Space Dilation / Constriction

BdS

BdS

Registered Senior Member
Since space only contains 1 main property distance, distance is the only thing that can be changed to warp or curve SPACE-time with the presence of mass. If mass causes Space distance to dilate or constrict it might explain a bit.

Example:

Let’s analyse Earth’s mass and what it’s doing to the space occupied and influenced by it.

At Earths sea level = 6,378.13 km radius, example: space distance density would be dilated or constricted in a volume or area at the given radius.
At sea level radius, 1m of space has a constricted distance of 1.0621m
At sea level radius + 10m, 1m of space has a constricted distance of 1.0612m
At sea level radius + 20m, 1m of space has a constricted distance of 1.0603m
At sea level radius + 30m, 1m of space has a constricted distance of 1.0594m
Etc…

The constricted space distance values are just examples and not real space distance constricted or dilated values.

The “changing space distance dilation” at different radius's is what “curved space-time” is mapping.

You could probably work out the real values by using the gravitational time dilation at sea level = x then reverse calculate the amount to space distance dilation is required to slow the clock down by that of space distance contraction.


This might be what is causing gravity! Objects located in “curves” are attracted / move toward higher space distance density areas or move down the curve...
 
BdS said:
This might be what is causing gravity! Objects located in “curves” are attracted / move toward higher space distance density areas or move down the curve...
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Have you considered reading up a little on general relativity?
You're sorta tryin' to reinvent the wheel here.
 
BdS said:
Since space only contains 1 main property distance
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Gravity warps spacetime not just space. If just space was warped then a thrown baseball, a fired bullet and a photon would all follow the same trajectory.
 
BdS:
BdS said:
Since space only contains 1 main property distance, distance is the only thing that can be changed to warp or curve SPACE-time with the presence of mass.
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General Relativity says that the TIME can also be changed. Hence "spacetime".

I'm not sure that "distance" is a property of space, anyway.
If mass causes Space distance to dilate or constrict it might explain a bit.
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Well, it does. The general theory of relativity explains how it happens, quantitatively.
The “changing space distance dilation” at different radius's is what “curved space-time” is mapping.
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Not in General Relativity. Curvature and distance intervals aren't the same thing.
You could probably work out the real values by using the gravitational time dilation at sea level = x then reverse calculate the amount to space distance dilation is required to slow the clock down by that of space distance contraction.
Click to expand...
If you're going to use time dilation anyway, what's the point of your space contraction/dilation?

I was under the impression your aim was to throw out time dilation.
This might be what is causing gravity! Objects located in “curves” are attracted / move toward higher space distance density areas or move down the curve...
Click to expand...
Okay. So you have an idea.

I agree with DaveC that it looks a lot like you're trying to reinvent the wheel. We already have an excellent theory of curved spacetime. The task you have ahead of you, then, is to show that your idea leads to a more useful (or more correct) description of reality than Einstein's.

You'll need to sort out the mathematical, quantitative formulation of your hypothesis next, then calculate some results that can be compared to real-world experiments and observations. That's what Einstein, and many who followed in his footsteps, did with GR.

How far have you got so far in determining exactly how (and, perhaps, why) your distance dilation/contraction works, quantitatively? Does your theory have a set of axioms, for instance? Are there any derived results? Or are you just at the stage of imagining possibilities?
 
James R said:
I'm not sure that "distance" is a property of space, anyway.
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What properties does space have?

James R said:
Not in General Relativity. Curvature and distance intervals aren't the same thing.
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So what is Curvature in GR and what is curving?

James R said:
If you're going to use time dilation anyway, what's the point of your space contraction/dilation?
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To discuss how gravitational time dilation works with space distance density and how it might be what is causing gravity. Motion time dilation works differently.

James R said:
If you're going to use time dilation anyway, what's the point of your space contraction/dilation?
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To explain how gravitational time dilation is being dilated physically through space distance density.

James R said:
I was under the impression your aim was to throw out time dilation.
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Only trying to figure out how it works physically.

James R said:
I agree with DaveC that it looks a lot like you're trying to reinvent the wheel.
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Nope, I'm inspecting the wheel and trying to understand how it works. I know you guys dont need to because you know everything already.

James R said:
We already have an excellent theory of curved spacetime.
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Pity nobody really understands it. Can you tell us what and how curves work?

James R said:
The task you have ahead of you, then, is to show that your idea leads to a more useful (or more correct) description of reality than Einstein's.
Click to expand...
Nope, I agree his theories/models produces the correct results. I'm trying to describe how they work physically.

James R said:
Does your theory have a set of axioms, for instance? Are there any derived results?
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Yes exactly like GR. I'm just trying to decipher its fundamental physical workings.

James R said:
How far have you got so far in determining exactly how (and, perhaps, why) your distance dilation/contraction works, quantitatively?
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I know you dont like to discuss things...

James R said:
Or are you just at the stage of imagining possibilities?
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Yes, I took advice from the best...
Imagination is more important than knowledge. For knowledge is limited to all we now know and understand, while imagination embraces the entire world, and all there ever will be to know and understand. -Albert Einstein
 
BdS said:
Yes, I took advice from the best...
Imagination is more important than knowledge. For knowledge is limited to all we now know and understand, while imagination embraces the entire world, and all there ever will be to know and understand. -Albert Einstein
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Yes he also published his general theory over 100 years ago which answers a lot of your questions.
I would also check out Minkowski regarding space time and his treatment of Einstein's work.
FWIR Einstein hated it but then came to accept it. He was a very smart man.
 
BdS said:
Yes, I took advice from the best...
Imagination is more important than knowledge. For knowledge is limited to all we now know and understand, while imagination embraces the entire world, and all there ever will be to know and understand. -Albert Einstein
Click to expand...

I have a suspicion that If Einstein knew what this quote would end up being used for, and mischaracterized as meaning, he would have never said it. For one, he had a disdain of "authority", and even said that the cruelest joke fate ever played on him was to make him one. IOW, he would not want anyone to follow what he said just because he said it.
Now to the quote: While he said imagination is more important than knowledge, he did not say that knowledge was unimportant. To take a page from his own life, when he realized that he did not have the knowledge in higher mathematics needed to complete General Relativity, he went out and sought that knowledge. Imagination might have set him on the path, but he needed already existing knowledge to blaze that path to its end.
The most imaginative architect in the world can't design a viable building without a knowledge of structural engineering.
 
BdS:
BdS said:
What properties does space have?
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It depends on what model of "space" you want to use, I guess.

For example, in the theory of relativity there are spatial and time coordinates (which transform from one reference frame to the next). Then there are various tensors (e.g. the curvature tensor) and other quantities (e.g. the spacetime metric) that describe how the coordinates interact and transform, as well as how distances and time intervals are to be measured using the coordinates. I guess that, if you like, you could call all of these things "properties of space". I'm not sure if I would.
So what is Curvature in GR and what is curving?
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The spacetime manifold is curving. Curvature describes a set of mathematical relationships in the model, essentially.
Nope, I'm inspecting the wheel and trying to understand how it works. I know you guys dont need to because you know everything already.
Click to expand...
Are you being sarcastic? Where have I claimed that I already know everything? There are lots of things I don't know.
Pity nobody really understands it.
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It is not true that nobody understands the general theory of relativity. However, a more than superficial understanding of it requires quite a high level of mathematics as a prerequisite. Most people do not have the mathematical background required to understand the mathematics of the theory. But some do.
Can you tell us what and how curves work?
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I'll give you a simpler example, as an analogy. Consider a curve in two dimensions. We can represent that curve on an x-y plot as a function $y=f(x)$.

Without showing you how it is derived, I can tell you that the curvature at any point on such a curve is given by the following mathematical formula:

$$C=\frac{|f''(x)|}{[1+(f'(x))^2]^{3/2}}$$​

where $f'(x)$ is the first derivative of the function and $f''(x)$ is the second derivative.

This looks complicated, but I'll give you a specific example or two.

Consider the line $y=f(x)=2$. Clearly, on an x-y graph, that is just a straight line. Applying the formula above, we have $f'(x)=f''(x)=0$, and so we easily see that $C=0$. Our line has zero curvature.

Next, consider a slightly more complicated straight line: $y=f(x)=7x$. For that line we have $f'(x)=7, f''(x)=0$. Plugging into the formula for the curvature, we again see that $C=0$, as expected.

How about a parabola, then? Consider $y=f(x)=x^2$. The derivatives in that case are $f'(x)=2x, f''(x)=2$. So, for the parabola, the curvature is:

$$C=\frac{2}{[1+4x^2]^{3/2}}$$​

Notice that the curvature is no longer a constant; rather, it varies depending on where you are on the curve. For instance, at $x=0$ (the apex of the parabola), the curvature is $C=2$. The magnitude of C, 2 in this case, is a measure of how "curvy" it is at that point. If we pick a point a little to the right, at $x=1$ and calculate we find:

$$C=\frac{2}{5^{3/2}}=0.18$$​

At $x=1$ the parabola is not as tightly curved, compared to $x=0$. If we look at the general curvature formula, we can see that our parabola becomes less and less "curvy" as $x\rightarrow \infty$.

So, you get the idea that this measure, C, quantifies our common-sense notion of how curved a line is.

In general relativity, things are more complicated. We're dealing with curvature in four dimensions (curvature of a spacetime manifold), and the spacetime at a single point can potentially curve in different directions by different amounts.

Of course, all of this is just maths. The power of general relativity is that it tells us why spacetime curves. Matter and energy cause the curvature, and we can quantify exactly how much and what kind of curvature a given amount of mass, say, will cause. GR also allows us to calculate how objects will move in the curved spacetime (under the influence of gravity).
I know you dont like to discuss things...
Click to expand...
??
What am I doing with you now?
 
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James R said:
BdS:

It depends on what model of "space" you want to use, I guess.

For example, in the theory of relativity there are spatial and time coordinates (which transform from one reference frame to the next). Then there are various tensors (e.g. the curvature tensor) and other quantities (e.g. the spacetime metric) that describe how the coordinates interact and transform, as well as how distances and time intervals are to be measured using the coordinates. I guess that, if you like, you could call all of these things "properties of space". I'm not sure if I would.

The spacetime manifold is curving. Curvature describes a set of mathematical relationships in the model, essentially.

Are you being sarcastic? Where have I claimed that I already know everything? There are lots of things I don't know.

It is not true that nobody understands the general theory of relativity. However, a more than superficial understanding of it requires quite a high level of mathematics as a prerequisite. Most people do not have the mathematical background required to understand the mathematics of the theory. But some do.

I'll give you a simpler example, as an analogy. Consider a curve in two dimensions. We can represent that curve on an x-y plot as a function $y=f(x)$.

Without showing you how it is derived, I can tell you that the curvature at any point on such a curve is given by the following mathematical formula:

$$C=\frac{|f''(x)|}{[1+(f'(x))^2]^{3/2}}$$​

where $f'(x)$ is the first derivative of the function and $f''(x)$ is the second derivative.

This looks complicated, but I'll give you a specific example or two.

Consider the line $y=f(x)=2$. Clearly, on an x-y graph, that is just a straight line. Applying the formula above, we have $f'(x)=f''(x)=0$, and so we easily see that $C=0$. Our line has zero curvature.

Next, consider a slightly more complicated straight line: $y=f(x)=7x$. For that line we have $f'(x)=7, f''(x)=0$. Plugging into the formula for the curvature, we again see that $C=0$, as expected.

How about a parabola, then? Consider $y=f(x)=x^2$. The derivatives in that case are $f'(x)=2x, f''(x)=2$. So, for the parabola, the curvature is:

$$C=\frac{2}{[1+4x^2]^{3/2}}$$​

Notice that the curvature is no longer a constant; rather, it varies depending on where you are on the curve. For instance, at $x=0$ (the apex of the parabola), the curvature is $C=2$. The magnitude of C, 2 in this case, is a measure of how "curvy" it is at that point. If we pick a point a little to the right, at $x=1$ and calculate we find:

$$C=\frac{2}{5^{3/2}}=0.18$$​

At $x=1$ the parabola is not as tightly curved, compared to $x=0$. If we look at the general curvature formula, we can see that our parabola becomes less and less "curvy" as $x\rightarrow \infty$.

So, you get the idea that this measure, C, quantifies our common-sense notion of how curved a line is.

In general relativity, things are more complicated. We're dealing with curvature in four dimensions (curvature of a spacetime manifold), and the spacetime at a single point can potentially curve in different directions by different amounts.

Of course, all of this is just maths. The power of general relativity is that it tells us why spacetime curves. Matter and energy cause the curvature, and we can quantify exactly how much and what kind of curvature a given amount of mass, say, will cause. GR also allows us to calculate how objects will move in the curved spacetime (under the influence of gravity).

??
What am I doing with you now?
Click to expand...
Thanks for the tutorial on curvature in algebra. It's not something I was ever taught.
 
James R said:
It depends on what model of "space" you want to use, I guess.
Click to expand...

The one where space distance dilates/contracts causing our measurement of time to dilate, and creating a "curve transition" with a variable radial space distance dilation/contraction.
 
And how the variable radial space distance dilation/contraction ("VSDDC") from the distance of a mass object m1, causes a physical attraction potential for other mass m2 m3... objects located in m1 influenced space. It can be modeled as a curve...
 
earth.jpg

I used to see an image likes this and just see the curve. Now I look at it and see it's not only the curve that matters, its also the amount the space distance is stretched to create the curve.

I've never understood how curves cause gravity, I think of it like this. A ball on the top of a hill representing a mass and the hill curved spacetime. The ball has potential and will roll down the hill, if you think mass in curved spacetime is moving down a curve, answer this. When the mass rolls down the hill there is friction between the ball and the hill causing the ball to roll or gain spin. When mass is moving down curved spacetime why doesn't it roll or tumble? is there no friction between mass and curved spacetime? If no then, how does curved spacetime influence mass to move?

I get stuck here.
 
BdS said:
View attachment 6528

I used to see an image likes this and just see the curve. Now I look at it and see it's not only the curve that matters, its also the amount the space distance is stretched to create the curve.

I've never understood how curves cause gravity, I think of it like this. A ball on the top of a hill representing a mass and the hill curved spacetime. The ball has potential and will roll down the hill, if you think mass in curved spacetime is moving down a curve, answer this. When the mass rolls down the hill there is friction between the ball and the hill causing the ball to roll or gain spin. When mass is moving down curved spacetime why doesn't it roll or tumble? is there no friction between mass and curved spacetime? If no then, how does curved spacetime influence mass to move?

I get stuck here.
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Have you read any of the replies? Balls do tumble, that is what the earth is doing when it orbits the sun but there are two distinct ways of doing the mathematics which is the only real way of looking at gravity in any meaningful scientific sense.
 
BdS said:
When mass is moving down curved spacetime why doesn't it roll or tumble?
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Just on this point. Why would it? Remember that a body will keep on doing exactly what it is doing forever unless a force acts on it.
So a body in space travelling at velocity V, with a certain orientation will remain that way.
A body approaching a mass M will be accelerated,
but of all the mass at the same time unless it is significantly elongated.
By significantly I mean ridiculously elongated and I do not have the maths to illustrate that.
 
Pinball1970 said:
Just on this point. Why would it?
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Spacetime curves imply mass is interacting with the curve in some way so spacetime can tell mass how to move. How does spacetime influence mass to move? with friction or some other type of interaction between the mass and spacetime?

If it is a friction type of interaction mass would tumble down the curve while falling.
 
BdS:
BdS said:
I've never understood how curves cause gravity, I think of it like this. A ball on the top of a hill representing a mass and the hill curved spacetime. The ball has potential and will roll down the hill, if you think mass in curved spacetime is moving down a curve, answer this. When the mass rolls down the hill there is friction between the ball and the hill causing the ball to roll or gain spin. When mass is moving down curved spacetime why doesn't it roll or tumble? is there no friction between mass and curved spacetime? If no then, how does curved spacetime influence mass to move?

I get stuck here.
Click to expand...
First of all, about the ball on the hill analogy, notice that you mentioned two forces there. It is not gravity that causes a ball on a hill to roll. Gravity just pulls downwards. The rolling is caused by the friction force, which is due to contact between the atoms in the ball and the atoms in the hill. A ball on a frictionless hill will slide down the hill, but it won't start to roll.

Second, you need to realise that, in the curved spacetime picture of gravity, gravity does not exert a force on objects. Or, to put it another way: in the general theory of relativity, gravity is not a force. Instead, the apparent attraction we see between masses comes from those masses following the curvature of the local spacetime (which includes the curvature created by the presence of other mass).

Gravity is not required to "influence mass to move". Newton's law of inertia says that an object will continue to move at constant velocity unless it is acted on by a force. If gravity is not a force, then all objects move at constant velocity under gravity.

But if we drop a ball, it clearly speeds up as it falls. How can I say that it is moving at constant velocity, then? The problem is that, although the ball has no force pulling it down (because gravity isn't a force), we have a force on us that is stopping us from falling down with the ball. The floor or ground is pushing up on us with a certain force. If the ground wasn't there, we'd be falling with the ball, and we wouldn't see it speeding up. It would remain stationary relative to us.

What objects do in curved spacetime is that they just move with constant velocity through the spacetime, unless there are forces on them - and gravity isn't one of those forces. But spacetime can be curved, so the closest thing to a straight line - especially when there are other masses nearby - might not be truly "straight".

If you're falling freely under gravity next to a falling ball, you feel no force and you don't speed up relative to the ball. But you will speed up relative to somebody who is "at rest" with the ground pushing up on their feet. It is not that you are accelerating. It is actually the person with the force on them who is accelerating. Why don't they go anywhere, then? Answer: because they are accelerating in a curved spacetime (curved by the Earth's mass, that is).

Hope this helps.
 
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BdS said:
Spacetime curves imply mass is interacting with the curve in some way so spacetime can tell mass how to move. How does spacetime influence mass to move? with friction or some other type of interaction between the mass and spacetime?

If it is a friction type of interaction mass would tumble down the curve while falling.
Click to expand...
Space-time isn't a "thing or "substance". It is just a combination of the 3 spatial and 1 temporal dimensions( degrees of freedom of motion). And when it it said that space-time "curves" what it is referring to is that the rules of geometry governing it deviates from the Euclidean rules and is non-Euclidean.
 
Here is an excellent video that shows spacetime's behaviour. It demonstrates very succinctly how paths across its surface are geodesically straight but pass through space in a curved fashion (like a falling apple does).

It shows that an apple attached to a branch is actually following a curved path through spacetime because it is constrained to the branch. Only when the apple falls from the branch and moves in free fall does it resume its straight path through space time.


A few of the key take aways here are:

1. Gravity does not curve space time. That's a mistake. Spacetime is curved - and the effect of that curvature is what we call gravity.

2a. The natural/default state of things is free fall, when no forces are acting on it. The object follows a straight path (as one would expect when no forces are in play).
2b. Only when there are constraints imposed on an object (such as being attached to a tree) is it forced to deviate from its natural path.
 
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I'm leaning toward there is no physically curved space. SPACE is only distance dynamics that we've modeled with a curve. Curves just represent how much the space distance is dilated over radius's, volumes, areas. The angle of the curve over a segment is how much the space distance is dilated for that segment. Max curve angle is vertical 90deg which represents? the max amount space distance can dilate, which would probably come back to something with c in meters as max dilation over a 1m or something like that.
 
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