Last section ended with the idea that the speed of light is the same in all inertial frames. Now let's connect this to the idea of spacetime and events. Two astronauts moving at constant speeds relative to one another will measure the speed of light from all sources of light to have the exact same value which we write as a lowercase c. A constant speed is just the distance traveled by the time that has elapsed. Einstein realized that one way to explain why two astronauts moving relative to each other measure the same speed of light is because the two astronauts do not agree on the definitions of space and time. Instead of thinking about space and time as separate concepts, Einstein realized that he needed to consider the combination of both space and time into a concept he called spacetime. The universe consists of four dimensions. Three of those dimensions are spatial moving in the up-down dimension, the left-right dimension, and the forward back dimension. The last dimension is time, the past future dimension. Although, we don't say something moves in time, just that the flow of time itself moves us towards the future and away from the past at a speed of one second per second. Let's exercise our imagination to better understand how humans perceive time. Our senses collect information from the space around us but we exist only at a single moment in time. None of our senses can perceive the passage of time directly or changes in time for that matter. The best humans can do is to create memories of the past which allows us to affect change in their future environment. In that sense, we only experience a narrow slice of time. So, how do we effectively imagine what a four-dimensional spacetime looks like? Well, let's start by considering an easier picture with fewer dimensions altogether. Suppose my fingers are limited to motion in only one spatial dimension like walking along my arm. I can move them forwards along my arm or backwards along my arm. But it's too narrow for left and right and my fingers are too weak for up and down. In essence, I've compressed three dimensions of space into a single dimension. So now, my fingers' position can be characterized by a single point along a line. If the fingers walk along my arm from elbow to hand, it takes some amount of time. Since we've got my fingers' distance on the horizontal axis, let's now plot time along the vertical axis. This diagram is called the spacetime diagram. Since we humans only see a narrow slice of the spatial dimensions, we need to reveal how my fingers' position changes with time. This curve, for example, shows that my fingers walk back and forth across my arm and also move forward in the time dimension. If we mask everything but a narrow slice, we get back to the original representation of my fingers position in space. This path is my fingers worldline. Since photons must travel at the speed of light, a plot of position of a photon on a spacetime diagram will zoom outwards in a perfectly straight line. Normally, this line is drawn so that the light ray makes a 45-degree angle from the space and time axes. Anything that travels at speeds less than light such as people and rockets have worldlines that stay in the region between the time axis and the worldline of the light ray. The only way to escape from this region is to move faster than the speed of light. This diagram only shows light moving to the right. But light can also move to the left. And the left moving light will also be represented by a line that makes a 45-degree angle to the space and time axis. This diagram shows only one dimension, the left-right dimension. But there is also a back and forth dimension that comes in and out of the screen that we aren't showing. Light also travels at 45-degree angles to the back and forth dimension's axis. The two-dimensional surface that light can travel on is called the light cone. In addition, there is a third dimension, up and down and it would be really difficult to show this dimension in a drawing of this sort. In a spacetime diagram, the light cone defines the boundary of spacetime events that a person or any object that travels at speeds slower than light can experience. People can travel upwards in the time dimension in directions that stay inside the light cone. Experiencing events outside of the light cone would require that we can travel faster than light. This means that people and all objects with mass are confined to our own personal light cones. It's hard to convey what spacetime actually is. One way to visualize spacetime is to imagine a three-dimensional object and then try to extend its dimensionality across time. A person is human-shaped in three dimensions but in four-dimensional spacetime, a person is a long tube that includes the person in the past, present, and future. If you slice this four-dimensional tube in the time dimension, a three-dimensional version of the person at that moment in time is the slice. The four-dimensional spacetime we live in is similar to a block of cheese if we reduce spacetime to only two dimensions. We can imagine the ends of this cheese as the two space dimensions and the length of the cheese as the time dimension. So a hole in Swiss cheese becomes a cheese being, living inside of a block of cheese time or space cheese or space cheese time. You get the idea. A cheese being at rest thinks of time running along the long axis of the cheese and the two-dimensional space that it lives in is the flat end of the cheese. Humans are all powerful higher dimensional beings with a cheese knife and we can slice up the block of cheese into thin slices. Each slice of cheese represents a single moment of time as experienced by the cheese being. At one end of the cheese there are no cheese beings but as we slice through their time dimension, we discover the birth of a cheese being growing to larger sizes and eventually disappearing. Just like our four-dimensional human tube. From our perspective, a cheese being has been born, lived a fruitful life and died a cheesy death. Here's where things get interesting though. A different cheese being that moves at a constant speed through the cheese will slice up the cheese in different direction. The moving cheese being will see different size slices and think the times and sizes are different as if the cheese spacetime itself were somehow warped. However, if we were to take the same cheese block and slice it up in yet another direction, we can do it such that both observers agree on where the bubbles are in spacetime but they can't agree on how it was sliced. We can only speculate whether Einstein used cheese to describe spacetime but if he did surely we can all agree that it must have been tasty.
