## Friday, July 27, 2018 ... /////

### Einstein's breakthrough was far deeper, more philosophical than assumed

Some days ago, we had interesting discussions about the special theory of relativity, its main message, the way of thinking, the essence of Einstein's genius and his paradigm shift, and the good and bad ways how relativity is presented to the kids and others.

Newton has introduced mathematics to the thinking about the physical phenomena including the accelerated motion of objects. This mathematics was compatible with the common sense and it allowed the people to think as reductionists. I think that most people who can pronounce "relativity" understand this viewpoint.

The world is composed of various objects – particles, solid objects, fields – and they obey some differential equations with time as the independent variable. These equations may be written down, solved, and exploited. The intuition is that the world is composed of many things, each works in some way, and we are learning how they work one by one.

So Newton has introduced some reductionism as a basis for science – and the world could be divided to objects and pieces that evolved according to some differential equations. The differential equations are a bit hard and most people aren't good at them – but they sort of understand the intuition behind them.

In this whole framework, it was assumed – because it really seemed obvious – that there were objective values of the relevant quantities describing the location and shape of "things" that were a function of time $t$; and all the objects were embedded in the three-dimensional flat Euclidean space $\RR^3$. A copy of that space – with objects at some locations – existed at each moment of time. Details weren't known from the beginning but the basic framework seemed clear forever. You could only change the precise shape of the differential equations – including the forces – and you could construct larger objects from more elementary ones (which I will later describe as the invention of "constructivist" theories).

The elementary objects could have been understood and the understanding of these objects or "stuff" wasn't terribly different from the work of inventors such as Edison – that's why I embedded the diagram of the light bulb. Because the speed of light is so tightly incorporated into special relativity, many people end up thinking that Einstein was similar to Edison. Just like Edison grabbed a light bulb and optimized it, Einstein played with another object, light, and theoretically understood what it does and how it moves.

But that's a wrong lesson. Special relativity isn't about light itself. It's about the amazing role of the speed called the speed of light – and the speed of light isn't the speed of light only. Instead, it is also the speed of light, aside from other things.

Light is a casual name for some electromagnetic waves – or photons – but the speed of light is also the speed of gravitational waves – and gravitons – and, in principle, other things (I think that photons and gravitons are the only massless particles in Nature – gluons are massless as well but they're confined). Well, it's the speed that all massless objects move by; and all massive objects may approach arbitrarily closely from below. The speed $v$, energy $E$, and rest mass $m_0$ obey:$\frac{E}{m_0 c^2} = \frac{1}{\sqrt{1 - v^2 / c^2}}$ For massless objects such as photons and gravitons, $m_0=0$ and the left hand side is infinity whenever $E\neq 0$ which means that the right hand side must be infinite, too. That's the case when $v=c$. Massless objects simply must move by the speed of light. On the other hand, when $m_0\gt 0$, the ratio $E / m_0 c^2$ may also be arbitrarily high if you pump up the kinetic energy. Then $v$ goes up and approaches $v\to c$ from below – but it can never quite reach it, let alone surpass it.

Those who understand this rather basic stuff know that special relativity isn't exclusively about light. It's really about the space and time – which must be unified into the spacetime. Space, time, and spacetime affect everything that can live or move within them – which really means everything (as well as every thing) in our real lives.

The postulates become the "beginning", not the "end"

That's the main far-reaching point that the people tend to misunderstand. You know, special relativity may be phrased as a system of facts derived from two axioms – we really call them postulates in theoretical physics:

1. the laws of physics have the same form in all inertial frames (that are moving by a constant velocity relatively to each other)
2. the speed of light is measured to be the same constant, $c=299,792,458\,{\rm m/s}$, in all inertial frames
The first statement operationally means that if you make experiments inside a train that is moving uniformly, and you can't see outside, you can't determine whether the train is moving or it is at rest (and you can't measure the speed).

If you interpret this statement in a strong way – so that even the measurement of the light that comes outside cannot help you to determine the speed of the train – then the second postulate follows from the first one as a special example.

In Newton's physics, the first postulate (the principle of relativity) was true – because Newtonian mechanics respected the so-called Galilean relativity. You could change all the velocities of all objects by $\vec V$, a constant:$\vec v_i \to \vec v_i + \vec V$ and everything obeyed the laws of physics just like before. The simple additive shift of all the velocities corresponded to a simple change of the vantage point – if things seemed to obey the laws of physics in one inertial frame, they had to obey the laws of physics in another frame as well.

However, Newton assumed that the light was made of particles, the curpusles, when the inertial frame was switched, those had to change their speed additively as well. So if light were emitted from a source to have a speed $|\vec v_{\rm light}| = c$, then the speed had to look different in generic, other reference frames. (Even those who believed that light was made of waves thought that the speed of those waves looked different to observers in motion.)

Well, the simple Galilean transformation didn't touch the time at all, $t\to t$. You know that the Galilean group was replaced by the Lorentz group $SO(3,1)$ or the Poincaré group – which also allows spacetime translations. The Galilean group is a "contraction" of the Lorentz group; the Lorentz group is a "deformation" of the Galilean group.

I think that people who have been sufficiently exposed to relativity – at least a few successful hours, if I try to quantify it in some way – understand these statements about group theory. There exists some Lorentz group that mixes the space and time and Newton's space and time didn't mix in this way. But I think that even most of the people in the world who would claim that they understand this statement still misunderstand relativity. And it boils to the title of the blog post.

My experience is that most laymen and amateur physicists still think about the constancy of the speed of light and the Lorentz transformation as about some derived facts, some properties of objects such as light bulbs and the light itself. They think that physicists "grab stuff", like the light, look at it, and they determine that the stuff has some properties and moves so that it's compatible with the relativistic formulae and symmetry.

With this (wrong) perspective, Einstein's postulates and the Lorentz symmetry remain permanently unnatural and eternally challenged. These people tend to think: So far it's worked but it's really a coincidence and when physicists look at new things or they look more closely, the formulae will be found to be inaccurate and the symmetry will be seen to be approximate. It will probably break down at some point.

But that's not the conclusion that Einstein – or anyone who really understands modern physics – would make.

In reality, it's extremely likely that all tests of special relativity (within freely falling frames or locally, so that I get rid of gravity in some way) will confirm this theory of Einstein's in the rest of this century and the next one and many others. Why? Because Einstein has found new principles that seem to agree with all the tests so far nontrivially and incredibly accurately, yet a priori surprisingly, and that's quite some evidence that these principles are perfectly true.

Most quantitative statements about Nature are approximate. When we say that the Sun is 150 million kilometers away, it's not surprising that a precise measurement yields a slightly different figure – in fact, the right figure oscillates with seasons and depends on the treatment of the Sun's and Earth's nonzero size, too. Indeed, it's a good habit to expect some error margin in most of such statements.

However, in physics and science, there may also be statements that are true exactly, some ultimate principles, postulates, axioms, or theorems of Mother Nature or God. They are meant to be perfectly true – exactly like religious dogmas. When someone believes in statements that are perfectly true, doesn't it mean that he's religious – and what he pretends to be science is therefore a kind of faith, a religion?

Well, not necessarily. The real difference between the "scientific dogmas" and the "religious dogmas" is that the "scientific dogmas" have passed some empirical tests that were nontrivial to start with. But the dogmas have succeeded. The religious dogmas – such as the virginity of Mary – haven't really passed empirical tests, at least not tests that you (an independent scientist who isn't satisfied with the brainwashing by others) could reproduce in your lab (your lab shouldn't be in your bedroom because the virginity test would then be negative, anyway).

OK, so Einstein found some postulates which imply the mixing of space with time, Lorentz transformations as symmetries, and he wanted us to believe that these claims are exact. Is it good science that we're supposed to believe in some "new scientific dogmas"? Yes, it is. The point is that these "new dogmas" aren't a completely new, unprecedented creation. If you look carefully, you will see that they're just competitors to – and because they work very well, replacement for – some other "scientific dogmas" that people had believed before Einstein.

Einstein has articulated those postulates – "scientific dogmas" – and derive lots of implications which have the same truth value and reliability – "derived scientific dogmas". Did he make science more faith-based? Not at all. It's actually great that he articulated those dogmas and other propositions – and looked at the evidence that tells us something on their validity (yes, they seem true) – because it's more scientific to clearly articulate propositions and to judge them than to remain silent or assume that everything is clear!

If you think about special relativity rationally, you must understand that $SO(3,1)$ was just proposed as a replacement for the Galilean group, the spacetime was proposed as a replacement for the space and time that didn't mix, the maximum cosmic speed became a replacement for the belief that the speed of an object may always be increased towards infinity, and all other statements of relativity replace some non-relativistic statements. The point of special relativity is the "reform" of all these qualitative statements – and then the measurement of the key parameter, $c$, becomes just a subsequent small task for experimenters.

A funny fact is that many of these non-relativistic statements that were replaced by their relativistic counterparts hadn't even been clearly articulated before Einstein – but they were believed, anyway. For example, Einstein found out that the simultaneity of events is relative: it depends on the inertial system. That "dogma" is clearly a replacement of the opposite non-relativistic dogma: the simultaneity of events is absolute.

Did the physicists before Einstein spend their days by screaming that the simultaneity of events is absolute? They didn't. It was an assumption that they were making all the time. All of science totally depended on it. But it seemed to obvious that they didn't even articulate that they were making this assumption. When they were describing the switch to another inertial system, they needed to use the Galilean transformation and at that moment, it became clear that they were assuming something. But everyone instinctively thought that one shouldn't question such an assumption. No one has even had the idea to question it. And that's why they couldn't find relativity before Einstein.

Einstein has figured out that some of these assumptions were just wrong and he replaced them with "new scientific dogmas". He ate the apple in the Garden of Eden. The clearly articulated alternatives – Einstein's and the silently believed predecessor of Einstein's dogmas – could have been compared and be sure that Einstein's dogmas were found to be right and the non-relativistic ones were found to be wrong. The difference becomes really obvious when speeds of object become comparable (or even very close) to the speed of light.

Once again, Einstein has replaced the "old scientific dogmas" that looked so obvious that they weren't even discussed; by "new scientific dogmas" that are a little bit more abstract, must be abstract, and may be empirically shown to be superior. Now, if you're rational, you see that Einstein clearly won a match against Newton. So if you were certain about Newton's dogmas, you should simply replace them by Einstein's dogmas and be equally certain about them as you were previously about Newton's dogmas. That surely improves your understanding of the Universe because Einstein's dogmas may be proven to be strictly better than Newton's dogmas! If you question Einstein's postulates much more than you questioned Newton's axioms, it means that you have an irrational preference for theories that don't seem to work too well empirically and it's bad.

OK, Einstein found the right new principles or postulates or axioms or dogmas. And this very methodology – the search for the "new and better dogmas" – is one of Einstein's more general contributions to science. A physicist should really question things because even some of the assumptions that seem so obvious that no one even articulates them may be wrong and may be replaced by much deeper and more accurate replacements. The quantum mechanical revolution has applied Einstein's general philosophical strategy and found something even deeper than relativity.

Einstein was very aware of this change of methodology – by which he really started modern physics. As a teenager, I liked to read a book of his essays ("Mein Weltbild") many times. He was rather modest about this change of the perspective, too. Because of the focus on the "search for correct axioms and derivations starting with these axioms", he considered relativity to be a "principled theory" of physics. The other class of physical theories were "constructive theories". I basically started with them – it's the reductionism where things are made of pieces.

In this classification, relativity was an example of a principled theory but Einstein pointed out that he wasn't really the first physicist who made this change of the perspective. Thermodynamics did it before relativity. Like relativity, thermodynamics was also built around some basic laws – the laws of thermodynamics.
The first law of thermodynamics is that you can't build the perpetuum mobile of the first kind.

The second law of thermodynamics is that you can't build the perpetuum mobile of the second kind.
It sounds simple and logical. Just to remind you, the perpetuum mobile of the first kind produces energy and never stops; the perpetuum mobile of the second kind spontaneously transmits heat from a colder object to a hotter one.

Like in relativity, these basic laws of thermodynamics may be interpreted as general axioms – "scientific dogmas" – and physicists are invited to behave as mathematicians who try to derive interesting "theorems" out of these "axioms" (which may be applied to more specific situations).

Even in the case of thermodynamics, a too "constructivist" person may fail to understand the power of the "valid principles" and the methodology based on the "scientific dogmas". Well, if you don't get that the principles above are almost certainly general – and there is quite some evidence that they're true – you are at risk of spending your life by trying to construct the perpetuum mobile! The men who have spent years with this futile exercise don't see the forest through the trees. They're not capable of thinking in terms of big statements – like the "scientific dogmas". Whenever they add a new building block to their candidate machines (a metallic handle, water, electricity, and lots of other things), they believe to have a much higher chance to succeed although they have failed so far. They don't get discouraged because they're blind to the main negative arguments against their hopes – and they're blind because these statements are too "big", too "general" for them. The constructors of the perpetuum mobile don't understand or don't believe general statements and principles. If you close your eyes and overlook universal laws and big-picture statements, the perpetuum mobile may look like a matter of patience.

We know e.g. the first law of thermodynamics – the energy conservation. It holds for some laws of physics (e.g. the Standard Model) whose equations may be written down. But the energy conservation doesn't really depend on the Standard Model Lagrangian too much. It's not some derived property of more detailed, constructed laws of physics. Instead, you should think of the Standard Model as a set of equations – a theory of a certain kind – that obeys the energy conservation and lots of other, stronger principles.

What's going on? As I promised you, we're really changing the starting point. The little pieces and point masses and the differential equations that they "possess" are no longer the starting point. Instead, you start with some well-chosen principles – you must be a good enough physicist to find the laws of thermodynamics or the postulates of relativity – and then you guess the right microscopic equations from a list of candidates that obeys the principles. Can you see the difference? The thermodynamic founding fathers and Albert Einstein added a fundamental step at the very beginning – the guessing of the right "new scientific dogmas". And the next work for scientists actually follows after those!

This extra step at the beginning has made the work of theoretical physicists deeper and more philosophical. When this new principled perspective was born, many deep theoretical physicists have been switched
from Edison-like characters who play with the basic pieces of light bulbs and their equations

to Einstein-like chaps who try to outline the best possible "metalaws" that the Edison-like characters should better obey in order for them to find something useful.
The postulates of relativity, the laws of thermodynamics, and similar principles are deeper and more far-reaching than any single particular statement about the behavior of any particular elementary particle or another object. In some sense, Einstein became a boss of all the people who later constructed relativistic (classical or quantum) field theories. He wrote the general laws of relativity that define the general framework – what is allowed and what is not – and the constructivist physicists may only invent or change "relative details".

It's not a perfect analogy but I must mention it: the role of physicists such as Einstein was changed to the role of America's founding fathers who needed to write and enforce some foundational documents for Edison to succeed later.

Do you get my point? When modern physics began, physics became much more philosophical. Philosophers used to look for the "right dogmas" as well except that it hasn't ever led to anything that would be useful to understand Nature. Modern physicists have actually found general principles that do apply to Nature and that seems to work. Modern physicists are the only successful philosophers in this very sense.

Ironically enough, the amateur physicists who love to present themselves as "philosophers" – a "philosopher" is basically a self-described physicist who is ignorant of physics according to all actual physicists, so a "philosopher" is basically synonymous with a "crackpot" – usually misunderstand this point (that physics has become more philosophical). The Czech crackpot and "reformer of relativity" named Jan Fikáček – an ex-boss of Mensa Czechoslovakia – is an excellent example of that.

All these people love to immediately jump into some technicalities. They never really think about their starting point too deeply because they think that the right starting points are obvious. But that's completely wrong. The search for (and selection of) the right principles that define the rough rules of the game for all the subsequent dirty work has become the most important part of theoretical physics. It's a work that philosophers had wanted to do – but only modern physicists could do it well. And the contemporary "philosophers" i.e. self-confident crackpots are the group of people who maximally misunderstand the need to pick the right principles in physics.

Bonus: there is a related point I want to make. Brian Greene posted an innocent comment about dark matter and prizes:

Someone disagreed with that:

And:

You know, some of the people want to keep theory and experiments separated, and all stuff like that. It's bizarre because the whole point of the scientific method is that theories and experiments intensely interact with each other. But you can see what drives Federico Lelli, Peter Yoachim, and a majority of similar "empirical activists". They just want to praise some dull, obedient observations, even in the absence of any interpretation, and say that the interpretations and theories don't matter.

But science could never work like that. The viable interpretations are actually the ultimate goal of the experiments and only when viable interpretations appear, the experiments become important and truly trustworthy. In this sense, the people who find the correct interpretations – probably some theorists – are more important and their work is essential for making the experimenters important, too.

An ally gave a good example:

The Pioneer anomaly was just some artifact of some instrumental mess. I have already forgotten what caused it. It's known and there was no new physics behind it. But that's a textbook example of a surprising observation without an impressive interpretation – without a new theory that naturally explains the observation. When you have surprising observations without good theories, it usually means that the observation is rubbish. You just shouldn't mindlessly believe isolated surprising observations. It's a part of the scientific attitude to reality that you realize that lots of isolated surprising claims may be rubbish and only when there's some synergy between them which is consistent with some theory, they may be really trusted.

The belief in isolated, very surprising empirical or experimental statements is basically synonymous with the belief in miracles and – even though the "empirical activists" think that such a belief is maximally scientific – that's actually very unscientific.