Relativity IV: The Speed of Light

Hello, and welcome back to MPC! Last week, we spoke about the constant nature of time. This week we will be pulling together ideas from last week’s post and the “Michelson-Morley Part 2” post in order to get a better understanding of the importance of the speed of light.

Hopefully, you noticed the quotation marks around the word “constant” in last week’s blog post. As those quotations suggest, and as was alluded to at the end of that post, everything I told you about time being constant was a lie. For example, I mentioned how 30 minutes to you is the same thing as 30 minutes to me, and 1 second to me is the same thing as 1 second to you. Yes, this was lie.

How can that be? Does one of us just have a bad watch?

Nope, that’s not it.

Is one of us using a different timezone?

Nope, that’s not it either. What can it possibly be then? Well, I ask you to think back to the “Michelson-Morley Part 2” post. In that blog post, I presented a scenario in which I was a ray of light (traveling at the speed of light, of course) and you were traveling towards me at 100 m/s. We mentioned that, despite your motion towards me and the concept of the Galilean transformation, you would still see me as traveling at the speed of light. If anything, it may seem like that was a lie. Our everyday experience tells us that you should see me as moving slower if you were traveling towards me than if you were stationary, and everyday experience also tells us that my 5 minutes is the same as your 5 minutes. Nonetheless, scientific theories and experiments support the former, but not the latter.

Now, we must ask ourselves how it is possible for light to always appear to be traveling at the same speed, regardless of the observer’s (in the previous example, you were the observer) motion. Things are about to get counterintuitive, but I ask you to throw away all of your preconceptions about how our world works. This may be difficult, but, if you decide to do this, you will emerge from the next few blog posts with an even better understanding of the world than you have ever had before. Let’s get started.

When you hear the word speed, what do you think of? Hopefully, you at least think of distance and time. Specifically, when you think of speed, the following probably comes to mind:

speed = distance / time

Up until now, we have assumed that speed is simply a result of distance and time. In other words, if I were to ask you to measure the speed at which a car is traveling, you would probably decide to figure out how far the car has traveled and how long it took the car to travel that far. This is perfectly fine! However, why don’t we try flipping this scenario? What if instead of speed always being determined by distance and time, distance and time were determined by speed? This idea may sound confusing, but let me give you an example similar to one that you have probably encountered:

Al is watching a baseball game. He knows that the pitcher pitches the ball at 100 m/s. The distance from the pitcher’s mound to home plate is 10 m. How long does the pitch travel for?

This question should be simple. We know our speed and distance, and using our formula (or intuition), the ball must have traveled for 0.1 seconds. Notice how the answer we get is dependent on the given speed.  Let me ask a somewhat similar question now:

Al is watching a rocket ship in outer space via a camera that is stationary in space. Oscar is watching the same rocket ship in outer space via a camera that is on the front of the space ship. Both Al and Oscar see an asteroid approaching the rocket ship. Al sees the asteroid travel 150 meters before hitting the rocket ship. Because of the unique view Oscar has (which is moving relative to Al’s view), Oscar sees the asteroid travel 300 meters before hitting the rocket ship. Both Al and Oscar know that the asteroid is traveling at 50 meters per second. How long does it take for the asteroid to collide with the rocket ship?

If Al were to carry out the calculations, he would get 3 seconds. If Oscar were to carry out the calculations, he would get 6 seconds.

How does that make any sense? Does someone on the moving rocket ship have more time to act than the engineers in Houston (who are “stationary”)?

Not really (the Galilean transformation would come into play here, as we are not working with light; therefore, the speed would not be 50 m/s to both Al and Oscar). But this idea was simply meant to demonstrate a concept: time does not have to be constant. Just because I measure an event to take 5 seconds, that does not mean that you will measure the same event to take 5 seconds. Your 5 seconds and my 5 seconds may be different — 6 seconds to Oscar is 3 seconds to Al! I hope that you can see the connection between this and our predicament with light: in both cases we know the speed before we know distance and/or time. In other words, perhaps our previous scenario with the car and ray of light does make perfect sense, it is just that we have made “silly” assumptions such as time being a constant.

Indeed, this is exactly what we have done. All scientific evidence seems to suggest that, instead of the speed of light adapting to our conditions (such as our distance and our time), our distance and times adapt to make the speed of light always the same. If you think that this is mind-blowing, just wait for the next few blog posts, where we will be talking about special relativity. See you then!

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