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Why do you assume there is a bridge? Or even if there is one, why do you assume that descriptions of that bridge in a mathematical language is at all possible?

Why do you assume there is a bridge? Or even if there is one, why do you assume that descriptions of that bridge in a mathematical language is at all possible? We do know that mathematical frameworks cannot be at the same time totally complete and internally consistent. Would it be a stretch to assume descriptions of our physical reality could have the same restriction? General relativity and Quantum mechanics are relatively complete in describing our physical reality, however they are not consistent with each other. Perhaps if we ever find a description that is consistent, it won’t be complete. Perhaps grand unified theories are simply a mathematical impossibility.

mr_toad 3y ago
> We do know that mathematical frameworks cannot be at the same time totally complete and internally consistent. It would be troubling to think that physical reality was inconsistent.
GoblinSlayer 3y ago
Mathematical completeness is a mathematical concern and is irrelevant for physics, because physics and mathematics have different notions of existence.
jakeinspace 3y ago
It’s sort of incomprehensible that there wouldn’t be, even if that bridge is forever incomprehensible to us. There are boundaries between where GR and QM are predictive, so presumably, unless there’s some strange smooth transition of equations between those two regimes (which would itself lend itself to a mathematical theory), then there must be a consistent set of equations which explain both regimes consistently and simultaneously.
- runarberg 3y ago
  Coming from psychology this feels alien to me. In psychology there is a definite boundary between individual behavioral dynamics and population behavioral dynamics. There is no smooth transition between the two, either you describe the individual or you describe a group, you cannot do both (even thought debates about IQ here on HN will have you believe otherwise) and there is certainly no smooth transition. How is the boundary between GR and QM different from the boundary of psychology and sociology?
  - jakeinspace 3y ago
    Im neither a psychologist nor a physicist, but I think one can analogize population vs individual behaviour to condensed matter physics versus particle physics. Condensed matter physics finds emergent behaviour in large clumps of stuff that would, in principle, be totally predictable from first principles (the standard model), but which in practice are quite difficult to guess a priori. Different scales lend themselves to different tools, since nonlinear dynamics (chaos) makes it intractable to apply bedrock reductionist formulae to large systems. The higher order behaviour of complex systems is in no way less interesting or true, I would argue, than the seemingly simpler behaviour of very small systems. In contrast to condensed matter vs the standard theory (QM basically), QM vs GR has fundamental incongruities, since both theories make claims about what happens at the same scale. Only one (or most likely neither) can be correct at the event horizon and center of a black hole.
  - PopePompus 3y ago
    I would say it is completely different. In physics, quantum mechanics gives extremely precise and verifiable predictions of the outcomes of experiments within a certain range of physical conditions. So does general relativity. In contrast, psychology has no mathematical model that will, for example, accurately predict what I am going to eat for lunch, nor is there a model that predicts the exact outcomes of elections. Since physics has two models which are exquisitely precise in different size regimes, but which are mutually incompatible, you have a definite puzzle about what happens in situations where the effects of both theories should be important. There are no exquisitely precise and accurate mathematical models of anything in the social sciences, as far as I am aware.
  - dotnet00 3y ago
    The difference would be that the laws of physics are much more rigorous than the 'laws' of psychology/sociology. Outliers in the latter aren't necessarily indicative of anything wrong with theory in general, while even a single outlier in anything in the former is indicative of an incomplete model. There are various results in physics which should be predictable via both GR and QM independently. The results should be the same as both models are supposed to be describing the same thing, so it follows that there should be some sort of gradual transition as one set of effects gradually comes to dominate over the other. Otherwise we'd see a single point in the data where QM stops being accurate and GR takes over, but despite investigating so many different scales, we have not seen any such cutoff point.
eouwt 3y ago
> We do know that mathematical frameworks cannot be at the same time totally complete and internally consistent. I take it you're referencing Godel's theorems here, but "consistent" and "complete" have rather technical (and somewhat limited) meanings within that context, so it's not clear to me how they'd usefully map onto the potential relationship between QM and GR?
- simiones 3y ago
  That's a very good point. In particular, "complete" refers to the ability of the mathematical-logical system to prove every statement that is true within that system, in terms of the system. This property is completely irrelevant to a theory like QM or GR - it is only relevant for a system that aims to be a universal foundation for mathematics (a formal language in which any mathematical statement whatsoever could be precisely formally encoded, and then proven or disproven).
simiones 3y ago
The problem with this line of thinking comes from the way the problem is posed. The reality is worse for both GR and QM. QM is not a theory about small particles: it is a theory that describes the evolution of any object whatsoever. It just happens to be completely wrong for large objects. And even if we accepted that there is some objective cutoff points between "small objects" and "large objects" (the "objective collapse" interpretation), it would still be wrong, because it predicts effects like gravitational lensing don't exist. Conversely, GR is also a theory about any size of object; and it is also completely wrong when tested on small objects, as it predicts effects like the self-interference of particles don't exist. And again, even if some kind of objective boundary existed between the domains of GR and QM existed, that would need to be incorporated into the maths of both of them, and questions about behaviors close to that margin would arise.
- cthalupa 3y ago
  >because it predicts effects like gravitational lensing don't exist. But we use gravitational lensing, and the amount of lensing is predicted by GR? I don't understanding this statement. Is there some additional affect around lensing we should see if quantum gravity is a thing?
  - simiones 3y ago
    No no; I'm saying that if you apply QM as it exists today to describe the motion of light beams around the sun, you will not get any effect similar to gravitational lensing. Since gravitational lensing is a real effect that we have clearly seen, it means that QM as it exists today is just wrong (in its predictions about how light moves around the sun). GR does of course predict gravitational lensing. However, if you used the formulae of GR to compute the motion of photons passing through a double-slit experiment, the solution would show two different bright spots, corresponding to the two slits; in reality, we see an interference pattern. So GR is also wrong. By definition, a (correct) theory of quantum gravity would predict both gravitational lensing and the way photons behave in a dobule-slit experiment (otherwise, we would say that either the theory is wrong, or it is not a theory of quantum gravity). However, no such theory exists today, at least none that doesn't contradict other observations.

mr_toad 3y ago

> We do know that mathematical frameworks cannot be at the same time totally complete and internally consistent. It would be troubling to think that physical reality was inconsistent.

GoblinSlayer 3y ago

Mathematical completeness is a mathematical concern and is irrelevant for physics, because physics and mathematics have different notions of existence.

jakeinspace 3y ago

It’s sort of incomprehensible that there wouldn’t be, even if that bridge is forever incomprehensible to us. There are boundaries between where GR and QM are predictive, so presumably, unless there’s some strange smooth transition of equations between those two regimes (which would itself lend itself to a mathematical theory), then there must be a consistent set of equations which explain both regimes consistently and simultaneously.

runarberg 3y ago
Coming from psychology this feels alien to me. In psychology there is a definite boundary between individual behavioral dynamics and population behavioral dynamics. There is no smooth transition between the two, either you describe the individual or you describe a group, you cannot do both (even thought debates about IQ here on HN will have you believe otherwise) and there is certainly no smooth transition. How is the boundary between GR and QM different from the boundary of psychology and sociology?
- jakeinspace 3y ago
  Im neither a psychologist nor a physicist, but I think one can analogize population vs individual behaviour to condensed matter physics versus particle physics. Condensed matter physics finds emergent behaviour in large clumps of stuff that would, in principle, be totally predictable from first principles (the standard model), but which in practice are quite difficult to guess a priori. Different scales lend themselves to different tools, since nonlinear dynamics (chaos) makes it intractable to apply bedrock reductionist formulae to large systems. The higher order behaviour of complex systems is in no way less interesting or true, I would argue, than the seemingly simpler behaviour of very small systems. In contrast to condensed matter vs the standard theory (QM basically), QM vs GR has fundamental incongruities, since both theories make claims about what happens at the same scale. Only one (or most likely neither) can be correct at the event horizon and center of a black hole.
- PopePompus 3y ago
  I would say it is completely different. In physics, quantum mechanics gives extremely precise and verifiable predictions of the outcomes of experiments within a certain range of physical conditions. So does general relativity. In contrast, psychology has no mathematical model that will, for example, accurately predict what I am going to eat for lunch, nor is there a model that predicts the exact outcomes of elections. Since physics has two models which are exquisitely precise in different size regimes, but which are mutually incompatible, you have a definite puzzle about what happens in situations where the effects of both theories should be important. There are no exquisitely precise and accurate mathematical models of anything in the social sciences, as far as I am aware.
- dotnet00 3y ago
  The difference would be that the laws of physics are much more rigorous than the 'laws' of psychology/sociology. Outliers in the latter aren't necessarily indicative of anything wrong with theory in general, while even a single outlier in anything in the former is indicative of an incomplete model. There are various results in physics which should be predictable via both GR and QM independently. The results should be the same as both models are supposed to be describing the same thing, so it follows that there should be some sort of gradual transition as one set of effects gradually comes to dominate over the other. Otherwise we'd see a single point in the data where QM stops being accurate and GR takes over, but despite investigating so many different scales, we have not seen any such cutoff point.

eouwt 3y ago

> We do know that mathematical frameworks cannot be at the same time totally complete and internally consistent. I take it you're referencing Godel's theorems here, but "consistent" and "complete" have rather technical (and somewhat limited) meanings within that context, so it's not clear to me how they'd usefully map onto the potential relationship between QM and GR?

simiones 3y ago
That's a very good point. In particular, "complete" refers to the ability of the mathematical-logical system to prove every statement that is true within that system, in terms of the system. This property is completely irrelevant to a theory like QM or GR - it is only relevant for a system that aims to be a universal foundation for mathematics (a formal language in which any mathematical statement whatsoever could be precisely formally encoded, and then proven or disproven).

simiones 3y ago

The problem with this line of thinking comes from the way the problem is posed. The reality is worse for both GR and QM. QM is not a theory about small particles: it is a theory that describes the evolution of any object whatsoever. It just happens to be completely wrong for large objects. And even if we accepted that there is some objective cutoff points between "small objects" and "large objects" (the "objective collapse" interpretation), it would still be wrong, because it predicts effects like gravitational lensing don't exist. Conversely, GR is also a theory about any size of object; and it is also completely wrong when tested on small objects, as it predicts effects like the self-interference of particles don't exist. And again, even if some kind of objective boundary existed between the domains of GR and QM existed, that would need to be incorporated into the maths of both of them, and questions about behaviors close to that margin would arise.

cthalupa 3y ago
>because it predicts effects like gravitational lensing don't exist. But we use gravitational lensing, and the amount of lensing is predicted by GR? I don't understanding this statement. Is there some additional affect around lensing we should see if quantum gravity is a thing?
- simiones 3y ago
  No no; I'm saying that if you apply QM as it exists today to describe the motion of light beams around the sun, you will not get any effect similar to gravitational lensing. Since gravitational lensing is a real effect that we have clearly seen, it means that QM as it exists today is just wrong (in its predictions about how light moves around the sun). GR does of course predict gravitational lensing. However, if you used the formulae of GR to compute the motion of photons passing through a double-slit experiment, the solution would show two different bright spots, corresponding to the two slits; in reality, we see an interference pattern. So GR is also wrong. By definition, a (correct) theory of quantum gravity would predict both gravitational lensing and the way photons behave in a dobule-slit experiment (otherwise, we would say that either the theory is wrong, or it is not a theory of quantum gravity). However, no such theory exists today, at least none that doesn't contradict other observations.