Can SR be mathematically proven to be self-consistent?

[JohnWisp]

Hi,

SR is a mathematical theory with axioms.

Can anyone provide a math proof of self consistency?

Thanks

 

[micromass]

http://en.wikipedia.org/wiki/Godel_incompleteness

 

[Fredrik]

The mathematics of SR is just the set $\mathbb R^4$ with some functions defined on it. This means that if it's inconsistent, it would have had to inherit an inconsistency from the real numbers, which would have had to inherit an inconsistency from the rational numbers, which would have had to inherit an inconsistency from the natural numbers, which would have had to inherit an inconsistency from the axioms of set theory. So if SR is inconsistent, all of mathematics falls with it.

 

[micromass]

I am pretty good at this.

But, I may only ask questions.

Can you explain how a theory like SR which contains number theory in its logic can prove its own consistency?

Thanks

SR uses notions from mathematics such as set theory. Since ZFC is used, Godel's theorems apply.
If you want to circumvent Godel, then you'll need to use another set theory than ZFC. And you'll need to phrase SR in that setting. Good luck with that.

 

[WannabeNewton]

Why in the world are you conflating mathematical axioms with physical axioms John? A good example of a mathematical theory is ZFC set theory which is built up from a set of mathematical axioms. SR is not a mathematical theory in this sense; it uses math but that is different.

 

[Dale]

Closed for moderation and cleanup.

 

[Dale]

I will reopen the thread, but remind the participants that one of PF's rules forbids:

•Challenges to mainstream theories (relativity, the Big Bang, etc.) that go beyond current professional discussion

Therefore if you wish to argue that SR is inconsistent then you must provide a reputable mainstream scientific source discussing the inconsistency. We can then discuss that particular work.

The mathematical framework of SR is pseudo-Euclidean geometry. I personally have never seen any mainstream scientific source attacking the self-consistency of SR and/or pseudo-Euclidean geometry using Goedel's work or any other work. One reason, as WannabeNewton points out, is that SR is a PHYSICAL theory, not a mathmatical one. Another is that Goedel's theorem shows that you cannot prove consistency, which is different from proving inconsistency. Merely stating that Goedel applies does not in itself demonstrate any inconsistency in SR.

To my knowledge there are no known inconsistencies of SR either with itself or with experiments within its domain of applicability. As a result the prevailing opinion is that it is, in fact, self-consistent, even if Goedel's theorem prevents any formal proof. Any assertions to the contrary (i.e. assertions that it is not self-consistent) must be supported with mainstream scientific references, per the forum rules.

 

[Dale]

JohnWisp, in a previous thread you mentioned that you do not know how to calculate the time on a clock. IMO, you would be much better served asking about that than following this line of criticism. You do not yet know enough about SR to have an informed opinion about its self-consistency.

 

[Fredrik]

The purely mathematical part of SR consists of definitions of terms like "Minkowski spacetime" and "proper time". The part that's not just mathematics consists of correspondence rules, i.e. statements that tell us how to interpret the mathematics as predictions about results of experiments.

There are at least two correspondence rules that are included in every theory of matter in the framework of SR, so they can be considered part of the framework, rather than part of the specific theories. These two tell us how to measure time and length. In principle, each theory could come with its own set of additional correspondence rules, but in reality, they are going to be very similar. The main difference is going to be between the classical theories and the quantum theories.

People who naively think that SR is inconsistent always try to prove it inconsistent by attacking results like the twin paradox. Since the twin paradox is just the counterintuitive values of the proper times of the three sides of a triangle in a plane, an inconsistency in the twin paradox would be an inconsistency in the purely mathematical part of SR. So it makes sense for a person who's trying to prove SR inconsistent to focus on the mathematics.

An inconsistency in the twin paradox would force us to abandon at least one of the following concepts: the set $\mathbb R^4$, the metric, integration of functions along a world line. Since ZFC set theory ensures that these things make sense, it would force us to abandon ZFC set theory, and therefore essentially all of mathematics. This is of course utterly ridiculous. It means that if SR is inconsistent, then everything else is too.

This is why I find it so annoying when people who haven't even bothered to learn SR (or mathematics) are trying to convince us that SR is inconsistent.

People who instead try to argue that SR is just wrong would need to focus on the correspondence rules instead (unless they think that there's a stupid blunder that we're all making in our calculations). Of course, the correspondence rule that gives us the twin paradox is just the statement that for any two events A,B on the world line of a clock, the time that the clock says has elapsed from A to B is equal to the proper time of the part of the clock's world line from A to B. And as most of us know, this agrees extremely well with the results of experiments, unlike the alternatives that these crackpots would have us consider instead.

 

[Dale]

This is why I find it so annoying when people who haven't even bothered to learn SR (or mathematics) are trying to convince us SR is inconsistent.

Same here, particularly when they are aware that they lack the knowledge to calculate the very thing they assume is inconsistent.