By: Adam Koberinski
In the current state of theoretical physics, there are very few clues as to what will be important in building a theory of quantum gravity. Due to the extremely high energies and exotic conditions under which both gravity and quantum effects are known to both be relevant, experimental data on quantum gravity is hard to come by. With little else to guide theoretical work, physicists have often turned to theoretical puzzles for guidance.
One of the most well-known puzzles in contemporary quantum gravity research is the cosmological constant problem. This problem arises when one tries to understand the way that vacuum physics in quantum field theory will play a role in gravity. According to the standard account, matter is described by quantum field theory, and even states with no matter present still have energy. Since no matter is present, this state is known as the vacuum state, and its associated energy is known as vacuum energy. If we take to heart the lesson from general relativity that all energy gravitates (think about the relationship between mass and energy E=mc^2) then the vacuum energy should have observable effects on gravity. The problem is that the size of that effect is predicted to be dozens of orders of magnitude larger than what is actually observed.
Standardly, this problem is taken as a motivating issue to be solved by a future theory of quantum gravity. Schneider (2020) has argued that problems like the cosmological constant problem play an important role in guiding speculative physics; by highlighting inconsistencies and ambiguities that arise in merging general relativity and quantum field theory, the cosmological constant problem forces one to disambiguate and make foundational choices in current and future theories. My own previous work has taken a more critical stance on the standard interpretation of the problem. I argue that the motivating argument is heavily flawed, and that there is little to no ground on the side of quantum field theory to motivate taking vacuum energy density to be physically real. I elaborate on this in a forthcoming paper as well. In effect, I am arguing against one choice of interpretational strategy that is often used by physicists to motivate the problem.
Koberinski (2017) outlines three major steps required to formulate the cosmological constant problem, and casts doubt on each of them. First, one must accept that quantum field theory implies the presence of something that can play the role of a semiclassical vacuum energy. Second, one must accept that quantum field theory accurately predicts the magnitude of this vacuum energy density. Finally, one must accept that vacuum energy density couples to gravity in the standard way. The details of these assumptions are a bit too involved to spell out here, but none of these steps is straightforward.
In more recent work, Professor Chris Smeenk and I are taking a step back to examine the the implications of the cosmological constant for a popular approach to modern physics, known as the effective field theory approach. If we treat our current best theories of physics as effective field theories, this means that we expect them to be low-energy limits of some more fundamental field theory, in such a way that we can make quantitative statements about the error involved in approximating the full theory — whatever that may be — with our current theories instead. One key assumption required for effective field theories to work is the decoupling assumption: that physics at high energy scales decouples from physics at low energy scales. We claim that the cosmological constant problem highlights a failure in decoupling, and therefore shows a limitation in the effective field theory approach.
In response to this failure of decoupling, we provide three possible amendments to the EFT approach:
Accept the conclusion of the problem: The setup for the cosmological constant problem is correct, and we need to reconsider how to think of measured input parameters like particle masses and vacuum energy. Specifically, we should take the observed values as “anthropically selected” from an ensemble of possible values. This is where one encounters recourse to a multiverse, within which pocket universes take on different values for each of the fundamental set of constants. This strikes us as misguided, given the plausibility of the following two responses.
Modify the current effective field theories: Although the effective field theory concepts apply, the cosmological constant problem shows us that we have overlooked something that will change the problematic scaling behavior. Most of the proposed solutions to the cosmological constant problem in the literature fall into this category. By adding new physics (in the form of supersymmetry, extra dimensions to spacetime, etc.) one can save the effective field theory approach from the apparent failure of decoupling.
Reject the applicability of the effective field theory approach: The cosmological constant problem is a reductio ad absurdum of the starting assumption, namely that we can or should always treat gravity as a low-energy effective field theory. The problem indicates that we cannot take an approach built on flat-space quantum field theories as the basis for a treatment of quantum fields coupled to gravity (at least in the most straightforward way). On this last approach, one is left to question the foundational assumptions of effective field theory, and to survey the space of possible alternatives.
We endorse the third option: the failure of decoupling in the cosmological constant problem should be taken to signal the limitations of the effective field theory approach. It turns out that effective field theories rely quite heavily on the properties of the spacetime background on which they are defined. In the absence of gravity, quantum field theories are defined on a highly symmetric relativistic spacetime known as Minkowski spacetime. Once we add gravity to setup, however, Minkowski spacetime is no longer an appropriate background. According to general relativity, gravity is actually spacetime curvature; masses curve spacetime, and what we think of as gravitational orbits are actually the straightest paths possible in the curved spacetime.
Though there has been some success in using effective field theory methods with simple gravitational interactions (those for which the spacetime has certain global time symmetries, or those which “look like” Minkowski spacetime far away from the masses in question), we think it is too quick to generalize from the success of limited models to the applicability of effective field theories everywhere in general relativity.
If effective field theories don’t work for gravity, where do we go from here? Various approaches to quantum gravity lead to theories that don’t fit well into the effective field theory framework. For example, in string theory, nonlocal interactions fall outside of the scope of effective field theories. Further, string theory implies a duality symmetry between high-energy and low-energy physics in the theory. We should therefore expect decoupling to fail if string theory is the correct theory of quantum gravity. By coming to terms with the limitations of effective field theories, perhaps the path will be cleared for a new way forward.