This is an extract from the OPIP book. Previously, (B)obby argued to (A)lice that progress in physics may come from developing a better understanding of how human thinking could be flawed. Note: This post has the “Speculative Theories”-tag to indicate that what is being said should be taken with a grain of salt.
B: Humans tend to accept concepts as reality that have never been observed in practice. One such example is the endless extrapolation of phenomena, assuming that things can go on forever, i.e., the concept of infinity. Not only has this never been observed, but it is, in principle, impossible to observe and validate in practice. Why, if it cannot occur in the reality in which we live, is it unquestionably accepted as part of our reality? Surprisingly, the concept of infinity is alive and well in several areas of physics today.
A: Assuming infinity isn’t real, can we derive anything useful from this insight?
B: Maybe we can. For example, think about how something—let’s call it an “atom” for now—moves through space. Have you ever thought about how many different locations it’s passing through? According to our traditional model, space is continuous, which means it can be separated into ever smaller and smaller chunks. Hence, an atom can be described as passing through an infinite number of locations. However, as we said infinity doesn’t exist, something about this model must be wrong.
A: Yes, and that’s not a new insight. Most physicists agree that at a certain scale, the so-called Planck length, our traditional concept of space loses its meaning.
B: That’s true, but can you see what’s happening here? A relatively sophisticated concept in physics has been re-derived in a new and surprisingly simple manner.
A: Perhaps, but it doesn’t quantify it as the Planck length, which has a value of 1.616255 × 10−35 meters.
B: That’s true; this still needs to be derived in the alternative way. In any case, deriving existing knowledge in new ways is always interesting, as it confirms and solidifies our current understanding. Also, it may lead to other insights that are indeed new.
A: What are other examples where infinity is assumed and we need to adjust our view of the world?
B: Another example is the size of the universe. Some theories in physics postulate an infinitely large universe. However, as infinity is a human invention, this cannot be. It may be difficult for us to picture a finite universe, as our understanding of 3-dimensional space is that it cannot be limited. Therefore, we need to adjust our models so that the question “What’s behind the observable universe?” becomes nonsensical.
A: Any other thoughts on the topic of infinity?
B: It’s interesting to see how some concepts in physics question the existence of infinity in certain aspects, without going one step further and generalizing it. Doubting infinity means nothing other than saying “everything has a limit or maximum value.” When Einstein postulated the maximum speed in our universe, the speed of light, he did exactly that. But it was only limited to the maximum of a certain phenomenon, not questioning infinity as a whole. Hence, the new postulate “there is no infinity” is at a higher level, from which the conclusion “also speed cannot be infinite” is logically derived. When Einstein stated the maximum speed, it wasn’t derived. Einstein just postulated it, and drew conclusions from it, which led to many interesting revelations. But how did he arrive at the assumption that there is a maximum speed in the universe? He is quoted as having said:
“There is no logical way to the discovery of these elemental laws. There is only the way of intuition, which is helped by a feeling for the order lying behind the appearance.”
Well, assuming the thoughts mentioned before are correct, Einstein was wrong in this specific case. There is a logical path to it, as it can be derived from the higher principle that there is no infinity.
A: This might be true for the “there is a maximum speed” part of Einstein’s postulate. However, he made it more concrete by stating that it’s the speed of light. This being the maximum, that’s not directly derived from the insight that there is no infinity, right?
B: Yes, that’s true. However, the key part is the realization that there is a maximum speed. Once you’ve accepted that, and start looking for what that maximum speed could be, you must be really blind to not at least come up with the hypothesis that it could be the speed of light. I mean, it shines directly into your eyes.
A: Is deriving insights from higher principles a requirement to make progress in physics?
B: I cannot say if it’s always required, but it undoubtedly plays a key role in deepening our understanding of the laws of nature. I like the analogy by Richard Feynman, where he describes people observing a chess game without knowing the rules, trying to figure out what’s going on. For instance, they notice that the bishops always remain on squares of the same color. Why is that? Eventually, they realize that bishops move diagonally on a check-pattern board. That logically explains it. Of course, why the board is checkered or why bishops move diagonally are the next questions to explore. However, that’s the essence of progress in comprehending the world—attaining a higher level of understanding that allows us to make sense of our observations.
A: Coming back to the non-existence of infinity, does it allow us to derive any other insights?
B: It may. Allow me to brainstorm a little, and be lenient with what I’m about to say. Postulating that everything has a limit could allow us to draw conclusions about other related elements, not just the ones being currently discussed. For example, we know since Leibniz that the (kinetic) energy of a system can be described as follows (this is the only formula I’ll bother you with today):
Energy = 1/2 Mass x Velocity2
For example, a car in motion has a certain amount of energy based on its mass and velocity (speed), which becomes evident if it hits a wall. If the car has a higher mass, it would mean more energy, causing more damage to the wall. The same with higher speed.
What implications does the formula have if we assume there is no infinity and that velocity has a maximum value? It would mean that if the velocity is already at its limit, or close to it, if we put more energy into the system, the mass has to increase. The idea that an object’s mass increases as it moves faster is a prediction of special relativity.
A: I see why you say “Please be lenient with me on this.” A proper physicist would just rip it apart. First, the formula you mentioned is from classical physics and has nothing to do with relativity theory. Second, the concept of relativistic mass is outdated and not used in modern physics. Third… but do I even need to go on?
B: Not needed. I get your point. But please also try to get mine. It doesn’t matter if it’s true in every detail. My main point is that making a postulate about one concept or element can have implications for others that are connected to it.
A: Alright.
B: Also, even if that idea is wrong as well, it’s not conducive to progress in physics—or any other field for that matter—to create an atmosphere that discourages sharing of early ideas. It would lead people to withhold their ideas, thereby eliminating the chance they could inspire others, potentially sparking genuinely good concepts. I’ll delve deeper into the importance of “baloney-brainstorming” and the “manifesto for the half-baked idea” later on.
A: Okay, back to infinity. You’re saying the postulate that infinity doesn’t exist could have various implications.
B: Yes. Physicists should scrutinize all areas where the concept of infinity still occurs in our current models and consider how to adjust them to make the concept obsolete.
The book continues by elaborating on other potential thinking mistakes, and what conclusions can be drawn from it. Get it here.
