Einstein's Special Theory of Relativity - An Easy (I hope!) Explanation

Our brains are wired for survival purposes for a 3 dimensional and very slow moving environment. Compared to the speed of light, the everyday objects that our brains perceive and reason about are barely moving at all. Our common sense about how the world works is specialized for dealing with an almost non-moving or static environment (again, that's compared to the speed of light).

What this means, is that what our common sense tells us about our sluggish everyday world is mostly correct but otherwise it's judgements cannot be trusted when dealing with extremely fast things.

So when experiments and mathematics tell us things that are contrary to our crude perceptions about how things should work, we find it to be totally bizarre!

Our everyday common sense tells us that if while standing on a moving barge we hit a golf ball off the front, the speed of the barge adds to the speed of the golf ball. If we were to shine a flashlight in the same direction as we had hit the ball we would find that the speed of the barge does not add to the speed of the light beam. Its speed would be the same as if the barge were not moving at all.

The best minds of the 19'th century were stumped by this fact because it totally violated a very basic and seemingly self evident notion of how things are supposed to work.

In 1905, Einstien explained that this was simply the way that light behaved and that it only seemed strange because our common sense notions of how relative speeds were supposed to add up were only true for very slow moving objects (as compared to the speed of light).

Interestingly, the theory of electromagnetism, developed in the 19'th century by James Clerk Maxwell, also predicted this fact that the speed of light was unaffected by the speed of its source.

Note: In this explanation I'm trying to avoid excessive 'relative to this, relative to that' verbiage. Unfortunately, this can leave things somewhat vague. In the golf ball example above, to someone watching from the shore, the golf ball appears to move at a speed equal to the speed of the barge plus the speed of the ball relative to the barge. Our common sense says that this should be true regardless of how fast the ball leaves the barge. However, this doesn't hold up if we do the same experiment with a beam of light.

So the speed of light is unaffected by the speed of its source. Let's see what falls out of this...

Imagine having two horizontal mirrors facing each other and that one mirror is spaced above the other by the distance d. Also imagine that there is a pulse of light that bounces vertically between the two mirrors as shown in the left part of the drawing below.

The time it takes for the pulse of light to do a round trip (from the top mirror to the bottom mirror and back to the top) is twice the distance d divided by the speed of light. This device would actually make a great clock since the pulse can be relied on to always travel at the same speed while doing its round trips and thus always counting out consistent time intervals.



Suppose our "light clock" were traveling sideways at a very high (but constant) speed. Now the pulse would follow the "saw tooth" path shown on the right side of the drawing. The light must travel a greater distance now to make a round trip. Since its speed is the same as before (remember, the speed of light is not changed by the speed of its source), it will take longer to make a round trip.

So our "light clock" takes longer to count out its intervals. Another way of saying this is that the clock "ticks" more slowly.

Note that if the speed of light were not constant, the horizontal speed of the clock would have added to the speed of the pulse. Then, the light clock would not have slowed down since the pulse's greater speed would have compensated for the longer distance of the "saw tooth" path.

Stifle that yawn. This result has great significance as I will explain in the next section.

Suppose you are the person who is taking this photo and the other guy seems to be drifting toward you. Are you moving toward him or is he moving toward you? The answer is yes to both questions.

From each person's point of view, he is stationary, and the other guy is moving. Relativity states that everyone's frame of reference is valid. The observations that you make from your frame of reference is just as valid as those made by some one else on a different reference frame.

Now, back to the light clock... It's very feasible to hook up the light clock to an LED display that reads out seconds, minutes, and hours. Now lets say you choose a frame of reference that's "stationary." That way you get a clock that's keeping time "properly" (don't want a slow running clock, thank you very much!) So your light clock is behaving like the one on the left side of the drawing above.

But as always, someone comes along (at an extremely fast speed) to spoil your day. From his point of view, you're the guy that's moving, not him. From his equally valid point of view, your light clock is behaving like the one on the right side of the drawing above. And of course, to him your clock is counting out its intervals very slowly and your LED is counting out those seconds, minutes, and hours way too slow. Since you're stationary relative to your clock, it's working just fine as far as you are concerned. Now you try to tell him this and you speak at a normal rate (about 4 words/second by your clock). To him you are speaking 4 words/second relative to your very very slow clock. You sound like an old fashion phonograph record that is set to a very slow speed.
And of course since he is moving relative to you, his speech sounds equally slow.

This effect is called time dilation.

Time dilation is present even at the slow speeds that we are used to. But it's so tiny that our senses can't detect it. 60 miles/hour or even 3000 miles/hour is too slow compared to the speed of light at 186,000 miles/second or 669,600,000 miles/hour. At 60 miles/hour the triangles in the drawing above would have such a tiny base that they wouldn't look any different from the vertical photon path of the stationary clock. So the stationary clock and the 60 miles/hour clock "practically" keep the same time.

In the section that describes how the light clock works I wrote:

"Suppose our light clock were traveling sideways at a very high (but constant) speed. Now the pulse would follow the "saw tooth" path shown on the right side of the drawing."

I omitted an explanation for why the pulse would follow a saw tooth pattern. This prompted the following question from a reader:

"If the speed of the boat does not add to the speed of the photon, then when we move our light clock sideways, the photon should not zig zag, but go straight down and miss the bottom mirror."

Here is the explanation:

Suppose the two mirrors were on a very fast moving boat and a flash bulb on the bottom mirror emits a brief flash of light that propagates outward. To someone riding on the boat, the light flash would expand away from the bulb at the speed of light. He would describe this as an expanding hemisphere of light (diagram). From his point of view, the light source is not moving, so to him, the expanding hemisphere would always be centered about the flashbulb.

This person would see that any light that's captured by the two mirrors would be bouncing up and down between them. There would be no saw-tooth pattern.

Someone watching from the shore would see a different scene. He would not see the hemisphere of expanding light moving along with the boat. That's because the light would be moving faster than c on the leading surface of the hemisphere and slower on the trailing surface. This is not allowed by relativity.

So the person on the shore would see a stationary hemisphere of expanding light. To him, the boat (and it's two mirrors) would be moving away from the center of this hemisphere (the mirrors are moving toward the left in the diagram).

To him, light that's moving straight up would miss the top mirror. The two mirrors would only capture light moving along the diagonal path shown in the diagram. The light would appear to bounce between the mirrors in a zig-zag or sawtooth pattern.

We're at the end of the explanation here. However, you might be wondering how it is that the light hemisphere can be stationary with respect to the person on the moving boat and the person on the shore. These two people are moving relative to each other so it seems to be a contradiction. This paradox arises from the requirement that the speed of light remain constant to all observers which itself seems paradoxical.

There is no explanation for this that your intuition or common sense will readily grasp. As was mentioned at the beginning of this lens, our brains are wired to function in a very slow moving 3D spatial environment.

The only way to "understand" this paradox is by turning to abstraction and introducing a four dimensional abstract (or real?) space called space-time. If this interests you click here.