Why are four dimensions insufficient?
Are calculations more accurate if we include ten or eleven dimensions?
Will our lives be ruined in some way if we assume that there are only four?
Quantum mechanics is peculiar , you could totally ignore it and plan a rockets path to Pluto , but a Scanning tunnelling microscope uses it to image individual atoms.
Very tiny particles and energies seem to have minimum sizes to exist , thus the term "Quantum" because tiny masses and energies tend to be found in particular quantities and multiples of these.
When a single quanta of mass or energy is being studied ,Heisenberg tells us , it is impossible to get a measurement of its position and its velocity , you have to settle for either learning its position or its velocity. This is because it requires a quantum of energy to report the fact and the impingement of the reporting quantum changes the state of the single quantum under study reporting one fact and destroying the other. You don't notice this effect on a baseball , a baseball can be impinged by billions of photons with no perceptible effect on its position and velocity , so many facts can be learned by watching a baseball as it passes , but observing an electron as it passes means the electron is necessarily interacting with energies or masses that have profound effect on its direction and speed. It is as if the only way to observe a baseball was to bounce a tennis ball off of it.
The position of an electron in quantum mechanics is described in terms of odds. There is an envelope of possible positions and a range of possible speeds , energy states , spins etc. the electron is considered to be 50% in the position and state it is 50% likely to be AND (not or) 25% in the position and state it is 25% likely to be AND (not or) 15% in the position and state it is 15% likely to be. An electron viewed in this way seems to be a cloud with thin and thick bands. Not so much a particle at all, if a measurement is taken of the electrons position it will seem like a particle that left a single track , but if a measurement is taken of the electrons energy state, its wavelike effects will predominate. If allowed to pass through two slots an electron can pass through both of them , or a single one of them depending on how you measure the electron as it passes .
Tunnelling is an effect of Quantum Mechanics that is getting a lot of use , it is very likely that you own a device that incorporates a tunnelling diode , these are pretty common. Tunnelling is finding an electron in a place that it has no business being , it takes a certain amount of energy for an electron to pass the barrier of a Diode , but at lower energies than this a certain number of electrons show up on the other side of the barrier as if they had dug a tunnel through the barrier. This is amazing ,but dependable ,and produces a device of very great sensitivity . Without the quantum mechanical understanding of this effect it might be hard to build your cell phone . But how exactly is there a 2% chance that an electron will appear on the wrong side of a barrier that should be electron proof? Why does it seem as if each electron is 2% there? I am reaching the limits of my ability to elucidate because my understanding peters out here.
The existence of extra dimensions helps explain the porosity of tiny barriers and the behavior of tiny particles , but this is never observed on a large scale , it is as if any dimension above the main three spacial ones have no stability over a long range and fold themselves into small packages unnoticeable at the scale we live in , and temporal dimentions about the same.
I read about this stuff now and then it is fun and good exercise , whatever I manage to get my mind around successfully seems like an accomplishment, but the really advanced stuff is always a good bit in frount of what I grock.
