On YouTube there is a channel that I like to watch called MinutePhysics. Normally the short videos are pretty good and the channel creator does a good job at explaining some common (and some uncommon) physics in a short and intuitive way. So I was rather surprised when he posted a video about common misconceptions in physics that itself perpetuated common misconceptions in physics. Here's the video for you to watch so I can refer to it.
There are two things that are problematic in this video that I want to address. I will give a short explanation here and then a longer explanation further down.
- Teaching Newtonian gravity is not lying. He is trying to make the point that light, even if it is massless, is still affected by gravity, which Newtonian gravity does not predict. True, but he makes his point by saying that teaching Newtonian gravity is lying to students. Newtonian gravity is still alive and well and is fundamental to of almost all undergraduate and even graduate (and post graduate) areas of study. The idea that teaching Newtonian gravity is wrong is a big misconception and this video simply perpetuates the misconception.
- Just because you have an equation that you can stick numbers into and a calculator to calculate it out to an arbitrary number of digits of precision does not mean that it has have physical meaning. I have to fight this misconception every semester with almost all of my students. It is harder to fight this misconception than it is to fight the "misconception" of a Galilean vs. Lorentz transformations.
1. Teaching Newtonian gravity is not lying.
The misconception that Newtonian gravity is fundamentally wrong, and therefore useless, is so prevalent among people that when mostly well informed individuals ask me about my research they are shocked to learn that I still use Newtonian gravity. They usually say something along the lines of, "I rememeber learning about Newton in high school/college, but you are probably way beyond that." They would be even more shocked to learn that most of the cutting edge research in physics uses Newtonian gravity and not relativity. It seems like every semester I have at least one or two students who express the idea that everything undergirding Newtonian gravity is wrong and that therefore all the collective wisdom, intuition, insight and knowledge of people who have used Newtonian gravity, or even Newtonian physics in general, is somehow invalid.
2. An equation and a calculator do not make reality.
Every semester I have to fight a major misconception with my students. I don't mean the pre-meds who take the introductory physics classes, or the "I don't know what I'm doing with my life students, but I have to take this class to get some sort of degree." students. I mean physics majors who are in their senior year and who have been through many physics classes already. I have to fight the misconception that just because the students have an equation and a calculator or computer that can calculate something to an arbitrary number of digits, that the result, to that precision, has meaning for the real world. This is a misconception that physicists of all stripes have to fight every day. And unfortunately this short video perpetuates this myth.
Let's take the sheep example. He gives an example of a sheep riding a train and says if you have a train going 2 mph and a sheep on the train is moving forward at 2 mph with respect to the train then,
2 mph + 2 mph = 4 mphwhich he promptly declares to be false. He then proceeds to give a short explanation of how to add velocities in special relativity and produces the equation for adding velocities in special relativity (for those who want to know he is merely pointing out the difference between a Galilean vs. a Lorentz transformation. One assumes light has no speed limit and the other one does. But, by his definition what he presents is also false, since a Lorentz transformation is also incomplete, so he merely traded one misconception for another. Fail.).
But, according to him, if we want to be honest we have to use the special relativistic equation and see that the sheep is only moving 3.999999999999999964 mph. That is a difference of 0.000000000000000036 mph. The problem is, how did he measure that? No really! That is a perfectly valid question in physics, I am not just trying to ask a trite, funny question. If he claims that the sheep is actually moving 0.000000000000000036 mph slower than it should because of special relativistic effects then he will have to actually measure that. The problem is (as many, many, many, many of my professors over the years have pointed out), the sheep is made up of atoms. You can't calculate something, get a result and say, "This is how the world works." because you are ignoring the fact that everything is made up of real matter. You can't separate that fact or you will end up in trouble.
To give you an idea of why this is problematic let's take our result, the difference of 0.000000000000000036 mph, and see what this means. Suppose the sheep and the train move together for one hour, what would be the difference in how far they have moved based on this difference?
0.000000000000000036 mph x .44704 (m/s)/mph = 1.61e-17 m/s
(that's meters per second instead of miles per hour)
1.61e-17 m/s * 3600 s = 5.8e-14 m
So if you let the sheep walk on the train and let the train go for one hour, then after one hour the difference that you would expect between using a relativistic vs. a non-relativistic calculation would be 5.8e-14 m or about 60 femtometers. To give you an idea of how small this is that is about 4 times larger then the nucleus of a uranium atom. Not 4 times larger than a Uranium atom, 4 time larger than the nucleus, which is very, very, very small. This distance is still about 3000 times smaller than the radius of an atom.
So is it wrong to use Galilean transformations and Newton's laws? No. If you can find me a wooden meter stick that has tic marks that go down into the femtometer range then you could say that Newton was wrong. But if you can't actually measure that accurately then it is wrong to say that the standard way we think about adding velocities is wrong. Just because someone came up with an equation and you can stick the numbers into a calculator and get a result does not mean that it has any real world interpretation.
Now, as a physicist I am well aware of relativity, but this is an abuse of it. To say that Newton (and Galileo) were wrong because they didn't have access to a meter stick which measured femtometers, is itself wrong. To ignore real world considerations and then calling people who have to (and had to) deal with those real world considerations wrong is to ignore something fundamental about physics, and that is we live in a real, physical universe. And you can't ignore that fact. Even when teaching relativity.
[PS: If you want to see another example of abuse of equations, consider "Why Pigs Don't Diffract Through Doorways".]