Timeline for How could something have negative mass?
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| Apr 13, 2017 at 12:39 | history | edited | CommunityBot |
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| Jan 1, 2012 at 10:35 | comment | added | David Z | @AnamitraPalit: Regarding the quantum mechanical definition of (effective) mass, as far as I know that has nothing to do with restrictions on the velocity of particles, so it is not relevant here. | |
| Jan 1, 2012 at 10:32 | comment | added | David Z | In the context of my answer $i = \sqrt{-1}$. That is all. | |
| Jan 1, 2012 at 9:36 | comment | added | Anamitra Palit | @Sam L.:In the context of the answer to Corb's question by David Zaslavsky the value of $i=+1$ is relevant. We may have consistent formulations where i=+1. You will find such an indication in my last comment[as well as in my first one]. | |
| Jan 1, 2012 at 8:57 | comment | added | Sam | @Anamitra: If you set $i^2 = 1$ but $i \ne 1$, then you have simply given a new name to $-1$... Note that for such a "definition": $(i-1)(i+1) = i^2 - 1 = 0$. So $i=\pm 1$. Also $i$ is usually not defined by $i^4 = 1$ (or rather can not be defined in such a way), but to be a solution to $X^2 + 1 = 0$ (which itself has some degeneracy, but not in an essential way). | |
| Dec 31, 2011 at 12:07 | comment | added | Anamitra Palit | @Ron Maimon:If i=+1 [in a restricted manner]there is a possibility of spacelike intervals getting converted to timelike ones.How would you take that?We may write:$i^2 \times i^2 \times i^2 \times i^2\times i^2 \times i^2 $=(-1)*(-1)* (-1)*(-1)*(-1)*(-1)=1$=> $i^12=1$=> $[i^12]^{1/4}=(1)^(1/4)$=>$i^3=[1,-1,i,-i]$ =>$i^2\times i=[1,-1,i,-i]$ There is a possibility of i=1 in this formulation | |
| Dec 31, 2011 at 11:40 | comment | added | Anamitra Palit | @David Zaslavsky:The Quantum Mechanical mass of a particle is given by:$m*=\hbar^2(\frac{d^2 E}{dk^2})^{-1}$.This may have a negative value and has nothing to do with antiparticles.The negative value of QM mass finds use in the band theory of semiconductors. How would you relate this to the non-observance of negative mass in your answer? | |
| Dec 31, 2011 at 10:43 | comment | added | Ron Maimon | @Anamitra Palit: this is a valid (but unusual) algebraic idea--- people generally do this sort of thing in physics by using the Pauli matrix $\sigma_x$ which is (0,1;1,0), which is separate from "i", which can be taken to be (0,-1;1,0) or $i\sigma_y$ (this is a real matrix). You find both objects used all over. Mathematically, "i" is more elegant because it produces a division algebra which is algebraically complete. Neither is useful for the neutrino, because tachyonic neutrinos don't explain OPERA. | |
| Dec 31, 2011 at 8:05 | comment | added | Anamitra Palit | $i^4=1$ contains two assignments:$i^2=1$ and $i^2=-1$. We may supress the first assignment by the power of definition.What happens if we don't do that and accept a mathematical formulation where $i^2=1$ could be used in certain situations?[This is a speculative notion and I am not staking a claim]. Regarding negative mass:The quantum mechanical mass of a particle may be negative . The quantum mechanical mass of an electron may be negative--this information is well known. We might have an analogous situation with the neurtrinos[ a speculative suggestion] | |
| Dec 31, 2011 at 6:15 | history | answered | David Z | CC BY-SA 3.0 |