From: mk_thisisit
Modern physics faces a significant challenge as new observations, particularly from advanced telescopes, show a decreasing agreement with established theories [00:00:00], [00:04:16]. This unprecedented level of disagreement between theory and experiment in the history of science suggests that physics is at a crossroads [00:00:08], [00:05:22], [00:05:26]. One area of re-evaluation is the fundamental concept of arithmetic, specifically how basic operations like addition, subtraction, multiplication, and division apply to physical quantities across different scales [00:01:09].
The Challenge to Standard Arithmetic
The core of the problem lies in how nature “adds” quantities versus how humans do with conventional arithmetic [00:01:19], [00:01:45]. For instance, while 2 + 2 = 4 is an “indisputable truth” in standard arithmetic, and 1 + 1 = 2 [00:01:19], [00:01:26]:
- Adding the speed of light to the speed of light results in only one speed of light, not two [00:01:31], [00:01:35]. This is explained by the fact that adding speeds is a physical process, representing the passage from one moving system to another [00:01:55]. When speeds become large, they stop adding in the simple, linear way we expect [00:02:10].
- This leads to questions: if speed, which is distance divided by time, behaves strangely, then perhaps distance or time, or even division itself, don’t add up normally either [00:02:43], [00:02:51].
Scale-Dependent Arithmetic
The idea of generalized arithmetic suggests that fundamental mathematical operations may behave differently depending on the scale of the quantities involved [00:03:00].
- Small Numbers: For everyday items like apples, 1 + 1 = 2 [00:03:15].
- Large Numbers: When considering enormous quantities, such as the number of hydrogen atoms in the universe, it’s questioned whether adding this number to itself truly doubles it in a physically meaningful way [00:03:22], [00:06:04]. The argument that adding large numbers like hydrogen atoms is inaccurate from a mathematical standpoint is considered [00:00:14], [00:06:48]. An example is given comparing the number of hydrogen atoms to the possible positions of knobs on washing machines in a city, where the latter can be an astronomically larger yet “imaginable” number that still adds up conventionally [00:06:18].
- Micro, Meso, and Cosmic Scales: It appears there are different physics for the micro-world, our “meso” world, and the cosmic scale [00:00:27], [00:03:53], [00:04:04]. Observations from new telescopes reveal objects that shouldn’t exist according to current theory, like stars older than the universe or objects three times too big [00:04:22].
- Paradoxes: The ancient Greek paradox of the heap of sand (Sorites paradox) illustrates this problem: subtracting one grain from a heap still leaves a heap, but repeated subtractions eventually make it cease to be a heap, highlighting the issue of continuous small changes leading to a qualitatively different result [00:08:25]. Similarly, adding small increments of speed, if done enough times, would eventually exceed the speed of light, which is not possible according to the theory of relativity [00:08:08]. This suggests that even small additions might carry subtle corrections that accumulate over many operations [00:09:07], [00:09:12].
Implications for Cosmology: Dark Energy and Dark Matter
The concept of a new arithmetic has profound implications for understanding cosmological phenomena:
- Dark Energy: There’s a significant discrepancy between the theoretical estimate and experimental measurement of the cosmological constant associated with dark energy. Theoretical calculations are off by a factor of 10^120 compared to experimental results [00:04:40], [00:05:06], [00:05:15]. It’s proposed that modifying the arithmetic of time in a specific way could eliminate the need for dark energy while still matching experimental observations [00:00:43], [00:16:26], [00:16:32], [00:17:44]. This means that for very long durations (billions of years), the rule for adding time might change, similar to how speeds add differently at high velocities [00:16:55], [00:17:24].
- Dark Matter: While dark energy might be explained by modified time arithmetic, dark matter is not as easily explained away by similar “arithmetic tricks” [00:17:48]. Some alternative theories suggest dark matter could be a quantum effect, like fluctuations of spin connection [00:18:19].
The Interplay Between Mathematics and Physics: Arithmetic as Physics
The discussion raises fundamental questions about the relationship between mathematics and physics:
- Relativity of Arithmetic: It’s proposed that arithmetic itself might be relative, similar to time in relativity, with different arithmetic rules for different physical quantities or groups [00:11:54], [00:12:02], [00:12:08].
- Changing Arithmetic vs. Changing Distance: One perspective is that we change the arithmetic operations (addition, etc.) while keeping the concept of distance the same [00:12:38], [00:13:40]. The alternative view is to maintain standard arithmetic but modify the concept of distance itself, which is explored in mathematics as metrics [00:13:44], [00:13:47], [00:20:25], [00:20:30].
- Numbers have two structures: arithmetic (for counting/combining quantities like apples) and for measuring distances [00:12:50]. These two structures are not inherently linked and can be separated [00:13:33], [00:20:49]. The common practice of treating them as the same may be a result of human “laziness” that science needs to overcome [00:21:10], [00:21:25].
- Mathematical Interpretations of Geometric Principles: This mirrors concepts in geometry. Instead of curved space as in general relativity, one could interpret gravity as a flat space with a “metric tensor field” that defines distances, similar to an electromagnetic field [00:22:02], [00:22:17].
The Sub-Quantum Level and Consciousness
Beyond arithmetic, a profound question in physics is whether there exists a sub-quantum level, deeper than current quantum physics [00:23:06], [00:23:21]. It’s hypothesized that if consciousness is not a classical phenomenon (and is experimentally known to involve quantum processes like photosynthesis), it might reside at a level deeper than quantum mechanics, as the quantum level is seen as statistical, while consciousness involves awareness and probability reduction [00:24:04], [00:24:08], [00:24:13].
Conclusion
The current state of physics suggests a paradigm shift where the fundamental rules of arithmetic, long considered universal, may need to be re-evaluated. This could lead to a generalized arithmetic where operations behave differently depending on the scale or context, particularly for concepts like speed and time [00:11:54], [00:12:02]. This means the seemingly simple question “How much is 1+1?” could, in a broader physical context, depend on how “one” is defined and what it means to “add” [00:26:30], [00:26:42]. The exploration of these concepts represents a new frontier in the interplay between mathematics and physics.