Quantifying the Universe with Brian Cox
Part One: The Power of Quantum Mechanics
The Early Glimpses of Quantum Mechanics
Quantum mechanics emerged from the effort to describe matter and understand atoms and molecules. In 1610, Johannes Kepler, famous for his laws of planetary motion, wrote "On the Six-Cornered Snowflake." While walking in a snowstorm on the Charles Bridge in Prague, realizing he had no New Year's gift for his benefactor, he noticed the symmetry of snowflakes. This led him to ponder why all snowflakes share a similar structure. He concluded it must be related to the building blocks of nature. Although he didn't know about the water molecule's shape (H₂O) as we do now from quantum mechanics, his insight was remarkable. He even said he was "knocking on the doors of chemistry" in the English translation of his book.
The Origins of Quantum Mechanics
Quantum mechanics also grew from attempts to explain curious experimental findings. In the late 1890s and 1900, there was a problem with calculating how hot objects radiate light. Max Planck made a revolutionary proposal in 1900. He suggested that a hot object only emits light in little packets, which later became known as photons after Einstein's work. Planck thought this was a calculational device, but the appearance of Planck's constant in the calculation was crucial. The relationship between the energy of the photon (E), the frequency of the light (f), and Planck's constant (h) is given by E = hf. This is considered the beginning of modern quantum mechanics.
Einstein's Impact on Science through the Photoelectric Effect
When Planck introduced photons, he didn't believe they were real. He thought it was a mathematical trick related to how matter oscillates. In 1905, Einstein wrote a paper on the photoelectric effect for which he won the Nobel Prize. The photoelectric effect is the observation that when light shines on a metal, electrons can be emitted. However, if the light has too long a wavelength (low frequency), no electrons are emitted, no matter how bright the light. Einstein explained this by saying that light can be thought of as a stream of photons. If a photon doesn't have enough energy to knock an electron out of the material, no electrons will emerge. This was the first time it was suggested that the quantization of the electromagnetic field was a property of light itself, not just how matter emits light. At the time, this was very controversial, as shown by a letter Planck wrote years later recommending Einstein for an award, where he said Einstein's belief in the reality of photons should not be held against him.
The Conflict between Quantum Physics and Classical Theory
Teaching quantum mechanics in universities has changed over the last few decades. Instead of teaching it historically, which can lead to confusion, it's now more common to start with the theory as it is understood today. A good introduction is the property of particles called spin. In classical theory, a coin can be either heads or tails. In quantum mechanics, a quantum coin can be in a superposition of heads and tails, meaning it can be a combination of both states, like 30% heads and 70% tails. Particles like electrons have a spin property that can be up or down, but they can also be in a superposition of these states. The probabilities in quantum theory are fundamental, not due to incomplete knowledge as in classical probability theories. This simple property is the source of many intellectual challenges and confusion in quantum mechanics.
The Double Slit Experiment
The double slit experiment is a simple yet powerful experiment that encapsulates the properties of the quantum world. In this experiment, electrons are emitted from an electron gun towards a barrier with two slits and a screen behind it. If electrons were just particles, we would expect them to hit the screen mostly opposite the slits. However, what is observed is a pattern of stripes on the screen, with areas of high and low electron density. This is the same pattern that would be seen if waves were sent through the slits, due to interference. The experiment becomes even more interesting when electrons are sent one at a time. They still create the same interference pattern, as if each electron explores both paths through the slits and interferes with itself. The Feynman Lectures, volume three, first chapter, offer an excellent description of this experiment. The mathematics of calculating the pattern is relatively simple, but the interpretation of what it means for the nature of reality is still a subject of debate.
Part Two: The Fundamental Measurements of Nature
Defining the Universe: Properties of Nature
When we think about the size of things, we usually refer to ourselves. Units like the foot or meter are historically based on the human body. However, these are not fundamental to the structure of the universe. Max Planck came up with a system of units based on fundamental constants of nature. These constants include the speed of light (a universal speed limit for massless objects), Newton's gravitational constant (which describes the strength of gravity), and Planck's constant (associated with quantum theory, such as the uncertainty principle). These three constants allow us to define the Planck length, which is about 10⁻³⁵ meters.
Insights from the Planck Scale
The Planck length has several astonishing implications. For example, the entropy of a black hole (the amount of information hidden within it) is equal to the surface area of the event horizon in square Planck lengths. Additionally, if we try to observe something very small by shining light on it, as we approach the Planck length, the energy required to do so is so high that we form a black hole. This suggests that the Planck length is a fundamental property of the universe. However, there are theories with extra dimensions in the universe. If these extra dimensions exist and can be detected at energies similar to those at the Large Hadron Collider, the Planck scale could change, and the Planck length could be larger than currently measured.
The Chandrasekhar Limit: A Quantum Mechanical Calculation
The Chandrasekhar limit is a beautiful calculation that shows the relationship between fundamental properties of the universe and observable phenomena. It calculates the maximum mass of a white dwarf star that can be held up by quantum mechanical processes. As a star collapses, electrons are confined, and due to the uncertainty principle and the Pauli exclusion principle, they start to jiggle faster, creating a pressure that can hold the star up. However, as the electrons approach the speed of light, there is a limit to this pressure. The calculation shows that the maximum mass of such a star is 1.4 times the mass of our sun. This limit can be expressed in terms of the Planck mass (a fundamental mass calculated using the speed of light, Planck's constant, and Newton's gravitational constant) and the proton mass.
The Breakdown of Our Comprehension of Scale
The Planck length is unimaginably small. If a proton were expanded to the size of our solar system, something the size of the Planck length would be about the size of a virus or a living cell. Our comprehension of scale starts to break down when we move beyond distances we can experience in our daily lives. We can understand distances up to a few thousand miles, but when we start to talk about the distance to the Sun (93 million miles), the nearest star (about four light years away), or the size of the Milky Way galaxy (about 100,000 light years across), it becomes inconceivable. The most distant object we can see, the cosmic microwave background radiation, was emitted 380,000 years after the Big Bang and has been traveling for 13.8 billion years. The place that emitted this radiation is now about 46 billion light years away, and the universe may be infinite in extent.
Part Three: The Frontiers of the Future
The Opportunities of Space Colonization
We are on the verge of becoming a space-faring civilization. The development of reusable rockets by companies like SpaceX and Blue Origin has made access to Earth orbit cheaper, leading to an increase in industrialization in space. There will be more space stations, scientific research, space tourism, and communication satellites. This is an exciting opportunity, but it also comes with challenges, such as managing conflicts between satellites and allocating orbits. Beyond near-Earth orbit, there are opportunities for mining asteroids, which could provide unlimited resources and reduce competition and environmental damage on Earth. However, we need to develop a regulatory framework for space, which requires international collaboration.
Humanity's Influence on the Universe
When we consider the size and scale of the universe, it's easy to feel insignificant. However, we may be remarkably valuable if the number of civilizations in the universe is rare. Additionally, life has already transformed the Earth, and it's possible that in the future, our civilization could expand and start to affect larger structures in the universe. We could build cities on Mars, terraform planets, and even influence the lifetime of stars. In a billion years, if our civilization becomes an interstellar one and understands the quantum theory of gravity, it may be able to play a central role in the far future of the universe. The Omega Point cosmology, proposed by Barrow and Tipler, suggests a scenario where life in the far future is so powerful that it can control the collapse of the universe and make it immortal. While this is highly speculative, it shows that life may not always be insignificant on a cosmic scale.
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