General Relativity Quantum Mechanics and the new String Theory

[sebastien]

Hi everyone again

Here is a quote from the book 'A brief history of time" by Stephen Hawking (I am currently reading this book )

'In order to talk about the nature of the Universe and to discuss questions, such as does the universe have a beginning or an end, you have to be clear about what a scientific theory is. I shall take the simpleminded view that a theory is just a model of the Universe, or a restricted part of it, and a set of rules that relate quantities in the model to observations that we make that we make. It exists only in our minds and does not have any other reality. '

Thankyou, and hope that this helped ,
Sebastien.

[sjastro]

If we are going to start quoting individuals here is G.H Hardy one of the greatest Pure Mathematicians of the 20th century.

"... and there is no sort of agreement about the nature of mathematical reality among either mathematicians or philosophers. Some hold that it is 'mental' and that in some sense we construct it, others that it is outside and independent of us ... I believe that mathematical reality lies outside of us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our 'creations', are simply our notes of our observations."

The whole point is that there is no definitive answer.

Steven

[shane.mcneil]

Well from my completely ignorant point of view: I always thought that the "mathematics of the universe" is a real thing waiting to be discovered, but how can you be sure that you have actually got it right? We may have a theory that seems right, but that doesn't mean that somehow someday it wont be contradicted. So we "invent maths" in the hope that we've worked out the real maths, but how do you know that you have found a fundamental truth/fact? So we just go with what we've worked out and change it as the need arises, never being quite sure. But it's better than sitting at home watching the grass grow. (Unless you really like grass that is)

I hope I just made sense.

Shane

[Robh (Rob)]

Originally Posted by shane.mcneil

Well from my completely ignorant point of view: I always thought that the "mathematics of the universe" is a real thing waiting to be discovered, but how can you be sure that you have actually got it right? We may have a theory that seems right, but that doesn't mean that somehow someday it wont be contradicted. So we "invent maths" in the hope that we've worked out the real maths, but how do you know that you have found a fundamental truth/fact? So we just go with what we've worked out and change it as the need arises, never being quite sure. But it's better than sitting at home watching the grass grow. (Unless you really like grass that is)

I hope I just made sense.

Shane

Shane,

In physics, we might form an hypothesis based on our observations and measurements of the Universe at large.
A large enough body of evidence might upgrade the hypothesis to a theory. Continued confirmation from observation and measurement might lend further support to the theory, as might confirmation of any predictions made by the theory. Example, the Big Bang Theory. However, a real world observation that contradicts the theory will result in its modification or, possibly, its downfall. A theory can be proven false but it cannot be proven true.

Observation and measurement may lead us to discover a mathematical relationship in nature e.g. the relationship stated by Pythagoras' Theorem. However, the proof of any theorem is logically deduced from the axioms and defined rules of mathematics. In Euclidian (plane) geometry, every theorem can be proven from a small number of axioms. For example, we can prove Pythagoras' Theorem. It just so happens that our measurements confirm the theorem because the local geometry is flat. The relationship is not true for triangles drawn on a sphere.
Mathematical theorems do not depend on continued observations of the Universe to be upheld. A theorem is proven to be true.

Now, consider a new field of maths derived as a purely conceptual system. It may or may not have a practical application. Its theorems do not depend on the physical Universe for their truth. Example, the field of complex numbers was a creative concept long before it found any applications in physics.

Regards, Rob.

[xelasnave]

String theory is not theory it is no more than fancy..if not refer me to some experiments or other evidence called for before a hypothisis can be elevated to the high level of scientific theory.
Speculation is not science and string "ideas" are no more than high class speculation....in my humble view.
alex

[shane.mcneil]

Thanks for that explanation Rob. Yes I see that a mathematical theorem can be proven true. I guess I was more talking about the application of those theorems to the real world. As you said theories can be proven false but not true. I just find sometimes that ones tend to talk in absolutes whereas I tend to think in terms of "this appears to be the case..."

Just a question about maths in general though, the fact that mathematics works the way it does, is that a reflection of preexisting laws too? If the real world is a reflection of mathematical laws, are mathematical laws a reflection of something else?

Regards Shane

[Robh (Rob)]

Originally Posted by shane.mcneil

Just a question about maths in general though, the fact that mathematics works the way it does, is that a reflection of preexisting laws too? If the real world is a reflection of mathematical laws, are mathematical laws a reflection of something else?

Regards Shane

Well, that debate continues...
The views by G.H. Hardy and Stephen Hawking as quoted earlier by Steven and Sebastian (see posts 81 & 82) are two opposite extremes of this debate.

Regards, Rob.