Why is learning still hard and what can we do about it?

How many people truly understand general relativity? Or quantum field theory? Or any other challenging subject?

If you spend enough time in academia you slowly but steadily realize that the number is tiny. Even most students and professors of physics don’t understand the best fundamental theories of nature that we have.

And what about the billions of people who never studied physics at a university? There might be a few autodidacts here and there but the number remains tiny.

This is puzzling if you think about it. Many people have a deep interest in understanding fundamental ideas that explain how the world works. Yet hardly anyone reaches an understanding beyond a superficial level. Many would love to contribute to our communal quest to decipher the source code of the universe. Yet an incredibly large talent pool is locked out from participating.

The only possible explanation is that it’s still incredibly hard to learn challenging subjects.

But why? And how can we improve the situation?

Let’s start by talking about three observations that answer the first questions.

1.) To some extent, learning has to be challenging. However, this idea has been fetishized.

To quote Sönke Ahrens:

“Learning requires effort, because we have to think to understand and we need to actively retrieve old knowledge to convince our brains to connect it with new ideas as cues.”

Unfortunately, lots of teachers (especially at the university level) take this whole idea to a level that I can only as absurd. They leave out crucial details and tell the students they should figure it out themselves knowing fully well that this is too difficult of a problem and the students don’t have time for it. They select homework problems solely under the aspect that they’re sufficiently difficult irrespective of how much students can learn from them. They don’t follow any grand plan that cumulates in a series of “aha”-moments. They don’t even try to design the lectures in a way that makes them enjoyable. The mantra seems to be “the more I confuse the students the better”.

Sometimes this is intentional, sometimes it isn’t. There are many facets of this problem:

  • If you confuse the students they are less likely to ask questions. Each questions potentially challenges your status and hence it’s a good strategy to avoid them.
  • Most university professors are too busy with other obligations to have sufficient time to prepare for their lectures.
  • Professors don’t get selected for their teaching skills. Metrics like the number of citations are far more important.

These observations lead us directly to the next point.

2. Current educational institutions are mostly about signalling.

Institutions focus on metrics (grades, citations) that primarily select people who are conscientious and conformist and tells us little about understanding. (If you doubt this, just try take a slightly non-standard position in an oral exam.)

Or as Sanjoy Mahajan puts it:

“Traditionally taught science and mathematics teach little except obedience.”

This point has been elaborated on by many much more gifted writers, so I’ll just refer you to them in case this is a new idea for you. Good starting points are:

One often overlooked aspect I want to emphasize is that this also affects textbooks. Most textbooks are not written to help the reader understand. Instead, they’re written to signal how smart the author is. That’s why most textbooks are impossible to understand. And to make matters worse, these textbooks get recommended over and over again because if you recommend a book that’s difficult to understand, you signal how smart you are.

The problems of the traditional learning institutions lead us to the next observation.

3. There hasn’t been a revolution in learning despite the internet

Despite all the possibilities offered by the internet, no one has yet come up with a framework that actually puts them to use to make it dramatically easier to learn challenging subjects.

Yes, there are a few nice lectures freely available online. But this was never the bottlenecks and thus hasn’t improved the situation in any significant way. Excellent textbooks have been available since ages and are superior to lectures anyway.

A book allows you to go jump around and move through the information on your own pace. This is extremely cumbersome in video lectures. And if anything, online lectures are worse than real world lectures (which are already an awful medium) since it’s much easier to get distracted. Funny cat videos are always just one click away. (And no, there aren’t different learning types.)

Moreover, the flexibility to start the course whenever you want and to pick from lots of different lectures usually leads to analysis paralysis and hinders learning.

For quite a while I thought that there is nothing we can do about it. I was convinced that there are some intrinsic flaws (e.g. proximity to cat videos) that makes online learning ineffective.

But this isn’t true. It’s just that all current online learning frameworks are missing one or several essential puzzle pieces. Online learning has not to be synonymous with recording a bunch of videos and putting them in a MOOC.

Essential Aspects of Effective Learning Environments

To understand which puzzle pieces are potentially essential to create an environment that makes it possible to understand even the most challenging topics, it makes sense to analyze what universities are doing. While universities are far from optimal learning environments, this analysis will allow us to understand what is missing in current online learning frameworks. Once we’ve identified these puzzle pieces we can discuss how they can be realized and improved upon in an online setup.

So, let’s ask ourselves: What does a university provide to help students learn challenging subjects? There are at least the following eight puzzle pieces:

  • Community
  • Support
  • Guidance
  • Accountability
  • Credentials
  • Feedback
  • Content

With this list in mind, it becomes clear why most online learning experiments have failed so spectacularly. Many of them primarily focussed on providing content online, which is really just one tiny aspect and certainly not the bottleneck.

MOOCs typically don’t foster any sense of community, offer only limited support, feedback, guidance, or accountability (if any), and only provide credentials that are hardly worth anything. If we then add to this that the content is usually just a recording of mediocre lectures, the package doesn’t look enticing.

Of course, as discussed above, universities are hardly any better in most aspects. And some MOOCs are excellent at mimicking the university experience online. But the difference is that universities get away with their far from optimal package since they provide sufficient accountability and incentives (credentials) to make students endure the whole thing.

Universities are simply not the gold standard of learning experiences that they are often thought to be. Moreover, if you try to mimic something there are necessarily some losses along the way. Just to name two examples:

  • A video recording of a lecture is never as good as a live lecture since you can’t see everything at once.
  • Online certificates simply don’t have the same standing as established offline certificates.

So while the university package might be just good enough, due to these losses the online equivalent no longer crosses the threshold.

To illustrate this point, let’s rate how good universities are at providing the essential puzzle pieces listed above. I would say:

  • Community: 7/10
  • Support: 3/10
  • Guidance: 3/10
  • Accountability: 10/10
  • Credentials: 10/10
  • Feedback: 5/10
  • Content: 4/10

In total, we have 42 out of 70 possible points. (Feel free to put in your own ratings.)

Now what happens if we mimic the same thing in an online environment? In my experience, a typical result can be rated as follows:

  • Community: 2/10
  • Support: 3/10
  • Guidance: 2/10
  • Accountability: 1/10
  • Credentials: 2/10
  • Feedback: 2/10
  • Content: 3/10

Certain aspects are mimicked quite okay while others are almost completely lost. I might be a bit negative here but in my book we end up with 15 out of 70 possible points. Even if you’re a bit more generous, the result is certainly below the threshold (say 40 points) that separates effective and ineffective learning experiences.

With these observations in mind, we can finally think about how we can design more effective learning environments.

Revolutionizing Learning and Teaching

An exhaustive discussion of how each puzzle piece can be improved and implemented in an online setup requires several additional articles. The following list merely offers a few starting points.

  • Community. In theory, this should be the easiest part to improve in an online setup. The internet is a tool that connects people and hence should make it easier for communities to form. Unfortunately, this rarely happens when it comes to online learning. Most online communities are too open, too heavily moderated, too anonymous, and focus solely on text messages. Most people don’t feel comfortable shouting stuff from the rooftops for the whole world to hear. Moreover, it’s quite hard to make friends solely by exchanging topic-specific text messages. As a result, no real sense of community emerges. The rise of smaller private communities supplemented by virtual conferences, virtual book clubs and virtual co-studying places have the potential to improve the situation dramatically.
  • Network. Similar comments as for community building apply. An additional aspect is that it’s possible to network online simply by putting yourself out there. Most people remain invisible. Hence, if you’re interested in some topic and regularly publish things related to it, opportunities will show up at your door step.
  • Support. The way universities offer support is far from optimal. Lecturers are annoyed by questions since they make it harder to get through all the material. Tutoring sessions mostly focus on homework platforms and there is rarely any time for discussions. In contrast, online platforms like StackExchange are great at providing answers to specific questions. However, so far, the platforms function solely on a voluntary basis and are quite impersonal. Respondents typically don’t know your full background and the context of your question, and it’s simply a matter of luck if someone qualified feels motivated to answer your questions. This certainly limits the quality of answers. In addition, most platforms suffer from overmoderation. A paid full-time staff of tutors and a more decentralized, personal approach would improve the situation.
  • Guidance. There are quite a few learning curricula and learning roadmaps available online for most topics. However, these one-size-fits all curricula are far from optimal for individuals. Moreover, they are hardly ever detailed enough to provide enough guidance for individual decisions. Personal mentoring could solve these problems but also automated solutions could work.
  • Credentials: Online credentials exist but are not a good solution. They’re just the same (already bad) thing slightly worse. One proposed solution are college equivalence degrees. Although they could represent an improvement, they, like their offline equivalents, would inevitably get corrupted by the cobra effect. So, instead of the mimicking something intrinsically flawed, the opportunity should be used to replace it with something better. Credentials signal conformity and conscientiousness but certainly not deep understanding, creativity and high agency. To improve the situation, we could replace exams by projects and hence credentials by portfolios.
  • Feedback. Some MOOCs allow students to get feedback on their solutions of homework problems. However, homework problems (offline like online) are often primarily designed to keep students busy and to filter out certain types of students. Solutions would be to create exercises that help the students deepen their understanding (e.g. by explaining what they’ve learned to others) and to get real-world feedback on their projects.
  • Accountability. This is something universities are good at and that current online learning frameworks are lacking. A solution is to offer paid courses for small cohorts with a fixed starting and end date and regular virtual meetings.
  • Content. Despite of all tech innovations, books are still the best medium if you want to understand something deeply. You can read a book far away from all distractions, move through it at your own pace and jump between chapters. But this doesn’t mean that all books are automatically great or that no improvement is possible. In fact, as mentioned above most textbooks are impossible to learn from. And there are many ways of how even good textbooks can be further improved. A great example is to include multi-level content. Moreover, ideally textbooks are supplemented by something more human to provide all the little social cues that get lost when we try to transfer information in text form.

The message to take away is that attempts to create new learning environments are doomed to fail if they ignore one or several of the essential puzzle pieces.

But, of course, it’s not enough to just throw ideas out there. In the past, I’ve primarily focussed on the “content problem” by writing reader-friendly textbooks and by building a multi-layer wiki since I didn’t understand the bigger picture. Currently, I’m working on something that tackles remaining puzzle pieces too. So if you find the ideas outlined above interesting and want to get involved, feel free to send me a message.

PS: It’s a fun exercise to rate different online learning products and platforms using the 8 criteria discussed above. I would love to hear who gets the highest rating in your book!

How I learned to learn physics

“You do not understand an argument, until you’ve found the major flaws in it. For any problem complex enough to be interesting, there is evidence pointing in multiple directions. ”


While there are many models that try to encapsulate how learning and understanding works, I recently came across one particular model that I keep thinking about and find extremely useful.

The model is a simple 3-level model and was proposed by Nat Eliason here.

The model describes remarkably well how I reached maturity in my thinking about different physics topics and since Nat didn’t mention physics, I want to discuss some examples below.

But first, a short summary of the model.


Level 1

Level 1 is called “Blind Ideology“. Everyone starts at this stage for any given topic. This stage is

“characterized by the wholesale adoption of the beliefs, attitudes, and lifestyles that were thrust onto you by your upbringing and environment. [….] Level 1 thinkers have an ideology they’re fixed to, and their blindness to it makes them throw out contrary opinions as heresy.”

A great example is diet. Here, Level 1 means that you eat what your parents taught you to eat, which in most cases is the standard Western diet.

Level 2

Level 2 is called “Chosen Ideology“. At this stage, people realize that the first best thing they were taught isn’t the best thing that exists and they become obsessed with another ideology. As Nat describes it

“If you know someone who believes in something and is annoying about it, they’re most likely at Level 2.”

We reach Level 2 after a “Moment of Clarity“. During such moments we realize that we have been driving with blinders on.

For the diet example above, Level 2 means that you become obsessed with something like Low-carb, Paleo, Veganism etc. At this stage, you are convinced that, for example, Paleo is the only way to go and every other way to eat is stupid.

Level 3

Finally, there is Level 3, which is called “Ideology Transcendence“. At this stage, we are able to sample the best bits from pre-packaged belief systems. At Level 3 we realize that no pre-packaged ideology is a perfect fit for us and we start developing our own. We start studying all ideologies that are out there and pick from each one only those parts that are of use for us.

The step from Level 2 to Level 3 is only possible through lots of Moments of Clarity. Only when we are exposed to lots of contrarian points of view, we can recognize the flaws in every pre-packaged belief systems. To reach Level 3 we must read books and articles that make us uncomfortable.

Regarding the diet example, Level 3 means that you recognize that different people respond differently to different diets. Everyone has different genes and therefore everyone has to experiment to find a diet that is a good fit. However, no pre-packaged diet can be a perfect fit for everyone.

A good test if you’ve already reached Level 3 are “Brake Lights”:

“When you react emotionally to information, any information, that’s a sign of Level 1 or Level 2 thinking. If you truly had a well-rounded stance on a topic and cared about enhancing your understanding of it, you would not react emotionally to anyone else’s opinion.”


It’s important to note that at Level 3 there is a “Strange Loop“. After enough time you will build an ideology of your own by picking the best stuff from other ideologies and adding something of your own. However, as soon as this happens you are again back at Level 2 since you are again following an ideology. Then, you must again search for flaws in your thinking and get exposure to contrarian points of view. In other words, Level 3 starts again. Level 3 is a stage of constant deliberate uncertainty.

The notion “Strange Loop” was coined by Douglas Hofstadter in his book “Gödel, Escher, Bach“:

“The “Strange Loop” phenomenon occurs whenever, by moving upwards (or downwards) through levels of some hierarchical system, we unexpectedly find ourselves right back where we started.”

In some sense this a miniature version of the whole scientific process. We can never know anything in the real world with 100% certainty. The only thing we can talk about is the level of confidence we have in a given theory, model or idea. Ultimately, today’s paradigm-shifting theory will become tomorrows standard theory and will again be replaced by another paradigm-shifting theory.

Nat discusses several other examples and most importantly ways to actively “level up”. It’s much better than this short summary and I highly recommend reading it.

But now, let’s discuss what all this means for physics.

Physics beyond Ideologies

Quantum Mechanics

  • Level 1 is the standard “Shut up and Calculate” approach that everyone learns in the lectures and standard textbooks.
  •  Level 2 thinking is becoming obsessed with, for example, “Bohmian Mechanics” or the Everretian “Many-Worlds interpretation”.
  • Level 3 thinking is realizing that none of these approaches is entirely correct and starting to develop your own way of thinking about quantum mechanics.

Gauge Symmetry

  •  Level 1 thinking is that gauge symmetry is a neat trick to derive the Lagrangian of the Standard Model and otherwise only necessary to prove renormalizability.
  • Level 2 thinking is becoming obsessed with the geometrical interpretation of gauge symmetry in terms of fiber bundles or with the idea that gauge symmetries aren’t fundamentally important after all but merely redundancies in our description.
  •  Level 3 is when you realize that gauge symmetries are indeed only redundancies, but carry a lot of physical meaning that isn’t captured by fiber bundles or the “neat idea” narrative.

Quantum Field Theory

  •  Level 1 is again the standard “Shut up and Calculate” approach that everyone learns in the lectures and standard textbooks. For quantum field theory this meany learning how to calculate Feynman diagrams and path integrals without caring about their meaning.
  •  Level 2 thinking is becoming obsessed with, for example, Supersymmetric Quantum Field Theory or String Theory.
  •  Level 3 thinking is realizing that none of the existing “beyond QFT” frameworks is the final answer. Maybe there are no quantum fields after all, since every time we took the field idea seriously we ended up with horribly wrong predictions (Monopoles, Strong CP violation,  Domain Walls etc.).

General Relativity

  •  Level 1 is the conventional narrative that in General Relativity there is no longer a gravitational field, but instead, gravity is merely a result of the curvature of spacetime.
  • Level 2 is the realization that you can turn this whole idea around and argue that the essence of general relativity is that there is no spacetime at all but only interacting fields. The only thing that exists are points where spacetime trajectories of field excitations meet. Only this way spacetime emerges. Another possible Level 2 understanding is “GR is the unique theory with no absolute object”, as coined James L. Anderson in his book Principles of Relativity Physics. (I actually have a friend who is really obsessed with this idea.)
  •  Level 3 is… I have no idea. I find the level 2 idea outlines above extremely cool and I guess this means I am stuck at level 2 for now. But if you know any articles that could help me improve beyond Level 2, please send them my way.

Some thoughts on how to level up in physics

After reading Nat’s essay I started thinking about how I could actively improve my learning process by taking the various 3 levels into account.

I started by assessing at what level I current am for various topics. (It turned out I’m still at level 1 or 2 for many physics topics).

Then I started to think about how I can get from Level 1 to Level 2. The crucial step here is recognizing that there is more than what we learn in lectures and the standard textbooks.

Level 2 ideas usually can’t be found in textbooks. Instead, they must be actively discovered. Often it’s just a side remark in a paper, book, blog post or at StackExchange that initiates the moment of clarity. Afterward comes a period of “going down the rabbit hole” where I try to trace any reference and comment on the alternative approach.

Finally, after enough research, I slowly realize that the alternative approach I became obsessed with is not the final answer. Level 3 thinking requires that I recognize that there is more than one reasonable idea of how to go beyond what we learned in lectures and textbooks.

To stay at Level 3 I must be constantly exposed to ideas that challenge my current beliefs. If I become too certain of a given idea I fall back to Level 2. Level 3 is uncomfortable and lonely.

To summarize: To level up you must read broadly. If you only stick to the books that your professor recommends you will stay at Level 1. Read books and articles by experts, read blog posts, read comments at StackExchange or at the PhysicsForums, read stuff by weird unknown guys. It doesn’t matter as long as they do not all repeat the standard story over and over again. As soon as some alternative approach sparks your interest it is necessary to dig deep and understand it from all possible angles. While it is extremely helpful to become obsessed during this phase, this obsession should always end after some time. At some point, it is always necessary to recognize that there is no universal pre-packaged answer.

Why there is rarely only one viable explanation

“Nature is a collective idea, and, though its essence exist in each individual of the species, can never in its perfection inhabit a single object.” ―Henry Fuseli

I recently came across a WIRED story titled “There’s no one way to explain how flying works”. The author published a video in which he explained how airplanes fly. Afterward, he got attacked in the comments because he didn’t mention “Bernoulli’s principle”, which is the conventional way to explain how flying works.

Was his explanation wrong? No, as he emphasizes himself in the follow-up article mentioned above.

So is the conventional “Bernoulli’s principle” explanation wrong? Again, the answer is no.

It’s not just for flying that there are lots of absolutely equally valid ways to explain something. In fact, such a situation is more common than otherwise.

The futility of psychology in economics

Another good example is economics. Economists try to produce theories that describe the behavior of large groups of people. In this case, the individual humans are the fundamental building blocks and a more fundamental theory would explain economic phenomena in terms of how humans act in certain situations.

An economic phenomenon that we can observe is that that stock prices move randomly most of the time. How can we explain this?

So let’s say I’m an economist and I propose a model that explains the random behavior of stock prices. My model is stunningly simple: humans are crazy and unpredictable. Everyone does what he feels is right. Some buy because they feel the price is cheap. Others buy because they think the same price is quite high. Humans act randomly and this is why stock prices are random. I call my fundamental model that explains economic phenomena in terms of individual random behavior the theory of the “Homo randomicus”.

This hypothesis certainly makes sense and we can easily test it in experiments. There are numerous experiments that exemplify how irrational humans act most of the time. A famous one is the following “loss aversion” experiment:

Participants were given \$50. Then they were asked if they would rather keep \$30 or flip a coin to decide if they can keep all \$50 or lose it all. The majority decided to avoid gambling and simply keep the \$30.

However, then the experimenters changed the setup a bit. Again the participants were given \$50, but then they were asked the participants if they would rather lose \$20 or flip a coin to decide if they can keep all \$50 or lose it all. This time the majority decided to gamble.

This behavior certainly makes no sense. The rules are exactly the same but only framed differently. The experiment, therefore, proves that humans act irrationally.

So my model makes sense and is backed up by experiments. End of the story right?

Not so fast. Shortly after my proposal another economist comes around and argues that he has a much better model. He argues that humans act perfectly rational all the time and use all the available information to make a decision.  In other words that humans act as “Homo oeconomicus”. With a bit of thought it is easy to deduce from this model that stock prices move randomly.

This line of thought was first proposed by Louis Bachelier and you can read a nice excerpt that explains it from the book “The Physics of Wall Street” by James Owen Weatherall by clicking on the box below.

Why stocks move randomly even though people act rational

But why would you ever assume that markets move randomly? Prices go up on good news; they go down on bad news. there’s nothing random about it. Bachelier’s basic assumption, that the likelihood of the price ticking up at a given instant is always equal to the likelihood of its ticking down, is pure bunk. this thought was not lost on Bachelier. As someone intimately familiar with the workings of the Paris exchange, Bachelier knew just how strong an effect information could have on the prices of securities. And looking backward from any instant in time, it is easy to point to good news or bad news and use it to explain how the market moves. But Bachelier was interested in understanding the probabilities of future prices, where you don’t know what the news is going to be. Some future news might be predictable based on things that are already known. After all, gamblers are very good at setting odds on things like sports events and political elections — these can be thought of as predictions of the likelihoods of various outcomes to these chancy events. But how does this predictability factor into market behavior?
Bachelier reasoned that any predictable events would already be reflected in the current price of a stock or bond. In other words, if you had reason to think that something would happen in the future that would ultimately make a share of Microsoft  worth more — say, that Microsoft  would invent a new kind of computer, or would win a major lawsuit — you should be willing to pay more for that Microsoft  stock now than someone who didn’t think good things would happen to Microsoft , since you have reason to expect the stock to go up. Information that makes positive future events seem likely pushes prices up now; information that makes negative future events seem likely pushes prices down now.
But if this reasoning is right, Bachelier argued, then stock prices must be random. think of what happens when a trade is executed at a given price. this is where the rubber hits the road for a market. A trade means that two people — a buyer and a seller — were able to agree on a price. Both buyer and seller have looked at the available information and have decided how much they think the stock is worth to them, but with an important caveat: the buyer, at least according to Bachelier’s logic, is buying the stock at that price because he or she thinks that in the future the price is likely to go up. the seller, meanwhile, is selling at that price because he or she thinks the price is more likely to go down. taking this argument one step further, if you have a market consisting of many informed investors who are constantly agreeing on the prices at which trades should occur, the current price of a stock can be interpreted as the price that takes into account all possible information. It is the price at which there are just as many informed people willing to bet that the price will go up as are willing to bet that the price will go down. In other words, at any moment, the current price is the price at which all available information suggests that the probability of the stock ticking up and the probability of the stock ticking down are both 50%. If markets work the way Bachelier argued they must, then the random walk hypothesis isn’t crazy at all. It’s a necessary part of what makes markets run.
– Quote from “The Physics of Wall Street” by James Owen Weatherall


Certainly, it wouldn’t take long until a third economist comes along and proposes yet another model. Maybe in his model humans act rational 50% of the time and randomly 50% of the time. He could argue that just like photons sometimes act like particles and sometimes as waves, humans sometimes act like as a “Homo oeconomicus” and sometimes as a “Homo randomicus” . A fitting name for his model would be the theory of the “Homo quantumicus”.

Which model is correct?

Before tackling this question it is instructive to talk about yet another example. Maybe it’s just that flying is so extremely complicated and that humans are so strange that we end up in the situation where we have multiple equally valid explanations for the same phenomenon?

The futility of microscopic theories that explain the ideal gas law

Another great example is the empirical law that the pressure of an ideal gas is inversely proportional to the volume:

$$ P \propto \frac{1}{V} $$

This means if we have a gas like air in some bottle and then make the bottle smaller, the pressure inside the bottle increases. Conversely, if we have a bottle and increase the pressure, the gas will expand the volume if possible. It’s important the relationship is exactly as written above and not something like $ P \propto \frac{1}{V^2}$ or $ P \propto \frac{1}{V^{1.3}}$. How can we explain this?

It turns out there are lots of equally valid explanation.

The first one was provided by Boyle (1660) who compared the air particles to coiled-up balls of wool or springs. These naturally resist compression and expand if they are given more space. Newton quantified this idea and proposed a repelling force between nearest neighbors whose strength is inversely proportional to the distance between them squared. He was able to show that this explains the experimental observation $ P \propto \frac{1}{V} $ nicely.

However, some time afterward he showed that the same law can be explained if we consider air as a swarm of almost free particles, which only attract each other when they come extremely close to each other. Formulated differently, he explained $ P \propto \frac{1}{V} $ by proposing an attractive short-ranged force. This is almost exactly the opposite of the explanation above, where he proposed an attractive force as an explanation.

Afterwards other famous physicists started to explain $ P \propto \frac{1}{V} $. For example, Bernoulli proposed a model where air consists of hard spheres that collide elastically all the time. Maxwell proposed a model with an inverse power law, similar to Newton’s first proposal above, but instead preferred a fifth power law instead of a second power law.

The story continues. In 1931 Lennard–Jones took the now established quantum–mechanical electrical structure of orbitals into account and proposed a seventh-power attractive law.

Science isn’t about opinions. We do experiments and test our hypothesis. That’s how we find out which hypothesis is favored over a competing one. While we can never achieve 100% certainty, it’s possible to get an extremely high quantifiable confidence into a hypothesis. So how can it be that there are multiple equally valid explanations for the same phenomenon?


There is a great reason why and it has to do with the following law of nature:

Details become less important if we zoom out and look at something from a distance.

For laws of ideal gases this means not only that there are lots of possible explanations, but on the contrary that almost any microscopic model works. You can use an attractive force, you can use a repulsing force or even no force at all (= particles that only collide with the container walls). You can use a power law or an exponential law. It really doesn’t matter.

Your microscopic model doesn’t really matter as long as we are only interested in something macroscopic like air. If we zoom in all these microscopic models look completely different. The individual air particles will move and collide completely different. But if we zoom out and only have a look at the properties of the whole set of air particles as a gas, these microscopic details become unimportant.

The law $ P \propto \frac{1}{V} $ is not the result of some microscopic model. None of the models mentioned above is the correct one. Instead, $ P \propto \frac{1}{V} $ is a generic macroscopic expression of certain conservation laws and therefore of symmetries.

Analogously it is impossible to incorporate the individual psychology of each human into an economic theory. When we describe the behavior of large groups of people we must gloss over many details. As a result, things that we observe in economics can be explained by many equally valid “microscopic” models.

You can start with the “Homo oeconomicus”, the “Homo randomicus” or something in between. It really doesn’t matter since we always end up with the same result: stock markets move randomly. Most importantly, the pursuit of the one correct more fundamental theory is doomed to fail, since all the microscopic details get lost anyway when we zoom out.

This realization has important implications for many parts of science and especially for physics.

What makes theoretical physics difficult?

The technical term for the process of “zooming out” is renormalization. We start with a microscopic theory and zoom out by renormalizing it.

The set of transformations which describe the “zooming out” process are called the renormalization group.

Now the crux is that this renormalization group is not really a group, but a semi-group. This difference between a group and a semi-group is that there is no unique inverse element for semi-group elements. So while we can start with a microscopic theory and zoom out using the renormalization group, we can’t do the opposite. We can’t start with a macroscopic theory and zoom in to get the correct microscopic theory. In general, there are many, if not infinitely many, theories that yield exactly the same macroscopic theory.

This is what makes physics so difficult and why physics is currently in a crisis.

We have a nice model that explains the behavior of elementary particles and their interactions. This model is called the “standard model“. However, there are lots of things left unexplained by it. For example, we would like to understand what dark matter is. In addition, we would like to understand why the standard model is the way it is. Why aren’t the fundamental interactions described by different equations?

Unfortunately, there are infinitely many microscopic models that yield the standard model as a “macroscopic” theory, i.e. when we zoom out. There are infinitely many ways to add one or several new particles to the standard model which explain dark matter, but become invisible at present-day colliders like the LHC. There are infinitely many Grand Unified Theories, that explain why the interactions are the way they are.

We simply can’t decide which one is correct without help from experiments.

The futility of arguing over fundamental models

Every time we try to explain something in terms of more fundamental building block, we must be prepared that there are many equally valid models and ideas.

The moral of the whole story is that explanations in terms of a more fundamental model are often not really important. It makes no sense to argue about competing models if you can’t differentiate between them when you zoom out. Instead, we should focus on the universal features that survive the “zooming out” procedure. For each scale (think: planets, humans, atoms, quarks, …) there is a perfect theory that describes what we observe. However, there is no unique more fundamental theory that explains this theory. While we can perform experiments to check which of the many fundamental theories is more likely to be correct, this doesn’t help us that much with our more macroscopic theory which remains valid. For example, a perfect theory of human behavior will not give us a perfect theory of economics. Analogously, the standard model will remain valid, even when the correct theory of quantum gravity will be found.

The search for the one correct fundamental model can turn into a disappointing endeavor, not only in physics but everywhere and it often doesn’t make sense to argue about more fundamental models that explain what we observe.

PS: An awesome book to learn more about renormalization is “The Devil in the Details” by Robert Batterman. A great and free course to learn more it in a broader context (computer science, sociology, etc.) is “Introduction to Renormalization” by Simon DeDeo.