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"Discoveries" about the mathematical structure of these theories are actually incredibly important even if no current day experiment can conceivably test them.

"Discoveries" about the mathematical structure of these theories are actually incredibly important even if no current day experiment can conceivably test them. Special and general relativity were discoveries made in this way (at least to an extent), and now general relativity is important for the proper functioning of technology as "trivial and boring" as GPS. Even earlier in our history, much of thermodynamics was developed in a similar fashion. See the sibling comment for another version of this argument, but finding the weird mathematical coincidences between the competing mathematical theories of nature is very useful. In other words, there are mathematical and logical tests that can be as important as experimental tests for the progress of our understanding of nature.

muxator 8y ago
Came here to (wrongly) correct your statement, as I remembered that the only relevant effect was from special relativity. It turns out it is the exact opposite: general relativity effects prevail [0]. Thanks for forcing me to check! > Special Relativity predicts that the on-board atomic clocks [...] should fall behind clocks on the ground by about 7 microseconds per day [...] due to the time dilatation effect of their relative motion. > Further, the satellites are in orbits [...] where the curvature of spacetime due to the Earth's mass is less than it is at the Earth's surface. A prediction of General Relativity is that clocks closer to a massive object will seem to tick more slowly [...]. A calculation using General Relativity predicts that the clocks in each GPS satellite should get ahead of ground-based clocks by 45 microseconds per day. > The combination of these two relativitic effects means that the clocks on-board each satellite should tick faster than identical clocks on the ground by about 38 microseconds per day (45-7=38)! [0] http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps....
ketralnis 8y ago
They're incredibly important, but they shouldn't be touted as facts until there's some consensus that they are facts
- krastanov 8y ago
  Mathematical theorems (especially no-go theorems, one of the most powerful tools in physics) are at least as much of a fact as an experimental measurement. I can concede that a pop-sci outlet should be clear about what is an experiment and what is a mathematical theorem, but was it really not clear in this case? This is a sincere question, and I care to hear your opinion: do you believe that a reader of phys.org would need more than a glance at the article to know this is a discovery about the mathematics of general relativity, not an engineering breakthrough in the creation of a scifi-like hyperdrive?
  - naasking 8y ago
    > Mathematical theorems (especially no-go theorems, one of the most powerful tools in physics) are at least as much of a fact as an experimental measurement That's an overstatement. Measurements are more important than theory. We cannot form theories without measurements, and yes theories inform our measurements, but science always begins and moves forward with measurements.
    - krastanov 8y ago
      General relativity, quantum computing, some parts of thermodynamics/information theory/statistical physics, some parts of quantum field theory, some parts of condensed matter physics are all things that started as purely mathematical statements. I am not trying to diminish the monumental importance of empirical measurements, but please do not diminish the importance of logical consistency and mathematical constraints. We can say a lot about our universe with great certainty even though in same cases making direct measurements is orders of magnitude beyond our technology.
      - dbasedweeb 8y ago
        GR was amazing, but it wasn’t well known and accepted until the first measurements confirmed it. Quantum Computing is still very much up in the air, but it’s also weird to bring it up in this context, because QM is one of the most tested theories of all time. QED In particular is tested to the most decimal places of any prediction, ever. It’s also weird to act as though GR and QM started out in a vacuum, instead of what they really were, which was based on centuries of math, theory, and experiment. Edit: Unrelated, but I see you’re a fellow Greg Egan fan, good to meet you! Planck Dive has to be one of my all time favorites.

muxator 8y ago

Came here to (wrongly) correct your statement, as I remembered that the only relevant effect was from special relativity. It turns out it is the exact opposite: general relativity effects prevail [0]. Thanks for forcing me to check! > Special Relativity predicts that the on-board atomic clocks [...] should fall behind clocks on the ground by about 7 microseconds per day [...] due to the time dilatation effect of their relative motion. > Further, the satellites are in orbits [...] where the curvature of spacetime due to the Earth's mass is less than it is at the Earth's surface. A prediction of General Relativity is that clocks closer to a massive object will seem to tick more slowly [...]. A calculation using General Relativity predicts that the clocks in each GPS satellite should get ahead of ground-based clocks by 45 microseconds per day. > The combination of these two relativitic effects means that the clocks on-board each satellite should tick faster than identical clocks on the ground by about 38 microseconds per day (45-7=38)! [0] http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps....

ketralnis 8y ago

They're incredibly important, but they shouldn't be touted as facts until there's some consensus that they are facts

krastanov 8y ago
Mathematical theorems (especially no-go theorems, one of the most powerful tools in physics) are at least as much of a fact as an experimental measurement. I can concede that a pop-sci outlet should be clear about what is an experiment and what is a mathematical theorem, but was it really not clear in this case? This is a sincere question, and I care to hear your opinion: do you believe that a reader of phys.org would need more than a glance at the article to know this is a discovery about the mathematics of general relativity, not an engineering breakthrough in the creation of a scifi-like hyperdrive?
- naasking 8y ago
  > Mathematical theorems (especially no-go theorems, one of the most powerful tools in physics) are at least as much of a fact as an experimental measurement That's an overstatement. Measurements are more important than theory. We cannot form theories without measurements, and yes theories inform our measurements, but science always begins and moves forward with measurements.
  - krastanov 8y ago
    General relativity, quantum computing, some parts of thermodynamics/information theory/statistical physics, some parts of quantum field theory, some parts of condensed matter physics are all things that started as purely mathematical statements. I am not trying to diminish the monumental importance of empirical measurements, but please do not diminish the importance of logical consistency and mathematical constraints. We can say a lot about our universe with great certainty even though in same cases making direct measurements is orders of magnitude beyond our technology.
    - dbasedweeb 8y ago
      GR was amazing, but it wasn’t well known and accepted until the first measurements confirmed it. Quantum Computing is still very much up in the air, but it’s also weird to bring it up in this context, because QM is one of the most tested theories of all time. QED In particular is tested to the most decimal places of any prediction, ever. It’s also weird to act as though GR and QM started out in a vacuum, instead of what they really were, which was based on centuries of math, theory, and experiment. Edit: Unrelated, but I see you’re a fellow Greg Egan fan, good to meet you! Planck Dive has to be one of my all time favorites.