It seems like it's a given that the laws of physics that govern our universe are consistent, and that inconsistency somehow is a reason to doubt an explanatory theory (such as famously Godel's spinning universes leading to an inconsistency that caused Einstein to doubt his own theory).


Along these same lines, if our universe was found to be inconsistent, what would that mean? How would it physically manifest?

Edit: I don't feel like the argument of "it would make science meaningless or make constants not exist" it necessarily true. See Paraconsistent Logic or Dialetheism for some examples.

Edit$^2$: My question was intended to be less phiosophical, and more about what kinds of explanatory or simplifying benefits allowing contradiction would give to attempted models of physics. Or if such a program has been attempted - because so far I don't see any apparent reason why we avoid it.

Edit$^3$: Really the answer to "what would that mean?" is a philosophical one, hence the long discussion that doesn't belong here, sorry. My opinion is that it may simply be a mathematical simplification similar to imaginary numbers that gives us a different and helpful perspective. But I don't know.

  • $\begingroup$ There wouldn't be any constants if the universe was inconsistent. Experiments wouldn't yield any meaningful information because patterns would be nonexistent. This is my personal opinion: science assumes that truths do not change. And this allows for repetition to be possible. And that repetition provides the data from which scientist can construct or confirm theories laws, etc. $\endgroup$ – CoffeeIsLife Apr 5 '14 at 4:19
  • $\begingroup$ Godel's incompleteness and consistency theorems apply only to specific formal mathematical systems, and say nothing about about the universe. $\endgroup$ – baldrik Apr 5 '14 at 4:23
  • $\begingroup$ Well, just because a system is inconsistent doesn't mean that it's dysfunctional. It just means it works differently, but there's still relatively meaningful results that can often be obtained (see naive set theory). $\endgroup$ – Phylliida Apr 5 '14 at 4:31
  • $\begingroup$ @baldrik You're mistaking Godel's work in logic for his work on general relativity. He did, in fact, work on this topic as well. $\endgroup$ – Danu Apr 5 '14 at 8:03
  • $\begingroup$ @Danu Yes I did, I noticed that after I made the comment. Which is why I posted an answer. A lesson in reading the question properly. $\endgroup$ – baldrik Apr 5 '14 at 8:04

Physics is about studying the behavior of nature at an elementary level, gathering experimental data, and organizing the data into consistent mathematical models. By which I mean the mathematics in the models are consistent. The physical postulates that determine the mathematical model ( as additional axioms for the interpretation of the mathematics in physical variables) allow predictions for new experiments to be made. If the predictions are inconsistent with the measurements, the postulates are invalidated, i.e. the physical theory is falsified and a new mathematical model will be sought which will be consistent ( postulates included) with the data, old and new.

The above is an encapsulated history of physics from the time Newton started using mathematics in an organized fashion to explain and predict observations.

What has been happening is that the newer theories ( postulates and mathematical models) have been such as at the limits the older theory is recovered. Example : special relativity reduces to Galilean relativity at the low energies. Thermodynamics emerges from statistical mechanics. etc.

Thus if we got some surprising data which the mathematical models + physical postulates for the universe cannot describe , i.e. inconsistent results , a new mathematical model will be devised with new physics postulates which will, at the limits of the variables, be consistent with the previous physical theory.

In physics, I cannot conceive of an inconsistency that would not be resolved in this manner, by some mathematical tools or others. Thus physics theories are consistent as far as our measurements and observations stretch, by construction.

  • $\begingroup$ Thanks, but I think you're missing the point. You're talking about inconsistencies between predictions of a model and observed results, that are by necessity separate from the model. I agree those need to agree, or physics wouldn't work. What I was talking about was when you obtain a contradiction in your model: when you prove that something and the negation are both true. I went looking for references, and this article seemed to give a pretty good overview of some ways paraconsistent logic can be used for physics. $\endgroup$ – Phylliida Apr 5 '14 at 21:56
  • $\begingroup$ I am sorry, but as a physicist, if there exists a basic contradiction in my model ( mathematics + physical postulates) I would throw the model away. If the contradiction is outside the area of applicability of my model I will define the model as validated within the area of applicability and inaccurate and false outside. Newtonian physics works perfectly in its area of applicability and fails out side. It is still a valid model . You are ignoring that in physics "model" also includes the area of applicability. $\endgroup$ – anna v Apr 6 '14 at 3:56
  • $\begingroup$ I glanced at your reference and it is not something that has to do with physics . The truth value of physics is given by the experiment. In my view inconsistencies with concepts in the mathematical models are only due to lack of good definitions and postulates when using the mathematics of the model. For example expecting physical objects at the micro scale to be definable in the same way as macroscopically. $\endgroup$ – anna v Apr 6 '14 at 4:09

Along these same lines, if our universe was found to be inconsistent, what would that mean? How would it physically manifest?

This is key to seeing that "is the universe consistent?" is a meaningless question. A mathematical theory can be inconsistent but the universe can't.

Also true for "if our universe was found to be contradictory, what would that mean? How would it physically manifest?" So if two mathematical models produce different physical predictions at least one of them is wrong.

Can a model be based on maths that is not self consistent or even contradictory still make good physical predictions? I don't know. I'm guessing no for models that make any predictions for, as anna v put it in her answer, "the behavior of nature at an elementary level"

  • $\begingroup$ I see, thanks. I think this question explained why inconsistent systems are meaningless as well. $\endgroup$ – Phylliida Apr 5 '14 at 4:36
  • $\begingroup$ However, there are systems like paraconsistent logic, which show that contradictions don't necessarily have to make things meaningless. $\endgroup$ – Phylliida Apr 5 '14 at 4:38
  • $\begingroup$ Sure, I think that is only relevant though if you believe in Max Tegmark's MUH. Tegmark is one hoopy frood $\endgroup$ – baldrik Apr 5 '14 at 5:03
  • $\begingroup$ Personally I'd agree with Scott that that argument is somewhat devoid of content. My question was less about philosophy, and more about what further explanatory powers allowing a contradictory system would allow. I don't think such a theory (MUH) is really necessary, personally, though that tends to philosophy myself. $\endgroup$ – Phylliida Apr 5 '14 at 5:10
  • $\begingroup$ Tegmark makes an appearance in the thread, the whole thing is worth a read. I agree it is somewhat devoid of content, and is mostly philosophical, now. Not sure the border between philosophy and science is so fixed. The question "Is the wave function real?" would have been judged to be on the philosophical side, but I think it is now a scientific question. MUH is way, way out there though. $\endgroup$ – baldrik Apr 5 '14 at 5:24

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