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Time and entropy
Rovelli, Connes, Hawking, Penrose: why time flows one way, and whether it is fundamental at all.
The reading track
- 01
A black hole's entropy depends only on its surface area, not its interior volume, hinting that the universe itself might be a holographic projection.
The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics · Leonard Susskind · 2008
Susskind explains the discovery by Jacob Bekenstein and Stephen Hawking: a black hole's entropy is measured by its event horizon's area. When an object falls in, its information is not lost but etched onto that surface. This defies our intuition, since entropy usually scales with volume. For instance, a solar-mass black hole has a horizon area of about 10^7 square meters, yet its entropy is 10^77 units, enormous compared to an ordinary star. This relationship led to the holographic principle, suggesting our entire three-dimensional space might be a projection from a two-dimensional surface.
The entropy of a black hole is proportional to the area of its event horizon, not its volume. This is a deep statement, suggesting that the information about everything that fell into the black hole is stored on its surface, like a kind of hologram.The Black Hole War, Chapter 1: The Black Hole War Begins
Why it matters The notion that information resides on surfaces rather than volumes is timely as debates over the universe's initial entropy and the nature of time intensify, with this book bridging thermodynamics and quantum gravity.
- 02
Time's direction exists because the universe began with extremely low entropy, and this rare initial state makes the past distinct from the future.
The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics · Roger Penrose · 1989
Penrose argues that the second law of thermodynamics — entropy increases over time — does not explain time's direction. The key is that the universe started in a state of incredibly low entropy, far lower than a black hole of the same mass. For instance, at the Big Bang, the universe's entropy was about 10^10 times smaller than the maximum possible. This extremely special initial condition creates the arrow of time: things evolve from order to disorder. Without it, processes would be reversible, and memory and causality would vanish. Penrose calls this the initial entropy problem, which he considers unsolved by current physics.
The arrow of time is a consequence of the extremely special initial conditions of the universe, particularly the low entropy of the Big Bang. Without this condition, time would be symmetric, and past and future would be indistinguishable.The Emperor's New Mind, Chapter 7: Cosmology and the Arrow of Time
Why it matters The Rovelli–Penrose debate over the universe's initial entropy is central to our shelf, and this book explains Penrose's view that the initial conditions are a fundamental mystery, not a byproduct of quantum gravity.
- 03
The arrow of time is not a fundamental law but an effect of how we perceive the world at a macroscopic scale.
The Order of Time · Carlo Rovelli · 2017
Rovelli shows that fundamental laws of physics, both classical and quantum, are time-symmetric. The difference between past and future emerges only when we look at macroscopic systems, where entropy increases. For instance, a cup of coffee cools down but never heats up spontaneously. This happens because there are so many microscopic states that the probability of finding the system in an ordered state decreases. Rovelli calls this privileged perspective our ignorance, since we cannot track every molecule. Thus, thermal time, defined by entropy increase, replaces fundamental time.
The difference between past and future is not a fundamental property of the laws of nature. It arises only when we look at the world from a privileged perspective, that is, from our ignorance of the microscopic state of things.The Order of Time, Part I: The Crumbling of Time, Chapter 2: The Direction of Time
Why it matters This idea explains why sudden market fluctuations seem unpredictable: they are effects of our ignorance of the microscopic details of transactions.
- 04
Spacetime is not a passive backdrop but a quantum entity with a granular, discrete structure at the smallest scale.
Reality Is Not What It Seems: The Journey to Quantum Gravity · Carlo Rovelli · 2014
Rovelli explains loop quantum gravity, where spacetime is made of interwoven quantum loops. At the Planck scale, about 10^-35 meters, space becomes granular, and time disappears as a fundamental variable. For instance, an atom of space cannot be divided further. This means there is no universal time, only relations between events. The theory requires no background, unlike general relativity. Rovelli emphasizes this is a hypothesis, not experimentally confirmed, but it offers a coherent picture of the universe at the quantum scale.
Space and time are no longer a fixed background on which events unfold. They are themselves dynamical entities, which fluctuate and become quantized at the Planck scale.Reality Is Not What It Seems, Chapter 7: Quantum Gravity, section 'The End of Space and Time'
Why it matters This perspective helps understand why extreme volatility can arise from local interactions without a global cause, similar to quantum fluctuations of spacetime.
- 05
Black holes are not mere holes in spacetime but real thermodynamic objects with entropy and temperature, linking gravity to thermodynamics and quantum mechanics.
Black Holes and Time Warps: Einstein's Outrageous Legacy · Kip Thorne · 1994
Thorne explains the revolutionary discovery that black holes have entropy proportional to the area of their horizon, not their volume. This means information about what fell into the hole is stored on its surface, like a hologram. Hawking showed that quantum effects near the horizon cause the hole to emit thermal radiation, losing mass and slowly evaporating. For example, a black hole with the Sun's mass would have a temperature billions of times lower than the cosmic background and would take 10^67 years to fully evaporate. This discovery created the information paradox: if the hole evaporates completely, does the information about what fell in disappear? The answer is still debated and directly links black hole entropy to the foundations of quantum mechanics and gravity.
Bekenstein argued that a black hole must have an entropy proportional to the area of its event horizon, and Hawking showed that this entropy is real: black holes emit radiation and evaporate, confirming that they have a well-defined temperature and entropy.Capitolul 11 — Găurile negre și entropia
Why it matters In the context of discussions about risk and volatility in markets, the idea that information can be stored on surfaces and that seemingly simple systems hide thermodynamic complexity offers a powerful analogy for understanding systemic risks.
- 06
The relational interpretation holds that quantum properties are interaction-dependent, not absolute.
Helgoland: Making Sense of the Quantum Revolution · Carlo Rovelli · 2020
Rovelli extends Niels Bohr's idea that quantum measurement creates reality: any interaction between two quantum systems defines relative properties. For instance, an electron's position does not exist until it interacts with another system, like a detector. This eliminates paradoxes such as Schrödinger's cat, since states are defined only relative to an observer. Rovelli emphasizes this is an interpretation, not a new theory, but it offers a coherent picture of quantum mechanics without collapse or hidden variables.
A quantum property is not a property of an object in itself, but a property of how that object relates to another. Reality is made of relations, not of substances.Helgoland, Chapter 4: The Relational Interpretation, section 'Quantum Mechanics Is a Theory of Information'
Why it matters This idea explains why market information is context-relative: an asset has no intrinsic value but one defined by interactions between participants.
- 07
Time does not flow the same for everyone — a clock moving very fast or sitting near a huge mass runs slightly slower.
Relativity: The Special and General Theory · Albert Einstein · 1916
Picture space and time as a stretched elastic sheet. A heavy planet bends it, just like a heavy ball bends a stretched blanket. Other objects passing by slide along that curve, which we call gravity. The heavier the mass, the stronger the curve — and the stronger the effect on time.
Why it matters Without this correction, the GPS in your phone would be wrong by kilometers every day.
- 08
If you are in a closed cabin on a smoothly moving ship, no experiment inside can tell you whether you are moving or standing still.
Dialogue Concerning the Two Chief World Systems · Galileo Galilei · 1632
Galileo asked readers to imagine tossing a ball or pouring water below deck on a perfectly smooth ship. Everything behaves exactly as it would on land. From this he drew the bold conclusion that Earth could be moving through space without us feeling it directly.
Why it matters That same idea about relative motion led, centuries later, to Einstein's theory.
- 09
Heat always flows from hot things to cold ones, never the other way, and this simple rule is what gives time its forward direction.
Seven Brief Lessons on Physics · Carlo Rovelli · 2014
Pour warm milk into a cup of cold tea: they mix and reach the same temperature. That never happens in reverse on its own. Rovelli shows that this simple rule about heat, not some mysterious law, explains why the past differs from the future and why time seems to move forward.
Why it matters The idea explains why every machine loses some energy as heat, no matter how well it is built.
- 10
If all scientific knowledge were lost and only one sentence could survive, the most useful one would be that everything is made of tiny, ever-moving atoms.
Six Easy Pieces · Richard Feynman · 1994
Feynman said water, air, and rocks look very different but are all made of tiny atoms that pull and push on each other. When it is hot, atoms move faster and bump harder. From this one idea alone, you can explain why ice melts or why smells spread through a room.
Why it matters The same idea underlies chemistry, biology, and the materials that phones are made from.
- 11
A black hole pulls everything toward it so strongly that not even light can escape, but even black holes can slowly evaporate.
A Brief History of Time · Stephen Hawking · 1988
Think of a black hole as an extremely deep funnel: anything falling too close to the edge can never come back out. Hawking discovered, though, that new particles keep appearing at the funnel's edge, straight out of empty space. Given enough time, the black hole loses energy and, in theory, disappears completely.
Why it matters The radiation Hawking discovered is still a key test for any future theory of quantum gravity.
- 12
An object stays at rest or keeps moving steadily unless something pushes it, and the same force pulling an apple down also keeps the Moon in orbit.
Philosophiae Naturalis Principia Mathematica · Isaac Newton · 1687
Newton realized gravity does not stop at your roof. It pulls an apple from a tree and the Moon overhead the same way. The difference is speed: the Moon moves sideways so fast that it keeps falling toward Earth without ever hitting it. He linked sky and ground with one set of rules.
Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon.
Why it matters The same equations still send satellites into orbit and rockets to other planets.
- 13
Death is nothing to us and does not concern us at all.
Despre natura lucrurilor · Lucretius · -55
Lucretius argues that as long as we exist, death is not present, and when death comes, we no longer exist. There is no sensation or suffering after death. Just as the years before birth do not bother us, the years after should not frighten us. This frees man from the fear of death.
Therefore death is nothing to us, nor does it concern us a bit.Cartea III, versul 830
Why it matters In a culture obsessed with longevity, this idea offers a way to live without anxiety about death, focusing on the present.
- 14
Religion has been able to prompt such great evils.
Despre natura lucrurilor · Lucretius · -55
Lucretius, an Epicurean poet and philosopher, criticizes religious superstition that, in the name of gods, has justified atrocities. He cites the sacrifice of Iphigenia, killed by her own father to appease an imaginary storm. The mechanism is fear of divine punishment, which makes people commit acts they would otherwise reject.
So great the evils which religion could prompt.Cartea I, versul 101
Why it matters Today, the phrase warns against any ideology that demands suffering in the name of a higher ideal, whether religious or political.
- 15
Nothing vanishes into nothingness; everything breaks down into its basic components.
Despre natura lucrurilor · Lucretius · -55
Lucretius rejects the idea that things can be completely annihilated. What we call death or destruction is actually a rearrangement of matter into its component parts, atoms. For example, a dried leaf does not vanish; it decomposes into the soil, feeding other plants. This is a materialist view that explains transformation, not disappearance.
Therefore no thing returns to nothing, but all things return dissolved into their elements.Cartea I, versul 248-249
Why it matters This idea helps us see loss or endings as transformation rather than total disappearance, offering a less frightening perspective on death.
- 16
The living power of the human mind triumphed and went beyond the known boundaries of the world.
Despre natura lucrurilor · Lucretius · -55
Lucretius praises the philosopher Epicurus for daring to think beyond superstitions and the limits imposed by religion. The human mind, through reason and curiosity, can overcome any barrier, even the 'flaming walls of the world' – that is, cosmic or mental boundaries. For instance, scientific discoveries that challenged religious dogmas illustrate this power.
Therefore the lively force of his mind prevailed, and he marched far beyond the flaming walls of the world.Cartea I, versul 72-73
Why it matters Today, it encourages us not to blindly accept authority or tradition, but to use our minds to explore and understand the world more deeply.
- 17
Death does not affect us because when it is, we are not.
Despre natura lucrurilor · Lucretius · -55
Lucretius, following Epicurus, argues that death is not an experience we can undergo. While we exist, death is absent; when death arrives, we cease to be. Therefore, it makes no sense to fear something we will never feel. The fear of death stems from a confusion: we imagine ourselves present as spectators of our own disappearance.
Therefore death is nothing to us and does not concern us in the least.Cartea III, versul 830
Why it matters Today, this idea can free us from existential anxiety and help us focus on the life we live, not on its end.
- 18
Nothing arises from nothing through divine intervention; everything has a natural cause.
Despre natura lucrurilor · Lucretius · -55
Lucretius states the fundamental principle of Epicurean atomism: the universe is governed by natural laws, not divine whims. Every phenomenon has a material explanation based on the motion and combination of atoms. For instance, rain is not a divine sign but a physical process. This idea rejects superstition and paves the way for science, showing that the world can be understood rationally.
Nothing is ever begotten of nothing by divine power.Cartea I, versul 150
Why it matters In an age of misinformation, this principle reminds us to seek natural causes and evidence, not mystical explanations.
- 19
What is beneficial to some can be harmful to others.
Despre natura lucrurilor · Lucretius · -55
Lucretius observes the relativity of perceptions and effects: nature does not provide universal reactions. Food that nourishes one person can poison another, due to differences in constitution or tolerance. This applies morally or socially too: what seems good in one context may be bad in another. For example, competition motivates some but paralyzes others.
What is food to one, is to others bitter poison.Cartea IV, versul 637
Why it matters In daily life, this thought teaches us not to generalize and to respect the diversity of individual experiences.
- 20
If we accept that nothing comes from nothing, we understand everything has a natural origin.
Despre natura lucrurilor · Lucretius · -55
Lucretius restates the atomist principle as a starting point for a scientific worldview. Believing that nothing comes from nothing means rejecting miracles and arbitrary divine interventions. Everything that exists arises from prior combinations of matter. For instance, a plant grows from a seed, not from thin air. This premise underlies rational investigation of nature.
First, if we believe that nothing can be created from nothing.Cartea I, versul 159
Why it matters Today, this principle anchors us in critical thinking and helps us distinguish facts from fictions.
- 21
Nature knows no absolute loss, only continuous transformation.
Despre natura lucrurilor · Lucretius · -55
Lucretius rejects death as annihilation, seeing change instead as a rearrangement of atoms. Nothing truly vanishes; matter breaks down and reassembles into other forms. A rotting trunk feeds the soil, from which new plants sprout. The same energy that was in a man passes into tree, air, worm. Death is not an end, but a step in an endless cycle.
For all things change, but nothing perishes.Cartea I, versul 670
Why it matters It helps you see losses as transformations, not endings. In grief or failure, this Stoic perspective offers comfort and clarity.
- 22
Subjective perceptions make the same experience completely different for different people.
Despre natura lucrurilor · Lucretius · -55
Lucretius, an Epicurean poet and philosopher, highlights the relativity of pleasure and pain. What is beneficial or pleasant for one individual can be harmful or unpleasant for another, depending on nature, upbringing, or context. For example, one person's favorite music can be torture for another. The mechanism is biological and psychological: each person has a unique constitution and personal associations that color experiences.
What is food to one, is to others bitter poison.Cartea 4, versul 637
Why it matters In daily life, this idea teaches you not to judge others' preferences and to be tolerant of differences.
- 23
Light behaves not like a smooth wave but like tiny particles called photons, and the chance a photon lands somewhere comes from adding up little spinning arrows.
QED: The Strange Theory of Light and Matter · Richard Feynman · 1985
Picture a tiny clock hand spinning fast along every possible path light could take. Each path gets its own spinning arrow. Scientists add all those arrows together like tiny vectors. The length of the final arrow tells you how likely light is to arrive there. It sounds strange, but it works perfectly.
The theory of quantum electrodynamics describes Nature as absurd from the point of view of common sense. And it agrees fully with experiment. So I hope you can accept Nature as She is — absurd.QED: The Strange Theory of Light and Matter, introducere
Why it matters This idea underlies lasers, the chips inside phones, and fiber-optic internet.
- 24
Two particles that once touched can stay linked forever, so measuring one instantly affects the result of the other, no matter the distance.
Speakable and Unspeakable in Quantum Mechanics · John Stewart Bell · 1987
Imagine two magic dice that, no matter how far apart they are thrown, always show linked numbers. Bell showed with a precise calculation that no hidden trick can explain this — the link is genuinely real. Einstein called it spooky action at a distance and did not like it at all.
Why it matters Quantum entanglement is now the basis for ultra-secure communication technologies.
- 25
Beneath the separate things we see, there may be a deeper level where everything is folded together into one whole.
Wholeness and the Implicate Order · David Bohm · 1980
Bohm compared the universe to a hologram: even from a small piece, you can rebuild the whole picture. Particles that seem far apart might actually be linked through a hidden level. His idea is not fully proven yet, but it inspired new ways of thinking about connections in physics.
Why it matters Similar concepts show up today in debates about quantum entanglement over long distances.
- 26
You cannot know both exactly where a particle is and exactly how fast it moves — the universe itself sets that limit.
Physics and Philosophy: The Revolution in Modern Science · Werner Heisenberg · 1958
Try photographing a fast-bouncing ball in a dark room using a flash. The flash shows where the ball is but also nudges it, changing its speed. Tiny particles work the same way, except the limit is not your camera's fault — nature itself is built that way.
Why it matters This principle explains why quantum computers are so hard to build and control.
- 27
Light and matter have two faces — sometimes acting like a wave, sometimes like a particle — and no single experiment shows both at once.
Atomic Physics and Human Knowledge · Niels Bohr · 1958
Think of a coin that can land heads or tails, but never both in the same toss. An electron is similar: in one experiment it spreads out like a wave, in another it acts like a tiny ball. Bohr called this complementarity: both faces are real, but you see them one at a time.
Why it matters The idea changed how scientists understand what it even means to "measure" something.
- 28
Before you look, a quantum particle can be in several states at once — the puzzle is that the rules seem to say a big object could be too.
The Present Situation in Quantum Mechanics · Erwin Schrödinger · 1935
Schrödinger imagined a cat sealed in a box, linked to a random quantum event. By the strict rules, the cat would be, on paper, both alive and dead until you open the box. He did not actually believe this — he wanted to show how strange the theory gets at a large scale.
Why it matters The paradox is still used today as a test for the limits of quantum computers.