Why does the Universe look the same in all directions?

We’ve all heard of the Big Bang – the beginning of our universe; starting as a tiny, extremely dense and hot point that rapidly expanded. While this theory explains everything around us in space with incredible accuracy, there are some aspects of the Big Bang and its implications that still have scientists confused. The horizon problem is one such problem, and it will be the topic of this piece.

 

We live in a universe that looks the same in all directions. In particular, the cosmic microwave background (CMB) is uniform in all directions. The CMB is the cooled remainder of the first light that ever travelled through the universe – it is considered a “shockwave” of the Big Bang.

 

The Horizon Problem boils down to this – the only way for two regions to have the same conditions, is that they are close enough together for information to be passed between them – so they can “balance out” to the same state. Our universe has a speed limit – the speed of light – and nothing can travel faster than this. In one second, light travels 300,000 kilometres. Here is the problem, if two regions are far enough apart that light has not had enough time to travel between them, then the regions cannot exchange information and hence are isolated from each other. There is a limit to how far their light can have travelled – their horizon. So how can two separated regions of space be in the same state, when they have not interacted? Imagine you are at a party, and only get to interact with people in your vicinity – you do not mingle with the people at the opposite side of the room; thus you haven’t exchanged information – it’s the same idea.

 

 

So how have scientists proposed we solve the horizon problem? A leading theory that speaks to scientists is inflation. Inflation means that the universe began to rapidly expand mere fractions of a second after the Big Bang, as quick as a flash before the more gradual expansion associated solely with the Big Bang. This suggests that the separated regions in question interacted before inflation began. Prior to inflation, the universe was a singularity or point, and the regions were much closer together than if there had only been expansion associated with the Big Bang. The theory of inflation to solve the horizon problem was first suggested in the 1980’s and since then, scientists have produced more than 200 inflationary models. Space missions to test the validity of some of these models have so far shown that the universe obeys the simplest inflationary models.

 

References:

The Horizon Problem (2017), Bahia Si Lakhal and Ameur Guezmir, DOI:10.1088/1742-6596/1269/1/012017

 

From Eternity to Here, chapter 14, “Inflation and the Multiverse:” Sean Carroll

 

Image credit: Wikipedia – https://en.wikipedia.org/wiki/Horizon_problem

 

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Physics or Philosophy: Can science explain the existence of our universe?

HISTORY OF PHYSICS:

Today, we’re taking a trip down memory lane to explore the historical roots of physics as a discipline. It may surprise you to learn that physics was once considered a branch of philosophy!

In ancient Greece, philosophers like Aristotle and Plato pondered the nature of matter and motion, positing that everything in the world was made up of four basic elements: earth, air, fire, and water. Fast forward a few centuries, and the Renaissance brought experimentation and observation to philosophical inquiries. This led to scientists like Galileo and Descartes using rigorous methods to test their philosophical ideas, eventually laying the foundation for modern physics.

But wait, there’s more! Physics continued to be closely linked to philosophy for centuries to come, with philosophers exploring questions related to space, time, and the nature of reality. It wasn’t until the 20th century that physics emerged as a separate discipline, with the development of quantum mechanics and relativity transforming our understanding of the universe.

So what does this all mean in today’s day and age? While physics has come a long way from its philosophical roots, it still remains an interdisciplinary field that draws on insights from philosophy, mathematics, and other areas of science. And yet, in our current era of fake news and anti-science sentiment, it’s more important than ever to remember the rigorous methods and critical thinking that led to the development of modern physics.

LIMITATION OF SCIENCE

Science has undoubtedly transformed our understanding of the universe and helped us make sense of the world around us. But in our quest for knowledge, we must also acknowledge the limits of science and our own understanding of the universe. One area where this becomes especially apparent is in the relationship between science and religion, particularly when it comes to the question of deities.

Many people today use science to justify the belief that there are no deities. They point to the scientific method, empirical evidence, and the lack of a need for a supernatural explanation for natural phenomena. And yet, at the heart of physics lie fundamental constants – values that are thought to be unchanging and universal. These constants, such as the speed of light and the gravitational constant, govern the behavior of the universe and the laws of physics as we know them.

The existence of these fundamental constants raises important questions about the nature of the universe and our own limitations in understanding it. We have no explanation for why these constants take the values that they do, or why they are even necessary in the first place. Some have argued that the existence of these constants points towards a divine creator – an explanation that science cannot disprove or verify.

But this does not mean that science and religion are irreconcilable. In fact, many scientists and religious individuals alike acknowledge the limits of science and the importance of faith and spirituality in their own lives. And to paraphrase the physicist and theologian John Polkinghorne, science cannot tell us why the universe exists, but it can tell us how it works. In other words, science and religion can both offer valuable insights into the universe and our place in it.

WHAT HAPPENS NEXT?

But as our understanding of the universe continues to evolve, how will the relationship between physics and philosophy change going forward?

One area where physics and philosophy have traditionally overlapped is in the exploration of fundamental questions about the universe – questions that may be beyond the scope of empirical observation and experimentation. For example, questions about the nature of time, space, and causation have long fascinated both physicists and philosophers, and may require a combination of both disciplines to fully understand.

Another area where physics and philosophy may continue to intersect is in the realm of ethics and morality. As we develop new technologies and push the boundaries of what is possible, we must also grapple with the ethical implications of our actions. Philosophers have long pondered questions of morality and the nature of the good life, and their insights may be valuable in guiding us as we navigate the ethical dilemmas posed by advances in physics and technology.

But as physics becomes increasingly specialized and technical, there may be a growing divide between the two disciplines. Physicists may be more focused on empirical observation and mathematical models, while philosophers may be more focused on conceptual analysis and ethical considerations. Bridging this divide may require a renewed emphasis on interdisciplinary collaboration and a willingness to learn from each other’s perspectives.

SHOULD WE FAVOUR SEPARATION?

There is a growing debate about whether physics and philosophy should remain closely linked or whether they should be allowed to diverge.

On the one hand, some argue that the separation of physics and philosophy would be a bad thing. They argue that philosophy provides a critical lens through which we can view scientific discoveries and their implications. For example, questions about the ethical implications of new technologies or the nature of scientific inquiry itself may require philosophical inquiry in addition to empirical observation.

Moreover, philosophy provides a broader perspective on the human condition and our place in the universe. Philosophers have long pondered questions of meaning, purpose, and morality, and their insights can help guide us as we navigate the complex world of science and technology.

On the other hand, others argue that the separation of physics and philosophy may be a necessary step towards progress. As physics becomes increasingly developed, it may require a more focused approach that emphasizes empirical observation and mathematical models over conceptual analysis and ethical considerations. In this view, philosophy may be seen as a distraction or even an obstacle to scientific progress.

 

To a quote Albert Einstein:

“The most beautiful thing we can experience is the mysterious. It is the source of all true art and all science. He to whom this emotion is a stranger, who can no longer pause to wonder and stand rapt in awe, is as good as dead: his eyes are closed.“

So, as we continue to push the boundaries of human knowledge, it is important to remember that physics and philosophy are not mutually exclusive, but rather complementary fields of inquiry. By embracing interdisciplinary collaboration and open-minded inquiry, we can continue to make new discoveries about the universe and our place in it, while also grappling with the ethical and existential questions that have fascinated philosophers for centuries.

 

References:

Albert, D.Z. (2003) Time and chance. Cambridge (Mass.): Harvard University Press.

Kant, I. and D., M.J.M. (2020) The critique of pure reason. S.I.: Duke Classics.

Polkinghorne, J.C. (2016) Faith of a physicist – reflections of a bottom-up thinker. Princeton University Press.

Feature Image: https://www.thesistinechapel.org/the-creation-of-adam
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Chaos Theory – A Brief Summary

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What came first, energy or matter… or space?

The question of if matter or energy came first is an interesting philosophical question that has been pondered for centuries. It is known that matter and energy are inextricably bound, mass is a form of energy – the reason things have mass is because they have internal stored energy. I like to imagine mass as like a dial of how much energy is stored in an object. Einstein’s energy-mass equivalence E = mc2, tells you exactly how much energy is stored; however, it evokes that mass is energy, but energy is not mass… Matter is a kind of energy so it can’t be first, there can’t be a universe with matter and no energy. For this reason, it is pretty clear that energy must have come first.
When thinking about if (matter/energy) or space came first, things get a bit more complicated. The short answer is that we don’t know as there is currently no observational evidence which can really tell us. As far as we know, both have always existed in some form but when we go all the way back to the Big Bang, our models become unable to make predictions about this topic. According to the uncertainty principle the generation of matter is not allowed. It certainly doesn’t seem to allow violation of baryon and lepton quantum numbers which is required for matter generation. Anyway, since space is also very homogenous and isotropic, matter must have been evenly distributed before the expansion of space happened, so that the expansion can smooth everything out and enlarge the gravitational artifacts allowing for matter to collapse into our galaxies. This is actually our best-known model which can answer the question of why everywhere looks the same on the largest scales, known as the theory of cosmic inflation.
This leads us to our conclusion that (1) Matter must have existed before space began expanding significantly, because of how uniform it is today, and (2) Unless the law of energy conservation is violated somehow, the energy must also have existed at this time.

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Spaghettification.

Spaghettification may sound like a new diet trend on how to get thin as spaghetti. Yet if this were true, the method to achieve this is the most extreme yet. Spaghettification is a term in astrophysics coined by Stephen Hawking in his book, A Brief History of Time; it is described as the vertical stretching and horizontal compression of objects into elongated and thinned shapes in a very strong non-homogeneous gravitational field. Basically, spaghettification is a process which turns you (a human) into spaghetti when the difference in the strength of the gravitational field from your head to your toe is very strong. This causes your body’s length to become stretched and to maintain the volume of your body (and ensure there is no net change in volume), the width of your body is compressed. Therefore, your head is pulled up, your feet are pulled downwards, your right side is pulled to your left and your left side is pulled to your right. Almost like a nightmare rollercoaster that leaves you in the shape of a spaghetti and ultimately, dead due to the extreme pressure that this process causes.

A visual of an astronaut undergoing spaghettification;

For spaghettification to occur, the difference in gravitational field strength needs to be quite noticeable . Spaghettification is most commonly known to occur in black holes, specifically after the event horizon. The event horizon is a point where an object cannot escape a black hole and ultimately, it is sucked into the black hole’s singularity (a point of infinite density at centre of a black hole). After this point, the gravity caused by the singularity in a black hole causing the gravitational gradient (difference in strength of the gravitational field) becomes noticeably different from head to toe. Because this process is not constant across the entire body, the force of gravity is unequal and therefore stretches the body. If it was equal across the body, there would be no observable spaghettification.

Luckily for us, humans have been immune to spaghettification, but this happens all the time to other objects in space. Every time that an object with mass is sucked into a black hole, this process occurs. Any object from a small asteroid to a star undergoes spaghettification on passing the black holes event horizon. Our solar system is only 1000 light-years away from the nearest black hole. So thankfully, we have a while before we have to imagine our Earth turning from a meatball into spaghetti.

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It’s Time for Time Crystals

To a layperson, the words “Time Crystal” probably evokes images of scientific magic, like phasers, flying DeLoreans and flubber. Real-world time crystals are likely not as exciting as whatever sci-fi gobbledygook you might have imagined (Physicists are very good marketers). But their potential applications in quantum computing are genuinely something to pay attention to in the coming years.

Google’s sycamore microprocessor. In 2021, Google’s Quantum AI team, in collaboration with researchers from the Max Planck Institute for Physics of Complex Systems, Stanford and Oxford managed to create a 20-atom time crystal on the sycamore microprocessor chip. Credit: Erik Lucero

 

The earliest modern proposal of time crystals was made in 2012 by Nobel Laureate, Frank Wilczek in his paper titled ‘Quantum Time Crystals’. To understand Wilczek’s proposal, we should first consider a regular crystal. Crystals are ordered periodically in space. The pattern of a crystal repeats across space.

This is ‘discrete space translational symmetry’. In the crystal structure above, you have to walk some discrete distance to get from one black atom to the closest black atom, and the same distance to get from one white atom to the closest white atom. Crystals are said to spontaneously break ‘continuous space translational symmetry’ as the crystal is not spatially homogenous. Wilczek wondered if there was a system that could break ‘continuous time translational symmetry’ spontaneously. Rather than the discrete ordering of atoms, this system would be characterised by the discrete temporal ordering of events. He dubbed such a system a ‘Time Crystal’ 1. The idea is that time crystals repeat some state periodically after some period of time. What could this look like? Wilczek originally supposed a superconducting ring of atoms carrying a current. The ring is threaded by a small magnetic flux. This generates a constant current in the lowest energy or ‘ground’ state. The charged particles could then be ordered to travel in “lumps” that complete the loop in a constant period, indefinitely, giving us our conditions for a time crystal [1].

Wilczek’s time crystal exists in thermal equilibrium – The system does not require any energy exchange with the surroundings. If the indefinite motion of charge around the ring seems wrong to you, you’re not alone. What Wilczek proposed is ‘Perpetual Motion’ in the ground state. The idea of macroscopic perpetual motion has been discredited among scientists since the 1700s. Technically, Wilczek’s proposal doesn’t violate the current laws of thermodynamics, as no mechanical work can be extracted from the ground state system [2]. However, Wilczek’s superconductor model was shown to be impossible in a paper from Patrick Bruno in equilibrium in 2012.2 Kablamo! Your theory is dead, Wilczek. It was good while it lasted.

Woah, not so fast. What if we also let go of our equilibrium condition. What if we allowed an external energy source to drive the system. And what if our system was arranged so that none of this energy was absorbed or dissipated by the system, so it could behave as though it was in equilibrium. A paper from Yao et al suggested just this in 2016! Yao et al posited that an array of 1D ions could be created as shown.

Certain isotopes have a ‘spin-state’. The concept of spin is too complex to dissect in this blog. The spin axes align parallel and antiparallel with each other as these states are lower energy than random orientations due to their interacting magnetic fields. Suppose these alignments are along the z axis. Normally, as our system would tend towards equilibrium, the arrangement of these spins would randomise. This is ‘thermalisation’. But we want temporal order so we can’t permit this to happen. What if the atoms were radiated with pulses of electromagnetic radiation which caused each of the spins to rotate 180 degrees about the x-axis.

This sort of system is a ‘Discrete Time Crystal’ because the atoms return to their initial state after some multiple integer of the period of the driving force. It’s not spontaneous like Wilczek originally suggested, but it’s good enough. The period of the time crystal would be twice the period of the laser as it oscillates between the two states. Imperfections in the laser could destabilise the ions if the interaction strength between ions is not strong enough. Additionally, if the interaction is too strong, the system would thermalise. The existence of such a system outlined by Yao et al was confirmed by Monroe et al in 2016. They used an array of ten 171Yb+ ions which were oscillated using a Raman laser.

The paper from Yao et al also suggests that this periodic behaviour should continue for extended periods of time if the driving beam is stopped (provided that the frequency of the laser was sufficiently high). These so-called ‘Pre-Thermal Time Crystals’ were observed by Monroe et al in 2021.

In 2021, the researchers at Google’s Quantum AI team, in collaboration with researchers from Stanford, Oxford and the Max Planck Institute of Physics of Complex Systems managed to create a time crystal of 20 qubits on Google’s Sycamore processor [3-4]. Not to be outdone by Google, two physicists from the University of Melbourne, Philipp Frey and Stephan Rachel, managed to create a time crystal of 57 qubits using IBM’s Brooklyn and Manhattan processors [5-6].

 

Quantum Computing

One possible pathway for quantum computing is spintronics. Currently data in computers is binary. It consists of an array of 1s and 0s. These 1s and 0s are bits. In quantum computing, information is stored by ‘Qubits’, which can be 1, 0 or a ‘superposition’ of the two. The essence of spintronics is using the spin-states of particles as our qubits. One of the challenges of quantum computing is finding a sustainable way of storing these 1s and 0s as information across long periods of time in an energy-efficient manner. These systems are easily disturbed by heat and the preservation of the memory often entails cooling the qubits to temperatures on the scale of tens of millikelvins [7]. The stable oscillations of the discrete time crystals could open the door to long-term, energy-efficient, quantum-memory storage.

 

The future of quantum computers is, however, still uncertain. What does the future hold for time crystals? Time will tell.

 

1 Wilczek was not the first to use the term ‘Time Crystal’ to describe periodically repeating systems. Biologist Arthur Winfree gave the name to biological systems that repeat periodically in his book, The Geometry of Biological Time in 1980.

2 Additionally in 2015, a paper from Haruki Watanabe and Masaki Oshikawa purported to disprove time crystals in equilibrium. However, this proof contained a discrete error, as outlined in the appendix of a paper from Khemani et al [8]. However the authors of this paper agreed that the conclusion of the falsified proof is likely correct.

 

 

References

[1]: Zakrzewski, J., 2012. Crystals of Time. [online] Physics. Available at: <https://physics.aps.org/articles/v5/116> [Accessed 10 May 2022].

[2] Andersen, T., 2021. Here’s how time crystals really work. [online] Medium. Available at: <https://medium.com/the-infinite-universe/heres-how-time-crystals-really-work-b487fbe03523> [Accessed 12 May 2022].

[3] Mi, X., Ippoliti, M., Quintana, C. et al. Time-crystalline eigenstate order on a quantum processor. Nature 601, 531–536 (2022). https://doi.org/10.1038/s41586-021-04257-w

[4] University, S., 2021. Time crystal in a quantum computer | Stanford News. [online] Stanford News. Available at: <https://news.stanford.edu/2021/11/30/time-crystal-quantum-computer/> [Accessed 11 May 2022].

[5] Frey, P. and Rachel, S., 2022. Realization of a discrete time crystal on 57 qubits of a quantum computer. [online] science.org. Available at: <https://www.science.org/doi/10.1126/sciadv.abm7652> [Accessed 13 May 2022].

[6] Cho, A., 2022. Physicists produce biggest time crystal yet. [online] Science.org. Available at: <https://www.science.org/content/article/physicists-produce-biggest-time-crystal-yet> [Accessed 13 May 2022].

[7] Moss, S., 2021. Cooling Quantum Computers. [online] datacenterdynamics.com. Available at: <https://www.datacenterdynamics.com/en/analysis/cooling-quantum-computers/> [Accessed 10 May 2022].

[8] Khemani, V., Moessner, R. and Sondhi, S., 2019. A Brief History of Time Crystals. [online] Available at: <https://arxiv.org/pdf/1910.10745.pdf> [Accessed 12 May 2022].

 

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The Cosmic Symphony: A Brief Exploration of String Theory

According to theoretical physicist Michio Kaku, “in string theory, all particles are vibrations on a tiny rubber band; physics is the harmonies on the string; chemistry is the melodies we play on vibrating strings; the universe is a symphony of strings, and the ‘Mind of God’ is cosmic music resonating in 11 dimensional hyperspace” [1]. This post will not attempt to cover the physics behind the need for an 11-dimensional hyperspace. Instead, it will provide an insight into the beauty of a remarkable theory, which has the potential to be the theory that physics has strived for since its inception: the theory of everything.

 

The Edge of Knowledge

Currently, there are two core theories upon which the entirety of modern physics is built. The first is quantum mechanics, which allows us to understand the universe at the smallest scales, giving us an insight into the behaviour of atoms; and their even smaller constituents, electrons and quarks. The second is Einstein’s theory of general relativity, which allows us to understand the universe at the largest scales, giving us an insight into the behaviour of stars and galaxies. Both of these theories have been tested rigorously and the accuracy of the predictions made by these theories is incredibly precise. We have used these theories to make remarkable advancements in technology and the world has derived great benefit from them. However, quantum mechanics and general relativity cannot both be right. Our best understanding of the movement of the heavens and of the building blocks from which our universe is created directly contradict each other. 

 

This seems like it should create an urgent problem which needs to be solved immediately, but the contradiction has not caused many issues in most physics research, as each theory applies to very different extreme circumstances which do not overlap much. Quantum mechanics is used when we would like to study things that are small and light (like atoms) and general relativity is used when we study things that are large and heavy (like stars and galaxies). However, when we encounter things that have a mix of these properties, we get into trouble. When we’d like to study the centre of a black hole or the beginning of the universe, we encounter situations where immense masses have been crushed into a tiny scale (small and heavy).  Which theory do we use here? It would appear that we need a combination of the two. However, when we try to bring these two theories together, we get chaotic and nonsensical results. The laws of physics break down. Clearly, if we want to advance our understanding of the centre of black holes, we need something more.

 

Superstring Theory

Physicists have discovered that through the lens of superstring theory, the conflicts between quantum mechanics and general relativity are resolved. In superstring theory (or string theory for short) we no longer need to change the theory we use depending on the situation. One theory of the universe fits all situations. For the first time in human history, we have a theory that has the capacity to explain the entirety of the known universe. We have a candidate for the theory of everything. 

 

The Fabric of The Universe

Figure 1    [2]

String theory states that the elementary particles in our universe (the smallest known building blocks of our universe) are not actually indivisible little balls, but instead tiny loops called strings. In Figure 1, the apple is shown on increasingly smaller scales, starting off with the whole apple, then the atoms, the protons and neutrons, the elementary particles (electrons and quarks) and then finally, strings.

 

Musical Strings

Figure 2     [2]

In order to understand how the strings in string theory operate, it’s helpful to first think about more familiar strings, such as those on a violin. Each string on a violin can experience a huge number of different vibrational patterns called resonances. Examples of these vibrational patterns are shown in Figure 2. Each different vibrational pattern will create a different musical note. The resonance patterns consist of a number of peaks (top of the wave) and troughs (bottom of the wave) that are equally spaced across the length of the string. Each different resonance pattern will have a different number of waves and troughs that fit between the two ends of the string.

 

The strings in string theory operate in a similar way in that different resonance patterns have different numbers of peaks and troughs that can fit across a given length but now instead of the peaks and troughs fitting inside a straight line, they now fit inside a loop as shown in Figure 3. 

Figure 3     [2]

The first loop has two peaks and two troughs, the second has four peaks and four troughs, the third has eight peaks and eight troughs. Just like the resonance patterns in violin strings give rise to different musical notes, the different resonance patterns on a fundamental string give rise to different masses and force charges. So, the properties of a ‘particle’ are determined by the vibrations of its internal string.

 

Mass Visualised Through Strings

Figure 4     [3]

Let us cast our minds back to the violin strings. The energy of a given vibrational pattern will depend on the amplitude (vertical distance between the peaks and troughs) and wavelength (the horizontal distance between 2 peaks) as shown in Figure 4. The energy of the vibrational pattern increases as the amplitude increases and the wavelength decreases. This makes sense intuitively, because we can see that more frantic vibrational patterns have higher energy and the calmer vibrational patterns have lower energy. In Figure 2, the vibrational patterns increase in energy as you move downwards, as their wavelengths decrease and they become more frantic in appearance. We can also imagine plucking a violin string more vigorously (supplying more energy) will cause the string to vibrate more frantically and plucking a string less vigorously (supplying less energy) will cause the string to vibrate more calmly.

 

From special relativity, we know that energy and mass are equivalent (E=mc2); which means that if the mass of an object increases, its energy increases, and vice versa. Therefore, the mass of an elementary particle is determined by the vibrational pattern of its internal string.  Whilst a heavier particle will have an internal string vibrating more energetically, a lighter particle will have an internal string vibrating less energetically. The forces of the universe are explained by detailed aspects of the string’s vibrational pattern.

 

So, we can see that in string theory, the properties of matter can be determined by investigating the vibrations of the fundamental strings that make up our universe. This is a sharply different perspective from pre-string theory physicists, who claimed that each of the elementary particles that make up our universe were “cut from a different fabric”. Each particle was viewed as being made up of different “stuff”, for example, electrons were made up of “stuff” with negative electric charge and neutrinos were made up of “stuff” with no electric charge. String theory breaks this notion and declares that all “stuff” is the same, tiny vibrating strings. Different elementary particles are strings vibrating at different notes, joining together in enormous numbers to form planets, stars and galaxies – creating a cosmic symphony.

 

Definitions

Term Definition
The Theory of Everything A hypothetical theoretical framework explaining all known physical phenomena in the universe.
Elementary particle The smallest known building blocks of the universe (examples include electrons, quarks and neutrinos).
Quarks Elementary particles that make up the nucleus of an atom.
Neutrinos Elementary particles with no electrical charge.

 

Further Reading

The Elegant Universe ~ Brian Greene

The Cosmic Landscape ~ Leonard Susskind

 

References

[1] Lubin, G., 2014. String Field Theory Genius Explains The Coming Breakthroughs That Will Change Life As We Know It. [online] Business Insider. Available at: <https://www.businessinsider.com/michio-kaku-talks-about-coming-breakthroughs-2014-3?r=US&IR=T> [Accessed 12 May 2022].

[2] GREENE, B. (1999). The elegant universe: superstrings, hidden dimensions, and the quest for the ultimate theory.

[3] Courses.lumenlearning.com. 2022. Waves and Wavelengths | Introduction to Psychology. [online] Available at: <https://courses.lumenlearning.com/atd-bhcc-intropsych/chapter/waves-and-wavelengths/> [Accessed 12 May 2022].

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What are Superconductors?

Dutch physicist, Heike Kamerlingh Onnes, discovered superconductivity in 1911. Onnes was studying the electrical properties of mercury when he found that its electrical resistance completely vanished when it was at a temperature of 4.2 K (close to absolute zero). An electric current was applied to this supercooled mercury, then the battery was removed. The electric current remained the same in the mercury at the same value. This discovery had massive implications for the energy industry, and if utilised could solve looming energy crisis.

Although the discovery of superconductors was in 1911, the understanding of how they work was not put forward until 1957. Physicists John Bardeen, Leon N. Cooper and Robert Schrieffer developed the theory that to create electrical resistance, the electrons in a metal need to be free to move and bounce around. In super cold conditions, under the material’s critical temperature, the electrons inside the metal become less mobile, allowing them to pair up. This prevents them from moving around. These electron pairs are called Cooper pairs and are very stable at low temperatures.  As there are no electrons free and mobile, the electrical resistance disappears completely.

Superconductors experience many phenomena, one being the Meissner Effect. When a superconductor is below its critical temperature, it expels its magnetic field. When the temperature is above the critical value, a magnetic field is able to pass through the material. Below the critical temperature, the magnetic field cannot pass through the material and instead must go around it. Surface currents that flow without resistance then develop to create magnetization within the superconducting material. This magnetization is equal and opposite to the applied magnetic field, which results in the cancelling out of the magnetic field everywhere within the superconductor. This means the superconductor has a magnetic susceptibility of -1, and it exhibits perfect diamagnetism. Diamagnetic materials are repelled by by a magnetic field, hence the superconductor is repelled by the magnetic field. One way to display this phenomena is to place a magnet above a superconductor. The magnet is observed to ‘float’ above the superconducting material. This is because repelling force can be stronger than gravity, allowing the magnet to levitate above the superconductor.

Fig1: Meissner EffectFig 2: Meisnn

The implementation of superconductors have not been so straightforward. Superconductors only operate at temperatures close to absolute zero, and the energy costs of cooling these materials to these temperatures are enormous. Despite this, it is very likely to encounter a superconductor in everyday life. Many MRI machines use superconducting magnets, as normal magnets would melt due to the heat of even a little bit of resistance. As superconductors have no electrical resistance, no melting occurs, and the electromagnets can generate the necessary magnetic fields for the safe operation of MRIs.

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The Future of Self-Driving Cars

Have you ever gotten into a car, and as soon as you drive onto the main road, particularly at rush hour, there is some sort of traffic congestion? The answer is yes for pretty much everyone reading this of course. Now, imagine what it would be like if you never experienced a traffic jam again. What about being able to sit down and read a book while your car takes you to your destination? Now, you’re probably thinking either that I am crazy, or you probably already know about self-driving cars.

Self-driving or automated cars are cars which incorporate the use of vehicular automation, which uses artificial intelligence among other things. According to SAE International, there are six levels of automation in vehicles: level 0 providing no automation whatsoever, level 1 providing hands on or hybrid control, level 2 is hands off, level 3 is eyes off, level 4 is mind off and level 5 means the steering wheel is totally optional.

Currently, we are at level 2, where we can let the car do the steering, accelerating and braking, while us humans still need to be well aware of what is happening and be ready to intervene when needed.

There has been steady progress in this field over that past number of years, although unfortunately a little slower than expected. However, Alphabet, the parent company of Google, has recently announced that it had begun carring employees in electric Jaguar I-Pace SUVs without human backup drivers. So, it is clear that we are getting somewhere.

So, how long will it be until our dream of escaping those terrible traffic predicaments and endulging in the latest Sally Rooney novel in the driving seat (or “driving” seat, I should note)? Well, fully autonoumous vehicles will probably take a good few decades before we see them flying down the M50, but their safety, efficiency, convenience and cost, along with many other factors, will make them ever-present in the years to come.

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Warp Drives: Not just a Hollywood Plot Device?

Introduction

Have you ever envisioned yourself sitting alongside Han and Chewie in the Millennium Falcon travelling through hyperspace seeing the stars form streaks across your windscreen? Or do you rather fancy yourself on the USS Enterprise and its iconic warp drive? Worry not, because as I am about to explain in this blog, warp drives and faster-than-light (FLT) travel might actually “be possible” according to physics with some caveats.

 

Image depicting travel of a spaceship through a wormhole by curving spacetime around it . Source : [4].

Interstellar travel and its difficulties

It is quite well-known that given our current technological limitations, that feasible interstellar travel is impossible. One of the reasons for this is the large amount of fuel required to carry out these journeys which we simply do not have or have an efficient source of. Another reason is special relativity which states that the faster an object travels, its ‘relativistic’ mass or mass due to an object’s motion increases tremendously and becomes infinite at the speed of light. This has the effect of requiring more and more energy as the spaceship is to go faster and faster, finally needing an infinite amount of energy to get the spaceship to the speed of light! With these in mind, let us see how a hypothetical warp drive would work

 

General and special relativity

Special relativity forms a subset of general relativity which holds under very small regions of 4D spacetime that can be considered to be flat[2]. Thus, general relativity does not impose restrictions on the speed of light, only that special relativistic restrictions must hold ‘locally’ including the limit on the speed of light[2].

Warp drives and general relativity

In 1994, theoretical physicist Miguel Alcubierre published a paper based on his work on general relativity proposing a solution to Einstein’s field equations of general relativity. According to Einstein’s field equations, one can calculate the deformation of the 4D spacetime, that Einstein predicted we live in, by a ‘distribution of mass and energy’[1]. Alcubierre did the reverse and, using a particular configuration of spacetime, was able to figure out the mass and energy distribution that produced it. The configuration he proposed was that of a bubble of flat spacetime containing the spaceship with a region of compressed spacetime in front of the ship (which can be thought of as spacetime being destroyed similar to the Universe collapsing in the Big Crunch) and a region of expanded spacetime behind the ship (which can be thought of as the spacetime being created just as the Universe expands with the Big Bang)[2]. This “warped” region can push this pocket of flat spacetime containing the spaceship to arbitrary velocities including faster than light without the spaceship having to move.

 

 

Image depicting the warped spacetime as proposed by Alcubierre. The region dipping down as shown compresses spacetime and is felt as the force of gravity, known by us all. The region projecting up is more unusual and expands spacetime as described and can be thought of as “antigravity”[1]. These two regions work together to push the flat region in the center, containing the spaceship, forward at any arbitrary velocity .Source : [5]

Thus, for a spaceship at the center of this bubble, it would find itself at rest or even moving slightly with respect to a relatively flat portion of spacetime, thereby having its velocity less than the “local” speed of light within the flat region of the bubble. Moreso, the spaceship being at rest or close to it in the flat spacetime region, it would not experience any of the relativistic effects such as length contraction, time dilation or mass expansion. So, the spaceship stays at rest within the pocket volume of flat spacetime, but this pocket moves as it is pushed by the “warped” region of spacetime.

 

Too good to be true?

Although the warp drive configuration of spacetime or known as the “Alcubierre metric” is a valid solution of Einstein’s field equations, to produce it is to open up a whole new assortment of problems.

One of the major problems is that the Alcubierre metric requires negative energy density to produce it[2]! This seems impossible to produce, however, there have been observed effects in quantum field theory that gives rise to negative energy densities under certain scenarios such as the Casimir effect[2], but what is this Casimir effect?

In quantum vacuum, quantum field theory predicts there are fluctuations in electromagnetic energies that produce electromagnetic waves at all wavelengths[3], but if two perfectly conducting, uncharged plates are brought close together, only those waves having nodes at either plate will fill the space between similar to standing waves on a guitar string[3]. This reduces the number of possible waves compared to that in free vacuum which reduces the energy density inside the cavity compared to outside[3]. With the energy density outside being close to zero, there is a small negative energy density created inside the cavity that results in a negative pressure inside that cavity which results in the plates being pushed together or attracted to one another. This is known as the Casimir effect.

 

Image depicting the Casimir effect with limited number of electromagnetic modes inside the cavity due to constraints resulting in a negative energy density with respect to the surrounding, producing a force on the plates. Source : [6]

As shown with the Casimir effect, negative energy densities do exist on a quantum scale, however, this is way too small for the amount of negative energy we require. Another viable solution of Einstein’s equations is a wormhole (also called Einstein-Rosen bridges) that require the same negative energy constraint in order to work[2]. In order to produce stable wormholes, “exotic matter” having negative energy density is required but this is completely hypothetical[2].

 

Another problem that Alcubierre warp drives brings is that it creates the possibility for making “closed time-like curves” which open up violations of causality[2] (such as effect happening before cause!). A well-known example is the grandfather paradox: if you travel back in time and kill your grandfather before your parent was born, they never would have been born and neither would you so who went back in time to kill your grandfather?

 

 

Conclusion

Thus, it can be seen, no matter how exciting building a warp drive to cruise by countless galaxies we can only dream of visiting may seem, we are still limited by our current technology. And although the need for the impossible negative energy can be overcome by using positive energy instead and with a slightly modified spacetime metric[1], the amount of energy required would be still phenomenal. Moreover, care must be taken to ensure that the spaceship and its inhabitants do not fall prey to the massive tidal forces at the boundaries of the moving “bubble” of spacetime.

So, to conclude, although  warp drives still seem like they belong on our television screens and on the pages of our books, the promising physics behind it give us hope that somewhere a long time from now, we may visit a galaxy far, far away.

 

REFERENCES:

[1]: Gast R, Spektrum. Star trek ’s warp drive leads to new physics [Internet]. Scientific American. [cited 2022 May 13]. Available from: https://www.scientificamerican.com/article/star-treks-warp-drive-leads-to-new-physics/

[2]: Alternate view column AV-81 [Internet]. Washington.edu. [cited 2022 May 13]. Available from: https://www.npl.washington.edu/av/altvw81.html

[3]: Stange A, Campbell DK, Bishop DJ. Science and technology of the Casimir effect. Phys Today [Internet]. 2021;74(1):42–8. Available from: http://dx.doi.org/10.1063/pt.3.4656

 

IMAGE SOURCES:

[4]: https://commons.wikimedia.org/wiki/File:Wormhole_travel_as_envisioned_by_Les_Bossinas_for_NASA.jpg

[5]: https://commons.wikimedia.org/wiki/File:Alcubierre.png

[6]: https://commons.wikimedia.org/wiki/File:Casimir_plates.svg

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