Parth G | Physics Diagrams That Suck (Quantum Mechanics) | When Physics Goes Wrong Ep.1 @ParthGChannel | Uploaded 4 years ago | Updated 2 hours ago
What happens when the physics we study is based on sloppiness (to some small degree)?
Hey everyone, I'm back with a fairly short video this time! I wanted to start a new series where I discuss two main ideas: firstly, what happens when physics begins to break down (such as when quantum mechanics and general relativity disagree) and secondly, what happens when physicists themselves use silly conventions (such as conventional current - why is this still a thing?!).
In this video, I wanted to ease us into talking about these concepts. Therefore, I decided that the focus of this video would be to talk about certain energy - position diagrams that are commonly drawn when physics students are taught basic quantum mechanics. These diagrams are used to represent the position of a charged particle such as an electron, when it encounters what is known as a potential barrier. I discussed this in detail in my previous video about Quantum Tunneling, so check that out if you haven't seen it already.
The problem with these diagrams is that the wave function of the electron, found by solving the Schrodinger Equation in every distinct region, is also displayed on these diagrams. Since the wave function commonly takes the form of an oscillating wave, this brings up the misconception that the energy of the electron is changing as we move from left to right. However, this is not the case. The energy of the electron is actually constant, and it is the energy eigenvalue found when solving the Schrodinger Equation. The wave function fluctuations only tell us about fluctuations in the probability distribution of the electron.
So what we really need is another axis - one which will show the fluctuation of the wave function without any chance of being interpreted as a fluctuation in the actual energy of the electron. There are a couple of ways to draw this. The first is to draw the axis off in the third dimension and turn the graph into a 3d diagram. The issue with this is that 3d diagrams are difficult to draw and even more difficult to interpret. It works fine when information is being transferred on a computer, with some sort of interactive 3d software, but not so much on paper. Another alternative is to draw the axis in the same plane as the original graph, but on the right hand side of the graph. This way we have two vertical axes, one which shows the energy of the electron, and the other which shows the fluctuation in its wave function. However there are problems with this too. The diagram becomes way too clunky and easy to misinterpret, and there still needs to be a clarification for the reader, so they understand how to correctly interpret the diagram.
I also discuss how wave functions need not be real, which is why drawing them is in reality quite difficult. However, we should take all these diagrams with a pinch of salt. After all, they only exist so as to provide readers with a simplistic visualisation of the scenario being studied. All in all therefore, I come to the conclusion that the diagrams physicists currently draw, are justifiable (despite all the problems they have).
I hope you enjoyed this video. If you did, please leave it a thumbs up and don't forget to subscribe. If you want to follow what I get up to on a more day-to-day basis, follow me on Instagram @parthvlogs
What happens when the physics we study is based on sloppiness (to some small degree)?
Hey everyone, I'm back with a fairly short video this time! I wanted to start a new series where I discuss two main ideas: firstly, what happens when physics begins to break down (such as when quantum mechanics and general relativity disagree) and secondly, what happens when physicists themselves use silly conventions (such as conventional current - why is this still a thing?!).
In this video, I wanted to ease us into talking about these concepts. Therefore, I decided that the focus of this video would be to talk about certain energy - position diagrams that are commonly drawn when physics students are taught basic quantum mechanics. These diagrams are used to represent the position of a charged particle such as an electron, when it encounters what is known as a potential barrier. I discussed this in detail in my previous video about Quantum Tunneling, so check that out if you haven't seen it already.
The problem with these diagrams is that the wave function of the electron, found by solving the Schrodinger Equation in every distinct region, is also displayed on these diagrams. Since the wave function commonly takes the form of an oscillating wave, this brings up the misconception that the energy of the electron is changing as we move from left to right. However, this is not the case. The energy of the electron is actually constant, and it is the energy eigenvalue found when solving the Schrodinger Equation. The wave function fluctuations only tell us about fluctuations in the probability distribution of the electron.
So what we really need is another axis - one which will show the fluctuation of the wave function without any chance of being interpreted as a fluctuation in the actual energy of the electron. There are a couple of ways to draw this. The first is to draw the axis off in the third dimension and turn the graph into a 3d diagram. The issue with this is that 3d diagrams are difficult to draw and even more difficult to interpret. It works fine when information is being transferred on a computer, with some sort of interactive 3d software, but not so much on paper. Another alternative is to draw the axis in the same plane as the original graph, but on the right hand side of the graph. This way we have two vertical axes, one which shows the energy of the electron, and the other which shows the fluctuation in its wave function. However there are problems with this too. The diagram becomes way too clunky and easy to misinterpret, and there still needs to be a clarification for the reader, so they understand how to correctly interpret the diagram.
I also discuss how wave functions need not be real, which is why drawing them is in reality quite difficult. However, we should take all these diagrams with a pinch of salt. After all, they only exist so as to provide readers with a simplistic visualisation of the scenario being studied. All in all therefore, I come to the conclusion that the diagrams physicists currently draw, are justifiable (despite all the problems they have).
I hope you enjoyed this video. If you did, please leave it a thumbs up and don't forget to subscribe. If you want to follow what I get up to on a more day-to-day basis, follow me on Instagram @parthvlogs
