The ancient Greek philosopher Aristotle wrote in his manuscript on Physics 2373 years ago: “If everything that exists has a place, place too will have a place, and so on ad infinitum.” Is the notion of space being continuous `without limit’ justified?
Before elementary particles were discovered, water was thought to be a continuous fluid. This is a good approximation on large scales but not on molecular scales where the interactions among elementary particles matter.
Similarly, spacetime has been thought to be a continuum since ancient times. While this notion appears consistent with all experimental data on large spatial or temporal scales, it may not be valid on tiny scales where quantum effects of gravity matter. An analogy can be made with the illusion of a movie which appears continuous when the frame rate is high enough and the spatial pixels are small enough for our brain to process the experience as seamless. Since our brain is made of elementary particles, the temporal and spatial resolution by which it senses reality is coarser by many orders of magnitude than any fundamental scale by which spacetime is discretized.
The pixel length-scale would naturally be the time-bin times the speed of light, which is a fundamental constant of nature in all frames of reference — according to Albert Einstein’s Theory of Relativity. Gravity represents the curvature of spacetime and any discretization must be related to its quantum nature.
The unification of quantum mechanics with gravity remains an unsolved puzzle, flagged by the unsolved information paradox of black holes as well as the unknown nature of the singularities of black holes and the Big Bang. We currently have no theory at hand with robust predictions that solve these mysteries of quantum gravity. Could the culprit be that we made a fundamental mistake in thinking about spacetime as continuous whereas in reality it has a discrete nature, just like the molecules of water?
In 1955, John Wheeler suggested that quantum uncertainties of spacetime would be of order unity at the Planck scale, leading to large fluctuations in spacetime topology which he termed “spacetime foam.”
If spacetime is discrete, the motion of particles through it would resemble a computer simulation. In such a case, the motion would not be smooth and its jumps would result in new discontinuous events for an observer that resolves the Planck scale.
When reaching the pixelization scale of Wheeler’s “spacetime foam,” we would notice that the movie of reality is composed of discrete snapshots separated by the fundamental bins of time, with each frame composed of discrete pixels of space. Could this explain the mysterious vacuum mass density, labeled dark energy, or the independently mysterious dark matter?
The Planck mass is 19 orders of magnitude larger than the proton mass. This translates to a length scale that is 25 orders of magnitude smaller than the size of an atom and a time scale that is 43 orders of magnitude shorter than a second. The age of the Universe is 61 orders of magnitude longer than the Planck time and the dark energy density is 122 orders of magnitude smaller than the Planck density. Given this mismatch, the discretization of spacetime encapsulated in Wheeler’s concept of quantum-gravity has no obvious connection to the present-day universe.
But could the connection be more subtle? Observationally, the astrophysicist Moti Milgrom showed that the need for dark matter appears when the gravitational acceleration in the outskirts of galaxies drops below a threshold value equal to the speed of light divided by the age of the Universe. If this threshold acceleration is dictated by vacuum fluctuations, then the need for dark matter might be related to vacuum mass density which gives the current age of the Universe through the inverse of the square root of its product with Newton’s constant. Given such a link, the mass density of the vacuum would have been defined by the threshold acceleration squared, in analogy to the way that the energy density of an electromagnetic field relates to the square of the field amplitude in quantum electrodynamics.
Linking dark matter to dark energy as the two unsolved mysteries of modern cosmology would have been equivalent to killing two birds with one stone. But as of now, there is no viable path for doing so. Certainly not within conventional thinking about quantum gravity.
It is possible that future physicists will be able to unify quantum mechanics and gravity in a way that would unify dark energy and dark matter. But as of now, the two mysteries are thought to be unrelated. Mainstream physicists are engaged in the experimental search for dark matter particles while suggesting in the context of the string theory landscape that there are 10 to the power of 272,000 possible values for the vacuum mass density and the one we observe in our part of the much larger multiverse, was selected by the requirement that we exist. This “anthropic principle” suggests that the vast majority of the other possible vacuum states do not allow life-as-we-know-it on the surface of Earth-like planets around Sun-like stars because the cosmic background is short-lived.
So far, I did not subscribe to anthropic reasoning because it cannot be falsified. My hope is that by meeting an advanced scientific civilization we could learn more. If we encounter smarter students in the class of intelligent civilizations within the Milky Way galaxy, they might explain to us what lies inside a black hole or what happened before the Big Bang. In particular, their quantum-gravity engineers could show us a recipe for making a baby universe in the laboratory. These engineers will bring a scientific interpretation to Genesis 1:1, “In the beginning God created the heavens and the earth.”
Rather than suggesting that everything is possible in the multiverse and we represent one out of 10 to the power of 272,000 possibilities in the string theory landscape, we might realize that our universe was constructed by engineers. In such a case, our existence stemmed from their choice and not from an arbitrary random process. Realizing that we are not orphans of quantum fluctuations of the vacuum will assign a new meaning to our cosmic existence.
ABOUT THE AUTHOR
Avi Loeb is the head of the Galileo Project, founding director of Harvard University’s — Black Hole Initiative, director of the Institute for Theory and Computation at the Harvard-Smithsonian Center for Astrophysics, and the former chair of the astronomy department at Harvard University (2011–2020). He chairs the advisory board for the Breakthrough Starshot project, and is a former member of the President’s Council of Advisors on Science and Technology and a former chair of the Board on Physics and Astronomy of the National Academies. He is the bestselling author of “Extraterrestrial: The First Sign of Intelligent Life Beyond Earth” and a co-author of the textbook “Life in the Cosmos”, both published in 2021. His new book, titled “Interstellar”, is scheduled for publication in August 2023.