That would leave the underlying theories of physics without topological qualities. What would near and almost mean. In addition, the theories wold also be devoid of geometric character. That is bad news when one considers that the General Theory of Relativity is a reduction of gravitation...
If a particle with non-zero rest mass is accelerated from rest its mass increases as its speed increases.
A photon does not need to be accelerated to go at light speed. Its rest mass is zero. Any particle with rest mass zero will go at light speed without being pushed.
The Cable T.V. (so-called) science programs just love to tell us the civilization will be ended by the next Carrington Event. It wont. A lot of people will probably die, but civilization will not be ended and recovery is possible by using direct current generators locally to power DC motors...
We can cobble together DC generators which can power DC moters that can turn AC alternators w.o. using transformers. This can power water delivery systems and other critical infra-structure elements. It may not be first class power, but we can get it going in fairly short order. This will...
The Moon has no atmosphere so it cannot be terraformed. Mars has water from which fuel can be made. With labor and terraforming Mars could support human life independent of help from Earth. Not so, the Moon.
Even so, I think we should established habitats on the Moon and use it as a...
The easiest way I have found to understand energy flow in an electric circuit is by means of Poynting vectors. The electron move in the wire (slowly) because of potential difference. The electrons have the field E and the motion produces the magnetic field S. The Poynting vector E x S tells...
A relation is a set of pairs. which would include the empty set. So if A has a elements (a not = 0) and B has b elements (b not = 0) then the set of relations between A and B is the set of subsets of A x B This tells you all the ways of matching elements of A with elements B including...
Here is a "must read" Please read http://science.uniserve.edu.au/school/curric/stage6/phys/stw2002/sefton.pdf
Sefton demolishes the "garden hose" analogy and shows power is transmitted as a field effect. The electric and magnetic fields produce the Poynting Vector field which is really what...
Homework Statement
I need a pointer to a proof of the following items:
if div X =0 then X = curl Y for some field Y.
if curl X = 0 then X = grad Y for some field Y.
Can anyone provide a pointer to a proof?
Thanks.
Bob Kolker
Homework EquationsThe Attempt at a Solution
Suppose an ice cube is in a vessel and it is at a temperature slightly below 0 degrees Cesius. Suppose further that the inside of the vessel is a vacuum. If the temperature of the vessel is increased to slightly above zero Celsius and the vacuum is maintained would the state change in the ice...
The gravitational force exerted by Earth (at the surface) is function of its mass which does not change of the planet stops turning. Our weight would increase slightly everywhere but at the poles because the turning of the Earth exerts an outward centrifugal force on bodies which is subtracted...