Tag Archives: quantum mechanics

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 Wibbly Wobbly of Continuum

The series Continuum is a time travel science fiction TV show that follows the adventures of City Protective Services (CPS) law enforcement officer Kiera Cameron (Rachel Nichols) as she attempts to stop the self-proclaimed freedom fighters known as “Liber8”. It is easy to dismiss many science fiction shows dealing with time travel for the simple reason so many of them are done badly. Continuum is different in that there is an underlying mystery. A big part of that mystery is the motivation of an older Alec Sadler (William B. Davis) and the principles on which Continuum’s time travel is based.

The Continuum World of 2077

Continuum LogoIn 2077, the future of this world is both a distopian and Orwellian. World governments have somehow failed and, by implication, we assume so too has democracy. This has given way to a corporate controlled government that monitors and records every moment of a person’s life. People are born indebted and indentured to  the Global Corporate Congress until they pay off their life debts.

Among the largest corporations in the North American Union and possibly the world is SadTech, owned by Alec Sadler — a genius responsible for inventing and developing much of the technology we see in the world of Continuum. This hasn’t only made Sadler one of the richest men in the world but possibly one of the most powerful.

In an attempt to end the corporation’s rule over the people, Liber8 leader, Edouard Kagame (Tony Amendola) attempts to bring down the Corporate Congress by blowing up the building where a scheduled meeting is to take place thereby killing all 20 members. To Kagame’s surprise Sadler is the sole survivor. Sadler gives Kagame a time travel device to allow Liber8 to escape into the past; Sadler’s full intentions are unknown.

Upon arriving in 2012, Kiera meets and befriends a younger Alec Sadler (Erik Knudsen) who is coming to terms with the loss of his father and has decided to follow his father’s work and research. The beginnings of much of the “tech” that Keira uses was developed by Alec’s father. The young Alec posits two likely time traveling scenarios, both of which have their roots in physics. Evidence for both scenarios has been presented over the course of the first season and they both seem equally valid. The first is a “time loop” where conditions can not be altered. Everything that is happening has already happened and will give way to the future that Kiera knows. The second is an alternate time line and the very presence of both Kiera and Liber8 have altered Continuum’s 2077 future.

Time Loop

The first possibility is the “time loop” where the older Alec, knowing of his interactions in 2012 with Kiera, deliberately sends her back in time. This fulfills the events in the past and allow the future to progress in the way it has. All the events we see in 2012 have already happened and none of the Continuum characters can deviate from that. In a sense, everything is preordained. One of the most tantalizing clues, though unrelated, clues is the presence of Mr. Escher, the unknown head of the high security government agency, Section 6, who vouches for Kiera to the Vancouver Police Department.

Time Loop hypothesis for Continuum

“Ascending and Descending” is a lithograph print by the Dutch artist M. C. Escher which was first printed in March 1960. This perpetual loop illustrates the concept of the time loop used in Continuum.

This name may be a hidden clue that supports the the Time Loop theory. It may  Continuum’s writers way of telling viewers which of the two theories are correct. The name may have been taken from the Dutch artist, Maurits Cornelis Escher or M.C. Escher, who is best known for his mathematically inspired artwork. Escher was known for his depictions of impossible realities, especially those that related to infinite loops in some way. The “Ascending and Descending” litographic print is an artistic depiction of the “Penrose stairs“, an impossible object created by Lionel and Roger Penrose . The reality bending idea of the Penrose Stairs was used in the 2010 movie “Inception”.

Visual Time Loop in Continuum using a Mobius strip and ants

The ants crawl along a Möbius strip. This is another illustration of the principle of a time loop in the TV series Continuum.

In addition to impossible objects, Escher’s art also features insects. One of his paintings, Möbius Strip II (Red Ants), shows an ant walking along a surface with only one side — a Möbius strip. This strip looks very much like the infinity symbol. If an ant was to start at one point on the strip it will eventually return to that same point. We can create a Möbius strip of our own by twisting one end of a strip of paper by one half-turn and gluing the ends together. This object was dicovered independently by August Ferdinand Möbius and Johann Benedict Listing in 1858.

If this name is really a clue, then it add credibility to the time loop hypothesis. It could also mean that the reason that the older Sadler sends Keira back into time isn’t just to preserve the future but because he has to; he knows and recalls his interactions with this time traveling cop in his past.

This raises the question, can Kiera or Liber8 do anything to change the future? Does it mean that every little action, from the coffee they drink in the morning to the time they go to bed at night, has already been scripted? Can they do anything that might create a time paradox?

To resolve the problem of time paradoxes, which is permitted in some solutions of Einstein’s Theory of General Relativity, Russian physicist Igor Dmitriyevich Novikov came up with his self-consistency principle . In simplest terms, the Novikov self-consistency principle says that if an event exists that would give rise to a paradox, or to any “change” to the past whatsoever, then the probability of that event is zero. This means that it is impossible to create time paradoxes.

Some may find this idea unpalatable as it interferes with our ideas of free will and destiny. Does it mean that Kiera and Alec and all of Liber8 are doing nothing more than following a script from which they can never deviate? Well, not entirely. The Novikov self-consistency principle does not imply that time traveler have no free-will. It just says that the results of their actions can not produce inconsistent results. Kiera can choose what to have for lunch but not stop the bombing of the building even if she tried. If she succeeded, her actions would be inconsistent with how events unfold in the future.

Alternate Timelines & the Many Worlds of Continuum

Alec also considers the possibility that Kiera’s and Liber8’s presence may have altered the time line making the fate of 2077 is uncertain. But what does that mean for the inhabitants of 2077 if Liber8 or even Kiera make a change in the present? Do they “blink” out of existence just like old Biff Tannen in Back to the Future II? No, they don’t have to and quantum mechanics may provide an answer.

To resolve some of the strange results observed in quantum mechanics, physicist Hugh Everett came up with his Many-Worlds Interpretation in 1957 . In this version of quantum mechanics, at every single instant of the tiniest portion of a second the Universe is splitting into countless billions of parallel universes. Thus our Universe branches out in which every possibility exists. The arrival of Kiera and Liber8 in the past results in a a new branch and a new alternate reality. This idea was seen in the 2009 Star Trek reboot. This spells bad news for Kiera as she can only travel to the future of the new time-line she is already in. Getting home or to the timeline she came from is an impossibility.

So which is it?

It’s difficult to say which of the two hypotheses are true as the series has given evidence to support either hypothesis. In “A Test of Time”, Kagame decides to test these theories of time travel. If Liber8 were to kill Kiera’s grandmother, then the threat posed by this future cop would literally cease to exist. While Kiera manages to save her grand-mother, Matthew Kellog’s (a former Liber8 member) teenage grandmother is killed in a confrontation between Kiera and Liber8.

Matthew’s continued existence provides no clear answers as Alec explains at the end of the episode. While we are certain who Kiera’s grandmother was, we are not quite sure in Kellog’s case. For all we know, Kellog could have been mistaken about the young girl’s identity and she was never his grandmother. The young girl could also have been Kellog’s grandmother and though she died thus preventing Matthew’s future birth, Kellog’s journey through time might protect him from this causality paradox. It does mean that the future can be changed which gives Liber8 even more incentive to succeed.

The good and bad guys in Continuum

If the future is a bad place to live and Kiera is trying to preserve the future, does that mean she is the bad guy? Liber8’s methods and motivations, while they are extreme, are to free the world from a tyrannical and oppressive system from ever taking place. Both sides are fighting to save the future they believe in. Liber8 seeks to create a better world while Kiera is trying to preserve her family’s existence. Neither knows if that is even possible.

It all comes down to one man, the older Alec Sadler and his ultimate goal and motivations. Young Alec discovers at the end of the season finale that he is the reason that Kiera is now living in the past. Did he send Kiera and Liber8 to save the future or to preserve it? Whatever the answer, we are going to have to wait for the answer in future episodes.

Further Reading