On Time and Entropy

(and everything inbetween)

Many people when asked to define time would say something along the lines of “How long something takes to move from A to B?” But what does that mean, anyway? Define “long,” then. Is it a unit of distance? That can’t be because time is not distance (or are they inseparable?). So, what does time mean, then? More specifically, what does it mean to me? It’s a valid question, as historically in the eyes of physics, time is not as absolute as was once thought.

To me, our definition of time is inextricably linked to our own flawed sensory perception of the world around us. You see, time does not exist in and of itself outside of the spatial dimensions. Does time move in one “direction” uncompromisingly wayward as an arrow? No. Time is no tangible thing but we perceive it in relation to tangible things. Clocks are the universe’s time keepers. But no matter how you build them or look at them, they are just devices built with repetitive motion. The “time” or interval between complete cycles is called the unit “time.” But really, it’s a physical phenomenon that exists only in the spatial dimensions. An atomic clock pretty precisely repeats its oscillations, such that it repeats the same movement in the spatial dimensions with exact distance. There is no inherent absolute time in the universe. This is part of Einstein’s special relativity that did away with the Galilean concepts of a master clock. Any physical phenomenon taken from an inertial frame will be spatially dependent on the position of the observer. Einstein’s time dilation equations are as good as any example to evidence this.

So…Here’s a thought:

If all matter in the universe is at rest, does any time pass?

Are we frozen in time like a paused movie or has the universe just ceased to change spatially whilst time keeps trudging along, well, forever? These two situations depict a reality in which time is spatially dependent and one in which it is spatially independent, respectively. I advocate the former — that a universe at rest means the end of time. This is why time and space are inseparable.

So, if you can define the spatial dimensions as the way matter is arranged in the universe and their topographic relation to each other and you take it face value that no two things can be in the same place in the same inertial reference frame*, then perhaps “time” is just the “order” in which matter progresses throughout the universe.

Of course, this brings up many complications such as: what keeps the sequence of matter in the universe from going in reverse? If the laws of physics guide how matter moves, perhaps, the single guiding rule that holds dominion over everything in the universe is that the universe can only proceed toward ever increasing entropy. Perhaps this is our notion of “time,” and the only law governing the direction of the state of matter and energy in the universe.

To elucidate this a bit further, for myself and others. The second law of thermodynamics states that universal entropy must always increase. Even if one can describe a system whereby entropy decreases such as certain nonspontaneous reactions with the right temperature, the second law still holds because it talks about Universal entropy. It all depends on where you draw your system boundaries as to whether your system obeys the second law or not, but the universe always does. It is like achieving a process of greater than 100% efficiency. It’s impossible.

Thus, to imagine this a little further, allow me to draw a diagram. Imagine we are starting with a universal inertial reference frame.

For clarity, let us define a few parameters concerning these diagrams. Each individual snapshot is an inertial moment or reference frame. The yellow-green-neon band will be called a “permutation.” This is one possible subset of eventualities in which the universe can progress whilst following the laws of physics. This is what I propose most closely fits with our definition of “time.” Let us differentiate this from another concept which I will arbitrarily call a “combination” which can be thought of as the middle collection of frames. These are individual possibilities originating from a previous frame. However, they are not simultaneously possible as these are time-independent and thus, simultaneity would infer objects being in the same place at the same time. Lastly, the starting reference frame (our current reality — in yellow) is part of a combination of other possible reference frames. It is just depicted in isolation for clarity of conveyance.

Does this definition of “time” hint toward multidimensionality?

If so, is there a physical bridge between dimensions? And, if we are to select this instant as our initial reference frame, what does that say about all of the reference frames that came before it and those which will come afterwards? Is there a universal pattern?

To begin to answer these questions, we would need to have an idea if multidimensionality and crossing dimensions are possible or not. We would need to rely on empirical observations and experimentation which up until now has yet to detect multidimensionality. So maybe we will never know if these ideas are possible or not. But we can still ask ourselves, what would it “look” like if they were true and what would be the consequences?

Let us go back to the inertial reference frame at this instantaneous moment. If this is the current state of affairs in the universe (our starting inertial frame), then what law(s) guide the way matter and energy interact from here on out? What overarching commandments decide why, for example, a chemical reaction will occur instead of not occurring? I postulate that all possible eventualities in the universe, taken from an initial reference frame must obey only these two laws:

The progression of matter and energy in the universe that follows from a starting inertial reference frame must proceed such that**:

1. It follows the second law of thermodynamics.

2. It follows all other known and unknown laws of physics.

This might at first sound like I am pulling off a hat trick. Of course the universe will act insofar as to follow the laws which guide it! Why separate the laws of physical into the second law and them “all others?” Certainly this is a logical fallacy, circulus in probando. But I would implore there’s something to be learned from this.

To start, of all the possible arrangements of matter and energy in the universe (we can trivially define as close to infinite) we can only know one inertial reference frame for sure: the one we are on***.

So what do the past and future “look” like? First let’s examine the case of the latter. Since we defined the laws that guide our possibilities, a curious case emerges.

I have heretofore defined entropy loosely as synonymous with disorder or randomness. Let us delve deeper into what it means and its repercussions on this diagram. Entropy is a thermodynamic quantity that represents the unavailability of a system’s thermal energy for conversion into mechanical work. Thus, as the universe progresses (it helps to think of this as time in the usual way we perceive it) and entropy increases, less and less thermodynamic “free energy” is available to do work and thus, we reach the eventuality of the “heat death” of the universe whereby temperature differences or other processes may no longer be exploited to do work. Thus, in the future, as the universe increases towards maximum entropy (thermodynamic equilibrium), our possible inertial frames dwindle down to just one. This is what that would look like:

Eventually, abiding by the laws of physics and the second law of thermodynamics, we will reach a “final” inertial reference frame in which no other possibilities of arrangement of matter and energy in the universe are possible.

If this is true, does it mark the end of the universe? And if this is indeed the “end” of the universe, then what was the “beginning”?

Conclusions

If one follows logically that abiding by the second law and all other laws of physics will arrive to a single inertial reference frame, the “heat death” of the universe, then it should follow that there were infinitely many inertial reference frames at the “beginning.” There is no reason to assume that the same physical laws which guide us from our current reference frame to the last were different in the past. Thus, working your way backwards, you may assume that universal entropy, and thus “randomness,” which can be taken loosely as the total number of possible inertial reference frames in one instant (a “combination”) must have been infinite at the very beginning.

If the beginning of the universe held infinitely small entropy and the end of the universe holds infinitely large entropy, maybe we have it wrong in the first place.

Maybe they are not beginnings and ends at all.

Maybe they are cyclical. Perhaps infinitely large and infinitely small are the same thing. I like to think of it much like asymptotic graphs, which your professors would always tell you increase ever so closely to a “limit” (as if imposed by a God) but never actually reach it because then all the math breaks down. Maybe, just maybe, depending on the dimensionality of the universe (10-dimensions as per string theory, but who knows), the beginning and end of the universe are the same thing. Perhaps multidimensionality exists. Perhaps we are living, as if on a lower dimensional surface on an even higher-dimensional reality (perhaps infinite as well).

My conclusions are not novel, at least not in the sense that they are groundbreaking science or even philosophy. My conceptualization, at least to my understanding, is compatible with our current understanding of the universe. My only goal in this essay was to shed a little bit of light on the concept of “time” and how I, for one, understand it.

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*An inertial reference frame is a time-independent frame of reference that describes space-time homogenously and isotropically. Think of it as a ‘snapshot’ of the universe.

** These two laws can really be summed up into one, but they are kept separate in order to emphasize something.

***Assuming an ideal world, in which we could detect and measure all known matter and energy in the universe

NORBERT WEINER ON ENTROPY.

In Gibb’s Universe order is least probable, chaos most probable. But while the Universe as a whole, if indeed there is a whole Universe, tends to run down, there are local enclaves whose direction seems opposed to that of the Universe at large and in which there is a limited and temporary tendency for organization to increase. Life finds its home in some of these enclaves.

Until next time… SEE YOU, SPACE COWBOY…