In this blog post, we will follow the reasoning from Galileo to Mach to explain the concept of the relativity of speed and position in an easy and interesting way.

Galileo and the concept of inertial reference frames

Galileo Galilei is an indispensable figure in the development of modern kinematics. He emphasized that the difference in dynamics between a state of rest and a state of constant motion cannot be detected from within. In other words, objects that appear to be at rest and objects moving at a constant speed cannot be distinguished from the perspective of an observer inside them. This can be considered the origin of the concept of inertial frames in classical mechanics. To explain this, Galileo proposed an interesting thought experiment.
He asks us to imagine that we are in a room with a fish tank in which a fly and a butterfly are flying freely and a goldfish is swimming leisurely. This room is not a simple stationary space, but is actually the cabin of a large ship. Galileo points out that the physical phenomena occurring in this cabin cannot be distinguished at all, regardless of whether the ship is stationary or moving smoothly at a constant speed.
The flies and butterflies would fly around naturally regardless of the ship’s movement, and the goldfish would swim smoothly in the water regardless of the ship’s motion. This thought experiment provides a very powerful insight. In reality, the Earth revolves around the sun at a speed of about 30 km per second and rotates once a day. However, no one feels dizzy when the Earth rotates. This is because, even though the Earth’s rotation and revolution are accelerated movements, the effect of the acceleration we can measure is negligible. This fact clearly explains Galileo’s argument about physical systems in uniform motion, or inertial frames.
According to Galileo, objects moving at a constant speed cannot know their own speed. In other words, physically meaningful speed is only relative to other objects, and it is impossible to define speed that transcends an absolute reference point. Galileo’s thinking became the basis for the concept of relativity and led to new horizons in physics.

Leibniz: Philosophy of relative distance and space

Gottfried Leibniz further expanded Galileo’s concept of inertial reference frames philosophically. He believed that if the concept of speed cannot transcend an absolute reference point, then the concept of position cannot be defined from an absolute reference point for the same reason. This view can be considered the beginning of modern theoretical physics, as it represents the convergence of philosophy and physics.
Like speed, position can ultimately only be defined in relation to other objects. For example, the statement “I am two meters away from the wall of this room” makes sense, but the statement “I am absolutely at this point” has no physical meaning. Based on this concept of relativity, Leibniz proposed a new definition of time and space.
According to him, time is a concept given by the sequence of events, and space is merely the distance between events that occur simultaneously at each moment. In other words, space is not a single entity, but a relational structure based on the configuration of events. This idea rejects the concept of absolute space and is summarized as a philosophical position that seeks to understand space as a relational entity.

Newton’s absolute space: the pinnacle of classical mechanics

However, Isaac Newton assumed an absolute space and time scale that could objectively define motion. He believed that there was an “absolutely stationary space” that could describe all physical phenomena regardless of the position or motion of any observer. For Newton, absolute space was the standard for all motion, and therefore, the speed defined in that space was absolute.
For example, just as we can measure the height of mountains and buildings in absolute terms based on sea level, measuring the motion of objects based on absolute space results in objective and definitive motion rather than relative motion. In this way, Newton accepted Galileo’s concept of inertial reference frames, but took a different direction from existing philosophical interpretations by viewing space itself as a substance.

Clarke vs. Leibniz: The Bucket Experiment and the Space Realism Debate

Samuel Clarke, a student of Newton, defended his teacher’s position and engaged in a full-scale debate with Leibniz. He attempted to prove the existence of absolute space using the example of non-inertial motion, particularly rotational motion.
Clarke presented his argument through his famous “bucket experiment.” Imagine a bucket with no handle hanging in the air and spinning around. If the bucket is empty, we have no way of knowing whether it is spinning or the universe around it is spinning. However, if the bucket contains water, the water will be pushed toward the outer wall when the rotation begins. This movement is caused by centrifugal force, and observers can objectively confirm that the rotation actually exists and that it belongs to the bucket.
At this point, Clark asks the question, “Around what is the water rotating?” The answer is absolute space. Leibniz believed that space was only relative and not real, but Clark argued that the physical phenomenon of rotation proved the reality of space. In the end, the debate seemed to be temporarily settled in favor of the existence of absolute space.

Mach’s principle: The universe’s counterattack beyond absolute space

However, at the beginning of the 19th century, another thinker brought a new twist to the debate. Ernst Mach argued that rotational motion could be explained without the concept of absolute space. He believed that if all matter in the universe moved in a certain way, physical phenomena could be explained without assuming the existence of absolute space.
Mach’s argument is based on the following thought experiment. If there is only one bucket filled with water in the entire universe, and that bucket is rotating on its own, would the water spill out? Mach believed that it would not. The phenomenon of water flowing outward is actually caused by the bucket rotating relative to all matter in the universe. In other words, rotation is not absolute, but is determined by its relationship to other matter in the universe.
Although this thought experiment cannot be directly reproduced in reality, Mach’s theory showed the possibility that Leibniz’s relational view of space could also provide a consistent interpretation of non-inertial motion. Mach’s principle had a profound influence on Einstein’s general theory of relativity and paved the way for the end of the concept of absolute space and time.

Conclusion: Absolute and relative, a never-ending quest

The concept of inertial reference frames, which originated with Galileo, fundamentally changed human understanding of the concepts of “motion,” “velocity,” “position,” and “space” through Leibniz, Newton, Clark, and Mach.
Within the framework of classical mechanics, absolute space seemed to be a valid interpretation, but philosophical reflection and natural scientific observation gradually revealed the relational and relative nature of space and time.
This discussion goes beyond the realm of physics and extends to the way we perceive the world, that is, to the question of phenomena and reality, standards and perspectives. Depending on where we stand, the world can appear completely different. This is not merely a scientific proposition, but also a starting point for epistemological reflection.