2.1 The block universe
A simple picture of a block universe would be, say, a house brick standing on its end, with the vertical direction representing time, and space being represented by horizontal sections at different levels through the brick – the higher the level, the later the time. A more accurate representation of the block universe would incorporate “curved” geometries, including those described by general relativity where mass and energy are intrinsic components, but that wouldn’t change the simple-picture case that we are going to make for a block universe.
To make this picture more substantial, we’re going to need special relativity. The figure shows a Minkowski diagram, where space is plotted in the horizontal direction and time is in the vertical direction. The plot is drawn from Alice’s point of view – we say that the plot is in Alice’s frame of reference. Because of Einstein’s postulate that the speed of light is the same for all observers, we have to specify the frame of reference. Minkowski diagrams are scaled so that it takes light one vertical time unit to travel one space unit horizontally. So light paths in Minkowski diagrams are always at 45º to the vertical and horizontal in any observer’s frame of reference.
On the left of the Minkowski diagram, Alice sends two light beams to two equidistant mirrors, one on her left and one on her right. You can see the two beams drawn slanting diagonally upwards at 45º to the left and 45º to the right towards her mirrors. Since they reach the mirrors at the same time, they are reflected back to Alice and arrive at the same moment.
Bob is travelling towards Alice at such a high speed that his time axis is noticeably bent towards Alice in her reference frame by 11º. (So Bob covers 1 × tan (11º) = 0.2 space units in one time unit: 20% of the speed of light.) Bob has the same arrangement of two equidistant mirrors, and you can see the light paths leaving Bob, reflecting from the mirrors and arriving back at Bob at the same moment.
So why is Bob’s space axis tilted at 11º instead of being horizontal, coincident with Alice’s space axis? It is because of the requirement for light paths to be drawn at 45º for all observers (or, in other words, because the speed of light is the same for both Alice and Bob). The paths form a rectangle rather than a square as in Alice’s case, because that is the only way in which the reflected light paths can meet at the same point, given that Bob’s time axis is bent rather than vertical in Alice’s reference frame. If you try to draw the 45º paths hitting the two mirrors on a dotted line which is horizontal rather than tilted at 11º, and then reflecting back to Bob, you will find that they don’t get back to Bob at the same moment.
So, as a general rule, in Minkowski diagrams drawn in one observer’s rest frame, the time and space axes of another observer moving with respect to the first are tilted at the same angle, respectively, to the vertical and to the horizontal. We say that the axes are “scissored” in the direction of travel.
In a Minkowski diagram, any two events on an observer’s space axis, or on a grid line parallel to their space axis, happen simultaneously. This means, though, that in Alice’s reference frame, events which are simultaneous for Bob (such as his light beams hitting his two mirrors) are not simultaneous for her. You can see this in the diagram, where the right-hand beam hits Bob’s right mirror at a point which is below the point where the left-hand beam hits Bob’s left mirror. This relativity of simultaneity has profound consequences, as you will see in the next diagram.
Bob is approaching Alice. If Bob is moving with constant speed relative to Alice, then, in her reference frame, Bob’s time and space axes are inclined like scissor blades with respect to her own time and space axes. This has the effect that an event in Alice’s future can be already in Bob’s past.
Now we have all the information we need to see why the universe can be called a “block universe”.
This diagram is drawn in Alice’s reference frame where Bob is approaching Alice, just as in the previous diagram. When Alice is at the origin of her axes, M, then, in her reference frame, Bob is at that moment at point U, which we may take to be the origin of his axes.
As we saw above, Bob’s time and space axes are “scissored” in the direction of his motion, which has the effect that, instead of his space axis being horizontal and coincident with Alice’s, it intersects her world line at point Q, which is some time in her future.
Also on Alice’s world line, still in her future, but below Bob’s space axis, and so in Bob’s past, is event T. I have marked it with a star; it doesn’t matter what the event is – it could be, say, the spin outcome of Alice’s 60º experiment. The importance of event T is that, being in Bob’s past, the outcome of the event – say, spin-down – is fixed, because it has already happened for Bob, which means that it is fixed for Alice, too, even though it is still in her future.
We can extend this scenario (of Bob approaching Alice) to any event at any spacetime point in the universe: for any given moment for Alice, who may be anywhere in the universe, there is an event in her future which is already in Bob’s past at that same given moment. Ultimately, this means that every event, anywhere in the universe, from the moment of creation to the very last event in time, is fixed. In other words, our universe is not a three-dimensional structure which evolves with time – it is a fixed, four-dimensional structure which does not evolve at all.
Ultimately, the fact that events in the block universe are fixed means that the block universe is a structure. It will be important later to appreciate that this structure is not a structure within spacetime – it is a structure of spacetime, with events embedded in it. It defines a spacetime. To put it another way, while the events in our universe make a pattern in spacetime, the spacetime pattern, including all the events, is a pattern, or structure, at a more fundamental level – one which clearly cannot be constructed from the very properties, like spacetime, that are defined by the structure itself! For lack of a better name, we call this a mathematical structure, and we are now ready to see what this means for our universe and our multiverse.
