# Space-Time

People assume that time is a strict progression of cause to effect, but actually—from a non-linear, non-subjective viewpoint—it's more like a big ball of wibbly wobbly…timey-whimey…stuff.

*Doctor Who*, a popular science fiction show in the UK. They're, of course, making fun of the complicated, nonsensical explanations of time in science-fiction shows that take themselves a little more seriously, but you'd be hard pressed to find an accurate description of time in such a genre. Our current understanding of time and space is surprisingly non-intuitive but nonetheless interesting. For the better part of human history, the ideas of space and time were regarded as completely separate phenomena - until Albert Einstein turned this concept on its head in 1905 with his theory of Special Relativity. After that, most physicists stopped regarding space and time as completely separate concepts and instead recognized that they shared a deep relationship that surprised everyone.

Let us begin with a little history. Around 1860, physicist James Clerk Maxwell published what we now call "Maxwell's Equations," four equations that describe the laws of electrodynamics. He didn't really come up with all of them, but he was the first person to group them together and make them what we call self-consistent. Surprisingly, when looked at together, the equations predicted electromagnetic waves that travel at the same speed we knew light travelled at. Physicists of course eventually found out that light is really just electromagnetic waves. These equations are considered one of the crowning achievements of 19th century physics, but they had a slight problem. Maxwell's equations predicted that light travel at what physicists call c, or 300 million meters per second. But his equations didn't say what speed that was with respect to. This is a subtle point, so we'll use sound as an example. If I tell you that sound travels at about 340 meters per second, we know that means sound travels at that speed with respect to air, because air is the medium that sound travels through. In fact if you saw a gunshot fired off, the sound from it would get to you sooner if the wind were blowing in your direction. But physicists had no idea what the medium would be for light. To solve this they reasoned there *had* to exist what was referred to as "ether," some medium light travels through that must propagate the entire universe.

Physicists tried to measure the velocity of this "ether" in 1887 in the Michelson-Morley experiment. They measured the speed of light coming from the sun at different times during the year. Earth travels at very different velocities during different times of the year, because it travels around the Sun. So based on the differences in the speed of light from the sun at different times of the year, physicists hoped to measure the velocity of the ether. This would be like measuring the speed of sound to determine which direction the wind is blowing, in theory it can be done. The surprising result was that the speed of light coming from the sun seemed to be constant throughout the year. At the time, the experiment was considered a failure, but in actuality, it did not fail. Physicists did not measure the velocity of ether, because well, ether doesn't exist.

This is about where Einstein enters the picture. He reasoned there wasn't any ether and instead hypothesized that light always travels at c, which should always be measured regardless of how fast you're moving. This is an extremely radical concept. For example, if someone shined a flashlight at you, and you traveled toward him at half the speed of light, classical physics intuition would tell you that when you measured the speed of the light coming out of the flashlight, you would measure one and a half times the speed of light due to the fact you're traveling towards it. This is certainly how sound works, but Einstein said no - you will always measure light to be traveling at c regardless of how fast *you're* moving. To most, that probably doesn't make any sense.

It turns out the only way this can happen is if space and time do some pretty funky things when objects start moving. Einstein figured out these funky things with Gedanken Experiments, or more colloquially *thought* experiments. These are just simple situations one could think of, applying the fact that c is constant. One concept that emerged was length contraction. When an object is observed moving very quickly (close to the speed of light), it'll get shorter in the direction it's moving. For instance, if a meter stick passed by you at half the speed of light, its length would only measure 87 centimeters instead of one meter (which is 100 centimeters.) But what if the meter stick was stationary, but you passed it at the speed of light? Would you get all squished up? It turns out this question is ambiguous. If someone was standing next to the meter stick and watched you zoom by at half the speed of light, they would observe you to be all squished up. But you would still measure the meter stick to be 36 centimeters. This is a non-intuitive aspect of relativity - there is no preferred reference frame, and people passing one another will observe the *other* person to be squished up, but not themselves. Believe it or not, this actually makes sense, but only when the next concept is added.

The other weird thing that happens when objects start moving quickly is time moves slower for them; we call this time dilation. For instance, if you observed a clock pass by you near the speed of light, it would be ticking slower than your own clock. This is the principle of the "twin paradox." If you had a twin and he left on a spaceship for 50 years travelling near the speed of light and came back to earth, much less time would have passed for him, because time was moving slower for him. Technically, at least from the perspective of your twin in the spaceship, your clock would be moving slower too. The magic happens when he turns the spaceship around, but the details are a little complicated.

So we know when you see an object travelling quickly, it will shrink, a spatial property, and it's clock will slow down, a temporal property. If we propose that time and space have to look the same if we start moving and then stop again, the result is what is known as a Lorentz transformation. A Lorentz transformation is just a bit of math that tells us how space and time behave if we start moving in a particular direction. It also turns out you can get all the things discussed about time dilation and length contraction from a Lorentz transformation, but there are other interesting consequences. The most interesting, in my opinion, is the breakdown of simultaneity. It turns out that if I observe two things that happen at the same time, another person who is moving relative to me will observe them to *not* happen at the same time. This is a necessity based on what I've said about length contraction, and we can look at a fun paradox to see this has to be true.

Imagine two people named Alice and Bob are standing on a train, Alice in the front and Bob in the back. Also imagine they're approaching a tunnel the same length as the train, and traveling close the speed of light. According to Alice and Bob, the tunnel will be shorter than the train (length contraction), so it would actually be possible for them both to look up after Alice has passed through the tunnel but before Bob has and both see the sky. But let's look at this from the viewpoint of a third person watching from somewhere on the ground, not on the train. According to the observer on the ground, the train is shorter than the tunnel (again, length contraction), so there should never be a moment that Alice could look up and see sky at the same time as Bob before he enters the tunnel. How are we to reconcile this apparent paradox? The answer is the breakdown of simultaneity. Alice and Bob looking up happened at the same time. . . according to them on the train. But according to someone on the ground, these two events happen at completely different times. According to the person on the ground, Bob will look up before Alice and see the sky, Bob will enter the tunnel, and *then* Alice will look up. In fact, the longer the train is, the bigger the difference in time will be between when Bob and Alice look up. The time difference actually depends on a spatial separation. The time difference will also be larger according to the person on the ground the faster the train moves. Crazy.

So that's our modern understanding of time, to a certain extent. The time you observe someone to measure depends both on where they are located and how quickly they're moving with respect to you. Given this property, it really doesn't make sense to think of space and time as two completely separate quantities - they depend on each other, which is why physicists often just say "space-time." This was one of the starting points for modern physics, which continued to redefine how we look at the world through the world through the 20th century. Our modern understanding of space and time is even more complicated today, but Einstein was the first to propose that they share a deep relationship.