Dear George,

Tut tut my friend.

Try this on for size.

From 'Improbable Research - Research that makes people LAUGH and then THINK'.

http://www.improbable.com/airchives/paperair/volume7/v7i3/angels-7-3.htm

Surely laughing and thinking are two of the more pleasurable human activities (not discounting sex of course and about a dozen other vices) so shouldn't we be all for things that allow us to do just that?

Here are some snippets;

“According to Thomas Aquinas, it is impossible for two distinct causes to each be the immediate cause of one and the same thing. An angel is a good example of such a cause. Thus two angels cannot occupy the same space. This can be seen as an early statement of the Pauli exclusion principle. (The Pauli exclusion principle is a pillar of modern physics. It was first stated in the twentieth century, by Pauli.)”

and

“One of the first reported attempts at a quantum gravity treatment of the angel density problem that also included the correct end of the pin was made by Dr. Phil Schewe. He suggested that due to quantum gravity space is likely not infinitely divisible beyond the Planck length scale of 10exp-35 meters. Hence, assuming the point of the pin to be one Ångström across (the size of a scanning tunnelling microscope tip) this would produce a maximal number of angels on the order of 1050 since they would not have more places to fill.”

finally

“Assuming that each angel contains at least one bit of information (fallen / not fallen), and that the point of the pin is a sphere of diameter of an Ångström (R=10exp-10 m) and has a total mass of M=9.5*10exp-29 kilograms (equivalent to that of one iron atom), we can use the Bekenstein bound on information to calculate an upper bound on the angel density. In a system of diameter D and mass M, less than kDM distinguishable bits can exist, where k=2.57686*10exp43 bits/meter kg. This gives us a bound of just 2.448*10exp5 angels, far below the Schewe bound.”

In fact I think it would make an excellent university assignment.

Dear George,

You said;

“Well, since the Earth orbits the Sun, its velocity (a vector) with respect to the Sun cannot be constant. From Wikipedia: “To have a constant velocity, an object must have a constant speed in a constant direction. Constant direction constrains the object to motion in a straight path (the object's path does not curve).””

I think you might find the critical words are 'with respect to the Sun'.

Of course the Earth changes its absolute velocity as it orbits the Sun because of the nature of the elliptical orbit, slower at the pointy ends but quicker through the flat sides.

Yet an observer on the Sun sees the Earth travelling through each 10th of an arc in the same amount of time therefore exhibiting, with respect to themselves, a constant velocity.

Dear WmTrevor,

Thank you for the links.

They might need to be treated with a degree of caution as most are about 15 years old and there has been a lot more work done on Gravity.

One explanation has a logic problem;

“If a star collapses into a black hole, the gravitational field outside the black hole may be calculated entirely from the properties of the star and its external gravitational field before it becomes a black hole.”

So even if this black hole sucks in another star its gravitational field can never grow in size from its original strength?

But I do like this one;

“The key point is that electromagnetic interactions (and gravity, if quantum gravity ends up looking like quantum electrodynamics) are mediated by the exchange of *virtual* particles. This allows a standard loophole: virtual particles can pretty much "do" whatever they like, including traveling faster than light, so long as they disappear before they violate the Heisenberg uncertainty principle.”

Virtual particles? – I think we have found our modern day angels.

Dear Poirot,

This could possibly be just an issue of terminology so can I rephrase my statement to;

....If the Sun instantly disappears then it is difficult to comprehend the Earth falling toward the warp in the fabric of space and time caused by an imagined Sun for eight minutes...

Remember this field is moving as the Sun moves in relation to the Earth. Experiments show that the Earth is 'falling' toward where the Sun is now not the position indicated by the light reaching the Earth.

The quandary is how does the field keep moving after the Sun is gone?

csteele,

Regardless of terminology, the warp would dissipate at the speed of light - not instantaneously.

Do you reckon?

"One explanation has a logic problem;"

Does it, csteele?

"So even if this black hole sucks in another star its gravitational field can never grow in size from its original strength?"

The 'it' in the sentence, “If a star collapses into a black hole, the gravitational field outside the black hole may be calculated entirely from the properties of the star and its external gravitational field before it becomes a black hole.” clearly refers to the 'subject' of the star (the one that collapses) at the point in time rather than space (get the joke?) of it becoming a black hole.

Here's the spin on black hole astrophysics doing the rounds over the past few days...

http://www.space.com/19980-monster-black-hole-spin-discovery.html

Let us know if you notice anything inconsistent with those older links, above.

Dear WmTrevor,

Thanks for the link.

I managed the following on the quiz;

“You Scored 78%”
“You answered 7 out of 9 questions correct!”
“If you got 7 to 9 correct, you'd make Einstein proud. If you got 4 to 6, you're ready to apprentice to Stephen Hawking. If you got 3 or less right, it's time to review your black hole basics.”

Which was lucky as the last thing I wanted was some stranger reviewing my 'black hole basics'.

Hint – the one about the Sun being replaced by a black hole of equal size is a bit tricky.

To the quote;

“The gravity doesn't have to get out of the black hole.  General relativity is a local theory, which means that the field at a certain point in spacetime is determined entirely by things going on at places that can communicate with it at speeds less than or equal to c.  If a star collapses into a black hole, the gravitational field outside the black hole may be calculated entirely from the properties of the star and its external gravitational field before it becomes a black hole”

Yet I would have thought if it increases in size, as it gathers more matter, gravity or rather the effects of the gravitational field do escape to impact things outside the event horizon.

Where am I going wrong?