I had decided to follow an Oxford University Summer School (2026) on the subject “Understanding Space and Time”.
One of the recommended reading was “The Order of Time“ by Carlo Rovelli.
I decided to create this book review along the lines of personal revision notes. I’ve tried to hit the key points, and I’ve added some links to videos describing many of the scientific concepts outlined in the book.
Rovelli is quite active is presenting a discussion his ideas, and you could easily save yourself a lot of time by just listening to him talk about this book. In fact at the end of my book review I’ve list a series of video links.
What the reviewers wrote?
You can’t get any better than the books receptions, as described in Wikipedia.
Writing for The Guardian, Ian Thomson praised the “lucid” writing, translation, and compared it to Seven Brief Lessons on Physics, describing it as “a deeper, more abstruse meditation” but “jargon-free”. Cosmologist Anthony Aguirre, in a generally positive review, noted that some portions of the book “occupy a frustrating ground between too technical and not technical enough”. Literary Review noted Rovelli’s skill for presenting complex and even unexplainable concepts in an accessible form, “the brevity and elegance of which belie its depth”.
What did I think of the book?
I did not expect to enjoy the book, but I did. I also expected to be more confused at the end, than at the beginning. But I do feel that I learned something, even if I still doubt the real meaning of what I read. There is a rational foundation, that appears to lead to irrational or counter-intuitive conclusions. So for me this is a work in progress.
Did I find the writing “lucid”? At times, but the key idea could merit greater clarity. Did I find it frustrating? Occasionally, the inclusion of the poetry, etc. left me cold, but I enjoyed the mention of the great names of the past. I would have like a more punchy attack on the key messages. Was it accessible and brief? Yes. Was it elegant? Not sure what that really means, but it was not stuffy. Also elegance can be an obstacle to clarity, and the key messages were not clear enough underlined. A short summary at the end of each chapter would have been nice.
Will I re-read it? Not sure, probably not. But if I did, it would be with a marker pen in hand.
Preface - Perhaps Time is the Greatest Mystery
In just over four pages Rovelli wanted to stress the apparent everyday nothingness of time, “we inhabit time as fish live in water”. Yet the structure of time is not “uniform, universal flowing”, and we don’t know how time actually works.
He asks the question “Why do we remember the past and not the future?” Which on the surface, appears pretty stupid. I took this as a warning sign. Either this book will be a fast, stupid read, or it will be challenging, where every word may have a deeper meaning.
Part One is a summary of how physics sees time today. Part Two is about time as a “strange, alien world”, and Part Three is about what gives us “our time” with “a past that is different from the future”.
Part One - THE CRUMBLING OF TIME
Loss of Unity
The Slowing Down of Time starts with the statement that “time passes faster in the mountains than it does at sea level”.
And its not just clocks that slow down, but also physical processes. Someone living in a valley will have lived less (aged less) than someone who lived on the top of a mountain. In the valley there is less time than on the mountain top, so even plants will have grown less.
But the difference is small, about 1 nanosecond per day, per 10 metres.
This does not mean that cells, etc. grow differently due to gravitational time dilation in general relativity. It just means that a mountain plant grows according to its time, and the valley plant grows according to its slightly slower time.
For a height difference of 1000 m, that would be ~100 nanoseconds per day, when compared to cell division that takes a number of minutes. So molecular reactions, metabolism, and cell division, would be slightly slower. but so would be the measurements instruments used, so locally nothing would appear different.
So time is slightly slower deeper in a gravitational field. This means that all processes (including cell growth) are proportionally slower. But a plant in a valley does not “grow more slowly” in any meaningful biological sense, it simply experiences slightly less time.
The above video is about paradoxes in relativity, and is useful background for the video below.
In the below video, you might want to find out how you can actually measure the difference between two clocks, one in a valley and the other on a mountain top.
In his book Ravelli highlights:-
- Einstein understood that time does not pass uniformly everywhere before clocks were developed to measure the difference.
- What appears obvious to us that time passes at the same speed everywhere, is not true.
- That the Sun and Earth do not attract each other, but they act on (modify) what is between them, i.e. space and time.
- In fact a mass slows down time around itself. So it does this little more in valleys, and a little less on mountain tops.
- This fall because of this slowing down of time. If time passes uniformly, as in interplanetary space, things don’t fall. But on Earth things fall to where time passes more slowly.
- Our feet are on the ground because our whole body inclines naturally to where time runs more slowly, i.e. it passes more slowly for our feet than for our head.
Which tells the true time? The one in the valley, or the one on the mountain? There is no true time (or truer time), there are two times that change relative to the each other.
But there are not just two times, there are a multitude of times, each point in space has it time, which in physics is called proper time.
Physics describes how time evolves in local time, and how local times evolve relative to each other. Physics first describes how things evolve in their own times (not ‘in time’), and then how those “things” evolve relative to each other.
Loss of Direction
Setting aside the measurement of how much time passes, there is also the question about how time flows? We cannot change the past, and the future is uncertain. But in the elementary laws that describe the mechanisms of world there is no such difference. All but one of these laws can be run forwards and backwards in time.
There is just one basic law of physics that distinguishes the past from the future.
The arrow of time appears only where there is heat. Remember that heat cannot pass from a cold body to a hot one.
Below is an extensive video by Stephen Wolfram of a great but lesser know physicist, Sadi Carnot. And I can highly recommend Wolfram’s website.
And below there is another video by Sean Carroll (check out his podcasts) on that same “arrow of time”.
It was Clausius who introduced a quantity that measures this irreversible progress of heat in only one direction, named from the Greek, entropy S. This can increase or stay the same, but it can never decrease, in an isolated process.
This is second law of thermodynamics, the first being the conservation of energy.
Check out Wolfram’s “Computational Foundations for the Second Law of Thermodynamics“.
But our story turns to Ludwig Boltzmann, another less well known, but highly influential physicist.
Sadi Carnot thought heat was a substance, but heat is actually the microscopic agitation of molecules. More heat is just more agitation. Boltzmann understood that natural disordering leads gradually to less specific situations. It does not say why in the past things were more ordered. Rovelli phrases this increasing disorder as a blurring of the world. As there are more and more possible disordered configurations, and entropy is precisely the quantity that counts how many are the different configurations that our blurred vision does not distinguish between. Heat and entropy belong to an approximate statistical description of nature.
The physical laws, that link events of different times, are symmetrical between future and past. In a microscopic description, there can be no sense on which the past is different from the future. Boltzmann concluded that the differences between the past and the future refers only to our own blurred vision of the world.
This blurring is not our vision, but that our description of heat, temperature and the passage of heat from hot to cold is blurred, and only in this blurring does the difference between the past and the future appear. So there is nothing intrinsic about the flowing of time.
The End of the Present
Speed Also Slows Down Time, but what does that mean?
Let’s look at those two people, one in the valley and one on the mountain top.
But now they are both in the valley, one is sitting stationary, and the other is walking around. Time passes more slowly for the one who keeps moving. They will age less quickly, their watch will mark less time passing, they will have less time to think,… For a moving object, time contracts.
What does that mean? To know that, you need to have two clocks at a place, then for one clock to move and return to that same place, so a comparison can be made. The only answer is that the reference point is where the two clock separated and were brought back together. In spacetime it is the straight line between the two events where time is maximum, and the speed relative to this line is the one that slows time. The question has no meaning if the clocks are not brought back together again.
Imagine phoning someone and asking what they are doing now. You cannot know what they are doing now, because the time the message arrives to you, it is no longer now. At best you can know what they were doing some very short time ago.
Rovelli claims that the fact that “now” does not exist for that other person, is the “most astounding conclusion arrived at in the whole of contemporary physics”. Asking what they are doing now has no meaning, and that our “present” does not extend throughout the universe.
So how far does our “now” extend? If we measure time in nanoseconds, our “now” is probably just a few metres. If it’s a 10th of a second, then our “now” can cover the entire planet. In this case we have a past, a future, and an expanded present between them. But the idea of a “present of the universe” is meaningless.
Rovelli describes special relativity as the discovery that the temporal structure of the universe defines an order between events that is partial, not complete. There exists an expanded present that is a set of events that are neither past nor future. So every event has its past, its future and a part of the universe that is neither past not future. The light cone that defines that expanded present is extremely brief (nanoseconds) and almost imperceptible. A common present does not exist, it is a structure made up entirely of light cones. The idea that the universe exists “now” in a certain configuration, and changes together with the passage of time is meaningless.
Take your time, and follow Rovelli…
The Loss of Independence
It is interesting to not forget that time (meaning “to divide”), only started to organise our lives when mechanical clocks appeared (14th century Europe). But the clocks in bell-towers were set by sundials, which determined the moment when the sun was its midpoint, at that place. It was only with the telegraph in the 19th century that synchronising clocks started. Time zones appeared only in 1883. It was an intriguing detail, that Rovelli noted that Einstein, as a patent officer, dealt specifically with the synchronisation of clocks for railway stations.
Rovelli also noted that for Aristotle, time was the measurement of change. He believed that if nothing changed, there was no time. Newton would contend that another time existed, a “true” time that passes regardless of things and of their changes. This “true” time is not directly accessible, only indirectly, through calculation.
Which is a more efficient description of the world?
Time is “absolute, true and mathematical”. Rovelli comes into his own with the little side stories, namely that Leibniz dropped the “t” because he believed in the nonexistence of absolute Newtonian time “t”.
What is There, is about space, just as “when” is about time. Aristotle apparently defined “space” or “place” of a thing, as “what surrounds that thing”. Newton introduced “absolute, true and mathematical” space in itself, which exists even where there is nothing. So for Newton there could be “empty” space. Aristotle argued that between two things there is always something, not nothing.
Today there is no experimental evidence to support the existence of “absolute, true and mathematical” space.
Einstein would argue that time and space, beyond tangible matter, do exist. They are real. But they are not absolute, and not independent from what happens. They are made up of fields.
Fields that form, for example, the texture of electromagnetism, but also there is a gravitational field. A texture that forms spacetime. So Newton was right, a field exists even without matter. Its stretching and bending is the origin of the force of gravity, and is called curved spacetime. But Newton was wrong is thinking time was independent from things, and Aristotle was right is saying that “when” and “where” were always located in relation to something.
The Quanta of Time
Rovelli’s pet topic is quantum gravity, and in particular loop theory. A theory set in opposition to string theory.
But it looks looks some concordance exists, and it would appear that our nice spatio-temporal sheet has been replaced with the idea that there are a myriad of times, but they can only have certain values. Rovelli mentions “granularity, indeterminacy and relational aspect of physical variables”.
Granularity means that time can only have certain values, i.e. Planck Time. This is incredibly small, and unmeasurable today. This idea of quantisation of time also implies that certain values of time don’t exist. So time does not flow uniformly, and a minimum of time does exist. This does not sound so stupid, since everything, even light, appears to be made of bits, and the idea of continuity was invented because we could not see the bits.
And not to out done, there is a Planck Length, a minimum length below which it becomes meaningless. It also is an incredibly small length.
Indeterminacy means it is not possible to predict “where an electron will appear tomorrow”. Until it is seen (detected) it has no precise position, it is in a “superposition”.
Like the electron, spacetime can be a “superposition” of different configurations. This can mean that the difference between past and future can fluctuate, e.g. and event can be before and after another event.
Relations, means fluctuations that occur when something materialises only in relation to another physical object, e.g. an electron hits a screen, or collides with a photon. The idea is that the “cloud of probability” collapses, and an election materialises at a point on the screen, etc. More telling is that the collision is in fact between two clouds of probabilities “a superposition of configurations” that their collapsing into a particular configuration is determined in relation to a third object.
I’m now going to tread carefully. For it would appear, just as the electron and the screen, time and space also behave in the same way. The gravitation field that determines duration and physical intervals is not only influenced by masses, it is also a quantum entity that does not have determined values until it interacts with something else.
And “when it does, the durations are granular and determinate only for that something with which it interacts, but they remain indeterminate for the rest of the universe”.
It would appear that spacetimes (plural) fluctuate, superimpose one above the other, materialising at certain times with respect to particular objects.
So there is no single time. there are different durations for every trajectory, and time passes “at different rhythms” according to place and according to speed.
It is not directional, and the difference between past and future does not exist in the elementary equations of the world. Its orientation is merely a contingent aspect that appears when we look at things and neglect the details.
The substratum that determines the duration of time is not an independent entity, different fro the others that make up the world. It is an aspect of a dynamic field.
And does not exist below a minimum scale.
PART TWO - THE WORLD WITHOUT TIME
The World is Made of Events, not Things
So in dumping singularity, direction, independence, the present, and continuity, at least Rovelli keeps the world as a network of “events” that “occur”.
Nice touch, a kiss is an event, not a thing.
Equations that don’t include time, does not mean they are frozen. It just means that events don’t occur in an orderly fashion. Equations include variables that change in relation to each other, our world is one of impermanence.
Events are spatially and temporally delimited. Some types of things, like a stone, are just long events. It’s a complex vibration of quantum fields, that keeps it shape, before eventually disappearing in dust.
And we will understand the world by studying change, and not things. Newton’s mechanics, Maxwell’s equations, quantum mechanics, etc. describe how events happen, not how things are.
Dynamics as Relation
We must look to quantities and properties that we see continuously changing. Some quantities change regularly with respect to others. Rovelli looks for “a theory that tells us how the variables change when others change”. This is not time, it’s just relations between variables.
Events happen, change occurs, but not in an orderly succession, the temporal structure of the world is more complex. Temporal relations between events exist, but at the same time, the world without a time variable is not a complicated one. It’s a net of interconnected events, where variables in play adhere to probabilistic rules. which we know for a good part how to write.
Rovelli’s loop gravity includes no time variable. The variables describe fields that form matter, photons, electrons, other components of atoms, and the gravitational field.
The fields manifest themselves in granular forms, elementary particles, photons and quanta of energy, or rather “quanta of space”. These elemental grains form space. The spatiality of the world consists of a web of interactions. Interactions that do not dwell in time, but only exist as incessant interactions. This interaction is the happening of the world, it is the minimum elemental form of time, that is neither directional nor linear.
It does not have a curved or smooth geometry, and quanta manifest themselves in the interaction. The probabilities that something will happen depend on the occurrence of something else.
There is no complete geometry of everything that happens, because things that happen are triggered by interactions with the physical system involved in the interaction.
You cannot look at this world, because there is no outside to it.
The elemental quanta of the gravitational field exist at the Planck scale, they are the elementary grains that in interacting determine the extension of space and the duration of time.
Spatial adjacency tie the grains of space into webs, in “spin networks”. A ring in the spin network is called a “loop”.
The webs transform into each other in discrete leaps, becoming structures called “spinform”.
These leaps appear to us as the smooth structure of spacetime. On a small scale, the theory describes a “quantum spacetime” that is fluctuating, probabilistic and discrete.
So the idea is that space and time are not containers, but are approximations of a quantum dynamic that knows no space nor time. There are only events and relations (between events).
PART THREE - THE SOURCES OF TIME
Time is Ignorance
Complex things emerge from a much simpler world. time emerges from a world without time.
Thermal molecular mingling, never changes the total amount of energy in any isolate system.
Between time and energy there is close bond. Knowing the energy of a system, and how it is linked to other variable, is the same as knowing how time flows. And energy is conserved in time, it cannot vary, even if everything else varies. Thermal agitation is just a series of configurations that always have the same energy.
The classical arguments is that a macroscopic state is defined by the energy, which is defined by the time.
But its possible to say that our blurred view of a macroscopic state, is a mingling that preserves energy, and this generate time.
Rovelli stresses that a macroscopic state chooses a particular variable that has some of the characteristics of time. Time is just the effect of blurring. The number of possible microscopic configurations is entropy, and the blurring of those configurations itself determines a time, a “thermal time”. That microscopic “thermal time”, when related to the thermodynamics of macroscopic states, resembles what we usually call “time”. But it is not a universal time, it is simply due to the blurring, or incompleteness of a description.
When an interaction renders a position of a molecule, the state of the molecule is altered. The same applies for speed. What materialises first is speed, then position. But the order matters, and a particles state is different if its velocity is measured first, then its position. This is called “non-commutativity” for quantum variables, because position and speed, “do not commute”.
Non-commutativity determines the order, and has a germ of temporality in determining two physical variables.
It would appear that the time determined by macroscopic states and the time determined by quantum non-commutativity are aspects of the same phenomenon.
The intrinsic quantum indeterminacy produces the blurring, thus ensuring that the unpredictability of the world is maintained, even if it were possible to measure everything that is measurable.
This blurring and indeterminate image of reality determines a variable, thermal time. This is tied to thermodynamics, and hence to heat. But it does not yet distinguish between past and future, it has no direction, and lacks flow.
Perspective
The entire difference between past and future may be attributed solely to the fact that the entropy of the world was low in the past.
Our vision is blurred, because we can only see an infinitesimal part of what actually is happening around us. From this blurring, the concept of heat and entropy are born, and these are linked to the flow of time. Entropy depends explicitly on blurring. It depends on what we can’t register, because it depends upon the number of indistinguishable configurations. Entropy is not arbitrary, it’s just relative, like speed.
Entropy also depends on the way we are blurring the world, and that depends on the variables of the world we interact with. The entropy of the world in the far past appears very low to us. This could be simply because we interact with the world through a very small number of variables. We determine the particular macroscopic description we use, and the lower entropy of the past universe might be more down to us than to the universe itself.
The low initial entropy of the universe might be due to the particular way in which we (our physical system) interact with it. It may just be our particular subset of the universe that is orientated in time.
Objectivity is a good thing in science, but it maybe useful to view the universe from our particular perspective (our point of view). “Indexicality” is when words have different meanings every time they are used, depending on where, how, when, and by whom it is used. The idea is that we should not confuse the temporal structure of the world “as seen from outside”, with what we observe as part of it (within it). From within we interact with only a small number of the variables of the universe. What we see is blurred image, which suggests that the dynamic of the universe is governed by entropy, which measures the amount of blurring (as we see it).
To summarise so far…
So at a fundamental level, the world is a collection of events not ordered in time.
These events manifest relations between physical variables that are, a priori, on the same level. Each part of the world interacts with a small part of all the varia-bles, the value of which determines the state of the world with regard to that particular subsystem.
A small system S does not distinguish the details of the rest of the universe, because it interacts only with a few among the variables of the rest of the universe. The entropy of the universe with respect to S counts the (micro) states of the universe undistinguishable by S. The universe appears in a high-entropy configuration with respect to S, because (by definition) there are more microstates in high-entropy configurations, and therefore it is more likely to happen to be in one of these microstates.
As explained above, there is a flow associated with high-entropy configurations and the parameter of this flow is thermal time. For a generic small system S, entropy remains generally high along the entire flow of thermal time, perhaps just fluctuating up and down, because, after all, we are dealing here with probabilities, not fixed rules.
But among the innumerable small systems S that exist in this extraordinarily vast universe where we happen to live, there will be a few special ones for which the fluctuations of the entropy happen to be such that at one of the two ends of the flow of thermal time entropy happens to be low. For these systems S, the fluctuation is not symmetrical: entropy increases.
This growth is what we experience as the flowing of time. What is special is not the state of the early universe: it is the small system S to which we belong.
It is the law announced by Clausius, ∆S ≥ 0, and deciphered by Boltzmann that is guiding us: entropy never decreases. Having lost sight of it, in search of the general laws of the world, we rediscover it as a possible perspective effect for particular sub-systems.
What Emerges from a Particularity
If energy is conserved, why do we constantly need new energy?
The truth is that there is plenty of energy and it is not consumed. It’s not energy that the world needs in order to keep going. What it needs is low entropy.
Energy (be it mechanical, chemical, electrical or potential) transforms itself into thermal energy, that is to say, into heat. It goes into cold things, and there is no free way of getting it back from there to reuse it. In this process, the energy remains the same but the entropy increases, and it is this which cannot be turned back.
The second law of thermodynamics demands it.
What makes the world go round are not sources of energy but sources of low entropy. Without low entropy, energy would dilute into uniform heat and the world would go to sleep in a state of thermal equilibrium. There would no longer be any distinction between past and future, and nothing would happen.
Near to the Earth we have a rich source of low entropy: the Sun. The Sun sends us hot photons. Then the Earth radiates heat towards the black sky, emitting colder photons. The energy that enters is more or less equal to the energy that exits. Consequently, we do not generally gain energy in the exchange (gaining energy is global warming). But for every hot photon that arrives, the Earth emits ten cold ones, since a hot photon from the Sun has the same energy as ten cold photons emitted by the Earth. The hot photon has less entropy than the ten cold photons, because the number of configurations of a single (hot) photon is lower than the number of configurations of ten (cold) photons. Therefore, the Sun is a continual rich source of low entropy.
Where does the low entropy of the Sun come from?
From the fact that, in turn, the Sun is born out of an entropic configuration that was even lower, i.e. the primordial cloud from which the solar system was formed had even lower entropy. And so on, back into the past, until we reach the extremely low initial entropy of the universe.
But the increase in the entropy of the universe if not rapid, like the sudden expansion of gas in a box. It is gradual, it takes time.
A pile of wood, for example, lasts a long time if left alone. It is not in a state of maximum entropy, because the elements of which it is made, such as carbon and hydrogen, are combined in a very particular manner (ordered) to give form to the wood. Entropy grows if these particular combinations are broken down. This is what happens when wood burns, its elements disengage from the particular structures that form wood and entropy increases sharply (fire being an irreversible process). But the wood does not start to burn on its own. A pile of wood is in an unstable state until something comes along to make it burn, it does not collapse. The flame is a process that opens a channel through which the wood can pass into a state of higher entropy.
There are situations which impede and hence slow down the increase ot entropy throughout the universe.
In the past, for instance, the universe was largely an immense expanse of hydrogen. Hydrogen can fuse into helium, and helium has a higher entropy than hydrogen. But for this to happen a star must ignite for hydrogen to begin to burn into helium. What causes stars to ignite? Another process that increases entropy, the contraction due to gravity of one of the large clouds of hydrogen that sail throughout the galaxy. A contracted cloud of hydrogen has higher entropy than a dispersed one. But the clouds of hydrogen are so vast that they take millions of years to contract. Only after they have become concentrated do they manage to heat up to the point that triggers the process of nuclear fusion.
The ignition of nuclear fusion opens the door that allows the further increase in entropy, hydrogen burning into helium.
The entire history of the universe consists of this halting and leaping growth of entropy. It is neither rapid nor uniform, because things remain trapped in basins of low entropy until something opens a door on to a process that finally allows entropy to increase. The growth of entropy itself open new doors through which entropy can increase further. Over the course of this irregular trajectory, large or small portions of the universe remain isolated in relatively stable situations for periods that can be very prolonged.
Living beings are made up of similarly intertwined processes. Photosynthesis deposits low entropy from the sun into plants. Animals feed on low entropy by eating. Inside every living cell, the complex web of chemical processes is a structure that opens and closes gates through which low entropy can increase. Molecules function as the catalysts that allow the processes to intertwine, or, conversely, they put a brake on them. The increase of entropy in each individual process is what makes the whole thing work. Life is this network of processes for increasing entropy – processes which act as catalysts to each other. It isn’t true, as is sometimes stated, that life generates structures that are particularly ordered, or that locally diminish entropy. It is simply a process that degrades and consumes the low entropy of food. It is a self-structured disordering, no more and no less than in the rest of the universe.
I’ve copied a large portion of the book in this last section, because it serves as a kind of reminder where Rovelli is going.
I will admit my mind started to drift with the last three chapters. In part because I felt that Rovelli was musing, and I did not want to become even more confused.
