34 ܫ ݀݁݊ ݐ ݅ ݕݐ ݈݁݁݉݁݊ ݐ ݂ ݏ ݈ܿܽܽ ݎ ݉ ݑ ݈ ݐ ݈݅݅ܿܽ ݐ ݅݊: 1࢜ ൌ ࢜ ܦ ݅ ݎݐݏ ܾ݅ ݐݑ ݅ ݒ ݅ ݕݐ ݂ ݏ ݈ܿܽܽ ݎ ݉ ݑ ݈ ݐ ݈݅݅ܿܽ ݐ ݅݊ ݓ ݅ ݐ ݄ ݎ ݁ ݏ ݁ܿ ݐ ݐ ݒ ݁ܿ ݐ ݎ ܽ݀݀݅ ݐ ݅݊: ܽሺ࢛ ࢜ሻ ൌ ࢛ܽ ܽ࢜ ܦ ݅ ݎݐݏ ܾ݅ ݐݑ ݅ ݒ ݅ ݕݐ ݂ ݏ ݈ܿܽܽ ݎ ݉ ݑ ݈ ݐ ݈݅݅ܿܽ ݐ ݅݊ ݓ ݅ ݐ ݄ ݎ ݁ ݏ ݁ܿ ݐ ݐ ݂݈݅݁݀ ܽ݀݀݅ ݐ ݅݊: ሺܽ ܾሻ࢜ ൌ ܽ࢜ ܾ࢜ 9 Again, from these axioms, it is possible to deduce a vast amount of physical knowledge related solely to vector mathematics and, in conjunction with a few others, can be extended to cover many related studies. For example, the dynamics of point particles can be deduced from newton’s laws of motion which are almost axioms: ܣ ݊ ܾ݆݁ܿ ݓ ݐ ݈݈݅ ܿ݊ ݐ ݅݊ ݑ ݁ ܽ ݐ ܿ݊ ݐݏ ܽ݊ ݒ ݐ ݈݁ܿ݅ ݑ ݕݐ ݈݊݁ ݏݏ ܽܿ ݐ ݁݀ ݊ ܾ݁ ܽ ݂ ݎ ܿ݁ ࡲ ൌ ݀݉࢜ ݀ ݓ , ݐ ݄݄݅ܿ ݂ ݎ ܿ݊ ݐݏ ܽ݊ ݐ ݉ܽ ݏݏ ܾ݁ܿ݉݁ ݏ ࡲ ൌ ݉ࢇ ݒܧ ݁ ݕݎ ܽܿ ݐ ݅݊ ݄ܽ ݏ ܽ݊ ݁ ݑݍ ݈ܽ ܽ݊݀ ݏ ݅ ݐ ݁ ݎ ݁ܽܿ ݐ ݅݊ However, these are not quite axioms as they are not independent as the first one can be derived from the second by setting F =0 you get a =0, which means that the object will continue at constant velocity. Furthermore, the statement that every action has an equal and opposite reaction comes from the law of conservation of momentum, which, along with the other conservation laws is generally assumed to be axiomatic for physics. Therefore, F =m a is the only axiom required, in fact, along with the definitions of time and energy, as the duration of movement, and the integral of force with respect to time, respectively, it is sufficient as the basis of all of classical mechanics. 10 I will now advance the discussion to newer theories, firstly, quantum field theory, our principle theory of particle interactions. This has been described in an axiomatic form by Arthur Wightman.These axioms are of principle concern to both mathematicians and physicists, one of the millennium problems 11 being the realisation of these axioms in the case of Yang-Mills fields. However, they require an understanding of complex mathematics and so stating them will offer very little. Similarly, general relativity requires a reasonable knowledge of vector mathematics, however, it has been summarised by a set of axioms about the equivalence of both inertial and accelerated observers. This seemingly innocuous statement actually has a profound impact on physics at a grand scale as it is possible, with these axioms to show that light has a fixed, finite speed which is the maximum speed at which anything is capable of moving, a fairly unintuitive fact. Similarly, these axioms can prove that mass bends space time in such a way that is seen as gravity to an observer. Unfortunately the mathematics required for this proof was
9 http://en.wikipedia.org/wiki/Vector_space 10 http://www.marinsek.com/files/axiomatic_of_mechanics.pdf 11 Devlin, Keith J. (2003) [2002]. The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time . New York: Basic Books
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