Quantum Reality (I): The Measurement Problem

Quantum mechanics. It’s weird, complex, and highly esoteric. Physicists have used quantum theory to make incredibly successful predictions – calculating everything from the energy levels of the hydrogen atom to the anomalous magnetic moment of the electron, to incredible precision. Yet despite all this, the implications of quantum mechanics remain mysterious.

I think the main barrier to understanding what quantum mechanics has to say about reality is that there has never been a clear consensus on what quantum mechanics is fundamentally about – and very few physicists have bothered to really answer that question.

Again, this is in part due to the influence of the philosophy of logical positivism, which also so affected the debate about the nature of time. Whatever reality underlies physics is not something that can be empirically observed, so physicists have mostly concerned themselves with predicting measurement results, without really seeking to go further with the more philosophical questions.

So by something of a historical accident, the main concepts of quantum theory were developed without any clear specification of what they really meant, or how they related back to the reality that we observe. And the interpretations of the theory have multiplied every since.

A Brief History of Quantum Mechanics

In the same year, 1905, that Albert Einstein produced his special theory of relativity, he also made a huge contribution to the other pillar of modern physics, quantum mechanics. His discussion of the photoelectric effect showed that the energy of electromagnetic radiation is absorbed and emitted in discrete amounts – quanta of energy – where the amount of energy in each discrete unit is proportional to the frequency of the radiation.

This suggested that a wave of electromagnetic radiation could somehow also behave as if was made of particles. This insight led another physicist, Louis de Broglie, to propose a radical hypothesis, the other half of wave-particle duality: that particles could somehow also behave as if they were waves. And indeed, it was discovered that they can. Electrons and other particles diffract and form interference patterns like waves, with wavelengths inversely proportional to their momentum. In the weirdness of quantum mechanics, this behaviour persists even at the level of individual particles.

The duality between particles and waves is what prompted Erwin Schrodinger to formulate what is probably the most fundamental equation of quantum mechanics – Schrodinger’s equation. This is where the modern form of quantum mechanics began, and the mathematics of the theory began to eclipse its physical interpretation.

In crafting his theory, Schrodinger looked for an equation that would have the correct mathematical behaviour before anything else – he wanted a wave equation that would produce the relationships between energy and frequency on one hand, and wavelength and momentum on the other, that were seen in the experimental indications of wave-particle duality.

And indeed, he did find such an equation, and used it to correctly predict the energy levels of the hydrogen atom. But the fundamental object in his equation was now a complex-valued mathematical entity called a wavefunction, and what it represented physically was something of the mystery, even to Schrodinger.

(This, by the way, is where imaginary numbers made their first appearance in quantum physics. They show up in Schrodinger’s equation not because of any physical reality they represent, but because they are a convenient way to get the periodic wave behaviour that he wanted. Imaginary numbers entered into quantum mechanics a second time in a similar way, when Paul Dirac was trying to find mathematical objects that would obey certain relations for his equation.)

The wavefunction was retroactively interpreted by most physicists to represent a probability amplitude, a complex quantity with a phase, which allows it to produce wave-like interference effects, and a magnitude, related to the probability that a quantum system may be found in a certain state. The fact that the wavefunction is viewed as the fundamental object of physics is one of the main things that makes quantum mechanics so difficult to understand.


There is a serious conceptual problem with considering the wavefunction as a probability amplitude and simultaneously considering it to be a complete description of the physical system. This is the measurement problem, and it involves the quantum mechanical phenomenon of superposition.

I apologise for the next few paragraphs. I could not figure out how to describe this phenomenon concisely without using a few arbitrary variables. (For a more in-depth explanation, with better examples, David Albert’s book Quantum Mechanics and Experience is a decent resource.)

A quantum system in a superposition of two states, lets say A and B, is such that, when you make a measurement that can determine whether it is in A or B, there is some probability of the system being found in state A and some probability of it being found in state B. (This is just an operational definition: I’m afraid it really tells you nothing about what a superposition is like.)

Let’s say that the probability of it being found in each state is 50%. The strange thing about quantum mechanics is that such a system does not behave as a system that has a 50% probability of being in A and a 50% probability of being in B. We would expect it to behave half the time as if it were in state A and half the time as if it were in state B, but in many cases it does not do that. In fact, a system in superposition of states A and B can exhibit behaviour that neither states A nor B themselves can.

(A well-known example of such extraordinary behaviour is the double-slit experiment, where a particle ends up in a superposition of going through two slits in a screen, creating an interference pattern that cannot be created by particles known to be going through one of the slits.)

So a system in a superposition of states A and B is not in state A, and not in state B, because it shows behaviour that neither state individually can show. But it is always found in exactly one of A or B when it is measured, so in some sense it is not in neither A nor B, and it not in both A and B. A superposition is a very strange, seemingly contradictory state of affairs.

Now, a very important feature of quantum mechanics is that the equation which governs the wavefunction (that is, Schrodinger’s equation) preserves superpositions. This means: if the equation says that state A evolves into state C, and that state B evolves into state D, then the equation says that a superposition of A and B evolves into a superposition of C and D.

This feature leads directly to the measurement problem.

The Measurement Problem

The measurement problem comes about when we ask quantum mechanics to describe what happens when we take a measurement to find the state of a quantum system. To do this, we have to treat the measurement apparatus as second quantum system, interacting with the first. (Which, if quantum mechanics is an accurate description of physical reality, is exactly what the measurement apparatus should be.)

Let’s consider the system I described above, in a superposition of states A and B (with 50% probability of being found in each). A measurement apparatus that can accurately determine whether this system is in A or B should have the following properties:

  • When it interacts with a system in state A, it evolves to the state “displaying result A”.
  • When it interacts with a system in state B, it evolves to the state “displaying result B”.

These properties, combined with the fact that the equations of quantum mechanics preserve superpositions, directly imply that:

  • When the measurement apparatus interacts with a system in a superposition of states A and B, it evolves to be in a superposition of “displaying result A” and “displaying result B”.

And this is in direct contradiction to the experimental results. Because what actually happens is this:

  • When the measurement apparatus interacts with a system in a superposition of states A and B, it has a 50% chance of displaying result A, and a 50% chance of displaying result B. (For the system described above. In general, the chances depend on the superposition.)

These are two very different situations. If the measurement apparatus is in a superposition of displaying two different results, it is not displaying one or the other, or both, or neither. Instead, it is some strange mode of existence that we really do not understand. (The usual illustration of the role of superposition in the measurement problem is, of course, is the story of Schrodinger’s cat.)

It gets worse. According to the operational definition I gave earlier, if the measurement apparatus is in a superposition of two different states, that means that when the apparatus itself is “measured,” it has some probability of being found in either state. So how do we “measure” the measurement apparatus? Well, we simply look at the readout and see which result it displays.

But if we ourselves are physical systems, then according to quantum mechanics, what happens when we look at the measurement apparatus is that we ourselves enter into a superposition of “seeing result A” and “seeing result B”. This is even more blatantly in opposition to the evidence. We have direct introspective access to our own experiences, and no experimenter has ever reported experiencing a superposition of mental states. We know what we experience if we know anything at all, so either quantum mechanics is wrong, or we are wrong – possibly about everything.

I should note here that when a macroscopic system like a measurement apparatus enters into a superposition, what almost inevitably happens is a phenomenon called decoherence. After decoherence, the different states of the superposition no longer interfere with each other and can evolve independently. So if a superposition of states A and B experiences decoherence, its subsequent evolution could be described completely in terms of the way that systems definitely in state A or B would evolve. This suppresses some of the strange behaviour characteristic of quantum systems.

But decoherence does not remove the measurement problem. Decoherence does not cause the measurement apparatus to definitely enter one state or the other: the superposition still exists, it just behaves more simply. The measurement apparatus is still in this strange mode of existence where it is not displaying result A, and not displaying result B, and not both, and not neither.

So, if the wavefunction is a complete description of a physical system, and the standard equations of quantum mechanics are correct and apply to the whole universe, then the “measurement” process that is supposed to resolve superpositions – and the resulting process of wavefunction collapse – never actually occurs.

But in order for quantum mechanics to make predictions that match our experience, and for the interpretation of the wavefunction as a probability amplitude to make any sense, wavefunction collapse must occur. The measurement problem reveals that the standard interpretation of quantum mechanics is either inconsistent, incorrect, or incomplete.

We can also see the measurement problem as revealing a different conceptual problem with quantum mechanics: the standard interpretation of quantum theory introduces an unacceptably vague and ad-hoc division between quantum systems (for which the wavefunction obeys the Schrodinger equation) on one hand, and classical systems (or measurements, or observers, inducing collapse in the wavefunction) on the other. There is no non-arbitrary way to precisely define this division, so as long as it persists, quantum mechanics cannot be regarded as a complete theory of physics.

In my post after next, I will explore the various ways we can resolve the measurement problem and interpret the empirical evidence for quantum mechanics in a coherent way. But first, I want to explore some further aspects of quantum weirdness.

Relativity and the Nature of Time

In my exploration of the nature of reality, my experience of the passage of time, and change, has led me to believe in presentism and the A-theory of time, and I have found that a number of philosophical objections to this position are unable to defeat it. But there is one more challenge to face, and not a few physicists and philosophers think that eternalism defeats presentism on this point alone.

So now, I have finally come to the question of what implications Einstein’s theories of relativity have on the nature of time.

As they are traditionally formulated, these theories are not about space and time, but about spacetime. Space and time are inextricably bound together, and where we draw the line between them depends upon what coordinate system we use to describe reality. The intertwining of space and time in relativity physics is one of the main motivations for thinking that time is just another dimension, like the three dimensions of space, and that non-present times are like distant spatial locations.

The other significant reason to believe in eternalism on the basis of relativity physics is the fact that Einstein’s theories do not feature any relation of absolute simultaneity. If there is an objective present, it appears to pass without leaving any trace of which distant events are truly simultaneous with each other, and which ones are not.

Relativity Theory

Einstein’s special theory of relativity was motivated by a couple observations. First, the reigning physics of that time, Newtonian mechanics, implied that an observer who was not being acted upon by any forces would not be able to determine by any experiment whether he was moving or at rest, except relative to other objects.

Measuring the speed of something requires us to know the distance between two points in space at different times. If we have a way to know that, we can use that knowledge to trace a point in space across time: two points at different times are really the same point if the distance between them is zero. Alternatively, if we have a way to trace points across time, along with a way to measure the distance between two points at the same time, then we can put them together to find the distance between points at different times.

Now, Newtonian mechanics does not give us any way to determine which points at different times are the same. In other words, it gives us no notion of absolute rest, no way to determine whether we are staying at one point in space or moving from one to another. (Newton himself believed that there was such a thing as absolute rest, but the laws of physics that he devised did not require it and could not discover it.) But we can stipulate a relation of being at the same point relative to some object: being the same distance away in the same direction from that object. This specifies a reference frame or a coordinate system that we can use to describe reality.

So only relative motion, not absolute motion, is detectable by physics. If you’ve ever been on an airplane you have seen this in action: provided the plane is flying smoothly in a straight line and there is no turbulence, if you don’t look out the window, you can forget that you are moving at hundreds of kilometers per hour. Einstein believed this property would have to be satisfied by whatever physics came after Newtonian mechanics as well. Specifically, his first postulate was that the laws of physics have the same form in all inertial reference frames, that is, all reference frames from the perspective of an observer not being acted upon by any external forces.

Second, by Einstein’s day, experiments had been devised to measure the speed of light. These experiments measured it to be the same in all directions, no matter the state of motion of the observer. This is what motivated Einstein’s second postulate, that the speed of light is constant in all directions. (At first glance this sound just like a restatement of what the experiments discovered – but that isn’t exactly the case, and I’ll talk about why in a moment.)

Now, these experimental results were very surprising. According to Newtonian mechanics, relative velocities simply add together. If I am standing by the road and see a car moving past me at 20 km/h, and the driver of that car sees another car moving away from him, in the same direction, at 60 km/h, I would expect to see the second car moving at 80 km/hr – not the same 60 km/h that the driver of the first car sees. Yet the experimental results implied that two observers moving relative to each other measure the exact same speed of light.

So, while the equations of electromagnetism predicted that light would travel in the same speed in all directions, the general expectation was that these equations would only be correct in one specific reference frame: the rest frame of the “aether” through which light was thought to propagate. One of the main goals of these experiments was to discover just which reference frame was at rest relative to the aether. And the apparent answer was, “all of them are.” It seemed that no matter how fast or in which direction you are moving, the aether is there moving with you.

Einstein’s second postulate says that the speed of light appears to be the same in all directions because it is the same in all directions, no matter your state of motion, and no matter the counterintuitive implications of that fact. To clarify things, however, I want to compare Einstein’s theory of special relativity to a rival interpretation of the data.

The Lorentz Aether Theory

Even before Einstein entered the scene, there was an explanation of these experimental results, known as the Lorentz aether theory. Contrary to the theory of special relativity, it postulates that there is one reference frame in which the speed of light was the same in all directions – the rest frame of the aether – and that in this reference frame, all the laws of physics share a special mathematical symmetry with the equations of electromagnetism, called Lorentz symmetry.

The Lorentz theory turns out to imply that any physical system that was moving relative to the aether rest frame would contract along the direction of its motion, and that any physical processes in such a system would slow down. A ruler moving in a direction along its axis gets shorter, and a moving clock ticks at a slower rate, compared to the same ruler or clock at rest. These two effects work together to make it appear that the speed of light is the same in all directions, even relative to a moving reference frame (when, in reality, it is the same in all directions only in the aether rest frame).

When I say that the Lorentz aether theory makes it appear that the speed of light is the same in all directions, what I mean is it implies that the two-way speed of light will be measured to be the same in all directions, by all observers. (The two-way speed of light is the average speed of a flash of light as it goes from point A to point B and back.) This matches the empirical evidence: the speed-of-light-measurement experiments all measure the two-way speed, not the one-way speed. Which is why Einstein’s second postulate is more than a restatement of the experimental results: it is about the one-way speed instead of the two-way speed.

The effects of length contraction and time dilation that affect moving systems make it so that the two-way speed of light is always measured to be the same. But even more than that, they make it impossible to measure the one-way speed of light. In order to measure the one-way speed, you would have to have synchronized clocks separated by some distance. But it turns out, in the Lorentz theory, that you cannot correctly synchronize distant clocks unless you know how fast you are moving relative to the aether rest frame.

How might we synchronize two distant clocks? Well, one way is to synchronize two clocks that are not separated in space – that can be done easily – and then separate them. But to do that we have to move at least one of them. Moving the clock relative to the aether frame causes it to tick more slowly, so it gets out of sync.

Maybe we can separate them very slowly, so that the effect of time dilation is negligible? No, not if we are moving relative to the aether – the reduction of the time dilation effect is exactly cancelled out by the increase in time it takes to get the same distance away, so the clocks are still out of sync after separation. This procedure only works correctly if you already know that you are at rest relative to the aether.

Here’s another procedure we can use to synchronize distant clocks. Send a flash of light (or a radio signal, or some other light-speed message) to your friend, who is waiting to receive your signal some distance away. When he receives it, he immediately sends a signal back to you, and sets his clock to zero. Then you wait until you receive his signal.

The seemingly natural thing to do at this point is to set your clock so that it would read zero halfway in between when you sent your signal and when you received his. But that would only be correct if the time it took for your signal to reach your friend was the same as the time his signal took to get back to you – that is, if the two signals travelled at the same speed in your reference frame. But that will only be the case if you are at rest relative to the aether.

So, we can only measure the one-way speed of light if we can synchronize distant clocks, and to synchronize distant clocks we need to know our speed relative to the aether. And the only way we could know that is by measuring the one-way speed of light. There seems to be a grand conspiracy in the laws of physics that prevents us from detecting the motion of the aether. The Lorentz theory tells us there is one correct reference frame from which to describe reality, and then it prohibits us from ever finding it.

In contrast, what Einstein’s theory of special relativity really says is that every inertial reference frame is the correct one. The speed of light is constant in all directions, not just in appearance, but in actuality. Rather than being unable to know how to correctly synchronize our clocks, it says we can synchronize them no matter how fast or which way we are moving. Since synchronizing clocks is just the same as determining whether two distant events are simultaneous, special relativity says we can determine simultaneity.

What happens when we do that, though, is that the simultaneity of distant events is relative to one’s reference frame. An observer who is moving relative to you can find different answers about the order of events. If two events A and B are far enough apart in space (far enough that a light signal could not travel from one to the other in the time that passes between them), it is possible for you to discover that A happened before B, while at the same time she discovers that B happened before A.

Since special relativity says both answers are right, any notion of absolute simultaneity must be discarded. (In contrast, the Lorentz aether theory says the only correct answer is the one obtained in the aether rest frame.) Unless you are willing to say that what exists is relative – which is an incoherent notion, as far as I can see – this means that eternalism must be true if the usual understanding of relativity theory is correct.

Nowadays, the Lorentz theory that I have described is generally regarded as an unorthodox interpretation of special relativity theory, rather than as a separate theory in its own right. For one thing, it doesn’t need the aether, which can be understood merely as an abstract designator for the preferred reference frame. But most importantly, the Lorentz theory is empirically equivalent to the usual interpretation of special relativity: it makes exactly the same predictions about what we can observe and measure.

Because of this empirical equivalency, Einstein’s postulates can never be experimentally verified over the postulates of the Lorentzian interpretation. Deciding between them is not strictly a question of science, but of philosophy.

The Argument from Relativity

Since the Lorentzian interpretation is a coherent one, the argument for eternalism from relativity cannot just be that physics proves that presentism is false. The usual spacetime interpretation implies eternalism, but the Lorentzian interpretation is perfectly compatible with there being an objective present, and it has exactly the same degree of experimental validation.

So the argument from relativity has to be that the spacetime interpretation is better than the Lorentzian interpretation, or any other empirically equivalent interpretation that is compatible with an objective present. That would allow us to conclude, by inference to the best explanation, that we should believe the spacetime interpretation over other interpretations, and so infer that eternalism is true.

But when I take everything into consideration, I don’t think it is clear that the spacetime interpretation is better than the Lorentzian interpretation. In fact, in some ways the opposite seems to be the case. Given that I have reasons for believing in presentism, I have reasons for preferring an interpretation compatible with presentism as long as one is available.

So let’s compare the spacetime interpretation to the Lorentzian interpretation of relativity. The spacetime interpretation is, in some sense, simpler than the Lorentzian one: it does not have a permanently hidden absolute reference frame. But in another sense, it is more complicated: it requires that everything in the past, present, and future all exist; while the Lorentzian interpretation can get by with just the present.

Perhaps the advantage of the spacetime interpretation lies in its elegant explanation of why all the laws of physics obey Lorentz symmetry: because the geometry of spacetime constrains them to be that way. In the Lorentzian interpretation, on the other hand, the laws of physics are just inexplicably conspiring to hide the correct reference frame.

However, in another area, the spacetime interpretation lacks explanatory power and fails to cohere with our experience in a major way: we cannot explain why we have the “stubbornly persistent illusion” of the passage of time, as Einstein called it, if there is no objective present and all times exist on an equal level. The Lorentzian interpretation can explain this, since it is compatible with presentism – and it can at least explain the mechanisms that hide the correct reference frame, its own “illusion,” even if it cannot say why those mechanisms are in place.

In fact, the presentist can offer an anthropic explanation for why the laws of physics are Lorentz symmetric, and for why the related equivalence principle of general relativity should hold: they must be that way in order for observers like us to exist. These relativistic principles imply that physics acts the same way for systems in motion as for those at rest, and the same way for systems in free-fall (for instance, in orbit around a star) as for those under no gravitational influence. This means that all physical entities, from atomic nuclei to planets, stars, and galaxies, can maintain their structure and equilibrium states while in various states of motion, which is surely important for the existence of complex life.

So the spacetime interpretation does not provide an overwhelming explanatory gain over the Lorentzian interpretation, and it loses out in other areas. Without further compelling reasons to believe in eternalism, the Lorentzian interpretation, or something akin to it, is a perfectly reasonable belief.

Alternative Presentist Interpretations

It may not even be the case that a presentism-compatible interpretation of relativity necessarily lacks the explanatory resources of the spacetime interpretation. One philosopher, Dean Zimmerman, suggests a way that the explanatory mechanisms of the spacetime manifold can be retained in a presentist interpretation. His proposal works like this:

  • Physics is described on a four-dimensional spacetime manifold, as in the standard interpretation of relativity.
  • The geometric structure of the manifold is retained, and explains the Lorentz symmetry of the laws of physics.
  • The objective passage of time is represented by a privileged foliation of the spacetime manifold: a way of dividing it into three-dimensional slices (“leaves” of the foliation) representing the universe at successive instants.
  • The fourth dimension of the manifold is re-interpreted not as a direction of time, but as a direction of inertial accessibility: points in that direction can be reached by things moving at speeds less than the speed of light.
  • One interpretation is that the whole four-dimensional manifold exists, but only one slice of it is occupied by the universe at any instant, and the universe constantly moves “forward” through the manifold as time passes.
  • Alternatively, the four-dimensional manifold can be seen merely as a mathematical construct, representing the non-Newtonian kinematical structure of the three-dimensional universe.
  • There is no single correct answer to how much time passes between two leaves of the foliation: that depends on how you measure it, which depends on how you are moving.
  • A natural choice of how to measure time even allows us to agree with the standard interpretation that the relative speed of light is constant and the same in all directions. (We just have to recognize then that apparent simultaneity differs from absolute simultaneity.)

This strategy works with Einstein’s theory of general relativity just as well.And another philosopher, Tom Crisp, shows (in his essay “Presentism, Eternalism, and Relativity Physics”) that there is yet another way of formulating general relativity that is naturally compatible with presentism.

(Note: in conversation with a physicist I learned that it is a little trickier than that to reconcile GR and presentism: it is possible to evolve spacetime geometry incompatible with the kind of foliation required by presentism, even when you start out with compatible initial data. So a restriction is required which is highly ad-hoc, or quantum corrections of the right sort are needed to avoid the problematic configurations.)

These alternative interpretations show that presentism does not require the aether reference frame of the Lorentzian interpretation, or its corresponding notion of absolute rest, or even an absolutely correct answer to the question of how much time passes between two events – it only requires that there is a correct answer to the order of events. All that presentism and absolute simultaneity imply, in the context of relativity physics, is that there is a correct way of foliating the spacetime manifold. And not even the weirdness of black holes prevents such a foliation from being possible.

Ultimately, presentism is not ruled out by relativity physics, since all it really does is introduce a preferred foliation to the spacetime theory. The only real argument from relativity against presentism is that physics implies we can never determine what the preferred foliation is, so it is simpler to go without it. But since our experience of the passage of time supports presentism, we have good reason to believe that such a foliation exists, whether or not we can find it. (Zimmerman’s essay, linked above, shows how the existence of a privileged foliation is a natural inference, given common-sense intuitions about reality.)

And the fact that we cannot find the preferred foliation is not really that much of a problem. All it means is that there are physical limits on our ability to determine whether or not events that are distant from each other are simultaneous. And since the speed of light is so incredibly fast relative to the time and distance scales of our experience (and since most large-scale structures in the universe are not moving anywhere near the speed of light relative to us), this turns out not to be that much of a limitation. For all practical purposes, we can still place quite good bounds on what is simultaneous with our present experience and what is not.

(In technical language, for every leaf of the privileged foliation, the leaf must lie entirely outside of the light-cones emanating from every one of its points. Since the speed of light is very high from our perspective, the light-cones open up quickly, constraining where the present leaf can lie to a thin region of spacetime.)

So while presentism may be burdened by an unknowable privileged foliation, that is much less of a cost to pay, in my mind, than eternalism’s persistent and unexplained illusion of the passage of time.

Quantum Mechanics and Relativity

Finally, it is worth noting that some of the difficulties in uniting the theory of general relativity with quantum mechanics can be traced, conceptually, to the eternalist interpretation of relativity. Furthermore, some of the conceptual problems with quantum mechanics itself may be resolved by adopting an interpretation that is compatible with presentism. I will explore this issue more in the next few posts. For now, I will say that if the correct interpretation of quantum mechanics or quantum gravity requires a privileged foliation of spacetime, that is all the more reason to believe in presentism.

At least one philosopher has argued that if it turns out that quantum theory requires a privileged foliation, this is worse rather than better for presentism, because now we have a “coordination problem” to deal with: the foliation privileged by quantum theory may not be the same as the one privileged by the objective passage of time.

But that is an extremely weak objection. It is perfectly reasonable to think that changes in reality are produced by causes, and that the equations of the correct quantum theory describe cause-and-effect that is happening to the most basic physical things that exist. Which means that if presentism is true, and real change is change in what exists, we have every good reason to believe that the quantum-theoretical foliation could not possibly be distinct from the foliation required by presentism. (Zimmerman responds to this objection in more detail towards the end of his paper.)

So I think that revisiting a presentist theory of time really could broaden avenues of research towards a theory of quantum gravity, and a better understanding of our universe.

The Nature of Time

So, what can I conclude about the nature of time? All my experiences of change and the passage of time powerfully support presentism and endurantism as their best explanation. And none of the arguments against presentism in favour of eternalism are strong enough, when clearly examined, to convince me that my common-sense interpretation of my experience is all wrong.

So, I believe that presentism and endurantism are true. Only the fleeting present moment exists, but there are things that endure through time, changing and remaining the same. The physical universe is a changing three-dimensional entity, rather than a four-dimensional entity with time as an internal dimension but which itself exists timelessly and unchanging.

We can still do physics from a four-dimensional perspective, and we can even still explain phenomena by citing the structure of the spacetime manifold. But given any four-dimensional description of spacetime, there is a unique way of slicing it into three-dimensional spaces so that it correctly represents the objective history of the universe.

Now that I have tackled what Einstein’s theories of relativity say about reality, in my next series of posts I am going to explore the other pillar of modern physics: quantum mechanics. And in fact, I think there is an interpretation of quantum theory that coheres with our common sense as well.

Presentism and Eternalism

Over the last two posts, I’ve been exploring the nature of time and change. Based on what I have considered so far, my belief is that:

  • The A-theory of time requires presentism, and vice versa; while the B-theory of time requires eternalism, and vice versa.
  • Endurantism requires presentism, and eternalism requires perdurantism.

More detail on these different positions, and my reasons for believing these assertions can be found in the previous posts, but briefly:

  • The A-theory holds that there is an objective present, while the B-theory holds that the present is only subjective.
  • Presentism holds that only the present exists, while eternalism holds that all times exist.
  • Endurantism holds that things can persist through time while remaining one and the same entity, while perdurantism holds that they cannot.

The main question now is whether presentism or eternalism is true. As I’ve examined the arguments for and against these positions, I’ve come to believe that, in fact, presentism and the A-theory are the correct theories about the nature of time. In this post and the next, I’ll share my reasons why.


Experience of Time and Change

Presentism and endurantism are supported by our constant experience of change and the passage of time. We experience the present, remember the past, and anticipate the future. The future continually approaches and the past continually grows farther away; we cannot choose to move through time the way that we can move through space. Because of this, it is natural to believe that the past and future are in some way less real than the present.

Furthermore, we directly experience enduring through time, changing while still being the same entity. We directly experience change in what exists, either through ourselves changing in what experiences we have, or through each of our experiences changing into the next. This dynamic experience of time gives us properly basic grounds for belief in both endurantism and presentism. Because of this, according to the principle of critical trust, we must have strong reasons against the A-theory and presentism to be able to rationally reject them.

It may be argued that it is possible to explain our subjective experience of the passage of time from an eternalist perspective. The argument goes like this: according to presentism, the dynamic experience of an observer, S, is simply described by S having experience E1 at time t1, and experience E2 at time t2, and so on. But since the same description can be given within the framework of eternalism, there is no difference from the perspective of the observer.

This is not quite correct, however. First, the correct description according to eternalism is actually that S1 has E1 at t1, while S2 has E2 at t2, where there are two different observers, because nothing can endure through time if eternalism is true. Second, presentism adds to its description the explanation that S has its changing experiences because they reflect an objectively changing reality. Eternalism needs to provide an explanation for our subjective experience of the passage of time, not just a description.

At best, the eternalist could say that S is a four-dimensional entity, that S1 and S2 are two of its temporal stages, and that there is a cause-and-effect relationship between the different temporal stages. However, if S can be said to experience E1 and E2 at different times, it can only be because its temporal parts have those experiences. And it makes no sense to say that S has those experiences successively: S exists as it does eternally and cannot change.

So the eternalist needs to explain why S1 and S2 have the have the illusory experience of persisting from one moment to the next. The cause-and-effect relationship between the temporal stages allows one stage to play a role in determining what the next stage experiences, but that does nothing to explain the illusion of time’s passing. And since it is the temporal parts themselves that seem to have the experiences, their part-whole relationship with S seems irrelevant.

Even if there was an explanation for how we could have an illusory dynamic experience of time within a four-dimensional eternalist universe, it might not be the best explanation for our experience of time, and it would not override the properly basic beliefs grounded in that experience. (At best, it would enable other arguments for eternalism to override those properly basic beliefs.) Without other arguments in its favour, such an explanation would be on par with a skeptical explanation of our experience of physical reality, such as one in terms of everything being a dream or an artificial simulation.

Therefore, just as we are rationally justified in believing in the external physical world on the basis of our experience, so we are rationally justified in believing in the objective passage of time, and our endurance through it, on the same basis, unless there are powerful arguments to the contrary.

The Ship of Theseus

I’ve appealed to common-sense intuitions about the nature of change to argue for endurantism, and via endurantism to argue for presentism. But there is an argument against endurantism that I have not considered. It comes in the form of a classic philosophical thought experiment: the Ship of Theseus.

As the story goes, Theseus sets out on a long seafaring voyage in his ship. Along the way, parts of the ship wear out and are gradually replaced. By the time Theseus returns, every single component of the ship has been replaced. Is it still the same ship as when it left? If so, what makes it the same, since none of the original parts remain? If not, when did it become a different ship?

For a different spin on this story, imagine you have an axe. After using the ax for a while, you replace the axe-head. Then you use it for a while longer before replacing the handle. A little while later your friend comes to help you chop wood, but he doesn’t have an axe of his own. Fortunately, you kept the old axe-head and handle around, and they are still functional. So you put them together to make a second axe. Which axe, now, is the one you started with?

These thought experiments are meant to show that objects like ships or axes cannot actually endure through time. Whether the ship of Theseus remains one and the same throughout the voyage, or which of the two axes is one and the same as the original, seems to just be a matter of perspective. If that is the case, then many ordinary objects composed of separable or replaceable parts – even our own bodies, which are constantly replacing cells and molecules – do not endure through time.

However, I do not think these thought experiments succeed at proving it impossible to formulate an objective principle by which we could say these objects exist and endure from one moment to the next. Maybe we can find an appropriate criteria of physical continuity for solid objects, for example. Or perhaps the structure and essential activity of living organisms provides a unifying principle by which we can identify them across time.

Moreover, these stories do not apply at all to metaphysically simple entities: that is to say, objects that are not composed of separable parts. Immaterial minds are usually conceived of as being metaphysically simple, if they exist. Fundamental particles like electrons or photons, or maybe their underlying quantum fields, could also be placed in this category.

But ultimately, even if it the story of the Ship of Theseus succeeds in showing that ordinary objects do not endure through time – that what we think of as trees only exist for an instant as one stage in a whole tree-history, for example, or that we should really think of trees as being more like processes than objects – I still think my experience of being an individual perspective enduring through time is powerful enough to justify believing it. And my experience of the passage of time still justifies the intuition that each momentarily existing stage of a tree really changes into the next, rather than continuing to exist eternally.

So even considering the Ship of Theseus story, I still find my belief in presentism, and in my own endurance through time, to be reasonable.

Rationality and Moral Responsibility

Presentism is further supported by two other arguments for endurantism, given that endurantism and eternalism are incompatible:

First, some philosophers have argued that reasoning and rational thought are only possible if endurantism is true. Since we can only think at a finite speed, we must endure through time to consider the premises of a rational argument and then draw the correct conclusion. Otherwise, there is one entity that considers some premises, and a different entity that draws a conclusion. There may be a cause-and-effect relationship between those two entities, but that seems insufficient for the ground-and-consequent relationship between the relevant propositions to be truly perceived, which is what is required for rationality. (Though, perhaps if the cause-and-effect relationship involved is dependent on the meaning of premises and the conclusion, this argument for endurantism can be overturned.)

Second, moral responsibility is only coherent if endurantism is true. We must endure through time to be responsible for our past actions. Otherwise, our past selves are literally not the same persons as we are, and all punishment is actually carried out on a different person than the one who committed the deserving offence. Holding anyone morally responsible for past actions becomes unjust if endurantism is false. Since our moral intuitions are also a source of properly basic beliefs (as I will argue in a future post), this provides good reason to accept endurantism, and presentism along with it.

Causation and the Direction of Time

Presentism also allows us a stronger concept of cause-and-effect, which I have argued is a fundamental part of reality. According to eternalism, causation is merely a relation of a past entity or event playing a role in determining a future event. But according to presentism, causes actually bring their effects into existence, producing objective changes in reality. This coheres better with my intuitive concept of causation.

Finally, presentism provides a good explanation for the direction of time and causality: it is an intrinsic feature of reality, the direction in which reality is objectively changing. But without an objective present, eternalism cannot explain the direction of time. The most fundamental laws of physics are symmetric under time-reversal. (Well, to be more precise, they are symmetric under time-reversal combined with charge-reversal and parity-reversal, but there is no reason to think that those symmetries are fixed independently of fixing a direction for time.) If there is no objective present, the laws of physics cannot provide any reason that we should experience time as passing in the forward direction rather than the reverse, or any reason to think that earlier events cause later ones rather than the opposite.

Often, it’s suggested that the arrow of time is determined by the direction of entropy increase, through the second law of thermodynamics. But that is simply making an observation of what needs to be explained, not an explanation itself. If presentism is true, we can give a statistical explanation for why entropy increases with time. But if eternalism is true, this explanation is unavailable, and there is no explanation that I have found for why time should increase with entropy.

So there are a number of good reasons to think that presentism is true. Let’s see if the reasons in favour of eternalism are comparable.


Grounding and Reference

Even prior to the arrival of Einstein’s theories of relativity, presentism was (and still is) thought to face a number of philosophical difficulties. The first difficulty is how the truth of past and future tensed statements is to be grounded in reality, if only the present is real. The second is how we can refer to past and future events or entities, and even stand in various relations with them, if they do not actually exist. These difficulties are presented as arguments against presentism, and therefore, for eternalism.

While I’ll concede that eternalism can handle these difficulties, I believe that with a little thought, presentism is capable of handling them as well. To see how presentism can do this, it is crucial to recognize that time is analogous to modality: if presentism is true, different times are like different possible worlds.

Presentism thus has much in common with actualism, the philosophical belief that merely possible entities do not exist. The causal account of modality, which I find very reasonable, is an actualist theory, since it grounds possibility and necessity in actual properties and states of affairs. Similarly, I think it is plausible that past and future truths may be grounded in present states of affairs.

It seems quite natural to me to suppose that certain rates of change, or related quantities like momentum, are among the actual properties that entities have. Given such properties, the laws of nature (which are themselves a result of existing causal powers) are able to ground any deterministic facts about the past or future from just the present facts.

The grounding of any indeterministic facts about the past or future are a more difficult hurdle, but again, I do not think it is insurmountable. If there are facts of a certain special kind that are true in reality, facts which I will call subjunctive conditionals of indeterminacy, then these are sufficient (along with existing causal powers and rates of change) to ground past and future indeterministic facts as well.

Here begins a long aside on these subjunctive conditionals:

Subjunctive conditionals of indeterminacy are facts about what effect a given indeterministic cause would produce, if it were in a given sufficiently well-specified circumstance. They include what are often called counterfactuals of freedom, assuming for the sake of example that humans have free will and are capable of self-determined actions. These are facts like: if it were the case on such-and-such a day that it looked like it was about to rain, John would refrain from mowing his lawn and read a book instead. Or for another example: if were the case that the past history of the universe was so-and-so, this particular uranium atom would decay at precisely this time.

I think it seems reasonable to believe that certain subjunctive conditionals like this are true. Specifically, the following statement is plausible to me:

Restricted Law of Conditional Excluded Middle


  • Q is a proposition expressing the occurrence of a cause C bringing about an effect E, and
  • P is a proposition fully specifying the history leading up to Q, including all the factors that could influence C up to the moment of its bringing about E,

Then, either:

  • If it were the case that P, Q would be true; or
  • If it were the case that P, Q would be false.

After all, since P fully specifies the circumstances of Q, it seems like there is no other option. The laws of logic force it to be the case that there would be a fact of the matter about what happens in circumstance P, so it seems natural to me to think that there is a fact of the matter about what would happen, if P were true.

As a close analogy, if it is going to rain tomorrow, the proposition that it will rain tomorrow is true today, whether we know it or not. If future-tensed statements describing what will be actual are true, I don’t see why subjunctive statements describing what would be actual cannot be true as well.

I am proposing that there are facts, subjunctive conditionals of indeterminacy, which help to ground the truth of non-present tensed propositions. This, of course, raises the question of what grounds the truth of the propositions expressing the subjunctive facts.

For now, my answer to that is effectively: just the subjunctive facts themselves. If indeterministic causes are possible, and I think they are, then in some sense, the facts about what effects they produce are going to be bare, rock-bottom features of reality. They can have explanations, but they cannot have logically entailing conditions, or be determined in any way. Subjunctive conditionals of indeterminacy are a natural stopping point for these fundamental contingent features.

(How do I reconcile my belief in the Principle of Sufficient Reason with the existence of these brute contingent subjunctive facts? Well, I would say that all such facts still have an explanation: they are explained by the fact that the relevant state of affairs would have a cause if the antecedent of the subjunctive conditional were true.)

I’ll be writing more about these subjunctive conditionals in the future, and when I do I will probably try to expand on my reasons for thinking they exist. That will be a while down the road, though.

Here ends the aside.

Further to all that, some presentists have suggested that presently existing things could have backwards-looking or even forwards-looking properties, which ground the truth of past or future statements much like the causal powers of things ground the truth of modal statements. (For example, properties like having been stepped on by a dinosaur 100 million years ago.) And I think that is not an entirely unreasonable thing to believe, though it may be objected that such properties cannot be physical properties.

Now, if past and future truths can be grounded in present reality as I have suggested, then problems with referring to non-present entities can be resolved as well. Specifically, I think we can take a sort of figuralist perspective to help discern the real content of statements with references to non-present entities, as opposed to merely their literal content. And I think that an intensional temporal logic can go a long way in helping us formally represent that real content, in order to reason about it clearly.

Philosopher Ned Markosian gives a good summary, in his paper here, of different ways we can interpret statements about non-present entities, in a way that is consistent with presentism. (I think the strategies he presents in Sections 3.5 to 3.8 of that paper are the strongest ones, and since I am a nominalist about abstract objects, I think 3.1 and 3.2 describe viable options as well. Sections 3.7 and 3.10 nicely demonstrate the presentist view that different times are analogous to different possible worlds.) Dean Zimmerman’s essay here also gives a good response to the objection from grounding non-present truths.

Ultimately, then, I don’t believe presentism poses any threat to the truth or meaning of statements about non-present entities, and this significantly weakens this objection to presentism as an argument for eternalism.

Inconsistency of the A-Theory

A second philosophical argument, this time against the A-theory of time specifically, may be used as an argument for the B-theory (and thus, for eternalism). It is known as McTaggart’s Paradox, after the philosopher who famously presented it as part of an argument that time itself is unreal. (McTaggart’s argument, incidentally, is where the terms “A-theory” and “B-theory” originated.)

The paradox is that if you take a series of events in time, all of the events must have all three of the properties of being past, being present, and being future. After all, the present was future and will be past, the past was present, and the future will be present. But these properties are incompatible with each other – an event cannot have more than one of them. So the A-theory of time is self-contradictory.

The obvious response to the paradox is that no event has the property of being past, present, and future all at the same time. At any single time, every event only has one of these properties. No contradiction after all.

Of course, McTaggart anticipated this response. But he believed that in order to say something like “this time was future, is present, and will be past,” the A-theorist had to be speaking of a higher-order time series, in which the normal time series resides and changes in what A-properties it has. This leads to an infinite regress of ever higher-order time series, which seems absurd.

However, McTaggart was wrong about the need for a higher-order time series, and I think his mistake was in trying to formulate the A-theory from the perspective of eternalism, where all the events in the series always exist. From the perspective of presentism, no such absurdity appears.

In a presentist interpretation, McTaggart’s paradox is actually an instance of the problem of temporary intrinsics, specifically applied to the endurance and change of times, which are understood as being abstract objects analogous to possible worlds. Then, either no regress of time series is needed (because times so understood are just representations of the way that reality was, is, or will be; they are not points in time itself), or the regress is a harmless one (because the higher-order time series are just representations of time contained within representations of reality; and particularly from a nominalist perspective, because these representations are just concepts, not objects with their own existence).

So McTaggart’s paradox fails to do any damage to presentism. It does, however, provide another reason for believing that the A-theory requires presentism to be consistent.

Thus far, the arguments for eternalism have failed to overcome my powerful justification for believing in an objective present, which is grounded in my experience of the passage of time. But I have not yet weighed presentism against what many philosophers find to be its greatest challenge: Einstein’s theories of relativity. I will complete my exploration of the nature of time with that topic, in my next post.