Understanding the theory of relativity

As I mentioned in my last post, I'm reading a biography on Einstein. Not surprisingly, a good portion of the book is devoted to the portion of his life where he developed the theory of relativity - commonly simplified to the equation that relates energy and mass, E=mc². There's more to it than this - read on if you're interested in getting Aaron's simplified summary (or you can go to the wiki for a much more detailed explanation, or just read a book or two :).

Special Theory of Relativity

The theory of relativity was actually developed in two stages, starting with the Special Theory of Relativity. Einstein would not fully complete the general theory of relativity until 10 years after the release of his special theory of relativity. The reason it's called the relativity theory (as far as I can tell) is that it exposes a relativity in a number of measurements that were previously thought to be constant - specifically, it outlines the relativity of time, mass, and dimensions. This means that time, mass, and dimensions are all relative depending upon the observer. There is no absolute or correct frame of reference, though on Earth we all share a frame of reference which allows us to experience time, mass, and dimensions similarly.

Despite all this relativity, the speed of light does not appear to be relative to the observer. A useful method of comprehending this is by imagining you're standing by the rails for an oncoming train at night. The train has a headlight at it's front end, and the train is speeding towards you at 200 mph. The light from the headlight of the train will still be measurable as the constant speed of light - 299,792,458 meters / s (186000 miles/second). It does not travel faster even though it's being broadcast from a source that is moving relative to you. This would not be the case if the conductor threw a water balloon at you from the moving train. The water balloon would slow down quickly due to air resistance, but it's initial speed would be the speed of the train + the speed of the conductor's throw. Ouch.*1

The reason the speed of light appears to be non-relative is because as an object approaches the speed of light, it's mass increases and time slows (decreases) relative to an observer. Light is moving at the maximum speed allowed in our universe at any given moment. Light (photons) have no mass, so the increase in mass is irrelevant.*2 The current belief is that it's impossible for an object with mass to be accelerated to the speed of light, and it's impossible for a massless object to not move at the speed of light. *3

Time changes depending on your frame of reference, which makes time relative. As a consequence, time passes differently for objects moving at extremely different speeds. This is, to an extent, common knowledge at this point. We've likely all heard of the experiments where a clock was sent into space and orbited at high speed while a control clock was left on the earth...and the clocks having different times when they are brought back together. A less discussed consequence is relativity of simultaneity - that is, that something that appears simultaneous for one observer will appear so to an observer moving at a high speed. Thematically, this is easy to understand, though it seems counter intuitive.

Perhaps the most difficult consequence of relativity to accept is that is changes the perceived dimensions of an object. Time being slowed is unusual, but time is already somewhat abstract, so conceptually it's not that difficult to accept. An increase in mass is unusual, but not groundbreaking. Accepting that an object will have different dimensions (it decreases in length relative to the direction of movement to the observer's frame of reference) is the most difficult for me to accept or understand.

As a final point (which may not have been introduced until Einstein later developed the general theory of relativity), there's an interesting thought experiment to help us comprehend our universe and hopes to answer the question of a finite or infinite universe (both of which seem impossible). The universe is, in a sense, both. It wraps around itself, so that traveling far enough in a single direction will eventually bring you back to where you started. This is difficult to imagine in a 3-dimensional world...and that's what the thought experiment is for!

Imagine a 2 dimensional being on a 2 dimensional world - for example, a dot on a piece of paper with no thickness, only a surface. As it stands, the dot can travel to the edges of the paper, and, well, find an end. Now imagine the paper is curled to create a sphere. To us, this paper becomes a 3-dimensional object, but to our 2 dimensional dot, there is no change. He doesn't know the paper "curves" in a way he could never understand. In addition, there are now no more edges to his universe. That was the explanation Einstein gave for our universe - sadly I don't yet know enough about physics to see where this theory is at currently.

I may try to simplify the General Theory of Relativity in a later post (the primary difference is that it encompasses gravity) but I don't feel that I understand it sufficiently yet.

*1 - This would not be true if the sum of the velocities of the train and the power of the conductor's water-balloon throw exceeded the speed of light, due to the velocity addition formula.

*2 - The Large Hadron Collider is a particle accelerator. What it does is increase the velocity of a two protons to near the speed of light (greatly increasing their mass relative to us) and then run them into each other. The plan is to observe the effects of this collision)

*3 - Light (photons) can be slowed when it enters a refractive substance. When photons slow, they gains mass (from atoms in the refractive substance). This new particle, a photon with mass, is called a polaritron. Light has been slowed to 38 miles per hour.