Gravity?

[Dauphin]

Originally posted by Adalbertus


What I think you mean is that the two bodies should fall to each other at different speeds depending on the frame of reference.

Errr. not quite.

When two electrons are moving parallel to each other they are repelled from each other by the electric force, and attracted by the magnetic force. A massless electron pair moving and approaching c would have these forces cancel each other out.

This scenario is reconciled to the pure electric treatment (electrons frame of reference) by saying they are experiencing time dialation. Hence magnetism is often referred to as a relativistic correction to the electric force.

Presumably gravity should be analagous. As two test masses approach c, they should accelerate towards each other at a decreasing rate, no? If they don't then what is the reconciling feature.

[Adalbertus]

What i have some trouble in visualising is how something that is (more or less) "drawing" a closed curve in a 3 dimensions representation is said to "draw" a straight line in a 4 dimensions one.

You've answered that part already in your post, in four dimensions the path of the moon is a sort of spiral.

When I add the time dimension I have to say that, in fact, the Earth never returns to the same space-time point, for time as elapsed. We would have a kind of cilindrical elipse, but hardly a straight line, wouldn't we?

In some sense, it is. The problem is that we normally think to know what is a straight line. Then you have to define it in some way. The most practical way is to take the paths of the light in vacuum as straight lines, also in four dimensions.
On earth, this fully agrees with our notion of straight lines.
One of the first tests of General Relativity was to take a photograph of the sun and surrounding starts during a solar eclipse, and of the same stars later when the sun was far away. One has found that the stars that appeared close to the sun apparently moved apart, and that even stars were visible that should have been hidden by the sun. The reason is that the gravitational field was such that the sun attracted the light (from a flat geometry point of view), or that spacetime around the sun was curved.
Note that we cannot know the "truth" about the geometry. We can measure the universe as we like to. You can make up a theory with a flat spacetime, and an attractive force of the sun to light. The only problem is that this theory would become way more complicated than the theory with a curved spacetime is.
(To get a better notion of the problems with a curved geometry you might find something in a good atlas, when it comes to the problems of drawing a world map. It is impossible to draw a flat world map in which all shortest paths on earth show up as straight lines on the map. Things are similar in a curved spacetime).

So the next thing you'll probably ask is the following: The deflection of light by earths gravity is not noticeable, one has a hard time to see this from the sun, why is the path of the moon so much more curved than that of light?

The answer: Earth curves spacetime but the moon does, too. This gives a far stronger effect than of the earth alone. And the path of the moon is not very strongly curved. You can see this by a short estimate: The velocity of light is the conversion factor time - space. The moon is a bit more than a light second away from us. It takes one month for a turn around the earth. Which is that said spiral has a ratio of radius :thread height of about 1:2419200. To me, this is quite straight.

In fact gravity is roughly 10^17 times weaker than elecromagnetism. This is a huge number and is thus far, completely unexplained.

The antropic principle would simply state that if gravity were as strong as electromagnetism, everything had ended up in a black hole or complete void, as gravity is (at least mostly) attractive; thus there were nobody to notice that situation. Of course it doesn't help here.
I just had a look in a handbook of physics, and found a table of the strengths of the fundamental forces
strong interaction 1
electromagnetism 1/137
weak interaction 10^-14
If the numbers are comparable to what you state, gravity should go in as something like 10^-19, which I would not see as too far off. Electromagnetism and weak interaction were the first to be unified.

[Dauphin]

Lets try and kill this thread

If you want to talk coincidental numbers -

Why is the ratio of the electic force between an electron and proton to the gravitational force between an electron and proton the same as the ratio of the size of the universe to the size of the electron, which is also the square root of the number of particles in the universe?

e²/ G m_p m_e = 10⁴⁰ = ct * m_e c² / e²

Which incidentally is the square root of the number of particles in the universe

[Lancer]

Damn that's a good question.

This thread isn't teaching me about gravity sadly, though that's entirely my fault I'm sure. No, what this thread is teaching me is how deeply stupid I am compared to those who can debate such stuff. I am unable to wrap my brain around any of this very interesting but perplexing read. Ahh well, to each their own, but I tell you what, my hat is off to you all.

Now, I'm very much looking forward to being perplexed by the answer to SD's question...

Who can answer it?

[Adalbertus]

If you want to talk coincidental numbers -

Given the error some of your data have, such as "number of particles in the universe" or "size of universe", it's rather coincidental orders of magnitude.

Let's discuss real numbers, small ones:
We perceive four dimensions, one of which (time) is somewhat weird.
We perceive four fundamental forces, one of which (gravity) is somewhat weird.
Why?

This thread isn't teaching me about gravity sadly, though that's entirely my fault I'm sure

Maybe it's not only your fault, there are many intelligent people who don't have a clue on general relativity. And there are two inherent difficulties: Most people who are untrained in university maths have difficulties in understanding geometries other than the usual Euclidean, or a spacetime other than our normal Galilean. And even if they did there are huge problems in communication inherent to the subject: To get some decent and mathematically correct understanding of GR, you have to take a one year's course at the university (I didn't get through all of it because of other interests...), after having done physics for some time. It is close to impossible to fit the essentials of what you've learned in this time into a post which roughly stays in limits (Imagine writing a data compression software such as zip which reduces the size of any given file by a ratio of 1:10000). And scientists aren't really famous for their communication skills.

[Dauphin]

Originally posted by Adalbertus

Given the error some of your data have, such as "number of particles in the universe" or "size of universe", it's rather coincidental orders of magnitude.

The size of the "causal" universe is known to with an order of magnitude, as is the size of the electron.

The number of particles in the universe is correct to within an order of magnitude if space is flat (which it appears to be).

[Adalbertus]

Order of a magnitude. Exactly what I mean. I wouldn't try to find any meaning in it. OTOH, astrophysicists seem to be quite happy if reality fits to theory by an order of magnitude...

[Dauphin]

Did you know I was going to take a PhD in astrophysics/cosmology, but dropped the idea at the last moment?

[KrazyHorse]

This thread isn't teaching me about gravity sadly, though that's entirely my fault I'm sure. No, what this thread is teaching me is how deeply stupid I am compared to those who can debate such stuff. I am unable to wrap my brain around any of this very interesting but perplexing read

Gravity's simple. Tensor algebra isn't. Nothing in this world should have four indices tagged on it.

[Adalbertus]

Gravity's simple. Tensor algebra isn't. Nothing in this world should have four indices tagged on it.

Gravity isn't quite thqt simple, because its geometry collides with normal imagination.
Tensor algebra. Tsts. Differential geometry and exterior calculus rocks. Gets you rid of most nasty indices unless you want your result in coordinates

edit: thqt??? s*** french kezboqrds!