In 1915, Albert Einstein wrote a letter to the philosopher and physicist Moritz Schlick, who had recently composed an article on the theory of relativity. Einstein praised it: ‘From the philosophical perspective, nothing nearly as clear seems to have been written on the topic.’ Then he went on to express his intellectual debt to ‘Hume, whose Treatise of Human Nature I had studied avidly and with admiration shortly before discovering the theory of relativity. It is very possible that without these philosophical studies I would not have arrived at the solution.’

More than 30 years later, his opinion hadn’t changed, as he recounted in a letter to his friend, the engineer Michele Besso: ‘In so far as I can be aware, the immediate influence of D Hume on me was greater. I read him with Konrad Habicht and Solovine in Bern.’ We know that Einstein studied Hume’s Treatise (1738-40) in a reading circle with the mathematician Conrad Habicht and the philosophy student Maurice Solovine around 1902-03. This was in the process of devising the special theory of relativity, which Einstein eventually published in 1905. It is not clear, however, what it was in Hume’s philosophy that Einstein found useful to his physics. We should therefore take a closer look.

In Einstein’s autobiographical writing from 1949, he expands on how Hume helped him formulate the theory of special relativity. It was necessary to reject the erroneous ‘axiom of the absolute character of time, viz, simultaneity’, since the assumption of absolute simultaneity

unrecognisedly was anchored in the unconscious. Clearly to recognise this axiom and its arbitrary character really implies already the solution of the problem. The type of critical reasoning required for the discovery of this central point [the denial of absolute time, that is, the denial of absolute simultaneity] was decisively furthered, in my case, especially by the reading of David Hume’s and Ernst Mach’s philosophical writings.

In the view of John D Norton, professor of the history and philosophy of science at the University of Pittsburgh, Einstein learned an empiricist theory of concepts from Hume (and plausibly from Mach and the positivist tradition). He then implemented concept empiricism in his argument for the relativity of simultaneity. The result is that different observers will not agree whether two events are simultaneous or not. Take the openings of two windows, a living room window and a kitchen window. There is no absolute fact to the matter of whether the living room window opens before the kitchen window, or whether they open simultaneously or in reverse order. The temporal order of such events is observer-dependent; it is relative to the designated frame of reference.

Once the relativity of simultaneity was established, Einstein was able to reconcile the seemingly irreconcilable aspects of his theory, the principle of relativity and the light postulate. This conclusion required abandoning the view that there is such a thing as an unobservable time that grounds temporal order. This is the view that Einstein got from Hume.

Hume’s influence on intellectual culture is massive. This includes all areas of philosophy and a variety of scientific disciplines. A poll conducted with professional philosophers a few years ago asked them to name the philosopher, no longer living, with whom they most identify. Hume won, by a clear margin. In Julian Baggini’s estimation, contemporary ‘scientists, who often have little time for philosophy, often make an exception for Hume’. Before saying more about Hume’s permanent relevance, we should go back to the 18th-century early modern context. His influence is due to his radical empiricism, which can’t be fully understood without examining the era in which he worked.

The dominant theory of cognition of early modern philosophy was idea theory. Ideas denote both mental states and the material of our thinking. A mental state is, for example, a toothache, and the material of our thinking are thoughts, for example, of a mathematical object such as a triangle. The clearest proponent of the theory of ideas was the French philosopher René Descartes, for whom philosophical enquiry is essentially an investigation of the mind’s ideas. In one of his letters, he explains why ideas are so important: ‘I am certain that I can have no knowledge of what is outside me except by means of the ideas I have within me.’ If we wish to gain any certainty in our investigations of any aspect of the world – whether the object of our investigation is the human mind or some natural phenomenon – we need to have a clear and distinct idea of the represented object in question.

Hume’s theory of ideas differs from Descartes’s because he rejects innatism. This view goes back to Plato’s doctrine of anamnesis, which maintains that all learning is a form of recollection as everything we learn is in us before we are taught. The early modern version of innatism emphasises that the mind is not a blank slate, but we are equipped with some ideas before our birth and sensory perception. Hume starts at the same point as his fellow Briton and predecessor, John Locke. The mind begins to have ideas when it begins to perceive. To ask when a human being acquires ideas in the first place ‘is to ask when he begins to perceive; having ideas and perception being the same thing,’ writes Locke in An Essay Concerning Human Understanding (1689). Drawing on this insight, Hume devised his copy principle.

Hume submits that we get the idea of time by perceiving change

Perception, for Hume, is divided into ideas and impressions. The difference between the two is a difference of degree, not kind. Impressions are more forceful and lively than ideas. For instance, I remember that as a kid I put my finger on our living room’s fireplace window. When I had my finger on the glass, I felt pain (impression), and now I have a recollection of that perception (idea). All simple ideas resemble some simple impressions. Ideas are copies of impressions. If any term is to be meaningful, it needs to be attached to an impression-based idea. In his later work An Enquiry Concerning Human Understanding (1748), Hume proposed to use his copy principle as a cognitive test that would ‘banish all that jargon, which has so long taken possession of metaphysical reasonings, and drawn disgrace upon them’. This is how the principle should be applied:

When we entertain, therefore, any suspicion, that a philosophical term is employed without any meaning or idea (as is but too frequent), we need but enquire, from what impression is that supposed idea derived? And if it be impossible to assign any, this will serve to confirm our suspicion.

Can we annex the term ‘absolute time’ to some impression-based idea? Here we can already see ‘the type of critical reasoning required’ for the discovery of special relativity that Einstein talks about. The copy principle is important for understanding Hume’s philosophy of time. How do we acquire the idea of time in the first place? He presents his argument in the second part of the first Book of his Treatise, where he submits that we get the idea of time by perceiving change. It ‘can never be convey’d to the mind by any thing stedfast and unchangeable’, Hume writes. Change is observable either in the succession of objects or in their relative motions. A good example of succession is the sequence of musical chords. We do not get time’s idea from a single ongoing chord. Instead, there must be a succession: chord, pause, chord, a different chord, and so on. Another source for the idea of time is observable relative motion. Perceiving motion causes an idea of time because ‘every moment were distinguish’d by a different position’ of the moving object.

Time, as it appears to us, is made of indivisible moments that are parts of succession. In the interpretation offered by the philosopher Donald L M Baxter in Hume’s Difficulty (2007), a single moment cannot have a duration. Something counts as a duration only if it is a temporal complex. We must perceive a change with respect to moments; otherwise we could not abstract the idea of time. There is an analogy that I have suggested earlier for understanding Hume’s reasoning on this matter. Imagine a stationary observer in front of a huge grey wall. The wall is evenly painted, and it covers the observer’s whole visual field. In this scenario, there is nothing changing in front of her. The wall is a steadfast object. It has no duration. Such an unchangeable object cannot be the source for the idea of time alone. Now, if something is changing, like a blue object moving in front of the wall, then the observer will be able to acquire the idea of time through the object’s change of place. Although the wall is a steadfast object, the moving item is not. When it is moving, it is changing its location with respect to the observer. However, this change is relative to the observer’s viewpoint. If the observer would be moving together with the object at the same relative velocity, there would be no change and therefore no duration in her viewpoint.

Hume’s philosophy of time shows the fundamental relevance of the relation between an observer and a reference object. There is no evidence for absolute, self-existing time. Nor is there evidence for one universal time. There are different times, depending on the observer/reference-object relation. It is not ‘possible for time alone ever to make its appearance’, as ‘time is nothing but the manner, in which some real objects exist,’ writes Hume. Based on this dictum, in his 2007 biography of Einstein, Walter Isaacson alludes that Hume’s rejection of absolute/universal time ‘would later echo in Einstein’s theory of relativity’.

Hume’s empiricist notion of time stands in contrast to influential pre-relativity accounts of time. Take Isaac Newton’s concept of time in his classical dynamics. He argues for absolute time in his monumental Principia: Mathematical Principles of Natural Philosophy (1687). In the context of the argument, Newton claims that the quantity of time (along with space, place and motion) is ‘popularly conceived solely with reference to the objects of sense perception’. Then he goes on to distinguish between absolute, mathematical time and relative, measurable time, like clock time. Absolute time exists substantially by itself. Its existence is independent of change. Whatever physical there is in the Universe, and however it moves, it does not have an influence on time itself. Time has a definite structure: it flows equally and unidirectionally. Consequently, the time difference between two simultaneous events is zero, and the time difference between two successive events is not zero. Everyone would agree on this, according to Newton. Temporal order and direction is grounded in time itself.

Initially, it might seem that Newton is committed to some dubious metaphysical speculation by assuming utterly unobservable entities. The philosopher Tim Maudlin notes in Philosophy of Physics (2012) that Newton’s position is, to the contrary, perfectly intuitive:

It sounds as if Newton is postulating some weird, ghostly, unfamiliar entities, but most people conceive of the physical world in terms of absolute space and time. For example, craftsmen and scientists continually try to improve the design of timepieces, to produce clocks that are ever more accurate and precise. But what is it for a clock to be ‘accurate’? What we want is for the successive ticks of the clock to occur at equal intervals of time, or for the second hand of a watch to sweep out its circle at a constant rate. But ‘equal’ or ‘constant’ with respect to what? With respect to the passage of time itself, that is, with respect to absolute time.

Another highly influential view of time that differs from Hume’s is embodied in Immanuel Kant’s transcendental idealism. Kant presents this argument in his major work, Critique of Pure Reason (1781). Here, he clearly criticises Newton’s position, according to which time exists by itself. According to Adrian Bardon in A Brief History of the Philosophy of Time (2013), Kant focuses on the adverbial use of the concept of time, not on its substantive use. This means that we experience things temporally, not in time. Time is not a thing in itself; it is a subjective human precondition. In Kantian terminology, time is an a priori form of sensibility. Kant doesn’t think that time is an innate idea. Rather, our minds impose the temporal order we experience. He puts the point as follows:

Time is not an empirical concept that is somehow drawn from an experience. For simultaneity and succession would not themselves come into perception if the representation of time did not ground them a priori. Only under its presupposition can one represent that several things exist at one and the same time (simultaneously) or in different times (successively).

It is stunning how Humean Einstein is in his opposition to Newton and Kant. The application of concept empiricism gave Einstein the means to discard the absolutist and transcendental arguments. Postulating that light’s speed is the same in all directions, the empiricist argument destroys absolute simultaneity. There is no time itself that exists independently of the selection of the frame of reference, as Newton has it. And time is not grounded in human intuition, because it is an empirical concept, unlike how Kant thought. Hume would very much nod to this conclusion. Absolutist argument invokes an utterly imperceptible structure of time, and the transcendental argument leans on a priori factors of cognition. The copy principle rules out both. For Hume as for Einstein, time is an empirical concept.

However, the Hume-Einstein connection should not be exaggerated. It would be wrong to say that Hume anticipated the scientific theory of relativity. There is simply no way that he could have predicted it. The theory was a product of an industrialised society that emerged after he wrote his Treatise. Einstein’s original paper, ‘On the Electrodynamics of Moving Bodies’ (1905), was the result of critical reflection of the 19th-century electromagnetic physics, as encoded in Maxwell’s equations.

The opening section of the original publication concerns Michael Faraday’s law of electromagnetic induction. Einstein presents a thought experiment with a magnet and a coil, by which he extends the principle of relativity to electrodynamics. Consequently, absolute electric fields, as well as absolute quantities of time and space, had to be relativised. Moreover, in the definition of simultaneity in the original publication, Einstein focuses on clock synchronisation. Along with electromagnetic induction, which is of the utmost importance in energy production, the synchronisation of clocks is also very much an aspect of the industrialised society: the 19th century saw an increase of train traffic that required considerable improvements of timekeeping. None of this could have been known to Hume.

Yet there is still something profoundly intriguing about Hume’s views. He did envisage a philosophy of time that is consistent with the relativity theory, and his critical reflection enabled him to articulate a view very much against common sense. This is what special relativity also did. The ramifications of abjuring absolute and universal time are astonishing. Due to time dilation, a parent can be younger than their child. Many philosophers have argued that relativity is consistent with an eternalist and static view of the world: the past, the present and the future are all equally real; there is no definite flow of time from earlier to later. Hume could not see the implications so specifically, of course, but he was conscious that his views on time were against the natural philosophical mainstream and the intuitions of an everyday conception of the world:

I know there are some who pretend that the idea of duration is applicable in a proper sense to objects, which are perfectly unchangeable; and this I take to be the common opinion of philosophers as well as of the vulgar.

Because of his strict empiricism, Hume cannot accept the notion of time itself that is independent of change. There is no sensory evidence for universal, self-sustaining time that flows equably, no matter what: ‘Ideas always represent the objects or impressions, from which they are deriv’d, and can never without a fiction represent or be apply’d to any other.’ As Baxter comments: ‘There is no observable evidence that the structure of time is uniform across space.’ This is very close to the kind of reasoning that pertains to Einstein’s argument for the relativity of distant simultaneity.

Despite many contributions from Hume’s side, there is a notable discrepancy between his views and the metaphysics required by relativity. This incongruity is related to sceptical doubts concerning metaphysical realism. Hume is usually taken to be an agnostic about the existence of mind-independent entities, such as objects, events and causal powers. In everyday life, he certainly believed in the continuous existence of a world-out-there. Here’s the problem, though. The copy principle maintains that impressions cause our ideas. But what causes the impressions in the first place?

The event-realism in relativity is in tension with Hume’s radical and sceptical empiricism

Hume is a radical empiricist and therefore agnostic on whether our impressions are caused by natural events that happen before and independent of our perceptions. In the third part of the first Book of the Treatise, he puts the point as follows:

As to those impressions, which arise from the senses, their ultimate cause is, in my opinion, perfectly inexplicable by human reason, and ’twill always be impossible to decide with certainty, whether they arise immediately from the object, or are produc’d by the creative power of the mind, or are deriv’d from the author of our being. Nor is such a question any way material to our present purpose. We may draw inferences from the coherence of our perceptions, whether they be true or false; whether they represent nature justly, or be mere illusions of the senses.

Our perceptions can be caused by mind-independent nature, by our minds themselves, or by God. This is a thoroughly sceptical remark: there is no way to tell which of the three – or perhaps more – options is the right one. In Hume’s view, we cannot even think of reality itself, because we cannot form an idea of a thing in itself. This would be an object without any sensory qualities, something ‘beyond the reach of human conception’, he writes. As we don’t have an idea of a self-existing reality, we don’t have a reason to believe in it. This follows from what the Hume scholar Miren Boehm in 2013 called a ‘No Reason to Believe’ principle: if we are to believe in something, we must have its idea. We don’t have the idea of an external reality. No matter how much we think about the problem, we cannot reason our way out of the sceptical challenge.

How is the problem of metaphysical realism relevant to special relativity, and the philosophy of time? The theory requires that an event happens before and independent of it being observed. As all signals travel slower than or at the speed of light, the sending of the signal happens before the receiving of the signal. Although the corollaries of special relativity are mind-boggling, the theory is in this regard commonsensical. Think about an example like this. On New Year’s Eve, I see a firework in the sky. There is a physical event, the explosion, in a space distant to me. Light and sound waves propagate with finite velocities; it takes time before I receive information of the explosion. It must be that the event took place before my visual and auditory perceptions. If I didn’t shoot the rocket or have anything to do with the causes that brought it up to the sky, it must be that the explosion happened entirely independent of me. Yet the explosion caused my visual and auditory impressions.

Einstein himself had deep sympathies with realist philosophy; so much that the indeterminacy of quantum mechanics was repugnant to him. The event-realism in relativity is in tension with Hume’s radical and sceptical empiricism. One should allow a distinction between perceptions and physical events, and agree that our perceptions are caused by natural events that occur independently of us. Hume’s rigidly empiricist stance does not countenance such a conclusion.

The Hume-Einstein connection is multifaceted, and raises fascinating connections between science and philosophy. When examining the nature of time, we enter a grey area in which physics and philosophy overlap. This is the proper field for natural philosophy, a combination of ambitious philosophical thinking and scientific acumen. Hopefully, natural philosophy will not be only a thing of the past, but we will revive it.