pendulum = gravity

yet another way i can prove your theories wrong.


i am not going to waste my time going too deep here (if i dont have too) but pendulums sway back and forth because gravity. read more http://en.wikipedia.org/wiki/Pendulum

discus.

(pendulum pictured below)

Because of gravity?  I say it's because of acceleration.  Nice try though.

Because of gravity?  I say it's because of acceleration.  Nice try though.

lol, i will get to the bottom of this. i am sure there is fact in what i said that can prove you wrong but i haven't the time currently to research.

ps i am gonna bring this site up in my class. lol my teacher will get a kick out of it, and prove you wrong.

lol my teacher will get a kick out of it, and prove you wrong.

Hopefully they'll come up with some original arguments.

ps i am gonna bring this site up in my class. lol my teacher will get a kick out of it, and prove you wrong.

Einstein says I'm right.  I doubt your teacher is smarter than Einstein.

Einstein says I'm right.  I doubt your teacher is smarter than Einstein.

Hardly.

While Einstein would agree that an acceleration causes a pendulum to swing, he would probably say that it was an acceleration caused by the mutual attraction of the pendulum and the Earth (i.e. Gravity)

He would almost certainly not say that it was due to an upward acceleration of a flat-earth.

he would probably say that it was an acceleration caused by the mutual attraction of the pendulum and the Earth (i.e. Gravity)

Doubtful.  Einstein did not believe that matter attracts other matter.

He would almost certainly not say that it was due to an upward acceleration of a flat-earth.

I bet he would.

This has been brought up previously, Geoguy and engineer both know what the reasons are, as they have been explained in the other thread, which I beleive they participated in.

Fe cannot explain it, and Enstein didn't beleive in a flat earth, nor can he agree with someone that was born after he died.

Fe cannot explain it,

I just did.

Yeah clearly this is not a proof of gravity vs the ever accelerating Earth at all.  Both scenarios would result in the same outcome.

I also think it is very important to understand what Einstein had to say about gravity - which is essentially that matter distorts space.  The so called force of attraction between two bodies in RE theory is essentially a fictitious force.  It's not that the items attract each other, it's that they bend the space and that causes them to move together.  This is a pretty simplified explanation but there are plenty of more detailed descriptions out there.

http://en.wikipedia.org/wiki/Fictitious_force

That's a good starting point.

Gravity as a fictitious force

All fictitious forces are proportional to the mass of the object upon which they act, which is also true for gravity. This led Albert Einstein to wonder whether gravity was a fictitious force as well. He noted that a freefalling observer in a closed box would not be able to detect the force of gravity; hence, free falling reference frames are equivalent to an inertial reference frame (the equivalence principle). Following up on this insight, Einstein was able to show (after ~9 years of work) that gravity is indeed a fictitious force; the apparent acceleration is actually inertial motion in curved spacetime. This is the essential physics of Einstein's theory of general relativity.

*Also note Biblicul that I'm backing up something I say with sources again. :shock:

centrifugal force is a ficticious force...  :cry:

Doubtful.  Einstein did not believe that matter attracts other matter.

Excuse me? Gravity *is* matter attracting other matter, and Einstein most certainly believed in it. He just postulated that the mechanism behind the attraction is that massive objects warp space-time, and the space time warping causes objects to accelerate relative to a reference frame in which the massive object is stationary.

Yes, but Einstein's theory of general relativity says that in a small enough space, it is impossible to distinguish between gravity and acceleration.  Pendulums included.

Quote from: "Erasmus"

Doubtful.  Einstein did not believe that matter attracts other matter.

Excuse me? Gravity *is* matter attracting other matter, and Einstein most certainly believed in it. He just postulated that the mechanism behind the attraction is that massive objects warp space-time, and the space time warping causes objects to accelerate relative to a reference frame in which the massive object is stationary.

THE CURVATURE OF SPACE-TIME.  Sorry, somedays I just feel like yelling that at the top of my lungs sometimes.

Excuse me? Gravity *is* matter attracting other matter, and Einstein most certainly believed in it.

No, really, he didn't.  "Matter attracting other matter" is a description of a force, which Einstein definitely stated that gravity was not.  Gravity is just an observed effect of the geometry of spacetime.  Einstein believed exactly what beast described -- that matter tells space how to curve, and space tells matter how to move.

Quote from: "skeptical_scientist"

Quote from: "Erasmus"

Doubtful.  Einstein did not believe that matter attracts other matter.

Excuse me? Gravity *is* matter attracting other matter, and Einstein most certainly believed in it. He just postulated that the mechanism behind the attraction is that massive objects warp space-time, and the space time warping causes objects to accelerate relative to a reference frame in which the massive object is stationary.

THE CURVATURE OF SPACE-TIME.  Sorry, somedays I just feel like yelling that at the top of my lungs sometimes.

There's no need to shout. Especially when you are simply using a different word which means the same thing. From Merriam-Webster: "warp: a twist or curve that has developed in something originally flat or straight."

Would you be happier if I said that the presence of mass and energy causes the metric tensor which describes the geometry of the pseudo-riemannian manifold representing spacetime to be locally non-euclidean?

As to Erasmus' comment: you are right, there is no force involved, but rather an influence of curved spacetime causing objects to move inwards near massive objects in the absense of any force. Whether or not the word "attract" appropriately describes this behavior is a problem with the vagaries of the English language. In any case, Einstein would say that the motion of the pendulum *is* due to the fact that the surface of the earth is accelerating upwards in a local inertial frame.

Would you be happier if I said that the presence of mass and energy causes the metric tensor which describes the geometry of the pseudo-riemannian manifold representing spacetime to be locally non-euclidean?

No, since it's part of the definition of a manifold that it is everywhere locally euclidean.  I would, however, be happy if you replaced "locally" with "on large scales" or something to that effect.

Quote from: "BOGWarrior89"

Quote from: "skeptical_scientist"

Quote from: "Erasmus"

Doubtful.  Einstein did not believe that matter attracts other matter.

Excuse me? Gravity *is* matter attracting other matter, and Einstein most certainly believed in it. He just postulated that the mechanism behind the attraction is that massive objects warp space-time, and the space time warping causes objects to accelerate relative to a reference frame in which the massive object is stationary.

THE CURVATURE OF SPACE-TIME.  Sorry, somedays I just feel like yelling that at the top of my lungs sometimes.

There's no need to shout. Especially when you are simply using a different word which means the same thing. From Merriam-Webster: "warp: a twist or curve that has developed in something originally flat or straight."

Would you be happier if I said that the presence of mass and energy causes the metric tensor which describes the geometry of the pseudo-riemannian manifold representing spacetime to be locally non-euclidean?

As to Erasmus' comment: you are right, there is no force involved, but rather an influence of curved spacetime causing objects to move inwards near massive objects in the absense of any force. Whether or not the word "attract" appropriately describes this behavior is a problem with the vagaries of the English language. In any case, Einstein would say that the motion of the pendulum *is* due to the fact that the surface of the earth is accelerating upwards in a local inertial frame.

I failed to read the whole paragraph.  Forgive me.

Quote from: "skeptical_scientist"

Would you be happier if I said that the presence of mass and energy causes the metric tensor which describes the geometry of the pseudo-riemannian manifold representing spacetime to be locally non-euclidean?

No, since it's part of the definition of a manifold that it is everywhere locally euclidean.  I would, however, be happy if you replaced "locally" with "on large scales" or something to that effect.

When you say "manifolds are locally euclidean" you mean that manifolds are locally homeomorphic to n-dimensional euclidean space (or diffeomorphic in the case of smooth manifolds) which, of course, they are. But here we're talking about pseudo-riemannian manifolds, which have geometry as well as topology, and so when I said "locally non-euclidean" I meant locally non-isometric to euclidean space. It's generally understood that in the context of geometry, "euclidean" means "isometric to euclidean space" and not just homeomorphic.

Edit: and no, I do not mean "on large scales." I mean locally! As in, no neighborhood in the vicinity of a massive object is isometric to flat space.

Quote from: "Erasmus"

Quote from: "skeptical_scientist"

Would you be happier if I said that the presence of mass and energy causes the metric tensor which describes the geometry of the pseudo-riemannian manifold representing spacetime to be locally non-euclidean?

No, since it's part of the definition of a manifold that it is everywhere locally euclidean.  I would, however, be happy if you replaced "locally" with "on large scales" or something to that effect.

When you say "manifolds are locally euclidean" you mean that manifolds are locally homeomorphic to n-dimensional euclidean space (or diffeomorphic in the case of smooth manifolds) which, of course, they are. But here we're talking about pseudo-riemannian manifolds, which have geometry as well as topology, and so when I said "locally non-euclidean" I meant locally non-isometric to euclidean space. It's generally understood that in the context of geometry, "euclidean" means "isometric to euclidean space" and not just homeomorphic.

Edit: and no, I do not mean "on large scales." I mean locally! As in, no neighborhood in the vicinity of a massive object is isometric to flat space.

You speak funny numbers.

when I said "locally non-euclidean" I meant locally non-isometric to euclidean space. It's generally understood that in the context of geometry, "euclidean" means "isometric to euclidean space" and not just homeomorphic.

...

As in, no neighborhood in the vicinity of a massive object is isometric to flat space.

Hm... I really felt like the whole point of the equivalence principle was that on small enough scales, curved spacetime has, approximately, a minkowski metric.  Wouldn't this make it locally isometric to flat space?

Quote from: "skeptical_scientist"

when I said "locally non-euclidean" I meant locally non-isometric to euclidean space. It's generally understood that in the context of geometry, "euclidean" means "isometric to euclidean space" and not just homeomorphic.

...

As in, no neighborhood in the vicinity of a massive object is isometric to flat space.

Hm... I really felt like the whole point of the equivalence principle was that on small enough scales, curved spacetime has, approximately, a minkowski metric.  Wouldn't this make it locally isometric to flat space?

And, on small enough scales, Quantum Mechanics decides to bite General Relativity on the ass.

Quote from: "skeptical_scientist"

when I said "locally non-euclidean" I meant locally non-isometric to euclidean space. It's generally understood that in the context of geometry, "euclidean" means "isometric to euclidean space" and not just homeomorphic.

...

As in, no neighborhood in the vicinity of a massive object is isometric to flat space.

Hm... I really felt like the whole point of the equivalence principle was that on small enough scales, curved spacetime has, approximately, a minkowski metric.  Wouldn't this make it locally isometric to flat space?

No, it would make it locally approximately isometric, which doesn't really get you anywhere. For example, a sphere is a sphere, and the curvature at any point of a sphere is nonzero, whereas the curvature at any point in euclidean space is nonzero. However, as we all know by virtue of living on a sphere (or at least debating the possibility), if you zoom in a lot, it's pretty close to being flat. But no matter how much you zoom in, it's still not perfectly flat, it's just good enough you can't tell - the approximation gets very good, but it's never perfect.

No, it would make it locally approximately isometric, which doesn't really get you anywhere. For example, a sphere is a sphere, and the curvature at any point of a sphere is nonzero, whereas the curvature at any point in euclidean space is [zero]. However, as we all know by virtue of living on a sphere (or at least debating the possibility), if you zoom in a lot, it's pretty close to being flat. But no matter how much you zoom in, it's still not perfectly flat, it's just good enough you can't tell - the approximation gets very good, but it's never perfect.

Okay, I get that... but I thought the fact that the approximation can be made arbitrarily good by getting arbitrarily local is the point of the equivalence principle.  But okay, I'll stand corrected on the "locally euclidean" issue.

It can be made arbitrarily good, but that is not the same as exact. We can find arbitrarily good approximations to 0 among the positive numbers, but we can't find an exact match. We can get something very close to a flat disc by cutting it out of a very large sphere, but for a sphere of any finite radius, a disc cut out will not be exactly flat.

So, back on topic.  Cheech, what did your teacher have to say?