Wednesday, August 11, 2021

Math Madness

 


The exercise for today is to map the set of all positive integers into the space  between zero one one … using my trusty version of set theory.

Since this space can be described by a set of rational numbers (1/4, 9/77, 17/209, etc. ),  to map the infinite set of integers, we need to set the denominator of all these fractions to infinity.  Then all integers easily map into the numerators of this set of rational numbers … as 1/infinity,  2/infinity, … ip to infinity/infinity  .…  and since any number divided by infinity equals zero … adding up the set of all these rational numbers (equivalent to zero) totals to the number value of one!


Perhaps this paradox can be resolved by positing that  the last number in the above rational number set  (infinity/infinity) is equal to one.  Not very satisfying … but it works.


STAND UP FOR MATHEMATICS!

Photon Mass

 


Does a photon have any mass? Science  says no … yet sunlight is able to propel objects that have solar sails (large surfaces like above) Here is one attempt at an answer from Physlink.com explanation:


“Indeed, photons have no mass. However, they DO have energy and momentum. It turns out that energy and momentum are the requirements that make a solar sail work, not mass.”


However, momentum is defined as “mass times acceleration” and, if photons have no mass, how can they have any momentum?  Also energy is scientifically synonymous with power … whose units are “Newtons times mass” … again this mass thingie.


So, it seems that they have some mass, however tiny, as a requisite for a photon’s ability to push a solar sail (a large thin metallic surface orthogonal to the sun’s rays.)


But things get much more complicated:


There are more issues with photons … one being that they are slightly repelled when they pass by an object of massive gravity.  But, if photons have any mass, wouldn’t they be bent toward the massive object instead of away from it? (I know, I know, Einstein attributes this to a “warp in the space-time continuum”). 


However, black holes have such enormous gravity that light can’t escape them. Does this not suggest that photons have mass?


Signed,

Perplexed


Afterward: Scientists agree that electrons can be comprised of a neutrino and a photon … neither of which has mass  … yet electrons have a very small mass. From whence?


Another afterward:  Curious thought … we see from the above that, if photons have any mass, it is extremely small. And if a photons mass equals its energy … then perhaps it  mass (from e = mc^2) might be equivalent to e/c^2. That would be very very very very  small!


STAND UP FOR PHOTONS!