Falsifiability
Offline I was watching a documentary based on Brian Greene's "The Elegant Universe" at http://www.pbs.org/wgbh/nova/archive/int_phys.html a while back.
One thing that I've been pondering about is the notion of mathematically sound, but supposedly unfalsifiable hypotheses. Would you say that being mathematically sound is reasonable evidence for belief? I think a while back somebody posted here that there was a mathematical model being published soon that showed that as we go back towards the time of the big bang, the universe never actually gets infinitelly small, and I think it was supposed to make some statements about what form the universe was in "before" that. Again, how is it testable? How is it falsifiable? And how much does it matter? Presumably it is taken more seriously than mere wild speculation, but what do the resident scientists have to say about this kind of thing?
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In general mathematical models build of physics. Physics is derived from mathematics then tested. For example, Newton developed Calculus to help explain physical forces.
So in essence mathematics is the language of physics.
As for mathematically sound hypothosesis, the general rule is yes. Relativity, for example, was mathematicaly derived then experimentally conformed.
actually no.
Back in the day, there used to be a mathematically beautiful and highly complex theory called loop vortex theory. They thought (and "proved", through calculation), that all particles were vortexes in the "ether", or a universal substance. The theory was perfectley mathematically sound. It resembled string theory very much. However, no experiment was put forth to prove it, and it was eventually discovered that the ether did not exist.
I feel string theory is the same way. If you cannot have experiments to back up your theory, then it is simply false. Quantum theory and the theory of relativity were indeed only mathematical approximations for their time, but have since been proven by experiment. If string theory is ever to be fully accepted as science, it will have to have experimental evidence. Otherwise, it is simply a matter of mind games, nothing more than philosophy.
String Theory is testable. We just need to wait until L.I.S.A and the LHC to come on line.
But yeah, math is good, but experiments should come after.
I should have said, math is a good tool for developing theories. Experiments confirm/deny them.
Well, math is the deductive end of an inductive field.
Mathematics is certianly VITAL to all sciences, but its deductive nature can lead to problems, and has. In any deduction, the conclusion is only as valid as the premises it is based upon. When said premises have not been fleshed out with empirical data, we can run the risk of fooling ourselves.
Sometimes, it honestly seems to me that quantum physiscists will simply add a new dimention to get the problem to work out. Sure, it makes the deduction sound, but it does not necessarily make it valid.
Validation in science will always come from the empircial. From the observable and testable.
That is not to say that cutting edge theories in M-Theory and what not are to be scoffed at. It should be expected that there could be decades of work to be done in order to flesh out or confirm such ideas. In the mean time, we work with what are determined to be plausible and likely mechanisms.
For example, the next generation of space telescopes may finally lay to rest the idea of a unique universe made during a single big bang, or an oscillating universe model - as it should be powerful enough to pick out the "ripples" in the cosmic background radiation we'd expect were the universe oscillating.
In the mean time, both theories have serious merit and fit the data we observe. We simply need BETTER data to make the dinstiction between a single BB or mutiple ones.
I am against religion because it teaches us to be satisfied with not understanding the world. - Richard Dawkins
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In this case, who would agree that "m-theory" is not deserving of the term of "theory"? It doesn't have the same level of evidence as evolution, or gravity, etc?
Personally, while I can appreciate that this model of the universe or others may mathematically represent the universe we observe quite well, without falsification and evidence, I have no problems clasifiying it in the same category as theories that involve 'ether'. I have no problems with saying that I don't know, there is no dishonour in it.
Since I've never come across an argument that says I need to make this decision with a lack of compelling evidence, surely I am rational in NOT making that decision while I wait for and gather evidence?
Well, you have to remember that math can be used for things we cannot physically mearuse, such as the mass of the Earth, or the radius of an Hydrogen atom.