From: mk_thisisit
Physics currently faces significant challenges in fully describing reality, particularly when attempting to reconcile seemingly disparate theories like quantum mechanics and general relativity. These challenges highlight the limitations of current mathematical descriptions and the need for new empirical observations [00:19:23].
Predictability and Randomness in Quantum Mechanics
One fundamental challenge arises from the nature of prediction in quantum mechanics. According to Professor Andrzej Dragan, the behavior of a single electron is fundamentally unpredictable, and there is no mathematical law that can predict its fate [00:08:48]. This contrasts with classical physics, where, theoretically, if all initial conditions were known, a system could be 100% predictable [00:22:50].
- Statistical vs. Individual Prediction: While probability theory can describe the statistics of many quantum events, it cannot predict the outcome of a single event [00:08:59]. This is a form of understanding, even if it doesn’t provide individual prediction [00:21:29].
- Empirical Evidence: Experimental results, including those recognized by a Nobel Prize, have demonstrated that there is no local and deterministic model for the behavior of a single electron [00:09:29]. This suggests that conventional deterministic mathematics may not fully apply [00:09:47].
- Fundamental Non-Determinism: The idea that some phenomena are fundamentally non-deterministic, rather than merely appearing random due to insufficient knowledge, is a concept that some physicists, like Einstein, found difficult to accept [00:23:05].
Limitations of Mathematical Descriptions
Current theories, while approximating reality, often contain internal contradictions or fail in certain scenarios [00:12:08].
- Singularities in General Relativity: General relativity, for example, features singularities within black holes, points where mathematics “stops working” [00:12:13]. While mathematicians may view this as a “missing point” in space-time that can be completed (albeit with loss of properties), physicists see it as a failure of the theory to describe reality [00:29:21].
- Classical Mechanics Failures: Even classical mechanics can exhibit unpredictable behavior in specific theoretical setups, such as a ball on a uniquely shaped hill. In such cases, standard differential equations may not have a unique solution, making prediction impossible [00:25:10].
- Internal Contradictions: Classical electromagnetism, classical mechanics, and quantum mechanics are all described as internally contradictory [00:12:53]. Quantum field theory, in particular, is noted for mathematical inconsistencies like “infinity minus infinity equals zero” [00:13:13].
The Quest for Quantum Gravity
The most significant goal in modern physics is the unification of gravity and quantum mechanics into a quantum theory of gravity [00:29:43].
- Lack of Empirical Observations: A major hurdle is the current lack of empirical observations to guide the development of such a theory [00:19:23]. There are “infinitely many” theoretical approaches to quantum gravity, but no clear way to determine which, if any, is correct without experimental data [00:30:36].
- Experimental Challenges: Currently, there are ideas for experiments to determine if gravity itself is quantum, or if a quantum theory of gravity is even necessary [00:32:27]. Such experiments might become feasible within 20 years [00:32:41].
- Penrose’s Perspective: Roger Penrose, a Nobel laureate, believes that quantum theory itself might fail when confronted with the theory of gravity, leading to a completely different, non-quantum theory that only reproduces quantum theory in borderline cases [00:33:03].
Holographic Theory
One interesting theoretical development related to quantum gravity is the holographic theory. This theory suggests that the description of reality might involve fewer dimensions than it seems, much like a black hole’s entropy depends on its surface area rather than its volume [00:35:10]. It proposes connections between different theories, for instance, that quantum gravity in a certain number of dimensions might correspond to a theory on the surface of that space in a different number of dimensions [00:35:23]. While the specific example of anti-de Sitter space, often used in this context, does not describe our reality, the underlying mathematical idea of hyperbolic space and the reflection of its interior on its edge is a powerful concept [00:35:40].
The Interplay of Mathematics and Physics
The interplay between mathematics and physics is crucial. Many fundamental physical theories, such as Einstein’s theory of gravity, would not have been created without advanced mathematics like Riemannian differential geometry [00:06:30]. While mathematics is often considered the language of physics, it is also acknowledged that physicists sometimes invent the necessary mathematical tools, such as calculus [00:06:50]. Mathematicians are often inspired by physics in their research [00:17:47], and physics owes a lot to mathematics [00:18:25].
Penrose's Three Existences
Roger Penrose postulates three existences:
- Mathematical Existence: Found in Platonic ideas [00:13:48].
- Physical Laws: Embodied in elementary particles and interactions like electromagnetism and gravity [00:13:55].
- Mental Existence: Human consciousness [00:14:04]. This framework suggests that while mathematics might not have an ambition to describe reality, its tools are indispensable for physicists [00:14:11].