No Matter, Ergo No Space-Time (?)

Schrödinger’s cat is a renowned thought experiment in the world of physics. It was devised by physicist Erwin Schrödinger in 1935 to illustrate the problems behind the Copenhagen interpretation of quantum mechanics. In simple terms, his experiment states that:

If you place a hypothetical cat and something capable of killing the cat (such as a radioactive atom) in a box and then seal it, you would not be able to tell whether the cat is alive or dead for as long as the box remains shut. As such, until the box is opened, the cat would be (in some sense) both “dead and alive” at the same time.

Graphic representation of Schrödinger’s cat. / Source: Wikipedia.com

That said, allow me to put a metaphorical pin on this fact. I promise that it will make a comeback later on, so try to keep it in mind. For the time being, though, let’s set our focus on the main topic of this essay, shall we?

So, here we go!

Physics, just like many other branches of science, can be characterised by the presence of debate. You’d think that, since physics is a science and since science is (by its own definition) factual, it’d be easy to achieve a consensus among physicists. After all, we have at our disposal all THE facts of nature (or, as we affectionately call them, the “Laws of Physics”), and discussing such things seems nonsensical.

Yet, us physicists enjoy taking part in debates, because we’re keenly aware that, in spite of our best efforts, not all facts are created equal. In fact, many “facts” that we take for granted are purely theoretical and stand on shaky grounds between being a truthful reflection of reality and mere speculation.

Thus, enter matter and space-time!

As you probably already know, matter is anything that has mass and takes up space, whereas space-time is simply the union of space (a boundless three-dimensional extent) and time (literally defined in physics as “what a clock reads”).

The manner in which these two concepts relate to one other is as follows:

Matter needs a) space in order to have a relative position and direction, and b) time so that there’s a continued sequence of existence happening in a [seemingly] permanent succession.

On the other hand, spacetime needs matter, because its curvature is directly related to the energy and momentum of whatever matter and radiation are present.

Simply put, matter determines how spacetime curves or shapes itself, while spacetime decides how matter moves within it.

However, now that we’ve determined this correlation, that begs the question: Can spacetime exist in spite of the lack of matter? And therein lies our present conundrum, my dear reader, for the answer to such a question can be posed as either a conceptual yes or a resounding no.

Allow me to elaborate upon that.

To a physicist, it is unclear whether matter can or cannot exist without spacetime and vice versa. That is because we have two opposing theories battling it out to become the official “rulebook” of the natural laws that govern our Universe. These are: general relativity, our best theory of spacetime, and quantum field theory, our best theory of matter. [*]

So, for starters, let’s talk about general relativity, a geometric theory that, as devised by Einstein in 1915, establishes the current description of gravitation in modern physics. In order to do so, it generalises special relativity and refines Newton’s law of universal gravitation, providing a unified description of how the relationship between spacetime and matter establishes gravity as a geometric property of spacetime. This association is then specified by the Einstein field equations, which relate the geometry of space-time with the distribution of matter inside it.

As it turns out, physicists have found ways to solve such equations by prescinding matter. One such solution is the Schwarzschild metric. Considered an exact solution to the Einstein field equations, it places the gravitational field outside a spherical mass, assuming that the electric charge and angular momentum of the mass, as well as the universal cosmological constant, are all zero. Such a definition basically represents a spherically symmetric and static black hole in a vacuum or the so-called Schwarzschild black hole. Thus, considering that black holes are merely regions of spacetime, we find ourselves in the presence of a matter-less Universe where spacetime can still exist.

Graphic representation of a black hole. / Source: Google images.

Another possible solution, albeit less likely, can be found in Wheeler’s geons (an abbreviation for the phrase “gravitational-electromagnetic entity”). As stated by theoretical physicist John Archibald Wheeler, a geon is a nonsingular electromagnetic or gravitational wave that is held together in a confined region by the gravitational attraction of its own field energy. The wave would then make it possible for electrons, quarks, and other particles to be represented as excitations of the gravitational field. To that end, the stress–energy-momentum tensor is net-zero everywhere, denoting that there are only gravitational waves. This signifies that, right now, as I’m typing this on my computer, there’s only spacetime and virtually no matter.

Additionally, a third solution can be found when taking into account Minkowski space. Created by mathematician Hermann Minkowski, Minkowski spacetime lays down the foundation for a four-dimensional manifold, where there are three space dimensions and one temporal dimension. It then equips spacetime with an indefinite non-degenerate bilinear form, also known as the Minkowski metric. As a consequence, it presupposes the existence of flat spacetime in the absence of matter.

Graphic representation of the subdivision of Minkowski spacetime. / Source: Wikipedia

That being so, we can safely say that general relativity concedes that there can be spacetime without matter.

But what about quantum field theory?

As a theoretical framework, quantum field theory (or QFT, for short) combines classical field theory, special relativity, and quantum mechanics, which allows it to construct the physical models of subatomic particles used in particle physics. From this then arises what we know as the Standard Model of particle physics, or the theory that “quantifies” three of the four known fundamental forces (the electromagnetic, weak, and strong interactions, but no gravity) in the Universe, and that establishes the classification of all known elementary particles.

Accordingly, this theory argues that there is never such a thing as “no matter”. Space is nothing but an agitated mass of fields, where particles emerge and fade out of existence faster than the blink of an eye. That is to say that, by its very nature, quantum field theory cannot consent to there being spacetime without matter.

Now, with all that’s been said, can you see how this relates to Schrodinger’s cat?

No? That’s okay. I’ll explain the analogy.

As you’ve probably noticed by now, the reason I mentioned Schrödinger’s cat earlier has nothing to do with how the space-time continuum could exist with or without matter. (Though I’ll admit that that could be an interesting topic for another essay). Instead, I was trying to point out the following:

Under certain circumstances, current knowledge cannot produce a definitive answer, so the possibility of a simultaneous yes and no result must be accepted. However, this can only be the case until new knowledge, that makes it possible to conceive an indisputable answer, is acquired.

Therefore, as it is now, we’ll have to settle for the idea that we just can’t open the box that keeps Schrödinger’s cat imprisoned. At least not until there’s sufficient technology available to do so. And by then, would it even matter whether the cat is dead or alive? Maybe yes. Maybe not. But if the time ever comes, only our inherent curiosity shall be the judge of that.

Thanks for reading. (:

Photograph of the Milky Way galaxy as seen from Earth. / Source: Google images.

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