ost people now think that space and time are not fundamental properties.
It's now generally believed that for a theory of quantum gravity to
be successful, space-time has to emerge from it. The question of how
that happens has become a hot topic, with heated debates among physicists
as to which of many competing theories is the best choice. The general idea
is that lack of background independence would be fatal to a theory of gravity.
Emergence happens when some property of matter is explained by some lower-level phenomenon that is necessary for it. One example is temperature, which is explained by collisions between molecules or atoms. An individual atom or molecule cannot have a temperature, but when many atoms collide with each other, the collective body has a temperature.
Having a background means the theory proposes a bunch of objects that already have a duration and are separated in space. Even though the objects may be Planckianly small, the fact that they're separate objects means that space and time have been ‘smuggled in.’
Figuring out how to avoid this is a tall order philosophically as well as physically. The tricky part is that we're unable to describe forces and objects without implicitly assuming that they exist. If they exist, where are they? If they don't exist, how can they do something? If there are two of something, it means they're separated in space. Our common idea of “existing” is that something occupies space and moves in time. If those objects and forces do neither, then they are nowhere forever. In other words, by our common definition, they don't exist. We're almost desperate enough to turn to philosophers to help us with this.
The other approach is to tweak the formulas until we get something that is formally equivalent to a metric in general relativity, and then declare the problem solved. It's the equivalent of the “shut up and calculate” mantra in quantum mechanics.
Dimensions up the wazoo
In ordinary 26-dimensional bosonic string theory, which is the simplest one, all quantum states represent bosonic particle states, which are energy. To get fermions, which are particles of matter like electrons and quarks, we also need superstring theories. This cuts it down to 9+1 dimensions (nine space plus one of time). Superstrings have supersymmetry, which predicts gigantic particles that are unlikely ever to be detected. There are five different ten-dimensional superstring theories. They're all mathematically related, so it was proposed to call them M-theory, which is not a string theory at all but talks about 2-branes and 5-branes, which are different from the D-branes in string theory. M-theory has eleven dimensions (10 + 1). Nobody knows whether all those extra dimensions are curled up, lost in history, or hiding behind the sofa. Also, no one knows what M stands for.
You know your theory is asymptotically approaching incomprehensibility when it takes a whole paragraph just to tell you how many dimensions it has.
High numbers of dimensions don't just come from physicists. Some philosophers proposed solutions to the “measurement problem” in quantum mechanics by claiming that the wave function is too complicated to fit in normal 3D space, so particles live in 3N space, where N is the number of particles in the universe. This is called wavefunction realism (see Vera Matarese's critical discussion in Quantum Mechanics and Fundamentality and Alyssa Ney's defense of the idea in The World In a Wave Function).
What do physicists say?
Advocates of string theory are naturally inclined to believe that their theory is background dependent. Philosopher Tiziana Vistarini, in the popular-style book The Emergence of Spacetime In String Theory, repeatedly asserts that it is. But physicists are more circumspect. For example, Harold Erbin in String Field Theory: A Modern Introduction says:
What is the status of background independence in string theory? The worldsheet formulation requires to fix a background (usually Minkowski) to quantize the theory and to compute scattering amplitudes. Thus, the quantum theory is at least not manifestly background independent. On the other hand, the worldsheet action can be modified to a generic CFT [conformal field theory] including a generic non-linear sigma model describing an arbitrary target spacetime. . . . From this point of view, the classical theory can be written as a manifestly background independent theory, and this provides hopes that the quantum theory may also be background independent, even if non-manifestly.
Background independence in SFT [string field theory] is thus the statement that the theories characterized by different CFTs can be related by a field redefinition. [p.328]
In other words: no, but we can change it. The temptation, as always, is to redefine the problem until it goes away, so we can get the critics off our back and go on to more interesting problems. Philosopher James Read in Background Independence in Classical and Quantum Gravity compared 18 different definitions and concluded: maybe yes, maybe no. Depends how you define it.
It's generally assumed that space came from somewhere, possibly during cosmic inflation. This suggests that at very high temperatures space might be converted into something else. But that doesn't tell us whether space is fundamental or not.
Maybe it doesn't even matter. The real issue is that thinking about emergence represents two fundamentally different approaches. The physical way is to say that the theory would have to explain, conceptually, what space is. The other way, which is a lot easier, is to see if the mathematics can be made into something that looks like the formulas in relativity.
We had the same problem in the question of consciousness, where the debate revealed that there was no clear definition and everyone was talking about something else. Some people even claimed that consciousness doesn't exist and there was no 'hard problem' at all. Maybe it's like the question “what is life?” which obsessed people for over a century and then became meaningless.
So, what the question really represents is a debate about the direction of physics. It's not just an academic question. It will determine whether physics remains tethered to the real world, or whether its theories gain accuracy but lose the benefit of simplicity, as Ptolemaic astronomy did, and risk getting swept away.
jul 22 2024, 6:46 am
