From: mk_thisisit
Current cosmological observations reveal a significant discrepancy between theoretical predictions and experimental results, indicating a critical juncture in the history of science [00:00:04], [00:04:21]. This poor agreement is particularly evident in the context of phenomena like dark energy and dark matter, suggesting that fundamental understandings of the universe, possibly even arithmetic itself, may need revision [00:00:10], [00:05:22].
The Problem of Dark Energy
One of the most striking issues in modern physics is the problem of dark energy [00:04:40]. Assuming the existence of dark energy, there is a specific parameter known as the cosmological constant. Experimentally, this constant should be approximately 10^-40 [00:04:50]. However, theoretical estimates based on current physics yield a value of 10^80 [00:05:06]. This represents a colossal difference of 10^120 between the theoretical and experimental results, an unprecedented disagreement in the history of science [00:05:15].
This discrepancy highlights a critical crossroads in physics [00:05:26]. The universe, when viewed through new telescopes, increasingly shows less agreement with established theories [00:00:00]. Objects are detected that shouldn’t exist, stars appear older than the universe, or structures are three times too big [00:04:23].
Rethinking Dark Energy: The Arithmetic of Time
One proposed alternative to the standard model of dark energy suggests that dark energy may not exist at all [00:00:43], [00:15:50]. Instead of adding new terms to equations, one could question the underlying mathematical structure itself, specifically the arithmetic of time [00:16:24].
In this model, it is suggested that while standard addition (e.g., one second plus one second equals two seconds) holds true for small time intervals, the rule for adding time might change for very long durations, such as billions of years [00:16:48], [00:17:28]. This is analogous to how speeds do not simply add linearly at very high velocities, but rather combine differently as dictated by the theory of relativity [00:02:10], [00:08:12], [00:17:30]. Even at small scales, corrections to arithmetic exist, but they are often too minute to observe [00:09:07], [00:17:37].
By modifying the arithmetic of time in a specific way, it’s possible to eliminate the need for dark energy and still match experimental observations, including the expansion of the universe, consistent with the standard model [00:17:44], [00:20:05]. This model posits that space remains flat with ordinary arithmetic, while only time’s arithmetic is modified [00:19:19], [00:19:38].
Dark Matter
Similar to dark energy, dark matter represents another significant mystery of the universe [00:15:21]. Everything we observe is made of elementary particles, but a large “dark component”—dark matter and dark energy—remains unknown, inferred only by subtracting what is known from the total [00:15:29]. While the “arithmetic of time” approach can potentially eliminate the need for dark energy, it is not as straightforward to apply the same trick to eliminate dark matter [00:17:48].
Some alternative theories attempt to explain dark matter as a quantum effect, such as fluctuations of spin connection, rather than a new particle [00:18:10], [00:18:24].
Arithmetic and Physics
The discussion surrounding dark energy and dark matter also raises fundamental questions about the nature of arithmetic itself. The concept that arithmetic might be relative, like time in relativity, suggests that different types of arithmetic could apply to different scales or physical quantities [00:11:54].
One perspective proposes that the numbers used for counting and those used for measuring distances (metrics) might be distinct concepts that have been, out of convenience, treated as the same [00:13:28], [00:20:43]. This means one could maintain standard arithmetic while changing the concept of distance, or vice versa [00:13:35], [00:13:40]. For example, in the context of dark energy, the proposal is to change the arithmetic of time while keeping the geometry of space as flat [00:19:19].
This implies that arithmetic might be more akin to physics than pure mathematics, where its rules are dictated by the physical processes observed in the universe [00:01:09], [00:01:45], [00:20:13].