How Do We Actually Know The Big Bang Happened

TITLE: How Do We Actually Know the Big Bang Happened? CHANNEL: Physics Explained DATE: 2026-03-29 ---TRANSCRIPT--- This video is sponsored by Squarespace, the big bang of website builders. You’ve probably heard it said that the universe began with a big bang, an unimaginably dense, searing hot state from which everything we see today emerged. And you’ve probably also heard that the universe is expanding, that the very fabric of space itself is stretching. But that immediately raises a deep question. How could we possibly know that from our position on a small planet looking up at the points of light in the sky? How can we draw conclusions about the origin of the entire universe? To answer that, we need a strategy. First, how do we measure the universe at all? When we look up at the night sky, how can we tell what is nearby, what is distant, and how far away anything really is? Second, what are those faint fuzzy objects scattered across the sky? Are they small structures within our own galaxy or entire galaxies lying far beyond it? Third, what does the light reveal? Why do so many of them appear to be moving away from us? And why do the most distant seem to recede the fastest? Fourth, if the universe is expanding today, what does that imply about the past? If everything is moving apart now, must the universe once have been smaller, denser, and hotter? And finally, if that picture is true, did the early universe leave anything behind? Is there any surviving trace that would allow us to test whether this story really is true? Because if it did, then the evidence should still be with us today. Not just in the light that fills the universe, but in the very matter it contains. So, if you’re ready for the story of our creation, let’s begin. Long before telescopes were invented, astronomers noticed a simple fact using the naked eye. Some stars in the night sky look brighter than others. And so the Greek astronomer Hypus, working in the 2n century BCE, began classifying stars by how bright they appeared in the sky. The brightest stars were called first magnitude stars and slightly fainter stars were called second magnitude and then third, fourth, fifth, all the way down to sixth magnitude which was roughly the faintest a human observer could see with the unaded eye. Later the Greek philosopher and astronomer Tomy preserved and popularized this kind of ranking in his famous work the almagist. Then in the 19th century, the English astronomer Norman Robert Pogson took this ancient hippocy scale and put it on a precise mathematical footing. He defined the system so that a difference of five magnitudes corresponds exactly to a factor of 100 difference in observed flux. That is the amount of light energy from the star arriving at us per unit area. That means a one magnitude step corresponds to a flux ratio of 100 raised to the power of 1/5 which is around 2.512. So now the old visual scale becomes quantitative. In other words, a star of magnitude 1 has about 2.512

• the observed flux of a star of magnitude 2. A magnitude 2 star has about 2.512 times the observed flux of a magnitude 3 star and so on. And after five such steps, the total factor is 2.512 raised to the power of 5. And this is equal to 100. And so this is how Pogson set up the scale. The magnitude scale changes in equal steps 1 2 3 4 5. But the observed flux changes in equal factors, a factor of 2.512 each time. So if we want to preserve Hypocus’ old step scale, but now tie it to something astronomers can actually measure, we need a mathematical function that converts repeated multiplication into simple addition. That function is the logarithm. For example, if you take the logarithm to the base 10 of the number 10, you get the answer one. Likewise, the logarithm of 100 gives the answer two and the logarithm of a thousand gives the answer three. So we see that each time the original quantity is multiplied by 10, the logarithm of that quantity only increases by one. And that’s exactly the behavior we need. Equal ratios in observed flux should correspond to equal differences in apparent magnitude. So if two stars have observed fluxes f_sub_1 and f_sub_2 and apparent magnitudes m_sub_1 and m_sub_2 then the difference in apparent magnitude must be related to the logarithm of the flux ratio. Pogson’s law can therefore be written as m_sub_2 - m1 = -2.5 * log of f_sub_2 / f_sub_1. Now you might legitimately ask where did this exact equation come from? So let’s connect it back to Pogson’s definition. If you recall, he defined a difference of five magnitudes as corresponding to a factor of 100 difference in observed flux. And so we can check our equation works by subbing this information back into our equation. And we get 5 = -2.5 * log of 1 / 100. And if we calculate the logarithm, we see that the right hand side becomes -2.5 * -2. And this is simply equal to five. And so we see that the left and right hand sides match and our equation is consistent with Pogson’s definition. Now using this scale, we can compare and quantify how bright different objects appear in our sky. Very bright objects like the moon or the sun can even have negative apparent magnitudes while much fainter objects invisible to the naked eye and only seen through telescopes have larger positive apparent magnitudes. Now, it’s important to note that so far we’ve only been talking about how bright objects appear to us from Earth. But that immediately raises a problem. When we see two stars in the sky, how do we know which is actually more luminous? A very luminous star that is far away can appear just as bright as a much dimmer star that is closer. And a dim star that is very close can even appear brighter than a more luminous star that is further away. So apparent magnitude on its own is not enough. That leads to the next obvious question. How do we measure the distance to stars? Because if we know the distance and we know their apparent magnitude, then we can determine how luminous they truly are. For nearby stars, the answer is parallax. As Earth moves around the Sun, a nearby star appears to shift slightly against the background of much more distant stars. It’s the same effect you see if you hold up a finger and look at it first with one eye and then the other. The closer the object, the bigger the apparent shift. This gives astronomers a direct geometric method for measuring stellar distance. If we label the distance between the earth and the sun as one astronomical unit and call the distance to the star d then the angle p we call the parallax angle. Then using basic trigonometry we can write that tan of p is equal to 1 au / d. And therefore if we rearrange we find that d is equal to 1 au / tan of p. But because stars are so far away, the angle P is extremely small. In this case, we can use the small angle approximation saying that tan of P is roughly equal to P. And so the distance becomes approximately 1 AU / P. Now, astronomers define a unit of length known as a parseek, where one parseek is the distance at which a star has a parallax of one arcsec. And an angle of 1 arcseconds to p / 648,000 radians. And if we sub this into our distance equation, we find that one parseek corresponds to a distance of around 26,265 times the distance from the earth to the sun, which is approximately equal to 3.26 light years, which is the distance light would travel in 3.26 years. Now, parallax is extremely powerful, and you can actually see it in action. For example, in these images from NASA, you can see the parallax effect. These animations compare the positions of two of the closest stars, Proxima Centuri and Wolf 359, as seen from Earth and from NASA’s New Horizon spacecraft, which is now over 4 billion miles away. The shift is small, but it’s measurable. And from this tiny shift, we can determine the distance to these stars. So, parallax works beautifully for nearby stars, but it quickly breaks down for more distant ones and certainly for galaxies. Before we continue, just a quick note about something that’s gradually becoming an extension of this channel, the Physics Explained website. One thing I’ve realized making these videos is that not every idea fits into a single upload. Some things just need to be written out properly, lecture notes, animations, or slower, more detailed explanations. That’s where Squarespace comes in. It makes that process straightforward. You can write things out clearly, organize them into pages, and refine ideas over time without everything feeling fragmented. The editor is really intuitive as well. You can lay things out how you want, combine text with diagrams or visuals, and structure explanations in a way that actually makes them easier to follow. And because everything’s builtin, hosting, design, and publishing, you don’t have to think about the technical side at all. You can also set up your own domain directly through Squarespace, so everything lives in one place under a name that fits the project. If you’d like to try it yourself, head to squarespace.com for a free trial. And when you’re ready to launch, go to squarespace.com/physicsexplained to get 10% off your first website or domain. Now suppose you could take every star in the sky and place all of them at exactly the same distance from the Earth. Then distance would no longer affect how bright they appeared. Any differences in brightness would then be due only to differences in the stars intrinsic luminosities. And that is the idea behind absolute magnitude. The magnitude that a star would have if it were placed at a distance of 10 parex is called its absolute magnitude and it’s denoted by a capital m. By contrast, the magnitude we actually observe from earth is the apparent magnitude which we’ve already seen and is denoted by little m. So little M tells us how bright the star looks. Whereas capital M tells us how bright it really is in the sense of how bright it would appear if all stars were compared from the same standard distance of 10 parex. So let’s see if we can derive a relationship between big M and little M. To do that, consider a star of luminosity L and suppose its actual distance from Earth is D parex and let its apparent magnitude be M and let the flux we receive from it at Earth be equal to F subscript D. Now imagine placing that same star at the standard distance of 10 parex. its magnitude there would be its absolute magnitude capital m and the flux we would receive we label as f subscript

10. We can now use pogson’s law but this time we can replace the fluxes inside the logarithm with their physical expressions. Since the star radiates with luminosity l uniformly in all directions the flux that we receive at a distance d is equal to l / 4 d ^ 2. This is simply the stars luminosity spread over the surface of a sphere of radius d. If instead the star were placed at a distance of 10 parx, the flux we would receive would be equal to l / 4 * 10^ 2. Substituting these expressions into pogson’s law, we obtain the following result. Next, we can cancel lots of the terms inside the logarithm and we obtain the following result. Then using the laws of logarithms, we can pull down a factor of 2 and then rewrite this expression as -5 log of 10 + 5 log of d. And this simplifies to 5 log of d minus 5. And so we arrive at the expression little m - big m= 5 log dus 5. This equation is known as the distance modulus equation and it relates the distance to a star d to its absolute magnitude capital m and its apparent magnitude little m. We can also rearrange this equation to obtain an expression for the distance d. And this makes something very powerful clear. If we know the absolute magnitude of a star and we can measure its apparent magnitude as seen from Earth, then this equation allows us to determine the distance to the star. But how could we ever know the absolute magnitude of a distant star in the first place? We can’t travel to these stars and check how luminous they are directly. So, how on earth do we determine their intrinsic luminosity? Unless nature gives us a clue. Unless there exists some class of stars whose true luminosity is encoded in something else, something we can observe directly. And that is exactly what Henrietta Swan Levit discovered. Levitt was born in Lancaster, Massachusetts in 1868. And in 1892, she graduated from Harvard’s Society for the Collegiate Instruction of Women, later known as Radcliffe College. After her studies and following a period of illness that would eventually leave her seriously hard of hearing, she began working as a volunteer at the Harvard College Observatory analyzing photographic plates as part of a team of women working under the supervision of Edward Charles Pickering. There Levit developed a particular expertise for identifying and cataloging variable stars, especially a class of stars known as Sephiid variables. The prototype of this class of variables known as delta CPI had been identified as a variable star in 1784 by John Goodrich. Its brightness was seen to rise and fall with striking regularity. And if you measure that change over time and plot it, you find a distinctive pattern, a rapid climb to maximum brightness followed by a more gradual decline. This behavior could not be explained as a simple eclipse and it pointed instead to an entirely new kind of star. We now understand the origin of this variability. A sephiid is a pulsating star, one that repeatedly expands and contracts. And as its outer layers compress, their physical properties change in a way that alters how radiation passes through them. This drives the regular cycle of brightening and dimming that we observe. And it was these sepied variable stars that came to fascinate Henrietta Swan Levit. After spending months measuring and cataloging them, she became intrigued by the fact that different stars exhibited different periods of variation and also the fact that their apparent brightness seemed to differ as well. But brightness posed a fundamental problem. As we’ve already noted, a star that is intrinsically dim may appear bright if it’s nearby, while a truly luminous star may appear faint if it’s very far away. At first glance, the situation seemed hopeless. But Levit was undeterred, and her breakthrough came when she turned her attention to the small melanic cloud, a star system observable from the southern hemisphere. Because the cloud is vastly farther away than it is wide, she reasoned that any difference in distance between two seafoods within it would be negligible compared with the enormous distance from the cloud to Earth. To a very good approximation, all of these stars could therefore be treated as lying at the same distance from Earth. And that changed everything. You see, if two stars are at the same distance, then any difference in their apparent brightness must reflect a genuine difference in their intrinsic luminosity. So if one seed appears brighter than another, it really is more luminous. And this was the key insight that Levit needed. Through careful and painstaking analysis, Levit identified 25 seed variables in the small melanic cloud and recorded both their periods and the observed maximum and minimum magnitude values. She then plotted the data with period on the x-axis and magnitude on the y-axis, plotting both the maximum and minimum apparent magnitude values. And the result was striking. A clear trend emerged. Longer period stars were generally brighter than shorter period stars and the points traced out a smooth curve. In a moment of brilliance, Levit realized that if instead of plotting the period, she plotted the logarithm of the period. The data fell into a near perfect straight line. As Levit wrote, a straight line can readily be drawn amongst each of the two series of points corresponding to maxima and minima. thus showing that there is a simple relation between the brightness of the variables and their periods. She also noted that the logarithm of the period increases by about 0.48 for each increase of one magnitude in brightness. What had been a trend was now a law. The longer the period of a sephiid, the brighter it truly is. Levit published a result in 1912 in the Harvard College Observatory Circular under the unassuming title periods of 25 variable stars in the small melanic cloud. Noting that a remarkable relation between the brightness of these variables and the length of their periods will be noticed. Never has a discovery so profound been so understated. The power of Levit’s discovery was that it was now possible to compare any two seafoods in the sky and determine their relative distance from Earth. If two seafoods have the same period, then they have the same intrinsic luminosity. So if one appears say 16 times less bright than the other, it must be four times further away by the inverse square law. But although astronomers could now establish relative distances between seafiids, they still did not know the absolute distance to any of them. They could say one was 10 times further away than another, but not how far away either star actually was from Earth. What was needed was a way to independently measure the distance to just one seed in order to calibrate the relationship. And that breakthrough came through the combined efforts of astronomers including Harlo Chappley and the Danish astronomer Aina Herzbrung who used techniques such as parallax to determine the distance to a nearby seafood. And that changed the distance problem completely. If you recall the distance to a star depends on both the absolute and apparent magnitude and you could measure the apparent magnitude but the absolute magnitude was unknown. But now Levit’s work filled in the missing piece. By measuring the period of oscillation of a variable star, you could use her plot along with the calibration to read off the absolute magnitude and then use the measured apparent magnitude to find the distance d. That’s what made seafood so revolutionary. They extended distance measurements far beyond the reach of parallax. And that mattered because in the early 20th century, astronomers still did not know what the universe actually contained. Today, the word galaxy sounds completely familiar, but a 100red years ago that was not established at all. There were many who believed that the Milky Way was all that existed. In the 19th century, astronomers could see many faint fuzzy objects in the sky, especially the spiral nebula. But they didn’t know what those objects actually were or how far away they were. In the 1840s, William Parsons, the third Earl of Ross, used the Leviathan telescope of Parson’s Town to reveal the spiral structure of some of these nebula, most famously handdrawing the spiral nebula M51, what today we recognize as a spiral galaxy. But at the time, these were mysterious objects. Were these small nearby objects inside our own Milky Way? Or were they enormous stellar systems far beyond it, island universes in their own right? That question came to a head in the 1920 Chappley Curtis Great Debate. Harlo Shappley argued that the Milky Way was essentially the whole universe and that the spiral nebula lay within it. Heba Curtis argued that the spiral nebula were separate stellar systems, other galaxies. The debate did not settle everything on the spot, but it crystallized the central questions that required answering. Namely, what are these spiral nebula? How far away are they? And how can we possibly know? And this is exactly where Levit’s work on sephiids changed everything. Levit had shown that sephiid variable stars obey a period luminosity relation. The longer the period, the greater the stars intrinsic luminosity. Once that relation was calibrated, seafards could be used as standard candles. If you could spot a seafood in some distant object such as a nebula, measure its period, infer its absolute magnitude, and compare that with its apparent magnitude. Then you could calculate the distance. Suddenly, a fuzzy spiral nebula was no longer just a shape in the sky. It became something whose distance could in principle be measured. And the astronomer who would fully exploit the power of Levit’s discovery was Edwin Pal Hubble, perhaps the most famous astronomer of the 20th century. Hubble fell in love with astronomy as a young boy. According to later accounts, his grandfather built him a small telescope when he was 8 years old. Yet, despite that early fascination, his father wanted him to pursue a more respectable profession. and Hubble tried for a time to satisfy both duty and desire. At the University of Chicago, he studied mathematics, astronomy, and philosophy while also spending a year as a student laboratory assistant to the physicist Robert Milikin, who would later win the 1923 Nobel Prize for his work on the electron and the photoelectric effect. At the time, the department was led by Albert Mikkelson, whose famous work with Edward Moley had dealt a devastating death blow to the ether hypothesis and who in 1907 became the first American to win a Nobel Prize in the sciences. Hubble then won a road scholarship to the University of Oxford where in keeping with his father’s wishes he studied jurist prudence rather than astronomy. But Hubble held on to his dream of one day becoming an astronomer. And when his father died in 1913, Hubble returned to the United States and abandoned law for good. As Hubble later recalled, “I chucked the law for astronomy, and I knew that even if I were second rate or third rate, it was astronomy that mattered.” Hubble was determined to work at the observatory that housed the world’s most powerful telescope. And that meant Mount Wilson in California. It already possessed a superb 60-inch telescope, and the even more formidable 100in Hooker telescope was being completed. Hubble was offered a job there, and after the war, he joined in the autumn of 1919. Over time, he gradually worked his way up the pecking order, gaining access to more and more telescope time. And then on the night of October 5th, 1923, using the 100inch Hooker telescope, Hubble turned his attention to the Andromeda Nebula, a faint spiral-shaped patch of light in the sky, long debated to be either part of our own galaxy or an island universe far beyond it. The viewing conditions that night were poor. Even so, Hubble managed to obtain a 40-minute exposure. After developing the photographic plate, Hubble noticed a new speck that he had not seen before. He assumed it was probably either a photographic defect or perhaps a nova, a star that suddenly brightens dramatically before gradually fading again. The following night, conditions were better, and he repeated the exposure. This time, he noticed the same spec again along with two others, each of which he marked with the letter N for NOVA. Hubble was eager to compare his new plate with earlier photographs of the same region of the Andromeda Nebula to see whether his Novi were genuine. And when he did, he realized that two of the specs really were new Novi. But the real shock was that the third spec was not a nova at all. It was a seafared variable. The object appeared on some earlier plates but not on others, revealing that its brightness changed over time. In a rush of excitement, Hubble crossed out the N for nova and scribbled vah for variable. An image that has become one of the most famous markings in the history of astronomy. For this was the first seafied ever discovered in a spiral nebula. Hubble immediately realized what it meant. By measuring the period of the oscillating variable star, he could then use Levit’s period luminosity relation to calculate the distance to this star. And from that, he could estimate the distance to the nebula itself. Finally settling the great debate once and for all by confirming whether the Andromeda nebula really did exist outside or inside our own Milky Way galaxy. When Hubble studied the data, he found that the sei had varied with a period of 31.415 days, which according to Levit’s period luminosity law corresponds to a luminosity of around 7,000 times greater than that of our sun. Then by comparing its absolute magnitude with its apparent magnitude and using the equation we derived earlier he estimated the distance to the star and therefore to Andromeda and found a value of around 900,000 light years. Now given that the Milky Way itself was thought to be roughly 100,000 light years across the implication was unmistakable. Andromeda could not possibly be part of our galaxy. If you imagine zooming out, then Hubble’s measurements clearly place the Andromeda nebula far outside the Milky Way galaxy. The result was so extraordinary that Hubble chose to be cautious. Rather than announce his result immediately, he waited and tried to gather more evidence. Remarkably, after taking several more photos of Andromeda, he found a second seafood that told the exact same story. The conclusion was undeniable. Andromeda was not in the Milky Way. So, finally, in 1924, Hubble revealed his findings in a letter to Chappley, the very astronomer who believed that the spiral nebula lay within our own galaxy. When Shappley read Hubble’s letter, he reportedly remarked, “Here is the letter that has destroyed my universe.” And in that one moment, humanity’s picture of the cosmos changed forever. The spiral nebula were not nearby wisps of gas. At least some of them were entire galaxies lying at immense distances far beyond our own. The universe suddenly became vastly larger and vastly richer than many had ever imagined. The story was picked up by the New York Times on November 23rd, 1924, and a formal report was read aloud by Henry Norris Russell at a joint conference of the American Association for the Advancement of Science and the American Astronomical Society on the 1st of January 1925. Russell pointed out that Hubble’s work had expanded 100fold the known volume of the material universe and had apparently settled the long muted question of the nature of the spiral nebula. But Hubble’s discovery did more than just reveal that galaxies lay far beyond our own. It opened up a deeper question. What are these galaxies doing? And the key to answering that question lay not in their positions but in their light and in what happens when that light is spread out. Since the work of Isaac Newton in the 17th century, it had been known that if you take a triangular glass prism and pass white light through it, the light disperses forming a beautiful continuous spectrum of colors. Later, as the wave theory of light was developed by figures such as Thomas Young and Augustine Jean Frenel, the colors of the continuous spectrum came to be understood as corresponding to different wavelengths. Red at the long wavelength end of the visible spectrum and blue at the short wavelength end. White light such as that from the sun was therefore understood to contain a whole range of wavelengths, each refracted by a slightly different amount as it passed through the prism, producing the familiar rainbow continuous spectrum. But as instruments improved and sunlight could be examined with greater precision, something strange appeared. The spectrum that at first sight appeared continuous was not perfectly continuous at all. It was crossed by a series of dark lines at specific wavelengths. These dark features were first noticed by William Hyde Wallist in 1802 and then studied in far greater detail by Joseph von Frownhofer from 1814 onwards. These lines would eventually become one of the most important clues in all of astronomy. At around the same time, scientists were also studying what seemed to be a completely separate phenomenon. If you place a substance into a hot flame, the color of the flame changes. Sodium gives a bright yellow flame. Lithium a beautiful crimson red. And if you place copper in the flame, you get a characteristic ghouish green glow. And if you pass that light through a prism, you don’t see a continuous spectrum. Instead, you see bright lines at particular wavelengths and nowhere else. These patterns are known as emission spectra. In 1859 and 1860, Robert Bunson and Gustaf Kirkoff showed that each element has its own distinctive pattern of lines, a spectral fingerprint that can be used to identify it. Then came the crucial insight. Kirkoff realized that these bright emission lines also explain the dark lines in the sun spectrum. You see, if white light from a hot dense source passes through a cooler, lower density gas such as hydrogen and is then spread into a spectrum, the result is a continuous spectrum crossed by characteristic dark lines. Now, the remarkable thing is that the location of the dark lines are at exactly the same wavelengths as the bright emission lines that the gas would produce on its own. In other words, a gas absorbs the same wavelengths that it can emit. What had seemed like two different phenomena, bright lines from glowing gases and dark lines in sunlight, turned out to be two sides of the same physics. And this then transformed the dark lines in sunlight into a powerful new tool. They were no longer just odd features in the spectrum. They were telling us which elements were present in the sun’s atmosphere and spectroscopy soon delivered an even bigger surprise. During the solar eclipse of the 18th of August 1868, Jules Yansen observed a bright yellow spectral line in the sun’s chromosphere near the sodium lines. Norman Loia independently observed the same line on the 20th of October and with Edward Franklin proposed that it came from a new element which they named helium after Helios the sun god. The element was eventually identified here on Earth by William Ramsay in 1895 with a spectrum that perfectly matched what had been observed in the light from our sun. Light was no longer just a way of seeing. It allowed scientists to determine the very composition of distant objects. Today we understand the reason why each element has its own spectral fingerprint and it’s to do with the notion of quantization. In 1900, Max Plank introduced the idea of energy quanta to explain the ultraviolet catastrophe. And in 1905, Albert Einstein argued that light itself comes in discrete packets of energy with the energy of a photon equal to plank’s constant multiplied by the frequency of the light. Then in 1913, Neil’s bore produced the first successful model that explained the emission spectrum of hydrogen. He proposed that electrons could occupy only certain allowed energy levels and that light is emitted when an electron drops from a higher level to a lower one. The energy of that light is set by the gap between the energy levels and we can then equate this to the energy HF following Einstein’s relation. And then finally we can write this in terms of wavelength rather than frequency. If we then take this expression and rearrange for wavelength, we see that the wavelength and therefore the color of the emitted light depends on the energy gap between the two levels that the electron transition between. The bigger the gap, the smaller the wavelength and the bluer the light. Whereas a smaller energy gap corresponds to a larger wavelength and redder light. And so B could now explain the hydrogen emission spectrum as being due to electron transitions from the third, fourth, fifth, and sixth energy levels down to the second energy level. And he was able to derive a relationship which accurately predicted those energy levels. And his equation could then easily be tested by observing the locations and wavelengths of the emission lines. And because different atoms have different allowed energy levels, they produce different spectral lines. The full explanation for the spectra of all elements came later with quantum mechanics. But B’s model was the crucial breakthrough. And once these spectral lines were understood, physicists realized that they could use them to infer the composition of distant objects far beyond our own sun, namely other stars and even distant galaxies. By observing the faint light from these objects and passing it through a prism or defraction grating, the absorption lines could be used to deduce which elements were present. The seemingly impossible had been achieved. We didn’t need to travel millions of light years to find out what distant stars were made of. We simply needed to look at their light. But almost immediately, astronomers noticed something else very strange. Although the patterns of lines from distant stars look the same, the entire pattern was often shifted, sometimes towards longer wavelengths and sometimes towards shorter ones. What was required was an understanding of what this shift meant. Physicists began to quantify these shifts by defining what’s known as the red shift denoted by the letter zed which is simply equal to the change in wavelength divided by the unshifted wavelength lambda n where the change in wavelength is given by the observed shifted wavelength minus the unshifted laboratory wavelength. And we can see from this equation that if zed is greater than zero then the wavelength has increased and the light has been shifted towards the red end of the spectrum. And if zed is less than zero the wavelength has decreased and the light has shifted towards the blue end of the spectrum. And so we see that the larger the shift factor zed the greater the displacement of the pattern from its original laboratory position. But what does that actually mean physically? Well, for relatively nearby objects, the simplest explanation is provided by the Doppler effect, first described for sound by Christian Doppler in 1842. You’ve almost certainly experienced this. When an ambulance or police car races past you, the pitch of the siren suddenly drops as it goes by. Higher as it approaches, lower as it moves further away. or when a fast car whizzes past, the sound is compressed on the way in and stretched on the way out. What’s happening is that the motion of the source changes the spacing between successive wave crests. And the same is true for light waves. If a source that is emitting light waves moves away from an observer, the observer sees the distance between the crests increase. Whereas if that same source moves towards the observer, the waves bunch up and the wavelength decreases. And we can quantify this effect using simple mathematics. Imagine that a moving source emits a wave. And then let’s pause just before the next wave is emitted. If the time between emissions is t and the source is moving at speed v, then we can label the distance moved by the source as v * t. We can also label the distance the wavefront traveled in this time which is equal to ct where c is the speed of light. It then follows that the observed wavelength will be equal to lambda n plus vt. So we see that the observed wavelength is stretched. And then if we rearrange the first expression for t and then sub this into the observed wavelength equation, we find the following expression. And we can then pull out a factor of lambda n and we get the following equation. If we then recall the definition of the red shift from earlier and combine these two expressions then after the dust is settled we end up with the fact that zed is equal to v over c. And then if we rearrange this expression we can write that v is equal to c * zed. And this is the key working equation. It tells us that by simply measuring how much the spectral lines are shifted, we can infer a velocity along the line of sight. And this is exactly what astronomers began to do. Beginning in 1912, the astronomer Vesto Melvin Slifer began measuring the spectra of spiral nebula. And his first target was the faint light coming from the Andromeda Nebula. In 1913, he reported something remarkable. The spectral lines of Andromeda were not where they should have been. They were shifted, indicating a velocity of around 300 km/s. But in this case, the shift was towards shorter wavelengths, a blue shift. And that meant Andromeda was not moving away from us, but towards us at a speed far greater than any of the known stars at the time. Sliper’s next target was what we now call the Sombrero galaxy. But in this case, he found the opposite. Its light was redshifted, indicating an even more extreme velocity of around a thousand km/s. This time moving away from us. But that was just the beginning. Over the next few years, Slifer extended these measurements to more and more spiral nebula. And by 1917, he had measured the spectral shifts of 25 of them. And a clear pattern had emerged. In 21 out of 25, the spectral lines were shifted towards the red end of the spectrum. Then using the Doppler velocity equation, Sliper converted these shifts into velocities and found that many of these objects were receding at hundreds, even thousands of kilometers/s. Almost every spiral nebula he looked at appeared to be racing away from us. But this seemed to make no sense. After all, if these objects were unimaginably vast collections of stars, then surely gravity should be pulling everything together, not somehow driving everything apart. What was needed was more data and someone with the creativity to ask the right question. And that person was Edwin Hubble. Hubble became intrigued by these receding nebula, but he also realized that velocities alone were not enough. If he could determine their distances, then perhaps some deeper pattern would reveal itself. And he already knew how to do that. He just needed to find seated variable stars within the same systems whose spectra had been measured. Then he could use Henrietta Levit’s period luminosity relation to work out how far away they were. And so using the 100in Hooker telescope at Mount Wilson, Hubble turned his attention to the great mystery of the receding nebula. By 1929, Hubble had compiled a list of galaxies for which he had estimates of the distance and the recessional velocities. And as Sly had already found, almost all of them were redshifted. But the real insight came when Hubble plotted the data with distance on the x-axis and recessional velocity on the y-axis. As the points were placed on the graph, a clear trend emerged. They slanted upwards. So Hubble drew a straight line through them. The conclusion was breathtaking. If the measurements were to be believed, then the motions of galaxies appeared to follow a pattern. The recession velocity of a galaxy was directly proportional to its distance from us. If a galaxy was twice as far away, it was moving twice as fast, three times as far, three times as fast. The farther away a galaxy was, the faster it receded. Hubble expressed this in the simple relation V= H N D where V is the recession velocity, D is the distance and H n is what we now call the Hubble constant which represents the gradient of the line on the graph. From his initial data, Hubble inferred a value of about 500 km/s per mega parseek. Meaning that for every additional million parex of distance, the recessional speed increased by about 500 km/s. And yet, despite the astonishing implications of the result, Hubble was cautious. He did not rush to grand conclusions. When Hubble published his initial findings in 1929 under the modest title, a relation between distance and radial velocity among extragalactic nebula, he ended by noting that it is thought premature to discuss in detail the obvious consequences of the present results. Over the next two years, Hubble worked alongside his assistant Milton Humeson to gather even more data, pushing out to greater distances and expanding the sample. Hume’s path into astronomy was extraordinary. He had left school at the age of 14 and began working at Mount Wilson, first as a mule driver, hauling equipment and provisions up the mountain, and later as a janitor. But he became fascinated by the work of the astronomers, learning by watching and listening, and gradually worked his way into the observatory itself. Eventually, he became one of the most skilled observational astronomers of his age. Hubble and Hume made a formidable galaxy hunting team. Hubble focused on estimating the distances to galaxies while Hume became a master of measuring their spectra and red shifts. By 1931, Hubble and Hume had extended the list of galaxies for which they had both distance and velocity data. Then in 1931, they published a much more substantial joint paper, the velocity distance relation among extragalactic nebula. And this time the result was impossible to ignore. Whereas the 1929 plot had merely hinted at a linear relation, the 1931 data made it far harder to doubt. The trend now extended to much greater distances, and the linear relation between distance and recessional velocity stood out even more clearly. The Hubble law was here to stay. Their updated data suggested a value of about 558 km/s per mega parc. The result was extraordinary. Galaxies in every direction appear to be moving away from us and the farther away they were, the faster they were receding. The conclusion was staring Hubble in the face. The universe was expanding. Now, when you hear that all galaxies are moving away from us, you might naturally think that this means the Earth or perhaps our galaxy sits at the center of the universe. But this is a common misconception. To see why, imagine a simple model universe consisting of galaxies arranged in a uniform grid. At some time t1, they sit at fixed positions and at later times t2 and t3, the distances between all galaxies have increased. Now imagine you live in one of these galaxies. From your point of view, every other galaxy is moving away. And crucially, galaxies that are twice as far away have twice as much space between you and them to expand. So in the same amount of time they move twice as far. From your perspective, the universe obeys Hubble’s law. The farther away a galaxy is, the faster it appears to recede. But now choose a different galaxy and repeat the argument. Nothing changes. From there too, every other galaxy appears to be moving away with the more distant ones receding faster still. So either every place is the center of the universe or no place is. And the only consistent interpretation is that there is no center at all. The expansion is not galaxies moving through space away from a special point. It is space itself expanding everywhere at once. This idea lies at the heart of modern cosmology. On large scales, the universe is homogeneous, the same everywhere, and isotropic, the same in every direction. And in such a universe, Hubble’s law is exactly what you would expect. But now comes the even deeper implication. If the universe is expanding today, then in the past it must have been smaller. If we mentally run the cosmic film backwards, distances must shrink. Galaxies get closer together. And in this simple picture, all separations tend towards zero. And we can even estimate when this would happen. If we take Hubble’s law v = hn * d and rearrange it, we get d over v is equal to 1 / hn. Now d over v has units of time. It’s simply the time you would infer if something moving at speed v had traveled a distance d at the same speed. But here’s the crucial point. Hubble’s law tells us that the velocity is proportional to the distance. So if a galaxy is twice as far away, it is moving away twice as fast. And that means the ratio d over v is the same for every galaxy. Every galaxy, no matter how far away, gives you the same value. And that means every galaxy is telling you the same story. If you run the expansion backwards at this constant rate, they would all have been on top of each other at the same moment in the past. That common time is written as 1 / h n and is known as the hub time. It sets the natural time scale of the expansion and in this simplified picture gives an estimate for how long ago all distances in the universe would have shrunk to zero. So let’s now sub in the value for hno that Hubble and humans inferred in 1931 which was about 558 km/s per mega parc. This gives a Hubble time of roughly 1.8 billion years. And this provides an estimate for when all the galaxies that are currently rushing away from us would have all been at the same point. Now, in the 1930s, this result was both astonishing and deeply puzzling. Astonishing because it suggested the universe was not eternal, but had a finite past, a time when all distances were compressed to zero. but puzzling because the time scale was alarmingly short. You see, by the late 1920s, radioactive dating had already placed the age of the Earth in the billions of years. Estimates by Arthur Holmes, for example, suggested an age between about 1.6 and 3 billion years. So, Hubble’s result implied a universe that was uncomfortably young. In some cases, even younger than the Earth itself. Something was wrong. The resolution came over the following decades. In 1952, Walter Bardy showed that distances to galaxies had been systematically underestimated. The issue was that astronomers had been treating all seafood variable stars as the same when in fact there were two distinct types with different intrinsic brightnesses. That meant galaxies were actually farther away than Hubble had realized. And if the distances are larger but the velocities are the same, the expansion rate must be smaller and the universe older. Today the Hubble constant is known to lie around 70 km/s per mega par implying a universe about 14 billion years old, comfortably older than the Earth, which is now known to be about 4.5 billion years old. And so from a deceptively simple linear relationship between distance and velocity, we are led to an extraordinary conclusion. The universe is expanding and it was smaller in the past. But this is only the beginning. Because once you accept that the universe was smaller in the past, a deeper question immediately forces itself upon you. What was the earlier universe actually like? denser certainly, but also hotter, much hotter. And that’s not just a vague picture. It follows directly from the physics of light in an expanding universe. First, it’s important to appreciate that as the universe expands, the wavelength of freely traveling light is stretched to longer and longer wavelengths. This is known as cosmological red shift where the wavelength increases because the intervening space expands while the light is traveling. To make that precise, we introduce a simple quantity a. This is called the scale factor. You can think of it as tracking the size of the universe or more concretely the typical distance between galaxies. As the universe expands, these distances grow. So, a increases and crucially, the wavelength of light stretches along with it. And so, if we run the expansion backwards in time, it then follows that when the universe was smaller, when a was smaller, all wavelengths must have been shorter. But now if you recall the energy of a photon is given by E= HC over lambda. So shorter wavelength means higher energy. And in a thermal radiation field the characteristic photon energies are set by the temperature through the scale KT where K is Boltzman’s constant. So it follows that as wavelengths decrease the photon energy increases and this corresponds to an increase in temperature. And so we can say that T is proportional to 1 / lambda. And because lambda is proportional to a, it follows that the temperature is inversely proportional to the scale factor a. In other words, when the universe was smaller, it was much hotter. And we can visualize this. If we plot this result, we see that a universe that was 10 times smaller was 10 times hotter. A universe that was a thousand times smaller was a thousand times hotter. So when we follow the expansion backwards, the universe does not merely become denser. It becomes hotter and hotter until we are no longer talking about galaxies at all, but about a young universe filled with intense radiation and matter in a radically different state. You see, at ordinary temperatures, matter exists mostly as neutral atoms. Electrons are bound to nuclei. But at sufficiently high temperatures, atoms cannot survive. Collisions are too violent and the surrounding radiation too energetic for electrons to remain bound. Matter becomes ionized. So the early universe would not have looked anything like the transparent cosmos we see today. It would have been a hot plasma, a sthing mixture of free electrons, atomic nuclei and radiation. And in such a plasma, light does not stream freely through space. Free electrons scatter photons very efficiently. So photons would have been continually interacting with matter, exchanging energy and momentum. The universe would therefore have been opaque. And because these interactions were happening so rapidly, matter and radiation would have been held very close to thermal equilibrium. And this point is crucial. A system in thermal equilibrium produces radiation with a very specific spectrum, a black body radiation spectrum, which is characterized by a very specific shaped curve. So once you accept that the early universe was hot, dense, ionized, and full of rapid interactions, a remarkable conclusion follows. The universe should once have been filled with thermal radiation, not random light, not some arbitrary glow, a genuine black body radiation field. Now, as we’ve seen, as space expands, the temperature drops and the radiation cools. Photon energies fall and eventually the universe becomes cool enough for electrons and nuclei to combine into neutral atoms. Once that happens, the number of free electrons drops dramatically and with it the rate at which photons are scattered. Over a relatively short interval of cosmic time, the universe changes from opaque to transparent and photons are then able to travel almost freely through space. This epoch is usually referred to as recombination, while the moment at which the photons effectively begin free streaming is called decoupling or last scattering. To estimate when this happens, we consider the ionization energy of hydrogen which is 13.6 electron volts. This is the energy required to remove a ground state electron from hydrogen. On the other hand, for black body radiation, the mean photon energy is of order 3 KT. So if we set this equal to the ionization energy and then rearrange for temperature, we can estimate the temperature at which photons cause ionization of hydrogen and we find a value of roughly 5 * 10 4 Kelvin. However, this is a crude estimate and it’s far too high. The reason it’s too high is because even when the average photon energy falls far below the ionization energy of hydrogen, there are still photons in the high energy tail of the distribution that have enough energy to ionize hydrogen. And because there are roughly a billion photons for every barriion, even a tiny fraction of such photons is enough to keep the universe ionized. And so recombination actually takes place at a much lower temperature. A slightly more sophisticated and careful estimate shows that the temperature at which recombination occurs is around 3,000 Kelvin. Now here is the crucial step. A black body at this temperature has a peak wavelength given by V’s law. And if we sub in a value of 3,00 Kelvin, we find that at this moment in the universe’s history, most photons have wavelengths of around 10us 6 m, which is in the near infrared. But since that radiation has been traveling through an expanding universe ever since, every wavelength must have been stretched along with space itself. though that originally infrared radiation should today be shifted to longer wavelengths specifically shifted towards microwave radiation. So the prediction is already quite strikingly concrete. If the hot big bang picture is right, the universe today should be filled with relic microwave radiation. And there is an even sharper prediction. Because this radiation was once in thermal equilibrium, it should not just be some arbitrary microwave glow. It should retain the exact form of a black body spectrum simply cooled by the expansion of the universe. And this is an astonishing prediction to make before the radiation had ever even been clearly observed. And yet in 1964, the first hint of it appeared completely by accident. At the Bell Telephone Laboratories in New Jersey stood a highly unusual radio antenna, a 20 ft horn reflector originally built for satellite communication, but with exceptionally low noise, making it ideal for precision measurements. Two young radio astronomers, Arno Penzians and Robert Wilson, were tasked with turning it into a scientific instrument. They weren’t looking for the afterglow of the Big Bang. Their goal was far more mundane to make extremely precise measurements of microwave signals from the sky. But this kind of measurement is actually extraordinarily difficult. Any signal that they detected would be mixed with noise from multiple sources. the electronics of the detector, the antenna itself, and even the Earth’s atmosphere. Normally, astronomers can subtract this noise by comparing a source with a nearby empty patch of sky. But Pensas and Wilson were measuring the sky itself. So, they set out to carefully calibrate their instruments. And after subtracting all known sources of noise, they expected the signal to drop to zero. But it didn’t. Instead, they found a persistent excess, a faint microwave signal that was always there. It did not depend on where they pointed the antenna. It did not vary with time of day, and it didn’t change with the seasons. The pair checked everything. They recalibrated the instrument. They dismantled the antenna. They even removed a pair of pigeons nesting inside along with what Pensas delicately described as a white dialectric material. But the signal remained. And when they quantified it, they found something extraordinary. The excess microwave radiation corresponded to a temperature of about 3° Kelvin. A faint uniform glow just a few degrees above absolute zero coming from every direction in the sky. Could this be the relic afterlow of the Big Bang? the very same radiation released when the universe cooled enough for atoms to form and light first began to travel freely. If so, then the implication was extraordinary. Now, we found earlier that the temperature t was proportional to 1 / a where a was the scale factor. And therefore, a drop in temperature from 3,000K down to 3K means that the universe has expanded by a factor of about 1,000 since that moment, stretching the radiation’s wavelength by the same amount. But to test the idea, it was not enough to merely detect microwave radiation. Its energy density spectrum had to be measured to see whether it matched the exact black body curve expected from a once hot universe. That confirmation came gradually at first and then decisively. Measurements at different wavelengths showed that the radiation behaved exactly as thermal radiation at about 3K should. But the decisive breakthrough came in 1989 with the launch of Kobe, the cosmic background explorer, which measured the microwave background with enough precision to reveal that its spectrum matched the predicted black body distribution. extraordinarily well. This was not just some microwave glow. It was the cooled remnant of a hot, dense early universe. Kobe also revealed something even more remarkable. The radiation was not perfectly uniform, but contained tiny fluctuations in temperature at the level of about one part in 100,000. These minute ripples were the seeds from which later cosmic structure such as galaxies and galaxy clusters would eventually grow. Later missions pushed this picture even further. W MAP launched in 2001 and the plank satellite launched in 2009 mapped these fluctuations with far greater precision confirming again the black body nature of the radiation and revealing the fine structure of the early universe in extraordinary detail. From those patterns, cosmologists have been able to infer the contents of the universe, ordinary matter, dark matter, dark energy, as well as its geometry and evolution. By studying faint microwaves arriving at Earth today, we’ve been able to reconstruct the state of the cosmos when it was only a few hundred,000 years old. And so, we’ve arrived at the extraordinary conclusion of our story. The universe is expanding today, indicating that if we run the clock backwards, it must have been smaller, denser, and hotter in the past. It passed through a phase when matter and radiation were in thermal equilibrium. And when the cosmos became transparent, that radiation was released and began its journey across space, and we can still detect it today. The cosmic microwave background is not a vague hint or a poetic metaphor. It is direct measurable evidence that the universe really did emerge from a hot dense early state. So when we look up at the night sky and ask where we came from, the answer is not hidden beyond the reach of science. It’s written in the light itself, in the distances to the stars, in the spectra of the galaxies, in the expansion of space, and in the faint microwave afterglow that still fills the universe. From a small planet orbiting an ordinary star, we have learned that the cosmos had a beginning, that it evolved, and that its history can still be read today. And that may be the most astonishing fact of all, that the universe has left behind the evidence of its own creation and that beings like us have learned how to see it. And as always, a massive thank you to all my patrons and a special shout out to the following who have been incredibly generous with their support. Thank you so much. I couldn’t do it without you.