The laws of physics imply that the passage of time is an illusion. To avoid this conclusion, we might have to rethink the reality of infinitely precise numbers. If numbers cannot have finite strings of digits, then the future can never be perfectly preordained.
We feel as if we travel through perched exactly on the border between past and present, yet the present has no definite or specific structure within the laws of physics. Einstein combined time with space, as an extra dimension, with the three dimensions contained in the latter.
This is a point that bugs me: a dimension is a degree of freedom, by which we mean you can travel this dimension freely without altering your location in the other dimensions, however, we cannot travel time freely, meaning it does not offer us the required degree of freedom, so, is it really a dimension? Would treating time as something other than a dimension help us understand it better?
From this we get the space-time continuum, which acts as the background upon which dynamic processes play out.Einstein's equations present us a (block) universe where everything that is going to occur is effectively decided from the beginning (the initial conditions), leading him to purport that time is an illusion. Most physicists accept Einsteins predetermined time, as it falls directly out of General Relativity. The problem, is that Quantum Mechanics, as with gravity, does not quite agree with the classical perspective on time:
Classical Mechanics focuses on physical systems that are deterministic, and reversible. By deterministic, what we mean is that there are a set of logical rules that allow you to derive the state of the future, given its current state. By reversible, we mean that given the state of the system at some point in the future we should be able to derive the state of the system at some point in the past.( from [[The Nature of Classical Physics]])
At the quantum level, there are events that distinguish the past from the future, such as the collapse of the wave function, which makes the past and future around a measurement asymmetrical, and thus represents an irreversible change (or rather, a change that removes the reversibility of the system being observed). Also, because quantum mechanics are probabilistic, there are natural side effects that make time operate, behave, or appear probabilistically, as opposed to the deterministic nature of time in classical systems.
If we have a particle that is in a number of states simultaneously, we can't speak about the temporal nature of any of these states relative to a particle, because we can't say when any given state is inhabited by the particle.
Kant says (roughly) two different times must be successive, however, if we have a particle in two different states, at the same time, we have two different times coexisting, which isn't possible according to Kant's perspective on time as an intuition, or form of knowing. Recently, Swiss physicist Nicolas Gisin published a number of papers attempting to clarify the issue around time, claiming that the issue is largely a mathematical problem, returning to an old mathematical language referred to as Intuitionist Mathematics, rejecting the idea of numbers with infinitely many digits.
To Gisin, it becomes clear that time really passes, and new information is created, but also, this formalism dissolves the deterministic nature of time in Einstein's equations, allowing for a more probabilistic process to step forward.
In short, if numbers are finite and limited in their precision, then nature is imprecise, and thus unpredictable. This, however, raises a semantic question about whether or not the highest level of precision achievable by nature can be considered imprecise, when compared to our "synthetic" precisions.
Gisin came upon the realization that the deterministic representation of time afforded us by Einstein contains an implication that information is infinite.
Given a weather system, one of many complex-systems that we interact with, we know we can only predict it's behaviors in the future for so long, before it becomes unpredictable, however the classical nature of this system (not being small enough to be subject to quantum uncertainty), means that technically, we should be able to predict it if we could amass the information of all the components with the necessary precision.
The universe, being the next step, is a bigger system, with its own initial conditions, that, in order to predict everything that happens (or be the determinants of), would have to be infinitely precise in their measurements of the initial conditions.
There's some connection between infinity and everything that I think should be pointed out: everything is a kind of infinity, so in order to exactly control everything, or rather be responsible for the fine-ness of everything we experience, would require infinite precision.
The problem arising here is that information has a physical aspect, and requires energy and space for its existence. A specific volume of space, has a limit with regard to the amount of information it can hold. The densest information storage occurs within singularities, such as the one that birthed our universe. However, infinite information would require more space than is available within the singularity preceding the universe.
The Logic of Time
While acceptable in modern times, the advent of infinite numbers after decimal points was not warmly received when the idea was first put forth. Hilbert was in support of the idea, where as LEJ Brouwer felt that Mathematics was a construct, and as such, numbers are finite, their digits being the result of calculation or random selection, one at a time.
Brouwer also felt that numbers are processes, and can become ever more exact as digits reveal themselves via choice sequences.
Brouwers intuitionist take on mathematics has a pronounced effect on the field as we know it, the most outgoing of which is the removal of the excluded middle.
The law of the excluded middle is a law of classical logic, claiming that only one statement from and is necessarily true, and that the other is necessarily false.
This seems to be about speaking about the present as the boundary between two sets of times, that can not coexist, because the future, can not be the past- for any given present they must reside on either side of the present.
"Two different times must be successive, not coexistent, just as two different spaces must be coexistent, not successive." #Kant
A real number with infinite digits can't be physically relevant. - Gisin
Let's say and that we can derive further digits via choice sequences.
At this point, the sequence might only return 9's, in which case, at some point, the value will converge on exactly . However, if a number other than 9 pops up in the sequence, then x is less than , however, we won't know that until this digit is revealed. Thus we can never exactly say that x does, or does not equal .
If you try to cut the continuum in half, this number x is going to stick to the knife, and it won’t be on the left or on the rightThe continuum is viscous; it’s sticky. - Gisin.
Hilbert felt that the removal of this law was equivalent to handicapping a boxer, but the mathematical framework that called for it intrigued some of the greatest minds of the time, such as Gödel, and Hermann Weyl.
The Unfolding of Time.
Gisin and Posy noticed a connection between the digits of numbers in resulting from a choice sequence, and the physical notion of time, with materializing digits seeming to map on to the sequences of moments that comprise the present, and that the future being undecided, is the same as not being able to quite say whether or not
The lack of the law of the excluded middle is akin to indeterministic propositions about the future.
Gisin and another collaborator have reformulated (some) of [[Classical Mechanics]], with the same predictions as Newton, save for events being indeterministic, providing the conditions for uncertainty and [[The Arrow of Time]].
In this framework, the reason we cannot predict the behavior of chaotic-systems, such as weather systems, is that they're not the result of predefined initial conditions, that are precise down to Planckian levels, but rather the values that dictate their behavior precisely are chosen in real time: this means the future is "open", and that time is a creative unfolding, where "the new digits really get created as time passes".
Other physicists, such as Fay Dowker, are appreciative of Gisins efforts, agreeing that physics doesn't exactly line up with our experiences or intuitions, and that the nature of the mathematics we use to describe phenomena influences our understanding of time, and the prominence of Hilberts influence, "...is certainly static. It has this character of being timeless, and that definitely is a limitation to us as physicists if we're trying to incorporate [a new explanation] for something that's as dynamic as our experience of the passage of time."__ This also somewhat points to the issue of stagnation in physics.
Dowker is focused on the relationship between [[Quantum Mechanics]] and [[Gravity]], which is linked to time via [[Einsteins]] Theory of [[General Relativity]], and thinks this new perspective on time, may be useful in bridging the two main physical theories of reality, which to date, have been irreconcilable with each other.
Generally, like all other forces, at the sub-atomic level, gravity is negligible, as particles have very little mass, however, unlike the other forces, who "disappear" at the macro scale, gravity increases as objects become larger, and also is unquantized, or lacking in discernable quantum properties.
A main issue is the fact that [[General Relativity]] is a system based on [[Classical Mechanics]], yet [[Quantum Mechanics]] puts us in a situation where we have to ask, from where does a particle, that can be in two places at once, attain its gravity? The answer to this question is often called a [[Theory of Everything]] or a Theory of Quantum Gravity."
Quantum Uncertainty and Time.
The requirements for physicists, as far as solving the mystery of time are resolving the ultimately quantum nature of reality, and the classical nature of the space-time continuum. In QM, time is strict, and not flexible in the way that time is from the perspective of relativity, which states that time is not absolute for two observers, depending on certain conditions. Furthermore, making measurements in QM, results in the collapse of [[Wave Functions]], which makes time asymmetric, as the state of the location of observables are markedly different on either side of this collapse event. #Also, this collapse event interferes with the reversible determinism put forth by classical mechanics: if we're given a particle, and a definite location, post measurement, this doesn't give us any information about where the particle was prior to this point in history.
This is particularly disturbing because it seems to imply a real world loss of information, which violates the law of conservation.
While most physicists interpret quantum mechanics as a revelation that nature is indeterministic, some keep the deterministic, classical presentation of time alive, via the [[Many Worlds]] interpretation.
[Gisin, rather than trying to make QM deterministic, is attempting to provide a non-deterministic language for both classical and quantum phenomena.
The law of conservation treats information as something that can neither be created or destroyed, but via the addition of new numbers, related to the state of the universe, and the re-definition of this state over time, new information is being created.
This new perspective on time, and information, may help deal with the [[Black Hole Information Paradox]], because if it is possible that information is being created, it may well be possible that it's being destroyed. It seems particularly likely that there's a connection between movement through time, and the creation/destruction of information, as navigating the spatial dimensions doesn't seem to imply anything about the nature of information, whereas time does.
Another benefit of IM, is that it allows for a shift in our understanding of the conscious experience of time, with the fact that we experience the present as thick, more like a range of points on a timeline, than the singular point it (perhaps, mathematically) is. This is very similar to the "continuum being sticky", with regards to decimals, hinting that it may be the same process that undergirds our perception of now: in short, time can't be divided in two cleanly- it's like cutting honey. While there's still a lot of work to do with this theory, it seems to have drawn mostly positive reactions from the community, offering novel ways of thinking about the problem of time, information, and the fundamental nature of reality.