The trial and condemnation of Giordano Bruno was mainly based on arguments of philosophical and theological nature, and therefore different from Galilei's. Such elements contribute to unfairly devalue the scientific contribution of Bruno and do not properly account in particular for his contribution to physics. This paper discusses the contribution of Bruno to the principle of relativity. According to common knowledge, the special principle of relativity was first enunciated in 1632 by Galileo Galilei in his Dialogo sopra i due massimi sistemi del mondo (Dialogue concerning the two chief world systems), using the metaphor today known as "Galileo's ship": in a boat moving at constant speed, the mechanical phenomena can be described by the same laws holding on Earth. We shall show that the same metaphor and some of the examples in Galilei's book were already contained in the dialogue La cena de le Ceneri (The Ash Wednesday Supper) published by Giordano Bruno in 1584. In fact, Giordano Bruno largely anticipated the arguments of Galilei on the relativity principle. It is likely that Galilei was aware of Bruno's work, and it is possible that the young Galilei discussed with Bruno, since they both stayed in Venezia for long periods in 1592.I knew that Bruno was a Catholic monk who denied the divinity of Jesus and argued for many other heresies, and was executed. And I knew that he speculated about an infinity of worlds. But I did not that he had any legitimate scientific contributions.
There were ancient Greeks who argued for the motion of the Earth, such as Aristarchus of Samos, but his works have been lost and we don't know his arguments. Since we do not feel the motion of the Earth, he surely must have argued for some sort of relativity principle. Aristotle argued that our failure to feel the motion suggests that the Earth is not moving. So I do not see how the principle can possibly be due to Bruno or anyone of that time period.
This paper does show that Galileo could have met Bruno and gotten important ideas from him, including the relativity of a moving ship.
Modern relativity got started when James Clerk Maxwell observed that his theory of electromagnetism appeared to be incompatible with the relativity principle. He coined the word "relativity", and suggested an experimental test.