The Biggest Ideas in the Universe | 1. Conservation

Conservation of Momentum

In this video, Sean Carroll discusses the idea of conservation in physics, specifically conservation laws such as momentum and energy. He argues that the concept of conservation of momentum was crucial to the development of modern physics.

The Importance of Conservation Laws

• Conservation laws are fundamental principles in physics.

• The conservation of momentum is a particularly important law.

• Understanding conservation laws was crucial to the development of modern physics.

History of Conservation Laws

• Aristotle was one of the first great figures in the history of physics.

• Bertrand Russell's story about Aristotle's perspective on teeth is an unfair characterization.

• It can be difficult to understand the conceptual framework of thinkers who lived a long time before us.

Conclusion

• The concept of conservation is essential to understanding modern physics.

• The development and understanding of conservation laws, particularly momentum, were crucial to the transition from pre-modern to modern physics.

Aristotle's Physics and Motion

This section discusses Aristotle's view on motion and physics, including his observations of the world around him and his belief in natures or purposes behind objects' movements.

Aristotle's Observations

• Modern dental hygiene had not been invented yet, so it is likely that many people did not have the same number of teeth as adults that they had when they were children.

• Aristotle believed that men and women had different numbers of teeth, but this was based on incorrect data.

• Physics is the study of the stuff of which the universe is made and how that stuff changes, transforms, interacts, and moves over time.

Aristotle's View on Motion

• Aristotle observed a box sitting still on the surface of the earth. He noted that if someone pushed it, it would move in the direction of the push. However, if left alone, it would not spontaneously start moving.

• Objects with a lot of fire naturally go up while those with a lot of earth naturally go down according to Aristotle. He believed there was something like a purpose or desire behind objects' movements.

• Aristotle built up his logic to prove God's existence by stating that an initial unmoved mover was necessary to get things to move.

From Nature's Purposes to Patterns

This section discusses how physics shifted from explaining nature's purposes to understanding patterns through equations.

Eben Cena

• Eben Cena was a Persian polymath who lived in the Islamic Golden Age. He was a doctor and scholar who studied health, biology, physiology, and physics.

• Eben Cena came up with the principle of conservation of momentum in his spare time doing physics.

Shift to Patterns

• Physics shifted from explaining nature's purposes to understanding patterns through equations.

• Conservation of momentum is an example of this shift towards understanding patterns.

Motion and Aristotle's Ideas

In this section, the speaker discusses Aristotle's ideas about motion and how they were contradicted by the behavior of arrows in flight. The speaker also talks about Galileo's and Newton's contributions to our understanding of motion.

Aristotle's Explanation for Arrow Flight

• Aristotle believed that an arrow would slow down quickly unless something was pushing it.

• He explained that the air in front of the arrow was displaced by the arrow moving into it, and then that air moved around to the back and exerted a force on the arrow, keeping it moving.

• This explanation was not very good, as even other scholars at the time did not believe it.

Galileo's Insights on Motion

• Galileo argued that if something is moving in a straight line with no external influences acting on it, it will continue to move at a constant velocity.

• He believed there were two types of natural motion: circular and linear.

Newton's Laws of Motion

• Newton wrote down his laws of motion in his book "Principia Mathematica" in 1687.

• The first law states that something moving in a straight line with no forces acting on it will continue to move in that straight line until acted upon by an external force.

• The second law explains how things accelerate when acted upon by a force.

Conservation of Momentum and Energy

In this section, the speaker discusses the conservation of momentum and energy in Newtonian mechanics.

Momentum and Kinetic Energy

• Momentum is defined as mass times velocity.

• Kinetic energy is defined as 1/2 mass times velocity squared.

• Both momentum and kinetic energy are conserved in straight-line motion when mass and velocity are constant.

Conservation of Momentum vs. Conservation of Energy

• Conservation of momentum is easier to see than conservation of energy because energy can take different forms and convert from one form to another while the total amount of energy is still conserved.

• Empirically showing that energy is conserved can be difficult because there may be different forms of energy that have not been accounted for.

Elastic vs. Inelastic Collisions

• In an elastic collision, both momentum and kinetic energy are explicitly conserved.

• In an inelastic collision, only momentum is conserved while kinetic energy changes into some other form of energy.

• The classic example given in physics classes is two billiard balls bouncing off each other (elastic collision) versus two balls of silly putty sticking together (inelastic collision).

Emily du Chatelet's Contributions

• Emily du Chatelet was a mathematician who translated Newton's Principia into French and analyzed his equations beyond what he had done himself.

• She figured out that both momentum and energy are conserved under certain circumstances by dropping objects onto a surface that could deform and absorb the impact.

Conservation Laws and the Shift in Perspective

In this section, we learn about the concept of conservation laws and how they represent a shift in perspective from Aristotelian physics to modern physics. We also discuss Laplace's demon thought experiment and the idea of the clockwork universe.

The Concept of Conservation Laws

• One neutron can turn into a proton, electron, and an anti-neutrino while conserving both energy and charge.

• Conservation laws did not exist in Aristotelian physics. There was no way to determine what quantities were conserved for an object at rest.

• Modern physics shifted from a story of nature's teleology goals purposes favorite things to do to a story of patterns that allows us to predict what will happen next based on what is happening now.

Laplace's Demon Thought Experiment

• Pierre-Simon Laplace came up with the famous Laplace's demon thought experiment which assumes that there is a vast intelligence that knows the position and velocity of every particle or bit of stuff everywhere in the universe.

• According to Laplace, if you know everything about the present moment, then you can predict both future and past events with certainty.

• This idea represents a significant shift from Aristotelian physics where there was no place for purposes or nature.

The Clockwork Universe

• The universe is like a mechanism obeying rules rather than being alive according to modern physics.

• Conservation of momentum represents the transition from pre-modern to modern physics by changing how we think about what the universe is.

• A new problem arises in understanding ourselves as living beings in a universe that is not itself alive.

• Modern physics is based on an idealized world rather than the actual world, which raises questions about its applicability to real-world situations.

The Spherical Cow

• Physicists use idealized models like the spherical cow to simplify complex systems and make predictions.

• Idealized models are useful for making predictions but may not accurately reflect the real world.

The Spherical Cow Philosophy

In physics, the spherical cow philosophy allows us to ignore important features of the world and get an answer in a simplified context. This technique works well in physics but is not available in other areas of science.

Conservation of Momentum

• Conservation of momentum is a technique that works in a wide variety of physics circumstances.

• Nonlinear dynamics and other areas where objects interact strongly cannot ignore interactions.

• The spherical cow approximation works well for much of physics.

Physics is Easy

• Physics seems hard because it's easy. Hilariously inaccurate idealizations and approximations still allow us to learn something.

• Progress in physics is easier than progress in economics, biology, chemistry, or astronomy.

• Starting with conservation of momentum and the spherical cow philosophy will lead to more big ideas.

Conclusion

The spherical cow philosophy allows physicists to make progress by ignoring important features of the world. Conservation of momentum is a technique that works well in many situations. Physics may seem hard because we have learned so much about it, but it is actually easier than other sciences.