Understanding Gravity: Properties & Effects

[Morga]

Gravity seems to be a very unusual force. From what i understand:

Gravity can bend space-time
Gravity occurs with an object with mass
Gravity can attract objects through barriers
Gravity attracts each unit mass of an object with the same force.

Can people add and correct any misunderstandings please.

 

[mgb_phys]

And gravity is always attractive, there are no positive/negative masses.

This is what has made gravity so hard to combine with other forces in a single theory.

 

[Maxwell's Demon]

Gravity seems to be a very unusual force. From what i understand:

Gravity can bend space-time
Gravity occurs with an object with mass
Gravity can attract objects through barriers
Gravity attracts each unit mass of an object with the same force.

Can people add and correct any misunderstandings please.

Gravity is probably my favorite subject - the more we learn about it the more fascinating it seems to become. I have some corrections and additions for your list, I hope and expect the real experts around here will have more.

Let's begin by clarifying the nature of gravity in the light of General Relativity, which is by far the most successful model for gravity that we have - after a century, every test of GR has only validated it further*.

According to GR, gravity isn't really a 'force' at all (the idea of gravity as a force refers to the old Newtonian model of gravity), instead, gravity -is- the curvature of spacetime. Basically, the presence of mass/energy appears to distort the physical dimensions of spacetime. So a mass in a gravitational field isn't experiencing a 'force' at all...it
s simply following the geometry of the spacetime 'background' that it exists in. This explains why all masses 'fall' at the same rate. Another way of saying this is that inertial mass is equivalent to gravitational mass.

Another slight clarification would be to say that mass and energy are gravitationally equivalent: not only does matter 'bend' spacetime, energy does too. For example, when you wind up a clock, it actually becomes slightly heavier. Another example would be a battery: a battery weighs more when it holds a 'charge' (ie when it possesses chemical potential energy) than when it's charge has run out. We can't measure the difference in mass in these cases, but we know it's true because the same principle applies to other cases that we -can- measure directly.

Here's where it gets -really- interesting: there are actually -three- forms of gravitational field, and they're analogous to electromagnetic fields. The gravity that you and I know and love, is the 'static' gravitational field. It bears a resemblence to a static electrical charge, except with gravity, there's apparently only one form of 'charge' instead of two, and that one 'charge' attracts other like 'charges' (unlike electircal charges where likes charges repel).

Now if you think that accelerating a 'gravitational charge' (ie mass/energy) might create an effect analogous to a magnetic field, you'd be right. It turns out that a mass in motion generates a gravitomagnetic field (also called the 'Lense-Thirring effect' or 'frame-dragging'). Don't get confused - the magnetic field created by a moving electrical charge, and the gravitomagentic field created by a moving mass are completely different phenomena. But they do share some facinating similarities.

There's more. It appears that an -accelerating mass- will produce a 'gravitoelectric' field, which follows the rules analogous to electromagnetic induction.

Wikipedia has a nice introductory page deduicated to these 'gravitoelectromagnetic' phenomena: http://en.wikipedia.org/wiki/Gravitoelectromagnetism

And many physicists are anxiously awaiting on the analytical results of the Gravity Probe B satellite experiment, which was created at Stanford University to measure the gravitomagnetic field of the Earth (the results are due in the next few months): http://einstein.stanford.edu/

But we already have compelling evidence of gravitomagnetism from astronomical observations of black holes and quasars: http://www.physorg.com/news99917013.html

Now if we want to go way out to the leading edge of scientific investigation of gravitoelectromagetism, we'll find the work of European Space Agency physicists Martin Tajmar and Clovis de Matos, who shook the theoretical physics community last year with the tentative announcement that they may have created a gravitomagnetic field in a laboratory experiment by rapidly spinning a superconducting ring of metal. *Early indications are that for reasons still unknown, the intensity of this gravitomagnetic field may be about 30 orders of magnitude stronger than the field intenisty predicted by General Relativity under their experimental conditions - this would be, to the best of my knowledge anyway, the -first- time GR failed to predict the magnitude of a gravitational effect to within a neglible error. These researchers feel that their work may be the key to creating a quantum model of gravity, which is pretty much the Holy Grail of theoretical physics nowadays.

Here's their fascinating and controversial paper from last spring: http://arxiv.org/ftp/gr-qc/papers/0603/0603033.pdf

So we're only now beginning to examine the subtle intricacies of gravitational phenomena. Many feel that the current work will herald a revolutionary era of new applied physics akin to the days of Faraday, Maxwell, and Tesla, when applied electromagnetism changed the world.

Perhaps you'll agree as you delve deeply into this riveting subject...

 

[Danger]

Awesome post, Demon.
I've never heard of that ESA experiment. While I don't have time now, I look forward to reading that link. I probably won't understand most of it, but it certainly seems fascinating from the introduction.

The only thing that I would like to mention is that the theoretical 'negative matter' would actually produce repulsive gravity. As far as I know, there hasn't been any physical evidence that it actually exists.

 

[HallsofIvy]

Gravity does NOT "bend space time"- gravity IS bent space time.

 

[Loren Booda]

Are there any strong and (more directly) weak force analogs to gravity?

What are some simple introductions to GR using Einstein notation? Misner, Thorne and Wheeler's Gravitation is a bit above my head.

 

[rcgldr]

So a mass in a gravitational field isn't experiencing a 'force' at all.

So what it the cause of acceleration of masses towards (assuming both objects in free fall) each other if it isn't a force?

 

[Maxwell's Demon]

So what it the cause of acceleration of masses towards (assuming both objects in free fall) each other if it isn't a force?

In the old Newtonian model, space and time, the ‘background’ of action in the universe, were immutable and Euclidean. Put simply, the shortest distance between two points was always assumed to be a straight line, and any change in motion was attributed to forces acting on a mass.

General Relativity threw that idea right out the window. Einstein proved mathematically that space and time were, well, ‘flexible.’ And his theory described exactly how much spacetime (now unified under his model) ‘curves’ when matter is present. Another way of saying this is that spacetime ‘couples’ with matter/energy (mass and energy also became united within his theory – dude was a genius, you see). So gravity isn’t the action of a ‘force,’ it’s simply 4D geometry disregarding our Euclidian expectations of nature.

This all seemed pretty outrageous at the time Einstein presented this weird geometric solution for gravity. But not only did this crazy idea work, it worked better than the Newtonian gravity model…it explained the at-the-time inexplicable little anomaly in the precession of the perihelion of Mercury, among other things. Physicists were used to thinking of gravity as a force acting against a ‘flat’ background. That is, Newtonian gravity was a ‘background independent’ theory of gravity. Einstein explained that matter wasn’t experiencing a ‘force of gravity’ at all, but rather, it was simply following -the shortest distance between two points- in a curved 4D spacetime.

It may be useful to consider the situation of a falling body within a gravitational field. This is where we really see that there isn’t a force involved.

Imagine that you’re a cold rock in space drifting toward the Earth at a constant velocity (we’ll neglect the minor fluctuations in velocity induced by other nearby planets and such).

As you approach the Earth, your velocity toward it increases. It increases a little bit at a time when you’re far away, but the rate of the increase continues to grow as you get closer…but you don’t feel any force ‘pushing’ or ‘pulling’ on you at all. Your trajectory may also change – it seems like the Earth is coming at you faster and faster, and it’s even putting itself more and more directly in your path! Hark! From your point of view, you're not acccelerating toward the Earth - it's accelerating toward -you-. Even as you begin to enter the Earth’s atmosphere, you still don’t feel any ‘force of gravity’ at all – not the slightest nudge toward the Earth. In fact, the only force you’ll feel is a slight ‘push’ from directly ahead of you, from atmospheric friction. And finally, you’ll feel a force directly ahead of you as you rudely impact the Earth.

So the only force we feel here on the surface of the Earth, is the force of the dirt beneath our feet stopping us from conforming to the dictates of the curved spacetime all around us. If there were a hole all the way through the Earth, we’d move through it to the other side of the planet and back and forth…without ever feeling any kind of accelerating force: we’d feel ‘weightless’ and unperturbed at all times (except for incidental air friction effects).

Why? Because from our point of view, we’re actually stationary on this crazy, twisted background of 4D spacetime. In freefall, the only reason we think we’re moving is because the other objects around us don’t share our unique little frame of reference. But if we were wearing blinders, there’d be no way to tell whether we were drifting in space, orbiting a planet, or plunging toward a black hole, because as we’ve seen, gravity isn’t a force.

 

[Morga]

Gravity does NOT "bend space time"- gravity IS bent space time.

Oops i meant mass and energy bends space time.

Thanks a lot guys for the clarification on such an unusual subject!

 

[Maxwell's Demon]

Thanks a lot guys for the clarification on such an unusual subject!

Anytime, Morga. I forgot to mention gravity waves - we haven't seen those directly yet, but we can infer their existence from observing regions of unusually intense gravitational interactions, such as binary star systems containing neutron stars, and stars being pulled into black holes. Gravity waves radiate from extremely violent events, and they're basically a ripple in the spacetime metric of reality.

It might also be worth noting a special case called 'gravitational lensing.' It wasn't long ago that we first observed that we could see light from distant objects being distorted by intense gravitational fields lying directly between the Earth and a distant light source, just like light gets bent through a magnifying lens. But today astronomers are using the gravitational lens phenomenon fairly routinely to detect the presence of 'dark matter.'

I've often wondered if someday we'll find a way to artificially engineer gravitational fields to produce this effect to make the perfect space-based telescope.

 

[rcgldr]

Imagine that you’re a cold rock in space drifting toward the Earth at a constant velocity. As you approach the Earth, your velocity toward it increases. It increases a little bit at a time when you’re far away, but the rate of the increase continues to grow as you get closer…but you don’t feel any force ‘pushing’ or ‘pulling’ on you at all.

Replace that rock with a very long rod pointed at the earth, and the rod will experience a tension due to the variation of strength of the gravitational field

 

[blazes816]

Some questions for the great physics people.

http://www.astronomynotes.com/evolutn/grwarp.gif

In that picture, it shows spacetime being warped. The gravity. Well, two questions about that.

1) Why does the object, or earth, or my coffee cup, or me, or anything bend spacetime? What causes it?

2) If that's what cause gravity, what makes something follow that path?

For example, in this image http://blazes816.com/spacetime.gif , why would the chunck of ice (the blue thing) follow the green path (roughly), and not the red one? Wouldn't gravity have to pull it down in that pattern?

 

[Morga]

1) Why does the object, or earth, or my coffee cup, or me, or anything bend spacetime? What causes it?

Energy and Matter (Which is energy locked up) bend space time. Although i do not know why...

2) If that's what cause gravity, what makes something follow that path?

It doesn't follow a path it's traveling in a straight line. The space time is bent and it is traveling in a straight line through it.

For example, in this image http://blazes816.com/spacetime.gif , why would the chunck of ice (the blue thing) follow the green path (roughly), and not the red one? Wouldn't gravity have to pull it down in that pattern?

You have taken that picture out of context but i think what it means is that the red line is what we perceive, and the green is what has actually happened. So we can see the chunk of ice between the massive object because the light has traveled through bent space time around the object.

That's my interpretation anyway.

 

[Loren Booda]

All objects tested have followed the path predicted by general relativity. Mass or energy density warps spacetime. According to GR, objects moving between the same two points in spacetime, despite their having different velocities over different spatial distances, follow an identical, maximal path. Furthermore, general relativity is the most elegant, simple (and only) theory to make these predictions - as far as we can tell, without error.

 

[SpitfireAce]

"we haven't seen those directly yet, but we can infer their existence from observing regions of unusually intense gravitational interactions"... why aren't these "inferences" good enough? Is there some quantity that watching a light beam bend on Earth will allow us to measure, but that our astronomical observations won't? or is there some other possible explanation for the unusual interactions other than gravitational waves? What more do we need?

 

[turbo]

In a bit of a wrinkle, the folks at CERN intend to measure the gravitational infall rate of neutral anti-hydrogen and compare it to the infall rate of hydrogen. This is a critical test of the Weak Equivalence Principle.

http://athena.web.cern.ch/athena/

 

[Loren Booda]

Consider a Minkowski (special relativistic, 4-dimensional Euclidean space) cone local to a point in spacetime. In an inertial frame, matter spreads out most symmetrically - through spacetime as concentric hypercircles on the cone, like ripples from a point on a pond. Under acceleration, though, the conic section tilts (since there is a spatially preferential increase in velocity), and we can section the Minkowski cone at a given time into hyperbolas, parabolas or ellipses. With the aqueous analogy, if you were to view the ripples lit from above onto a slanting pond bottom, they might appear as ellipses.

Curvature in local spacetime, the ratio between changing velocity and associated spacetime surface area (in terms of c), is a constant relative to observer and object. Tracked in local spacetime, the trajectories of a bullet and a ball follow the same fundamental curvature due to gravity.

 

[rcgldr]

If gravity isn't a force, then why does it take a force to oppose it? For example, imagine a rocket "hovering" (as opposed to orbiting) somewhat near a planet using force to maintain it's distance from the planet. If gravity isn't the opposing force, then where is the equal and opposite force opposing thrust from the rocket's engine?

 

[SpitfireAce]

Your intuition about netforces and motion breaks down in a gravitational field... think about it this way... in flat space-time (not in a gravitational field)... an object will move at constant speed until acted upon by an outside force, in space-time with a curvature of so and so (in gravitational field), an object will accelerate toward the center at so and so many m/s^2 until acted upon by an outside force... the "natural state of motion" at a given dist. from the grav. field center is a certain acceleration, not constant speed... it doesn't take a force to accelerate something in a gravitational field, just like it doesn't take a force to move something at constant speed in flat space-time, you have to rethink things

You must change your definition of a force, here force isn't something that causes acceleration, force is something that opposes acceleration... (a common def. may be, force causes objects to move in unnatural states of motion and needed to keep them moving in these states of motion)

The force on you while you're on the surface of Earth (your weight) is caused by the Earth pushing up on you preventing you from accelerating, not by gravity pushing down on you, you feel a net force up, opposing your acceleration... (this force is analogous to the car seat pushing up against you're back when your car is accelerating, preventing you from moving at constant speed).. note the different directions of the forces and how they correspond to the respective definitions above

These notions are difficult to get used to because we simply don't think about them in this way, that's why it's simpler to just get rid of forces all together in General Relativity and instead talk about accelerations or curved paths

 

[Loren Booda]

The "hovering" is that force providing acceleration that opposes the rocket's tendency to follow a worldline, that is, to remain in an inertial frame. This natural state of the rocket is free-fall.

The trick is to discern reaction from action, the impulse of the rocket from the "forces" of gravity. In the reference frame of the rocket, one cannot differentiate gravity's acceleration on it from that of hovering, just that they measure a certain value overall. Gravity can therefore be seen as a force (or equivalently, as energy density), but more intuitively both as spacetime curvature. Recall that the deaccelerating gasses of the rocket in vacuo follow their own worldlines with their own inertial frames. Curvature is universal, where forces can sometimes be fictitious or insufficient.

 

[rcgldr]

in space-time with a curvature of so and so (in gravitational field), an object will accelerate toward the center

And why is this acceleration not considered to be the result of a force? I can agree with the theory that the curvature occurs, but it's my belief that gravity has multiple properties, one resulting in curvature, and one resulting in an attractive force that causes the acceleration. I don't see any conflict with gravity having both properties or any any other yet undiscovered properties.

fictitious forces

In my opinion, "fictitious force" is a bad term, I prefer the term "reactive force". Reactive forces (associated with accelerations) are just as real as actual forces, equal and opposite, the main difference is the real forces are the "cause", and the reactive forces are the "effect". In the real world, deformation and an increase in pressure at the point of application occurs because of both of these opposing forces.

 

[tabchouri]

And why is this acceleration not considered to be the result of a force? I can agree with the theory that the curvature occurs, but it's my belief that gravity has multiple properties, one resulting in curvature, and one resulting in an attractive force that causes the acceleration. I don't see any conflict with gravity having both properties or any any other yet undiscovered properties.

In my opinion, "fictitious force" is a bad term, I prefer the term "reactive force". Reactive forces (associated with accelerations) are just as real as actual forces, equal and opposite, the main difference is the real forces are the "cause", and the reactive forces are the "effect". In the real world, deformation and an increase in pressure at the point of application occurs because of both of these opposing forces.

The two points of view cannot be agreed of simultaneously : it is either a curvature of spacetime, either a gravity force (acceleration), NOT both.

The way i understand it, that acceleration is not a force,
it is not a result of gravitational force, even though you can consider as such if you consider the 4D spacetime as flat.

Rather, you can imagine that the presence of a mass creates a distorsion in the space time in its vicinity in a manner that makes all straight lines go towoards the center of that mass; THUS, any object near that mass -not experiencing any force on it and thus- having a constant velocity, will move toward that center -following the spacetime curves that converge to the center in any direction.
Besides, the further you get close to that center of mass, the more the space is contracted, and the more the object seems to move faster -from our point of view of flat 4D spacetime.

That's how I understand it, i hope not beeing very wrong.

 

[rcgldr]

Rather, you can imagine that the presence of a mass creates a distorsion in the space time in its vicinity in a manner that makes all straight lines go towoards the center of that mass; THUS, any object near that mass -not experiencing any force on it and thus- having a constant velocity, will move toward that center -following the spacetime curves that converge to the center in any direction.
Besides, the further you get close to that center of mass, the more the space is contracted, and the more the object seems to move faster -from our point of view of flat 4D spacetime.

So why would it take a constant force to maintain position from that center of mass, or in other words why does it take a force to oppose a non-force?

 

[wv8111]

gravity is not fully understood, the main defination I think describes it as a phenomenon which all objects with mass attract each other, and most think that gravity's source is the object with mass, I think, and I don't know if there ever was or is a theory that gravity orginates from space, as pressure on objects with mass. and that pressure becomes a constant on example Earth because its size does not change. gravity of course is invisible, but for example, if I were to fill the room I am in with say Stryo-foam peanuts for example, there would be a pressure from them exerted on my body from the peanuts, now say a larger person was placed in the same room with the same amount of peanuts, the pressure on their body would be greater.
Thinking that way, I believe Space before the big bang, was in fact infinet , then after the big bang matter existed, I think this matter would have had to displace something perhaps THEORY: there is a force ( an all-around pressure) from space that exerted on Planets, Stars ETC. That could cause gravity to occur on Earth and other places.,; the bigger the planet or star, the greater pressure.
I am well aware space does not have atomosphere, or pressure that we can detect, but; on the other hand; a Flea in that same room with the styro-foam peanuts, would feel no pressure and be able to move quite freely, and in the grand scheme of things that's how big we a humans are, and even smaller.
I have only been thinking about this a couple of days now, but wondering if this may be possible?
it is hard for me to believe that gravity can " just occur because an object has mass".
However I do find it easier to believe that instead of being pulled to earth, objects are being pushed., however its just a thought

 

[SpitfireAce]

away from mass objects travel at constant speed, you seem to readily accept this... it is just the default... now accept that near mass, objects accelerate towards the mass (at different accelerations depending on distance)... this is just the default... if you want you can say it's b/c of the geometry of some cosmic stage called space-time... if you want to keep using forces then just mind the considerations in my last post and you should be fine...

wv8111, this sounds to me like an old theory to answer the why of gravity... it said that the reason that there is a force of attraction between the sun and earth, is because there are little particles hitting the system from all around (inward pressure)... but the sun shields the Earth and vise versa, so the equilibrium is broken and the net effect of the particles is to push these two bodies together... however, since the Earth is revolving at constant speed, it was predicted that more of these force particles should hit the side of the Earth in the direction of the motion than the back side (if you run while its raining more rain drops hit your front than your back) and the effect of this would be to gradually decrease the Earth's orbital velocity... then it would spiral into the sun... since this doesn't happen, the theory was dismissed...

oh yeah, and welcome to physics forum wv and gost =)

 

[Gost_D]

What is the gravity? - see
http://arxiv.org/ftp/physics/papers/0703/0703043.pdf
Possible experiments -
http://arxiv.org/ftp/arxiv/papers/0707/0707.4657.pdf
(with the references)

 

[otas]

I found this old post, and you had a very interesting and informative for me disscusion.

away from mass objects travel at constant speed, you seem to readily accept this... it is just the default... now accept that near mass, objects accelerate towards the mass

Can it (accelaration towards mass) be explaind in following way?
It is because, we constantly moving through spacetime(going to the future) and if spacetime is bent, then shortest path towards the future is not to stay in same place in space, but move towards mass.
Also when we get closer to mass, then spacetime is bent even more and the shortest path becomes to move even more towards the massive object.

Is this idea completely wrong?



Regards,
Me :)

 

[denni89627]

The problem with that statement is that physics has yet to model the flow of time. Your future is not the same as mine, relativity will explain this. Entropy was later investigated as a benchmark for the flow of time, but it turns out entropy increases when we look to the past or the future of a particular frame of reference. This is tough to wrap your head around.

 

[Loren Booda]

I found this old post, and you had a very interesting and informative for me disscusion.





Can it (accelaration towards mass) be explaind in following way?
It is because, we constantly moving through spacetime(going to the future) and if spacetime is bent, then shortest path towards the future is not to stay in same place in space, but move towards mass.
Also when we get closer to mass, then spacetime is bent even more and the shortest path becomes to move even more towards the massive object.

Is this idea completely wrong?



Regards,
Me :)

Actually, in spacetime an object tends toward the longest path, I believe. This is due in part to the negative squared time term in the 4-D Pythagorean expression.

 

[otas]

Thanks for such quick answers.

Your future is not the same as mine.

So, is the following statement correct? :)
I am going to MY future, and the shortest path to MY future when I am near massive object (i.e. earth) is to go towards it (i.e. down).

It's just hard to accept that it is just a way it is near massive object (I understood that from SpitfireAce post)
I would like to have some argument in my head for that :)

Actually, in spacetime an object tends toward the longest path

But wouldn't it be longer distance for me in spacetime to go to mars, then to be on Earth's surface? Or it is related to the fact that I don't understand what you wrote about negative squered time? :)

 

[Loren Booda]

But wouldn't it be longer distance for me in spacetime to go to mars, then to be on Earth's surface? Or it is related to the fact that I don't understand what you wrote about negative squered time? :)

The awkward phrase about "negative squared time" refers to spacetime curvature. Please read on. I highly recommend the Wheeler book referenced below.

__________


"Bodies like the Earth are not made to move on curved orbits by a force called gravity; instead, they follow the nearest thing to a straight path in curved space, which is called a geodesic. A geodesic is the shortest (or longest) path between two nearby points.

The mass of the sun curves space-time in such a way that although the Earth follows a straight path in four-dimensional space-time, it appears to us to move along a circular orbit in three-dimensional space."

http://www.generationterrorists.com/quotes/abhotswh.html

__________


Moving bodies preserve the same curvature when viewed in three dimensions or spacetime.

See A Journey into Gravity and Spacetime by John Archibald Wheeler, page 9, etc.; Scientific American Library, 1999.

 

[Hernik]

I love when these old threads - Sleeping beauties :-) - come alive again.

I have another question regarding curvature of spacetime. Why does the curvature of space seem to depend on the relative velocity of the masses that pass each other.

For example when light passes a large mass it is not deflected from the cartesian straight line as much as an object passing with half the velocity. And an object passing with very small velocity is deflected even more. How does that fit the description of objects generally traveling in a straight line which just curves because of the curvature of spacetime - why does spacetime seem to curve less for a fast object than for a slow object?

Thanks, Henrik

 

[talhaarshad]

I think gravity is the property of that system in which two or more than two body exist.
all of you...What r u thinking about gravity?
Is gravity a force?
Is gravity a Energy?
tell me anyone pleasez what is it?

 

[Maxwell's Demon]

Talhaarshad:

“Is gravity a force?
Is gravity a Energy?
tell me anyone pleasez what is it?”

The short answer is, in my opinion, that gravity is a negative energy field that manifests as curved spacetime geometry.

Henrik:

“I have another question regarding curvature of spacetime. Why does the curvature of space seem to depend on the relative velocity of the masses that pass each other.

For example when light passes a large mass it is not deflected from the Cartesian straight line as much as an object passing with half the velocity. And an object passing with very small velocity is deflected even more. How does that fit the description of objects generally traveling in a straight line which just curves because of the curvature of spacetime - why does spacetime seem to curve less for a fast object than for a slow object?”

It’s easy to confuse the term ‘spacetime’ with just ‘space,’ because most of us aren’t accustomed to thinking of time as a dimension equivalent to a space dimension. And this gets even more confusing when we’re trying to visualize special relativistic effects and general relativistic effects simultaneously, which your example demands.

For clarity, let’s start by looking at these two spacetime effects individually.

A motionless body (with respect to the observer) that is far from gravitational influences, according to special relativity, moves through time at the greatest rate. In fact, such a body is moving through time at the equivalent of the speed of light (since 3e10cm/sec is equivalent to 1sec/sec by the constant C). So really you can see that nothing is ever motionless in both space and time – a body can move through space at a velocity approaching C, or move through time at a velocity approaching C, or it can move with some mixture of both factors which yields a net spacetime velocity of C. That’s special relativity in a nutshell.

Now we consider our small test mass in the presence of a body with an appreciable gravitational field. For starters, we know that time is dilated (moves more slowly) within a gravitational field, compared to the scale of time at a point far removed from such a field. And as you might imagine, the space dimension within a gravitational field is dilated by precisely the same factor (although inversely – space is contracted by the same degree that time is expanded within the region of the gravitational field). Together, these alterations in space and time define a vector field of acceleration pointed toward the center of mass of the body and this is the effect that we call gravity.

Now we can answer your question: “why does spacetime seem to curve less for a fast object than for a slow object?”

The path of a fast object passing by the Earth (let’s say that its velocity is 1/2C) will only be slightly curved *in space* but its path will be appreciably curved *in time.* For example, compared to a distant observer stationary wrt (with respect to) the Earth, time aboard our fast-moving test mass is approx .866 seconds elapsed for every second that elapses on the observer’s distant clock. The fast-moving clock passing the Earth is slowed by both the velocity of the body (special relativity) and by the gravitational field of the Earth (general relativity), yielding a significant temporal curvature.

The path of the same body as it passes the Earth slowly, on the other hand, will be curved significantly *in space,* but will be only negligibly curved *in time.*

As you might intuit at this point, the curvatures of both examples are in fact equivalent, because the spacetime curvature around a body of stationary matter is a static quantity.

Things get even more interesting however when we consider the ‘twisting’ of spacetime around a massive rotating body, which is known as ‘frame-dragging,’ the ‘Lense-Thirring effect,’ or ‘gravitomagnetism.’ But that’s a whole other ball o wax.

If you’re interested in learning more about this subject, I suggest reading some good papers on the Global Positioning System (GPS), because the GPS satellite and signaling network is essentially ‘applied special and general relativity,’ and its success is a testament to the validity of Einstein’s model of gravity and spacetime.

http://relativity.livingreviews.org/Articles/lrr-2003-1/

http://arxiv.org/abs/gr-qc/0507121

And as Loren Booda pointed out, Wheeler’s book ‘A Journey into Gravity and Spacetime’ is a wonderful primer for anyone who wants to grasp these concepts, without all of the daunting mathematics that usually accompanies this subject.