it's not more likely, it just does. If we couldn't re-derive all known laws of classical mechanics and thermodynamics from the large scale limit of quantum mechanics, than we would have rejected quantum mechanics as wrong (or incomplete) decades ago.
This paper seeks to show that some of the mathematical framework of quantum mechanics "pops out" of some intuitive (depends on your perspective i guess) machinery from classical mechanics. It doesn't really mean much fundamentlly, and doesn't really reflect the historical derivations of the equations, but it is interesting to look in retrospect how readily some of these equations pop out from seemingly basic frameworks.
Its also interesting to consider the actual historical discovery of these concepts, or any scientific concept that generalised existing theories to a far deeper and more unifying result (e.g classical -> quantum mechanics, newtonian mechanics -> general relativity). You are required to somehow develop a theory that not only extends beyond horizons currently seen, but also one that correctly replicates the theory it seeks to supercede. And of course, you are limited to theoretical tools you already know, since no-one has yet figure a way to reach into the future and pluck out a more suitable notation or mathematical framework. Its like a literary character trying to write the story it is embedded in.
Of course, there are always hints to the keen observer, especially tucked away at the foundations: much of special relativity unravelled itself directly from the laws of electromagnetics, since in the equation the speed of light is never specified, and the naive galilean assumption that everyone made - that time and space are absolute, and speeds must be specified relative to observers - was the veil obscuring our vision. If you take the courage to abandon the doctrine of absoluteness of time and space, and to declare that the speed of light doesn't need to be specified in terms of some preferred reference frame, since the speed of light is invariant for all observers everywhere throughout the universe, the intractable gulfs seperating what we know from what we don't vanish like a mirage, and meld together naturally into a more fundamental, and unified theory.
And we can take the same step again, by noticing the strange coinicdence that in Newton's theory of gravitation and mechanics, the inertial mass happens to exactly equal the gravitational mass, magically cancelling each others contribution. If we declare that these two phenomena are infact exactly the same thing seen from different perspectives, and we realise that the apparant difference between somebody accelerating and somebody falling is an illusion, obscuring the fact that both are simply bodies taking the shortest path through the warped 4-dimensional manifold of spacetime, we once again unify all of our observations into a elegant, geometric theory of immense power and stunning beauty, one that can peer into the hearts of dead stars, and into the birth of all things, despite being first revealed in the brain of an absent minded jewish man, sitting in a cluttered office filled with pipesmoke, in a time where europe was fragmented from the collapse of empires and feudal houses, with wars fought with bayonets and horses still in living memory.
This paper seeks to show that some of the mathematical framework of quantum mechanics "pops out" of some intuitive (depends on your perspective i guess) machinery from classical mechanics. It doesn't really mean much fundamentlly, and doesn't really reflect the historical derivations of the equations, but it is interesting to look in retrospect how readily some of these equations pop out from seemingly basic frameworks.
Its also interesting to consider the actual historical discovery of these concepts, or any scientific concept that generalised existing theories to a far deeper and more unifying result (e.g classical -> quantum mechanics, newtonian mechanics -> general relativity). You are required to somehow develop a theory that not only extends beyond horizons currently seen, but also one that correctly replicates the theory it seeks to supercede. And of course, you are limited to theoretical tools you already know, since no-one has yet figure a way to reach into the future and pluck out a more suitable notation or mathematical framework. Its like a literary character trying to write the story it is embedded in.
Of course, there are always hints to the keen observer, especially tucked away at the foundations: much of special relativity unravelled itself directly from the laws of electromagnetics, since in the equation the speed of light is never specified, and the naive galilean assumption that everyone made - that time and space are absolute, and speeds must be specified relative to observers - was the veil obscuring our vision. If you take the courage to abandon the doctrine of absoluteness of time and space, and to declare that the speed of light doesn't need to be specified in terms of some preferred reference frame, since the speed of light is invariant for all observers everywhere throughout the universe, the intractable gulfs seperating what we know from what we don't vanish like a mirage, and meld together naturally into a more fundamental, and unified theory.
And we can take the same step again, by noticing the strange coinicdence that in Newton's theory of gravitation and mechanics, the inertial mass happens to exactly equal the gravitational mass, magically cancelling each others contribution. If we declare that these two phenomena are infact exactly the same thing seen from different perspectives, and we realise that the apparant difference between somebody accelerating and somebody falling is an illusion, obscuring the fact that both are simply bodies taking the shortest path through the warped 4-dimensional manifold of spacetime, we once again unify all of our observations into a elegant, geometric theory of immense power and stunning beauty, one that can peer into the hearts of dead stars, and into the birth of all things, despite being first revealed in the brain of an absent minded jewish man, sitting in a cluttered office filled with pipesmoke, in a time where europe was fragmented from the collapse of empires and feudal houses, with wars fought with bayonets and horses still in living memory.