January 18, 2023 (Originally December 6, 2023)
I wrote this for a class, but thought I would add it here. I'm too lazy to fix the formatting errors, but maybe I'll come back to them later. I'm largely posting this after being inspired by Anson Ho's blog which I found very cool : )
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It explains the casualties within our universe and the concept of causality at all. As with many physical phenomena, the development from Newtonian to Quantum mechanics shakes up the principles we’ve come to understand about the universe. Statistical mechanics and quantum ideas propose that “the flow” of time could be symmetric and all events could be reversible.
What does this mean? Perhaps many of the theories that were once thought never to be possible, could be. For instance, the Penrose-Hawking Singularity Theorem posits a singularity that happens when massive stars cause gravitational collapse called a black hole. However, a variant suggests the theoretical existence of a White Star. In a black hole, light cannot escape, and with white holes, light cannot enter. As such, they can be considered black holes where time is reversed. With our current “Arrow of Time” model, this isn’t possible, but with statistical mechanics, it could be.
Beyond a better understanding of a key variable in the universe, there are philosophical motivations for exploring the arrow of time. Our ethics view “time” as a fundamental principle. What happened and when is what allows witnesses to give valid testimonies -- the fabric of our judicial system; it is the foundation of epistemology, and it gives meaning to hallmarks of how we live, plan and think.
It tides to the relativistic transitions within physics, where everything we understand is always concerning something else. It also is linked to the evolution of quantum mechanics and the probabilistic nature of our universe. All states that we exist in are perchance. And all other states remain a possibility; the odds just didn't work in their favour. Not everything in the universe is rational, but rather random, with the most “reasonable” events having a higher probability of occurrence.
It is probably beneficial to provide an overview of how our conceptions of time have come to be. In 50,000 BCE, we had the first inhabitants of Australia who believed in the interconnectedness of everything through time. The dead merely had souls that inhabited new living bodies, and it’s a very early allusion to the connectivity property of time being proposed today.
A more scientific frame came to be in 8,000 BCE with the lunar calendar in Scotland, which relies on months based on the phases of the Moon.[2] Then, the concept of hours was conceived alongside timekeeping in Egypt in 1250 BCE. A more formal understanding of the linearity of time began to cement itself, especially around 500 BCE.
Aristotle believed in before and afterness - a continuation of linearity. Time was countable and existed on a continuum, both of which were major properties - time could only appear through counting. Time could be understood through the amount of motion that was perceived.
In 1650, timekeeping established itself. Galileo proposed a pendulum clock that wasn’t fruitful in truly capturing time. Isaac Newton proposed the absoluteness, truthfulness and mathematical nature of time. There is an absolute time, and everyone perceives the rate at which passes to be the same at a steady state. This development happened in 1987. Then, the development of entropy helped solidify the notion of directionality when it comes to the concept. Entropy refers to the amount of chaos or “disorder” in a closed system and Carnot theorized that it must always increase but not decrease, which implies a directionality in time.
With Special Relativity and Einstein, the concept of relativity was unified with time, and it wasn’t absolute as proposed by Newton, with the exception of the speed of light. Then, the general relativity revolution proposed the interconnectedness of space and time, namely how they can be curved by mass in the universe and the existence of gravitational waves. Large masses like large stars can create singularities where they pull space-time down due to their heavy loads such that no light can escape.
In 1928, we started to question the single-directional nature of time. The physicist Arthur Eddington coined the term “arrow of time” and presumed it was connected to entropy. He posted that when the arrow of time is followed, we see more randomness in the state of the world (more chaos). Assuming chaos, randomness, and stochasticity could decrease, it was a product of moving backwards on the arrow of time. This measure of randomness was the sole physical identifier to determine whether the timing was moving forward or backward. As such, Eddington’s hypothesis links back to Carnot and the concept of entropy, specifically that the amont of chaos in a closed system or the universe could be expected only to increase and not decrease - the second law of thermodynamics. There is the condition that if you could go back in time, chaoticity would decrease; however, as long as this is not true, chaos can supposedly not decrease either.
In 1988, Hawking published “A Brief History of Time” it identified three different arrows of time: psychological, thermodynamic and cosmological. Psychological refers to our perception of time, the memories we consolidate and our human ability to think about the future; a thermodynamic arrow which relates back to entropy; and the cosmological conception which relates to how the direction of time is forward as the universe expands.
Emile Borel, in the 1920s, conceptualized that all arrows in the universe follow the same direction when referring to its subsystems like galaxies. Therefore, there is an “absolute direction” for the arrow of time in cosmology. Some questions arise in this entropic understanding of the arrow of time. For example, the Big Bang - linked with the conception of the universe itself was a highly entropic event that succeeded all events before it and as such, if there’s supposed to be a nondecrease in entropy, then the Big Bang and its entropy poses some questions.[6] Physicists, for the most part, have learned to take the Big Bang as a unique event because the second law of thermodynamics holds for the most part, but it’s a punctuated progression of entropy with the Big Bang.
With our understanding of the Big Bang, there’s also the hypothesized “Big Crunch,” which claims that the end of the universe will be when the arrow of time reverses, entropy and density increase, and the entire universe collapses. The Big Crunch is countered by the “Big Chill” or “Big Freeze” theory, which posits that the universe will expand forever and cool (decreasing in entropy).[7]
Therefore, it offers a timeline of the universe that is the reverse, starting with the Big Bang. This is a hypothesis that scientists believe to be untrue due to the accelerating, expanding universe and claim that heat death is a more probable event. However, it is still highly entropic, so it follows somewhat similar lines of thinking. The theory is associated with Alexander Friedmann, and his notions of the density of the universe.[8]
Another hypothesis is the idea of Cosmic Inflation, which can help to solve the “past hypothesis” problem pushed forth by Richard Feynman. The problem, as described previously, is related to the fact that entropy relatively decreased compared to the Big Bang. Cosmic inflation redefines entropy to have all other principles, which are related to heat particles, hold true. A higher-entropy case is where there’s a mixture of temperatures, and a lower-entropy state is one where they are more separate. Higher entropy is still the decrease in uniformity but is interpreted differently. The notion of direction is that it is difficult and statistically unlikely to have more uniformity where opposite ends of the temperature spectrum are separate, staying on their respective “sides.”[9]
Ultimately, the expanding universe, Hawking radiation, the ejection of extraterrestrial masses, its black holes, etc., amasses a large amount of entropy that keeps up with the understanding of thermodynamics.
Later in 2009, the paper Quantum mechanical evolution towards thermal equilibrium was published and ties into the thermodynamic conception of time that Hawking posits. It tries to explain the ergodynamic nature of dynamical systems like the universe. Ultimately, all microstates (possibilities) have an equal probability of occurring over a long enough time horizon. The implication is that in a system, every state has a chance of happening, especially if understood ergodically, where this probability is actually equal upon a final “heat death” when entropy reaches its maximum value. Ultimately, as a “physical system becomes entangled with its surroundings, it moves closer to equilibrium.” The one-way evolution of this universal property determines the direction of the arrow of time.
Another hypothesis starts with an understanding that the entire universe is a statistical event and there is not a single universe (or the only universe that exists isn’t the one we currently live in). As such, in these other universes, there are arrows of time that point in other directions. The proposed probability for an alternatively-pointing arrow is low,, but it remains possible within this frame of thinking.
However, we can refer back to statistical mechanics to conclude our understanding of why there isn’t a paradox. The second law of thermodynamics implies a high probability entropy will increase over time, but it’s not a certainty as with many phenomena described in the quantum era.
Einstein radically altered our perception of time with his theory of relativity. He proposed that time is not an absolute constant, but rather a variable dependent on factors such as velocity and gravity. Experiments have verified time progress inconsistently for observers in different reference frames, such as atomic clocks aboard satellites. This challenges the conventional view of time as a uniform flow experienced identically by all. Instead, relativity demonstrates time is relative, changing based on speed and gravitational forces, necessitating a reevaluation of our intuitive conceptions of time's continuity and invariance.
Examining the link between consciousness and temporal perception reveals intriguing connections between our cognitive processes and experience of time's passage. Studies investigating this connection suggest consciousness is pivotal in shaping our subjective timing. Theories propose neural mechanisms associated with awareness filter our sense of time's direction and progression. This prompts queries into how brain functions mould our understanding of time, illuminating the subjective nature of our temporal sensations and their potential impact on time's arrow.
Multiverse hypotheses present fascinating speculations regarding time's asymmetry across divergent realities. If parallel universes with varying laws exist, time's arrow may differ between these theoretical planes. This thought-provoking notion begets contemplation of how alternate domains could influence our comprehension of time's unidirectionality. It raises provocative questions about the possible effects of other worlds on the fundamental character of time, encouraging exploration of the multiverse concept's implications for our understanding of time's arrow.
As we understand, space exists in a vector space with magnitude in all directions; however, the same does not apply to time only moving in one direction as understood by its symmetry: T-symmetry or time-reversal invariance. More work is being done to test this empirically, and leaps in science allow for this to happen. Computer scientists, compared to physicists, think this is possible and use video as a tool for experiments: building an algorithm that can determine whether a given snippet of video is playing forward or backward, with an alleged 80% accuracy.[10]
The algorithm works by dividing a frame of video into many small squares and then dividing those into a 4 x 4 grid. From there, the direction and the distance of the small 4 x 4 grids are analyzed in terms of direction and distance across each frame. The training set consists of thousands of these 4 x 4 grids developed into better and better predictors that can determine whether a combination of words indicates motion going forward or backward. Ultimately, this is looking at time in a hyper-specific case with a proxy measure and doesn’t deal with it as a constituent of the universe, but it gives an analogy to how it could be measured in a cosmological context where motion isn’t (always) linear.
An image of the world can be built where every instance is a single frame: a slice of time that together makes up the universe's progression. Ultimately, frames are replaceable and must be played forward. When put together, you have a continuous representation of events happening. This helps us understand why we perceive the direction of time to be different, even if the equations that use time don’t make the differentiation. The individual frames might be the same, but their being played in succession contributes to our notions of experience.
This helps to cement the definition of the direction of causality with statistics. Ultimately, I understand when and if one factor affects something else. Events played in reverse make no sense because we cannot assess causality.
The concepts of uniformity and discreteness help to understand entropy. If you have milk and coffee as two separate things at an initial state and then you stir in the milk, you have increased the disorder as these two substances have combined. They become increasingly difficult to separate or rather be viewed in these separate forms or rather it’s in an “entangled state.” This reaffirms the asymmetry of thermodynamics.
Highly ordered states are improbable after time has passed and entropy increases, but they still remain possible. For example, if you had a deck of ordered cards that were shuffled, we understand that the ordered deck was likely the initial state.
There is the question of why we do not have an arrow of space and not time, especially since the universe is understood with the notion of “space-time,” and they are hyperconnected. Our universe in the 4-dimensional manifold that it is, perhaps we cannot use an “arrow” but rather some other form to describe directionality, but the question is largely unsolved.
Within philosophy, we grapple with eternalism, possibilism and presentism when it comes to time. Eternalism suggests that time helps to construct the universe, that it is the fourth dimension and that time is merely phenomenal. This is largely the view of the Endurantists.
Possibilists believe that the above is true. However, the future is merely possible and exists in probabilities. Compared to eternalism, it’s less deterministic about the state of the universe. This is largely the view of the Pendurantists.
Lastly, presentists believe that only what is experienced (temporally present) exists and is true, and therefore, there is only what exists now, not in the past and not in the future. Time is thus not an actual dimension or property since the universe doesn’t exist relative to it. There is a lack of continuity of time in this worldview.
Once again, we encounter this temporal asymmetry, where, at the very least, we perceive time to be moving in directions and it’s forward, and it’s also relative to our notions of the past through our memories, for example.
When thinking about causation, there’s the Grandfather paradox, which helps us understand why the directionality of time is an important consideration.
An aspiring killer’s grandfather has been dead for 30 years, and she wants to kill him. She comes across a time machine and is able to go back in time to see the grandfather she wishes to kill. In this universe, if her grandfather is killed, then the entire bloodline would cease to exist, including her. Therefore, if she’s never conceived, then how could she return to a universe where she exists? Assuming there are multiple universes, with multiple arrows of time, then the paradox is solved. In a case where there isn’t, the entropy of the system decreases when she successfully kills her grandfather: the universes with a dead grandfather that she killed and one where she did not exist separately. There is a question of whether moments in time that have already passed are separable and can reduce to a lower-entropy state. History remains consistent normally, and a paradox arises. This has been studied by Hawking with his Chronology-Protection Conjecture which argues for the (forward), unchanging direction of times and events that have passed without many worlds.
With an understanding of causal loops where the cause and effect are indistinguishable or a cause seems to be uncaused (i.e. the chicken vs. the egg question, the start of the universe, etc.): physicists believe that backward causation just isn’t possible.
A closed timelike curve (CTC) is a path in spacetime, theoretically conceptualized, that involves loops back into their own past - similar to causal loops that deal with more real-world phenomena. It allows an object to return to an earlier time and encounter itself or events from its own past. CTCs often imply causal loops, where an event causes itself to occur, raising paradoxes like the famous grandfather paradox in time travel scenarios. These loops challenge traditional notions of causality by suggesting that an effect could precede its own cause, creating logical inconsistencies.
Looking to the future, there is significant work still needed to further develop mathematical models of statistical mechanics with varying assumptions about time's flow and directionality. Advancing these representations will help deepen our understanding of time as a phenomenon.
This paper aims to provide an overview of the evolving scientific conceptions of the arrow of time within quantum mechanics and relativity alongside perception wrapped in a philosophical lens. While traditional views hypothesized time as fundamentally moving in one direction, modern physics theorizes alternative possibilities ranging from bidirectional to multiversal flows.
Gaining a broader perspective on time that acknowledges these alternative theories has important implications. It challenges us to reexamine default assumptions ingrained since childhood. A more open perspective could inspire novel solutions to problems by considering previously unimagined options. Experiments exploring empirical tests of time's directionality may yield surprising results, further shifting paradigms.
Exploring time's nature through the lens of diverse scientific disciplines holds promise for gaining new fundamental insights. Collaborations between fields may help conceive fresh ways to experimentally scrutinize long-held models. Such progress could substantially impact our understanding of time as a baseline component of reality with yet untapped mysteries.
