Leonard Kelley holds a bachelor's in physics with a minor in mathematics. He loves the academic world and strives to constantly explore it.
Smolin’s take on relational theory still blows my mind. Most would reasonably agree that the world is comprised of things and processes that happen to them. Vague, but technically right…right? Well, a thing is just a collection of objects that are all moving themselves in some fashion, so nothing is ever truly stationary. Nothing is just there, existing as a static object, but seems to be because of the convenience of using slices of time as we describe reality. But all things continue on, therefore how can we really talk about a thing?
Really, it’s just a collection of processes that we group based on the illusion of instant time slices. We perceive an illusionary reality, but only partially so. Instead of a classical reality, we have a world full of events which are the “smallest unit of change,” and isn’t tied to any specific object. It is a fundamental. How the events are connected to each other is what forms the relational universe, and an important relation between two events would be a causal relationship. Examples of this would be, “A implies B” or “C doesn’t imply D.” Time in a relational universe is crucial because it provides the storybook ordering of the events that lead to our current event (Smolin 50-5).
This is a universe where information is king, and the event is what transmits the information. This leads to an interesting implication courtesy of general relativity. Light cones are typically used as a visual for the range of space-time that information is conveyed, with the speed of light being the fastest method of information conveyance. Anything inside or on the cone has the potential to be causally related, but not over a continuous space-time as is typically depicted. Yes, our changes in events are still dictated by Einstein’s equations, especially those pertaining to gravity. The influence of gravity bends light rays, altering the shape of our cones. So, it therefore alters the causal events we are working with, but at what scale? (55-62).
If space-time were continuous then it could be at any scale from the massive to the tiny, making predictive power essentially nonexistent as we could develop any scenario to account for a casual relation. As it turns out, we cannot break time into an infinite number of units, for science has found absolute minimum values for things such as length and time. This is the Planck scale, which is ultimately a consequence of Planck’s constant (from quantum mechanics), the speed of light in a vacuum (from general relativity), and the gravitational constant (from Newtonian gravity) (Ibid).
According to the Planck scale, the absolute smallest length achievable is 10-33 cm and the smallest time unit is 10-43 seconds. This is huge (see what I did there?) because the Planck scale arises from the effects of quantum mechanics and gravity being on equal footing and also because it implies space-time isn’t continuous but discrete! (Ibid).
Going back to those light cones, we mentioned how anything on it or enclosed by it is causally connected, but gravity can bend and alter those paths. One of the best examples of this effect comes from black holes and their event horizons, beyond which we know nothing about the object. You can find out, of course, but it’s a one-way ticket. Once past that event horizon you will know what is there but will be unable to communicate it to the outside world. Does this viewpoint change at all in a relational universe? (70-3).
Well, we do have causally closed-off regions that we experience daily, for you and I are not privy to all the information we encounter on a daily basis. Black holes are just an extreme type of closed-off space. Another example is the expanding universe, especially post-inflation. During that period, something drove the universe to expand beyond the speed of light and then shut off, but that means certain parts of the universe are causally disconnected. We have thus established certain horizons which prevent information disclosure and this “are observer dependent concepts” (Ibid).
But black holes offer some other important insights into our relational universe, including am alternate justification for the discreteness of space time we proposed earlier as relationships and events. It is “the relationships that define the space, not the other way around.” The finite number of events and relationships hints at the discreteness we seek, but where is the experimental evidence to back this up? Enter thermodynamics, specifically entropy. Both were in terms of energy until the rise of quantum mechanics and atomic theory, where the motion of atoms and the conveyance of information led to revisions (95-100).
Temperature was the “energy of random motion” of the atoms while entropy was “a measure of information” pertaining to a system of particles. As a system progresses, the amount of information accessible to us diminishes, and in fact is a direct implication of an arrow of time. Entropy dictates possibly why time doesn’t go backward, for if it did then we could see events happening in reverse. If you go from less structured to more, it comes at the entropic cost of the larger scale, reducing the temperature elsewhere. No matter what, entropy reigns supreme (Ibid).
Now, apply temperature and entropic considerations to black holes. What does each mean in terms of black hole mechanics? It has been found that because of Hawking radiation that black holes do cool off over time as they evaporate away. And a radiating object must shrink. If something gets smaller then its surface area decreases, and for a black hole that has a direct correlation to entropy. That is because the surface of the black hole is a light cone, and so contains photons which govern information exchanges. All this point to “an atomic structure of space-time” which is discrete, for black hole thermodynamics and entropy give values based upon particle movement and so can be based upon events and relationships (101).
But before we get too far ahead of ourselves, a contradiction seems to appear when you think about black hole consumption behavior. As a particle is eaten by a black hole, we have removed something from its environment so around the black hole we have decreased entropy. Therefore, the entropy of the black hole should increase and because of entropy-surface area correlations the size should grow instead of shrink, right? It’s all about that space-time and the geometry of the black hole, for if it’s not continuous but discrete due to the motion of the atoms governing relationships and events then no entropic contradictions arise. Everything is still moving, it’s just that some of that info is in a hidden region and so entropic laws continue as expected (101-5).
Where else can this take us? I’ll continue to investigate and will report back here with any other new findings, so check back soon!
Smolin, Lee. Three Roads to Quantum Gravity. Basic Books, Great Britain. 2001. Print. -62, 70-3, 95-106.
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© 2022 Leonard Kelley