8.1 Classical Physics
What is Classical Physics? It covers the development of fundamental physical laws starting from the time of Newton to the twentieth century. The most significant contributions being Newton’s and Einstein’s laws.
They all have a central theme - The world we observe has matter changing dynamically in the arena of space and time. This matter is made of particles. These particles interact via forces. If we know the position and momentum of every particle of the universe at one point of time, we can predict the future and past of the universe and the particles inside it.
This could be a lot to swallow. Let me break it down.
- The world we observe has matter. Do not assume matter is just solid or liquid substances. It also includes gaseous substances. The chair you are sitting on is made of matter. The water you drink has matter. The air you breathe has matter in forms of nitrogen, oxygen and carbon dioxide.
- The state of matter changes dynamically in the arena of space and time. We see this happening all around us. Things move, break, melt, evaporate, condense, etc.
- Matter can be broken down further into smaller particles at different levels, each having their own properties. We have crystals, polymers, molecules, atoms, sub-atomic particles and so on.
- These particles interact via forces - Gravitational and electromagnetic forces. An apple falling from the tree is because of Gravitational force. Electric motors and Magnets work because of electromagnetic forces.
In the world of classical physics, if you know the state of all matter in a system at one time, you can predict the future and past of the matter in the system. Imagine that the whole universe is just a cube you cannot get out of or move around in. You are just a face stuck in a wall of the cube. All you can see are two balls in front of you which are bouncing inside the cube at the same speed and they do not hit each other and you cannot touch or control either of them. If the world follows the rules of classical physics, if you know the position, the speed and direction of the two balls at one moment, you can predict the future and past of the balls and by that, you know the future past of the entire universe you live in. You just have to apply the laws of physics to know where the balls will be after 100 years.
Fortunately for many and unfortunately for some, our universe is way more complex than one with a cube and two balls. We are far from predicting the future of the universe this way. But this is the basic idea behind the laws of Classical Physics. It should at least be theoretically possible to do so. How far did we reach when it comes to our ability to predict with the Laws of Classical Physics? That is what we will see in this chapter.
Newton’s Laws
We all have heard of Newton’s three laws of motion, especially the third law - Every action has an equal and opposite reaction. The third law has been used in silly dialogues in movies and books as much as it has been used in science. There is also Newton’s law of Gravitation which explains the effect of Gravitational forces between two objects. You know, the apple falling from the tree story.
You put them all together, and you have a basic set of laws which allow you to predict the trajectory of objects in our day-to-day life. You can calculate how hard and how high you have to throw a ball, for it to land in the basket ball net. But we don’t have the time to do these calculations in a real basketball game. And even if we did, we may not be able to actually throw the ball accurately based on our calculations. But Newton’s laws explain how these things work
Taken further, you can calculate how hard you have to throw an object so that it never falls back on the earth. This is the calculation they use in the rockets to determine how to send rockets out of the Earth’s atmosphere.
Maxwell’s equations on Electromagnetism
James Clerk Maxwell came up with an equation which describes how electromagnetic forces behave. What happens to magnets when they are brought near each other? How does electricity flow through conductors? We used to think that electricity and magnetism are fundamentally different phenomena. But they were both unified under one equation.
This equation is one of the most important equations used in our day-to-day life that explains the functioning of all the electrical appliances around us.
Einstein’s Laws of Relativity
With Newton’s Laws and Maxwell’s equations, we had a good toolkit that was capable of explaining most things we observe around us in our day-to-day life. Many thought that physics was very close to being finished. But there was one lingering issue which took years to figure out - The mystery about the speed of light.
Before Einstein came up with his Laws of Relativity, we made some fundamental assumptions about space and time. We treated them as different and absolute entities. If I measure the length in space as 20m, you will also measure the same. If I measure the time in my stopwatch as 20 seconds, as long as you start your stopwatch at exactly the same time, you will also record 20 seconds. And whether I travel or not in space doesn’t affect my time.
Forget the laws of physics. These are also basic concepts we live by. If Einstein’s Laws of Relativity weren’t a thing, I would have added them as brute statements in the layman’s system. But as it turned out, they were wrong assumptions.
The story goes like this. If you measure the velocity at which a car is coming towards you while you are standing on a road, and your friend measures the velocity at which the same car is coming towards him while he is in another car driving towards that car, your friend’s measurement of the velocity will be higher than your measurement. The velocity of any object is usually measured in relative terms. In our day-to-day life, we don’t normally talk about what the velocity is relative to. We just say that the train was going at a velocity of 80kmph and others assume that it was measured from the perspective of someone standing next to the railway track. In our example above, while your friend notices that the velocity he measured of the oncoming car is higher, he can just subtract his own velocity from the velocity he measured to calculate the speed you have measured.
In scientific terms, it is necessary to mention what the velocity is measured relative to. You could claim that you are stationary because you are sitting somewhere and reading this and hence your measurement is the absolute velocity of the car. But you are on the planet earth and earth itself is moving around the sun. The Solar system itself is going around the Galaxy and the Galaxy is also in motion with respect to the other galaxies. One common example that is used to explain relativity of motion is when you are in a train that is stationary on a platform and there is another train that is next to you. When one of the trains moves, it is sometimes hard to say which one is moving just by your visual perception. If your train accelerates, then you will feel it and that will give you a hint that your train is moving. And lack of that feeling gives you a hint that your train is really stationary. But otherwise, it is hard to say which one is moving.
Going back to your story, Maxwell’s equation and Michelson Morley’s experiment showed that the velocity of light is a certain high value (299,792 km per second) usually represented with the letter C. But what was it relative to? We just understood how speed is always measured relative to something else. It turned out that the velocity of light remains constant no matter what your state of motion is when you are measuring it. Whether you are standing on the road or driving a car towards the light source, you measure the same velocity of light.
Imagine you’re floating in deep space, far from any planet. You measure the velocity of light coming from the sun. Now imagine you do it again while racing towards the sun on a super-fast rocket. You’d expect the rocket measurement of velocity to be higher - like how a ball thrown at you feels faster if you’re running toward it. But with light, you get the same number both times. It doesn’t add up the way everyday velocities do.
Einstein took the idea and calculated what happens to our understanding of space, time, and other physical laws when we assume that the speed of light is constant irrespective of the state of motion of the observer. What resulted was his special theory of relativity. One famous outcome was the rest-energy formula E = mc². More generally, special relativity gives E² = (pc)² + (mc²)².
Then, Einstein used what is called the equivalence principle to develop the general theory of relativity. If you are in a lift that is on a free fall from a really tall building, the things in the lift float, similar to how things float in a spaceship that is not affected by any meaningful gravity. Under certain conditions - if you’re in a small space and only for a short time - they can be considered equivalent. Similarly, the feeling you get while resting on the earth is the same as the one you get when you are on a lift that is going up. Einstein saw this equivalence between the effect of gravity and an accelerating body and came up with the general theory of relativity.
The special theory of relativity is mathematically very accessible while the general theory of relativity gives you impostor syndrome if you try to understand it. But you don’t have to understand the mathematics of the theories to be stuck in awe of the implications of the theories, which are:
- Space and Time aren’t separate like we assumed. They are a single intertwined entity named spacetime.
- Space and Time aren’t absolute like we assumed. Imagine I am in a space station outside the solar system. You took a space ship from the station and travelled very close to the speed of light. The length of objects you measure is smaller from the length of the same object I measure. When you are travelling, the time elapsed in your clock will look slower than the time elapsed in my clock if I could observe you. And the time observed in my clock will look slower than your clock if you could observe me. When you do a round trip and come back to the station, the time elapsed in your clock will be slower than mine. These effects are called length contraction and time dilation.
- Objects with mass bend spacetime. As a result, if you go near a heavy planet, star or a blackhole, the time in your clocks will be slower than the time on mine. This is also how gravity really works. Because huge masses bend spacetime, it changes your path in spacetime in a way that you are pulled towards the huge mass and you perceive it as the gravitational force.
- There is a limit on how fast you can travel. You can’t travel faster than the speed of light.
- Mass and energy are inter-convertible. This is an interesting outcome of the theory of relativity, popularly known by the mass-energy equation E=mC^2.
The fact that time runs differently for different people, when one travels very close to the speed of light or travels very close to a black hole, is probably one of the most profound philosophical realisations from the theories of relativity that is heavily used in science fiction. Imagine this. If there is a black hole near us. You can go there and come back every hundred years on earth, which is probably just a year on your clock and see how human civilization evolves over such a long period of time. So, if you go on to live a hundred years on your clock, you could see the earth for about 10,000 years on the earth clock.
Philosophical implications of classical physics
Classical physics is a vast subject and I only touched the surface of it. I used too many simplifications that I am not particularly proud of. But to convey my thoughts about philosophy, what we have seen now is enough. There are two major philosophical implications from classical physics.
- Determinism - If the classical physics assumption that if we know the position and momentum of all particles in the universe, using the laws of classical physics we saw above and many more, we can predict the future state of the universe is true, does it mean that the universe’s fate is pre-written? But what about free will? We feel like we are in control of our actions. If it is all pre-determined, does it mean that free will is an illusion?
- Nature of space and time - This one is on relativity. The idea that spacetime isn’t absolute and can be bent breaks down or at least asks some difficult questions to many philosophies. For example, many religions rely on a God watching the world and affecting things in the world based on people’s actions. If time goes differently in different parts of the Universe and for different people, how does time flow for God? It’s not just Religion. Many philosophers before relativity wrote their philosophies on the fundamental assumption that space and time are absolute. Turns out they are not.
Further Reading
All The Feynman Lectures by Richard Feynman are good. The books listed above have some handpicked lectures which are particularly interesting.
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The Biggest Ideas in the Universe series by Sean Carroll if you want to get a little bit deeper into the Mathematics. Third book yet to be released at the time of writing.
Sean Carroll’s blog is also very good