What is being suggeted when it is proposed that space is curved?
General Relativity does not have a causal mechanism for the force of gravitation. Curved space is simply a measurement of a property of space unknown to the theory of general relativity. A mapping system for the effect of a g-field...but ignore me please I am a "crack-pot".
Note: I am not describing the theory of relativity from within the hermetically sealed system. This is an "outsiders" viewpoint.
One example that immediately springs to mind is that the shortest distance between two points is no longer a straight line but a curve, also you'll find that the angles of shapes drawn in curved space add up to different values than the same shapes in flat euclidian space.
how could a curved path between 2 objects be shorter than a straight one?
Could be because if you sent an object on it's merry way in whatever direction in space - It would follow a curved line. This would be in response to whatever gravitational influence is the greater of all the other gravitational influences. If you could have a situation where all gravitational influences were equal from all directions - You could send an object in a straight line, and boldly say that space is not curved.
If my statements are not true - Then space is curved.
Think of two points on the surface of a globe, you'll notice that the shortest path between the two is a curved one as well (this fact was well known to sailors in days of yore).
It depends arbitrarily on the system in which the distance is measured.
The "curvature" of space is a metaphor for the behavior of spacetime (e.g., in the presence of matter). For example, a gravitational field around some mass can be visualized as a well...like a drawdown curve around that object. The trajectory of an object that enters that drawdown area (enters the slope of the well) is altered accordingly based on the strength of the field (the slope of the curvature).
Given that Relativity only has 3 dimensions of space, it is not proposing a physical curvature of 3D space into a higher, 4th dimension of space. (although maybe into the 4th dimension as Time, but I'm less clear on that)
Phobos, it's more than a metaphor, the curvature of space in GR works exactly the same way as if it were curved into a 4th higher dimension of space (some people have a hard time understanding that though space is curved this way it doesn't at all imply that a fourth dimension of space exists, tho').
I'm inclined to think of gravity like this.
And that there is no curvature of space. I think of gravity as a wound out wave in a spiral fashion. The wave is the particle. Half of the wave (particle) is localized and the other half is not. The part that is not is the gravitational aspect of the wave (particle). The localized part of the wave is what we see as a particle (the localized wave).
So it is a metaphor that works!!!
It still fails to explain the force of gravity in its causal details.
In Sorce Theory, gravity is a refraction of the internal wave systems of the atom in response to an over-riding density gradient (g-field) in the unified field.
The curvature of space is the causal explantion of gravity!!!!!!!!
When your looking at curved space in GR it is exactly the same as looking at a curved topology which is a lot stronger relationship than the word 'metaphor 'implies'.
The problem with that is that it does not explain the behavior of light, ie how light can be affected by gravity if it is massless.
Your interpretation of mass is likely different than mine. Light on the loose coming from say another star ... I see as a wave that is planar in nature. Sort of like a pizza getting made at the parlor. The dude tosses the dough in the air with a spin - It grows in size. With a photon it never stops growing in that planar fashion. At least not until it gets localized, partially localized, (acted on?). A free ranging Photon will be affected in more or less the same way as two gravitational field lines affect each other.
It is the explanation of the effect of the causal mechanism. It is not an explanation of the mechanism itself. This is common knowledge that the mechanism of gravitation still is a mystery in the standard model.
Can you tell me exactly HOW mass curves space?
It is simply a map. Nothing more.
Mass curves space via gravity (I know you're not going to be happy with that but GR in terms of explaining the causes of gravity is a great improvemnt oin Newtonian physics).
The fact that gravitational fields produce the exact same results as curved space means it is perfectly correcvt to say mass curves space.
The first question is "What is being suggested when it is proposed that space has zero curvature?"
Around 1820 it occurred to Carl Gauss to wonder about this and the answer he came up with was to do an experiment to see if the sum of the interior angles of a large triangle---determined by surveying instruments----would come out to be 180 degrees.
Would this satisfy you, as meaning that some region of space is uncurved, or has zero curvature?
Before asking if space is curved in some region it would be good to know what exactly do you mean by saying that it is not curved or flat. I think this triangle idea of Gauss is very good, how about you?
If we measure a big triangle and the angles sum to more than 180 degrees we could say that the curvature is "positive".
Or if it came to exactly 180 degrees we could say it the curvature was zero. Is this OK?
With that idea of curvature, there is no reason to suppose space is flat in any region where there is matter and indeed if we put 3 satellites in orbit around the sun in a rougly equilateral triangle and had them flash laser beams back and forth to make a triangle and if we measured the sum of the interior angles very accurately it would most likely come out to be more than 180 degrees.
My post here is in response to the question asked by Mitch Bass at the start of the thread, so I will wait to see if he is still around and wants to reply to my post. If he doesnt that is fine and I will just let it be.
This depends on your view of space. My personal view is that space can't be curved, because it isn't there. One could expect the same results from a gravitational field or curved space, but one of em has to be wrong. Right?
I agree that it is an improvement over newtonian gravitation, but you are correct I am not at all convinced that the mechanisms of gravitation have been explained by relativity, especially when I have seen a good causal explanation.
Exactly. Einstein realized this when, in his speech at Leydon, he said that the concept of the ether is crucial to understand the notion of curved space. The problem is that the understanding of substance is incompatible with the principals of relativity. All of these problems can be resovled if one understands "space" to be a fluid frame of reference--an actual frictionless fluid compressible substance from which everything is made and the "fundamental" particles are simply disturbances in this substance (solitons, vortices, etc.).
but that is only because you can't travel through the earth... if you could dig through... a straight line would be the shortest path... so if you were traveling in space.. a straight line should be the shortest distance... unless you had to go around something?? no?
Yes, but what we're thinking about here is not two spacial dimensions being curved like the surface of the Earth but three spacial dimensions. The Globe is only one analogy to help visualize it.
Ya have to be careful when you (I, anybody) talk about "curved space". Not anybody around here draws this conclusion, but other people that don't know anything of the concepts.
Because, take the Earth for example. The thinking goes these people put together goes this way:
1) Gravity makes Earth orbit the Sun.
2) Gravitation is really a distortion of space, it curves space.
3) The ole' "rubber sheet analogy" ...
4) So, the Sun distorts space around itself via gravitation.
5) The Earth is just following this path (track) in space around the Sun that the Sun has carved out around itself, like a ball flowing around a dip in a rubber sheet.
Of course that's wrong .. the distortion of space is way too little for the Earth to be following (trying to be careful to pick a correct word) a physical track around the Sun that the Sun carved out of space.
The element of time is not brought into the picture above .. to make the closed loop the Earth appears to follow around the Sun, you have to bring in time, and you find out that the path Earth follows in orbiting the Sun is not a closed loop at all, it's a very-very lazy coiled loop.
I like the lazy coil description (for the earth's path in space time.
Can you estimate the excess angle in an equilateral triangle around the sun where the sides pass, say, a million km from center.
By how many microradians would the sum of the interior angles exceed pi radians or 180 degrees?
As a very rough estimate I get the excess angle is 18 microradians.
This is a small angle but at least it is the present moment and 3D rather than referring to something in 4D spacetime. And the basic technology is how surveying instruments work, so the example has a kind of concreteness. Maybe you can get a better estimate of the excess angle?
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