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The Discovery of the Higgs Boson: Week 2 Review Light Bulbs and Railroad Schedules

The second week of the FutureLearn course “The Discovery of the Higgs Boson” looks at physics of the 20th century–special relativity and quantum mechanics. These two branches of physics represented a fundamental shift in the way we view the world.

It may come as a surprise to some that these deep philosophical shifts have very unexpected origins. Our view of a quantized world came from the need to create a more efficient light bulb while the connection between space and time came from our need to run a more efficient railroad network and international time conventions.

Need for a more efficient light-bulb

Philipp Lenard

Hungarian physicist Philipp Lenard, discoverer of the photoelectric effect in 1902.

In 1902, Hungarian physicist, Philipp Lenard, winner of the 1905 Nobel Prize in Physics for cathode rays, observed that the energy of individual emitted electrons increased with light frequency–the photoelectric effect. This appeared to be at odds with Maxwell’s theory of electromagnetism which predicted that an electron’s kinetic energy should be proportional to light intensity. In 1905, Albert Einstein published a paper that explained the experimental data from the photoelectric effect. Based on Max Plank’s theory of black body radiation Einstein postulated that light energy was being carried in discreet quantized packets.

In 1894, German theoretical physicist Max Planck was commissioned by the German Bureau of Standards with the task of creating more efficient light-bulbs. To do so, Planck needed to find one that would emit as much visible light as possible with very little to no infra-red and untra-violet light. Planck knew from experiments at when an object is heated, it emits radiation in the form of black-body radiation. Planck turned his attention to this problem.

Black Body Radiation

Black body curves for various temperatures and comparison with classical theory of Rayleigh-Jeans. As the temperature decreases, the peak of the black-body radiation curve moves to lower intensities and longer wavelengths.

“Blackbody radiation” or “cavity radiation” is the characteristic radiation that a body emits when heated. This is seen in the form of a curve which peaks at a characteristic temperature where most of the radiation is emitted. Experiments showed that as the temperature changes, so too does the emitted radiation. When the wave picture of light was applied to this problem, it failed to predict the observed intensity for any given temperature.

Planck made several attempts to understand this problem. His first proposed solution in 1899 based on the entropy of an ideal oscillator, in what he called the “principle of elementary disorder”, failed to predict experimental observations. Planck revised his approach in 1900 using Boltzmann statistics to gain a more fundamental understanding of black-body radiation. This approach worked but Planck held an aversion towards statistical mechanics. He was also deeply suspicious of the philosophical and physical implications of its interpretation. His recourse was, as he later put it, “an act of despair… I was ready to sacrifice any of my previous convictions about physics.”

The central assumption behind his third attempt was the hypothesis, now known as the Planck postulate, that electromagnetic energy could only be emitted in quantized form. Planck didn’t think much of this method, regarding it as a mere trick. We know now that assumption is regarded as the birth of quantum mechanics. Try as he might, Planck struggled to grasp the meaning of energy quanta, going so far as to reject Einstein’s hypothesis and explanation of Lenard’s photoelectric effect. He was unwilling to completely discard Maxwell’s theory of electrodynamics.

Not everyone was convinced by Einstein’s hypothesis either, even after it was experimentally verified by Robert Millikan in 1914. Many physicists were reluctant to believe that electromagnetic radiation could be particulate in nature. Instead, it was believed that the observed energy quantization was the result of some constraint of matter and the way that it absorbs and emits radiation. It wasn’t until Compton’s experiments showed that light cannot be purely be explained as a wave that the idea of light quanta was accepted.

Train Schedules and Time Zones

The first passenger carriage in Europe, 1830, George Stephenson´s steam locomotive, Liverpool and Manchester Railway

The first passenger carriage in Europe, 1830, George Stephenson´s steam locomotive, Liverpool and Manchester Railway

The mid to late-19th century saw considerable and rapid improvements in transportation, communication and technology. One of these inventions, the steam locomotive, not only changed the way goods and people traveled but also the way we view time. Products could be moved more cheaply and much faster.

Before the invention of clocks, people marked the time of the day with apparent solar time or by noting the sun’s position in the sky. Local time was different for each town and settlement. With the invention of well regulated mechanical clocks, cities used local mean solar time. As clocks differed between towns by an amount corresponding to the difference in geographic longitude–a variation of four minutes for every degree of longitude–communication between towns and rail transport became awkward. The time difference between Bristol and London, for example, a difference of 2°35′ longitude, is about 10 minutes while the difference between New York and Boston is about two degrees or 8 minutes.

25-0621E.6LTime keeping on American railroads was even more confusing. Each railroad had their own standard of time time, usually based on the local time of its headquarters or main terminus. Each railroad schedule was published using the company’s own time and stations had a clock for each railroad, each showing a different time.

Non-uniform time zones weren’t just confusing. It was dangerous. The incidents of accidents and near-misses became more frequent as more people started using trains for travel. What was needed was a means to know exactly where trains were at all times. The use of time zones solves this problem and with it came the need to synchronize clocks at a distance.

It’s not surprising that many of Einstein’s though experiments concerns trains. As a young patent clerk, many of the inventions he reviewed focused on using light signals to synchronize clocks. Einstein took it a step further and realized that clocks moving with respect to each other would not tick at the same rate.

Physics students are familiar with Einstien’s Gedankenexperiments and that the power of abstract thought can allow one to fully visualize the consequences of an experiment without having to actually perform said experiment. Far from being esoteric examples, Einstein’s thought experiments are firmly grounded in reality and shares its origins in something as simple as a train schedule.

The Higgs Boson Course

In one of the course’s lectures, Peter Higgs says that when he teaches undergraduates special relativity, he ignores the way that Einstein did it and asks, “how do you realize the principle of relativity, which was what was formulated by Henri Poincare?” To do this, you have to abandon Newton’s assumption of absolute time. Peter Higgs is correct, the development of special relativity need not have had anything to do with the Michelson-Morley experiment. In Einstein’s case, it came about from the practical need to synchronize clocks.

The second week of the course builds on the previous week. Though the concepts are quite literally mind-blowing, the ideas and mathematics were conveyed in a way that makes it easy for students to grasp. The third week looks even more exciting as we combine both special relativity and quantum mechanics to make much deeper predictions about our world.

The Discovery of the Higgs Boson: Week 1 Review Conservation Laws and Physical Revolutions

Peter Higgs 2The Higgs boson has captured the world’s attention from the moment it was announced the Large Hardron Collider was being built to find it. The elementary particle’s discovery was announced by CERN on 4 July 2012 and is nothing short of monumental as it appears to confirm the existence of the Higgs field. This pervasive field is pivotal to understanding why some fundamental particles have mass. As interesting and exciting as this discovery may be, its consequences and implications remain out of reach for the general public. Future Learn, a privately company owned by Open University, along with the University of Edinburgh have started a seven week Massive Open Online Course (MOOC) “The Discovery of the Higgs Boson” to introduce the theoretical tools needed to appreciate this discovery.

The course starts with classical mechanics. While it may seem like a strange place to start, especially given the course’s goals, it is a good one. Rather than jumping straight into Quantum Mechanics, classical mechanics makes the mathematics is accessible to students, especially those who have completed A-Level Mathematics or done Calculus. The course doesn’t assume many of the fundamental conservation laws in physics are true but rather goes through the mathematically rigorous process of proving these concepts to students. This also allows students to see how the behavior of physical systems can be deduced. Though some of the physical principles will need to be revised as the course progresses, the mathematical tools students would have acquired remain the same. Student can thus build on what they have learned before.

An Evolutionary Revolution

One of the more interesting questions asked was, “Why is the Higgs boson discovery important?” Dr. Victoria Martin, a reader in particle physics at the University of Edinburgh, answers that in one of the course’s modules. In her video, she says the Sun is a massive burning ball of hydrogen and helium and it is a mystery why it all hasn’t burned up by now. She says the answer comes from Peter Higgs’ theory which predicts the Higgs boson. It predicts why the nuclear process in the Sun is slow enough that the Sun is still around after 4.6 billion years and provides just the right amount of light and heat to sustain life on Earth.

Science didn’t always believe that the Sun or the Earth, for that matter, was old. In the mid-nineteenth century, both Charles Darwin and Alfred Russel Wallace were making the case for biological evolution by natural selection. This theory described a process of slow, gradual changes over time and indicated the Earth had to be very old, at least hundreds of millions of years. This was supported by geologist observations of erosion rates.

Lord Kelvin

Photograph of William Thomson, Lord Kelvin.

This posed a problem for the most prominent theoretical physicist of the time, William Thomson, 1st Baron Kelvin, who saw evidence that disagreed with Darwin. This guiding light of the Industrial Revolution, whose work in thermodynamics contributed to the steam engine, was a devout Christian who believed in a much younger Earth and with good reason. In 1862, using the thermodynamics of heat conduction, Thomson initial calculations showed that it would take between 20-400 million years for a molten Earth to completely solidify and cool.

This large uncertainty of the Earth’s age were due to uncertainties about the melting temperature of rock. This did not deter Thomson who then set out to calculate the Sun’s age in 1868 using what he knew of the Sun’s energy output. Kelvin rightly assumed the Sun formed from a giant gas cloud and gravity eventually caused the cloud to collapse into a ball. As with any falling mass, the cloud molecules’ potential energy would be converted into kinetic energy. This raise in kinetic energy would turn into heat, raising temperatures to result in star formation in a process known today as the Kelvin-Helmholtz Contraction.

While we know today this is not the way stars generate all their energy, we know this is how the fusion process is started. Based on his assumption that the Sun built up all its heat as it was formed and radiating it away like a hot coal, Kelvin estimated the lifespan of the Sun to be about 30 million years.

The numbers posed a nagging contradiction–the Earth was older than the Sun. Thomson realized he needed to refine his calculations of the Earth’s age. In 1897 Thomson settled on an estimate that the Earth was somewhere between 20-40 million years old. This fit in nicely with his estimation of the Sun’s age.

Charles Darwin

Darwin, aged 45 in 1854, by then working towards publication of On the Origin of Species.

The age of the Earth was an important part to Darwin’s theory of evolution. As a geologist, he had conducted his own studies and concluded that the time needed to wash away the Weald, a valley in south-east England formed of the eroded remains of an anticline, would require 300 million years. Thomson believed that geologists were wrong to assume a steady rate of erosion. Floods and other natural disasters could accelerate this process. Thompson though the geologist’s thinking could use a dose of mathematical rigor. Though Darwin’s observations supported an old Earth, he was so bowled away by Thomson’s analysis that he removed any reference to time scales in later editions of his Origin of the Species.

A Quantum World

Thomson’s opponents argued that his time scales were too short for life to develop. He ignored them. With hindsight, it is easy to see that the brilliant Thomson was wrong and Darwin was right. But should we judge Thomson harshly for not listening to his opponents?

We must be careful when we judge the past and not look through the lens of our own experiences or biases. Thomson lived to 1907, to a time when radioactivity had firmly been established. The observation then by geologists that the Earth could be heated from within by radioactive decay meant that the Earth could be a lot older than Thomson thought. In fact, it was widely believed that the discovery of radioactivity invalidated Thomson’s estimates of the age of the Earth.

Higgs Boson

This image shows the Sun as viewed by the Soft X-Ray Telescope (SXT) onboard the orbiting Yohkoh satellite

Despite the discovery of radioactivity, Thomson refused to acknowledge this. He had strong reason to believe that the Sun was younger than 20 million years. Even with an old Earth, without sunlight, there could be no explanation for the sediment record on the Earth’s surface. It wasn’t until the discovery of fusion in the 1930s that this paradox was resolved.

While history has proven Thomson wrong in this debate, we must remember one thing. Given what we knew at the time, Thomson’s calculations and conclusions were correct–his science was sound. We can not fault Thomson for this.

The Higgs Boson Course

Higgs Boson Collision

Data from the CMS experiment, one of the main Higgs-searching experiments at the Large Hadron Collider. Image: CERN

The Higgs boson is the latest addition to our understanding of what happens in our Sun. Just like Thomson demanded a certain mathematical rigor, so too does “The Discovery of the Higgs Boson” course. The course recommends that the week’s module should take about two hours. Though it has been some time since I last sat in a Physics class and while the concepts and proofs were not entirely new, it does take some time to view the lectures and complete the exercises. I think students will realistically have to dedicate more than two hours to complete the week’s exercises.

Overall, it is a strong course that demands a lot of its students. I look forward to the rest of the course.