slowly than our typical experience. In reality, however, the opposite is true. If you found yourself suddenly going nearly the speed of light, the effect would be that time would feel as if it were passing normally for you and much more quickly than normal for everything around you. If you found yourself suddenly going the speed of light, everything around you would simply happen instantly.
To take that a step further, if you were able to travel a set distance at exactly the speed of light, it would be irrelevent how far the distance is. If your destination were a million miles away, you’d arrive instantly. If the destination were a trillion miles away, you’d arrive instantly. You wouldn’t be able to tell the difference. At least not until you stopped and discovered the universe had aged two months in that instant.
Thinking in this way, the cosmic speed limit suddenly makes sense. Not as the highest number of meters you can possibly traverse in one second, but the lowest number of seconds you can take to traverse one meter, or indeed any number of meters.
We often use this reasoning in reverse, when considering the idea of time travel. That is, that you can’t send information in to the past, because you can’t send information faster than light. Perhaps an easier way to look at it is that you can’t send information faster than light, because you can’t force information to travel a negative amount of time.
Another aspect of the speed of light that perhaps makes more sense in this context is the fact that it’s impossible to accelerate to the speed of light. That concept is not intuitive based on our everyday experiences. We aren’t used to the idea of a speed we can’t reach, in much the same way that we aren’t used to the idea of a speed we can’t exceed given sufficient technology. Your intuition tells you that if you are going nearly the speed of light, and you speed up a little, you’d be going the speed of light. Intuition is, of course, wrong.
However, if you approach the idea in the same manner we originally used to describe the car’s speed, it makes perfect sense. If I’m traveling at 1 meter per second, and I double my speed, then I’m now traveling at 1 meter per half second. Double it again, and I’m traveling at 1 meter per quarter second. Double it 5 more times, and we’re up to 1 meter per 0.003125 seconds. I think you see where this is headed. Double it as many times as you like.
In fact, you can double your speed an infinite number of times and it won’t matter. That fraction will get smaller and smaller, but it will never hit zero because there are an infinite number of decimal places at your disposal. Because you’re always taking some amount of time to travel that meter, you’ll never accelerate to the speed of light, which as we saw before, would require you to travel the meter in 0 seconds.
This of course led me to wondering if the opposite is true as well. If you can’t accelerate to the maximum speed in the universe, can you decelerate to the minimum? Could an object ever reach an absolute speed of zero? I’ll leave you to ponder that, but remember this: You might feel like you’re sitting perfectly still reading this, but your intuition is, of course, wrong again. Massively, hugely, mind-bogglingly wrong. I look forward to my next road trip.