Discoveries in physics in the first quarter of the 21st Century.

May 13, 2026May 13, 2026 by David D. Nolte

The Best Physics of the Century (So Far)

History of Dynamics
Black Hole, Cosmic Microwave Background, Event Horizon Telescope, Exoplanet, Gravitational Wave, Higgs Particle, LIGO, Nuclear Fusion, photon, Quantum computing, Quantum Information, Solar Neutrino Oscillation, Topological physics

Our century is now a quarter complete, from Y2K to today (2000 – 2025). What have been the greatest discoveries in Physics so far? And what do they portend for the rest of the century?

Every century of physics tends to have its own character:

• The 1600’s were the time of Galileo, Descartes, Huygens, Leibniz and Newton who created the science of dynamics out of nothing.

• The 1700’s were the time of du Chatelet, Maupertuis, Euler, Lagrange, and D’Alembert who constructed mathematical physics on the foundation of the calculus.

• The 1800’s were the time of Young, Fresnel, Hamilton, Maxwell, Boltzmann, and Lord Kelvin who completed the program of classical physics.

• The 1900’s were the time of Einstein and Bohr who invented relativistic and quantum physics and launched the grand program of unified forces.

Now we come to the 2000’s. What will this century be known for?

Two topics physicists have at the top of their mind today is Quantum and AI (and there is even quantum AI). But AI is merely a tool (though an important one that is radically changing how physics is done), and quantum is a catch-all (almost everything is quantum at its core).

So, what are the greatest breakthroughs of the 21^st Century so far? And what do they portend for the eventual “character” of 21^st-Century physics when seen in the rear-view mirror of history by the year 2100?

Single-photon Quantum Information (2001)

The century started on July 24, 2000, when a landmark paper was received by Nature magazine submitted by Emanuel Knill and Raymond Laflamme at Los Alamos National Lab in the United States with Gerald Milburn from the University of Queensland, Australia (collectively known as KLM). This little-heralded paper proposed a radical new idea in quantum information, an idea that would have profound effects on the development of quantum science for the coming quarter-century.

The idea was simply that quantum logic could be performed with single photons and linear optics [1]. Up to that point, most research on quantum optical computing was trying to get photons to interact with each other (which they really don’t like to do) in nonlinear media like crystals or trapped atoms. What KLM showed was that quantum information could be manipulated in general ways without interactions. The paper proposed a technique that could perform quantum logic in a universal way using only linear optical elements like single-photon sources, beam splitters, phase shifters, and single-photon detectors, introducing the novel idea of “measurement-based” quantum computing.

Recovery from Z Linear Optical Quantum Computing — Fig. 0. LOQC circuitry from the KLM paper.

In the quarter-century since the publication of the KLM paper, LOQC has steadily progressed via the development of single-photon sources and detectors. Today, numerous start-ups are pursuing LOQC, notably Xanadu in Toronto, Canada, and PsiQuantum in Palo Alto, USA and Brisbane, Australia. By 2100, this century will likely be viewed as the time when applications of quantum information reached their maturity. Where the 20^th century was a century of discovery of quantum phenomena, the 21^st will be the century when it was reduced to practice.

Solar Neutrino Oscillation (2001)

The sun is fueled by the fusion of hydrogen that generates electron neutrinos. The reaction looks like

where p is a proton (hydrogen), ²H is deuterium (a hydrogen nucleus with an extra neutron), e⁺ is a positron (the anti-matter form of an electron) and ν _e is an electron neutrino. This reaction accounts for 99% of the neutrinos generated by the Sun, calculated by the theoretical astrophysicist John Bahcall of the Institute for Advanced Study at Princeton University. Already by the late 1960’s it was suspected that too few of the neutrinos were being detected compared to predictions, so he teamed with Raymond Davis of Brookhaven National Lab to build an experiment to detect the flux of solar neutrinos. To shield the detector from cosmic rays, the experiment was placed at the 4850 level of the Homestake Gold Mine in Lead, South Dakota and operated from 1970 to 1994. The deficit of solar neutrinos was confirmed, and it was huge: Fully two-thirds of expected solar neutrinos were missing!

The simplest solution to the missing solar neutrinos was that they just weren’t there because, on their way to Earth from the Sun, they had converted to something else that was not detectedable. This conversion from one particle to another is possible if neutrinos have a non-zero (but extremely small) mass. If so, then an electron neutrino can convert to a muon neutrino, and if the distance is far enough, they can convert back. In other words, the nature of the neutrino particle is that its identity oscillates. This is called the solar neutrino oscillation, and by the time the neutrinos have arrived at Earth, two-thirds of them have converted to muon neutrinos.

There was a general reluctance to accept neutrino oscillations because it represented a departure from the Standard Model of particle physics and introduced uncomfortably small masses for neutrinos that otherwise behave like massless particles. Two experiments put these qualms to rest: the Super-Kamiokanda expeeriment in Japan and the Sudbury Neutrino Oscillation experiment in Canada. By the early years of the century, neutrino oscillations had been confirmed.

By 2100, the mystery of the ultra-small neutrino masses will likely have been solved. If the answer falls within the Standard Model, then this may be the crowning achievement that “completes” the standard model. If the answer falls outside the Standard Model, then this may be the beginning of a new chapter in high-energy physics.

WMAP and Planck (2003)

The Big Bang may have occurred 13.7 billion years ago, but that Bang echoes to this day across the Universe. At its inception, the reverberations were incredibly hot, but they have cooled now to a mere 3 degrees Kelvin. In 1987, Paul Richards and Andrew Lange at the University of California at Berkeley, recorded the peak of the Planck black body spectrum during a sounding rocket flight that carried a far-infrared spectrometer to the edge of space. (The dichroic bandpass filters in their spectrometer were the first far-infrared metamaterials. I designed and built them as a young grad student at Berkeley! [2]) This experiment was followed by the COBE satellite that measured the presence of minuscule fluctuations in the temperature, representing the original heterogeneity of the universe just after the Big Bang.

COBE flew for a year, followed in 1998 by the BOOMerAng experiment, led by Andrew Lange, that was suspended from a high-altitude balloon circling the South Pole for ten days. This experiment discovered the literal echoes of the Big Bang, acoustic oscillations, in other words, the “sound” of the Bang. It also established that the universe is gravitationally “flat”, which is a direct consequence of cosmic inflation. Once again, these findings were followed by a satellite experiment, the WMAP mission in 2003, that mapped these oscillations over the entire sky. Even finer resolution was obtained by the Planck mission in 2013, measuring higher harmonics of the sound oscillations. These oscillations in the early universe helped seed regions of slightly higher density that condensed into galaxies, leading to the large-scale structure of the universe that we see today.

Anisotropy of the cosmic background radiation — Fig. 2. Successively higher resolution views of the echos of the Big Bang from COBE (1992) to WMAP (2003) to Planck (2013). From Ref.

The 21st Century will likely be known as the time when the physics of the early universe was finally pinned down, and maybe even of what can before. The answers may tell us if there are parallel universes in a much larger metaverse.

Exoplanets (2009)

The Earth is not alone in the Universe. It is not even alone in our little neighborhood of the Milky Way. Within 50 light years it is estimated that there are about 1000 Earth-sized planets in the habitable zone of their respective stars. Why is 50 light years significant? It is because, within this century, the technology to explore those planets is likely to be developed. With the right designs, an unmanned probe could reach 50 light years from Earth within a century, and the time to call back home is only 50 years. So if a probe is launched in the year 2100, we could be receiving transmissions from the new planet by the year 2250.

This estimate of 1000 New Earths is the result of a quiet revolution in planetary science that has been unfolding over the past quarter century. The very first exoplanet was confirmed in 1995 by Michel Mayor and Didier Queloz. Today, as of the writing of this blog, there are 6,278 confirmed exoplanets. Most of these were disovered by the Kepler satellite that was launched in 2009.

Kepler exoplanet discoveries — Fig. 3. An artists rendition of several of the Earth-sized planets discovered by the Kepler satellite. From Ref.

By 2100, we will know where all the exoplanets are that are within 50 light years of Earth, and we will know which ones are potential inhabitable. It may even happen that signs of life on one of these planets will have been discovered. If so, then it is hard to imagine humankind NOT launching probes to visit those planets. If the right propulsion technology is developed, then those probes could be signaling back information from those planets as early as the year 2250…if anyone is still here to listen.

The Higgs (2012)

The crowning achievement of high-energy physics may also have been the last nail in the coffin. Throughout the second half of the 20th century, high-energy physics took the lion’s share of money and attention showered on physics. Beginning in the aftermath of the Manhattan Project, the search for the fundamental constituents of our universe at first found more and more particles, creating a “zoo” that resisted easy classification, until quarks were proposed that simplified the whole thing down into what is now called the Standard Model of Physics.

But one piece of the puzzle was still missing–the explanation of why particles have the masses they do. This missing piece was supplied by the theoretical physicist Peter Higgs in 1964 who proposed that point-like massless particles interacted with a “field” that permeated space. The interaction energy was equivalent to mass through Einstein’s famous E = mc², and the quantization of the field predicted the existence of a “Higgs Boson”. The search for the “Higgs”, as it is called for short, became the Holy Grail of Physics at the end of the last century.

Higgs production, decay and pair processes as Feynman diagrams — Fig. 4. Feynman diagrams that involve the generation of Higgs particles.

The discovery of the Higgs boson was announced on the 4th of July in 2012 [3]. It capped 80 years of progress in high-energy particle physics since the discovery of the positron in 1932. But it may also be the last. Since 2012, over the past 14 years, there have been no new “major” discoveries at the Large Hadron Collider (LHC). Most high-energy talks since then have been about speculative experiments seeking deviations from the Standard Model, but so far there is nothing new.

In the year 2100, looking back, the era of high-energy physics may be relegated to the 20th century, with the Higgs just a finishing touch that tipped over into the new millennium … Or sometime in the next 75 years there will be a discovery that goes beyond standard physics and opens a new chapter in the field. We will have to wait to see.

Gravitational Waves (2015)

Where were you on Nov. 11, 2015 at 10:30 am? Can you remember? I can! I was in a conference room in the Physics Building on the Purdue University Campus waiting with a small crowd of physicists for a news conference to begin. Everyone knew it would be something big. It was. They announced the first detection of a gravitational wave by the LIGO detector (the Laser Interferometric Gravitational Wave Observatory). In a way, it was anti-climactic because we all knew that LIGO would eventually see one. But it was also immensely dramatic, because it was the most sensitive measurement ever made by mankind. The displacement of the mirrors in the interferometer caused by the passing gravitational wave was a tiny fraction of a radius of a proton, yet the signal was as clear as a bell. It came from the merger of two 30 solar-mass black holes in a galaxy far, far away.

First detection of gravitational waves by LIGO — Fig. 5. The two LIGO recordings (at Hanfored and at Livingston) of the first detected gravitaitonal wave. From Ref.

By the year 2100, looking back, multi-messenger astronomy will have been a key part of the physics of the 21st century. Multi-messenger astronomy is when an astronomical event is detected across many detection modes, possibly including light, infrared, ultraviolet, x-ray, neutrino and gravitational wave detection. The field is just beginning and has a long way to go to integrate all these different ways of seeing into a complete picture of what happens out in the universe.

Topological physics (2016)

Of all the topics of this blog, this one is perhaps the most abstract. When we think of geometry, it is natural to think in terms of the symmetries that objects have. The last century was the pinnacle of geometric physics, where Einstein showed that gravity is a geometric property of warped space, where group theory classified all the ways that objects can be constructed and behave, and symmetry breaking was invoked to explain the hierarchy of physical forces.

The new century will be the time of topological physics, where symmetries of matter may not even matter, but the way that properties of matter are connected does. By “property of matter” I mean like the electronic states of a solid state material where the states are excluded from portions of state space, creating topology in abstract spaces. Such topological properties govern how freely currents can flow on surfaces but not in the bulk, or vice versa. In quantum systems, topological properties can protect quantum information from decoherence, which is the bane of most real-world implementations of quantum computers. For instance, by “braiding anyons” it is possible to create qubits that resist dephasing.

Braided anyons at Purdue — Fig. 6. Evidence for the braiding of anyons in the solid state. From Ref.

The importance of topology in physics was recognized with the 2016 Nobel Prize to David J. Thouless, F. Duncan M. Haldane, and J. Michael Kosterlitz for “Theoretical discoveries of topological phase transitions and topological phases of matter.”

Images of Black Holes (2019)

Why hasn’t this gotten a Nobel Prize yet? The imaging of black holes is a tour de force, requiring a telescope with the diameter of a planet, and requiring the collaboration of scientists from across that planet to make it all work.

The physics is straightforward. Everyone knows that bigger telescopes have better resolution, so the logical limit is a telescope the size of the Earth. This is accomplished by using interferometric detection, with data from widely spread millimeter-wave telescopes synchronized by an atomic clock in a network of telescopes known as the Event Horizon Telescope (EHT). The results are constructed numerically, as shown below.

Event Horizon Telescope (EHT) images of a black hole

Fig. 7. The EHT images (left) compared to the model (middle) and the blurred model (right) of the black hole in the M87 galaxy. From Ref.

The next logical step for this kind of imaging is a telescope array that is bigger than the Earth … much bigger! This could be accomplished with an array of Lagrange-point satellites, improving the resolution of the images. By the end of this century, we may be imaging the black holes in all the near-by galaxies.

More to Come?

What are the greatest outstanding problems of physics that may yet yield to solutions within this century? It is impossible to say for certain without a crystal ball, but there are some that are likely to be resolved in the next 75 years:

• Dark Matter: This is the 500 pound gorilla in the room. If most of the tangible universe is made of this stuff, then we had better get around to detecting it!

• Dark Energy: This is the other 500 pound gorilla in the room. If most of the intangible universe is made of this stuff, then we had better get a good understanding of it.

• Quantum Gravity: Of the four forces of physics (gravity, electro-magnetic, weak nuclear and strong nuclear) gravity stands apart in several ways, one of which is that there is no quantum theory for it. We have 75 years to fix this if it is to be a crowning achievement of 21st-Century physics.

• The Evolution of Life: I didn’t include any biophysics in my list of the best physics of the century mainly because I cannot point to a single revolutionary breakthrough of physics in this area. There has been a lot of good progress on the microphysics of biological systems, but nothing like discovering a Higgs boson. This could change if the origins of life turn out to be physics-based rather than just some chemistry.

• The Evolution of Intelligence: I think physics has more to say on the evolution of intelligence than on the evolution of life. Intelligence is the quintessential complex system, and the methods of theoretical physics may yet provide a clear answer to the question of “What is Intelligence?”.

• The Early Universe: This is just starting now with the James Webb Telescope peering into the dark depths of history–nearly to the Big Bang itself.

• Multiple Dimensions: String theory likes to live in 11-dimensional space, so what other parts of our physical universe live there too? Dark Matter? Dark Energy? Do all the extra dimensions need to be compact?

• The Arrow of Time: The physics of time is possibly the greatest unsolved problem in physics. Why does it only go one way?

• Singularity Physics: What happens at the center of a Black Hole? Do wormholes provide hyperspace bypasses? These questions may yet get answers from theoretical physics though likely not from the laboratory unless it is from an AMO analog.

References

[1] E. Knill, R. Laflamme and G. J. Milburn, A Scheme for Efficient Quantum Computation with Linear Optics, Nature 409 (6816), 46–52 (2001).

[2] D. NOLTE, A. LANGE and P. RICHARDS, Far-Infrared Dichroic Bandpass-Filters, Applied Optics 24 (10), 1541–1545 (1985).

[3] CERN. (2012, July 4). CERN experiments observe particle consistent with long-sought Higgs boson [Press release]. https://home.cern/news/press-release/cern/cern-experiments-observe-particle-consistent-long-sought-higgs-boson; ATLAS Collaboration. (2012). Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC. Physics Letters B, 716(1), 1–29. https://doi.org/10.1016/j.physletb.2012.08.020 Cited by: 13000+; CMS Collaboration. (2012). Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC. Physics Letters B, 716(1), 30–61. https://doi.org/10.1016/j.physletb.2012.08.021

August 17, 2023August 16, 2025 by David D. Nolte

Book Preview: Interference and the Story of Optical Interferometry

Interference: The History of Optical Interferometry and the Scientists who Tamed Light is available at Oxford University Press and at Amazon and Barnes&Nobles .

The synopses of the first chapters can be found in my previous blog. Here are previews of the final chapters.

Chapter 6. Across the Universe: Exoplanets, Black Holes and Gravitational Waves

Stellar interferometry is opening new vistas of astronomy, exploring the wildest occupants of our universe, from colliding black holes half-way across the universe (LIGO) to images of neighboring black holes (EHT) to exoplanets near Earth that may harbor life.

Image of the supermassive black hole in M87 from Event Horizon Telescope.

Across the Universe: Gravitational Waves, Black Holes and the Search for Exoplanets describes the latest discoveries of interferometry in astronomy including the use of nulling interferometry in the Very Large Telescope Interferometer (VLTI) to detect exoplanets orbiting distant stars. The much larger Event Horizon Telescope (EHT) used long baseline interferometry and closure phase advanced by Roger Jenison to make the first image of a black hole. The Laser Interferometric Gravitational Observatory (LIGO) represented a several-decade-long drive to detect the first gravitational waves first predicted by Albert Einstein a hundred years ago.

Chapter 7. Two Faces of Microscopy: Diffraction and Interference

From the astronomically large dimensions of outer space to the microscopically small dimensions of inner space, optical interference pushes the resolution limits of imaging.

Two Faces of Microscopy: Diffraction and Interference describes the development of microscopic principles starting with Joseph Fraunhofer and the principle of diffraction gratings that was later perfected by Henry Rowland for high-resolution spectroscopy. The company of Carl Zeiss advanced microscope technology after enlisting the help of Ernst Abbe who formed a new theory of image formation based on light interference. These ideas were extended by Fritz Zernike in the development of phase-contrast microscopy. The ultimate resolution of microscopes, defined by Abbe and known as the Abbe resolution limit, turned out not to be a fundamental limit, but was surpassed by super-resolution microscopy using concepts of interference microscopy and structured illumination.

Chapter 8. Holographic Dreams of Princess Leia: Crossing Beams

The coherence of laser light is like a brilliant jewel that sparkles in the darkness, illuminating life, probing science and projecting holograms in virtual worlds.

Holographic Dreams of Princess Leia: Crossing Beams presents the history of holography, beginning with the original ideas of Denis Gabor who invented optical holography as a means to improve the resolution of electron microscopes. Holography became mainstream after the demonstrations by Emmett Leith and Juris Upatnieks using lasers that were first demonstrated by Ted Maiman at Hughes Research Lab after suggestions by Charles Townes on the operating principles of the optical maser. Dynamic holography takes place in crystals that exhibit the photorefractive effect that are useful for adaptive interferometry. Holographic display technology is under development, using ideas of holography merged with light-field displays that were first developed by Gabriel Lippmann.

Chapter 9. Photon Interference: The Foundations of Quantum Communication and Computing

What is the image of one photon interfering? Better yet, what is the image of two photons interfering? The answer to this crucial question laid the foundation for quantum communication.

Photon Interference: The Foundations of Quantum Communication moves the story of interferometry into the quantum realm, beginning with the Einstein-Podolski-Rosen paradox and the principle of quantum entanglement that was refined by David Bohm who tried to banish uncertainty from quantum theory. John Bell and John Clauser pushed the limits of what can be known from quantum measurement as Clauser tested Bell’s inequalities, confirming the fundamental nonlocal character of quantum systems. Leonard Mandel pushed quantum interference into the single-photon regime, discovering two-photon interference fringes that illustrated deep concepts of quantum coherence. Quantum communication began with quantum cryptography and developed into quantum teleportation that can provide the data bus of future quantum computers.

Chapter 10. The Quantum Advantage: Interferometric Computing

There is almost no technical advantage better than having exponential resources at hand. The exponential resources of quantum interference provide that advantage to quantum computing which is poised to usher in a new era of quantum information science and technology.

The Quantum Advantage: Interferometric Computing describes the development of quantum algorithms and quantum computing beginning with the first quantum algorithm invented by David Deutsch as a side effect of his attempt to prove the multiple world interpretation of quantum theory. Peter Shor found a quantum algorithm that could factor the product of primes and that threatened all secure communications in the world. Once the usefulness of quantum algorithms was recognized, quantum computing hardware ideas developed rapidly into quantum circuits supported by quantum logic gates. The limitation of optical interactions, that hampered the development of controlled quantum gates, led to the proposal of linear optical quantum computing and boson sampling in a complex cascade of single-photon interferometers that has been used to demonstrate quantum supremacy, also known as quantum computational advantage, using photonic integrated circuits.

From Oxford Press: Interference

Stories about the trials and toils of the scientists and engineers who tamed light and used it to probe the universe.

Available at Amazon

and at Oxford University Press

and at Barnes & Noble

July 26, 2023August 16, 2025 by David D. Nolte

Book Preview: Interference. The History of Optical Interferometry

This history of interferometry has many surprising back stories surrounding the scientists who discovered and explored one of the most important aspects of the physics of light—interference. From Thomas Young who first proposed the law of interference, and Augustin Fresnel and Francois Arago who explored its properties, to Albert Michelson, who went almost mad grappling with literal firestorms surrounding his work, these scientists overcame personal and professional obstacles on their quest to uncover light’s secrets. The book’s stories, told around the topic of optics, tells us something more general about human endeavor as scientists pursue science.

Interference: The History of Optical Interferometry and the Scientists who Tamed Light, was published Ag. 6 and is available at Oxford University Press and Amazon. Here is a brief preview of the frist several chapters:

Chapter 1. Thomas Young Polymath: The Law of Interference

Thomas Young was the ultimate dabbler, his interests and explorations ranged far and wide, from ancient egyptology to naval engineering, from physiology of perception to the physics of sound and light. Yet unlike most dabblers who accomplish little, he made original and seminal contributions to all these fields. Some have called him the “Last Man Who Knew Everything”.

The chapter, Thomas Young Polymath: The Law of Interference, begins with the story of the invasion of Egypt in 1798 by Napoleon Bonaparte as the unlikely link among a set of epic discoveries that launched the modern science of light. The story of interferometry passes from the Egyptian campaign and the discovery of the Rosetta Stone to Thomas Young. Young was a polymath, known for his facility with languages that helped him decipher Egyptian hieroglyphics aided by the Rosetta Stone. He was also a city doctor who advised the admiralty on the construction of ships, and he became England’s premier physicist at the beginning of the nineteenth century, building on the wave theory of Huygens, as he challenged Newton’s particles of light. But his theory of the wave nature of light was controversial, attracting sharp criticism that would pass on the task of refuting Newton to a new generation of French optical physicists.

Chapter 2. The Fresnel Connection: Particles versus Waves

Augustin Fresnel was an intuitive genius whose talents were almost squandered on his job building roads and bridges in the backwaters of France until he was discovered and rescued by Francois Arago.

The Fresnel Connection: Particles versus Waves describes the campaign of Arago and Fresnel to prove the wave nature of light based on Fresnel’s theory of interfering waves in diffraction. Although the discovery of the polarization of light by Etienne Malus posed a stark challenge to the undulationists, the application of wave interference, with the superposition principle of Daniel Bernoulli, provided the theoretical framework for the ultimate success of the wave theory. The final proof came through the dramatic demonstration of the Spot of Arago.

Chapter 3. At Light Speed: The Birth of Interferometry

There is no question that Francois Arago was a swashbuckler. His life’s story reads like an adventure novel as he went from being marooned in hostile lands early in his career to becoming prime minister of France after the 1848 revolutions swept across Europe.

At Light Speed: The Birth of Interferometry tells how Arago attempted to use Snell’s Law to measure the effect of the Earth’s motion through space but found no effect, in contradiction to predictions using Newton’s particle theory of light. Direct measurements of the speed of light were made by Hippolyte Fizeau and Leon Foucault who originally began as collaborators but had an epic falling-out that turned into an intense competition. Fizeau won priority for the first measurement, but Foucault surpassed him by using the Arago interferometer to measure the speed of light in air and water with increasing accuracy. Jules Jamin later invented one of the first interferometric instruments for use as a refractometer.

Chapter 4. After the Gold Rush: The Trials of Albert Michelson

No name is more closely connected to interferometry than that of Albert Michelson. He succeeded, sometimes at great personal cost, in launching interferometric metrology as one of the most important tools used by scientists today.

Albert A. Michelson, 1907 Nobel Prize. Image Credit.

After the Gold Rush: The Trials of Albert Michelson tells the story of Michelson’s youth growing up in the gold fields of California before he was granted an extraordinary appointment to Annapolis by President Grant. Michelson invented his interferometer while visiting Hermann von Helmholtz in Berlin, Germany, as he sought to detect the motion of the Earth through the luminiferous ether, but no motion was detected. After returning to the States and a faculty position at Case University, he met Edward Morley, and the two continued the search for the Earth’s motion, concluding definitively its absence. The Michelson interferometer launched a menagerie of interferometers (including the Fabry-Perot interferometer) that ushered in the golden age of interferometry.

Chapter 5. Stellar Interference: Measuring the Stars

Learning from his attempts to measure the speed of light through the ether, Michelson realized that the partial coherence of light from astronomical sources could be used to measure their sizes. His first measurements using the Michelson Stellar Interferometer launched a major subfield of astronomy that is one of the most active today.

Stellar Interference: Measuring the Stars brings the story of interferometry to the stars as Michelson proposed stellar interferometry, first demonstrated on the Galilean moons of Jupiter, followed by an application developed by Karl Schwarzschild for binary stars, and completed by Michelson with observations encouraged by George Hale on the star Betelgeuse. However, the Michelson stellar interferometry had stability limitations that were overcome by Hanbury Brown and Richard Twiss who developed intensity interferometry based on the effect of photon bunching. The ultimate resolution of telescopes was achieved after the development of adaptive optics that used interferometry to compensate for atmospheric turbulence.

And More

The last 5 chapters bring the story from Michelson’s first stellar interferometer into the present as interferometry is used today to search for exoplanets, to image distant black holes half-way across the universe and to detect gravitational waves using the most sensitive scientific measurement apparatus ever devised.

Chapter 6. Across the Universe: Exoplanets, Black Holes and Gravitational Waves

Moving beyond the measurement of star sizes, interferometry lies at the heart of some of the most dramatic recent advances in astronomy, including the detection of gravitational waves by LIGO, the imaging of distant black holes and the detection of nearby exoplanets that may one day be visited by unmanned probes sent from Earth.

Chapter 7. Two Faces of Microscopy: Diffraction and Interference

The complement of the telescope is the microscope. Interference microscopy allows invisible things to become visible and for fundamental limits on image resolution to be blown past with super-resolution at the nanoscale, revealing the intricate workings of biological systems with unprecedented detail.

Chapter 8. Holographic Dreams of Princess Leia: Crossing Beams

Holography is the direct legacy of Young’s double slit experiment, as coherent sources of light interfere to record, and then reconstruct, the direct scattered fields from illuminated objects. Holographic display technology promises to revolutionize virtual reality.

Chapter 9. Photon Interference: The Foundations of Quantum Communication and Computing

Quantum information science, at the forefront of physics and technology today, owes much of its power to the principle of interference among single photons.

Chapter 10. The Quantum Advantage: Interferometric Computing

Photonic quantum systems have the potential to usher in a new information age using interference in photonic integrated circuits.

A popular account of the trials and toils of the scientists and engineers who tamed light and used it to probe the universe.

Available at Amazon

and at Oxford University Press

and at Barnes & Noble

March 23, 2022August 16, 2025 by David D. Nolte

The Physics of Starflight: Proxima Centauri b or Bust!

The ability to travel to the stars has been one of mankind’s deepest desires. Ever since we learned that we are just one world in a vast universe of limitless worlds, we have yearned to visit some of those others. Yet nature has thrown up an almost insurmountable barrier to that desire–the speed of light. Only by traveling at or near the speed of light may we venture to far-off worlds, and even then, decades or centuries will pass during the voyage. The vast distances of space keep all the worlds isolated–possibly for the better.

Yet the closest worlds are not so far away that they will always remain out of reach. The very limit of the speed of light provides ways of getting there within human lifetimes. The non-intuitive effects of special relativity come to our rescue, and we may yet travel to the closest exoplanet we know of.

Proxima Centauri b

The closest habitable Earth-like exoplanet is Proxima Centauri b, orbiting the red dwarf star Proxima Centauri that is about 4.2 lightyears away from Earth. The planet has a short orbital period of only about 11 Earth days, but the dimness of the red dwarf puts the planet in what may be a habitable zone where water is in liquid form. Its official discovery date was August 24, 2016 by the European Southern Observatory in the Atacama Desert of Chile using the Doppler method. The Alpha Centauri system is a three-star system, and even before the discovery of the planet, this nearest star system to Earth was the inspiration for the Hugo-Award winning sci-fi trilogy The Three Body Problem by Chinese author Liu Cixin, originally published in 2008.

It may seem like a coincidence that the closest Earth-like planet to Earth is in the closest star system to Earth, but it says something about how common such exoplanets may be in our galaxy.

Artist’s rendition of Proxima Centauri b. From WikiCommons.

Breakthrough Starshot

There are already plans to send centimeter-sized spacecraft to Alpha Centauri. One such project that has received a lot of press is Breakthrough Starshot, a project of the Breakthrough Initiatives. Breakthrough Starshot would send around 1000 centimeter-sized camera-carrying laser-fitted spacecraft with 5-meter-diameter solar sails propelled by a large array of high-power lasers. The reason there are so many of these tine spacecraft is because of the collisions that are expected to take place with interstellar dust during the voyage. It is possible that only a few dozen of the craft will finally make it to Alpha Centauri intact.

Relative locations of the stars of the Alpha Centauri system. From ScienceNews.

As these spacecraft fly by the Alpha Centauri system, possibly within one hundred million miles of Proxima Centauri b, their tiny HR digital cameras will take pictures of the planet’s surface with enough resolution to see surface features. The on-board lasers will then transmit the pictures back to Earth. The travel time to the planet is expected to be 20 or 30 years, plus the four years for the laser information to make it back to Earth. Therefore, it would take a quarter century after launch to find out if Proxima Centauri b is habitable or not. The biggest question is whether it has an atmosphere. The red dwarf it orbits sends out catastrophic electromagnetic bursts that could strip the planet of its atmosphere thus preventing any chance for life to evolve or even to be sustained there if introduced.

There are multiple projects under consideration for travel to the Alpha Centauri systems. Even NASA has a tentative mission plan called the 2069 Mission (100 year anniversary of the Moon landing). This would entail a single spacecraft with a much larger solar sail than the small starshot units. Some of the mission plans proposed star-drive technology, such as nuclear propulsion systems, rather than light sails. Some of these designs could sustain a 1-g acceleration throughout the entire mission. It is intriguing to do the math on what such a mission could look like, in terms of travel time. Could we get an unmanned probe to Alpha Centauri in a matter of years? Let’s find out.

Special Relativity of Acceleration

The most surprising aspect of deriving the properties of relativistic acceleration using special relativity is that it works at all. We were all taught as young physicists that special relativity deals with inertial frames in constant motion. So the idea of frames that are accelerating might first seem to be outside the scope of special relativity. But one of Einstein’s key insights, as he sought to extend special relativity towards a more general theory, was that one can define a series of instantaneously inertial co-moving frames relative to an accelerating body. In other words, at any instant in time, the accelerating frame has an inertial co-moving frame. Once this is defined, one can construct invariants, just as in usual special relativity. And these invariants unlock the full mathematical structure of accelerating objects within the scope of special relativity.

For instance, the four-velocity and the four-acceleration in a co-moving frame for an object accelerating at g are given by

The object is momentarily stationary in the co-moving frame, which is why the four-velocity has only the zeroth component, and the four-acceleration has simply g for its first component.

Armed with these four-vectors, one constructs the invariants

and

This last equation is solved for the specific co-moving frame as

But the invariant is more general, allowing the expression

which yields

From these, putting them all together, one obtains the general differential equations for the change in velocity as a set of coupled equations

The solution to these equations is

where the unprimed frame is the lab frame (or Earth frame), and the primed frame is the frame of the accelerating object, for instance a starship heading towards Alpha Centauri. These equations allow one to calculate distances, times and speeds as seen in the Earth frame as well as the distances, times and speeds as seen in the starship frame. If the starship is accelerating at some acceleration g’ other than g, then the results are obtained simply by replacing g by g’ in the equations.

Relativistic Flight

It turns out that the acceleration due to gravity on our home planet provides a very convenient (but purely coincidental) correspondence

With a similarly convenient expression

These considerably simplify the math for a starship accelerating at g.

Let’s now consider a starship accelerating by g for the first half of the flight to Alpha Centauri, turning around and decelerating at g for the second half of the flight, so that the starship comes to a stop at its destination. The equations for the times to the half-way point are

This means at the midpoint that 1.83 years have elapsed on the starship, and about 3 years have elapsed on Earth. The total time to get to Alpha Centauri (and come to a stop) is then simply

It is interesting to look at the speed at the midpoint. This is obtained by

which is solved to give

This amazing result shows that the starship is traveling at 95% of the speed of light at the midpoint when accelerating at the modest value of g for about 3 years. Of course, the engineering challenges for providing such an acceleration for such a long time are currently prohibitive … but who knows? There is a lot of time ahead of us for technology to advance to such a point in the next century or so.

Figure. Time lapsed inside the spacecraft and on Earth for the probe to reach Alpha Centauri as a function of the acceleration of the craft. At 10 g’s, the time elapsed on Earth is a little less than 5 years. However, the signal sent back will take an additional 4.37 years to arrive for a total time of about 9 years.

Matlab alphacentaur.m

% alphacentaur.m
clear
format compact

g0 = 1;
L = 4.37;

for loop = 1:100
    
    g = 0.1*loop*g0;
    
    taup = (1/g)*acosh(g*L/2 + 1);
    tearth = (1/g)*sinh(g*taup);
    
    tauspacecraft(loop) = 2*taup;
    tlab(loop) = 2*tearth;
    
    acc(loop) = g;
    
end

figure(1)
loglog(acc,tauspacecraft,acc,tlab,'LineWidth',2)
legend('Space Craft','Earth Frame','FontSize',18)
xlabel('Acceleration (g)','FontSize',18)
ylabel('Time (years)','FontSize',18)
dum = set(gcf,'Color','White');
H = gca;
H.LineWidth = 2;
H.FontSize = 18;

To Centauri and Beyond

Once we get unmanned probes to Alpha Centauri, it opens the door to star systems beyond. The next closest are Barnards star at 6 Ly away, Luhman 16 at 6.5 Ly, Wise at 7.4 Ly, and Wolf 359 at 7.9 Ly. Several of these are known to have orbiting exoplanets. Ross 128 at 11 Ly and Lyuten at 12.2 Ly have known earth-like planets. There are about 40 known earth-like planets within 40 lightyears from Earth, and likely there are more we haven’t found yet. It is almost inconceivable that none of these would have some kind of life. Finding life beyond our solar system would be a monumental milestone in the history of science. Perhaps that day will come within this century.

By David D. Nolte, March 23, 2022

Life in a Solar System with a Super-sized Jupiter

There are many known super-Jupiters that orbit their stars—they are detected through a slight Doppler wobble they induce on their stars [1]. But what would become of a rocky planet also orbiting those stars as they feel the tug of both the star and the super planet?

This is not of immediate concern for us, because our solar system has had its current configuration of planets for over 4 billion years. But there can be wandering interstellar planets or brown dwarfs that could visit our solar system, like Oumuamua did in 2017, but much bigger and able to scramble the planetary orbits. Such hypothesized astronomical objects have been given the name “Nemesis“, and it warrants thought on what living in an altered solar system might be like.

What would happen to Earth if Jupiter were 50 times bigger? Could we survive?

The Three-Body Problem

The Sun-Earth-Jupiter configuration is a three-body problem that has a long and interesting history, playing a key role in several aspects of modern dynamics [2]. There is no general analytical solution to the three-body problem. To find the behavior of three mutually interacting bodies requires numerical solution. However, there are subsets of the three-body problem that do yield to partial analytical approaches. One of these is called the restricted three-body problem [3]. It consists of two massive bodies plus a third (nearly) massless body that all move in a plane. This restricted problem was first tackled by Euler and later by Poincaré, who discovered the existence of chaos in its solutions.

The geometry of the restricted three-body problem is shown in Fig. 1. In this problem, take mass m₁ = m_S to be the Sun’s mass, m₂ = m_J to be Jupiter’s mass, and the third (small) mass is the Earth.

Fig. 1 The restricted 3-body problem in the plane. The third mass is negligible relative to the first two masses that obey 2-body dynamics.

The equation of motion for the Earth is

where

and the parameter ξ characterizes the strength of the perturbation of the Earth’s orbit around the Sun. The parameters for the Jupiter-Sun system are

with

for the 11.86 year journey of Jupiter around the Sun. Eq. (1) is a four-dimensional non-autonomous flow

The solutions of an Earth orbit are shown in Fig.2. The natural Earth-Sun-Jupiter system has a mass ratio m_J/m_S = 0.001 for Jupiter relative to the Sun mass. Even in this case, Jupiter causes perturbations of the Earth’s orbit by about one percent. If the mass of Jupiter increases, the perturbations would grow larger until around ξ= 0.06 when the perturbations become severe and the orbit grows unstable. The Earth gains energy from the momentum of the Sun-Jupiter system and can reach escape velocity. The simulation for a mass ratio of 0.07 shows the Earth ejected from the Solar System.

Fig.2 Orbit of Earth as a function of the size of a Jupiter-like planet. The natural system has a Jupiter-Earth mass ratio of 0.03. As the size of Jupiter increases, the Earth orbit becomes unstable and can acquire escape velocity to escape from the Solar System. From body3.m. (Reprinted from Ref. [4])

The chances for ejection depends on initial conditions for these simulations, but generally the danger becomes severe when Jupiter is about 50 times larger than it currently is. Otherwise the Earth remains safe from ejection. However, if the Earth is to keep its climate intact, then Jupiter should not be any larger than about 5 times its current size. At the other extreme, for a planet 70 times larger than Jupiter, the Earth may not get ejected at once, but it can take a wild ride through the solar system. A simulation for a 70x Jupiter is shown in Fig. 3. In this case, the Earth is captured for a while as a “moon” of Jupiter in a very tight orbit around the super planet as it orbits the sun before it is set free again to orbit the sun in highly elliptical orbits. Because of the premise of the restricted three-body problem, the Earth has no effect on the orbit of Jupiter.

Fig. 3 Orbit of Earth for T_J = 11.86 years and ξ = 0.069. The radius of Jupiter is R_J = 5.2. Earth is “captured” for a while by Jupiter into a very tight orbit.

Resonance

If Nemesis were to swing by and scramble the solar system, then Jupiter might move closer to the Earth. More ominously, the period of Jupiter’s orbit could come into resonance with the Earth’s period. This occurs when the ratio of orbital periods is a ratio of small integers. Resonance can amplify small perturbations, so perhaps Jupiter would become a danger to Earth. However, the forces exerted by Jupiter on the Earth changes the Earth’s orbit and hence its period, preventing strict resonance to occur, and the Earth is not ejected from the solar system even for initial rational periods or larger planet mass. This is related to the famous KAM theory of resonances by Kolmogorov, Arnold and Moser that tends to protect the Earth from the chaos of the solar system. More often than not in these scenarios, the Earth is either captured by the super Jupiter, or it is thrown into a large orbit that is still bound to the sun. Some examples are given in the following figures.

Fig. 5 Earth orbit for T_J = 12 years and ξ = 0.071. The Earth is thrown into a nearly circular orbit beyond the orbit of Saturn.

Fig. 6 Earth Orbit for T_J = 4 years and ξ = 0.0615. Earth is thrown into an orbit of high ellipticity out to the orbit of Neptune.

Life on a planet in a solar system with two large bodies has been envisioned in dramatic detail in the science fiction novel “Three-Body Problem” by Liu Cixin about the Trisolarians of the closest known exoplanet to Earth–Proxima Centauri b.

By David D. Nolte, Feb. 28, 2022

Matlab Code: body3.m

function body3

clear

chsi0 = 1/1000;     % Earth-moon ratio = 1/317
wj0 = 2*pi/11.86;

wj = 2*pi/8;
chsi = 73*chsi0;    % (11.86,60) (11.86,67.5) (11.86,69) (11.86,70) (4,60) (4,61.5) (8,73) (12,71) 

rj = 5.203*(wj0/wj)^0.6666

rsun = chsi*rj/(1+chsi);
rjup = (1/chsi)*rj/(1+1/chsi);

r0 = 1-rsun;
y0 = [r0 0 0 2*pi/sqrt(r0)];

tspan = [0 300];
options = odeset('RelTol',1e-5,'AbsTol',1e-6);
[t,y] = ode45(@f5,tspan,y0,options);

figure(1)
plot(t,y(:,1),t,y(:,3))

figure(2)
plot(y(:,1),y(:,3),'k')
axis equal
axis([-6 6 -6 6])

RE = sqrt(y(:,1).^2 + y(:,3).^2);
stdRE = std(RE)

%print -dtiff -r800 threebody

    function yd = f5(t,y)
        
        xj = rjup*cos(wj*t);
        yj = rjup*sin(wj*t);
        xs = -rsun*cos(wj*t);
        ys = -rsun*sin(wj*t);
        rj32 = ((y(1) - xj).^2 + (y(3) - yj).^2).^1.5;
        r32 = ((y(1) - xs).^2 + (y(3) - ys).^2).^1.5;

        yp(1) = y(2);
        yp(2) = -4*pi^2*((y(1)-xs)/r32 + chsi*(y(1)-xj)/rj32);
        yp(3) = y(4);
        yp(4) = -4*pi^2*((y(3)-ys)/r32 + chsi*(y(3)-yj)/rj32);
 
        yd = [yp(1);yp(2);yp(3);yp(4)];

    end     % end f5

end

References:

[1] D. D. Nolte, “The Fall and Rise of the Doppler Effect,” Physics Today, vol. 73, no. 3, pp. 31-35, Mar (2020)

[2] J. Barrow-Green, Poincaré and the three body problem. London Mathematical Society, 1997.

[3] M. C. Gutzwiller, “Moon-Earth-Sun: The oldest three-body problem,” Reviews of Modern Physics, vol. 70, no. 2, pp. 589-639, Apr (1998)

[4] D. D. Nolte, Introduction to Modern Dynamics : Chaos, Networks, Space and Time, 2nd ed. (Oxford University Press, 2015).

January 23, 2022August 16, 2025 by David D. Nolte

The Doppler Universe

If you are a fan of the Doppler effect, then time trials at the Indy 500 Speedway will floor you. Even if you have experienced the fall in pitch of a passing train whistle while stopped in your car at a railroad crossing, or heard the falling whine of a jet passing overhead, I can guarantee that you have never heard anything like an Indy car passing you by at 225 miles an hour.

Indy 500 Time Trials and the Doppler Effect

The Indy 500 time trials are the best way to experience the effect, rather than on race day when there is so much crowd noise and the overlapping sounds of all the cars. During the week before the race, the cars go out on the track, one by one, in time trials to decide the starting order in the pack on race day. Fans are allowed to wander around the entire complex, so you can get right up to the fence at track level on the straight-away. The cars go by only thirty feet away, so they are coming almost straight at you as they approach and straight away from you as they leave. The whine of the car as it approaches is 43% higher than when it is standing still, and it drops to 33% lower than the standing frequency—a ratio almost approaching a factor of two. And they go past so fast, it is almost a step function, going from a steady high note to a steady low note in less than a second. That is the Doppler effect!

But as obvious as the acoustic Doppler effect is to us today, it was far from obvious when it was proposed in 1842 by Christian Doppler at a time when trains, the fastest mode of transport at the time, ran at 20 miles per hour or less. In fact, Doppler’s theory generated so much controversy that the Academy of Sciences of Vienna held a trial in 1853 to decide its merit—and Doppler lost! For the surprising story of Doppler and the fate of his discovery, see my Physics Today article.

From that fraught beginning, the effect has expanded in such importance, that today it is a daily part of our lives. From Doppler weather radar, to speed traps on the highway, to ultrasound images of babies—Doppler is everywhere.

Development of the Doppler-Fizeau Effect

When Doppler proposed the shift in color of the light from stars in 1842 [1], depending on their motion towards or away from us, he may have been inspired by his walk to work every morning, watching the ripples on the surface of the Vltava River in Prague as the water slipped by the bridge piers. The drawings in his early papers look reminiscently like the patterns you see with compressed ripples on the upstream side of the pier and stretched out on the downstream side. Taking this principle to the night sky, Doppler envisioned that binary stars, where one companion was blue and the other was red, was caused by their relative motion. He could not have known at that time that typical binary star speeds were too small to cause this effect, but his principle was far more general, applying to all wave phenomena.

Six years later in 1848 [2], the French physicist Armand Hippolyte Fizeau, soon to be famous for making the first direct measurement of the speed of light, proposed the same principle, unaware of Doppler’s publications in German. As Fizeau was preparing his famous measurement, he originally worked with a spinning mirror (he would ultimately use a toothed wheel instead) and was thinking about what effect the moving mirror might have on the reflected light. He considered the effect of star motion on starlight, just as Doppler had, but realized that it was more likely that the speed of the star would affect the locations of the spectral lines rather than change the color. This is in fact the correct argument, because a Doppler shift on the black-body spectrum of a white or yellow star shifts a bit of the infrared into the visible red portion, while shifting a bit of the ultraviolet out of the visible, so that the overall color of the star remains the same, but Fraunhofer lines would shift in the process. Because of the independent development of the phenomenon by both Doppler and Fizeau, and because Fizeau was a bit clearer in the consequences, the effect is more accurately called the Doppler-Fizeau Effect, and in France sometimes only as the Fizeau Effect. Here in the US, we tend to forget the contributions of Fizeau, and it is all Doppler.

Fig. 1 The title page of Doppler’s 1842 paper [1] proposing the shift in color of stars caused by their motions. (“On the colored light of double stars and a few other stars in the heavens: Study of an integral part of Bradley’s general aberration theory”)

Fig. 2 Doppler used simple proportionality and relative velocities to deduce the first-order change in frequency of waves caused by motion of the source relative to the receiver, or of the receiver relative to the source.

Fig. 3 Doppler’s drawing of what would later be called the Mach cone generating a shock wave. Mach was one of Doppler’s later champions, making dramatic laboratory demonstrations of the acoustic effect, even as skepticism persisted in accepting the phenomenon.

Doppler and Exoplanet Discovery

It is fitting that many of today’s applications of the Doppler effect are in astronomy. His original idea on binary star colors was wrong, but his idea that relative motion changes frequencies was right, and it has become one of the most powerful astrometric techniques in astronomy today. One of its important recent applications was in the discovery of extrasolar planets orbiting distant stars.

When a large planet like Jupiter orbits a star, the center of mass of the two-body system remains at a constant point, but the individual centers of mass of the planet and the star both orbit the common point. This makes it look like the star has a wobble, first moving towards our viewpoint on Earth, then moving away. Because of this relative motion of the star, the light can appear blueshifted caused by the Doppler effect, then redshifted with a set periodicity. This was observed by Queloz and Mayer in 1995 for the star 51 Pegasi, which represented the first detection of an exoplanet [3]. The duo won the Nobel Prize in 2019 for the discovery.

Fig. 4 A gas giant (like Jupiter) and a star obit a common center of mass causing the star to wobble. The light of the star when viewed at Earth is periodically red- and blue-shifted by the Doppler effect. From Ref.

Doppler and Vera Rubins’ Galaxy Velocity Curves

In the late 1960’s and early 1970’s Vera Rubin at the Carnegie Institution of Washington used newly developed spectrographs to use the Doppler effect to study the speeds of ionized hydrogen gas surrounding massive stars in individual galaxies [4]. From simple Newtonian dynamics it is well understood that the speed of stars as a function of distance from the galactic center should increase with increasing distance up to the average radius of the galaxy, and then should decrease at larger distances. This trend in speed as a function of radius is called a rotation curve. As Rubin constructed the rotation curves for many galaxies, the increase of speed with increasing radius at small radii emerged as a clear trend, but the stars farther out in the galaxies were all moving far too fast. In fact, they are moving so fast that they exceeded escape velocity and should have flown off into space long ago. This disturbing pattern was repeated consistently in one rotation curve after another for many galaxies.

Fig. 5 Locations of Doppler shifts of ionized hydrogen measured by Vera Rubin on the Andromeda galaxy. From Ref.

Fig. 6 Vera Rubin’s velocity curve for the Andromeda galaxy. From Ref.

Fig. 7 Measured velocity curves relative to what is expected from the visible mass distribution of the galaxy. From Ref.

A simple fix to the problem of the rotation curves is to assume that there is significant mass present in every galaxy that is not observable either as luminous matter or as interstellar dust. In other words, there is unobserved matter, dark matter, in all galaxies that keeps all their stars gravitationally bound. Estimates of the amount of dark matter needed to fix the velocity curves is about five times as much dark matter as observable matter. In short, 80% of the mass of a galaxy is not normal. It is neither a perturbation nor an artifact, but something fundamental and large. The discovery of the rotation curve anomaly by Rubin using the Doppler effect stands as one of the strongest evidence for the existence of dark matter.

There is so much dark matter in the Universe that it must have a major effect on the overall curvature of space-time according to Einstein’s field equations. One of the best probes of the large-scale structure of the Universe is the afterglow of the Big Bang, known as the cosmic microwave background (CMB).

Doppler and the Big Bang

The Big Bang was astronomically hot, but as the Universe expanded it cooled. About 380,000 years after the Big Bang, the Universe cooled sufficiently that the electron-proton plasma that filled space at that time condensed into hydrogen. Plasma is charged and opaque to photons, while hydrogen is neutral and transparent. Therefore, when the hydrogen condensed, the thermal photons suddenly flew free and have continued unimpeded, continuing to cool. Today the thermal glow has reached about three degrees above absolute zero. Photons in thermal equilibrium with this low temperature have an average wavelength of a few millimeters corresponding to microwave frequencies, which is why the afterglow of the Big Bang got its name: the Cosmic Microwave Background (CMB).

Not surprisingly, the CMB has no preferred reference frame, because every point in space is expanding relative to every other point in space. In other words, space itself is expanding. Yet soon after the CMB was discovered by Arno Penzias and Robert Wilson (for which they were awarded the Nobel Prize in Physics in 1978), an anisotropy was discovered in the background that had a dipole symmetry caused by the Doppler effect as the Solar System moves at 368±2 km/sec relative to the rest frame of the CMB. Our direction is towards galactic longitude 263.85^o and latitude 48.25^o, or a bit southwest of Virgo. Interestingly, the local group of about 100 galaxies, of which the Milky Way and Andromeda are the largest members, is moving at 627±22 km/sec in the direction of galactic longitude 276^o and latitude 30^o. Therefore, it seems like we are a bit slack in our speed compared to the rest of the local group. This is in part because we are being pulled towards Andromeda in roughly the opposite direction, but also because of the speed of the solar system in our Galaxy.

Fig. 8 The CMB dipole anisotropy caused by the Doppler effect as the Earth moves at 368 km/sec through the rest frame of the CMB.

Aside from the dipole anisotropy, the CMB is amazingly uniform when viewed from any direction in space, but not perfectly uniform. At the level of 0.005 percent, there are variations in the temperature depending on the location on the sky. These fluctuations in background temperature are called the CMB anisotropy, and they help interpret current models of the Universe. For instance, the average angular size of the fluctuations is related to the overall curvature of the Universe. This is because, in the early Universe, not all parts of it were in communication with each other. This set an original spatial size to thermal discrepancies. As the Universe continued to expand, the size of the regional variations expanded with it, and the sizes observed today would appear larger or smaller, depending on how the universe is curved. Therefore, to measure the energy density of the Universe, and hence to find its curvature, required measurements of the CMB temperature that were accurate to better than a part in 10,000.

Equivalently, parts of the early universe had greater mass density than others, causing the gravitational infall of matter towards these regions. Then, through the Doppler effect, light emitted (or scattered) by matter moving towards these regions contributes to the anisotropy. They contribute what are known as “Doppler peaks” in the spatial frequency spectrum of the CMB anisotropy.

Fig. 9 The CMB small-scale anisotropy, part of which is contributed by Doppler shifts of matter falling into denser regions in the early universe.

The examples discussed in this blog (exoplanet discovery, galaxy rotation curves, and cosmic background) are just a small sampling of the many ways that the Doppler effect is used in Astronomy. But clearly, Doppler has played a key role in the long history of the universe.

By David D. Nolte, Jan. 23, 2022

References:

[1] C. A. DOPPLER, “Über das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels (About the coloured light of the binary stars and some other stars of the heavens),” Proceedings of the Royal Bohemian Society of Sciences, vol. V, no. 2, pp. 465–482, (Reissued 1903) (1842)

[2] H. Fizeau, “Acoustique et optique,” presented at the Société Philomathique de Paris, Paris, 1848.

[3] M. Mayor and D. Queloz, “A JUPITER-MASS COMPANION TO A SOLAR-TYPE STAR,” Nature, vol. 378, no. 6555, pp. 355-359, Nov (1995)

[4] Rubin, Vera; Ford, Jr., W. Kent (1970). “Rotation of the Andromeda Nebula from a Spectroscopic Survey of Emission Regions”. The Astrophysical Journal. 159: 379

Single-photon Quantum Information (2001)

Solar Neutrino Oscillation (2001)

WMAP and Planck (2003)

Exoplanets (2009)

The Higgs (2012)

Gravitational Waves (2015)

Topological physics (2016)

Images of Black Holes (2019)

More to Come?

References

Chapter 6. Across the Universe: Exoplanets, Black Holes and Gravitational Waves

Chapter 7. Two Faces of Microscopy: Diffraction and Interference

Chapter 8. Holographic Dreams of Princess Leia: Crossing Beams

Chapter 9. Photon Interference: The Foundations of Quantum Communication and Computing

Chapter 10. The Quantum Advantage: Interferometric Computing

From Oxford Press: Interference

Chapter 1. Thomas Young Polymath: The Law of Interference

Chapter 2. The Fresnel Connection: Particles versus Waves

Chapter 3. At Light Speed: The Birth of Interferometry

Chapter 4. After the Gold Rush: The Trials of Albert Michelson

Chapter 5. Stellar Interference: Measuring the Stars

And More

Proxima Centauri b

Breakthrough Starshot

Special Relativity of Acceleration

Relativistic Flight

Matlab alphacentaur.m

To Centauri and Beyond

Further Reading

The Three-Body Problem

Resonance

Matlab Code: body3.m

References:

Indy 500 Time Trials and the Doppler Effect

Development of the Doppler-Fizeau Effect

Doppler and Exoplanet Discovery

Doppler and Vera Rubins’ Galaxy Velocity Curves

Doppler and the Big Bang

References:

Further Reading