Philosophical Contemplation on Einstein's Relativity: An Introduction

Hello there. I'm Shen, and I study Philosophy and Computer Science. This is the start of a three-part series on the Theory of Relativity, from a philosophical perspective.

All Philosophy is a pursuit towards being. Whether it is political philosophy (what is legitimacy?), epistemology (what is the truth?) or even just the personal contemplations of an individual life (see Montaigne's Essays), we must have some sense of the ontology of our human-reality, in order to conduct philosophical inquiry in the first place. But yet, it is important to ground our inquiries in the facticity of our human-reality – for if we let ourselves get carried away, we might end up talking about a metaphysics which have no correspondence to our human-reality at all – in other words, we would be simply "building castles in the clouds."

Hence, any rigorous metaphysical inquiry of metaphysics must at minimum acknowledge the insights of the empirical sciences. In particular, in order to investigate space and time, we must consult not only our phenomenological experience of spatiality and temporality – but also the physical foundation of space and time. After all, Physics is a component of our human-reality, for we live in an objective reality in which the phenomena that we experience are not simply subordinate to our will. With these thoughts in mind, I began a study of Einstein's Relativity – so that I can better understand the principles of our physics, and derive insights that will better inform me on further inquiries in metaphysics as a whole.

In this process, I completed a reading of Einstein's 1917 book Relativity: The Special and The General Theory, as well as a study of his 1905 paper On the Electrodynamics of Moving Bodies. These were highly satisfying readings, which I enjoyed greatly – and with these thoughts on my mind, I find myself ready to present some contemplations on Einstein's Special and General Relativity. This article is partly an explanation of Relativity, partly a review of Einstein's book – and wholly a reflection of my contemplations, as a Philosophy student reviewing Physics.

What is the Theory of Relativity?

To begin, what is the Theory of Relativity? What solutions does it offer, and what problems does it aim to solve?

Our human-reality is a spatial and temporal reality. We exist as beings with definite extension in space, as well as a location in time. Our existence is subject to empirical principles which apply to us irrespective of our internal desires – hence we live in an objective reality. One of the necessary conditions of this objectivity, is for the same empirical principles to apply to any human being, irrespective of their perspective. We must all be subject to the same natural laws, in order for these laws to be objective in the first place.

The student of Physics can surely agree to this conclusion, for it is essentially a formulation of a more familiar principle. This is the principle of Galilean Relativity, which states that the laws of Newtonian mechanics are true for observers in any reference frame. Whether you are "at rest," on a train, or jetting across the globe on an aircraft at 300 kilometers per hour – the kinematic equations and laws of motion are equally true for all of us.

Why do we call this principle Galilean Relativity? It is a principle of relativity, insofar that the events (i.e. the phenomena, for the student of Philosophy) of a system in any reference frame is directly relatable to any other reference frame. There will always exist some method of transformation, some function, that will allow you to take the event(s) of one reference frame, and translate it into the terms of another – in a way where this transformation will preserve the underlying laws and equations of Newton. And it is Galilean, because this principle was first expressed by Galileo Galilei, in his Dialogues Concerning the Two Chief World Systems – in the most charming little thought experiment, that I will reproduce for the pleasure of my readers below:

Shut yourself up with some friend in the main cabin below decks on some large ship, and have with you there some flies, butterflies, and other small flying animals. Have a large bowl of water with some fish in it; hang up a bottle that empties drop by drop into a wide vessel beneath it.

With the ship standing still, observe carefully how the little animals fly with equal speed to all sides of the cabin. The fish swim indifferently in all directions; the drops fall into the vessel beneath; and, in throwing something to your friend, you need throw it no more strongly in one direction than another, the distances being equal; jumping with your feet together, you pass equal spaces in every direction.

When you have observed all these things carefully (though doubtless when the ship is standing still everything must happen in this way), have the ship proceed with any speed you like, so long as the motion is uniform and not fluctuating this way and that. You will discover not the least change in all the effects named, nor could you tell from any of them whether the ship was moving or standing still.

In jumping, you will pass on the floor the same spaces as before, nor will you make larger jumps toward the stern than toward the prow even though the ship is moving quite rapidly, despite the fact that during the time that you are in the air the floor under you will be going in a direction opposite to your jump. In throwing something to your companion, you will need no more force to get it to him whether he is in the direction of the bow or the stern, with yourself situated opposite. The droplets will fall as before into the vessel beneath without dropping toward the stern, although while the drops are in the air the ship runs many spans. The fish in their water will swim toward the front of their bowl with no more effort than toward the back, and will go with equal ease to bait placed anywhere around the edges of the bowl. Finally the butterflies and flies will continue their flights indifferently toward every side, nor will it ever happen that they are concentrated toward the stern, as if tired out from keeping up with the course of the ship, from which they will have been separated during long intervals by keeping themselves in the air.

And if smoke is made by burning some incense, it will be seen going up in the form of a little cloud, remaining still and moving no more toward one side than the other. The cause of all these correspondences of effects is the fact that the ship's motion is common to all the things contained in it, and to the air also.

– Galileo, Dialogues Concerning the Two Chief World Systems.

What is the Problem of Galilean Relativity, which Einstein wishes to Solve?

Galilean Relativity is reasonable and convincing, for it broadly agrees with both our lived experience, as well as rigorous (and accessible) experiments. But yet, at the turn of the 19th century, Physicists began to encounter seemingly inexplicable phenomena, which Galilean Relativity is unable to account for. What were these difficulties, which pointed towards the insufficiency of Galilean Relativity? They laid chiefly in the field of electrodynamics – the study of the behaviour of moving electromagnetic bodies. And the two most apparent difficulties were on the electrodynamics of moving bodies, and the isotropy of the speed of light.

The Electrodynamics of Moving Bodies

Move a magnet in motion past a conductor at rest, and you'll generate a moving magnetic field. As the moving field perturbs the conductor, the moving magnetic field will induce an electric field in the conductor. The electric field in the conductor becomes observable as a measurable current on our multimeter. This is Faraday's Law of Induction in effect.

\[\nabla\times\vec E=-\frac{\partial \vec B}{\partial t}\]

But yet, there exists a puzzling asymmetry. For when we move a conductor in motion past a magnet at rest, there is no moving magnetic field. And yet, an electrical current is induced in the moving conductor nonetheless. There is no electric field anywhere to be found, as there is no magnetic field in motion.

Now, it seems reasonable for us to observe a current in the second case as well as the first, for moving a magnet past a conductor and a conductor past the magnet are the same interaction, seen from different perspectives (i.e. reference frames, for the Physics student). And yet, classical electrodynamics was unable to provide a singular account for both cases. For the latter case, a different mechanism of action has to be proposed, relating to the electromotive force instead. The details of both cases are not necessary for our investigation – but the key takeaway is that the theory of classical electrodynamics required two different accounts for the same underlying phenomena. The laws of our physical reality are not the same irrespective of our reference frame, but somehow, we have fundamentally different laws for what is essentially the same phenomena.

The (Anti-)Isotropy of the Speed of Light

Imagine a train, an embankment, and two observers – one on the train, and one on the ground. The observer on the train will perceive herself to be stationary, while the observer on the ground will perceive the observer on the train to move at the speed of the train itself.

If the observer on the train were to throw a ball towards the front of the train, the speed of the ball will appear to be the speed of the train plus the speed of the ball, for the observer on the ground. And likewise, if her ball were to be thrown towards the rear of the train, than the observer on the ground will perceive the ball to be the speed of the train minus the speed of the ball.

We use the word anti-isotropic to describe this phenomena, where the speed of the ball (as observed from the ground) is different, depending on whether the ball is thrown in one direction, or another. Naturally, for the observer on the train, the ball will move at the same velocity no matter which direction she throws it – but that is only true if we were on the reference frame of the train. As observers on the ground, the ball's velocity has to be anti-isotropic.

This anti-isotropy is not a violation of Galilean Relativity. For the velocities of the ball in respect to the train and in respect to the ground are merely quantities that refer to different reference frames. And there exists definite functions to "translate" the values from one reference frame to another – namely adding or subtracting the velocity of the train itself. This transformation preserves the kinematic equations and Newtonian laws of motion, so this anti-isotropy is a welcome sign that all is well in our physics.

At the close of the 19th century, Physicists tried to discover this anti-isotropy in the speed of light, and failed. Light, as an electromagnetic wave – must propagate within a definite medium, an electromagnetic field. This is the train from our analogy. And whatever our velocity is in relation to this field, we must be able to observe a similar anti-isotropy in the speed of light depending on whether we are moving with the motion of the field, or against the motion of the field.

Are we moving with the motion of the electromagnetic field, or against the motion of the electromagnetic field? Well, since the Earth orbits the sun in a circle, we would be moving both with the field, and against the field, at different points of our orbit.

Hence, a good way to uncover the anti-isotropy of the speed of light, is to measure it during different times of the year. This way, we will get to measure the speed of light while we are moving in different directions within this "lumiferous aether," and whenever we are aligned with it, light would move slightly faster, or slower, if we are moving against the aether.

But yet, despite the best and most exacting experiments of the Physcists of the time, we were unable to discover any anti-isotropy in the speed of light. The speed of light was the same, no matter our reference frame, in respect to the "aether." This culminated in the famous Michelson-Morley experiment of 1887, in which the existence of the "aether wind" was conclusively proven to be false.

This is a fatal problem for the Galilean Relativity of Classical Mechanics. Because now, there is a phenomena – the speed of light – which is the same no matter the observer's reference frame, or perspective. You could be traveling on a rocket at 95% the speed of light, and shoot a laser beam forwards – and that laser beam will move at exactly \(c\), for both you on the rocket – as well as me, an observer on the ground. Somehow, the speed of light is no longer objective, insofar Classical Mechanics is concerned. It has become a constant those constancy seems subjective to the observer's perspective – a metaphysical solipsism that is deeply troubling for our system of physics as a whole.

These are the two difficulties of Classical Mechanics, at the end of the 19th century. Somehow, the Galilean Relativity of Newton are unable to account for the theory of electrodynamics at all.

This is the background behind the project of Einstein's theory. We are faced with an incomplete system of physics, in which our laws of motion are invariant in respect to reference frame, but yet our laws of electrodynamics are not. But yet, it cannot possibly be the case that our laws are not invariant in respect to reference frame, for the laws of physics privilege no perceptual subject – it is an objective science.

Examples of this sort, together with the unsuccessful attempts to discover any motion of the earth relatively to the “light medium,” suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest. They suggest rather that, as has already been shown to the first order of small quantities, the same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good.
– Einstein, On the Electrodynamics of Moving Bodies

Concluding Remarks

What does it even mean to have physical laws which are not invariant in respect to a reference frame? Is this a possibility that we can tolerate in any case?

We cannot tolerate it. It would be a disastrous flaw within the ontology of our physics, for it destroys all possibility of objectivity. Physical laws must be the same no matter our perspective – both on the practical grounds of experimental physics, as well as on a priori principles of metaphysics too. To paraphrase Jean-Paul Sartre, any theory of knowledge presupposes a metaphysics. Ontologically, to state that physical laws are variant in respect to perspective, is to reduce our system of metaphysics to a dangerous solipsism – the world no longer has properties which are independent of my will.

This is where Einstein begins his pursuit. An attempt to furnish an account of physics, one in which both the laws of electrodynamics, as well as the laws of kinematics, are valid and invariant, for all reference frames. This is the problem of Galilean Relativity which Einstein's Relativity aims to solve.

We will examine Einstein's Special Relativity in the next installment of this series, followed by an account of Einstein's General Relativity as a whole. In particular, we will look at what Relativity means, in terms of the spatial and temporal condition of our human-reality.

Thank you for reading my article. For updates on the series, feel free to subscribe to my RSS feed. If you have any thoughts, comments, or feedback, feel free to contact me. I am particularly interested in conversations with Physicists and Physics students, who can help me further my understanding of Einstein. Write to me, and let me know of your thoughts!