From: mk_thisisit
Recent observations from new telescopes indicate a significant disagreement between theoretical predictions and experimental results in cosmology, marking a “breakthrough moment” in science [00:00:00]. This discrepancy suggests that traditional arithmetic operations, as commonly understood, may not universally apply in physics, particularly at extreme scales.
Inapplicability of Standard Addition in Physics
The concept of addition, which seems indisputable in everyday life (e.g., 2 + 2 = 4 [01:19:00]), appears to behave differently for certain physical quantities.
Speed Addition
A prime example is the addition of speeds. If you add the speed of light to the speed of light, the result is still the speed of light, not two times the speed of light [01:31:00]. This phenomenon, which is part of the theory of relativity, indicates that “nature understands something different by adding speeds than we do with a pencil and a piece of paper” [02:19:00].
This observation raises questions about whether other physical quantities, such as distance or time, might also behave differently under addition or other operations [02:43:00]. If speed is distance divided by time, and speed doesn’t add up normally, then perhaps distance, time, or even division itself might behave differently in extreme conditions [02:43:00].
Large and Small Numbers
The application of standard arithmetic to extremely large or small numbers in physics is also questioned:
- Large Numbers: When considering the number of hydrogen atoms in the universe, it is uncertain if adding this number to itself would yield twice the number [03:22:00]. While an example using washing machine knobs demonstrates that some large numbers can add conventionally, the context of fundamental physical quantities may differ [06:18:00].
- Small Numbers: Similarly, it is not definitively known if very small numbers behave the same way as the numbers we commonly deal with [03:39:00].
Varying Physics Across Scales
The universe exhibits different physical properties depending on the scale:
- Micro World: The physics of the micro world is distinct from our “Meso” world [00:27:00], [03:53:00].
- Cosmic Scale: The physics on a cosmic scale also appears to be different, depending on the model of the universe [00:33:00], [04:04:00].
This indicates that arithmetic properties for physical quantities might vary with scale, meaning arithmetic could be “relative” like time [11:59:00].
Implications for Dark Energy and the Cosmological Constant
A significant issue illustrating the limitations of traditional mathematics is the problem of dark energy.
- Discrepancy: The theoretical estimate for the cosmological constant, a parameter related to dark energy, is 10^120 times greater than the experimentally observed value [04:40:00], [05:01:00]. This represents an unprecedented “poor agreement between theory and experiment in the history of science” [05:22:00].
- Alternative Arithmetic: Some theories propose that dark energy may not exist at all [00:43:00]. Instead, by modifying the arithmetic of time in a specific way, it’s possible to eliminate the need for dark energy and achieve results that match experimental observations [01:09:00], [01:59:00], [02:00:00], [02:01:00], [02:03:00], [02:04:00], [02:06:00], [02:07:00], [02:08:00], [02:10:00], [02:11:00], [16:29:00], [17:28:00], [19:43:00]. For instance, while one second plus one second might equal two seconds, 5 billion years plus 5 billion years might not equal 10 billion years, especially if the universe’s age is 13 billion years [16:55:00]. This suggests that the rules for adding time change for sufficiently long durations, similar to how speeds add differently at high values [17:28:00].
Mathematics and Physics: A Reassessment
The current challenges suggest a fundamental re-evaluation of the relationship between mathematics and physics.
Arithmetic as a Physical Process
It is proposed that what we call “adding” in mathematics is, from the point of view of physics or nature, a physical process [01:45:00]. For example, adding speeds involves the passage of one system relative to another [01:57:00]. This implies that arithmetic should belong to physics, not mathematics [20:13:00].
Separation of Number Concepts
A key insight is that the numbers used for arithmetic (counting) and the numbers used for measuring distances (metrics) might not be the same [13:28:00]. Traditionally, these have been treated as identical for convenience, but science may be at a point where these “two separate ideas” need to be disentangled [20:49:00], [21:22:00].
This perspective allows for:
- Keeping traditional arithmetic while changing the concept of distance or metric [13:38:00], [20:27:00].
- Modifying arithmetic while maintaining existing distance concepts [13:40:00].
For instance, in a model where dark energy is eliminated, space retains its ordinary flat arithmetic, but time’s arithmetic is modified [19:19:00], [19:43:00]. This demonstrates that different dimensions can have different arithmetic properties [19:14:00].
Redefining Concepts
Similar to how geometry in the theory of relativity became a branch of physics, the metric (distance) can be viewed as a field defined on an ordinary flat structure, rather than an inherent geometric property [22:05:00]. This leads to equivalent models and highlights the profound interplay between mathematics and physics [22:26:00].
The Search for a Deeper Level
The current theoretical crisis points towards the possibility of a deeper level of reality than what quantum physics describes [23:23:00], [23:38:00]. This search for a “sub-quantum level” is motivated by the desire to understand phenomena like consciousness, which might operate at a more fundamental level than the statistical nature of quantum physics [23:42:00], [24:08:00].
These developments suggest that a paradigm shift may be underway, challenging long-held assumptions about fundamental mathematical operations in the context of physical reality.