What’s in it for me? Understand the concepts of space, time, and spacetime.
When was the last time you had a conversation with your neighbor about inflationary cosmology? How often do you discuss superstring theory with your partner? What? Never?
Well, if Sean Carroll had his wish, we’d all be talking about physics and offering our opinions on the latest theories in the same way that we discuss politics or the economy.
Although that’s not likely to ever happen, Carroll hopes that his book series The Biggest Ideas in the Universe will help people really learn about modern physics – even if they want nothing more than to remain amateur physicists. The first of the three books, Space, Time, and Motion, focuses on nine topics and explores each through a breakdown of the theory and analysis of equations.
Maybe Einstein’s equation would be a good place to start.
You’re probably thinking E=mc², right? Energy equals mass times the speed of light squared. Well, that might be important – but it’s just small beans.
When professional physicists talk about Einstein’s equation, they mean Einstein’s field equation for general relativity, or
Rµv - ½Rgµv = 8πGTµv
But don’t worry! In this Blink, we’re not going to present you with any other complex equations, what they mean, or how to solve them; that level of detail lies firmly in Carroll’s sphere. Instead, we’ll offer a taste of three of the biggest ideas in the universe – space, time, and spacetime – and perhaps whet your appetite to become an amateur, or even professional, physicist.
Space
You’re probably aware of the concept of space. It’s that “thing” where everything takes place. Where “objects” are located. But have you ever really thought about what space actually is? To start unpacking the concept, it might help to wind the clock back some 300 years.
In the early 1700s, there were two schools of thought. One posited that space was a substance and had an existence of its own – it was the “container” for everything else. The other considered space to be nothing at all. There was much discussion at the time, especially in a series of letters between Samuel Clarke in England – who agreed with Isaac Newton that space was indeed a substance – and the German Gottfried Wilhelm Leibniz, an adversary of Newton who believed space was relational. Leibniz’s death brought the exchange to an abrupt end in 1716, but by then, they’d talked about everything from space to free will to God.
Most physicists today agree with Newton: space is indeed a “thing.” Why do they believe that? Well, first, space isn’t empty. There are fields of one type or another – gravity, for instance – operating within it. And second, space (as part of spacetime) can change on its own.
At the moment, the whole picture still isn’t completely understood. We do know some basics, though. Take space’s dimensionality, for instance. Grab a couple of pencils, and tie them together at right angles. Then pick up a third, and tie it at the same intersection so it’s at right angles to the other two. Now pick up a fourth and tie it at the same intersection at right angles to the other three. That’s right! It’s not possible. You’ve just effectively demonstrated that space is three-dimensional.
Occasionally, physicists treat some things as having only one dimension – a stream of electrons moving rapidly along the length of a long wire, for example. Or having two – a thin film or the surface of a three-dimensional object. But although they can model systems as if they have just one or two dimensions, they in fact have all three. And when it comes to string theory or some other models, physicists envision even more than three dimensions. Not quite as simple as it first seems, huh? Well, you’ll be pleased to know that’s all beyond the scope of this Blink!
Having three-dimensional space, though, provides us with a neat explanation as to why the gravitational force between two objects is inversely proportional to the square of the distance between them. Imagine lines radiating out from the center of the sun – these represent lines of gravitational force. Now imagine another bigger sphere with the sun at its center. All the lines radiating from the sun pass through this sphere. Finally, imagine another even bigger sphere even further out. All the lines also pass through the radius of this megasphere. But due to its size, fewer lines pass through any given area compared with the first. The area of a sphere is proportional to its radius squared. So it follows that the gravitational force is inversely proportional to the square of the distance between two objects.
OK, enough about space for now. Let’s turn our attention to the next big idea in the universe: time.
Time
Consider two questions for a moment. First, “Can we meet up at 9:00 p.m.?” Second, “Want to watch this 120-minute-long movie?” Both utilize the concept of time, and we know exactly what the person asking means in terms of time.
But let’s push that up a notch and look at time in terms of the universe. Here, we can consider time to be a convenient way of labeling the slight changes that happen from moment to moment. Something “happens,” and there’s a transformation that takes place over time. Without time, there could be no transformation. No evolution from one moment to the next. No change.
Time also helps us locate ourselves in the future, like meeting at 9:00 p.m. – our when. Space allows us to specify our where – the café around the corner from work. If we don’t specify one or the other, then the information isn’t of much use. Bundling time and space together gives us the concept of spacetime, which we’ll explore in the next section. But before that, let’s discuss some more properties of time.
Time, like space, can be measured. We measure time using a clock, right? If we want to do this accurately, we need to use an instrument that changes reliably and in a way that can be compared to other clocks. Thankfully, there are many “clocks” in the universe – systems that have a predictable, regular motion in comparison to one another. The rotation of Earth around the sun is a good example: in one year, Earth rotates on its axis just over 366 times.
But there’s a big difference between time and space. Whether we like it or not, we travel through time. With space, we don’t always move – think of the COVID-19 lockdowns – but even when we do, time continues to flow. And time flows forward from the past to the future; each moment is dependent on the previous one. When we look at time from the present, we feel that the past is over, whereas the future is yet to come. The past has been recorded, but we can only predict the future. This direction of time is often known as the arrow of time.
Let’s compare time to space once more. You probably remember from the last section that there were two views about space – one said it was a substance itself, and the other said it was a convenient way of describing the location of objects in relation to one another. But nobody was questioning whether locations in space were real or not. When it comes to time, that isn’t the case.
First, we have the concept of presentism: the view that only the present moment in time is actually real. Moments in the past have gone, and those in the future are yet to come – so they aren’t real.
Eternalism, on the other hand, suggests that all moments in time are equally real. This way of looking at the universe is also known as the block universe view because it considers the real world to be a block of spacetime in four dimensions.
And there’s a third view: possibilism, which is sometimes called the growing present view. This view considers both the past and the present to be real – but not the future.
The truth is that all three approaches have their merits, and good arguments exist for each.
As far back as the sixth century BCE, the Greek philosopher Heraclitus expressed presentist views. He observed that it wasn’t possible to ever walk into the same river twice – at a different moment in time, it’s already become a different river. But Parmenides, a Greek philosopher from a century later, thought differently; he believed that the universe was simply eternal.
There’s still a lot about space and time that isn’t well understood. In the next section, we’ll turn our attention to the combination of the two: spacetime.
Spacetime
Back in Newton’s day, it would have been quite feasible to put space and time together and talk about a four-dimensional concept of spacetime. But it wasn’t until the theory of relativity was proposed in the early twentieth century that it really came into its element. With relativity, spacetime is reality; separating it into space and time is just a convenience for us mortals.
In his theory of special relativity, Einstein introduced new ways of thinking about length and duration. He also posited that the speed of light – the speed at which light travels through “empty” space – was an absolute limit; it would always be the same, even if the observer were also moving. But it wasn’t Einstein who ultimately proposed unified spacetime. It was his former professor, Hermann Minkowski.
For Minkowski, four-dimensional spacetime was flat, static, and infinite. But after working for ten years on how to incorporate gravity into the theory, Einstein realized that spacetime could also be dynamic and curved – and actually, it was the curvature that created what we experience as “gravity.” This theory is now known as general relativity.
So, just to distinguish these, when physicists refer to special relativity they’re talking about the theory of fixed flat spacetime without gravity. When they talk about general relativity, it’s dynamic spacetime where the curvature is responsible for gravity.
Let’s revisit that café around the corner from work, where we’re going to meet at 9:00 p.m. From your home to the café, “as the crow flies” would be the shortest distance. But you’re not a crow. In the real world, you have to walk down a couple of streets and turn a few corners to get there. Now let’s think about it in terms of spacetime too. In relativity theory technical speak, we have two events – two points in the universe with a time and location. So we have event A (at home at 8:30 p.m.) and event B (at the café at 9:00 p.m.). There are 30 minutes between the two events. Simple, right?
Yes, of course – and, well, also no! Yes, if we consider this in the old Newtonian world – but no if we consider it from an Einsteinian perspective. Why is that? Well, just as the crow’s route to the café is shorter than your actual route, in spacetime, the duration of the time you experience getting to the café – time you can measure on a clock you carry with you – isn’t the same as the universal coordinate time. You see, time is just like space here. It depends on the route through spacetime that you take. And this is where it all starts to get a bit complicated:
A straight line in space is the shortest distance between two points, but a straight path between two events through spacetime yields the longest elapsed time!
OK, definitely not intuitive. But why is it this way? Well, as Carroll says, “Because physics says so.” With the knowledge that physicists have today, this is a fundamental assumption upon which physics is built.
It might help if we consider what’s commonly known as the twin paradox – which, incidentally, isn’t a paradox at all; it’s just nonintuitive. Tom stays on Earth, while Barbara heads off into space in a rocket traveling close to the speed of light and then comes back to be with Tom. Tom moves through spacetime in a straight line. Although Barbara started from the same event as Tom and finishes at the same event, her route is definitely not straight. At their reunion, Barbara discovers she’s not as old as Tom – her clock has counted fewer minutes, hours, days, and years. If Barbara were traveling at 99 percent the speed of light for each year that she experienced, Bob would have experienced seven.
Obviously, this hasn’t been tested with humans due to our current technological limitations. But physicists have done experiments with elementary particles, and it’s beyond doubt that this phenomenon is real. And the equations? They back it all up too.
So if we’re all moving around in spacetime relative to one another, why don’t we notice the effects like Tom and Barbara do? It’s because we’re all moving much more slowly than the speed of light. For example, a car traveling at 65 miles per hour is going at approximately 10⁻⁷, or 0.0000001, times the speed of light. Effectively, in day-to-day life, we’d never be able to tell the difference.
Final Summary
It’s sometimes convenient to think of space as one- or two-dimensional – or, for physicists, to consider many more dimensions. But it can be demonstrated that space essentially has just three dimensions.
Most of us understand the concept of time in our day-to-day lives; unlike with space, we have no option but to travel through it, and our direction of movement is always forward. There are three views on which aspects of time are real. Presentism considers only the present to be real; possibilism builds on this and says the past is real too; and eternalism considers past, present, and future to be equally real. Each view has its own merits.
When we consider four-dimensional spacetime, the so-called twin paradox demonstrates that time is relative – depending on the route traveled through spacetime from event A to event B, two people can experience time differently.