It's harmful to teach wrong physics

In a discussion about the reasons of the accelerated expansion of the Universe (see also the first thread), a reader named BBB proposed that I was misunderstanding the goal of Carroll's claims that it's "wrong" to say that the negative pressure is the cause of the acceleration. Carroll's word "wrong" in "wrong way" doesn't necessarily mean that the physics is wrong, BBB argued; he may just say that it's "wrong" pedagogically and a completely different explanation "should" be presented instead.



Well, I think it doesn't matter for the indefensibility of Carroll's attitude. In fact, I think it's even worse when wrong claims are sold as physics to many people – while teaching or explaining physics to the laymen and beginners. When an individual believes a wrong idea about physics, he has the right to do so; no one is really infallible and the problem may be "localized". But when someone starts to teach wrong ideas as if they were physics, he is harming the whole society.

I will continue to use the would-be controversy about the "cause of the accelerated expansion" as my example – although I could think of hundreds of other examples that would be equally if not more apt and urgent. I am sure that Carroll must misunderstand some of the basic physics – that his proposal is not just about the obsession to spread lies among the laymen – but I will nevertheless pretend that I believe that he actually understands the physics and he only wants to make it "more popular".




Let's roll. Since the late 1990s, we have known that the expansion of the Universe isn't decelerating, as most cosmologists expected (because gravity is attractive and if you throw an apple into the clouds, it will be decelerating as well), but it is accelerating. What's the reason of the acceleration? The right answer is:

Relativity teaches us that the mass density – the only source of gravity in Newton's picture – is just one "component" of a "tensor" which has many components including the momentum density and the flux/current of energy and the flux of momentum (pressure etc)., the "stress-energy tensor". That's analogous to the insight that the total energy/mass is the time component of the energy-momentum 4-vector. Because these components are related by symmetries, all of them must have some impact on the curvature of the Universe.



This \(4\times 4\) table represents the components of the stress-energy tensor \(T_{\mu\nu}\). The numbers get mixed up with others in the table whenever one translates the observations of one observer to the coordinate system of another observer who is moving relatively to the first one.

The acceleration of the expansion is a property of the "curvature of the spacetime" and equations of GR show that it depends not only on the mass density \(\rho\), like Newton's gravity would, but on the combination \((\rho+3p/c^2)\). So a positive pressure, like the pressure inside a gas or a liquid, has the effect of increasing the gravitational attraction, i.e. it makes the Universe decelerate and ultimately shrink faster than we would expect just from \(\rho\).

On the contrary, we may theoretically imagine an environment with a negative pressure \(p\); after all, even ordinary solids may be either squeezed or stretched. If \((\rho+p/3c^2)\) is negative as well, the rate of the expansion will actually increase with time. We will get an accelerated expansion. So the evidence for the acceleration is the evidence that \((\rho+3p/c^2)\) is negative. The detailed evidence is compatible with the assumption that \(\rho\gt 0\), \(p=-\rho\). The latter is the relationship that holds for Einstein's "greatest blunder", the cosmological constant. That's sufficient for having \((\rho+3p/c^2)\lt 0\). More generally, environments filling the empty outer space which obey \(p=-\rho\) "approximately" are known as "dark energy". The adjective "dark" means that this environment contains no particles that would interact electromagnetically i.e. that would emit light. We can't see the "substance" filling this medium.

Carroll doesn't like the right explanation.




He calls this right explanation "the wrong way" for the following would-be reason:

[I]t’s not the slightest bit of help in bringing people to any real understanding. It simply replaces one question (why does dark energy cause acceleration?) with two facts that need to be taken on faith (dark energy has negative pressure, and gravity is sourced by a sum of energy and pressure). The listener goes away with, at best, the impression that something profound has just happened rather than any actual understanding.

Indeed, it's sometimes being said that when we answer a question in science, five new questions arise. In this case, the layman got an answer and just two mysterious facts – according to Carroll's counting – appeared. This is the normal situation for anyone who is studying and learning science. It's actually a reason why we learn and study.

There are so many problems with the philosophy behind Carroll's criticism that I don't know where to start. First, the extra two facts that the right explanation needs are true and important. A layman or beginner probably fails to see their importance or relevance for the question of acceleration from the beginning but that doesn't change the fact that these two insights are true and important. It's important to understand than in GR, the whole stress-energy tensor (including pressure) and not just the mass density affect the gravitational field; and it's important that we know viable physical theories (or concepts) that predict that the vacuum may have a negative pressure. If someone fails to grasp any of these points, he just can't be understanding why the Universe is accelerating according to modern physics.

Now, a layman – a listener – may legitimately fail to grasp anything or everything. It's not his job, after all. In that case, he will indeed end up with the impression that something profound has just happened but he doesn't actually understand what has happened. But that's the best possible outcome of the teaching after a full understanding! In particular, it's much better than the scenario in which the layman learns a completely wrong "answer" and is led to believe that it's the ultimate answer and he doesn't need anything else, anything deep. One does need that if he wants to understand the true reason behind the acceleration.

It's great if the layman gets the impression that something profound has happened because, you know, something profound has indeed happened! We usually use the term "relativity" for the body of these profound insights. We even celebrate Albert Einstein because he was the most important man who helped to find these profound insights!

It's also deeply misleading to say that the "two facts have to be taken on faith". That's just not how science works. These facts are believed to be true because there's very strong evidence – empirical evidence as well as derivations and calculations – supporting these two facts. It is dishonest for someone to describe important scientific insights as "faith" just because he finds them difficult (or because he finds them hard to explain to others). Science is not just about the faith. These are important scientific facts whether someone understands them or not.

The dark energy's having negative pressure is pretty much its defining property. Someone claiming to understand the concept of "dark energy" without knowing that it has negative pressure is dangerously deluded. In the same sense, the importance of the whole stress-energy tensor for the spacetime curvature is a basic implication of relativity (even special relativity). Special relativity clumps various quantities to 4-vectors and tensors and it says that the components of the 4-vectors or tensors behave in qualitatively analogous ways, ways that are related by symmetries. Time mixes with space, the total energy/mass mixes with the total momentum, the energy density mixes with the momentum density or the pressure and the stress, electric fields mix with magnetic fields when you switch to a different reference frame. That's also why the pressure must influence "something about the spacetime curvature" if the mass density can do it. This fact follows from the Lorentz symmetry or from the principle of relativity, if you wish. It is profound, indeed.

One doesn't understand relativity at all if this basic insight (about the relativity's ability to link the fate of previously independent quantities) is unfamiliar to him. It's OK for the society if he doesn't understand relativity – most people don't – but it's dangerous if he is led to believe that he has understood the essence of relativity or dark energy or the acceleration of the rate of the cosmic expansion if he clearly hasn't. It's important for everyone, experts and the laymen, to realize that they don't understand everything if they don't understand (and no one does, and it's true especially for the laymen). So if an "explanation opening new questions" leads to this feeling, it is a good outcome, too.

It may sometimes be hard to explain scientific concepts and discoveries – not only because they depend on numerous facts and their relationships and sometimes on difficult maths but also because they contradict some "intuition", some knee-jerk reactions of the beginners, preconceptions that people have before they learn the right answers. But to overcome these things is the mission of teaching and explaining – in some sense, it is the only mission. It's what teaching and explaining is all about. If we had known almost everything (or everything important) from the beginning, we wouldn't have to study and learn.

In particular, physics and cosmology isn't being explained with the purpose to make someone "feel good" whatever it costs. There are surely easier ways for most people to "feel good". If the "good feelings" are compatible with a successful explanation of physics or cosmology, it must be a "good feeling" about having learned something that is actually true. A person who loves science and learning probably likes to correct his invalid expectations and misleading preconceptions. Some people don't like to learn science – and they don't like to be told that their beliefs were wrong, either. But that changes nothing about the fact that teaching or explaining science is impossible without challenging and ultimately defeating the listeners' wrong expectations! That may sometimes be unpopular but it is critically needed.

Sean Carroll is among those who wouldn't hesitate for a second to bastardize science, to sell complete bullshit as physics if it helps him, if it makes him more popular among the stupid people. But by doing so, he is not popularizing physics. He is abusing, bastardizing, and contaminating physics and cosmology for the purpose of his own benefits. Such dirty populists should be spitted upon and pissed upon by all the people who have been decently educated, especially by all the aristocrats.

These conclusions are extreme because I was writing them under the aforementioned assumption that Carroll understands the right reasons and he's just proposing the wrong explanations to make "life easier for the laymen". The truth is somewhat different; much of the reason behind his delusions is that he misunderstands much of the basic physics himself. In that case, the right criticism of Carroll is less about his immorality and more about his stupidity and incompetence.

Let me copy the final paragraphs that contain a wrong explanation that Carroll calls "the right way":

You notice a couple of nice things about this [first Friedmann] equation. First, the pressure doesn’t appear. The expansion rate is simply driven by the energy density \(\rho\). It’s completely consistent with the first equation [the second Friedmann equation], as they are related to each other by an equation that encodes energy-momentum conservation, and the pressure does make an appearance there. Second, a constant energy density straightforwardly implies a constant expansion rate \(H\). So no problem at all: a persistent source of energy causes the universe to accelerate.

Banning “negative pressure” from popular expositions of cosmology would be a great step forward. It’s a legitimate scientific concept, but is more often employed to give the illusion of understanding rather than any actual insight.

Everyone who understands GR knows that this is just plain bullshit. The sign/existence of the acceleration is dictated by the quantity \((\rho+3p/c^2)\) and its sign. If it is negative, the expansion rate is increasing. If it is zero, the expansion rate is constant. If it is positive, the expansion rate is negative and the Universe is decelerating (as expected from attractive gravity).

It is just not true that the acceleration – and whether or not the expansion may slow down, stop, and revert in the future – depends on \(\rho\) only. The right quantity it depends upon is \((\rho+3p/c^2)\). Anything less complex than that is simply a lie. In particular, it's also impossible to identify the conditions for the acceleration with a property of the time derivative \(d\rho/ dt\).

It is not true that a constant energy density is necessary for the acceleration. After all, the energy density in our Universe is still decreasing (because the contribution from the dark matter and the visible matter is decreasing). The Universe might even be filled with stuff that has a constant \(p/\rho c^2\), for example by the cosmic domain walls with \(p/\rho c^2=-2/3\), and the energy density will still decrease while the expansion rate will accelerate!

Even if you neglected the fact that Carroll's constancy fails when \(p/\rho c^2\) is between \(-1\) and \(-1/3\) which are enough for an accelerated expansion, the comment about the "constant \(\rho\)" only captures one property of the cosmological constant which is in no way "the cause" of the acceleration. Carroll's "right way" is just like saying that Italy is a capitalist country because they have the Alps. They're not really the main nation that has the Alps, the Alps are neither necessary nor sufficient for capitalism, and they just have nothing to do with the question. Carroll's non-explanation doesn't explain why the mass density is capable of staying constant or decreasing more slowly than the dust's mass density – the reason for that is all about the negative pressure, too. Einstein's equations still imply a "covariant conservation of the stress-energy tensor" which means that the energy density can't evolve arbitrarily – the evolution is dictated by the pressure.

Similarly, it is not true that a constant energy density is a sufficient condition for the acceleration, either. An empty Universe with \(\Lambda=0\) has \(\rho=0\) which is constant but it is not accelerating. A negative-cosmological constant Universe has \(\Lambda\lt 0\) and \(\rho=\Lambda\lt 0\) and its expansion is even strictly decelerating, not accelerating. Carroll's claims that only the energy density and its persistence matter is just wrong in every interpretation. It's clear that if the right condition involves the pressure, you can't just eliminate it without spoiling the validity of the proposition.

And the whole "desire" to eliminate the pressure from the explanation (despite the pressure's critical importance) is completely pathological. The laymen should be led to think relativistically and in relativity, the pressure \(p\) is exactly as simple, legitimate, and natural as the mass density \(\rho\) – they're components in the same tensor. This relationship between \(p\) and \(\rho\) is not only true; it's also deeply spiritually satisfying; one can "feel" some of Nature's elegance and sexiness through similar insights. A listener who has a chance to understand modern physics will ultimately be happy about the right explanation. A priori, a layman might think that it's "simpler, prettier, and more natural" if only the energy density matters. But relativity with its symmetries should teach him that Nature respects a very different (and in this sense opposite) type of simplicity, beauty, and naturalness. All components of a 4-vector or tensor matter – they matter "qualitatively equally"; the equations showing their influence have totally analogous (if not "the same") form.

But let me spend some more time with the "moral dimension" of Carroll's sick claims. We hear that the right explanation is often employed to "give the illusion of understanding rather than any actual insight". This assertion displays the degree of enhanced arrogance that the Jews call "chutzpah" (another example: a murderer of his parents insists that he is found innocent because he is an orphan) because it's exactly (and only) Carroll's would-be explanation that explains nothing and gives the illusion of understanding rather than any actual valid insight.

In fact, it was designed with this very purpose in mind. It was designed so that the listeners don't have to ask any additional questions. Carroll was very open about his motives. With Carroll's wrong explanation, the debate is over. Everything is just due to the mass density, like in Newton's theory, we don't have to learn anything new, relativity doesn't force us to modify any opinions, there is nothing "profound" about relativity, and I am [Sean Carroll is] so great that I have [Carroll has] explained it so cleanly while others are muddled minds who have to bother you, dear listeners, with unnecessary complicated concepts such as pressure and dark energy.

Except that you haven't explained a damn thing, Mr Carroll, everything you say about the actual causes of the acceleration is wrong, and by your pumping of self-confidence into the minds of people who have been explained nothing about the actual physics, you are producing new pompous fools and aggressive idiots who understand nothing, who think that they never have to learn anything new or modify their opinions, but who still act as if they were understanding everything.

And that is very harmful to their environment, that is very harmful to the present and to the future of their communities and the human society at large. It's a much better idea to encourage the kids to have parties all the time (or whatever they like) than to teach them wrong physics.