The Universe in a Box: Simulations and the Quest to Code the Cosmos
Simulations and the Limits of Replicating Reality
One has to be incredibly clear about what we're trying to achieve when we perform a simulation. We know we never fully correctly solve the equations we're trying to solve, even if we could solve the equations we write down perfectly. We are not literally reproducing the Universe. We always have to start from the point that there is no perfect solution to this problem.
Simulations involve approximations and simplifications. We can't reproduce every single detail of the Universe. Instead, the goal is to find ways to simplify the problem and still gain insights and valid predictions about the patterns in our Universe or on our planet.
Some of the earliest attempts to simulate the Universe did not use computers at all. For example, in the 1960s, researchers at Lund University built a laboratory full of light bulbs to simulate the motion of stars in a galaxy. By measuring the intensity of light from the bulbs, they could use the inverse square law to approximate the forces of gravity.
These early "experiments" pioneered techniques like the "drift step" and "kick step" that are still used in modern simulations. The idea is to split up the complex motions into discrete steps - first calculating the forces, then moving the objects along their trajectories.
There are deep connections between simulations of different phenomena, like weather, climate, and galaxies. At a fundamental level, they are all dealing with "fluids" - materials that can be moved around and reshaped, described by equations like the Navier-Stokes equations.
While the specific circumstances differ, the underlying mathematical frameworks have a lot in common. Advances in solving the equations for one domain, like climate, can often be applied to another, like cosmology. The challenge is in capturing the right level of detail and approximating the small-scale processes that can't be fully resolved.
A key aspect of successful simulations is incorporating "feedback" effects, where small-scale processes like star formation or supernovae have large-scale impacts on the system being modeled. Since computers can't resolve all these micro-details, modelers have to introduce "subgrid rules" - approximations and parameterizations that capture the essential effects.
This is similar to how weather and climate models incorporate rules for cloud formation that can't be derived directly from the underlying equations. It's a necessary compromise to make large-scale simulations tractable.
Simulations also provide a way to explore the idea of a "multiverse" - running multiple versions of a simulation with slightly different parameters. This connects to the concept of the "many-worlds" interpretation of quantum mechanics, where parallel universes exist.
As quantum computers become more powerful, they may be able to directly simulate quantum systems in ways that classical computers can't. This could shed light on the nature of quantum gravity and the early universe, where quantum effects were dominant.
A key limitation of simulations is the sheer scale of the systems involved. Faithfully reproducing the Universe or even a galaxy would require computational resources on the scale of the entire Universe itself. Modelers have to make judicious choices about what to simplify and what to focus on.
There are also growing concerns about the energy use and carbon footprint of large-scale simulations, especially as the field of AI becomes more computationally intensive. However, cosmological simulations remain a tiny fraction of the global energy use of data centers and computing infrastructure.
Ultimately, the goal of simulations is not to replace the awe and wonder of the cosmos, but to enhance it. By gaining a deeper understanding of how the Universe works, we can appreciate its beauty and complexity on new levels. As the poet Whitman lamented, knowing the facts of science need not diminish the poetry of the night sky.
Part 1/7:
The Universe in a Box: Simulations and the Quest to Code the Cosmos
Simulations and the Limits of Replicating Reality
One has to be incredibly clear about what we're trying to achieve when we perform a simulation. We know we never fully correctly solve the equations we're trying to solve, even if we could solve the equations we write down perfectly. We are not literally reproducing the Universe. We always have to start from the point that there is no perfect solution to this problem.
Simulations involve approximations and simplifications. We can't reproduce every single detail of the Universe. Instead, the goal is to find ways to simplify the problem and still gain insights and valid predictions about the patterns in our Universe or on our planet.
Part 2/7:
The History of Simulation Experiments
Some of the earliest attempts to simulate the Universe did not use computers at all. For example, in the 1960s, researchers at Lund University built a laboratory full of light bulbs to simulate the motion of stars in a galaxy. By measuring the intensity of light from the bulbs, they could use the inverse square law to approximate the forces of gravity.
These early "experiments" pioneered techniques like the "drift step" and "kick step" that are still used in modern simulations. The idea is to split up the complex motions into discrete steps - first calculating the forces, then moving the objects along their trajectories.
The Commonalities Between Simulations
Part 3/7:
There are deep connections between simulations of different phenomena, like weather, climate, and galaxies. At a fundamental level, they are all dealing with "fluids" - materials that can be moved around and reshaped, described by equations like the Navier-Stokes equations.
While the specific circumstances differ, the underlying mathematical frameworks have a lot in common. Advances in solving the equations for one domain, like climate, can often be applied to another, like cosmology. The challenge is in capturing the right level of detail and approximating the small-scale processes that can't be fully resolved.
Feedback and Subgrid Rules
Part 4/7:
A key aspect of successful simulations is incorporating "feedback" effects, where small-scale processes like star formation or supernovae have large-scale impacts on the system being modeled. Since computers can't resolve all these micro-details, modelers have to introduce "subgrid rules" - approximations and parameterizations that capture the essential effects.
This is similar to how weather and climate models incorporate rules for cloud formation that can't be derived directly from the underlying equations. It's a necessary compromise to make large-scale simulations tractable.
The Multiverse and Quantum Simulations
Part 5/7:
Simulations also provide a way to explore the idea of a "multiverse" - running multiple versions of a simulation with slightly different parameters. This connects to the concept of the "many-worlds" interpretation of quantum mechanics, where parallel universes exist.
As quantum computers become more powerful, they may be able to directly simulate quantum systems in ways that classical computers can't. This could shed light on the nature of quantum gravity and the early universe, where quantum effects were dominant.
The Challenges of Scale and Energy Use
Part 6/7:
A key limitation of simulations is the sheer scale of the systems involved. Faithfully reproducing the Universe or even a galaxy would require computational resources on the scale of the entire Universe itself. Modelers have to make judicious choices about what to simplify and what to focus on.
There are also growing concerns about the energy use and carbon footprint of large-scale simulations, especially as the field of AI becomes more computationally intensive. However, cosmological simulations remain a tiny fraction of the global energy use of data centers and computing infrastructure.
The Beauty and Wonder of Understanding
Part 7/7:
Ultimately, the goal of simulations is not to replace the awe and wonder of the cosmos, but to enhance it. By gaining a deeper understanding of how the Universe works, we can appreciate its beauty and complexity on new levels. As the poet Whitman lamented, knowing the facts of science need not diminish the poetry of the night sky.