Having said that, i of course do not think we should stop looking to solve problems and attribute every inexplicables to anthropic principle and intelligent design. All i am saying is i dont know if everything is ultimately explicable by physical theories alone and there are very well respected brains who think so too. Hell, even stephen hawking thinks intelligent design is highly probable here. Also, lookie here just to confuse yourself a little more it is actually very enlightening, i learnt something. Even Professor Weinberg gives that as an explanation (to the problem of cosmological constant). Hence, using QFT and math to answer a very fundamental question like yours is like explaining science to religious people using scientific laws.įor those disagreeing fervently at the very appearance of the name of anthropic principle, see here. Spin statistics theorem and quantum mechanics itself was a huge leap of faith and we design the mathematics around the principles that we observe in nature. Physics is hugely empirical we go out, poke anthills, see what happens, write stuff down, try to predict things using theories and laws, if it doesnt work, we collect more data, refine theories and do the same thing again. Just as a side note, we also dont know 'why' there is lenz's law which states that a conducting loop resists change in flux.and there are many more such examples. But if there was no exclusion principle, all the fermions will favour ground state and the universe will be one big dull soup of homogeneous element. This is also not an answer to the question "why" is there pauli exclusion principle, like the rest. In other words, humans inferred the existence of pauli exclusion principle and from that, the abundance of heavier elements other than hydrogen of which we are made like carbon and oxygen which would not have formed if it werent for the exclusion principle.and then we thought to ourselves the only reason we were able to infer the existence of the exclusion principle was because it is there in the first place and helped us come into existence thereby letting us probe the laws of nature and trip on the exclusion y reading the last few lines again its an argument going in circles. if the laws were something else (read no pauli exclusion principle) then life forms would not exist. If you have heard of the anthropic principle, it states that the conditions and laws of physics are such that it would allow human aning. This is just my take on the pauli principle. This means that they can not be in the same state, as exchanging them would leave $\Psi$ unaltered as no minus sign would appear so fermions can not be in the same state (Pauli principle). However if the particles were fermions, the theorem says that $\Psi(1, 2)=-\Psi(2, 1)$ must hold. If the two states are the same, say $|\alpha\rangle$ ($\alpha$ is the label of the state), when I invert the two particles $\Psi$ does not change as the two bras are equal! $$\rm \Psi=|state\ of\ particle\ 1\rangle |state\ of\ particle\ 2\rangle$$ We can write $\Psi$ using the bra notation (the first ket being of particle 1 and the second one of particle 2): It states that the integers spins particles' wave function does not change if you swap the two particles, meaning If you define a boson as a integer-spin particle then you must see the spin-statistics theorem. When in physics you start asking a "why" question (like, why do magnets attract each others?), eventually you will inevitably find yourself in this situation, where the only possible answer you are left with is: "because that's how things work". Said in other words, there are no underlying or "deeper" principles or theories that can "explain" Pauli's principle from other more foundamental assumptions (yet?). This is not really an answer to the "why" question, as it is just an equivalent way to formulate the exclusion principle. $ \lvert \psi_1 \psi_2 \rangle = - \lvert \psi_2 \psi_1 \rangle,$Īnd show that there is a connection, given by the spin-statistics theorem, between spin and symmetry of the wavefunction, so that half-integer spin particles must be antisymmetric like in the above case. You can "derive" the impossibility for two fermions to have the same quantum numbers from the requirement for many-fermion states to be antisymmetric with respect to the exchange of any two particles, that is, This is a legitimate question but one for which you probably won't get any real, satisfying answer rather than just "because that's how nature works".
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