What is the biggest difference between mathematics and physics? Mathematics is a tool for humans to understand nature, a language for us to communicate with the Creator, and a symbol for human logical thinking. When I encounter a physical phenomenon, we must first conduct a qualitative and quantitative analysis of it and find out the physical laws it obeys, and then perform mathematical modeling and to write equations describing the physical system. Then you bring in the values of some specific conditions, and you are likely to get multiple mathematical solutions to this system, but only one of these mathematical solutions describes our objective physical reality. This is the biggest difference between mathematics and physics.
Mathematics is abstract logical thinking and a tool for human beings to understand nature. Physics is objective reality and a set of theories that describe the objective universe. It has only one solution and only one certain fact. For example, when we look up at the starry sky, especially when taking long-term time-lapse photography in the North Pole, if analyzed from a mathematical perspective, there are two possibilities, one is that the starry sky is rotating, and the other is that the earth is rotating, but there is only one viewpoint that is consistent with our physical reality. In addition, all the mathematical formulas of Newtonian mechanics are true in the state of time reversal, which means that a broken mirror can be reunited and a broken cup can be restored automatically. This is a real mathematical solution. But in our physical reality, time has an arrow, and it can only move forward, which denies the physical process of breaking the mirror and reuniting it.
The magic of mathematics is that sometimes certain physical processes follow the description of certain equations. This shows that nature has rules to follow, can be understood by us, and can be written in mathematical language. What's even more disgusting is that some equations were not derived. For example, the Schrödinger equation was pieced together by Schrödinger on a dark and windy night, and then became a basic assumption in quantum mechanics . His Ψ describes the evolution of microscopic particles over time. This Ψ is a mathematical solution to the Schrödinger equation. We did not know its physical meaning at the beginning, and neither did Schrödinger. At first he gave a wrong semi-classical explanation, and finally Bonn gave the correct probability explanation. Bonn also won the Nobel Prize in Physics in 1954.
This also shows that there is a difference between mathematics and physics. If you know mathematics, even if you come up with a correct mathematical solution, but you do not have keen physical intuition, you still do not know what kind of physical reality this solution describes. I believe everyone is familiar with the story of Dirac's prediction of positron , which is also a hint given by mathematical solutions. At that time, the four components were eliminated and corresponded to four solutions. Two of the solutions corresponded to the two spin components of the electron. These two solutions could completely describe the movement of the electron, and the other two solutions corresponded to the situation of negative energy. This led Dirac to predict the existence of positrons. The content of
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