Perhaps the best analogy is the Copernican Revolution of 1543. Before Nicolaus Copernicus – based on observation – we believed the Sun orbited around the Earth. Copernicus provided a new understanding which accounted for problems that couldn’t otherwise be solved. People’s day-to-day lives didn’t change. But now, the Earth orbited the Sun along with the other known planets. The thing that changed was our understanding of nature.
I. Introduction
Science makes progress when it develops concepts, frameworks of understanding, methods, techniques, or data that make it possible to uncover phenomena or test explanations of them. Thus, knowing where and how to look for discoveries and explanations is an important type of scientific progress.[1]
More than anything else, what follows can be thought of as knowing where to look for answers. But this goes beyond scientific progress; it determines how we view reality.
I’m an experimental physicist. I worked on various projects over the years, each requiring its own set of skills. In 2012 I began investigating something completely separate from our work. This sparked a series of discussions with a theoretical physicist friend of mine, Jim Bray. I was trying to understand how, over time, a sequence of single photons passing through a double-slit builds up an interference pattern. This resulted in an invention called the dual double-slit diffraction experiment. We’ll discuss this in detail in Section II.
Then, in 2013 I decided to start working on a fictional story that employed the dual double-slit diffraction experiment to validate the existence of the multiverse. I began using the more descriptive expression superposition test for Sisters of Infinity, and that’s carried forward here. This became a four-year effort to build a scientific framework on a literary foundation. The story is disconcerting. Enough so that I wasn’t able to finish it at the time. Perhaps I will someday. And I promise it has a happy ending.
Section III describes how the superposition test can be used. I’ve spent ten years reasoning through the details of how this would work. One of my areas of expertise is spectroscopic ellipsometry, which deals with changes in the polarization of light. This was very helpful. As an industrial scientist, the focus is on quickly solving technical challenges to develop practical applications. This website can be viewed with that in mind.
II. Superposition Test
The double-slit experiment is a phenomenon which is impossible to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery of quantum mechanics.
– Richard Feynman
The double-slit experiment consists of a light source, a barrier with two narrow slits, and a detector screen. When a beam of light is directed at the double-slits, diffraction causes each slit to act as a secondary source with light radiating outward. The light from these two sources creates an interference pattern on the screen.
This phenomenon was first described by Thomas Young to the Royal Society of London in 1803 and is sometimes referred to as Young’s interference experiment. It led to our understanding of light as waves. Surface waves on water do the same thing.
Interference is a characteristic of wave behavior. But individual photons will form dots on the screen indicating particle behavior. Thus the double-slit experiment displays both the wavelike and particle-like properties of light; a fundamental component of nature.
An interference pattern is formed by the superposition of two wavefronts, hence the need for two slits. Interference exhibits some unique effects. For example, if we observe which slit the photons go through, the pattern is lost. But perhaps most intriguing is what happens when a series of individual photons are directed at the slits one at a time. If photons had only particle-like properties, we would expect to see an image of the two slits.
Instead, individual photons form an interference pattern over time. It doesn’t matter if they’re separated by one second, a day, or centuries.
To accommodate a single universe, we’ve said the photon – a quanta of energy equivalent to one wavelength of light – splits in half, goes through both slits, and interferes with itself. Or that the photon’s wavefunction scatters at the double-slit, guiding the photon to the needed location. Both of these sound a little like Ptolemy’s epicycles.
Wavefunctions are complicated. We use mathematics to describe them very accurately. They look like equations to us. But what wavefunctions actually represent has been debated since the 1930s. One possibility is they’re purely mathematical but determine everything we observe. Or are they something real that can interact with the physical world? This fundamental choice determines how we perceive objective reality.
Perhaps a different explanation than imaginary wavefunctions scattering at double-slits is needed. One that can simplify everything. Let’s assume for a moment the wavefunction is real. It is in coherence with its environment until an observation occurs. Coherence means the wavefunction is spread out; it exists in an infinite number of possible states. This is referred to as superposition. When a photon is observed, its wavefunction must decohere to manifest the properties we see.
But what environment is the wavefunction decohering from? I’ll use what David Bohm called pre-space (there are several terms for this). Pre-space is where wavefunctions reside. It’s not our universe, or any physical reality. There isn’t a three-dimensional space like we’re accustomed to thinking of it. There’s no passage of time.
I didn’t appreciate all this when I invented the dual double-slit diffraction experiment in 2012. I was trying to understand how photons, passing one-at-a-time through a double-slit, form an interference pattern. The idea is that each photon’s wavefunction is in a superposition of states, some of which overlap other possible outcomes. This is known as the many-worlds interpretation, which was formalized by Hugh Everett III in 1957. The GE Global Research report on the invention states this concept as follows:[2]
In many-worlds, a single particle would exist as a superposition of entangled states across possible universal wavefunctions. So while interference between any two states might be infinitesimally small, there are a virtually infinite number of quantum states to interfere with. Hence, what we observe as an individual particle creates a diffraction pattern across all probability densities, of which our universe is one. In effect, the amplitude distribution of the double-slit pattern is produced each time a particle passes through the double-slits. Over time, an interference pattern has to be generated in our world. The issue now becomes: if it is a physical state that is interfering, is it possible to perform an experiment to test many-worlds?
We weren’t entirely sure what to make of this. The superposition test had nothing to do with the work we were performing. But the leadership team at GE Global Research was completely supportive throughout this process. What we decided to do was draft the report and contact experts who perform these types of experiments.
I talked to folks at the Institute of Optics at the University of Rochester, the National Institute of Standards and Technology (NIST), and NASA’s Jet Propulsion Labs. After a lot of discussions, I started working with Dr. Dmitry Strekalov at JPL’s Ultrafast Quantum Optics Lab. Dmitry and I put together a proposal in early 2016 to perform the test at JPL, but I wasn’t able to get the funding. I retired from GE at the end of 2016.
The superposition test is designed to create conditions that enable particles like photons to exist in a known state before they’ve decohered from pre-space. So they still overlap other possible outcomes.
This is achieved using quantum entanglement. The wavefunctions of two or more particles or entities are overlapped in pre-space; that is to say, they’re entangled. The superposition test directs entangled particles like photons at two double-slits. One double-slit generates a reference pattern, and the other double-slit is used to create a test pattern. Formation of the reference pattern requires observation of the photon. This sets the corresponding state of the test photon. For example, if we measure polarization, entanglement instantaneously establishes the polarization state of its twin. Instantaneously is faster than the speed of light. This doesn’t violate the Theory of Relativity since information is being conveyed, not matter or energy. In quantum physics, it’s because the photons are entangled in pre-space where the separations we perceive as space and time don’t exist. The test photon is now in a known state without having yet decohered. It won’t decohere until it’s observed and contributes to the test pattern. Until then, the test photon exists in an infinite superposition of possible states.
This enables the statistical comparison of hundreds of thousands of one-at-a-time entangled photon pairs. The null hypothesis is that the reference pattern and the test pattern should be identical other than their relative sizes. If they’re not, this indicates the test photons’ wavefunctions overlapped with different possible outcomes. A simple way to think about this is the test pattern would appear somewhat “fuzzy” compared to the reference pattern. The superposition test therefore allows us to measure variation due to quantum non-equilibrium:
where Non-equilibrium is defined as a function that conveys information about a phenomenon, or an observable change in a quantity.
If any of this seems unusual, we need to put it into context. Scientists have debated how to interpret quantum physics since it was first originated by Max Planck in 1900. Albert Einstein won a Nobel Prize in Physics by postulating that light is made up of quantum particles (photons) to explain the photoelectric effect. Virtually every aspect of what we observe in the quantum world is counterintuitive. The issue is that our interpretation determines how we define objective reality; the reality that exists independent of any conscious awareness of it.
In 1952 Erwin Schrödinger gave a lecture in Dublin where he told his audience what he was about to say “might seem lunatic.” He went on to assert that the mathematical formulation that won him the Nobel Prize seemed to be describing multiple histories, that they are “not alternatives but all really happen simultaneously.” We’ve been debating what this means for almost 70 years.
Albert Einstein and the philosopher Karl Popper began discussing quantum physics in the 1930s. In the 50s and 60s, Popper developed an interpretation that involved real existing probabilities. I remember this day distinctly. Jim Bray and I were sitting in his office describing the superposition test when one of the scientists asked us if we had ever heard of Popper’s experiment. Jim and I looked at each other and said no, we hadn’t. It turns out in 1980 Popper had devised a test to address the question of whether we live in a single universe (referred to as the Copenhagen interpretation). His experiment uses pairs of particles traveling in opposite directions. Each particle is directed at a single slit. He postulated that measuring the amount of diffraction obtained by adjusting the slit widths could determine which interpretation is correct.
Popper’s experiment lacked three key features. The first is the setup must enable the test photons to be in a known state before decoherence. The second is they have to sample a superposition of states. The third is double slits are needed for interference to occur.
If there are issues with any of this, we should emphasize the superposition test is specifically designed to evaluate if the many-worlds interpretation is accurate. It is falsifiable. But when performed successfully, the experiment will validate the following:
- Photon wavefunctions overlap with other possible outcomes
- Wavefunctions of photon-like particles in other outcomes overlap with our wavefunctions
- Quantum wavefunctions are part of objective reality
- Our universe consists of wavefunctions, matter, energy, space, and time
- We exist in a multiverse
The statement referenced earlier from the GE report refers to 1, 2, and 3. But these criteria are just five ways of saying the same thing; they are equivalent.
We have to speak to #3. Like I said before, wavefunctions are complicated. As a physicist, this takes precedence over the other four. It’s also the most difficult to grasp since wavefunctions exist in pre-space whereas objective reality comprises all possible outcomes. The seeming contradiction is resolved once we understand something in pre-space coincides with physical reality since what we observe is manifest by wavefunctions. There’s overlap between us and pre-space. Hence #4 – as incomprehensible as that may appear.
Even with the use of photons the superposition test will be challenging. Besides photons, the experiment also applies to other elementary particles as well as atoms and molecules. (Particles use spin instead of polarization.) I began thinking it may not be possible to measure non-equilibrium unless heavier particles like electrons or xenon atoms were used to increase the resolution of the fine structure in the patterns. These concerns have now been significantly reduced.
Researchers at Heriot-Watt University in Edinburgh, Scotland recently performed an extended Wigner’s friend experiment to record photons’ polarization states measured by different local observers.[3] Their test compared the polarization of photons in a known state with subsequent observations. The null hypothesis is these should be identical. Instead, the results demonstrated objective reality depends on its observation. Different observers see different realities. This apparent anomaly represents the intrinsic fuzziness of objective reality. Most importantly, the results validated criteria 1 and 3 above. Because of equivalency, the team at the Heriot-Watt University’s Institute of Photonics and Quantum Sciences discovered the multiverse.
III. Applications
A double-slit experiment forms an interference pattern over time using individual particles like photons. The superposition test utilizes entanglement to measure differences between photon pairs. This makes it possible to observe quantum non-equilibrium.
To understand this, we need to describe how the superposition test works. A pair of entangled photons from a source S are directed at two narrow double-slits. We don’t know which of the slits the photons will go through, how near the edge of the slit they will pass, or whether they’ll go through a slit at all. When a photon does pass through a slit, its proximity to the edge determines the amount it’s deflected. This is called diffraction, which produces an interference pattern.
Assume for a moment a pair of entangled photons pass through one of their respective double-slits. After enough repetitions, two interference patterns begin to form. But for any given iteration, the photons’ paths are entirely random:
Interestingly, the outcome of the superposition test is unaffected by the random sequence of paths. Interference patterns will build up over time irrespective of where a given photon lands. The test is designed to measure the difference in polarization states between photons, which are independent of the trajectories in the formation of the patterns.
The experimental design is primarily determined by the test distance and the corresponding sizes of the detector arrays. Sensitivity will increase with test distance. Resolution depends on the pixel density and responsivity of the detectors. The design can be optimized by excluding the side fringes with a series of dark matte baffles to eliminate optical vignetting and using only the central peaks as indicated here:
The superposition test may be conceptualized using a simplified version of the design, as shown in the following figure. Pairs of polarized entangled photons from the source S are directed at two double-slits. The reference photons pass through a vertical polarizing analyzer (polarizer). This establishes the corresponding polarization state of the test photons at the reference distance. The test distance is determined by the location of the second polarizer in front of the test pattern. This is used to analyze differences in polarization between the test and reference photons.
For example, design parameters for a functional test are given in the following table:
These conditions produce a test pattern with a central envelope approximately 5 cm wide and missing orders at ± 3 cm. This configuration would therefore require a 6 cm detector array.
The required number of photon pairs and measurement time are determined through a statistical analysis based on the design configuration. A difference in accumulated intensities between the reference and test patterns is indicative of non-equilibrium. Another way to say this is it won’t be possible to null out the intensity of the test pattern by rotating its polarizer 90° to horizontal.
This might seem unusual since we’re merely changing the distance between polarizers to evaluate the intensities (number of photons) forming the patterns. But the extended Wigner’s friend test measured non-equilibrium between polarization states due to a change in distance. Local observer independence has been demonstrated. This is unfamiliar to us because it’s due to non-coincidence in time. The same reason an individual photon in our universe can experience interference effects.
It’s unknown whether a simplified version of the superposition test can accurately resolve five standard deviations. That will likely require a more complex design.
The advanced version of the experiment will provide an additional method to confirm the results of the extended Wigner’s friend test. There are differences and similarities between the two approaches, but this will be at least as complicated to perform.
The advanced design uses an ancillary entangled source, S1, which provides pairs of photons with known polarization states. Comparison of the reference and test photons is accomplished using type-I fusion gates that allow nondestructive polarization measurements as described in Proietti et al. To determine differences between reference and test photons, we need to count only those photons contributing to the respective central envelopes. Like the extended Wigner’s friend test, a photon-counting process enables the binning of applicable events. Both reference and test photons must contribute to their respective interference patterns to be counted.
This affords a very accurate method for the comparison of polarization states. To provide the most meaningful results, pairs of photons from S1 and S0 should use similar fidelity, purity, and concurrence as Proietti et al. The reference patterns A0 and B0 are analogous to the facts measured by Alice and Bob’s friends in the extended Wigner’s friend test. Test patterns A1 and B1 correspond to facts measured by Alice and Bob.
Horizontally- and vertically-polarized photons from S1 are either transmitted or reflected by the fusion gates. Interaction with photons from S0 creates observables at A0, B0, A1, and B1. Coincidence with S1 causes variation in the transmission and reflection of S0 photons. The four combinations of S1 and S0 polarization orientations provide the following intensities:
Superscripts v, h, and ne correspond to vertical, horizontal, and non-equilibrium. Thus, S0ne at A1 and B1 are observables A1ne and B1ne; the direct measure of quantum non-equilibrium:
S0h at detector A0, and S0v at B0, are the maximum intensities from S0. These are observables A0max and B0max, respectively. The effects of non-equilibrium are given by S0h – S0ne at detector A1, and S0v – S0ne at B1; corresponding to observables A1min and B1min. Together these quantify relative overlap:
where Relative Overlap corresponds to the amount of non-equilibrium for a given experimental setup. Thus, the development of the advanced approach can provide a precise method for evaluating more complex phenomena.
As can be seen, the superposition test allows for the adjustment of several parameters, including wavelength, slit spacing and width (Karl Popper’s idea), and test distance. A determination of practical ranges for each defines an experimental space, as in the following example:
Using 0.10 mm double-slit widths, the maximum size of the central envelop occurs for λ = 2.1 μm, slit spacing = 0.40 mm, and test distance = 100 cm. Missing orders at ± 2 cm specify a 4x4x4 cm fusion gate and 4 cm-wide infrared detector arrays for A1 and B1.
Variation of wavelength, slit spacing, and test distance correspond to changes in energy, space, and time:
It may seem remarkable that we could discern differences representative of other possible outcomes by making adjustments to an experimental apparatus. This is feasible since we’re comparing variations in polarization states that are manifest by wavefunctions. Before observation, they’re in superposition in pre-space. The corollary is this should work virtually anywhere in the universe.
This suggests it might be possible to begin mapping how non-equilibrium varies with energy, space, or time. The easiest of these to understand is a change in space. Adjusting the slit width or spacing alters how the diffracted photons create an interference pattern. Similarly, photons with different energies diffract differently. This has the potential to register a change. Perhaps the most difficult to understand is an effect in time. Observed variations will mean our notions around the passage of time will become more complicated.
It’s essential to emphasize that non-equilibrium would be invariant within a uniquely singular universe. Measured variability would validate criteria 4 and 5. The observation of objective reality.
References
[1] F. Liu, X. Li, and Y. Shi, Scientific Breakthrough Study of Extenics, Procedia Computer Science 91, 10.1016/j.procs.2016.07.134 (2016).
[2] J. Johnson, J. Bray, and F. Ahmad, Proposed dual double-slit diffraction experiment, 2013PRO011, Class 1: Public (2013).
[3] M. Proietti, A. Pickston, F. Graffitti, P. Barrow, D. Kundys, C. Branciard, M. Ringbauer, A. Fedrizzi, Experimental test of local observer independence, Sci. Adv. 5, eaaw9832 (2019).