How does gravity curve spacetime?

[gravityblock]

Suppose gravity is the only force the object feels.

In Newtonian gravity, considering 3-acceleration:
1) It accelerates as it orbits
2) It accelerates as it falls

In Einstein gravity, considering 4-acceleration:
1) It does not accelerate as it orbits
2) It does not accelerate as it falls

Is #2 of Einstein's gravity a mistake or typo? I was not aware of this in #2 of Einstein's gravity.

My theory (idea) of gravity, considering e=mc2: <----- I can't believe I wrote this...lol
1) It does not accelerate as it orbits
2) It accelerates as it falls

Does an object accelerate as it orbits? I don't think so
Does an object accelerate as it falls? I think so

Now which theory of gravity above is correct (or more correct) according to what really happens?

Another question to you. When you drop a ball from a building that is 100ft. high, does the ball hit the floor? Of course it does, but one can say that it will never hit the floor because you can keep dividing the distance the ball is from the floor by 2. 100ft, 50ft, 25ft, 12.5ft...1in, 0.5in, 0.25 in, 0.125in, etc.. to infinity. According to this idea, it will never hit the floor, but this is not the observable affect, the observable affect says the ball hits the floor.

So, are you going to go with a theory that doesn't support the observable affects or will you go with what really happens?

If you're ready to choke me at this moment, that is not my intent.

 

[Jonathan Scott]

Is #2 of Einstein's gravity a mistake or typo? I was not aware of this in #2 of Einstein's gravity.

My theory (idea) of gravity, considering e=mc2: <----- I can't believe I wrote this...lol
1) It does not accelerate as it orbits
2) It accelerates as it falls

Does an object accelerate as it orbits? I don't think so
Does an object accelerate as it falls? I think so

Now which theory of gravity above is correct (or more correct) according to what really happens?

Another question to you. When you drop a ball from a building that is 100ft. high, does the ball hit the floor? Of course it does, but one can say that it will never hit the floor because you can keep dividing the distance the ball is from the floor by 2. 100ft, 50ft, 25ft, 12.5ft...1in, 0.5in, 0.25 in, 0.125in, etc.. to infinity. According to this idea, it will never hit the floor, but this is not the observable affect, the observable affect says the ball hits the floor.

So, are you going to go with a theory that doesn't support the observable affects or will you go with what really happens?

If you're ready to choke me at this moment, that is not my intent.

There are two different ways to think about gravity locally. You can either use the Newtonian view of gravity as an accelerating force, or use the Principle of Equivalence (part of GR) which says that being held in place against a local gravitational field is equivalent to being accelerated, and conversely being in free fall in a gravitational field is equivalent to zero acceleration. You can choose which view to use independently of whether you want to use Newtonian approximations or full GR.

If you want to understand for example what would happen inside a spaceship in various cases, you can use the Principle of Equivalence view. For example, when the spaceship is in free fall, with its engines turned off (regardless of whether that free fall is a closed orbit or something else), objects inside it will not experience any forces tending to move them to one side or another (at least over a short time scale). In contrast, if the spaceship either has its engines running (accelerating it) or is sitting on a planet (being held up against a gravitational field), objects inside will appear to experience a force proportional to their masses.

However, if you want to understand something relating to an orbit, you cannot use this Principle of Equivalence view, because the gravitational field strength and direction are not uniform over the whole region. Instead, you have to use some background coordinate system and describe the shape of the free fall paths (geodesics) relative to that coordinate system, which is equivalent to describing conventional accelerations relative to the coordinate system.

 

[atyy]

Is #2 of Einstein's gravity a mistake or typo? I was not aware of this in #2 of Einstein's gravity.

It wasn't a typo. Of course, that doesn't mean I got it right.

 

[jambaugh]

It may help to view the question in a different light. Einstein's equivalence principle doesn't say that "gravity is just curved space-time" or that "gravitational force is just the effect of an accelerated frame".

The critical point is that the division between a dynamic gravitational force and the effects of a curved space-time or choice of accelerated observer frame is not empirically meaningful. This goes both ways. "Geometry is just dynamics" as well as "(gravitational) Dynamics is just Geometry". Put another way, assuming some unification of all forces as components of one type of force, the gravitational component is precisely that component which can be expressed purely in geometric terms.

How this affects the OP question is this. Don't look for the mechanism by which "space-time is curved" but rather understand space-time as a mathematical construct we make prior to expressing the dynamics of an object. The choice of space-time geometry is a gauge condition. Just as you can choose your electromagnetic potential so that it is zero at some point, you can choose your space-time geometry so that dynamical gravitational forces are zero and "gravity is just the curvature of space-time".

Empirically distinguishing between geometry and dynamics is meaningless. We can't see geometry directly. We can only observe dynamic evolution of physical objects including clocks. As we do we typically have a mental picture of how things ought to behave if nothing affects them. This is our geometry. We then notice deviation from expectation and we call that the effect of a dynamical force. Einstein showed how we can transform the same behavior of the same physical system between distinct choices of geometry via the equivalence principle and then he showed how we must choose our geometry so that the dynamical force of gravity always disappears.

Now I haven't answered your question at all and this "spin" on the equivalence principle and GR doesn't change any of the empirical predictions of the theory. But it does, I hope, give a perspective in which you may formulate better more meaningful questions.

 

[DrGreg]

Is #2 of Einstein's gravity a mistake or typo? I was not aware of this in #2 of Einstein's gravity.

My theory (idea) of gravity, considering e=mc2: <----- I can't believe I wrote this...lol
1) It does not accelerate as it orbits
2) It accelerates as it falls

Does an object accelerate as it orbits? I don't think so
Does an object accelerate as it falls? I think so

Now which theory of gravity above is correct (or more correct) according to what really happens?

Another question to you. When you drop a ball from a building that is 100ft. high, does the ball hit the floor? Of course it does, but one can say that it will never hit the floor because you can keep dividing the distance the ball is from the floor by 2. 100ft, 50ft, 25ft, 12.5ft...1in, 0.5in, 0.25 in, 0.125in, etc.. to infinity. According to this idea, it will never hit the floor, but this is not the observable affect, the observable affect says the ball hits the floor.

So, are you going to go with a theory that doesn't support the observable affects or will you go with what really happens?

If you're ready to choke me at this moment, that is not my intent.

Acceleration, like almost everything else in relativity, is a relative concept. Strictly speaking, when you speak of something accelerating, you should specify relative to what. Nevertheless, the "what" isn't always specified and is then assumed to be a local inertial (free-falling) observer. Strictly speaking such acceleration should be called "proper acceleration" to avoid confusion.

In Newtonian gravity:

N1) An object in circular orbit has constant speed but continuously changing velocity, relative to Earth, and is therefore accelerating towards the Earth relative to Earth. If you don't understand this you need to brush up on your Newtonian physics before you can make sense of the rest of this.

N2) An object falling vertically downwards is also accelerating towards the Earth relative to Earth

In General Relativity:

GR1) An object in circular orbit is moving inertially, its velocity relative to itself (an inertial observer) is always zero, so its acceleration relative to a local inertial observer (itself) is zero.

GR2) An object falling vertically downwards is moving inertially, its velocity relative to itself (an inertial observer) is always zero, so its acceleration relative to a local inertial observer (itself) is zero.

In either case, it is still accelerating relative to Earth, but its "proper acceleration" is zero.

 

[MeJennifer]

GR1) An object in circular orbit is moving inertially, its velocity relative to itself (an inertial observer) is always zero, so its acceleration relative to a local inertial observer (itself) is zero.

Not just circular orbits.

 

[gravityblock]

Thanks to all who have taken the time to post a reply to my questions. I am sure I will not always ask meaningful questions when it comes to physics, but at least I'll be learning how to formulate better questions in these discussions.

Thanks

 

[jambaugh]

T[...] but at least I'll be learning how to formulate better questions [...]

Asking the right questions is the most important skill you can learn, even --I dare say-- more so than the mathematics.

 

[chis]

Gravity and Time are the same force.
Spacetime as Einstien intended it is merly a name for the matter dimention. The matter dimention is the one we percive ourselfs in. We see our environment in 3D, these dimentions are Antimatter, light and our dimension matter. Imagine a blind person reading brail where their hands are the matter dimention and the brail bumps are antimatter encapsulsted in light. The blind persons hands exert a presure on the brail bumps (gravity) and repeated presure would erase the bumps or in other words they would decay (time).

 

[Naty1]

Don't look for the mechanism by which "space-time is curved" but rather understand space-time as a mathematical construct we make prior to expressing the dynamics of an object.

But that is exactly what I wanted to do...to see if anyone yet understands a physical mechanism. I guess not yet.

 

[mehul ahir]

d

r stars & matter & energy in space infinite or finite?

 

[mehul ahir]

r stars & matter & energy in space infinite or finite?

 

[Hurkyl]

But that is exactly what I wanted to do...to see if anyone yet understands a physical mechanism. I guess not yet.

What do you mean by 'physical mechanism'? As I would understand such a phrase, our best theory of gravity says that matter* curving space-time is a 'physical mechanism'.

*: more accurately, stress-energy

 

[Phrak]

What do you mean by 'physical mechanism'? As I would understand such a phrase, our best theory of gravity says that matter* curving space-time is a 'physical mechanism'.

*: more accurately, stress-energy

Hey, Hurkyl. Not to disagree with you, but there are always the why questions, like "why should matter curve space?", which every once in a few hundred years leads to a deeper understanding. Or maybe matter doesn't curve space. Maybe matter is curved space.

 

[jtbell]

But that is exactly what I wanted to do...to see if anyone yet understands a physical mechanism. I guess not yet.

How would you distinguish a "physical mechanism" from a mathematical model? When we find the True Physical Mechanism for gravity, how will we know it?

 

[Naty1]

But that is exactly what I wanted to do...to see if anyone yet understands a physical mechanism. I guess not yet.

Math explains what happens, not necesarily why.

I simply wondered if there was an additional detail of understanding. Newtons laws explained a lot pretty well until Einstein came along and offered some deeper insights...but relativity is not the final answer either. Maybe magnetism would be an analogy...I think we understand pretty well why some materials are strongly magnetic and others are not...

Why SHOULD matter stress/energy curve space? Einstein had several different formulations...until the equivalence principle enabled him to discard the ones that did not fit...maybe we'll gain an understanding when we find out what "space" is...for now envisioning space time as a mathematical construct will have to do..but that doesn't mean it is the best we can do.

 

[jtbell]

I simply wondered if there was an additional detail of understanding.

We simply don't know yet, as far as I'm aware. Maybe a theory of quantum gravity will take us to a deeper understanding, if we can find one that can be verified experimentally. I'm not qualified to speculate in this area.

 

[Hurkyl]

Math explains what happens,

A slight correction: physics explains 'what happens'. Math tells us about math. e.g. while math might tell us that the kinds of 'particles' that are symmetric under 'infinitessimal rotation' can be categorized by half-integral 'spin', it's physics that tells us that particles exist and are (generally) symmetric under infinitessimal rotation.

not necesarily why.

What does "why" mean, really? In the operational sense, the question "why?" is a request to take a particular fact, and express it as a consequence of other facts. So, in order for the question "why?" to even make sense, you have to have accepted some category of facts in terms of which you will accept 'explanations'. This begs a question -- if the elements of our foundational scientific theories aren't acceptable as building blocks for 'explanation', then what is? And what is the justification for using those, rather than scientific ones?

 

[Hurkyl]

Just to make it clear: I'm not trying to marginalize imagination and innovation -- exploring for new ideas is an important part of science. But by the same token, one shouldn't marginalize the existing foundations of knowledge we do have -- it's not really fair to characterize it as merely something that will 'have to do'.

I get the feeling that you are leaning towards doing the latter, which is why I said something; if I am mistaken, then I apologize.

 

[atyy]

Newtons laws explained a lot pretty well until Einstein came along and offered some deeper insights...but relativity is not the final answer either. Maybe magnetism would be an analogy...I think we understand pretty well why some materials are strongly magnetic and others are not...

Why SHOULD matter stress/energy curve space? Einstein had several different formulations...until the equivalence principle enabled him to discard the ones that did not fit...maybe we'll gain an understanding when we find out what "space" is...for now envisioning space time as a mathematical construct will have to do..but that doesn't mean it is the best we can do.

Newton's gravity incorporates the equivalence principle. So can we describe it as spacetime curvature?

On Newton-Cartan Cosmology
Christian Rueede, Norbert Straumann
http://arxiv.org/abs/gr-qc/9604054

The main difference between Newton and Einstein is not curvature, but special relativity?