Newton vs. Leibniz: The Nature of Time and Space

You’ve probably heard the names  Isaac Newton and Gottfried Wilhelm Leibniz, two famous scientists with differing definitions of calculus. 

However, beyond their contributions to mathematics, these two great thinkers held fundamentally different views on a monumental question: What is the nature of time and space?

In his book “Principia,” Newton claims that there exists “an absolute time.” In other words, time does not depend on the events taking place within it. Newton argues that this absolute time flows uniformly and is not influenced by any external factors. For example, just because a star moves faster does not mean that time itself flows faster. 

If you asked Newton, if there were a universe in which absolutely nothing happened, would time still flow? his answer would be yes. Events happen in time, but they do not determine the nature of time itself.

Leibniz, however, would give the opposite answer. He explicitly challenges Newton’s view in the “Leibniz–Clarke Correspondence,” arguing that time is relational rather than absolute. 

He raises an interesting question: if absolute time exists independently of events, why didn't God create the universe one year earlier? Leibniz argues that, under Newton's view, God could have created the universe one year earlier, with exactly the same sequence of events taking place. 

He then asks another question: why would God choose this particular moment to create the universe rather than an earlier one?

This question brings us to one of Leibniz's core philosophical principles: the Principle of Sufficient Reason. Put simply, Leibniz believes that everything must have a sufficient reason for being the way it is. Returning to the question of creation, Leibniz argues that a perfect God would not act without sufficient reason. Therefore, if there is no reason for God to choose one particular moment over another, the assumption of absolute time seems to violate the Principle of Sufficient Reason.

However, if time is not an independent entity but simply an order of events, then the idea of the universe being created "one year earlier" becomes meaningless. Without an independent timeline against which to compare the two universes, there would be no difference between them. Therefore, Leibniz concludes that time is not something that exists independently of events, but rather the order of succession among them.

This difference extends to the idea of space.

Similar to absolute time, Newton believes that there exists an absolute space. 

Absolute space exists independently of any external objects or their relationships, and always remains still and immovable. Imagine an empty universe with only two identical balls, where the distance between them remains constant. The question is: are these two balls moving? 

Relative to each other, they are not moving. But Newton argues that although their relative positions remain unchanged, they could still be moving together relative to absolute space.

This leads to another question: how do we know whether an object is “actually” moving, rather than simply moving relative to another object?

Enter Newton’s bucket experiment:

In the first phase, the bucket starts rotating while the water initially remains still. The bucket and the water have relative motion, but the water surface remains essentially flat. 

Moving to the second phase, the water starts rotating with the bucket, and its surface begins to become concave. 

Eventually, the water rotates at approximately the same angular velocity as the bucket, meaning that there is barely any relative motion between them, yet the water surface is still concave.

Newton uses the fact that the water remains deformed in the bucket even if there is no relative motion between the two objects as proof of some other motion. 

In reality, Newton’s bucket experiment does provide strong evidence that rotation cannot be understood simply in terms of relative motion between the water and the bucket. However, Newton’s claim of absolute space is not overtly proved by this relation either. 

Centuries later, Albert Einstein approached the relationship between motion and spacetime from a different perspective through his theory of general relativity.

Returning to Leibniz, he believed that space is also relational. He brings up an interesting conundrum: if space is absolute, then when God created the universe, he could have placed the entire universe five meters farther east rather than in its current position. Why, then, did he choose this particular position? If absolute space is uniform, there would be no sufficient reason for God to choose one location over another. Once again, the notion of absolute space directly contradicts Leibniz’s Principle of Sufficient Reason.

Thus, Leibniz concludes that the two supposedly different universes are not actually two distinct possibilities. Rather, they are the same universe described in different ways!

Beyond Newton and Leibniz, other great thinkers, such as Descartes and Einstein, were also fascinated by the mysteries of time and space and made important contributions to our understanding of them. These questions have bugged physicists, philosophers, and scientists for centuries. Whether there is a definite answer to these questions or not, the thought process behind uncovering the mysteries of space and time have resulted in some of the most astounding discoveries of the nature of our universe. 

The question, however, remains: will we ever find a definitive answer to these questions? Or maybe these questions are absolute and eternal, independent of the flow of time.