Galileo's Ship and the Relativity Principle

TL;DR

This paper clarifies the ambiguity in the classical Galilean Relativity Principle by distinguishing between two inequivalent principles, demonstrating their different roles in physics, and extending the discussion to Einstein's relativity.

Contribution

It introduces the distinction between External and Internal Galilean Relativity Principles and analyzes their different implications in classical and Einsteinian physics.

Findings

EGRP and IGRP are distinct and play different roles in physics.

Many classical systems satisfy IGRP but not EGRP.

Einstein's relativity also involves two inequivalent principles.

Abstract

It is widely acknowledged that the Galilean Relativity Principle, according to which the laws of classical systems are the same in all inertial frames in relative motion, has played an important role in the development of modern physics. It is also commonly believed that this principle holds the key to answering why, for example, we do not notice the orbital velocity of the Earth as we go about our day. And yet, I argue in this paper that the precise content of this principle is ambiguous: standard presentations fail to distinguish between two principles that are ultimately inequivalent, the "External Galilean Relativity Principle" (EGRP) and the "Internal Galilean Relativity Principle" (IGRP). I demonstrate that EGRP and IGRP play distinct roles in physics and that many classical systems that satisfy IGRP fail to satisfy EGRP. I further show that the Relativity Principle introduced by Einstein in 1905-which is not restricted to classical systems-also leads to two inequivalent principles. I conclude by noting that the phenomenon originally captured by Galileo's famous ship passage is much more general than contemporary discussions in the philosophy of symmetries suggest.