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> What's an experiment we could do that verifies pi doesn't have an offset of 1e-1000? Quantum mechanics, the wave equation. Electron shells, photochemistry, g

> What's an experiment we could do that verifies pi doesn't have an offset of 1e-1000? Quantum mechanics, the wave equation. Electron shells, photochemistry, general chemistry, just about everything if we are talking about pi, or e, or i. 1 part off in trillions ^ trillions would impact the fusion of stars, the rates of chemical reactions, require adjustments to basic laws, violate conservation of energy as we know it, ... really obvious impacts. As in: "we would not be here" impacts. Cosmology has run experiments for us that ran billions of years. Contrast: Not everything can be tested with virtually unlimited precision, but basic mathematical constants in physics often can be. The gravitational constant is not testable like that. We don't have a mathematic derivation that we can leverage to test for violations like we do with pi, e, i, and other basic mathematical relationships that show up in physics. But often, even a tiny difference becomes obvious. We exist because the production of matter and anti-matter at the beginning of the universe was off by a tiny amount. Despite the small discrepancy, that there was a discrepancy is very clear. Another "we would not be here" test.

Dylan16807 2mo ago
> 1 part off in trillions ^ trillions would impact the fusion of stars, the rates of chemical reactions, require adjustments to basic laws, violate conservation of energy as we know it Pointing at entire fields is not helpful. Can you give me one specific measurement and an estimate of how far off it would be? > really obvious impacts. As in: "we would not be here" impacts. That sounds pretty nonsense to me. The range of possible values for life isn't that narrow. And relativity is already in there ruining any straightforward conservation of energy and mass by constantly shifting the weight of things as their state changes. But it still works just fine! And we don't know exactly how strong that effect is, which could hide all sorts of imprecision in the real world. It would not be obvious. > Not everything can be tested with virtually unlimited precision, but basic mathematical constants in physics often can be. I'm begging you, name a specific test. One that could tease out 1e-1000. > But often, even a tiny difference becomes obvious. We exist because the production of matter and anti-matter at the beginning of the universe was off by a tiny amount. Despite the small discrepancy, that there was a discrepancy is very clear. Another "we would not be here" test. And if the matter-antimatter imbalance was 1e-1000 it would be imperceptible. It would be less than one atom in the entire visible universe, by an unimaginable factor. It was somewhere around 1e-9, probably, sort of. Not that small at all.
- Nevermark 2mo ago
  > Pointing at entire fields is not helpful. Can you give me one specific measurement and an estimate of how far off it would be? You are dismissing my point, then asking me to make it. You can think of tests/measurements of values as falling into different classes. The strongest tests of all are for the critical values of systems. Because any discrepancy would result in entirely different system behaviors. Single highly accurate measurements are much lower on the rung. Complementing those are many tests with known statistical inaccuracy. Etc. Single tests? Every experiment involving quantum mechanics tests pi's role in those equations to a much lesser extent. Similarly, any test involving gravity tests the gravitational constant. But we have much stronger tests for pi in quantum mechanics that we do for g in gravitation. There isn't just one kind of measurement/test, there are many. And we want the strongest test we can make in any given situation. But of course, we can always perform weaker tests. Validating pi in quantum mechanics can be done with extreme robustness, because the entire theory depends on that value critically. Even the tiniest discrepancy would result in different physics compounding over all Plank space and time units, over billions of years and universe expansion, and we wouldn't be here. Of course, we can't rule out any discrepancy. But in this case, we can rule out discrepancies down to unimaginable infinitesimals. I doubt anyone even knows how to characterize how much of a discrepancy from pi would still be consistent with what we know. That tiny. The criticality is what gives us this far stronger test. Non-critical values cannot be tested this way. Pi can. Particular tiny ranges of stable constants in a stable 3-body system can (to a lesser extent, given the smaller system and higher bounds on criticality). Another way to view the systemic criticality of pi, is to recognize that pi is not just a representation for a particular magnitude, but a representation of conserved cyclic behavior. Any deviation from pi breaks cyclic behavior. Thus, the implications of pi in a theory, and our ability to test pi, are profoundly greater than for most other constants. Because the difference between cyclic vs. non-cyclic behaviors, is profound. Not just slightly different behavior, but entirely different behavior.
  - Dylan16807 2mo ago
    > Validating pi in quantum mechanics can be done with extreme robustness, because the entire theory depends on that value critically. Even the tiniest discrepancy would result in different physics compounding over all Plank space and time units, over billions of years and universe expansion, and we wouldn't be here. And if you had two separate copies of the universe, you could measure this compounding. But we only have one universe. How do we know which one we're in? > Any deviation from pi breaks cyclic behavior. Thus, the implications of pi in a theory, and our ability to test pi, are profoundly greater than for most other constants. Because the difference between cyclic vs. non-cyclic behaviors, is profound. Not just slightly different behavior, but entirely different behavior. Or it just knocks off the frequency by an absurdly small amount. But even if it did ruin cyclic behavior, how long are your cycles? The universe is only 1e61 planck times old. A discrepancy of 1e-100 would have no effect yet, let alone 1e-1000.

Dylan16807 2mo ago

> 1 part off in trillions ^ trillions would impact the fusion of stars, the rates of chemical reactions, require adjustments to basic laws, violate conservation of energy as we know it Pointing at entire fields is not helpful. Can you give me one specific measurement and an estimate of how far off it would be? > really obvious impacts. As in: "we would not be here" impacts. That sounds pretty nonsense to me. The range of possible values for life isn't that narrow. And relativity is already in there ruining any straightforward conservation of energy and mass by constantly shifting the weight of things as their state changes. But it still works just fine! And we don't know exactly how strong that effect is, which could hide all sorts of imprecision in the real world. It would not be obvious. > Not everything can be tested with virtually unlimited precision, but basic mathematical constants in physics often can be. I'm begging you, name a specific test. One that could tease out 1e-1000. > But often, even a tiny difference becomes obvious. We exist because the production of matter and anti-matter at the beginning of the universe was off by a tiny amount. Despite the small discrepancy, that there was a discrepancy is very clear. Another "we would not be here" test. And if the matter-antimatter imbalance was 1e-1000 it would be imperceptible. It would be less than one atom in the entire visible universe, by an unimaginable factor. It was somewhere around 1e-9, probably, sort of. Not that small at all.

Nevermark 2mo ago
> Pointing at entire fields is not helpful. Can you give me one specific measurement and an estimate of how far off it would be? You are dismissing my point, then asking me to make it. You can think of tests/measurements of values as falling into different classes. The strongest tests of all are for the critical values of systems. Because any discrepancy would result in entirely different system behaviors. Single highly accurate measurements are much lower on the rung. Complementing those are many tests with known statistical inaccuracy. Etc. Single tests? Every experiment involving quantum mechanics tests pi's role in those equations to a much lesser extent. Similarly, any test involving gravity tests the gravitational constant. But we have much stronger tests for pi in quantum mechanics that we do for g in gravitation. There isn't just one kind of measurement/test, there are many. And we want the strongest test we can make in any given situation. But of course, we can always perform weaker tests. Validating pi in quantum mechanics can be done with extreme robustness, because the entire theory depends on that value critically. Even the tiniest discrepancy would result in different physics compounding over all Plank space and time units, over billions of years and universe expansion, and we wouldn't be here. Of course, we can't rule out any discrepancy. But in this case, we can rule out discrepancies down to unimaginable infinitesimals. I doubt anyone even knows how to characterize how much of a discrepancy from pi would still be consistent with what we know. That tiny. The criticality is what gives us this far stronger test. Non-critical values cannot be tested this way. Pi can. Particular tiny ranges of stable constants in a stable 3-body system can (to a lesser extent, given the smaller system and higher bounds on criticality). Another way to view the systemic criticality of pi, is to recognize that pi is not just a representation for a particular magnitude, but a representation of conserved cyclic behavior. Any deviation from pi breaks cyclic behavior. Thus, the implications of pi in a theory, and our ability to test pi, are profoundly greater than for most other constants. Because the difference between cyclic vs. non-cyclic behaviors, is profound. Not just slightly different behavior, but entirely different behavior.
- Dylan16807 2mo ago
  > Validating pi in quantum mechanics can be done with extreme robustness, because the entire theory depends on that value critically. Even the tiniest discrepancy would result in different physics compounding over all Plank space and time units, over billions of years and universe expansion, and we wouldn't be here. And if you had two separate copies of the universe, you could measure this compounding. But we only have one universe. How do we know which one we're in? > Any deviation from pi breaks cyclic behavior. Thus, the implications of pi in a theory, and our ability to test pi, are profoundly greater than for most other constants. Because the difference between cyclic vs. non-cyclic behaviors, is profound. Not just slightly different behavior, but entirely different behavior. Or it just knocks off the frequency by an absurdly small amount. But even if it did ruin cyclic behavior, how long are your cycles? The universe is only 1e61 planck times old. A discrepancy of 1e-100 would have no effect yet, let alone 1e-1000.