Spacetime as a Wave Function

Amanda Gefter dives into complex physics in her book Trespassing on Einstein’s Lawn, and helps us better understand the challenges of modern physics research today. When we look out into space we see stars and planets and if we look really closely with telescopes we see asteroids, galaxies, and lots of dust floating through space. What physics tells us exists within the empty space between those objects (and indeed within all space) is spacetime. Spacetime is a thing. It bends and is warped by matter and it can ripple through the universe and change the physical matter that we can see and feel.


Gefter describes our complex understanding of spacetime as a wave function, describing probabilities of our observations. She writes, “When it comes to spacetime, though, there’s no such thing as spacetime at an instant, because spacetime contains all instants. And you can’t have spacetime evolve in time, because it is time. The only way forward seemed to be this: break four-dimensional spacetime into three dimensions of space and one of time, then describe the spatial portion as a wave function that can evolve relative to the dimension you called ‘time’.”


Gefter’s quote is how we as humans experience spacetime. We do not experience all instances of space and time at one exact moment, but instead we experience space and our movement through space over time. Here on earth, where things operate on scales that seem constant and continuous to us, this works. But once we start operating on different scales in different parts of the universe with different masses, different speeds, and different energies, the experience of three dimensional space and one dimensional time break down. Gefter continues:


“Different observers can slice up spacetime in different ways. So when we decide to quantize only the three dimensions of space, we have to choose certain coordinates to call ‘space’ and others to call ‘time.’ But whose space? Whose time? Making any kind of choice would suggest that one observer had a truer view of reality than all others. But that can’t be so. That was Einstein’s whole point: the laws of physics must be the same for everyone.”


What is so concrete and clear in our world and in our experiences as human beings falls apart on scales beyond those that we can observe unaided with our senses. The universe is more complex and more challenging than we often imagine, and the priors that we bring to conversations, thoughts, and observations impact the way we come to understand the universe. There is no absolute time from which we can measure the universe, because as soon as we set a specific reference clock, physics breaks down for another observer somewhere else in the universe at a different scale of mass and energy. Similarly, there is no clock sitting outside the universe ticking away the lifetime of the universe as a whole. Spacetime is relative according to Einstein, and while we may be able to break spacetime into a wave function that predicts probabilities of space throughout time, we have to understand that the way we break space and time apart is specific to our observation and that both space and time change for other observers who separate spacetime differently from ourselves.


But why is any of this important? With physics and a deeper understanding we can begin to see that we are not outside the universe and our observations are not at the center of the universe. We are matter arranged in a way that allows us to observe other matter. Our perspectives and views are incomplete and the observations and perspectives we adopt shape the reality we can measure. There is a parallel between physical science and social science in this way. We may not realize it but our brains turn us all into social scientists, walking around with a megacomputer carefully recording observations of human behavior and reality, analyzing patterns, and crunching data to help us understand our position. If we assume that our observations and our reference frame is the one absolute and correct frame, then we miss the fact that the reality we live in is relative to where and when we make observations and how we have chosen to separate different points and parts of that reality. Perhaps not everything in the social sciences is completely relative since we do live in a constrained world, but we should recognize that there are not any absolutes living outside of our universe measuring us or anything else from the outside.

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