A Guide to the Language of Relativity
Key Concepts Explained
This essay is a work in progress. More entries need to be added, and some of the links don’t work. Sorry about that!
This short guide sets out the basic vocabulary and ideas that run through the Block Universe Series. It isn’t a physics lesson so much as a translation exercise: a way of seeing how relativity reshapes a few key concepts we thought we already knew. It can be read straight through as a primer of some basic relativity ideas, but it is by no means exhaustive. It’s been structured as a series of short sections, some are mini essays, while others just extended glossary entries. This is to fulfill its main function as an explainer to the main essays on the block universe. Most link to other essays that show how these ideas play out in detail.
Think of this as the framework that lets us speak clearly about what relativity does (and doesn’t) say about time, simultaneity, and reality.
Reference Frames
Reference frames (or ‘frames of reference’, sometimes just ‘frames’ for short) are central to understanding relativity. In fact, relativity theory is largely about how to switch between different reference frames, so it’s important to be clear about what they are.
If you’re already familiar with reference frames, you might be tempted to skip this section. But there are a couple of points here - particularly towards the end - that will matter for the philosophical arguments in the later essays, so it’s worth a quick read even if the basics are familiar.
We’re talking about how we refer to an event’s location: in time and space. We need to know how far away it is, in what direction, and when it occurs. There are always many different ways of describing this, and some are better than others in different situations.
To describe a time and place accurately, the main things we need to know are: what units are we using? Hours? Minutes? Days? Miles? Kilometres? Light years? Centimetres?
Where are we measuring from? (We usually call that place the ‘origin’.) If I say the event happened ten metres away, I need to specify: ten metres from where? Where I’m standing? Where you’re standing? Greenwich? The centre of the Sun?
And ten metres in what direction? North? ‘Along the x-axis’? And if we’re going to use axes, which way are they pointing?
Once we know all this, we have a frame of reference. We can then describe when and where something happens unambiguously. But you might prefer to use a different frame of reference, so we need to know how to switch from my description to yours. That’s what relativity helps with.
If it’s ten metres from me, how far is it from you? I have to add our separation. But I don’t need to change the time.
On the other hand, if you’re also using a different time (perhaps you’re in a different time zone), then I have to adjust for that too.
It gets more complicated if you’re moving away from me. As time goes on, the separation gets bigger, so the distance I have to add changes, depending on when the event happens. So in that case, time will come into the adjustment.
This is all fairly mundane stuff, if a bit fiddly.
Relativity complicates things by telling us that we have to take distance and time into account even when we wouldn’t expect to. For instance, suppose your clock is ahead of mine. If we want to synchronise our clocks, we can’t simply add the necessary amount. It turns out that the adjustment depends on how far away you are, amongst other things. (There is more about exactly why this is so here.) This is the peculiarity that lies behind the Andromeda paradox.
That’s enough background for the first essay. If that’s all you’re interested in, you can stop here. But there are a couple of points worth noting that will matter for the later essays in the series, as well as adding a little more clarity to the first:
The Andromeda argument is mostly expressed in terms of ‘observers’, as I did in the first essay. But strictly speaking, we should really be talking about reference frames. Early books and articles on relativity used this more precise language almost exclusively, but it’s cumbersome. It saves time to say ‘for Mike’ or ‘for Melissa’, and I’ll follow that convention, but the more accurate phrasing would be ‘in Mike’s reference frame’ or ‘according to Melissa’s reference frame’.
If we wanted to be really pedantic, we would say something like ‘as measured according to the reference frame in which Mike is stationary.’ ‘According to Mike’ is much simpler. But we can lose sight of an important point: people (observers) have experiences and beliefs; reference frames do not.
A second point: any observer is free to use whichever reference frame they wish. There’s nothing special about the frame in which they happen to be stationary. Relativity guarantees that any observer is entitled to use a frame in which they’re stationary, but they’re under no obligation to do so. Practical considerations often favour other choices.
We do this all the time. When engineers launch a satellite into Earth orbit, they use a reference frame in which Earth is stationary. The satellite’s orbit is then easy to calculate. Or they might use a frame in which Earth is stationary, but spinning. But if they’re launching a probe to Mars, they’ll choose a frame in which the Sun is stationary, with Earth and Mars both orbiting it. If they used a frame in which Earth was stationary (which could be done), calculating Mars’s motion would become very complicated. Choosing the Sun as stationary means Earth and Mars both move in ellipses around it.
Relativity of Simultaneity.
The idea that different observers, moving past each other, will disagree about which distant events are simultaneous seems utterly bizarre when we first hear it. Is it really true that two people, momentarily in the same location as they pass, are experiencing different realities?
Well, no. It isn’t. So what exactly do we mean then? To explain, let’s first be clear what we mean by simultaneous.
The doorbell rings just as the clock strikes the hour. A bird lands on the windowsill just as you sneeze. These are examples of things happening at the same place and time. This is where our everyday idea of simultaneity comes from.
But when we extend this idea to events that occur in different places, the concept becomes tricky. The key insight is this: you can only be in one place at a time, so if two events happen in different places at the same time, then you can’t be present at both. So simultaneity of distant events isn’t something we can ever actually experience. It is something we deduce about events.
This is the key point: it is these deductions that different observers disagree about.
What’s more, they cannot make these judgements at the time they meet. They must wait until the signals (images, sounds, or other messages) from the distant events reach them. Then they can make calculations about which events happened first. But by then they will no longer be in the same place as each other (because they are moving past each other). The differences in their calculations arise from the fact that those signals will reach them at different times.
But surely they can take their different locations and velocities into account, and then they can agree? No. This is the new result from relativity. They will still get different answers to their calculations.
If you want to see exactly how this comes about, I explain it in detail here in the second explainer essay.
If you are willing to simply accept the idea for the time being, then the key takeaways are these:
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Observers moving past each other (Mike and Melissa, for instance) don’t disagree about experience, only about what they deduce from their experience.
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When they meet they don’t even disagree about this. It is only later that these different deductions can be made. Most importantly, for our purposes, deductions about what distant events were happening at the time they met.
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And if they understand relativity theory, they won’t even disagree about their calculations. Each will be able to make the calculations based on using either reference frame, and they will get precisely the same results.
The Constant Velocity of Light, c.
The velocity of light plays a crucial role in relativity theory, and there are some aspects that appear paradoxical. This speed is 300,000 km per second, but we call it c for short.
First, you can’t travel faster than light.
What if you’re going almost the speed of light, and then put in the same effort it took you to get to that speed? Won’t you now be going twice as fast?
It turns out, no, you won’t. Physicists do this all the time in particle accelerators. As the particles get closer to the speed of light, the extra energy they put in goes into increasing the mass of the electrons and other particles, and less and less goes into increasing the speed. It’s just the way the world is. The mathematical details are provided in this essay, but you don’t need the details to get the picture.
Second, the velocity of light is constant. At first sight this seems to be an innocuous statement, like saying the speed of sound in air is constant. But we mean something far more radical. The speed of sound may indeed be constant, but you can catch up with sound, and if you travel fast enough you can even overtake it and break the sound barrier. As we’ve seen, it’s absolutely impossible to break the light barrier.
But there’s more. It’s not possible to catch up with light even a little. Let me explain.
If you are travelling in a car at 25 kmph and I approach from behind at 35 kmph I will overtake you, and you will see me going 10 kmph faster than you. What we are using here is known as the addition law for velocities. You add or subtract velocities in a way I probably don’t need to spell out.
Now suppose there is some sort of explosion behind us. The sound of the ‘bang’ travels at 1235 kmph. It will be going only 1200 kmph faster than me, and only 1210 kmph faster than you, using the same velocity addition law.
But the flash of light from the explosion won’t behave like that. It will be going at speed c past a bystander. It will also be going at speed c past you, and at speed c past me!
Surely this doesn’t make sense? Well, it confused scientists too when they first discovered it. (And they did discover this, most famously through the Michelson-Morley experiment; it’s not just theory.) It took them decades to figure out what was going on.
The paradox was resolved by relativity theory. The solution, to put it simply, is that the law of velocity addition - just adding or subtracting velocities, as with the cars above - turns out to be wrong. It is very, very nearly correct. But not quite. The difference from the simple addition law is too small to notice at everyday velocities, which is why no one noticed it was inaccurate. But as the velocities involved get closer to the speed of light, the discrepancy increases.
This has important implications for the Andromeda scenario. Mike and Melissa, though moving relative to each other, will both observe the same light rays passing them at velocity, c. Even if they were travelling much, much faster than walking pace, this would still be true.
This matters, because it is the speed of light that sets the boundaries of the light cones, and it’s the boundaries of the light cones that determine which events we can influence and which we can’t.
And that is because the speed of light is the maximum speed possible. So signals (and therefore influences) can’t reach outside the light cones.
Absolute Versus Relative Past and Future
In the first main essay I distinguished between two senses of ‘past’ and ‘future’:
- Absolute past/future: events inside our light cones that can affect us or be affected by us
- Relative past/future: events behind or ahead of our world-slice, depending on our reference frame
The first of these - absolute past and future - is standard terminology in physics. The second is not standard, but I introduced it because proponents of the block universe regularly refer to events in the Elsewhere region as being ‘in the past’ or ‘in the future’ (meaning behind or ahead of someone’s world-slice). To analyse their argument clearly, we need some way to distinguish this sense of ‘past’ from the causal sense. Hence ‘relative past and future’ - relative, because it depends on which reference frame we use.
The generic diagram (Diagram 2) shows what is universal: the absolute structure of spacetime regardless of any particular reference frame. The absolute past and future are agreed upon by all observers, so they appear in the diagram. World-slices vary from person to person, so they’re not shown in the generic picture.
But what about my past? It makes sense to think of everything behind my world-slice as my past, doesn’t it, even if it isn’t everyone else’s?
Well, even that isn’t entirely straightforward. Just as we had to analyse our notion of simultaneity and adjust it, so we must now think about past and future with the same analytical eye. I’ll make some observations here and have much more to say about this in the second essay of the main series, as this goes to the heart of the block view of spacetime.
What do we usually mean when we say that something lies in the past or future? Classically, the relevant causal properties of past events are the following:
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We can’t, even in principle, have any effect on an event which lies in our past. We can’t change the past.
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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 usual way of deciding that it was indeed a past event.
And the future? Future events classically have the opposite properties:
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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.
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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 in terms of signals:
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Signals can reach us from the past, but not from the future.
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We can send signals into the future, but not into the past.
Now look again at Diagram 2, the basic spacetime diagram. It’s clear that events inside the past light cone have the classical properties we associate with the notion ‘past’. Signals can reach us from there, but not the other way around. Similarly for the future light cone. We can send signals to events there, but not receive them.
But what about events in the ’elsewhere’ region? They have a curious mixture of properties.
We cannot have any effect on events in that region, no matter how late they are - in other words, no matter how far ‘up’ the diagram they lie. This is a property these events share with the absolute past.
But unlike the absolute 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 absolute future, not the past.
This is one reason why physicists restrict the labels ‘past’ and ‘future’ to events inside the light cones - the absolute past and future, as they’re known. We see now more clearly why events outside the light cones don’t deserve those labels: they don’t have the classical causal properties of past and future – they have a mixture of them.
And here’s a crucial point: this is equally true of all the events throughout the ’elsewhere’ region, whether they are ahead or behind our world-slice. Events ‘behind’ our world-slice (in our ‘relative’ past) have exactly the same causal relation to us as events ‘ahead’ of our world-slice (in our ‘relative’ future). Neither can affect us, and we can affect neither.
In other words, events in the relative past and events in the relative future have exactly the same causal relation to us. This is quite different from the absolute past and absolute future, which have opposite causal relations to us: one can affect us, the other we can affect.
Event. A point in spacetime (where and when something happens).
World‑slice. The set of events an observer calls ‘simultaneous’ with a chosen local event.
Light cone. The set of events reachable by light signals from a given event (future cone) or which could have sent light to it (past cone).
Elsewhere. The region of spacetime outside the light cones.
Predetermination. The belief that the future is already fixed or “exists in advance.” Unlike determinism, it is a metaphysical claim about fate, not a physical claim about causation.
Spacetime Diagram. Essentially a distance/time graph like the ones we learn in school, but with time going up the page instead of to the right, and with features drawn from relativity theory.