## How Far Is It To The Edge Of The Universe?

If you were to go as far out into space as you can imagine, what would you encounter? Would there be a limit to how far you could go, or could you travel a limitless distance? Would you eventually return to your starting point, or would you continue to traverse space that you had never encountered before? In other words, does the Universe have an edge, and if so, where is it?

Believe it or not, there are actually three different ways to think about this question, and each one has a different answer. If you consider how far you could go if you:

• left today in an arbitrarily powerful rocket,
• considered everything that could ever contact us or be contacted by us from the start of the hot Big Bang,
• or used your imagination alone to access the entire Universe, including beyond what will ever be observable,

You can figure out how far it is to the edge. In each case, the answer is fascinating.

ReunMedia / Storyblocks

The key concept to keep in mind is that space isn’t how we normally conceive of it. Conventionally, we think about space as being like a coordinate system — a three-dimensional grid — where the shortest distance between two points is a straight line, and where distances don’t change over time.

But both of those assumptions, so thoroughly good in our everyday lives, fail spectacularly when we begin looking at the larger-scale Universe beyond our own planet. For starters, the idea that the shortest distance between two points is a straight line falls apart as soon as you start introducing masses and energetic quanta into your Universe. Because spacetime is subject to curvature, which the presence of matter and energy is the cause of, the shortest distance between two points is inherently dependent on the shape of the Universe between those points.

Christopher Vitale of Networkologies and the Pratt Institute

In addition to that, the fabric of spacetime itself does not remain static over time. In a Universe filled with matter and energy, a static, unchanging Universe (where distances between points remain the same over time) is inherently unstable; the Universe must evolve by either expanding or contracting. If Einstein’s General theory of Relativity is correct, this is mandatory.

Observationally, the evidence that our Universe is expanding is overwhelming: a spectacular validation for Einstein’s predictions. But this carries with it a series of consequences for objects separated by cosmic distances, including that the distance between them expands over time. Today, the most distant objects we can see are more than 30 billion light-years away, despite the fact that only 13.8 billion years have passed since the Big Bang.

Larry McNish of RASC Calgary Center

When we measure how distant a variety of objects are from their physical and luminous properties — along with the amount that their light has been shifted by the Universe’s expansion — we can come to understand what the Universe is made of. Our cosmic cocktail, at present, consists of:

• 0.01% radiation in the form of photons,
• 0.1% neutrinos, an elusive, low-mass particle almost as numerous as photons,
• 4.9% normal matter, made mostly of the same stuff we are: protons, neutrons, and electrons,
• 27% dark matter, an unknown substance that gravitates but neither emits nor absorbs light,
• and 68% dark energy, which is the energy inherent to space that causes distant objects to accelerate in their recession from us.

When you combine these effects together, you get a unique and unambiguous prediction for how far it is, at all times past and present, to the edge of the observable Universe.

E. Siegel

This is a big deal! Most people assume that if the Universe has been around for 13.8 billion years since the Big Bang, then the limit to how far we can see will be 13.8 billion light-years, but that’s not quite right.

Only if the Universe were static and not expanding would this be true, but the fact is this: the farther away we look, the faster distant objects appear to speed away from us. The rate of that expansion changes in a way that is predictable based on what’s in the Universe, and in turn, knowing what’s in the Universe and observing how fast objects expand tells us how far away they are. When we take all of the available data together, we arrive at a unique value for everything together, including the distance to the observable cosmic horizon: 46.1 billion light-years.

Frédéric MICHEL and Andrew Z. Colvin, annotated by E. Siegel

This boundary, however, is not an “edge” to the Universe in any conventional sense of the word. It is not a boundary in space at all; if we happened to be located at any other point in space, we would still be able to detect and observe everything around us within that 46.1 billion light-year sphere centered on us.

This is because that “edge” is a boundary in time, rather than in space. This edge represents the limit of what we can see because the speed of light — even in an expanding Universe governed by General Relativity — only allows signals to travel so far over the Universe’s 13.8 billion year history. This distance is farther than 13.8 billion light-years because of the Universe’s expansion, but it’s still finite. However, we cannot reach all of it.

E. Siegel, based on work by Wikimedia Commons users Azcolvin 429 and Frédéric MICHEL

Beyond a certain distance, we can see some of the light that was already emitted long ago, but will never see the light that is being emitted right now: 13.8 billion years after the Big Bang. Beyond a certain specific distance — calculated (by me) to be approximately 18 billion light-years away at present — even a signal moving at the speed of light will never reach us.

Similarly, that means that if we were in an arbitrarily high-powered rocket ship, all of the objects presently contained within this 18 billion light-year radius would be eventually reachable by us, even as the Universe continued to expand and these distances continued to increase. However, the objects beyond that would never be reachable. Even as we achieved greater and greater distances, they would recede faster than we could ever travel, preventing us from visiting them for all eternity. Already, 94% of all the galaxies in the observable Universe are beyond our eternal reach.

NASA, ESA, R. Windhorst, S. Cohen, and M. Mechtley (ASU), R. O’Connell (UVa), P. McCarthy (Carnegie Obs), N. Hathi (UC Riverside), R. Ryan (UC Davis), & H. Yan (tOSU)

And yet, there is a different “edge” that we might want to consider: beyond the limits of what we can observe today, or even what we can potentially observe arbitrarily far into the future, if we run our theoretical clock towards infinity. We can consider how large the entire Universe is — the unobservable Universe — and whether it folds in on itself or not.

The way we can answer this is based on an extrapolation of what we observe when we try to measure the spatial curvature of the Universe: the amount that space is curved on the largest scale we can possibly observe. If the Universe is positively curved, parallel lines will converge and the three angles of a triangle will sum to more than 180 degrees. If the Universe is negatively curved, parallel lines will diverge and the three angles of a triangle will sum to less than 180 degrees. And if the Universe is flat, parallel lines will remain parallel, and all triangles will contain 180 degrees exactly.

NASA / WMAP science team

The way we do this is to take the most distant signals of all, such as the light that’s left over from the Big Bang, and examine in detail how the fluctuations are patterned. If the Universe is curved in either a positive or a negative direction, the fluctuation patterns that we observe will wind up distorted to appear on either larger or smaller angular scales, as opposed to a flat Universe.

When we take the best data available, which comes from both the cosmic microwave background’s fluctuations and the details of how galaxies cluster together on large scales at a variety of distances, we arrive at an inescapable conclusion: the Universe is indistinguishable from perfect spatial flatness. If it is curved, it’s at a level that’s no more than 0.4%, meaning that if the Universe is curved like a hypersphere, its radius is at least ~250 times larger than the part that’s observable to us.

Smoot Cosmology Group / LBL

If you define the edge of the Universe as the farthest object we could ever reach if we began our journey immediately, then our present limit is a mere distance of 18 billion light-years, encompassing just 6% of the volume of our observable Universe. If you define it as the limit of what we can observe a signal from — who we can see and who can see us — then the edge goes out to 46.1 billion light-years. But if you define it as the limits of the unobservable Universe, the only limit we have is that it’s at least 11,500 billion light-years in size, and it could be even larger.

This doesn’t necessarily mean that the Universe is infinite, though. It could be flat and still curve back on itself, with a donut-like shape known mathematically as a torus. As large and expansive as the observable Universe is, it’s still finite, with a finite amount of information to teach us. Beyond that, the ultimate cosmic truths still remain unknown to us.

ESO and deviantART user InTheStarlightGarden

Follow me on Twitter. Check out my website or some of my other work here.

I am a Ph.D. astrophysicist, author, and science communicator, who professes physics and astronomy at various colleges. I have won numerous awards for science writing since 2008 for my blog, Starts With A Bang, including the award for best science blog by the Institute of Physics. My two books, Treknology: The Science of Star Trek from Tricorders to Warp Drive, Beyond the Galaxy: How humanity looked beyond our Milky Way and discovered the entire Universe, are available for purchase at Amazon. Follow me on Twitter @startswithabang.

## Why NASA And Apple Are Using This Startup To Test Their Electronics More Efficiently

When Danielle Wuchenich hatched the idea for measurement startup Liquid Instruments, she was not chasing worldly success but a faster process for discovering the secrets of space. Her solution—a tool which jams 12 different electrical signal and frequency instruments into a single device—ended up being useful on Earth, with Apple, NASA and Texas Instruments employing the tool to ensure that the electronics they’re developing work.

Now Liquid Instruments’ chief strategy officer, Wuchenich was a graduate student at Australian National University, working on creating a tool called a phasemeter to measure gravitational waves in space, something only of use to high-level researchers. But in conducting the routine electrical measurements required for her research, she encountered a problem:

Every time she wanted to measure voltage over time, signal frequency or signal transmission, Wuchenich had to rely on separate devices with separate software and user interfaces, each with hefty price tags. To avoid this headache, Wuchenich programmed the high-tech phasemeter to do multiple kinds of measurements. In so doing, Wuchenich landed on a universally viable application for an otherwise esoteric product.

Over three years, a twelve-person founding team—consisting of Wuchenich, her lab mates and principal investigator CEO Daniel Shaddock—turned prototype into product. Liquid Instruments began selling its device, dubbed Moku:Lab, in 2017, an 8-inch tool the company argues is not only more efficient than the competition, but cheaper. Moku:Lab costs $6,500, whereas all the tools the device replaces cost up to$60,000, the company estimates. Shaddock says the product has the potential to fundamentally change the test and measurement industry.

“In the old days you had a typewriter for writing letters and a calculator for calculating. And they did the job pretty well. Then along came the computer, and it can write letters, it can calculate things, but it can do a whole lot more,” says Shaddock. “We’ve stumbled upon the formula for the computer for the test and measurement industry.”

So far, investors and scientists are buying it. The startup has raised $10.1 million from Anzu Partners, ANU Connect Ventures and Australian Capital Ventures Limited at a valuation of$33.7 million, with its 2018 revenue coming to around $750,000, according to Wuchenich. And Liquid boasts some big-name customers, including NASA, Texas Instruments, Apple and Nvidia. Despite this early success, Robert W. Baird & Co. analyst Richard Eastman says Liquid Instruments faces a tough challenge breaking into an oligopoly dominated by five major companies—Keysight, Rohde & Schwarz, Tektronix, National Instruments and Anritsu. With several of these large players also selling single pieces of hardware that can make multiple measurements, Eastman is skeptical Liquid Instruments can make a dent. “I’m not sure it looks disruptive,” Eastman says. Also, Liquid Instruments will need to prove it offers comparable precision to its rivals. J. Max Cortner, president of the Instrument & Measurement Society, says while Liquid Instruments offers a unique product, its specs are in mainstream ranges, which may not be good enough for its customer base of highly trained researchers. “That’s going to be their dividing line, their frontier. How do they expand this easy-to-use concept into the physical extremes?” Cortner says. Wuchenich is hoping Moku:Lab’s ready-to-use software and a specialized computer chip called FPGA will separate it from the competition. She notes whatever Liquid Instruments loses on precision, it more than compensates with its low price point. “Bottom line—customers don’t want/can’t afford to overpay for specs they don’t need,” she wrote in an email. It’ll be an uphill battle for a small startup like Liquid Instruments to compete with behemoths whose customers have been loyal for decades. But for Colonel Brian Neff, who heads the department of electrical engineering at the U.S. Air Force Academy and uses Moku:Lab to train his students, Liquid Instruments is a formidable challenger. “There are advantages to this new way of thinking that I’d love to see some of the other players adopt, and if they don’t adopt, then I think it’s that’s just more promising for a company like Liquid Instruments to be able to come in and innovate a solution that hasn’t really been done to this point,” Neff says. Follow me on Twitter or LinkedIn. Send me a secure tip. I cover billionaires and venture capital for Forbes. I’ve covered startups and debates in the business world for Inc. and breaking news for The Associated Press, WBUR and Metro Boston. I recently graduated from Tufts University, where I served as editor-in-chief of The Tufts Daily. 50.8K subscribers In 2017, a Nobelprize was awarded for the direct detection of gravitational waves, as predicted by Einstein’s theory of General Relativity. But really we are still no sure that the events are indeed of astrophysical origin and not misidentified noise that originates on Earth. In this video I tell you what gravitational waves are, how to measurement (directly and indirectly), what the problem is with the existing direct detection, what’s the matter with LIGO’s Nobelprize winning figure, and what’s with the glitches. References: * Better climate predictions https://www.nytimes.com/2019/06/12/op… https://www.extremeearth.eu/ * Articles I have written recently about LIGO In English http://backreaction.blogspot.com/2019… In German https://www.heise.de/newsticker/meldu… * How can LIGO detect signals? https://arxiv.org/abs/gr-qc/0702079 https://arxiv.org/abs/gr-qc/0511083 * Plot was made by eye quotes: https://www.newscientist.com/article/… * List of LIGO/Virgo run 3 alerts and retractions https://gracedb.ligo.org/superevents/… ## Why the Laws of Physics Are Inevitable Compared to the unsolved mysteries of the universe, far less gets said about one of the most profound facts to have crystallized in physics over the past half-century: To an astonishing degree, nature is the way it is because it couldn’t be any different. “There’s just no freedom in the laws of physics that we have,” said Daniel Baumann, a theoretical physicist at the University of Amsterdam. Since the 1960s, and increasingly in the past decade, physicists like Baumann have used a technique known as the “bootstrap” to infer what the laws of nature must be. This approach assumes that the laws essentially dictate one another through their mutual consistency — that nature “pulls itself up by its own bootstraps.” The idea turns out to explain a huge amount about the universe. When bootstrapping, physicists determine how elementary particles with different amounts of “spin,” or intrinsic angular momentum, can consistently behave. In doing this, they rediscover the four fundamental forces that shape the universe. Most striking is the case of a particle with two units of spin: As the Nobel Prize winner Steven Weinberg showed in 1964, the existence of a spin-2 particle leads inevitably to general relativity — Albert Einstein’s theory of gravity. Einstein arrived at general relativity through abstract thoughts about falling elevators and warped space and time, but the theory also follows directly from the mathematically consistent behavior of a fundamental particle. “I find this inevitability of gravity [and other forces] to be one of the deepest and most inspiring facts about nature,” said Laurentiu Rodina, a theoretical physicist at the Institute of Theoretical Physics at CEA Saclay who helped to modernize and generalize Weinberg’s proof in 2014. “Namely, that nature is above all self-consistent.” ## How Bootstrapping Works A particle’s spin reflects its underlying symmetries, or the ways it can be transformed that leave it unchanged. A spin-1 particle, for instance, returns to the same state after being rotated by one full turn. A spin-12 particle must complete two full rotations to come back to the same state, while a spin-2 particle looks identical after just half a turn. Elementary particles can only carry 0, 12, 1, 32 or 2 units of spin. To figure out what behavior is possible for particles of a given spin, bootstrappers consider simple particle interactions, such as two particles annihilating and yielding a third. The particles’ spins place constraints on these interactions. An interaction of spin-2 particles, for instance, must stay the same when all participating particles are rotated by 180 degrees, since they’re symmetric under such a half-turn. Interactions must obey a few other basic rules: Momentum must be conserved; the interactions must respect locality, which dictates that particles scatter by meeting in space and time; and the probabilities of all possible outcomes must add up to 1, a principle known as unitarity. These consistency conditions translate into algebraic equations that the particle interactions must satisfy. If the equation corresponding to a particular interaction has solutions, then these solutions tend to be realized in nature. For example, consider the case of the photon, the massless spin-1 particle of light and electromagnetism. For such a particle, the equation describing four-particle interactions — where two particles go in and two come out, perhaps after colliding and scattering — has no viable solutions. Thus, photons don’t interact in this way. “This is why light waves don’t scatter off each other and we can see over macroscopic distances,” Baumann explained. The photon can participate in interactions involving other types of particles, however, such as spin-12 electrons. These constraints on the photon’s interactions lead to Maxwell’s equations, the 154-year-old theory of electromagnetism. Or take gluons, particles that convey the strong force that binds atomic nuclei together. Gluons are also massless spin-1 particles, but they represent the case where there are multiple types of the same massless spin-1 particle. Unlike the photon, gluons can satisfy the four-particle interaction equation, meaning that they self-interact. Constraints on these gluon self-interactions match the description given by quantum chromodynamics, the theory of the strong force. A third scenario involves spin-1 particles that have mass. Mass came about when a symmetry broke during the universe’s birth: A constant — the value of the omnipresent Higgs field — spontaneously shifted from zero to a positive number, imbuing many particles with mass. The breaking of the Higgs symmetry created massive spin-1 particles called W and Z bosons, the carriers of the weak force that’s responsible for radioactive decay. Then “for spin-2, a miracle happens,” said Adam Falkowski, a theoretical physicist at the Laboratory of Theoretical Physics in Orsay, France. In this case, the solution to the four-particle interaction equation at first appears to be beset with infinities. But physicists find that this interaction can proceed in three different ways, and that mathematical terms related to the three different options perfectly conspire to cancel out the infinities, which permits a solution. That solution is the graviton: a spin-2 particle that couples to itself and all other particles with equal strength. This evenhandedness leads straight to the central tenet of general relativity: the equivalence principle, Einstein’s postulate that gravity is indistinguishable from acceleration through curved space-time, and that gravitational mass and intrinsic mass are one and the same. Falkowski said of the bootstrap approach, “I find this reasoning much more compelling than the abstract one of Einstein.” Thus, by thinking through the constraints placed on fundamental particle interactions by basic symmetries, physicists can understand the existence of the strong and weak forces that shape atoms, and the forces of electromagnetism and gravity that sculpt the universe at large. In addition, bootstrappers find that many different spin-0 particles are possible. The only known example is the Higgs boson, the particle associated with the symmetry-breaking Higgs field that imbues other particles with mass. A hypothetical spin-0 particle called the inflaton may have driven the initial expansion of the universe. These particles’ lack of angular momentum means that fewer symmetries restrict their interactions. Because of this, bootstrappers can infer less about nature’s governing laws, and nature itself has more creative license. Spin-12 matter particles also have more freedom. These make up the family of massive particles we call matter, and they are individually differentiated by their masses and couplings to the various forces. Our universe contains, for example, spin-12 quarks that interact with both gluons and photons, and spin-12 neutrinos that interact with neither. The spin spectrum stops at 2 because the infinities in the four-particle interaction equation kill off all massless particles that have higher spin values. Higher-spin states can exist if they’re extremely massive, and such particles do play a role in quantum theories of gravity such as string theory. But higher-spin particles can’t be detected, and they can’t affect the macroscopic world. ## Undiscovered Country Spin-32 particles could complete the 0, 12, 1, 32, 2 pattern, but only if “supersymmetry” is true in the universe — that is, if every force particle with integer spin has a corresponding matter particle with half-integer spin. In recent years, experiments have ruled out many of the simplest versions of supersymmetry. But the gap in the spin spectrum strikes some physicists as a reason to hold out hope that supersymmetry is true and spin-32 particles exist. In his work, Baumann applies the bootstrap to the beginning of the universe. A recent Quanta article described how he and other physicists used symmetries and other principles to constrain the possibilities for those first moments. It’s “just aesthetically pleasing,” Baumann said, “that the laws are inevitable — that there is some inevitability of the laws of physics that can be summarized by a short handful of principles that then lead to building blocks that then build up the macroscopic world.” By: Natalie Wolchover 71 subscribers Computational Modeling Physics First with Bootstrap seeks to explore how modeling practices and computational thinking can be integrated and synergistically serve as important orienting frameworks for teaching physics. The project is supported by National Science Foundation and 100Kin10. ## 15 Gripping Facts About Galileo Albert Einstein once said that the work of Galileo Galilei “marks the real beginning of physics.” And astronomy, too: Galileo was the first to aim a telescope at the night sky, and his discoveries changed our picture of the cosmos. Here are 15 things that you might not know about the father of modern science, who was born February 15, 1564. ## 1. There’s a reason why Galileo Galilei’s first name echoes his last name. You may have noticed that Galileo Galilei’s given name is a virtual carbon-copy of his family name. In her book Galileo’s Daughter, Dava Sobel explains that in Galileo’s native Tuscany, it was customary to give the first-born son a Christian name based on the family name (in this case, Galilei). Over the years, the first name won out, and we’ve come to remember the scientist simply as “Galileo.” ## 2. Galileo Galilei probably never dropped anything off the leaning tower of Pisa. With its convenient “tilt,” the famous tower in Pisa, where Galileo spent the early part of his career, would have been the perfect place to test his theories of motion, and of falling bodies in particular. Did Galileo drop objects of different weights, to see which would strike the ground first? Unfortunately, we have only one written account of Galileo performing such an experiment, written many years later. Historians suspect that if Galileo taken part in such a grand spectacle, there would be more documentation. (However, physicist Steve Shore did perform the experiment at the tower in 2009; I videotaped it and put the results on YouTube.) ## 3. Galileo taught his students how to cast horoscopes. It’s awkward to think of the father of modern science mucking about with astrology. But we should keep two things in mind: First, as historians remind us, it’s problematic to judge past events by today’s standards. We know that astrology is bunk, but in Galileo’s time, astrology was only just beginning to disentangle from astronomy. Besides, Galileo wasn’t rich: A professor who could teach astrological methods would be in greater demand than one who couldn’t. ## 4. Galileo didn’t like being told what to do. Maybe you already knew that, based on his eventual kerfuffle with the Roman Catholic Church. But even as a young professor at the University of Pisa, Galileo had a reputation for rocking the boat. The university’s rules demanded that he wear his formal robes at all times. He refused—he thought it was pretentious and considered the bulky gown a nuisance. So the university docked his pay. ## 5. Galileo Galilei didn’t invent the telescope. We’re not sure who did, although a Dutch spectacle-maker named Hans Lipperhey often gets the credit (he applied for a patent in the fall of 1608). Within a year, Galileo Galilei obtained one of these Dutch instruments and quickly improved the design. Soon, he had a telescope that could magnify 20 or even 30 times. As historian of science Owen Gingerich has put it, Galileo had managed “to turn a popular carnival toy into a scientific instrument.” ## 6. A king leaned on Galileo to name planets after him. Galileo rose to fame in 1610 after discovering, among other things, that the planet Jupiter is accompanied by four little moons, never previously observed (and invisible without telescopic aid). Galileo dubbed them the “Medicean stars” after his patron, Cosimo II of the Medici family, who ruled over Tuscany. The news spread quickly; soon the king of France was asking Galileo if he might discover some more worlds and name them after him. ## 7. Galileo didn’t have trouble with the church for the first two-thirds of his life. In fact, the Vatican was keen on acquiring astronomical knowledge, because such data was vital for working out the dates of Easter and other holidays. In 1611, when Galileo visited Rome to show off his telescope to the Jesuit astronomers there, he was welcomed with open arms. The future Pope Urban VIII had one of Galileo’s essays read to him over dinner and even wrote a poem in praise of the scientist. It was only later, when a few disgruntled conservative professors began to speak out against Galileo, that things started to go downhill. It got even worse in 1616, when the Vatican officially denounced the heliocentric (sun-centered) system described by Copernicus, which all of Galileo’s observations seemed to support. And yet, the problem wasn’t Copernicanism. More vexing was the notion of a moving Earth, which seemed to contradict certain verses in the Bible. ## 8. Galileo probably could have earned a living as an artist. We think of Galileo as a scientist, but his interests—and talents—straddled several disciplines. Galileo could draw and paint as well as many of his countrymen and was a master of perspective—a skill that no doubt helped him interpret the sights revealed by his telescope. His drawings of the Moon are particularly striking. As the art professor Samuel Edgerton has put it, Galileo’s work shows “the deft brushstrokes of a practiced watercolorist”; his images have “an attractive, soft, and luminescent quality.” Edgerton writes of Galileo’s “almost impressionistic technique” more than 250 years before Impressionism developed. ## 10. Galileo wrote about relativity long before Einstein. He didn’t write about exactly the same sort of relativity that Einstein did. But Galileo understood very clearly that motion is relative—that is, that your perception of motion has to do with your own movement as well as that of the object you’re looking at. In fact, if you were locked inside a windowless cabin on a ship, you’d have no way of knowing if the ship was motionless, or moving at a steady speed. More than 250 years later, these ideas would be fodder for the mind of the young Einstein. ## 10. Galileo never married, but that doesn’t mean he was alone. Galileo was very close with a beautiful woman from Venice named Marina Gamba; together, they had two daughters and a son. And yet, they never married, nor even shared a home. Why not? As Dava Sobel notes, it was traditional for scholars in those days to remain single; perceived class difference may also have played a role. ## 11. You can listen to music composed by Galileo’s dad. Galileo’s father, Vincenzo, was a professional musician and music teacher. Several of his compositions have survived, and you can find modern recordings of them on CD (like this one). The young Galileo learned to play the lute by his father’s side; in time he became an accomplished musician in his own right. His music sense may have aided in his scientific work. With no precision clocks, Galileo was still able to time rolling and falling objects to within mere fractions of a second. ## 12. His discoveries may have influenced a scene in one of Shakespeare’s late plays. An amusing point of trivia is that Galileo and Shakespeare were born in the same year (1564). By the time Galileo aimed his telescope at the night sky, however, the English playwright was nearing the end of his career. But he wasn’t quite ready to put down the quill: His late play Cymbeline contains what may be an allusion to one of Galileo’s greatest discoveries—the four moons circling Jupiter. In the play’s final act, the god Jupiter descends from the heavens, and four ghosts dance around him in a circle. It could be a coincidence—or, as I suggest in my book The Science of Shakespeare, it could hint at the Bard’s awareness of one of the great scientific discoveries of the time. ## 13. Galileo had some big-name visitors while under house arrest. Charged with “vehement suspicion of heresy,” Galileo spent the final eight years of his life under house arrest in his villa outside of Florence. But he was able to keep writing and, apparently, to receive visitors, among them two famous Englishmen: the poet John Milton and the philosopher Thomas Hobbes. ## 14. Galileo’s bones have not rested in peace. When Galileo died in 1642, the Vatican refused to allow his remains to be buried alongside family members in Florence’s Santa Croce Basilica; instead, his bones were relegated to a side chapel. A century later, however, his reputation had improved, and his remains (minus a few fingers) were transferred to their present location, beneath a grand tomb in the basilica’s main chapel. Michelangelo is nearby. ## 15. Galileo might not have been thrilled with the Vatican’s 1992 “apology.” In 1992, under Pope John Paul II, the Vatican issued an official statement admitting that it was wrong to have persecuted Galileo. But the statement seemed to place most of the blame on the clerks and theological advisers who worked on Galileo’s case—and not on Pope Urban VIII, who presided over the trial. Nor was the charge of heresy overturned. By: Dan Falk Check out Brilliant: http://brilliant.org/biographics →Subscribe for new videos every Monday and Thursday! https://www.youtube.com/c/biographics… This video is sponsored by Brilliant. Visit our companion website for more: http://biographics.org Credits: Host – Simon Whistler Author – Steve Theunissen Producer – Jennifer Da Silva Executive Producer – Shell Harris Business inquiries to biographics.email@gmail.com Other Biographics Videos: Albert Einstein: A Pillar of Modern Physics https://youtu.be/VnVVuLIoSWI Satoshi Nakamoto: The Mysterious Founder of Bitcoin https://youtu.be/2Mlw_jVHq7U Source/Further reading: Galileo by Mitch Stokes Galileo and the Scientific Revolution by Laura Fermi https://www.youtube.com/watch?v=OgaV5… ## Amazon Is The Second Company To Report Tesla Solar Panel Fire Topline: Amazon is joining Walmart in pointing the finger at Tesla solar panels for fires on the roofs of their facilities in what is yet another hiccup for Tesla’s embattled solar business. • Amazon said Tesla solar panels caught fire in June 2018 at one of its warehouses in Redlands, California. • Amazon’s disclosure comes days after Walmart sued Tesla for breach of contract and gross negligence after seven stores experienced roof fires allegedly caused by faulty Tesla solar panels. Both companies later said they are working together to “addressing all issues.” • Amazon said it would not install any more Tesla panels. In a statement to Forbes, a Tesla spokesperson said in an email that the Amazon fire was an “isolated event” at one of 11 Amazon sites with solar panels. “Tesla worked collaboratively with Amazon to root cause the event and remediate. We also performed inspections at the other sites, which confirmed the integrity of the systems. As with all of our commercial solar installations, we continue to proactively monitor the systems to ensure they operate safely and reliably,” the statement continues. Amazon did not immediately respond to a request for comment. Tesla did not respond when Forbes asked whether the company has plans for broader inspections of both commercial and residential solar power installations. According to a Business Insider report, Tesla was aware of problems related to its solar panels. In the summer of 2018, around the same time as the Amazon fire, Tesla launched a secret internal project called Project Titan to replace what the company said were faulty “connectors” manufactured by Connecticut-based Amphenol, according to the report. “We have no reason to believe that Amphenol’s products are the cause of any issues related to the claims filed by Walmart against Tesla,” an Amphenol spokesperson said in a statement. Key Background: Tesla’s embattled solar business has been plagued by plunging sales, production delays and layoffs since CEO Elon Musk acquired solar company SolarCity for$2.6 billion in 2016.

Musk hasn’t tweeted about the Walmart or Amazon complaints, but instead announced a revamped pricing plan in an effort to boost the slowing solar panel business. The new pricing model allows residents in six states to rent solar power systems starting at $50 a month ($65 a month in California) instead of buying them up front.

I’m a San Francisco-based reporter covering breaking news at Forbes. Previously, I’ve reported for USA Today, Business Insider, The San Francisco Business Times and San Jose Inside. I studied journalism at Syracuse University’s S.I. Newhouse School of Public Communications and was an editor at The Daily Orange, the university’s independent student newspaper. Follow me on Twitter @rachsandl or shoot me an email rsandler@forbes.com.

Source: https://www.forbes.com/

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## The 5 Lessons Everyone Should Learn From Einstein’s Most Famous Equation: E = mc^2

If you’ve ever heard of Albert Einstein, chances are you know at least one equation that he himself is famous for deriving: E = mc2. This simple equation details a relationship between the energy (E) of a system, its rest mass (m), and a fundamental constant that relates the two, the speed of light squared (c2). Despite the fact that this equation is one of the simplest ones you can write down, what it means is dramatic and profound.

At a fundamental level, there is an equivalence between the mass of an object and the inherent energy stored within it. Mass is only one form of energy among many, such as electrical, thermal, or chemical energy, and therefore energy can be transformed from any of these forms into mass, and vice versa. The profound implications of Einstein’s equations touch us in many ways in our day-to-day lives. Here are the five lessons everyone should learn.

This iron-nickel meteorite, examined and photographed by Opportunity, represents the first such object ever found on the Martian surface. If you were to take this object and chop it up into its individual, constituent protons, neutrons, and electrons, you would find that the whole is actually less massive than the sum of its parts.

NASA / JPL / Cornell

1.) Mass is not conserved. When you think about the things that change versus the things that stay the same in this world, mass is one of those quantities we typically hold constant without thinking about it too much. If you take a block of iron and chop it up into a bunch of iron atoms, you fully expect that the whole equals the sum of its parts. That’s an assumption that’s clearly true, but only if mass is conserved.

In the real world, though, according to Einstein, mass is not conserved at all. If you were to take an iron atom, containing 26 protons, 30 neutrons, and 26 electrons, and were to place it on a scale, you’d find some disturbing facts.

• An iron atom with all of its electrons weighs slightly less than an iron nucleus and its electrons do separately,
• An iron nucleus weighs significantly less than 26 protons and 30 neutrons do separately.
• And if you try and fuse an iron nucleus into a heavier one, it will require you to input more energy than you get out.

Iron-56 may be the most tightly-bound nucleus, with the greatest amount of binding energy per nucleon. In order to get there, though, you have to build up element-by-element. Deuterium, the first step up from free protons, has an extremely low binding energy, and thus is easily destroyed by relatively modest-energy collisions.

Wikimedia Commons

Each one of these facts is true because mass is just another form of energy. When you create something that’s more energetically stable than the raw ingredients that it’s made from, the process of creation must release enough energy to conserve the total amount of energy in the system.

When you bind an electron to an atom or molecule, or allow those electrons to transition to the lowest-energy state, those binding transitions must give off energy, and that energy must come from somewhere: the mass of the combined ingredients. This is even more severe for nuclear transitions than it is for atomic ones, with the former class typically being about 1000 times more energetic than the latter class.

In fact, leveraging the consequences of E = mc2 is how we get the second valuable lesson out of it.

Countless scientific tests of Einstein’s general theory of relativity have been performed, subjecting the idea to some of the most stringent constraints ever obtained by humanity. Einstein’s first solution was for the weak-field limit around a single mass, like the Sun; he applied these results to our Solar System with dramatic success. We can view this orbit as Earth (or any planet) being in free-fall around the Sun, traveling in a straight-line path in its own frame of reference. All masses and all sources of energy contribute to the curvature of spacetime.

LIGO scientific collaboration / T. Pyle / Caltech / MIT

2.) Energy is conserved, but only if you account for changing masses. Imagine the Earth as it orbits the Sun. Our planet orbits quickly: with an average speed of around 30 km/s, the speed required to keep it in a stable, elliptical orbit at an average distance of 150,000,000 km (93 million miles) from the Sun. If you put the Earth and Sun both on a scale, independently and individually, you would find that they weighed more than the Earth-Sun system as it is right now.

When you have any attractive force that binds two objects together — whether that’s the electric force holding an electron in orbit around a nucleus, the nuclear force holding protons and neutrons together, or the gravitational force holding a planet to a star — the whole is less massive than the individual parts. And the more tightly you bind these objects together, the more energy the binding process emits, and the lower the rest mass of the end product.

Whether in an atom, molecule, or ion, the transitions of electrons from a higher energy level to a lower energy level will result in the emission of radiation at a very particular wavelength. This produces the phenomenon we see as emission lines, and is responsible for the variety of colors we see in a fireworks display. Even atomic transitions such as this must conserve energy, and that means losing mass in the correct proportion to account for the energy of the produced photon.

GETTY Images

When you bring a free electron in from a large distance away to bind to a nucleus, it’s a lot like bringing in a free-falling comet from the outer reaches of the Solar System to bind to the Sun: unless it loses energy, it will come in, make a close approach, and slingshot back out again.

However, if there’s some other way for the system to shed energy, things can become more tightly bound. Electrons do bind to nuclei, but only if they emit photons in the process. Comets can enter stable, periodic orbits, but only if another planet steals some of their kinetic energy. And protons and neutrons can bind together in large numbers, producing a much lighter nucleus and emitting high-energy photons (and other particles) in the process. That last scenario is at the heart of perhaps the most valuable and surprising lesson of all.

A composite of 25 images of the Sun, showing solar outburst/activity over a 365 day period. Without the right amount of nuclear fusion, which is made possible through quantum mechanics, none of what we recognize as life on Earth would be possible. Over its history, approximately 0.03% of the mass of the Sun, or around the mass of Saturn, has been converted into energy via E = mc^2.

NASA / Solar Dynamics Observatory / Atmospheric Imaging Assembly / S. Wiessinger; post-processing by E. Siegel

3.) Einstein’s E = mc2 is responsible for why the Sun (like any star) shines. Inside the core of our Sun, where the temperatures rise over a critical temperature of 4,000,000 K (up to nearly four times as large), the nuclear reactions powering our star take place. Protons are fused together under such extreme conditions that they can form a deuteron — a bound state of a proton and neutron — while emitting a positron and a neutrino to conserve energy.

Additional protons and deuterons can then bombard the newly formed particle, fusing these nuclei in a chain reaction until helium-4, with two protons and two neutrons, is created. This process occurs naturally in all main-sequence stars, and is where the Sun gets its energy from.

The proton-proton chain is responsible for producing the vast majority of the Sun’s power. Fusing two He-3 nuclei into He-4 is perhaps the greatest hope for terrestrial nuclear fusion, and a clean, abundant, controllable energy source, but all of these reaction must occur in the Sun.

Borb / Wikimedia Commons

If you were to put this end product of helium-4 on a scale and compare it to the four protons that were used up to create it, you’d find that it was about 0.7% lighter: helium-4 has only 99.3% of the mass of four protons. Even though two of these protons have converted into neutrons, the binding energy is so strong that approximately 28 MeV of energy gets emitted in the process of forming each helium-4 nucleus.

In order to produce the energy we see it produce, the Sun needs to fuse 4 × 1038 protons into helium-4 every second. The result of that fusion is that 596 million tons of helium-4 are produced with each second that passes, while 4 million tons of mass are converted into pure energy via E = mc2. Over the lifetime of the entire Sun, it’s lost approximately the mass of the planet Saturn due to the nuclear reactions in its core.

A nuclear-powered rocket engine, preparing for testing in 1967. This rocket is powered by Mass/Energy conversion, and is underpinned by the famous equation E=mc^2.

ECF (Experimental Engine Cold Flow) experimental nuclear rocket engine, NASA, 1967

4.) Converting mass into energy is the most energy-efficient process in the Universe. What could be better than 100% efficiency? Absolutely nothing; 100% is the greatest energy gain you could ever hope for out of a reaction.

Well, if you look at the equation E = mc2, it tells you that you can convert mass into pure energy, and tells you how much energy you’ll get out. For every 1 kilogram of mass that you convert, you get a whopping  9 × 1016 joules of energy out: the equivalent of 21 Megatons of TNT. Whenever we experience a radioactive decay, a fission or fusion reaction, or an annihilation event between matter and antimatter, the mass of the reactants is larger than the mass of the products; the difference is how much energy is released.

Nuclear weapon test Mike (yield 10.4 Mt) on Enewetak Atoll. The test was part of the Operation Ivy. Mike was the first hydrogen bomb ever tested. A release of this much energy corresponds to approximately 500 grams of matter being converted into pure energy: an astonishingly large explosion for such a tiny amount of mass.

In all cases, the energy that comes out — in all its combined forms — is exactly equal to the energy equivalent of the mass loss between products and reactants. The ultimate example is the case of matter-antimatter annihilation, where a particle and its antiparticle meet and produce two photons of the exact rest energy of the two particles.

Take an electron and a positron and let them annihilate, and you’ll always get two photons of exactly 511 keV of energy out. It’s no coincidence that the rest mass of electrons and positrons are each 511 keV/c2: the same value, just accounting for the conversion of mass into energy by a factor of c2. Einstein’s most famous equation teaches us that any particle-antiparticle annihilation has the potential to be the ultimate energy source: a method to convert the entirety of the mass of your fuel into pure, useful energy.

The top quark is the most massive particle known in the Standard Model, and is also the shortest-lived of all the known particles, with a mean lifetime of 5 × 10^-25 s. When we produce it in particle accelerators by having enough free energy available to create them via E = mc^2, we produce top-antitop pairs, but they do not live for long enough to form a bound state. They exist only as free quarks, and then decay.

Raeky / Wikimedia Commons

5.) You can use energy to create matter — massive particles — out of nothing but pure energy. This is perhaps the most profound lesson of all. If you took two billiard balls and smashed one into the other, you’d always expect the results to have something in common: they’d always result in two and only two billiard balls.

With particles, though, the story is different. If you take two electrons and smash them together, you’ll get two electrons out, but with enough energy, you might also get a new matter-antimatter pair of particles out, too. In other words, you will have created two new, massive particles where none existed previously: a matter particle (electron, muon, proton, etc.) and an antimatter particle (positron, antimuon, antiproton, etc.).

Whenever two particles collide at high enough energies, they have the opportunity to produce additional particle-antiparticle pairs, or new particles as the laws of quantum physics allow. Einstein’s E = mc^2 is indiscriminate this way. In the early Universe, enormous numbers of neutrinos and antineutrinos are produced this way in the first fraction-of-a-second of the Universe, but they neither decay nor are efficient at annihilating away.

E. Siegel / Beyond The Galaxy

This is how particle accelerators successfully create the new particles they’re searching for: by providing enough energy to create those particles (and, if necessary, their antiparticle counterparts) from a rearrangement of Einstein’s most famous equation. Given enough free energy, you can create any particle(s) with mass m, so long as there’s enough energy to satisfy the requirement that there’s enough available energy to make that particle via m = E/c2. If you satisfy all the quantum rules and have enough energy to get there, you have no choice but to create new particles.

The production of matter/antimatter pairs (left) from pure energy is a completely reversible reaction (right), with matter/antimatter annihilating back to pure energy. When a photon is created and then destroyed, it experiences those events simultaneously, while being incapable of experiencing anything else at all.

Dmitri Pogosyan / University of Alberta

Einstein’s E = mc2 is a triumph for the simple rules of fundamental physics. Mass isn’t a fundamental quantity, but energy is, and mass is just one possible form of energy. Mass can be converted into energy and back again, and underlies everything from nuclear power to particle accelerators to atoms to the Solar System. So long as the laws of physics are what they are, it couldn’t be any other way. As Einstein himself said:

It followed from the special theory of relativity that mass and energy are both but different manifestations of the same thing — a somewhat unfamiliar conception for the average mind.

More than 60 years after Einstein’s death, it’s long past time to bring his famous equation down to Earth. The laws of nature aren’t just for physicists; they’re for every curious person on Earth to experience, appreciate, and enjoy.

Follow me on Twitter. Check out my website or some of my other work here.

I am a Ph.D. astrophysicist, author, and science communicator, who professes physics and astronomy at various colleges. I have won numerous awards for science writing si…

Starts With A Bang is dedicated to exploring the story of what we know about the Universe as well as how we know it, with a focus on physics, astronomy, and the scientific story that the Universe tells us about itself. Written by Ph.D. scientists and edited/created by astrophysicist Ethan Siegel, our goal is to share the joy, wonder and awe of scientific discovery.

## How Long Does Quantum Tunneling Take?

The phenomenon known as “tunneling” is one of the best-known predictions of quantum physics, because it so dramatically confounds our classical intuition for how objects ought to behave. If you create a narrow region of space that a particle would have to have a relatively high energy to enter, classical reasoning tells us that low-energy particles heading toward that region should reflect off the boundary with 100% probability. Instead, there is a tiny chance of finding those particles on the far side of the region, with no loss of energy. It’s as if they simply evaded the “barrier” region by making a “tunnel” through it.

It’s very important to note that this phenomenon is absolutely and unquestionably real, demonstrated in countless ways. The most dramatic of these is sunlight— the Sun wouldn’t be able to fuse hydrogen into helium without quantum tunneling— but it’s also got more down-to-earth technological applications. Tunneling serves as the basis for Scanning Tunneling Microscopy, which uses the tunneling of electrons across a tiny gap between a sharp tip and a surface to produce maps of that surface that can readily resolve single atoms. It’s also essential for the Josephson effect, which is the basis of superconducting detectors of magnetic fields and some of the superconducting systems proposed for quantum computing.

So, there is absolutely no debate among physicists about whether quantum tunneling is a thing that happens. Physicists get a bit twitchy without something to argue over, though, and you don’t have to dig into tunneling (heh) very far to find a disputed question, namely “How long does quantum tunneling take?”

This is an active area of research, and one I’ve written about before. The tricky part is that the distances involved in quantum tunneling are necessarily very small, making the times involved extremely short. It’s also very difficult to ensure that you know where and when the process starts, because, again, the whole business needs to be quantum, with all the measurement and uncertainty issues that brings in.

In the old post linked above, I talked about a couple of experiments involving intense and ultra-fast laser pulses, which rip an electron out of an atom, and then deflect its path in a direction that varies in time. This is a really clever trick, and the experiments are impressive technical achievements; unfortunately, they don’t entirely agree, with some experiments suggesting a short but definitely not zero tunneling time, and others finding a time so short it might as well be zero. So the question isn’t completely settled…

The latest contribution to the ongoing argument showed up on the arxiv just last night, in the form of a new tunneling-time paper from Aephraim Steinberg’s group at the University of Toronto. This one uses the internal states of atoms tunneling through a barrier to make a kind of clock that only “ticks” while the atoms are inside the barrier region.

As with so many things involving atomic physics these days, the key enabling technology here is Bose-Einstein Condensation. They’re able to measure the tunneling of rubidium atoms (which many thousands of times bigger and heavier than the electrons in the pulsed-laser experiments) across a barrier a bit more than a micron thick (several thousand times the distance in the pulsed-laser experiments) because the atoms are incredibly cold and slow-moving. The temperature of their atom cloud is just a few billionths of a degree above absolute zero, and they push them into the barrier at speeds of just a few millimeters per second.

The big advantage this offers is that unlike electrons, which are point particles, atoms have complicated internal structure and can be put in a bunch of different states. This lets them make an energy barrier out of a thin sheet of laser light that increases the energy of the atom in the light. They can control the energy shift by adjusting the laser parameters to get any height they want— they can even “turn off” the barrier without turning off the laser, by making a small shift in the laser frequency, which is crucial for establishing the timing.

The laser also changes the internal state of the atoms in a way that varies in time, letting them use the atoms as a kind of clock. They prepare a sample that’s exclusively in one particular state, and set the laser up in such a way that it drives a slow evolution into a different internal state. They separate the two different states on the far side of the barrier, and measure the probability of changing states. Once they have that, it’s relatively easy to convert that into a measurement of how much time the atoms spent interacting with the laser.

They end up with a number that’s definitely not zero— between 0.55ms and 0.69ms— that agrees well with one of the quantum methods for predicting tunneling time, and disagrees with a “semiclassical” model very badly. It’s always nice to get this kind of discrimination between models; their method also gives them a nice way to separate out the perturbation that comes from making the measurement from the “clock” they’re using, which is a nice bonus.

As a fellow cold-atom guy, I find this experiment very impressive and convincing, and there’s potential to extend this to other cool tunneling-related measurements, maybe even tracking the atoms as they move through the barrier. Physicists being physicists, though, I expect the argument over what, exactly, this all means will continue— I’d be a little surprised if zero-tunneling-time partisans gave up without finding some feature of this system to claim as a loophole.

Arcane disputes aside, though, it’s worth taking a step back to note how absolutely incredible it is that we can even have a sensible conversation about something as arcane as the amount of time a tunneling atom spends in places where classical physics says it can’t possibly be. The technology we’ve developed for probing the weirdest of quantum phenomena over the last few decades is mind-boggling, and continues to get better all the time.

Disclosure: Steinberg and I worked in the same research group at NIST in the late 1990’s— he was a postdoc working on BEC and I was a grad student on a different project. I actually had dinner with him a week ago in Toronto, but we didn’t discuss this experiment.

I’m an Associate Professor in the Department of Physics and Astronomy at Union College, and I write books about science for non-scientists. I have a BA in physics from Williams College and a Ph.D. in Chemical Physics from the University of Maryland, College Park (studying laser cooling at the National Institute of Standards and Technology in the lab of Bill Phillips, who shared the 1997 Nobel in Physics). I was a post-doc at Yale, and have been at Union since 2001. My books _How to Teach Physics to Your Dog_ and _How to teach Relativity to Your Dog_ explain modern physics through imaginary conversations with my German Shepherd; _Eureka: Discovering Your Inner Scientist_ (Basic, 2014), explains how we use the process of science in everyday activities, and my latest, _Breakfast With Einstein: The Exotic Physics of Everyday Objects_ (BenBella 2018) explains how quantum phenomena manifest in the course of an ordinary morning. I live in Niskayuna, NY with my wife, Kate Nepveu, our two kids, and Charlie the pupper.

## Irish Teen Wins 2019 Google Science Fair For Removing Microplastics From Water

An Irish teenager just won $50,000 for his project focusing on extracting micros-plastics from water. Google launched the Google Science Fair in 2011 where students ages 13 through 18 can submit experiments and their results in front of a panel of judges. The winner receives$50,000. The competition is also sponsored by Lego, Virgin Galactic, National Geographic and Scientific American.

Fionn Ferreira, an 18-year-old from West Cork, Ireland won the competition for his methodology to remove microplastics from water.

Microplastics are defined as having a diameter of 5nm or less and are too small for filtering or screening during wastewater treatment. Microplastics are often included in soaps, shower gels, and facial scrubs for their ability to exfoliate the skin. Microplastics can also come off clothing during normal washing.

These microplastics then make their way into waterways and are virtually impossible to remove through filtration. Small fish are known to eat microplastics and as larger fish eat smaller fish these microplastics are concentrated into larger fish species that humans consume.

Ferreira used a combination of oil and magnetite powder to create a ferrofluid in the water containing microplastics. The microplastics combined with the ferrofluid which was then extracted.

After the microplastics bound to the ferrofluid, Ferreira used a magnet to remove the solution and leave only water.

After 1,000 tests, the method was 87% effective in removing microplastics of all sorts from water. The most effective microplastic removed was that from a washing machine with the hardest to remove being polypropylene plastics.

With the confirmation of the methodology, Ferreira hopes to scale the technology to be able to implement at wastewater treatment facilities.

This would prevent the microplastics from ever reaching waterways and the ocean. While reduction in the use of microplastics is the ideal scenario, this methodology presents a new opportunity to screen for microplastics before they are consumed as food by fish.

At 18 Ferreira has an impressive array of accomplishments. He is the curator at the Schull Planetarium, speaks 3 languages fluently, won 12 previous science fair competitions, plays the trumpet in an orchestra and has a minor planet named after him by MIT.

I am a geologist passionate about sharing Earth’s intricacies with you. I received my PhD from Duke University where I studied the geology and climate of the Amazon.

## How To Prove Einstein’s Relativity In The Palm Of Your Hand

Cosmic rays, which are ultra-high energy particles originating from all over the Universe, strike protons in the upper atmosphere and produce showers of new particles. The fast-moving charged particles also emit light due to Cherenkov radiation as they move faster than the speed of light in Earth’s atmosphere, and produce secondary particles that can be detected here on Earth.

Simon Swordy (U. Chicago), NASA

When you hold out your palm and point it towards the sky, what is it that’s interacting with your hand? You might correctly surmise that there are ions, electrons and molecules all colliding with your hand, as the atmosphere is simply unavoidable here on Earth. You might also remember that photons, or particles of light, must be striking you, too.

But there’s something more striking your hand that, without relativity, simply wouldn’t be possible. Every second, approximately one muon — the unstable, heavy cousin of the electron — passes through your outstretched palm. These muons are made in the upper atmosphere, created by cosmic rays. With a mean lifetime of 2.2 microseconds, you might think the ~100+ km journey to your hand would be impossible. Yet relativity makes it so, and the palm of your hand can prove it. Here’s how.

While cosmic ray showers are common from high-energy particles, it’s mostly the muons which make it down to Earth’s surface, where they are detectable with the right setup.

Alberto Izquierdo; courtesy of Francisco Barradas Solas

Individual, subatomic particles are almost always invisible to human eyes, as the wavelengths of light we can see are unaffected by particles passing through our bodies. But if you create a pure vapor made out of 100% alcohol, a charged particle passing through it will leave a trail that can be visually detected by even as primitive an instrument as the human eye.

As a charged particle moves through the alcohol vapor, it ionizes a path of alcohol particles, which act as centers for the condensation of alcohol droplets. The trail that results is both long enough and long-lasting enough that human eyes can see it, and the speed and curvature of the trail (if you apply a magnetic field) can even tell you what type of particle it was.

This principle was first applied in particle physics in the form of a cloud chamber.

A completed cloud chamber can be built in a day out of readily-available materials and for less than $100. You can use it to prove the validity of Einstein’s relativity, if you know what you’re doing! Instructables user ExperiencingPhysics Today, a cloud chamber can be built, by anyone with commonly available parts, for a day’s worth of labor and less than$100 in parts. (I’ve published a guide here.) If you put the mantle from a smoke detector inside the cloud chamber, you’ll see particles emanate from it in all directions and leave tracks in your cloud chamber.

That’s because a smoke detector’s mantle contains radioactive elements such as Americium, which decays by emitting α-particles. In physics, α-particles are made up of two protons and two neutrons: they’re the same as a helium nucleus. With the low energies of the decay and the high mass of the α-particles, these particles make slow, curved tracks and can even be occasionally seen bouncing off of the cloud chamber’s bottom. It’s an easy test to see if your cloud chamber is working properly.

For an extra bonus of radioactive tracks, add the mantle of a smoke detector to the bottom of your cloud chamber, and watch the slow-moving particles emanating outward from it. Some will even bounce off the bottom!

If you build a cloud chamber like this, however, those α-particle tracks aren’t the only things you’ll see. In fact, even if you leave the chamber completely evacuated (i.e., you don’t put a source of any type inside or nearby), you’ll still see tracks: they’ll be mostly vertical and appear to be perfectly straight.

This is because of cosmic rays: high-energy particles that strike the top of Earth’s atmosphere, producing cascading particle showers. Most of the cosmic rays are made up of protons, but move with a wide variety of speeds and energies. The higher-energy particles will collide with particles in the upper atmosphere, producing particles like protons, electrons, and photons, but also unstable, short-lived particles like pions. These particle showers are a hallmark of fixed-target particle physics experiments, and they occur naturally from cosmic rays, too.

Although there are four major types of particles that can be detected in a cloud chamber, the long and straight tracks are the cosmic ray muons, which can be used to prove that special relativity is correct.

Wikimedia Commons user Cloudylabs

The thing about pions is that they come in three varieties: positively charged, neutral, and negatively charged. When you make a neutral pion, it just decays into two photons on very short (~10-16 s) timescales. But charged pions live longer (for around 10-8 s) and when they decay, they primarily decay into muons, which are point particles like electrons but have 206 times the mass.

Muons also are unstable, but they’re the longest-lived unstable fundamental particle as far as we know. Owing to their relatively small mass, they live for an astoundingly long 2.2 microseconds, on average. If you were to ask how far a muon could travel once created, you might think to multiply its lifetime (2.2 microseconds) by the speed of light (300,000 km/s), getting an answer of 660 meters. But that leads to a puzzle.

Cosmic ray shower and some of the possible interactions. Note that if a charged pion (left) strikes a nucleus before it decays, it produces a shower, but if it decays first (right), it produces a muon that will reach the surface.

Konrad Bernlöhr of the Max-Planck-Institute at Heidelberg

I told you earlier that if you hold out the palm of your hand, roughly one muon per second passes through it. But if they can only live for 2.2 microseconds, they’re limited by the speed of light, and they’re created in the upper atmosphere (around 100 km up), how is it possible for those muons to reach us?

You might start to think of excuses. You might imagine that some of the cosmic rays have enough energy to continue cascading and producing particle showers during their entire journey to the ground, but that’s not the story the muons tell when we measure their energies: the lowest ones are still created some 30 km up. You might imagine that the 2.2 microseconds is just an average, and maybe the rare muons that live for 3 or 4 times that long will make it down. But when you do the math, only 1-in-1050 muons would survive down to Earth; in reality, nearly 100% of the created muons arrive.

A light-clock, formed by a photon bouncing between two mirrors, will define time for any observer. Although the two observers may not agree with one another on how much time is passing, they will agree on the laws of physics and on the constants of the Universe, such as the speed of light. When relativity is applied correctly, their measurements will be found to be equivalent to one another, as the correct relativistic transformation will allow one observer to understand the observations of the other.

John D. Norton

How can we explain such a discrepancy? Sure, the muons are moving close to the speed of light, but we’re observing them from a reference frame where we’re stationary. We can measure the distance the muons travel, we can measure the time they live for, and even if we give them the benefit of the doubt and say that they’re moving at (rather than near) the speed of light, they shouldn’t even make it for 1 kilometer before decaying.

But this misses one of the key points of relativity! Unstable particles don’t experience time as you, an external observer, measures it. They experience time according to their own onboard clocks, which will run slower the closer they move to the speed of light. Time dilates for them, which means that we will observe them living longer than 2.2 microseconds from our reference frame. The faster they move, the farther we’ll see them travel.

One revolutionary aspect of relativistic motion, put forth by Einstein but previously built up by Lorentz, Fitzgerald, and others, that rapidly moving objects appeared to contract in space and dilate in time. The faster you move relative to someone at rest, the greater your lengths appear to be contracted, while the more time appears to dilate for the outside world. This picture, of relativistic mechanics, replaced the old Newtonian view of classical mechanics, and can explain the lifetime of a cosmic ray muon.

Curt Renshaw

How does this work out for the muon? From its reference frame, time passes normally, so it will only live for 2.2 microseconds according to its own clocks. But it will experience reality as though it hurtles towards Earth’s surface extremely close to the speed of light, causing lengths to contract in its direction of motion.

If a muon moves at 99.999% the speed of light, every 660 meters outside of its reference frame will appear as though it’s just 3 meters in length. A journey of 100 km down to the surface would appear to be a journey of 450 meters in the muon’s reference frame, taking up just 1.5 microseconds of time according to the muon’s clock.

At high enough energies and velocities, relativity becomes important, allowing many more muons to survive than would without the effects of time dilation.

Frisch/Smith, Am. J. of Phys. 31 (5): 342–355 (1963) / Wikimedia Commons user D.H

This teaches us how to reconcile things for the muon: from our reference frame here on Earth, we see the muon travel 100 km in a timespan of about 4.5 milliseconds. This is just fine, because time is dilated for the muon and lengths are contracted for it: it sees itself as traveling 450 meters in 1.5 microseconds, and hence it can remain alive all the way down to its destination of Earth’s surface.

Without the laws of relativity, this cannot be explained! But at high velocities, which correspond to high particle energies, the effects of time dilation and length contraction enable not just a few but most of the created muons to survive. This is why, even all the way down here at the surface of the Earth, one muon per second still appears to pass through your upturned, outstretched hand.

The V-shaped track in the center of the image arises from a muon decaying to an electron and two neutrinos. The high-energy track with a kink in it is evidence of a mid-air particle decay. By colliding positrons and electrons at a specific, tunable energy, muon-antimuon pairs could be produced at will. The necessary energy for making a muon/antimuon pair from high-energy positrons colliding with electrons at rest is almost identical to the energy from electron/positron collisions necessary to create a Z-boson.

The Scottish Science & Technology Roadshow

If you ever doubted relativity, it’s hard to fault you: the theory itself seems so counterintuitive, and its effects are thoroughly outside the realm of our everyday experience. But there is an experimental test you can perform right at home, cheaply and with just a single day’s efforts, that allow you see the effects for yourself.

You can build a cloud chamber, and if you do, you will see those muons. If you installed a magnetic field, you’d see those muon tracks curve according to their charge-to-mass ratio: you’d immediately know they weren’t electrons. On rare occasion, you’d even see a muon decaying in mid-air. And, finally, if you measured their energies, you’d find that they were moving ultra-relativistically, at 99.999%+ the speed of light. If not for relativity, you wouldn’t see a single muon at all.

Time dilation and length contraction are real, and the fact that muons survive, from cosmic ray showers all the way down to Earth, prove it beyond a shadow of a doubt.

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Ethan Siegel Contributor

I am a Ph.D. astrophysicist, author, and science communicator, who professes physics and astronomy at various colleges.

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