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Jan
17
comment Why don't positive charges move?
They can move, but tend not to because they are held in place by other atoms.
Aug
26
comment How can we deduce the relation $m = \frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}$ between relativistic mass and rest mass in special relativity?
I remember Feynman did something involving analyzing collisions of masses in different reference frames, and concluding that, while $mv$ is not a conserved quantity, $\gamma mv$ is. It's therefore natural to modify either the definition of momentum or mass in order to maintain momentum conservation in relativity.
Jun
5
comment What's the basic premise of General Relativity?
The Doppler factor (1+v^2/2c^2) that follows after "for our purposes" is an approximation that comes from a Taylor expansion of the exact factor. And Taylor expansion comes from calculus.
May
25
comment What force is responsible for anti-gravity?
The triangle lifter you're referring to works by ionizing air and forcing it downward, producing lift. The Mythbusters crew tested it in a vacuum and it didn't work, so it's clearly not anti-gravity. It's just a highly inefficient way of obtaining lift.
May
5
comment QED photon propagator to one-loop order gets different answers
Well that's not really what you asked for. How about this: 152.78.192.50/hepwww/staff/D.Ross/qft/aqft3.pdf ?
Apr
20
comment Transforming an equation to the co-vector version
You're right. I've changed my answer to reflect this.
Apr
20
comment Transforming an equation to the co-vector version
It's true as long as $\frac{d}{d \lambda} g_{\mu \nu} = 0$, which is true for most choices of $\lambda$ when considering a timelike geodesic (which is usually what one's interested in) when there's a timeline Killing vector. In physical scenarios where there's no t-symmetry, i.e. the FLRW metric, one's generally not interested in test particles anyway.
Apr
19
comment How do forces work
Necessary classic: youtube.com/watch?v=wMFPe-DwULM
Apr
11
comment Einstein's theory tells us that gravity is a curve in space and time but how does that causes attraction in mass?
youtube.com/watch?v=DdC0QN6f3G4
Apr
4
comment Why does the index of refraction change the direction of light
The easiest way to answer this is, of course, with Fermat's Principle. But that may not be what you're looking for.
Mar
23
comment Universe Expansion and two tennis balls
Well, since we have no idea what "dark energy" actually is, that's a tough question to answer.
Mar
23
comment Universe Expansion and two tennis balls
You're not reading it wrong, but you're missing Jerry's point. The reason the universe is expanding is because it is filled with dark energy, i.e. there is a nonzero cosmological constant. By "clear the universe of all matter" it was assumed that dark energy should also be removed. Remove the DE and space doesn't expand. Leave it in and it will, albeit at a different rate than we observe because the normal matter in the universe helps to "counteract" the effect of DE.
Mar
22
comment Future light cones inside black hole
To add to this, you can't avoid falling toward the singularity any more than you can avoid growing older.
Mar
20
comment Einstein gravity versus Newton's gravity
youtube.com/watch?v=DdC0QN6f3G4
Mar
19
comment Generating artificial gravity by using rotation
This is a rather subtle issue. In General Relativity, observables (like time, distance, etc.) are dependent on the metric tensor field. The value of metric is determined by the energy/momentum distribution in spacetime. It is assumed in your problem that the objects involved have little effect on the metric. The metric of a rotating coordinate system (i.e. the rotating clock) yields the above result. If the ring, etc., were sufficiently massive then they too would have an effect on the metric.
Mar
15
comment Trying to speak correctly of spacetime intervals and how to compare them
Sure, why not? The signature of either (+,-,-,-) or (-,+,+,+) is completely arbitrary. As for your last question, you're free to invent any notation you like.
Mar
14
comment How can my water cool down more quickly?
Uh, yes it is...
Mar
13
comment A tensor summation question
Yes. Flat 3D space is usually called 'Euclidean.'
Mar
12
comment A tensor summation question
But it's only unambiguous when the metric is Euclidean, so getting into the habit of writing everything with lower indices is a bad idea. It also looks sloppier.
Mar
12
comment A tensor summation question
Because using upper indices represent vectors while lower indices represent covectors. They are functionals of each other. Using all lower indices is ambiguous because you can't tell which is which.