Everything is relative, my dear Bruno!

Even if special¹A. Einstein, 1905. Zur Elektrodynamik bewegter Körper, Annalen der Physik, n° 17, pp. 891 – 921. It can be read on line. An English version translated by George Barker Jeffery is available on line. and general relativity²A. Einstein, 1916. Die Grundlage der allgemeinen Relativitätstheorie, Annalen der Physik, n° 49, pp. 769 – 822. It can be read on line. An English version translated by Alfred Engel can be read on line. theories were introduced by Albert Einstein (1879 – 1955), the principle of relativity were introduced in Physics much earlier. It is called Galilean relativity and were introduced by … Giordano Bruno (1548 – 1600).

Of course, if this first form of physical relativity is qualified “Galilean,” it is because Galileo had something to do in its formulation. The introduction of this principle is one of the main elements of the epistemological revolution to which I referred earlier. This article is therefore a continuation of the series on the history of science that I started. It will also be the occasion, once again, to introduce some concepts that will be useful for future popularisation articles to come.

There and back again!

The introduction of the principle of relativity is related to the introduction of the heliocentric theory, that is to say, to the realisation that not only the Earth is not the centre of the World, but also that it turns on itself and around the Sun.

The observations of the planets had showed anomalies in their orbits. Thus, they sometimes seem to turn back before moving forward:

To solve the problems of the usual models of his time, Nicolaus Copernicus (1473 – 1543) indicated that the simplest way to explain the observations is that the Earth is not stationary, but should turn on itself and around the Sun³N. Copernicus, 1543. De revolutionibus orbium cœlestium, J. Petreium. It can be read on line. An English translation by Edward Rosen: N. Copernicus, 1992. On the Revolutions, Johns Hopkins University Press. It is available on line.. Rather, it matched best with the law of parsimony, that is to say that this explanation would require fewer assumptions than other models – I deal with the law of parsimony in another article. Not only is the model more parsimonious, but it also explains every observations, which was not the case with previous models.

Before Nicolaus Copernicus, Nicole Oresme (around 1320 or 1322 – 1382) had already presented the heliocentric system as credible⁴N. Oresme, 1377. Livre du Ciel et du monde.. However, Nicolaus Copernicus gave a mathematical demonstration, that is to say geometric, of its validity. It will be another important point of the upcoming revolution.

Aristotle and Giordano Bruno on the same boat

However, models in which the Earth was not the centre of the World had been proposed since antiquity, such as the one of Aristarchus of Samos (circa 310 – 230 BC), which is now known mostly through the presentation that made Archimedes (circa 287 – 212 BC)⁵Αρχιμήδης, Ψαµµίτης. It can be read on line. An English version can be read on line.. It is also likely that the heliocentric theory had appeared in India even before – as the purpose of this article is to discuss the introduction of the principle of relativity in physics and not the history of cosmological systems, I will not give many details about this history immediately, but use the comments to tell me if you are interested in me to do an article on this subject. Similarly, the idea that one can explain the world using mathematics probably appeared with Pythagoras (about 580 – about 495 BC).

However, these systems were abandoned and gradually forgotten because of the pre-eminence of the philosophical system (a term which included at that time all fields of knowledge) of Aristotle (384 – 322 BC). This system is often presented somehow as a caricature, which makes sometimes a little difficult to understand why its influence has been so great. I will try not to fall into this pitfall.

Aristotle had established a school, the Lyceum. In this school, he claimed to teach all the knowledge of the time. In this purpose, he has been working to produce a system whose ambition was to explain the entire world. He achieved this task through a logical system he had established, the Aristotelian logic. This resulted in an extremely coherent and comprehensive system. Another consequence is that questioning one element of this system quite inevitably result in questioning the entire system, so that there are little more than two alternatives: either to adhere to the entire Aristotelian system, or to reject it completely. Precisely, it was possible to make the Aristotelian system compatible with the Bible. As a consequence, for quite a long time, it was possible to explain the whole world only by using the Bible and the Aristotelian system. But for a few problems … As to question a single element caused the questioning of the whole system, for quite a long time, these problems were generally considered to be some artefacts that did not deserve much attention.

According to Aristotle, the Cosmos is delimited by the outer circle where the stars are located, in its middle the Earth stays still, and it is divided into two zones. The first one is the sublunary world (below the Moon), field of four elements – earth, air, water, fire – and subject to change, which is the world we live in. The second one, where the Sun, the planets and the stars are located, is the superlunary world (beyond the Moon), field of a fifth element (the quintessence) and of perfection. Rules applying in one of these worlds are not the same as those applying in the other one. In the superlunary world, everything is perfect, circles and spheres. In the sublunary world, the natural motion is rectilinear, air and fire are going up, while water and earth are going down⁶Ἀριστοτέλης. Περὶ οὐρανοῦ. It can be read on line. An English version translated by John Leofric Stocks: Aristotle, 1922. On the Heavens, Clarendon Press. It can be read on line.. The geocentric system of Claudius Ptolemy (90 AD – 168) is compatible with the Aristotelian system⁷Κλαύδιος Πτολεμαῖος, circa 150 AD. Μαθηματική σύνταξις. An English version: G. J. Toomer, 1998. Ptolemy’s Almagest, second edition.. According to Aristotle, the Earth cannot be rotating, otherwise the rectilinear motions would be altered, so that if an object from a height is dropped, for example from a tower, it would not fall at the foot of the tower. As we observe the objects thrown from a tower reached its foot, in the Aristotelian system it proves that the Earth is not rotating.

Giordano Bruno has contradicted this argument⁸G. Bruno, 1584. La cena de le Ceneri, J. Charlewood.. Indeed, he noticed that if one stands on a vessel moving in a straight line without changing the speed (we now name it a “uniform motion”), when dropping an object from the top of a mast of the boat, the object lands at the foot of the mast.

As it was difficult to make a clear video by experiencing on a boat, I climbed on a cart. However, the result is the same. If the cart is stationary, when I drop an object without initial velocity, it falls at my feet:

You have probably noticed that the film is slowed down, to 60 % of its original speed (and also highly cropped). The reason is that at normal speed, it is too short, you hardly see anything.

When the cart is moving according a straight uniform motion, then the object still falls at my feet:

Consequently, the fact that objects fall according a straight line cannot be considered as an evidence of the immobility of the Earth.

It also means that the observation depends on the point of view: for an individual on the vessel (or on the cart in my case), the object follows a straight vertical path which runs from the top to the bottom. For an observer on the waterside (for an observer near my camera), the object still describes a rectilinear trajectory, but this time it is an oblique one, from top to bottom and also in the direction of the vessel (the cart). The movement is relative to the point of view (it is now called the referential).

Giordano Bruno did not formalise this principle of relativity any further. He did not have much time to do so. Indeed, not only was he supporting the Copernican system, thus contradicting Aristotle, what could have been passed to him even then. But he also defended a series of opinions that the Church considered unacceptable. Indeed, he argued that the Universe was infinite and populated with worlds comparable to ours. Also, he was a pantheist, that is to say he considered God was not unique, but embodied into everything. But it is not over, as he proclaimed that Jesus Christ was not God, but a mere “clever magician,” that the Holy Spirit was the soul of the World, that Satan would ultimately be saved and still more audacities. He was therefore arrested by the Inquisition in 1592 and burned down in 1600. However, his writings attracted the particular attention of someone called Galileo Galilei (1564 – 1642) …

Galileo looking through the right end of the telescope

In a letter to Johannes Kepler (1571 – 1630) in 1597 (the latter was himself convinced of the validity of the Copernican model), Galileo indicates he subscribed to the validity of the Copernican theories for years⁹J.-P. Maury, 1986. Galilée, le messager des étoiles, Découvertes Gallimard sciences.. He also states that he dared not to publish anything then. To engage in the defence of Nicolaus Copernicus model, he first had to ensure that he was able to provide solid evidences.

In 1609, a former student of his told him about the invention of the Dutchman Hans Lippershey (1570 – 1619): the monocular. Many scholars of the time see it as a toy, but Galileo was not of this opinion. He manufactured several of these, with the aim to make astronomical observations.

The first astronomical object that Galileo has observed was the Moon. Quite soon, he noticed that it is not smooth and perfect, similar to polished crystal, as claimed by the Aristotelian model. On the contrary, it is mountainous. This is the proof he sought of the invalidity of the Aristotelian system¹⁰G. Galileus, 1610. Sidereus nuncius, T. Baglionum. Can be downloaded on line. An English version: A. Van Helden, 1989. Galileo Galilei, Sidereus Nuncius, or The Sidereal Messenger, The University of Chicago Press.. Moreover, if the Moon is mountainous, then it is not so different from the Earth. Consequently, it can be assumed, contrary to what Aristotle claimed, that physical laws are the same on the Earth as in the rest of the Cosmos. With these two premises, Galileo founded modern science: the laws of physics are universal and mathematics form the appropriate language to formulate them¹¹Galileo Galilei, 1623. Il Saggiatore. An English translation: Stillman Drake and C. D. O’Malley, 1960. The Assayer, in The Controversy on the Comets of 1618, University of Pennsylvania Press..

Several contradictions have been raised against Galileo’s work. Among them, quite legitimately, some pointed out that the operating principle of the telescope was not known, so it could not be certain that observations made with it was not some illusion. To answer this, Johannes Kepler carried out the physical and mathematical study of the telescope that validated the observations¹²J. Kepler, 1611. Dioptricae..

Again, the purpose of this article is not the history of cosmology, though it is exciting. So let summarize the following two decades by saying that refutations of Galileo’s works were numerous, which the latter opposed each time with very strong scientific arguments. Consequently, on the scientific ground, he clearly appeared to be triumphant. This has brought him several enmities, essentially political enmities, but very strong as well. Indeed, his complete refutation of the Aristotelian system was threatening the position of academics who had built their careers on this system. Unable to attack him scientifically, Galileo’s opponents turned the controversy into a religious one.

In 1624, Pope Urban VIII (1568 – 1644) asked Galileo to write a neutral presentation of both Ptolemy’s and Copernicus’ systems. Thus, in 1632 he published the Dialogue Concerning the Two Chief World Systems¹³G. Galilei, 1632. Dialogo sopra i due massimi sistemi del mondo, B. Landini. It can be read on line. An English translation by Stillman Drake: Galileo, 1953. Dialogue Concerning the Two Chief World Systems, University of California Press. (which I have already mentioned in a previous article). In his book, the Copernican model comes out clearly strengthened against the one of Ptolemy. Also, Galileo responds again to the argument of falling bodies according a straight line as a refutation of the mobility of the Earth. On this occasion, he formalised the principle of relativity:

‘Lock yourself with a friend inside the main cabin of a large boat and take with you flies, butterflies, and other small flying animals. Take a large tank of water with a fish in it, hang a bottle that is dripping into a large container beneath it. When the boat is stopped, carefully watch how the little animals are flying at speeds equal to all sides of the cabin. The fish swim indifferently in all directions, the drops fall into the container below, and if you throw some object to your friend, you do not need to launch the object stronger in one direction than in another, the distances being equal, and if you jump in with both feet, you cross equal distances in all directions. When you have observed all these things carefully (although there is no doubt that when the boat is stationary, things have to be this way), make the boat advancing to any speed that pleases you, provided that this speed is uniform [that is to say constant] and does not fluctuate on either side. You will not see any change in any of the mentioned effects and even none of them will tell you if the boat is moving or stationary.’

This means that immobility cannot be distinguished from a uniform motion without an external reference. In other words, an external reference is necessary to observe a uniform motion. The movement is thus a relative concept: station is equivalent to uniform rectilinear motion. Moreover, there is no privileged point of view, no absolute position, every point of view (every referential) is as valid as any other – using Galilean transformations (mathematical operations), one can switch from one point of view to another, that is to say change the referential.

Hence, while Giordano Bruno highlighted the fact that objects fall according straight lines is not a proof of the immobility of the Earth, Galileo showed that no matter how many observations you may do, the only way to determine if you are in (uniform rectilinear) motion is to use an external reference.

You can visualize the Galilean relativity in the video game Super Mario Bros.¹⁴S. Miyamoto et T. Tezuka, 1985. Super Mario Bros., Nintendo.. Indeed, in this game, when Mario reaches the centre of the screen, the sprite no longer advance into the screen, it is the floor that is moving beneath Mario’s feet. The game has adopted a point of view centred on Mario, so that the world seems to be moving rather than Mario:

I found the idea to use Super Mario Bros. as an example of Galilean relativity on the website e-Penser – several videos on this website have English subtitles.

Galileo will eventually be condemned to recant his theories in 1633 by the Inquisition, but at least was he not put into death. Nevertheless, he manages to publish a new book, in 1638, the Discourses and Mathematical Demonstrations Relating to Two New Sciences¹⁵G. Galilei, 1638. Discorsi e Dimonstrazioni matematiche intorno a due scienze attenanti alla mecanica ed i movimenti locali, L. Elzevier. It can be read on line. An English translation by Henry Crew and Alfonso de Salvio: Galileo, 1954. Dialogues Concerning Two New Sciences, Dover Publications Inc. It can be read on line.. During his career, he has also made significant contributions on falling bodies and fluid mechanics, which I will soon addressed, viewed from here.

Some kind of absolute

If everything was truly relative, then so would be this sentence, which therefore would be wrong …

I owe this good point to Étienne Klein.

Thus, contrary to what is implied by the title of this article, a variation on an assertion that can commonly be heard, Galilean relativity, just as special or general relativity, does not claim that everything is relative. Galilean relativity indicates that motion is relative to the referential from which it is observed. However, in this theory time is an absolute: two events seen simultaneously from a referential will still be perceived as simultaneous in any other referential. That is to say in a given time-line, a given event takes place on the same date regardless the referential. Also, physical principles apply in the same way when stationary or when in uniform motion – the latter is now called the principle of inertia, formalised by Isaac Newton (1643 – 1727), of whom I would treat soon.

In special relativity and general relativity (which is a generalisation of special relativity to gravitation), on the one hand motion is also relative, but time is also relative: simultaneity is not retained by change of referential, i.e. the date an event occurs depends on the referential. On the other hand, there is a limit speed, the speed of light, which is always the same whatever the referential. Moreover, general relativity indicates that the effects of gravity are equivalent to the effects of acceleration and that this is true regardless of the location in space-time (what is called principle of equivalence). Thus, relativity introduced by Albert Einstein pushes even further the principle of relativity. However, it indicates also that some things are absolute. I planed to also deal with special and general relativity in this web-log.

A continuing history

In this article I have introduced the principle of Galilean relativity, and also gave some insight about the notion of referential which will be discussed here again, especially when presenting Isaac Newton’s work. I have also indicated two fundamental principles of modern science. First, the universality of the laws of physics, that is to say that principles of physics apply in the same way at any point of the Universe. Secondly, the principle that mathematics is the good formalism for physics. These two principles are at the origin of the extreme fertility of physics since the Copernican revolution.

Furthermore, this story made me highlight two points that I think are important.

The first is that research is not the act of a single individual. Even if in Galileo’s time researchers’ publications had a single author, for instance the formalisation of the heliocentric model is the work of at least three different people: Nicolaus Copernicus theorised a model, Galileo made observations validating this model and Johannes Kepler produced the formalism to justify the validity of these observations. Similarly, the principle of Galilean relativity was introduced by Giordano Bruno and Galileo formalised it. If we can find in the history of sciences some cases, which in consequence became famous, of major contributions due to one single person, most important advances involve several researchers.

The second point lies in the status of the Aristotelian system. While it has long been considered as the supreme model, it is now often seen, a little caricatured, as an example of complete misdirection, the archetype of wrongness. One reason for this situation may be the difficulty to refer to the original texts. However, I think that there are also deeper causes.

First, it seems to me a fairly linear view of history is widespread. In this vision, the Middle Ages (about 1000 years anyway) are seen as a dark period of stagnation, even of regression. In this sense, the Aristotelian system is seen as a straitjacket that had to be break to regain the path of progress. However, it seems to me that things are significantly more complex.

Second, one often has a very aristocratic vision of science: some superior individuals would see a truth that others have failed to detect. I think this is not only a bad point of view, but even a dangerous one.

As I have already indicated, science is not so much about doubt than about the search for errors. Throughout this article, I voluntarily regularly used the modern term “model,” while at the time the term “system” was used: there was a hidden purpose – yes, I am a manipulator!

When facing a given phenomenon, we seek the elements that explain it, trying to take into account everything that has influence on this phenomenon and nothing else. This is what is called a model. One then seeks errors in this model, for instance using observations. Once the model validated, it can be used to make predictions and to understand some underlying mechanisms of the phenomenon, until we reach the limits of the model and propose a new one. In such a context, the errors of a model are a rich source of informations and have a real interest.

The Aristotelian system, as a system aspiring to explain the whole World in an intrinsically coherent model and as a synthesis of the essential knowledge of its time, was a contribution of importance. While it is now entirely refuted, its errors have nevertheless been extremely fruitful. The great names of science, without minimizing the importance of their contributions, were all wrong at one time, or had only partial explanations: much of the scientific work is to be wrong! Then to look for errors …

Therefore, the problem with the Aristotelian system was certainly not the system itself, but what have been done with it. That is, specifically, that it had been seen with this aristocratic point of view considering that some individuals understanding exceed the one of the masses, that these individuals thinking is intrinsically higher than any else. So that rather looking for errors, thus making science, people stuck in paraphrasing this system, that is to say into dogmatism.

It would be a shame to continue to do the same today, even in some reverse way …