Gravity = warping of spacetime (doesn't make sense)

In summary, the ball on a bedsheet analogy is not a good way to explain gravity because it does not demonstrate why the intrinsic curvature of space-time affects "straight" lines. This analogy is only used because there are no better analogies.
  • #36
http://img506.imageshack.us/img506/5015/spacetimelu3.jpg [Broken]

Keep in mind that each of the "gaps" between those lines is the same distance apart, so the region where the lines are curved inwards is "deeper".

Feynman explained it wonderfully (as he always does) by pointing out that if you drew a circle around the curved region, and calculated what the radius would be for that circle, upon actually measuring it you would come up with an excess radius!
 
Last edited by a moderator:
Physics news on Phys.org
  • #37
Max™ said:
Feynman explained it wonderfully (as he always does) by pointing out that if you drew a circle around the curved region, and calculated what the radius would be for that circle, upon actually measuring it you would come up with an excess radius!
What you measure really depends on what kind of observer.

In a Schwarzschild solution for a stationary observer at a certain distance from the 'center' the volume of a sphere surrounding it would indeed be larger than as would be expected by measuring the surface of this sphere.

However for a radially free falling (from infinity) observer this would not be the case.
 
  • #38
Yeah, but I was trying to avoid causing extra confusion, hence the simplified explanation as provided by Feynman.

:P
 
  • #39
Passionflower said:
What you measure really depends on what kind of observer.

In a Schwarzschild solution for a stationary observer at a certain distance from the 'center' the volume of a sphere surrounding it would indeed be larger than as would be expected by measuring the surface of this sphere.

However for a radially free falling (from infinity) observer this would not be the case.

I don't think the red part is true. But I'm not sure how exactly you envision the free faller to perform that measurement, of a sphere around a center that accelerates relative to him.

However, locally the free falling observer can measure tidal forces and thus the curvature of space time.
 
  • #40
A.T. said:
I don't think the red part is true. But I'm not sure how exactly you envision the free faller to perform that measurement, of a sphere around a center that accelerates relative to him.

However, locally the free falling observer can measure tidal forces and thus the curvature of space time.
The difference between two Schwarzschild r values is never equal to its proper distance except for a radially free falling observer (who is free falling from infinity, e.g. an observer free falling at escape velocity).

It is true that two free falling points a given distance away will not be able to maintain this distance without proper acceleration but that does not invalidate the above statement.
 
  • #41
This is probably the best description I've heard:"I think I'm probably going to inspire more questions than understanding here, but I'll give it a shot anyway.
General relativity is a geometric theory. That means it has to do with geometry more than anything else. John Archibald Wheeler called it "geometrodynamics," as an analogy to "electrodynamics," but the name never really caught on.
So we start by thinking very abstractly about geometry.
Remember your Euclidean geometry, from school? It's a very simple, very idealized geometry, with a basic logic that's easy to wrap your head around. Lines which are parallel at one point are parallel everywhere. The interior angles of a triangle always add up to half a circle. The distance between two points is a function of the relative positions of those two points. And so on.
Well it turns out Euclidean geometry is not the only possible geometry. It's possible to construct, by careful manipulation of the basic geometric postulates, geometries which are entirely consistent, but which are different from Euclidean geometry.
In the 1800s, a variety of mathematical discoveries made it possible to describe arbitrary geometries in a rigorous, consistent way. It's possible for straight lines to curve. It's possible to have a geometry in which lines are parallel at one point, converge at another point, diverge at another point and so on. It's possible to have a geometry in which translating the same triangle from one region to another changes the sum of its internal angles.
This might sound odd, but it really isn't. It's Euclidean geometry — the geometry of the infinite perfect regular plane — that's odd. In the real world, non-Euclidean surfaces are everywhere. The surface of the Earth is non-Euclidean; parallel lines on the Earth's surface inevitably converge and cross. The surface of a bedsheet is even more complexly non-Euclidean, because it has bumps and crinkles.
The point here is that geometry doesn't have to be Euclidean. It can be something else.
This is the insight that Einstein brought to physics. He started with the assumption that the speed of light is the same to all observers, regardless of how they're moving — this was a consequence of Maxwell's theory of light — and began to investigate the way coordinate systems transform between differently moving observers.
What he found was that the way coordinates transform is complex, intricate, counter-intuitive … and entirely consistent and sensible. It's hard to visualize, because we imagine the universe as being Euclidean — straight lines and all that — but it makes sense, and what's more in the decades since it's been directly measured. We now know that the geometry of our universe is not Euclidean.
To get more specific, let's consider the very special case of two observers moving inertially with respect to each other. To move inertially just means to be unaccelerated; an accelerometer carried by an inertial observer will read zero.
If these two observers are moving differently, but they both observe the same ray of light to have the same speed, then their definitions of distance and duration must disagree. This was a very profound insight! Distance and duration are not universal, and depend on how you're moving. This is the source of interesting phenomena like length contraction, time dilation and the relativity of simultaneity.
Einstein then moved on to think about acceleration. He'd cracked the problem of relative inertial motion, but what about accelerated motion? Where he began was with what came to be called the equivalence principle. This principle states that the outcome of a purely local experiment is not dependent on the location of that experiment in spacetime.
In less abstract terms, imagine you're in a small room with no windows. Say you went to sleep the night before and woke up there, with no knowledge of how you arrived. The room is stocked with every piece of scientific equipment you can imagine, from a simple spring scale all the way up to (somehow) a huge particle accelerator.
What experiment can you perform in that room that will tell you whether you're imprisoned somewhere on the surface of the Earth, or out in deep space in a rocketship moving with a constant acceleration of 1 g?
The answer is none. No experiment can tell you which of those is true.
Suddenly, the acceleration pushing your feet to the floor vanishes. You're in free fall. You — and all the expensive equipment in the room — float freely, like an astronaut in orbit.
What experiment can you conduct now that will tell you whether the engines of the spaceship have been turned off, leaving you to coast through deep space far from gravity, or the cables suspending your cell at the top of a tall tower have been cut and you're now plummeting toward the ground?
Again, the answer is none. Do all the experiments you like, and you will never be able to tell whether you're floating or falling.
This is the heart of Einstein's theory of gravitation: Falling is inertial motion. Standing still on the Earth's surface is acceleration.
Gravity, then, is not a force at all. It's a consequence of inertial motion through curved spacetime. The presence of stress-energy — a composite quantity that includes mass, charge, momentum, pressure, sheer stress and so on — changes the fundamental underlying geometry of spacetime. Objects that move through that curved spacetime along entirely mundane, inertial trajectories will be observed, by observers who are at rest relative to the source of gravitation, to accelerate and curve toward the ground, but in fact this is an illusion. The falling object is moving at a constant speed and in a straight line. It's just that in that region of spacetime, where the stress-energy is, straight lines intersect. They intersect at the center of mass of the gravitating body.
As the aforementioned Wheeler so famously put it, matter tells space how to curve, and space tells matter how to move.
That's about as deep into gravitation as I can get without bringing in mathematics. And it's a lot of maths. But that's the essence of it. Everything in the universe that isn't actually accelerating — remembering that acceleration is a purely local phenomenon that can be measured with an accelerometer — moves in a straight line at a constant speed. But depending on where you are, a "straight line" can look like a curved line, and "constant speed" can look like acceleration.
Gravity, in other words, is just an optical illusion."

- RobotRollCall (http://www.reddit.com/user/RobotRollCall)
 
<h2>1. How does gravity warp spacetime?</h2><p>According to Einstein's theory of general relativity, gravity is not a force between masses, but rather a curvature of spacetime caused by the presence of mass or energy. This curvature causes objects to follow the shortest path through spacetime, which we perceive as the force of gravity.</p><h2>2. Why is it difficult to understand the concept of gravity warping spacetime?</h2><p>The concept of gravity warping spacetime can be difficult to understand because it is not something we can directly observe or experience in our daily lives. It also requires a shift in thinking from the traditional Newtonian understanding of gravity as a force between masses.</p><h2>3. How does the warping of spacetime explain the motion of objects in the universe?</h2><p>The warping of spacetime explains the motion of objects in the universe by showing how the presence of massive objects, such as planets and stars, create a curvature in spacetime that causes other objects to move towards them. This explains the orbits of planets around the sun and the motion of galaxies in the universe.</p><h2>4. Can you provide an example of how gravity warps spacetime?</h2><p>An example of gravity warping spacetime is the phenomenon of gravitational lensing, where the light from distant objects is bent and distorted by the gravitational pull of massive objects, such as galaxies. This can be observed during a solar eclipse when the sun's gravity bends the light from stars behind it, making them appear in a different position in the sky.</p><h2>5. How does the concept of gravity warping spacetime impact our understanding of the universe?</h2><p>The concept of gravity warping spacetime has greatly impacted our understanding of the universe by providing a more accurate and complete explanation of how gravity works. It has also led to the discovery of new phenomena, such as black holes, and has allowed us to make more accurate predictions about the behavior of objects in the universe.</p>

1. How does gravity warp spacetime?

According to Einstein's theory of general relativity, gravity is not a force between masses, but rather a curvature of spacetime caused by the presence of mass or energy. This curvature causes objects to follow the shortest path through spacetime, which we perceive as the force of gravity.

2. Why is it difficult to understand the concept of gravity warping spacetime?

The concept of gravity warping spacetime can be difficult to understand because it is not something we can directly observe or experience in our daily lives. It also requires a shift in thinking from the traditional Newtonian understanding of gravity as a force between masses.

3. How does the warping of spacetime explain the motion of objects in the universe?

The warping of spacetime explains the motion of objects in the universe by showing how the presence of massive objects, such as planets and stars, create a curvature in spacetime that causes other objects to move towards them. This explains the orbits of planets around the sun and the motion of galaxies in the universe.

4. Can you provide an example of how gravity warps spacetime?

An example of gravity warping spacetime is the phenomenon of gravitational lensing, where the light from distant objects is bent and distorted by the gravitational pull of massive objects, such as galaxies. This can be observed during a solar eclipse when the sun's gravity bends the light from stars behind it, making them appear in a different position in the sky.

5. How does the concept of gravity warping spacetime impact our understanding of the universe?

The concept of gravity warping spacetime has greatly impacted our understanding of the universe by providing a more accurate and complete explanation of how gravity works. It has also led to the discovery of new phenomena, such as black holes, and has allowed us to make more accurate predictions about the behavior of objects in the universe.

Similar threads

  • Special and General Relativity
Replies
1
Views
1K
  • Special and General Relativity
Replies
8
Views
429
  • Special and General Relativity
2
Replies
41
Views
3K
  • Special and General Relativity
Replies
15
Views
2K
  • Special and General Relativity
Replies
15
Views
1K
  • Special and General Relativity
Replies
7
Views
1K
  • Special and General Relativity
Replies
30
Views
499
  • Special and General Relativity
Replies
7
Views
1K
  • Special and General Relativity
Replies
7
Views
1K
  • Special and General Relativity
Replies
7
Views
1K
Back
Top