It uses two people who are traveling in a parallel line northward as an example for reference. The two people appear to be equidistant, but still are moving closer together as they reach the pole because the earth is curved.

Though this individual example makes some sense for an object in motion and in orbit, as well as to why the time is diffrent, it does not explain why if I hold a cup in the air and let go it will fall to the ground. All things relative, the cup is not in motion and has no path to follow to be bent or moved. However, logic would lead one to assume that it will fall to the ground when I let go. What dictates that the warped space-time from the earth will specifically act on the cup now that it is let go? I understand the correlation between acceleration and gravity having the same effect, but the explanation I was given on space-time being bent by mass seems to have holes in it. Can someone with a decent knowledge of physics explain this to me? How, and more importantly why exactly does gravity work on the cup the way it does? How does stored kinetic energy work? Is the mass continualy bending space and time to draw everything closer it to it (which would explain the acceleration)?

Now, each and every piece of matter exerts a force upon each and every other piece of matter throughout the universe, no matter how far away it is. The force is dependent on the square of the distance, so that the force a galaxy 100 billion light years away exerts on your nuts is essentially zero. Let's assume the mass of your nuts is .05 kilograms.

F = (G * M1 * M2) / R^2

G(Newton's Constant) = 6.67e-11
M1= .05 kg
M2(assuming 100 billion suns with an average mass equal to ours) = 2e30 kg * 100e9 = 2e41 kg.
R= 100 billion light-years = 1e11 * 9.4e15 m = 9.4e26 m.

So, plug in, remembering to square the distance, and you get: 7.55e-25 N, or 0.000000000000000000000000755 N. Verry verrrrrry small, indeed.

Anywho, the idea is that everything attracts everything else, but when masses are highly disparate or distances are extreme, one's effect on the other is drastically altered. That's why the cup will fall when you let it go. Relativistic effects are generally undetectable in a classic example. They are there, and if you use relativity's equations to describe the cup's fall, you'll see them. Since the masses are disparate by 30 orders of magnitude, they don't rightly matter. You'd never miscalculate the time it takes for the cup to fall if you used classical equations.

Celestial bodies are a different story. You're dealing with huge masses, velocities, and exerted forces. And yes, the objects are bending space and time. That's why we can see some stars which are behind the sun; its gravity affects the light's path and deflects it towards us.

Now, the way relativity works is this: it's all relative. From earth's standpoint, the moon is travelling in an elliptical orbit around it. From the moon's viewpoint, it's going in a straight line. Depends on how you observe it.

Consider a ship traveling close to the speed of light. The people aboard that ship age much more slowly than then people on earth, who are essentially standing still. They don't experience time and more slowly, what they experience is a shortening of the distance traveled. Say they're going four light years away at such a speed that, to an observer on earth, it'll take five years to cover the distance. To an observer on the ship, however, it doesn't take five years to get there, but a much shorter interval. How can they both be right?

This is the crux of relativity. The person on the ship sees length dialation, so that the distance traveled appears far, far shorter that four light years. So he says, "Oh, great! We'll be there in six months, because it's only half a light year away!" So upon arriving, the person in the ship has only aged six months, but has travelled for five years.

Kooky, ain't it?

As to the why the cup falls, that's just how the universe works. Gravity is fundamental property of matter, a consequence of the Big Bang. It is by far the weakest of the fundamental forces, but it's still there.

If something were to have an aboslute velocity of zero relative to everything else in the universe wouldn't their time be going by at an infinite rate?

The time dialation equation probably dosn't relate to 1/v but it seems like it would.

In short.. nuts.

[ 11-22-2003: Message edited by: diadem ]

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Naimah had this to say about (_|_):
This got me thinking...

If something were to have an aboslute velocity of zero relative to everything else in the universe wouldn't their time be going by at an infinite rate?

The time dialation equation probably dosn't relate to 1/v but it seems like it would.

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wouldn't that be the same as matching speed with something else? isn't the point of this that there are no fixed points?

In short, it's not really right to say the cup isn't moving, and has no path. It is moving through time. I don't mean to make a quick cop-out with an answer like that, what I'm trying to say is that the "Curved path" analogy works for more than three dimensions: Yes, the physical dimensions curve, making parallel lines meet, etc. But so does the time dimension.

Though this is mutilating the theory beyond recognition, try to picture it as the "parallel lines" of the cup and earth in the direction of time meeting, the same way that you accept the idea that curved space makes physical parallel lines intersect.

It all centers on the concept of the "straightest lines possible" in a space, and the unusual paths they follow. But that's time-oriented straight lines, as well as space-oriented straight lines.

...I think I'm explaining this badly. I'll try again in the morning, when I'm not half asleep. I may be able to take a decent stab at Potential Energy then as well. Trying to explain these things may actually give me a shot at an intuitive grasp some day.

[ 11-23-2003: Message edited by: Chalesm ]

You are taking time and palacing it as an extra dimension on a grid. Just as the two travelers heading north were traveling in a straight path happened to be heading towards each other because of the curve of the earth, the cup, and more importantly everything close to the earth’s mass is approaching the earth as it passes through time because of the earth mass folding the grid by placing it onto another dimension that happens to be curved itself (representing mass or whatever). The mass of earth curves the 4 dimensional path of the cup and everything close to earth (that is constantly in motion in at least one axis because we are traveling forward through time) to make us head down towards earth.

Not to be a pain in the ass, but this still gives me more questions. First, this just changes the “gravity magically moving things towards things with greater mass” idea to a different level but doesn’t explain it. Why does the simple fact that there are a lot of atoms close together in something suddenly give it the ability to bend space-time? It’s the same problem, just a level deeper. If you say it’s just like putting a globe in the carpet of space that is assuming that the globe itself has mass and has gravity, and displacing the carpet somehow. That's creating a theroy using the assumption that's it's true in the proof. That’s like saying oh there’s a fifth dimensions and that’s the magical answer, or something equally vague. Another “magic answer” so to speak, hidden under new theory. This would make the criticism of Newton hypocritical, with the exclusion of how exactly items can interact through a vaccum and distances (but not why they do so when mass is incresed). (Then again, I’m aware there always will be an “unexplained” level. I suppose you answered the "how" but not the "why")

Second, ignoring my little whine there, does this mean that the curve is getting exponentially bigger, as in we are heading towards the earth at an increasing rate which would explain the coloration between gravity and acceleration?

[ 11-23-2003: Message edited by: diadem ]

It seems there are two questions here: why objects do what they do in relation to curvature and space, and why some consider general relativity more satisfying than Newton. I can somewhat answer the second, but I'm afraid that with the first I'm going to have give that annoying, unsatisfying answer you've likely anticipated.

In answer to the first:
I unfortunately have no truly satisfying answer to "why matter curves space", and I seriously doubt there is one, or that there ever will to be. In its heart of hearts, physics (and most of science) is observational, not explanitory. The theory of relativity isn't interesting because it explains why matter curves space, it's interesting because it found that if we compared what actually happens in the universe to a particular mathematical model, just about everything matched (even things we hadn't thought of before). Pretty much all theories are like this, if one considers them deeply enough.

I think the kind of "why" you're looking for isn't likely to show up; quantum theories of gravity try to explain it all in terms of gravitons, massless particles that every bit of matter throws back and forth, causing all the strange effects. But to be honest, introducing quantum mechanics is likely only going to screw things up further; if ever there were an unintuitive, unsatisfying theory, it's quantum, and looking to it for "why" is only going to make things worse. The fact that quantum gravity is a somewhat-contradictory mess is only icing on the cake.

So, relativity just says matter does curve space, because that seems to be the simplest and most straightfoward mathematical model to match observations. It doesn't even have a shot at why that I know of. So yes, calling it a "magic answer" with no explination may be annnoyingly apt.

In answer to your second question, though, in some ways relativity's non-answre is still more satisfying that Newton's. The assumptions it asks of us are a little less strange in some ways, as indeed you partially stated yourself. In Newton's theory of gravity, there's the strange little fact that gravity only effects matter. It's one of those points that we need to consider the ramifications of for a moment. Two or more bodies at any distance instantly know where the other mass is without anything in between changing. No signal is sent or recieved, as there is no medium for a signal in Newtonian gravity. There's no analogy for this in our ordinary existence, every mundane chain of cause and effect (and indeed, every non-mundane, strange effect we know of) must have some form of message between the cause and the effect. In newtonian gravity an object simply seems to "know" where every other object in the universe is without being told, and acts accordingly. Newton asks (in fact, requires) that we accept this strange notion of non-connected communication. This is what those textbooks are talking about when they condecendingly call newton a "magic force".

General relativity doesn't have this strange factor. The one thing it asks is that we accept that matter can bend space (which isn't quite as big an assumtion as it seems, as we can PROVE space does bend in certain circumstances. For example, if one got close to a big star and made a triangle, the angles would add up to more than 180 degrees). If we accept this, we now know why objects do what they do, the "signal" between two distant objects is sent as a wave through the curvature of spacetime itself. If we accept that each bit of matter adds it's own contribution of space-time curve, all the rest of general relativity follows.

I'm aware it is still a pretty unsatisfying answer, and the notion of any phyicist brushing off an older to theory as just "silly assumtions of obviously false properties" is going to ring a bit hipocritical to anyone, as our theories are pretty likely to be wiped out the same way by much nicer refinements. Physics can be annoyingly unsatisfying at times, and answering pretty much any "why?" is the prototypical situation.

That's why I always take philosophy with my phyics. One gives a founded, unsatisfying "how", and the other gives an unfounded, unsatisfying "why". But just occasionally they can feel just a touch satisfying together.

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Chalesm had this to say about Cuba:
For example, if one got close to a big star and made a triangle, the angles would add up to more than 180 degrees

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I am going to use this fact to boggle my math teachers. At the bottom of some question involving trigonometry/Pythagorean Theorem I'll put as a footnote 'assume the triangle is near a really big star'. and confuse the heckupo out of em. Mwahahaupo.

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Gunslinger Moogle had this to say about (_|_):
I am going to use this fact to boggle my math teachers. At the bottom of some question involving trigonometry/Pythagorean Theorem I'll put as a footnote 'assume the triangle is near a really big star'. and confuse the heckupo out of em. Mwahahaupo.

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Non-Euclidean space is fun.

And as a PS to Diadem: I can't really answer your second question about acceleration yet; I've yet to get a good explination of the analogy between acceleration and gravity; we haven't gotten to that section of the textbook. The curvature is quite definitely increasing as you get closer, though, I know that much. What you're saying seems plausible in light of that.

[ 11-24-2003: Message edited by: Maradon! ]

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Maradon! had this to say about dark elf butts:
Hay, did you guys know there are 4 simultaneous 24 hour days within a single 24 hour Earth rotation?

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^^^

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Maradon! had this to say about Jimmy Carter:
Hay, did you guys know there are 4 simultaneous 24 hour days within a single 24 hour Earth rotation?

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*chuckles ever so softly until it becomes a whimper*

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Gunslinger Moogle had this to say about (_|_):
*chuckles ever so softly until it becomes a whimper*

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As an interesting side note, Gene Ray was recently diagnosed as a schizophrenic.

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Maradon! must read alot of poetry:
As an interesting side note, Gene Ray was recently diagnosed as a schizophrenic.

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Is that the word we use for incredibly stupid raving fools these days?