Never Judge an Electron, We All Seek to Minimize Some Quantity Along our Path

How do you get from point A to point B? You are born, that’s point A. Goals are your point B. What your dream job is, who you want to be married to, where you want to be in life is the point B. How do you get from birth to this point in your life. Recognize I’m assuming these two points are constant, the present state of your life and your birth. I’m asking about the path that your life took in between. What is interesting is that there are numerous ways your life could be lived and still end up at the same present. You could go to a different school, have different friends, live in a different location, and perhaps still end up at the same present state of your life. Certain variables can change along your life’s path and not affect who you are now. The constants are what is interesting here. What are the watershed events that happened in your life that define you. Things that happened in your life that, if altered, would make you a completely different person. Desmond Hume said we are like rivers, we are constantly changing and flowing through ebbs and eddies but we are still the same river in a sense. There is still a thread of constant substance flowing through space and time that define us. Our individuality is a conserved current and summed up over time and space a conserved quantity, if you will in QFT language. Now, why did you take the path that you did? Why did the variables take the form that they did for you. We can find a deep commonality and connection with nature here. We can take any body, let’s say an electron, and say it has to go from point A to point B. Then we can ask which path it will take. For a pencil that I let go of, we know point A is my hand and point B is the ground. Now, what path will it take from my hand to the ground? It will travel in a straight line (assuming it has no initial velocity). It could have taken a lot of different paths between my hand and the ground and been the same pencil at the same spot in the present moment. Why not do some loop d’ loops on the way down? Well this is interesting, and the reason that I got into physics in the first place. The answer is that there is a quantity called the Lagrangian that we can calculate at each moment in space and time and add up for all those moments along a given path. Now we sum up the Lagrangian and get something called the Action for each possible path. The path with the lowest Action (really the extreme value of action if we are being completely honest), is the true path that the object will follow. What’s interesting about the Lagrangian is that it still holds up no matter how weird the universe gets. In special relativity time and space are interchangeable, relative, and elastic, but the Lagrangian is still true. In Quantum Mechanics space and time don’t really exist anymore but the Lagrangian still determines the equations of motion. In in general relativity when time and space have differing curvatures, the Lagrangian still gives us correct predictions. So it seems that electrons and all bodies want to minimized or maximize some quantity along the path that they traverse no matter what the world throws at them. Now, as I always say to students, never judge an electron because we all seek to minimize some quantity along our path. We seek to minimize pain, or we seek to maximize love. Maybe the Action is something an electron values the way we value happiness. This is said in jest, but it is still an interesting connection between us and nature. Always remember the common threads that run throughout the universe.


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