What If Space And Time Are NOT Real?

Thank you to Brilliant for supporting PBS. Physics progresses by breaking our intuitions, but we are now at a point where further progress may require us to do away with the most intuitive and seemingly fundamental concepts of all—space and time themselves. Physics came into its modern form as a description of how objects move through space and time.

They are the stage on which physics plays out. But that stage begins to fall apart on the tiniest scales and the largest energies, and physics falls apart with it. Many believe that the only way to make physics whole again is to break what may be our most powerful intuition yet.

In our minds, space and time  seem pretty fundamental, but that primacy may not extend beyond our minds. In many of the new theories that are pushing the edge of physics, spacetime at its elementary level is not what we think it is. We’re going to explore the “realness” of space and time over a few upcoming episodes.

We’ll ask: Do our minds hold a faithful representation of something real out there, and if not, why do we think about space and time the way we do? And if space and time aren’t fundamental, what is? What do space and time emerge from?

But today we’re taking the first step by exploring how the notion of absolute space and time in physics came about in the first place, and how that notion is beginning to fall apart. We have this sense of space as an extended emptiness - a volume waiting to be filled with matter - a regular, continuous, mappable … space, in which everything that exists is embedded. Meanwhile time is the continuous rolling of future into past through the present, all governed by the same unstoppable clock.

But this idea of space and time as having an existence “out there”, independent of its contents, became cemented in popular intuition relatively recently, at the same time that they became cemented in physics. However humans have been arguing over the reality or the fundamentalness of the dimensions for millenia. We can summarise the two main conceptions of spacetime as either relational— space as a network of positional relationships of objects —or absolute—a real entity that exists independently of objects, and rather, contains the objects.

The latter seems to have emerged only relatively recently. Let’s start with the ancients. They certainly thought a lot about space—after all, they had maps and they invented geometry.

But the geometries of Euclid and Pythagorus and others didn’t need the notion of space as an absolute entity—they were relational. For example, a triangle is defined by the relative lengths of its sides and its internal angles. You don’t need a coordinate grid to define a triangle—which is good, because the ancient Greeks didn’t have one.

Sure, their maps had longitude and latitude, but they didn’t have our own mathematical habit of gridding up empty space with x, y, and z axes. As such, they didn’t tend to think of empty space as having its own independent existence. The idea of the coordinate grid came much, much later.

Perhaps you’ve heard of the Cartesian coordinate system. X, y, and z axes, each at 90 degrees to the others and gridded up so that any point in space can be defined with three numbers - the value of the closest grid-mark on each of the axes. This idea feels pretty intuitive to many of us, but it wasn’t commonly used until after 1637, when the French  mathematician and philosopher Rene Descartes made it cool.

With the coordinate system, it became possible to represent abstract numerical concepts in spatial terms—for example, by graphing an algebraic function. But it also gave us a tool for describing arbitrarily large and  imaginary physical spaces—and this application would soon revolutionise all of physics. Regarding the actual nature of space, Descartes was firmly in the camp of philosophers like Plato, who didn’t believe in empty space.

Descartes said that space is only real as far as it defines the extension of objects and matter. But the invention of the first true mathematical coordinate system opened the door for a very, very different conception of space. And that new conception was almost entirely due to Isaac Newton.

He gave us a set of equations that could, apparently, completely describe the motion of objects and how those motions change through the forces of their interactions. Newtonian mechanics is built on Descartes’ coordinates, and assume a universal clock. Those mehcanics proved wildly  successful— revolutionary, really.

So much so that many, including Newton, began to see the foundational building blocks of the mechanics—the coordinate of space and time—as in some way physically real. Newton himself insisted that space is absolute; it exists completely independently of any objects within it. The empty volume implied by the Cartesian grid is a thing in itself.

And according to Newton time is also absolute. From Aristotle to Descartes, “time” was mostly understood as a counting of events. But In Newton’s view, there’s a single universal clock that keeps the same time for all observers--time passes “by itself ”, even in the absence of any change.

Newton also believed that there was an absolute notion of stillness. Like, a master frame of reference whose x, y, and z axes are unmoving, and if your position was fixed relative to those axes then you were truly still. This is contrary to the ideas of Galileo a century prior, who showed us that velocity is relative—the speed you measure for another traveller depends on your own speed.

The laws of physics are the  same in any non-accelerating, or inertial frame, and so all such frames are equal. While Newton accepted the  mathematical consequences of Galilean relativity, he  thought the difficulty we had in defining a preferred inertial frame was a limitation of the human mind, not of the universe. The success of Newtonian mechanics elevated the notion of the realness of space and time in everyone’s minds.

But there was one prominent naysayer. Newton had a nemesis. Or maybe it was Newton who was the nemesis to this guy.

Ok, he shared a mutually nemetical relationship with the German mathematician  Gottfried Wilhelm Leibniz. Their most famous rivalry was over the discovery of calculus, which they  figured out independently—with Leibniz probably getting to it first. Newton however accused him of plagiarism, and being by far the most powerful scientist of his day, secured the credit for himself.

But another point of contention between these  two was on the nature of space and time. Leibniz did not accept Newton’s assertion that these dimensions were in some sense real and independent of anything in them. Instead, he thought that both space and time were relational.

What does that even mean? Well, it means that objects exist, but they don’t live in a 3- or any other dimensional space. Rather, what we think of spatial separation is a quality of the objects themselves—or rather of the connection between them.

Exactly why Leibnitz thought this and rejected  Newton is a whole thing, that we don’t have time to get into right now. Instead, let me try to give you a sense of what it could mean for space to be encoded in objects or in their relationships, rather than existing independently to those objects. Let’s start by imagining only one dimension of space, represented as a line.

This is a Newtonian space, where every point represents an absolute position in a 1-D universe. We can put some particles in the universe. The position of each in space is defined by - well, its position in space—whatever grid mark it’s next to if we add a coordinate system.

The particles might have intrinsic or internal properties—say, mass, electric charge, etc. , but their position isn’t a quantity that’s intrinsic to the particle. In Leibniz’s view there is no space, so we get rid of the line.

The particles still exist, but they aren’t anywhere. They’re sort of just bundles of properties with no size or location. Space doesn’t exist so maybe we should place these particles on top of each other, but then again if location is meaningless we might as well separate them so we can see them.

Let’s add a new property to each particle that we’ll call X. X is what we call a degree of freedom—something about the particle that can take on different values, and it can change. Other degrees of freedom could be energy and phase and spin and so on.

X behaves in a particular way. For example, it can change freely. If it’s changing, then it keeps changing at the same rate and in the same direction.

Now these particles have no idea about each other's existence, except  in a special circumstance. For example, If two particles have values of X that are close to each other then those X values influence each other, changing the  rate at which the dials turn. Maybe they want to try to be more similar, or maybe they try to be more different.

If we were to represent these X values with position on a number line - an x-axis - then the behaviour of the particles looks just like particles moving around in space and attracting or repelling each other only when they’re close together. We can’t tell the difference between particles moving in space versus space-like behaviour emerging from a degree of freedom within the particles. This thought experiment isn’t explicitly what Leibniz described,  nor is it how things should really be to explain a universe like our own.

For one thing, we need 3 spatial dimensions, not one. X, Y, & Z would all have to be close to each other for particles to interact. Also, Leibnitz thought that position was  encoded in the relationship between particles, not in the objects themselves.

He gave his elementary particles names - monads - which among other things had rudimentary consciousness, and that space emerged from their first-person perspectives of each other. But we don’t actually need  those extra qualities--the idea of particles with interacting, internal degrees of freedom illustrates how space can emerge from the relationships between elements that are themselves not in space. So that’s Leibnitz on space.

He disagreed with Newton on time in a similar way, believing it to be a measure of the change intrinsic to each element, rather than a cosmic clock that kept the universe in sync. Of course Newton was the undisputed boss of science back then, and so his preference for absolute space and time won over the physicists, and ultimately found its way into the popular imagination. But who was really right?

Are objects in space and moving through time, or are space and time somehow in objects and their connections? Are the dimensions absolute or relational? The big next development seemed to support Newton.

Over the 19th century, our understanding of the phenomena of electricity and magnetism converged, revealing the existence of something called the electromagnetic field. A field is just some property that can take on a numerical value at all points in space. For example, temperature is a field defined in the air around you.

It’s emergent from the properties of the air particles. But the electromagnetic field doesn’t need particles. For the first time, it seemed that a field could be a property of space itself.

So, surely if space can have properties, then space must objectively exist. And more intrinsic properties emerged with the development of quantum mechanics—for example, space was shown to have a sort of energy even in the absence of particles—so-called vacuum energy. However, if we really want to decide whether space and time are real—to judge between Leibnitz and Newton—we need the ultimate arbiter.

We need the greatest expert of space and time that ever lived—and that’s Albert Einstein. We’ve talked about Einstein’s special and general theories of relativity many times before. Let’s just go over what the theory changed about our notions of the dimensions.

With special relativity, the separation of 3-D space and 1-D time ended. They became 4-D spacetime. Einstein showed that our motion through space and our motion through time are linked.

A clock moving relative to you ticks slower from your perspective. And then with general relativity we see that the presence of mass and energy stretch and warp both space and time. This causes straight line trajectories that we expect on a Cartesian grid to become curved, and the apparent change in an object’s path in the presence of mass is Einstein’s explanation of gravity.

Relativity overturned some of Newton’s notions about absolute space and time: that they are independent entities, that there’s a universal clock for time, and that there’s some sort of ultimate, rigid coordinate system for space. But what did these mean for the central question of this episode: what about the realness of space and time? Actually, spacetime in Einstein’s universe kind of feels even more substantial than before.

It’s like a fabric that can be warped. It can hold energy. It can even propagate waves—gravitational waves.

Einstein showed that empty space has properties, so it must be real, right? Well, maybe - but Einstein’s view is really a radical departure from Newton’s—to the extent that Einstein even called himself a Leibnizian. Newton believed in space as an underlying stage on which the particles and the fields danced.

But Einstein insisted that no such background existed—and that’s because to him, space and the gravitational field are the same thing. This field is not painted on top  of a coordinate system; rather, the coordinate system is a quality of the field. Absent this field there is nothing.

So all of this landed Einstein somewhere between Leibniz and Newton. He believed that there is an extended structure “out there” that can hold objects and on which distances and durations can be defined, but it’s not absolute and fundamental in the way that Newton thought. According to Einstein, Descartes was right, and so was Plato: there’s no such thing as empty space.

To quote Einstein,  "there is no space empty of field" So is Einstein the last word on the matter? Far from it. We know that general relativity breaks down on very small scales—smaller than around 10^-35 meters, which is the Planck length.

There it comes into hopeless conflict with quantum mechanics, and it becomes impossible to meaningfully define shorter distances. Just as it’s meaningless to define durations shorter than the Planck time. This conflict between Einstein’s theory and quantum mechanics is one of the major challenges and inspirations for progressing to the next level of physics.

And essentially all of the possible paths forward force us to rethink our understanding of the dimensions—whether multiplying their number as in string theory, or by having them emerge from elements that, themselves, do not exist within space—such as in loop quantum gravity, which we’ve discussed, or the cellular automata of Wolframs physics project, or in the entanglements between  elements on a holographic horizon, or from Arkani-Hamed’s amplituhedron among others. . If any of these latter are true, then Leibniz may have been onto something; space exists in the relationships between some sort of elementary… something, not as an absolute and physically real fabric.

Leibniz also had another controversial idea: he thought that space was in our minds. This isn’t the same as saying that reality is in our minds—it’s not even the same as saying that space doesn’t exist. Rather, Leibniz felt that whatever it is that’s out there that behaves like space only gains the subjective feeling of depth, breadth, height, and distance when our brains try to organise objects that are separated by an altogether more abstract property.

Kind of like how the subjective experience of red only exists when brains interpret a frequency of light. It’s incredibly difficult to imagine a universe without space or time. The dimensions seem hardwired into our brains.

Perhaps we need to break this preconception to move forward in physics. If so, we need to explore how and why our brains build our very convincingly spatial and temporal inner worlds. And we’ll do that in an episode very soon, and perhaps get closer to figuring out whether we live in an absolute or a relational spacetime.

Thank you to Brilliant for supporting PBS.  Brilliant is an online learning platform for STEM with hands-on, interactive lessons. Brilliant  is for curious learners, both young and old, professional and inexperienced.

Brilliant courses  teach you how to think (via interactive lessons and problem-solving activities/exercises. ) and  solve problems with interactive lessons in STEM. For example, Artificial neural networks  learn by detecting patterns in huge amounts of information.

Like your own brain,  artificial neural nets are flexible, data-processing machines that make predictions  and decisions. In fact, the best ones outperform humans at tasks like chess and cancer diagnoses. In this course, you'll dissect the internal machinery of artificial neural nets through  hands-on experimentation, not hairy mathematics.

You'll develop intuition about the kinds  of problems they are suited to solve, and by the end you’ll be ready to dive into  the algorithms, or build one for yourself. To learn more about Brilliant,  go to brilliant. org/spacetime Today we’re looking at your comments from  the last two episodes.

There was the one about how Earth really moves through the  universe, and then the one about how the nucleus is held together by meson exchange.  Starting with the motion of the Earth. Matt Thomas asks, when we put together all of  our motion through the universe, how fast are we moving relative to the CMB?

And what effect  does that motion have on our experience of time? The answer is that we’re moving at 368km/s  relative to the CMB. This isn’t unusual—most things in the universe have some relative  velocity like this.

But you’re right that there should be a time dilation relative to the  CMB. Let’s assume the frame of reference of the stuff of the Earth has on average been moving  at that speed over the history of the universe. Less time has passed in that reference frame  compared to the rest frame of the CMB—the Big Bang was more recent for our hypothetical moving  frame.

I figured it out—the difference is about 10,000 years. Pretty tiny compared  to the age of the universe. Karl Sheffield asks what is in  front of our path around the Galaxy?

Well, immediately in front: the interstellar  medium. The Sun’s heliosphere—a bubble containing its outward-flowing solar wind and  magnetic field—is plowing its way through very low-density gas and dust grains. There  are also bigger things that we can’t see easily—bits of rock or ice like oumuamua  that were ejected from other star systems.

There will be ejected planets, brown dwarfs,  black holes and other stellar remnants. In terms of stuff we can see—well we’re heading  in the direction of the star Vega, but Vega is also orbiting the galaxy and so we’re not going  to collide. That said, we do occasionally get close enough to a star or stellar remnant to mess  with orbits in our system, with the main danger being an increase in inner-solar system comets. 

That’s more likely when we’re passing through the disk and especially in a spiral arm. It’ll  be millions of years before that happens again. Moving on to the episode on  the strong nuclear force.

Fensox asks whether Hideki Yukawa eventually got  the recognition he deserves for discovery of the strong and weak forces. He did. He got the  1949 Nobel Prize for predicting the existence of the pi meson.

And his name is all over the  standard model—the Yukawa interaction governs the strong force part of the standard model  Lagrangian as well the Higgs coupling term. Several people asked how it is that the  exchange of virtual particles can cause particles to be attracted. After all, in  the analogy of particles throwing balls at each other, it seems that the exchange  of momentum should only push them apart.

The short answer is that the balls analogy  is a pretty limited one, and even the notion of virtual particles is something of a metaphor.  What’s really happening is that the quantum fields between and around the particles are disturbed in  a way that can be approximated as the work of many virtual particles. But those virtual particles  don’t simply originate at particle one and travel in a straight line to particle two.

They  can originate in a wide region governed by the uncertainty principle, including on the opposite  side of particle two. They can also have any mass, including complex masses. All of this enables  the virtual particles to transfer momentum in a way that pulls the particles together instead  of apart.

But really, these particles are a mathematical fiction to describe field  behavior. No balls are being thrown. Feelincrispy points out that I could easily just make something up and %99.

9 of  you would have no idea. I don't know if I agree with that, but otherwise I have no comment. sleekweasel asks how the  island of stability works, given that if a nucleus grows too big,  its mesons can't hold it together.

To remind everyone —the island of stability is  a region of the periodic table of very large nuclei that is theoretically more stable  than the current heavy end of the table that we've discovered at this point. Actually, I don’t really know the details of this. But fortunately Gareth Dean jumped  in to the comment section to answer, so I’m just going to read that.

He says: Nuclei aren't just blobs of particles,  they have 'nuclear shells'. When these are empty the few particles in them are far apart and  cannot exchange mesons. When they are full, lots of particles are packed close and can  bind strongly.

'Islands of stability' are places where the shells are full, binding  is strong and the nucleus is more stable. Regarding my use of the labradoodle to  illustrate the amount of force between adjacent protons in an atomic nucleus. Many of  you expressed interest in using labradoodles as some sort of standard unit of measurement. 

This is a little impractical because we’d need to use the mean weight of a statistically large number of labradoodles. But I personally volunteer to run the NIST labradoodle standards facility to  make sure those very good boys and girls get all their standard treats and pets. Many of you also  pointed out that a universe without labradoodles is not a universe they’d want to live in.

Also  agreed. Which brings us to Steve. Steve sees the elimination of the strong nuclear force and  with it the elimination of all chemistry, biology and life, as a promising way to rid the world of  labradoodles.

Steve, you’ve identified yourself as labradoodle-foe, and your name has been passed  to a secret elite team at the NIST labradoodle standards facility. They’ll be watching  you. In fact all labradoodles will be watching you.