Reading Date: Sep 29, 2022 ~ Nov 9, 2022
A present that is common throughout the whole universe does not exist
Physics describes how things evolve in their own time and how these times evolve relative to each other. Our present doesn’t extend throughout the universe. It is like a bubble around us. How giant this bubble is depends on how precise you define or sense the time difference.
The temporal structure of the universe is made of light cones. (Like what we learned in special relativity.) It defines an order between the events of the universe that is partial, not complete. The expanded present is the set of events that are neither past nor future. The spacetime does not have the order but can be distorted. Light cones tilt. The structure of the cones can even be such that advancing always toward the future and returning to the same point in spacetime (we can only advance to the future part of the cone).
The world is made up of events, not things. The fundamental physics theory doesn’t need to choose a privileged variable and call it “time”. It only needs to tell us how variables change with respect to each other. That is to say, what the relations may be between these variables. At the fundamental level, no special variable exists. (Wheeler-DeWitt equation)
Aristotle’s time v.s. Newton’s time v.s. Einsteins’ time, and to the quanta of time
Aristotle thinks that time is the measurement of change. It is our way of situating ourselves in relation to the changing of things. If nothing changes and nothing moves, then time ceases to pass, and there is no time. And so is the space Aristotle describes. It is relative and common.
Newton assumes the exact opposite. He thinks that there exists a true time that passes regardless, independently of things and of their changes. If all things remained motionless, this time would continue to pass. This true time he assumes is not directly accessible, and we can only obtain it through calculations. He also thinks that there is a space that is completely void, without any physical entity, even quantum particles.
Einstein took the synthesis of Aristotle’s and Newton’s thoughts on time and space. The time and space Newton had intuited the existence of, beyond tangible matter, do effectively exist. But they are in no way absolute, they are not different from the other substances of the world. They are not independent from things. This time and space is made up of field (gravitational field), just like other substances do, for example: light is made of EM field and electron is made of Dirac field.
The world is like a superimposition of canvases, like Dirac field, EM field, and gravitational field is only one among others. These fields can stretch and can jostles with the others. Because of the existence of quantum mechanics, the gravitational field, like all physical things, must necessarily have quantum properties: granularity, indeterminacy, and the relational aspect of physical variables.
The time and space measured are quantified. Time has a minimum interval of $10^{-44}$ seconds (Planck time) and space has a minimum interval of $10^{-33}$ centimeters (Planck length). It is not possible to predict time and space exactly, only possibilities. Spactime fluctuates too. The structure of light cones fluctuates at all points that distinguish among past, present, and future. This indeterminacy is resolved after interactions with something else.
Entropy and blurring
Entropy $S$, is a measurable and calculable quantity never decreases in an isolated process ( $\Delta S \ge 0$ ). Its nub is the fact that heat passes only from hot bodies to cold. This is the only basic law of physics that distinguishes the past from the future. Entropy also defines as $S = k \ln ( \Omega )$, where $\Omega$ is defined as number of configurations under a macroscopic state. The growth of entropy is nothing other than the increase of disorder.
Then what is configuration? For example, when we shuffle cards, we can always find some charactaristics that distinguish this card from others. Nothing is more special than the others if we look at all of its details (There will only be one configuration if we take everything into account). The notion of charactaristics or particularity only exist when we limit ourselves to notice only some certain aspects of the cards, which is seeing the universe in a blur vision. Entropy is the quantity that counts how many are the different configurations (microscopic states) that our blurred vision (macroscopic state we observed) does not distinguish between.
If we could take all the details into account, all microscopic state of the world, then there is no past and future. Since physical laws that link different times are symmetric between future and past, there is no sense of direction of time in microscopic state. The difference between the past and the future refers only to our own blurred vision of the world.
Time
Everything in the world becomes blurred when seen close up. Like clouds turn into fogs when we seen them close up. We think of things in terms of concepts that are meaningful for us, that emerge at a certain scale. Entropy, which comes from our own blurred vision, does not decrease give the direction of time. There is no sense of time in microscopic level, and time emerges from a world without time.
Knowing what the energy of a system may be is the same as knowing how things evolve (Hamiltonian mechanics), because the equations of evolution in time follow from the form of its energy. On the other hand, energy is conserved in time, and it is what we observed, a macroscopic state of equilibrium.
The usual way of interpreting time and state of equilibrium is to think that time is something absolute and objective; energy governs the time-evolution of a system; and the system in equilibrium mixes all configurations (microscopic states) of equal energy (macroscopic state). That is: to define macroscopic state, we first need to know energy, and to define energy we first need to know what is time.
We can think this the other way! Which is to interpret a macroscopic state as a mingling of microscopic states that preserves an enegry, and this in turns generates time. There is no privileged variable that acts like “time”. All the variables are on the same level, but we can only have a blurred vision of them described by macroscopic states. A macroscopic state (the blurred vision, which ignores the details) chooses a particular variable that has some of the characteristics of time. The blurring itself determines a particular variable called time. Time determines this way by a macroscopic state is called thermal time, and its behavior is the one most resembles to what we call time.
If we see from quantum system (microscopic state), how it determines a physical variable through “interaction” and the “noncommutativity” charactaristic of these interactions give a primitive form of the temporal order of this world. Due to this noncommutativity, the set of physical variables in a system defines a mathematical structure (von Neumann algebra), and there is an implicitly defined flow within this structure. The flow shown here and the thermal time have an extremely close relation. That is to say, the time determined by macroscopic states (thermal time) and the time determined by quantum noncommutativity (Connes flow) are aspects of the same phenomenon.
Thermal time is tied to thermodynamics (in equilibrium state). Since it does not distinguish the past and the future, there is no direction, it does not yet resemble the time we experience.
Our perspective and why does entropy never decrease (Carlo Rovelli’s answer)
The entropy of a system depends explicitly on blurring. The same microscopic configuration may be of high entropy with regard to one blurring and of low in relation to another. And blurring depends on actual, existing physical interactions, and it is a relative one. The entropy of A with regard to B counts the number of configurations of A that the physical interactions between A and B do not distinguish. That is to say, the entropy of the world does not depend only on the configuration of the world. It also depends on the way in which we are blurring the world, and this depends on what the variables of the world are that we interact with.
Why does the entropy never decrease or we can ask why does the entropy of the world in the far past appears very low to us? Perhaps it wasn’t the universe that was in a very particular configuration in the past (which holds low entropy), it is us, and our interactions with the universe, that are particular. How can a particular interaction between us and the rest of the world determine a low initial entropy? Perhaps it was in no particular configuration (low entropy). Perhaps we are the ones who belong to a particular physical system with respect to which its state can be particular. Think of it as a shuffled random deck of cards. If we look at the first six cards and commit them to memory, then we can see they are getting disordered.
Then why should there be such a physical system, in relation to which the initial configuation of the universe turns out to be special? Because in the vastness of the universe, there are innumerable systems and they interact with each other in ways that are even more numerous, there will surely be some that interact with the rest of the universe precisely with those variables that found themselves having a particular value in the past. It is unnatural to assume that the entire universe has been in a special configuration in the past, but there is nothing unnatural in imagining that the universe has parts that are special.
Similarly, there are physical systems that interact with the rest of the world through those particular variables that define an initial low entropy. With regard to these systems, entropy is constantly increasing. Therefore, the flow of time is not a characteristic of the universe, it is due to the particular perspective that we have.