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Against the Block Universe Part I

Why the Argument for Predeterminism Falls Down

2025 Aug 01

1 Introduction

Does special relativity imply that the future is predetermined and free will an illusion? Many have argued so, even some well-known physicists, basing their claims on the so-called block universe view of time.

The notion of space-time as a unification of space and time dates back over a hundred years to Hermann Minkowski, and was used by Einstein to develop his general theory of relativity. But the block universe idea goes further. Minkowski said that space-time can be viewed mathematically from a four dimensional perspective. Proponents of the block universe suggest this implies the whole of space and time is essentially already real, and hence fixed, like a block of stone. So nothing in it can be changed – not the past and, crucially, not the future. In other words, the future is already fully determined and we can have no influence over it.

But this is not implied by relativity theory. A closer look at the details of special relativity shows that the block idea overreaches. It misuses key concepts like simultaneity and causality; past and future. It introduces terms such as ‘real’ without defining them, confuses reference frames with observers, and it mistakes the mathematics of space-time for metaphysics. In this essay I aim to show how the block universe argument misfires, avoiding, on the one hand, the muddled arguments found in the philosophical literature, and on the other, the superficial discussions usual in popular treatments.

In part one of this essay I will focus on a version of the block argument sometimes called the Andromeda paradox, a thought experiment introduced by Roger Penrose in his book The Emperor’s New Mind. This is a useful argument to target in this discussion - it is simply laid out, unlike the somewhat convoluted discussions in philosophical journals, yet it rests on the same essential misconception common to the more subtle arguments found elsewhere. It is also fairly well known, and I can link to a BBC animation that sets it out! Part 2 of the essay will address these other arguments, including those of Rietdijk and Putnam who first introduced the block idea.

Here I will first explain the world-view of special relativity in section 2, in order to help the reader follow the reasoning behind the Andromeda paradox, which I will present in section 3. I will then go back in section 4 to explain how the relativistic world-view arises, particularly the novel ideas about simultaneous events. This discussion of relativity, though rather lengthy, will not be overly technical. Once this is done the reader will have a much clearer grasp of the key ideas, and will be in a position to decide for themselves whether they agree with my critique of the block argument in section 5. I will finish with some reflections on what the physics is really trying to tell us.

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2 Time in Special Relativity

Before turning to Einstein’s theory let’s consider our intuitive ideas about time. They might be summed up as follows:

• The universe unfolds through time with a moment, ’now’ which is universal. The same everywhere and for everyone.

• ‘Behind’ now lies the past, which has already happened, and ahead of it lies the future, which has not yet happened.

• Time always ‘flows’, from the past to the future, at the same rate everywhere, for everyone.

We can present these ideas in picture form:

This might be called a naive space-time diagram. This is basically what is often taught in school science or maths as a ‘distance/time graph’. In those graphs distance usually goes up the page and time to the right. In space-time diagrams time is always on the vertical axis. In this ‘2-D’ version only one dimension of space, or ‘distance’ is shown, to keep the diagram simple. Sometimes a more elaborate diagram is used, showing two distance axes - in other words, two dimensions of space. There’s one in the next section. Usually the 2-D version is good enough for the discussion, and they’re easier to draw!

In relativity theory each point on the diagram is called an event: a location in space at one instant in time. The line going across the page represents all the events that are happening now. The line going up the page represents a person’s journey from the past to the future. This path is called their world-line. This vertical world-line is that of someone who is stationary – they’re not moving either to the left or right.

These ideas about time underlie much of our reasoning about past and future, cause and effect. It’s a natural model, but SR challenges this entire picture, starting with the idea of a universal ‘now’

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The View from Relativity

Relativity tells us that this simple division of events into past, present, and future is not universal. Observers moving at different speeds are said to have distinct frames of reference, and in different reference frames time will pass at different rates. What’s more, these observers in motion will disagree about which events are simultaneous. There is no objective notion of a single, universal ’now’ that everyone can agree on.

The view from relativity theory can be pictured like this:

In the diagram the different regions of space-time are described with not three, but five labels.

• The Past is relegated to only the bottom quadrant
• The Future is at the top
• Now is only a point in the middle (not a line as in the naive diagram)
• Elsewhere is to the left and right
• The Light Cones are the two diagonal lines forming boundaries between the other regions

Diagram 3 below (found online) is a ‘3D’ version, featuring two directions in space. I include it to make the meaning of the labels in Diagram 2 clearer.

There are two cones. The Past Light Cone at the bottom and The Future Light Cone at the top.

The name light cone is used because the cones are the trajectories (world-lines) of rays of light. Imagine an explosion occurring at x, in the centre of the diagram. The flash of light spreading out from the explosion is an expanding sphere, but as only two space dimensions are shown it’s represented by an expanding cirlce, like ripples spreading out in a pond. Add the time dimension (up the page), and this expanding circle is represented by a cone.

Everything outside of the light cones is called ‘Elsewhere’. The upper cone ‘contains’ the future and the lower cone contains the past. Diagram 2 is essentially a cross-section of this diagram. In it the cones appear as straight lines, and the ‘Elsewhere’ region appears in two parts on the left and right.

The vertical and horizontal scales in the 2D diagrams are always chosen so that a ray of light is represented by a line at a 45 degree angle.

The disagreement about which distant events count as ‘now’ is what is meant by the peculiar phrase, ‘relativity of simultaneity’, or sometimes, ’loss of simultaneity’. It is a genuine result from special relativity which does lead to further insights into the nature of time, but its real significance is routinely misunderstood. Crucially for us, it is the central premise behind the block argument, so it’s important to have a grasp of what it means.

The phrase ‘relativity of simultaneity’ is rather unwieldy, but I have to keep talking about it, so from now on I will abbreviate it to RoS. While I am at it, I will usually shorten Special Relativity to SR. There’s a glossary of terms and abbreviations at the end of the essay.

So RoS is illustrated in Diagram 4, below, with another strange term – ‘world-slice’.

What does this mean? Look back at the ’naive’ diagram 1. The horizontal line there is a world slice – a set of all the events that an observer judges to be happening at the same moment. It’s like a ‘slice’ through space-time of all the current events. Again, in reality this slice is three dimensional because space is, but we call it a slice by analogy with the 2- or 3-D spacetime diagrams, where it is either a line (as in diagram 4 or flat plane, as in diagram 1

But each frame of reference has its own world slice. And the slices are ‘tilted’ relative to each other. That is, they cut in different directions. The whole block universe idea rests upon this novel idea, so I will devote a section to it before setting out the Andromeda paradox in the following secion.

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What do we mean by Simultaneous Anyway?

In everyday life we take the idea of simultaneity for granted. If you see two fireworks explode at the same time in the night sky, you naturally assume they happened at the same time, and don’t give it much thought. But in special relativity, simultaneity becomes a subtle, and surprisingly slippery, concept.

The key challenge is this: we can never actually be present at two simultaneous events. You can only be in once place at a time, so if two events happen in different places at the same time then you can’t be present at both.

Simultaneity is not something anyone ever actually experiences directly. It is something we deduce about events.

But making these deductions involves checking out things such as when the flash of the lightning reached us, what time our clock read at the time, and so forth - making measurements and calculations. But to do this you have to choose a reference frame within which you make your measurements. And relativity theory is all about different reference frames. It turns out the theory tells us that the results of these calculations about simultaneity will be different when using different reference frames. So observers in different frames will have different ideas about which events elsewhere count as simultaneous. That is, they will ‘slice’ the world differently. If you’re not happy about this, Part 2 of this essay will explain in more detail how this comes about. For now it’s enough to know that this is an uncontroversial result from SR.

What diagram 4 is telling us then is this: Mike and Melissa disagree about which events are happening ‘now’. This is why, in diagram 2, ‘Now’ is not a line, but just the point where we are at one moment (centre of the diagram). Because there is no universally agreed ’now’ at other locations, the line in diagram 1 is less significant, because it’s not something all observers would agree on.

I will explain the diagram and these strange ideas a little more in section 4. For now though, that’s enough background to be able to follow the block universe argument, so let’s look at that first.

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3 The Andromeda Paradox

As an aid I include a link to a lighthearted animation that spells out Penrose’s argument in more detail. I will summarize the argument here, and quote statements from both Penrose’s book and the animation. I also copy Penrose’s diagram (without permission!).

For those who are interested, here is a link to the animated short: youtube.

Penrose’s thought experiment consists of the rather fanciful idea of an alien invasion fleet being sent from the Andromeda galaxy two million light years away. From Penrose’s book:

Imagine two people walking slowly past each other in the street. The events on the Andromeda galaxy … judged by the two people to be simultaneous with the moment that they pass one another could amount to a difference of several days … For one of the people, the space fleet launched with the intent to wipe out life on the planet Earth is already on its way; while for the other, the very decision about whether or not to launch that fleet has not yet even been made!

Taking my cue from the animation I’ll call the observers Mike and Melissa, who meet and ‘high five’ while walking past each other at around the time the aliens are deciding whether or not to launch the fleet.

Let’s spell the argument out in detail, summarising the video animation:

Consider the moment Mike and Melissa high-five. According to the video:

Mike and Melissa are moving relative to each other, so they have different reference frames.

Which means they will have different world-slices (see Diagram 5).

Mike’s world-slice intersects the alien planet in Andromeda the day before the vote on whether to launch the fleet.

Melissa’s world-slice intersects the aliens in Andromeda a day later, just after the fleet has set out on its way.

So Mike thinks that the launch of the fleet is something that may, or may not, happen tomorrow, depending on the outcome of the vote.

But Melissa thinks the fleet has already set out on its way.

So the launch lies in Mike’s future, but Melissa’s past.

So Mike’s future has already happened, because SR tells us that neither Mike nor Melissa is more right than the other.

So the future is already set.

That is, all things that have happened and are happening and are going to happen, they already exist.

So the crux of this argument is the part that is highlighted – Mike’s future, or at least part of it, is ‘already’ in Melissa’s past. But we all know that the past is a fixed thing. You can’t change the past. So Mike’s future is a fixed thing, and can’t be changed.

To support the argument further, a similar point can be made about any event in Mike’s ‘future’, as long as it lies outside his light cone. Though neither the animation nor Penrose mention this, it is always possible, in those circumstances, to find an observer for whom that event lies in the ‘past’.

Here’s how Penrose sums it up:

"… If to either person the decision has already been made, then surely there cannot be any uncertainty. The launching of the space fleet is an inevitability."

In fact neither of the people can yet know of the launching of the space fleet. They can know only later, when telescopic observations from earth reveal that the fleet is indeed on its way. Then they can hark back to that chance encounter and come to the conclusion that at that time, according to one of them, the decision lay in the uncertain future, while to the other, it lay in the certain past.

It begins to seem that if anything is definite at all, then the entire space-time must indeed be definite! … The whole of space-time must be fixed, without any scope for uncertainty … there is no flow of time at all. We have just ‘space–time’

Penrose touches on a point here which some may think invalidates the argument - how can they reasonably be said to disagree about an event neither can know anything about? As he points out, what we are really saying is that, when they compare notes later, they will disagree about what had happened at the time they met. Statements such as ‘Mike thinks’ are shorthand for this. The argument could be rephrased in these terms for more precision, but it would be tedious to spell it out each time.

Another point about this phrasing: When we say ‘Mike thinks’, or ‘Melissa disagrees’ it is understood to mean ‘Mike is justified in thinking’, or ‘Melissa is justified in disagreeing’ - the justification lying in the details of SR. They’re not just being stubborn or unreasonable. Throughout the discussion I will assume all observers understand SR and have good reasons for their ‘thoughts’ or ‘beliefs’. This point will become important later.

In order to be clear about what RoS is really telling us, the next sections will examine more closely what Einstein’s theory tells us about the past and future. We will then be in a position to see where the Andromeda argument goes wrong.

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4 More about Special Relativity

In this section I will try to give an indication of why SR leads us to the peculiar picture of the world which I outlined in part 2, and represented in Diagram 2. The outline given there was enough to be able to follow the block argument. The extra discussion here will enable us to see the flaws in the argument, which I will return to in the next section. I don’t need to explain all of Einstein’s theory – just a few key ideas.

The Principles

Einstein’s special theory of relativity rests on two principles. These, together with one further result from the theory, are required to explain RoS, and thus the block universe idea.

P1. The Principle of Relativity - there is no preferred reference frame. Any frame of reference that isn’t accelerating is as valid as any other.

What this means in practice:

Moving at a constant rate feels exactly the same as standing still. Indeed anyone moving at a steady rate can reasonably consider themselves to be standing still, as far as the physics is concerned, even if they are, for instance, on a moving train. After all, we are all on a moving Earth even when ‘standing still’. So it’s perfectly valid for such an observer to insist that they are stationary, and other people are moving.

P2. The constant velocity of light - all observers will measure the same velocity for any light ray, relative to them.

Even observers who are moving at different speeds relative to each other. This is far from obvious, but is amply confirmed by experiment. This velocity is about 300,000 km per second. We call it ‘c’ for short.

P3. The speed of light is the maximum speed possible in the universe. Nothing can travel faster.

This is a further result that can be shown to follow from the first two principles.

These are all uncontroversial results from relativity theory, strange though they may seem if they are new to you. Together they shape the causal structure of space-time, represented by light cones.

Looking at Diagram 2 again, we see that any possible world-line starting at ‘O’ must lie ‘inside its future light cone’, i.e,, at an angle that is steeper than 45 degrees, since that angle represents the speed of light. A world-line, or trajectory that lay outside (i.e., at a shallower angle, in the diagram) would represent movement faster than the speed of light, which P3 tells us is impossible. This leads to the following important point:

It is impossible, starting from ’now’ in the centre of the diagram, for any object or signal to reach any point in the elsewhere region, as to do so would require travelling faster than light. It is equally impossible for any signal to reach us now from anywhere in the elsewhere region.

This allows us to see that SR tells us something new about past and future not just as chronological ideas - ‘before’ and ‘after’ - but in terms of cause and effect -

Only signals from events inside the past light cone (the lower cone) can reach us from the ‘past’. Only these events can influence our ’now’. These are also the only events we might conceivably have been present at in the past. Travelling at or below the speed of light we could not have reached here from anywhere outside that past light cone. This is why that region is labelled Past. Similarly, the only events in the future which we can be present at are those that lie inside our future light cone (the upper cone). And these are the only events we can have a direct effect on, which is why that region is labelled Future.

But there’s a bit more to it than that. Just as we cannot take for granted the idea of a universal now, or that time flows at the same rate for everyone (ideas we must actually abandon in the light of SR), so we must rethink what we understand by words such as ‘past’ and ‘future’, and related terms ‘before’ and ‘after’, as well as concepts such as causation. Otherwise we may be inadvertently using them in ways that do not accord with reality. The Andromeda argument relies to a large extent on taking a genuine result from SR and mixing it with pre-relativistic ideas. So we need to be clear about what these terms really mean.

What does it mean to say that something lies in the past or future? Classically, the relevant causal properties of past events are the following:

• We can’t, even in principle, have any effect on an event which lies in our past. We can’t change the past.

• The past can affect us. It is possible in principle for an event in the past to have had an effect on our present situation. It can leave a memory or other trace, for instance, which is our main way of deciding that it was indeed a past event.

And the future? Future events have the opposite properties -

• We can affect the future. Though we might not in practice be able to do so, in principle it is possible to have some effect on events which lie in the future.

• Future events cannot affect our present situation. They haven’t happened yet, so they can have no effect on ‘now’. In particular, we cannot yet know what happens there. We cannot remember the future.

In the language of physics we can restate these features by talking about signals:

Signals can reach us from the past, but not from the future, and We can send signals into the future, but not into the past.

Now look again at Diagram 2, the basic space-time diagram. It is clear that events inside the past light cone have the classical properties we associate with ’the past’. Signals can reach us from there. Similarly, for the future light cone. We can send signals to events there.

But what about events in the Elsewhere region? They have a curious mixture of the causal properties of past and future. Firstly, we cannot have any effect on events in that region, no matter how late they are - in other words, how far ‘up’ the diagram they lie. This is a property these events share with what I shall call the ‘causal past’, by which I mean events inside the past light cone. But unlike the causal past, events in the elsewhere region can have no effect on us either, no matter how early they were – how far ‘down’ the diagram they lie. In that, they share a property of the ‘causal’ future, not the past.

We see now that not only do events outside the light cones not deserve to be called either ‘past’ or ‘future’, but they possess a mixture of the causal properties of the past and future. And - an important point here - this is equally true of all the events throughout the ’elsewhere’ region.

Finally we are ready to pick apart the Andromeda block universe argument. With the clarifications above we can make short work of it.

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5 Refuting the Argument

Here is the argument restated in clearer terms, in light of the analysis we’ve carried out so far. This will help to pinpoint exactly where the fallacies lie:

1. Mike and Melissa are in the same location, but have different world-slices.

2. The launch of the fleet lies on Melissa’s current world-slice.

3. That event will not be on Mike’s world-slice until tomorrow.

4. In other words, what has just happened in Andromeda, as far as Melissa is concerned, will not happen till tomorrow, according to Mike.

5. So the future for Mike is already the past for Melissa.

6. Since it is a feature of the past that it cannot be influenced, then the future cannot be influenced either.

7. Since the future cannot be influenced, it is predetermined.

Let us examine these points in turn.

Points 1 to 3: All Correct

There is nothing at all wrong with statements 1 to 3. As we have seen, it is indeed the case that observers who are spatially close but moving differently will assign different sets of events as being ‘simultaneous’ with the same local event. This is a consequence of the relativity of simultaneity (RoS) and is illustrated in Diagram 4.

Point 4: Acceptable With Care

Statement 4 is also acceptable, as long as we bear in mind what we mean by expressions such as ‘as far as Melissa is concerned’ or ‘according to Mike’. It is important to remember that neither Mike nor Melissa has any knowledge of what is happening in Andromeda. Their statements about simultaneity concern only the assignment of coordinates within their own reference frames. I will have more to say about this later.3

So far, so good. But now the argument begins to falter.

Point 5: The Reasoning Slips

This is where we begin to go astray.

Firstly, not all of Mike’s future is the past for Melissa, even under the particular meaning of ‘past’ used here. Crucially, all of Mike’s causal future is also all in Melissa’s causal future, and vice versa. We could, however, say that some events in Mike’s future (in the coordinate sense) are already in Melissa’s past (also in the coordinate sense).

But these are not events in their causal future or past. Remember, they are in the elsewhere region; events that are spatially separated, or space-like separated, and thus cannot be causally connected.

Point 6: Some Events Cannot Be Influenced

Given the analysis of point 5, we can accept a modified version of statement 6: that some future events cannot be influenced. Which? Just those that lie ‘ahead’ of Mike’s current world slice, but outside his future light cone.

But this is not controversial! We already knew this, and demonstrated it in the previous section. And without bringing Melissa into it at all. It has nothing to do with determinism, but everything to do with the finite velocity of light, and its role as the maximum possible speed for transmitting influence.

This is a property shared by all events in the elsewhere region, as explained in the previous section. The above argument applies to precisely those events that lie in the ’elsewhere’ region, which we have already demonstrated we cannot have any effect on.

Point 7: Are Such Events Predetermined?

What now of statement 7? Are those events, which we cannot influence, predetermined?

No, they are not. They are simply out of reach. Statement 7 relies on a hidden assumption that seems innocuous if we don’t stop to think about it. We might put it like this:

6a. If we are powerless to influence a future event, then it must be predetermined.

This has a superficial appeal, but as we have seen it is not valid. In the light of relativity theory none of the events outside the light cone can be influenced. But that is not because they are predetermined – it is simply that they are too far away. No signal travelling at, or below, the speed of light can reach them, and the speed of light is the top speed. If we do insist on referring to some events in the elsewhere region as ’the future’ then we must concede that statement 7 is false.

Bringing in a second person’s reference frame was a red herring. It simply confused the issue, and disguised a sleight of hand. The supposed insight about determinism turns out to be a restatement of something we already knew: we cannot influence events outside our light cone. That has nothing to do with whether the universe is predetermined.

It’s akin to missing the last post at Christmas. If, come December 20th, you realise that your cards cannot now possibly be delivered before the big day, you don’t lament that you have no free will - you know it’s your own fault for leaving it too late.

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Glossary of Terms

Event: a single point in space-time

Frame of Reference: A choice of coordinates with which to refer to places, times, and events

c: The velocity of light (approx. 300,000 km/s)

SR: Special Relativity

RoS: Relativity of Simultaneity

World Slice: The set of all events that a given observer considers simultaneous with a particular event. Space-like separated / Spatially separated: Events that are outside each other’s light cones.

Time-like separated events: Events that are inside each other’s light cones.

Causal Past: Events lying inside our past light cone

Causal Future: Events lying inside our future light cone