Is the expanding universe really an illusion?

Traditionally, the standard model of cosmology holds that the universe began with a big bang, followed by continued expansion and cooling. However, a new study recently found that based on a clever mathematical trick, we can "zoom" the universe and the expansion may just be an illusion. Does this idea stand up to scrutiny?

By Ethan Siegel

Translation | Liu Hang

Image source: geralt/pixabay

Back in the 1920s, two parallel developments paved the way for our modern understanding of the Universe. On the theoretical side, we could deduce that a Universe filled uniformly with matter and energy would not be static and stable, but would either expand or collapse, if general relativity held true. On the observational side, we began to be able to observe galaxies beyond the Milky Way and determine that (on average) the farther away they are from us, the faster they are moving away from us.

Simply combining theory with observation, the concept of an expanding Universe was born, and it has stayed with us ever since. Our standard model of cosmology—which includes the Big Bang, cosmic inflation, the formation of cosmic structure, and dark matter and dark energy—is built on top of this model.

But is an expanding Universe absolutely necessary, or are there other possibilities? Recently, an interesting new paper[1] has attracted some attention. Theoretical physicist Lucas Lombriser argues that by making some changes to the equations of general relativity, the expansion of the Universe can be made to "disappear." In his scenario, the observed expansion of the Universe is simply an illusion. But does this fit with what we know about science?

In a vacuum, all light, regardless of its wavelength or energy, travels at the same speed: the speed of light in a vacuum. When we observe light from a distant star, the light we see has actually completed the journey from the source to the observer. Image credit: Lucas Vieira/Wikimedia Commons

Physics Equivalence

Sometimes we realize that there are multiple different ways of understanding the same phenomenon. If two ways are physically equivalent, then we know that there is no difference between them, and which one we choose is just a matter of personal preference.

Taking optics as an example, you can describe light as waves (as Huygens did) or as rays (as Newton did), and in most experimental situations both descriptions lead to the same predictions.
In the field of quantum physics, quantum operators act on quantum wave functions. You can choose to describe the particle with a wave function and let it evolve while the quantum operator remains unchanged; or you can keep the particle's wave function unchanged and let the quantum operator evolve.
Or, as is often the case in Einstein's theory of relativity, imagine two observers with clocks: one on the ground and one on a moving train. There are two different perspectives that can be used to describe this phenomenon equivalently: let the ground be "stationary" and the observer on the train experience the effects of time dilation and length contraction in motion; or let the train be "stationary" and the observer on the ground experience the effects of time dilation and length contraction.
As the word “relative” implies, if these scenarios give the same predictions as each other, then any one is equivalent to the other.

The revolutionary idea of ​​relativity, created by Einstein (and preceded by similar mathematical expressions by Lorentz, FitzGerald, and others), is that fast-moving objects appear to contract in space, while time dilates. The faster you move relative to a stationary observer, the more your length appears to contract, while time appears to dilate for the outside world. To an observer standing on the ground, the train appears to contract, while time dilates inside the train; to an observer on the train, the outside world experiences length contraction and time dilation. Image credit: C. Renshaw, IEEE, 1996

The latter scenario in relativity suggests that the coordinate transformations commonly used by mathematicians may give us some inspiration. We may be more accustomed to thinking about coordinates in the way that René Descartes did about 400 years ago: the directions/dimensions are perpendicular to each other, and the coordinate axes have the same scale, that is, the Cartesian coordinate system we have all learned.

But Cartesian coordinates aren't the only coordinate system that's useful. For example, if we're dealing with objects that have axial symmetry, we might prefer cylindrical coordinates; if we're dealing with objects that are symmetric about a central point, spherical coordinates might make more sense. If we're dealing with spacetime, in which the "time" dimension behaves fundamentally differently from the "space" dimension, then it's more convenient to use hyperbolic coordinates to relate space and time.

The great thing about coordinates is that they are just a choice. As long as you don't change the fundamental physics behind the system, you are completely free to choose any coordinate system you like to describe anything in the Universe.

Once the critical point of forming a black hole is crossed, everything inside the event horizon is squeezed into a singularity, at most one-dimensional. No three-dimensional structure can survive intact. However, an interesting coordinate transformation shows that every point inside the black hole corresponds one-to-one with a point outside, which raises the mathematically intriguing possibility that a small universe is bred inside each black hole. Image credit: vchalup / Adobe Stock
Redefining coordinates: "reverse" expanding universe

There is an obvious approach that we can try to apply to the expanding Universe. Traditionally, we note that distances in bound systems (such as nuclei, atoms, molecules, planets, and even star systems and galaxies) are constant over time; we can use them as "rulers" to measure distances very well at any given moment. When we apply this to the entire Universe, since we see distant (unbound) galaxies moving away from each other, we conclude that the Universe is expanding, and try to find a relationship for how the rate of expansion changes over time.

So why not think in reverse and redefine these coordinates: keep the distances between (unbound) galaxies in the Universe fixed, but let our "ruler" and other bound structures shrink over time?

This choice may seem rash, but in science, changing the way we look at a problem can reveal features that were not obvious in our original perspective, but become clear in our new one. The redefinition of coordinates is exciting—and that’s what Lombriser explores in his new paper. What conclusions might we draw about our biggest puzzles by taking this inverse perspective?

This clip from a medium-resolution simulation of cosmic structure formation, scaled down to the expansion of the Universe, shows billions of years of gravitational growth in a dark matter-rich Universe. Notably, at the intersections of the filaments, the filaments and the rich clusters of galaxies are primarily produced by dark matter; normal matter plays only a small role. Smaller-scale structure is inherently underestimated or "smoothed out" more as the simulation gets larger. Image credit: Ralf Kaehler and Tom Abel (KIPAC)/Oliver Hahn

Unlike the traditional cosmological view, we can reconstruct the Universe as static and non-expanding, at the expense of mass, length, and time scales all changing and evolving. Since our goal is to keep the structure of the Universe constant, we can't have expanding, curved space (with growing density inhomogeneities in it), so these evolutionary effects need to be mirrored somewhere else. The mass scale will have to evolve with the evolution of spacetime, as will the distance scale and the time scale. They must co-evolve in a precise way so that when combined to describe the Universe, they constitute the "inverse" of the standard explanation.

Another approach would be to keep the structure of the Universe constant, as well as the mass scale, length scale, and time scale, but at the cost of having the fundamental constants of the Universe co-evolve in a certain way so that all the dynamics of the Universe are "encoded" on them.

You might be tempted to object to both of these statements because our traditional view makes more intuitive sense, but as we mentioned before, if the math is the same and there are no observable differences between the predictions of either view, then they are both equally valid when trying to apply them to the Universe.

What would a non-expanding universe look like?

Want to explain the redshift in the Universe? In this new image, you can explain it in a different way. In the standard image:

Atoms undergo atomic transitions;
Releases photons of a specific wavelength;
This photon travels through the expanding Universe, becoming redshifted on its journey;
When the observer receives it, its wavelength is longer than the wavelength of the same atomic transition in the observer's laboratory.

There are many energy levels in an iron atom, and different rules for selecting electron transitions. Although many quantum systems can be controlled to achieve efficient energy transfer, there are no examples of biological systems operating in the same way. Image credit: Daniel Carlos Leite Dias Andrade et al., Conference: 25º CSBMM – Congresso da Sociedade Brasileira de Microscopia e Microanálise, 2015

In the laboratory, the only observation we can make is to measure the observed wavelength of the received photons and compare it to the wavelength of the laboratory photons. There is the possibility that there is an evolution of the mass of the electron, an evolution of Planck's constant (ℏ), and an evolution of the (dimensionless) fine structure constant (or some combination of constants). The redshift we measure for distant photons could be due to a number of different factors that are indistinguishable from one another. Remarkably, these multiple factors, appropriately extended, will give the same kind of redshift to gravitational waves.

As the balloon inflates, the coins stuck to its surface appear to move away from each other, with the "further away" coins moving away faster than the closer coins. Any light will be redshifted, and similar to the expansion of the balloon, the wavelength of light will be "stretched" to a larger value. This image explains the redshift of the universe very well. Image credit: E. Siegel/Beyond the Galaxy

In the same way, we can reconstruct how structure grows in the Universe. Typically, in the standard picture, we start with a slightly overdense region of space, a region with a density slightly above the average density of the Universe. Then over time:

The gravitational disturbance in this area will attract more matter than the surrounding areas;
This causes the space in this area to expand more slowly than the average expansion of the universe.
As the density grows, a threshold is eventually crossed, triggering gravitationally bound conditions;
This region began to gravitationally contract and formed parts of the cosmic structure, such as star clusters, galaxies, and even larger groups of galaxies.
Instead of tracking the evolution of the overdense regions of the Universe (in a sense, tracking the evolution of the density field), we can also consider the evolution of the mass scale, distance scale, and time scale instead. Similarly, we can choose to consider the evolution of Planck's constant, the speed of light, and the gravitational constant. The "growing structure of the Universe" we see may not be a result of the growth of the Universe, but rather these parameters are fundamentally changing over time, so that observables (such as structure and its observed size) remain constant.

Typical or "normal" overdense regions will gradually develop rich structure, while less dense "void" regions will have less structure. However, early small-scale structure is dominated by the highest-density regions (labeled here as "rarepeak"), which grow fastest and can only be observed in detail in the highest-resolution simulations. Image credit: J. McCaffrey et al., Open Journal of Astrophysics (submitted), 2023

If we take this approach, we can try to reinterpret some currently unexplained features of our Universe, no matter how unnatural it may seem. For example, there is the problem of the "cosmological constant," which for some reason seems to fill space with a field with an intrinsic constant energy density: an energy density that does not dilute or change as the Universe expands. This question was not important long ago, but it is important now, because the matter density has diluted below some critical threshold. We do not know why space has this non-zero energy density, nor why it takes on values ​​consistent with the dark energy we observe. In the standard picture, this is an unexplained mystery.

However, in this reconstruction, if the mass scale and the distance scale change according to the new construction, there is a relationship between the value of the cosmological constant and the inverse of the Planck length squared. And the Planck length changes as the Universe evolves, and its evolution is from the observer's perspective: the value we observe now is exactly the value observed at this moment. If time, mass, and length all evolve together, then the so-called "coincidence problem" in cosmology is eliminated. Any observer will observe the effective cosmological constant at their "present moment", which is important because their "present moment" is evolving with cosmic time.

Schematic diagram of the photon radiation density (red), neutrino density (black dashed line), matter density (blue), and dark energy density (dotted line) changing over time. In a new model proposed a few years ago, dark energy was replaced by the solid black line in the figure, which is observationally indistinguishable from the dark energy we assume. As of 2023, dark energy in an expanding universe can differ from the "constant" in the equation of state by about 7%; more differences are strictly constrained by the data. Image source: F. Simpson et al., Physics of the Dark Universe, 2018

In this case, they can reinterpret dark matter as a geometric effect of particle masses increasing in a convergent manner at early times. They can also reinterpret dark energy as a geometric effect of particle masses increasing in a divergent manner at late times. What is exciting is the different ways to reinterpret dark matter - where the expansion of the universe is reinterpreted as the result of the interaction of the axion scalar field (as a known dark matter candidate particle) with the field. The coupling of the axion scalar field with other fields introduces CP violation - one of the key ingredients to produce matter-antimatter asymmetry in our Universe.

The illusion of reality

Thinking about the problem in this way leads to many interesting potential consequences, and we should not discourage anyone from this type of mathematical exploration at this early "sandbox" stage. Someday, such ideas could form part of the theoretical foundation for going beyond the currently accepted standard model of cosmology.

However, even if this is interesting from a purely general relativity perspective, most modern cosmologists don't bother considering these issues, because even if they could experimentally observe and prove that these reconstructions are acceptable on a cosmic scale, it would completely contradict what we already observe on Earth.

When hydrogen atoms are formed, the spins of electrons and protons are equally likely to be parallel or antiparallel. If they are antiparallel, no further transitions can occur, but if they are parallel, they can quantum tunnel into lower energy states, emitting photons of a specific wavelength over very long timescales. Such transitions can be measured with an accuracy of one part per trillion and remain constant for decades, constraining Planck's constant, the speed of light, the mass of the electron, and their combination. Image credit: Tiltec/Wikimedia Commons

For example, consider the following view:

Changes in the properties of elementary particles, such as mass, charge, length or lifetime,
Or fundamental constants like the speed of light, Planck’s constant, or the gravitational constant change.
Our universe is only 13.8 billion years old, as far as we can see. We have been making very precise measurements of quantum systems in the laboratory for decades, with the most precise measurements showing the magnetic moment of the electron to an accuracy of 1.3 parts per trillion[2]. If the properties of particles or fundamental constants change, then our laboratory measurements will also change. And according to the theory reconstructed by Lucas Lomblisser et al., in the approximately 14 years since 2009, we should be able to observe changes from these precise measurements that are thousands of times more precise than our most precise measurements: a difference of about one part in a billion.

The magnetic moment of the electron was measured with extremely high precision in both 2007 and 2022, and the difference between them was less than one part in ten trillion (the limit of the accuracy of the early measurements), which showed that the fine structure constant had not changed.
The spin-flip transition of a hydrogen atom results in a beam with a wavelength of 21.10611405416 centimeters, with an uncertainty of just 1.4 parts per trillion, and it has not changed since it was first observed in 1951. As physicists have measured it more precisely over time, this has shown that Planck's constant has not changed.
The Eötvös experiment, which measures the equivalence between inertial mass (which is not affected by the gravitational constant) and gravitational mass (which is affected), has shown as of 2017 that the equivalence between the two "types" of mass is very significant, reaching one part in a trillion.

The equivalence principle states that there should be no difference between the acceleration due to gravity and the acceleration due to any other force in the universe. One depends on the gravitational constant and the other does not. The most precise test of the equivalence principle was done by the MICROSCOPE satellite, which has an accuracy of 10 to the negative 15th power, which is a way to constrain how the gravitational constant changes over time. Image credit: APS/Carin Cain

A striking feature of the standard view of the Universe is that all the laws of physics that apply here on Earth apply everywhere and at every moment in the Universe throughout its history. A cosmological view that fails here on Earth is far less interesting than one that succeeds everywhere and everywhere. If the traditional view of the expanding Universe agrees with physics here on Earth, and an alternative view that works well for the larger Universe but fails here on Earth, then we can’t say that the expanding Universe is an illusion. After all, physics here on Earth is the most real, most precisely measured, and most rigorously tested anchor point for us.

This is not to say that the journals that publish this kind of speculative, exploratory research—such as Classical and Quantum Gravity, the Journal of High Energy Physics, or the Journal of Cosmology and Cosmological Particle Physics—are not reputable and high quality; in fact, they are very prestigious. They are specialized journals in specific fields—more interested in theoretical explorations of the early universe than in the analysis and understanding of experiments. By all means, continue to explore realistic alternatives to standard cosmology (and particle physics). But don't pretend that throwing away all reality is a viable option. The only "illusion" here is the reality we observe and measure, and this is extremely important when it comes to understanding our universe.

References

[1] Lucas Lombriser 2023 Class. Quantum Grav. 40 155005, DOI: https://doi.org/10.1088/1361-6382/acdb41

[2] Phys. Rev. Lett. 130, 071801 DOI: https://doi.org/10.1103/PhysRevLett.130.071801

About the Author

Ethan Siegel is an astrophysicist, writer and science communicator who teaches physics and astronomy. Since 2008, his blog Starts With A Bang! has won many science writing awards, including the Best Science Blog Award from the British Physical Research Society. He is the author of Treknology: The Science of Star Trek from Tricorders to Warp Drive, Beyond the Galaxy, etc.

Ethan Siegel, Could the expanding Universe truly be a mirage?
https://bigthink.com/starts-with-a-bang/expanding-universe-mirage/, published in "Fanpu" with the author's permission.

Produced by: Science Popularization China

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