Exploring the Relationship Between Gravity and Spacetime

[GRB 080319B]

I believe most of my questions relate GR:

1.) I've heard of gravity likened to a bowling ball sitting on a spring mattress. The mattress is deformed or warped around the bowling ball, creating an indentation. The explanation discusses that this is analogous to a massive object, e.g. a star, warping the fabric of spacetime around itself. Is this understanding of gravity correct? Is gravity a force field at all or an aspect of the local topography of spacetime? Does the warping effect of a gravitational field warp the time dimension of spacetime and if so what effect does it have on time and how does it achieve this? Does a gravitational field cause length contraction and time dilation? I've heard that all massive objects exert a gravitational force on all other objects. If this is true does this mean that all of spacetime is warped by an omnipresent gravitational field and is this why spacetime is described as being curved? Do physicists visualize the force of attraction of a gravitational field as a vector space or in some other way? Are gravitational waves caused by an accelerating gravitational field, e.g. a bowling ball that is at rest on a water mattress being pushed, causing a ripple/wave in the water?

2.) Does gravity pull/attract objects through the time dimension as well as the space dimension, and if so what is the significance of this? Does the manipulation of time by gravity have any correlation with the inability to escape a black hole after passing through the event horizon?(I heard this has to do with something called light cones but I haven't the slightest clue of what they are or how they relate to gravity.)

3.) Is there any correlation between a gravitational field and a electromagnetic field? Do electric and magnetic fields create the same kind of warping in spacetime as gravity does? If so, is the geometry of spacetime warped in different ways for opposite charges and is this why opposite charges attract? In reference to the force of gravity acting like the bowling ball on a mattress, would like charges be similar to two depression meeting or two anti-depression meeting and repelling one-another? Do gravitational waves behave like or share any properties with electromagnetic waves? Do gravitational waves lose energy as they propagate through spacetime and are they absorbed and re-emmited like electromagnetic waves? Is gravity in any way similar to the property of electric charge and if so would the opposite charge of gravity be that of dark matter? If dark energy is expanding spacetime, which I assume to be true, does gravity contract spacetime between two massive objects or does it just create an attractive force between the particles and decrease the distance between them? Do electromagnetic fields expand or contract their local spacetime? Is light slowed down or does it lose energy when it interacts with a gravitational field, e.g. a car slowed down by speed bumps or pot holes in a road? Does the speed of light have anything to do with gravitational fields?

4.) I know that light, which is an electromagnetic wave, can be bent around a massive object's gravitational field. Is it possible for a gravitational wave to be bent by a strong electromagnetic field? I have heard that magnetars have a strong magnetic field, and that strong gravitational waves can be produced by the merger of two black holes. Are the statements in the previous sentence valid, and if so would it be possible to view the gravitational waves bending around a magnetar like Eddington viewed light bending around the solar eclipse of 1919?

I have no background in physics, so if any of these statements or questions are misconstrued , blatantly incorrect or unknown at this time feel free to correct them. Also, I apologize if some of my questions are redundant. Thank you.

 

[Mentz114]

Hi GRB 080319B:

Catchy moniker ! You've asked too many questions for one mere mortal to answer, but I'll have ago at section 1.

Is this understanding of gravity correct?

It is a rather poor analogy. The curvature is mathematically intrinsic and not the result of embedding in an extra dimension.

Is gravity a force field at all or an aspect of the local topography of spacetime?

General relativity ascribes gravitational effects to changes in the metric of space-time. I suppose you could call this the local intrinsic topography. There are no gravitational forces in GR, bodies follow worldlines dictated by space-time, and the energy and momentum of the body.

Does the warping effect of a gravitational field warp the time dimension of spacetime and if so what effect does it have on time and how does it achieve this?

Yes, space-time curvature will change the time and space components of the metric. Observers in different gravitational fields will observe each others clocks running faster or slower.

I've heard that all massive objects exert a gravitational force on all other objects. If this is true does this mean that all of spacetime is warped by an omnipresent gravitational field and is this why spacetime is described as being curved?

All matter attracts all matter.
Which space-time ? If there is no matter nearby, space-time could be very close to flat. Cosmological models do ascribe a global curvature to space.

Do physicists visualize the force of attraction of a gravitational field as a vector space or in some other way?

In GR there are no forces. In Newtonian gravity, the force is a vector ( which lives in a vector space ).

Are gravitational waves caused by an accelerating gravitational field

As I understand it, any moving matter will create gravitational wave ( although motion is relative and this sounds suspect).

I suggest you do a lot of reading. Gravity is not simple and has been intensely studied by a lot of smart people for a long time.

Of course, no one knows what gravity actually is.

 

[CJames]

It's easiest for me to think of it in terms of how light is effected by gravity. Light emitted from a gravitational body will be redshifted, which causes the time between each wave of light to increase. So if you imagine that the time between waves was one second when it was emitted, it will be more than that when it arrives higher up in the gravitational field. That causes clocks to tick slower lower down in a gravitational field. This causes a distortion in the measurement of time. And since you can use the speed of light and the time between two events to calculate a distance, this means you will also get distortions in the measurement of space. The result is that the radius of a circle around a gravitational body is larger than you would expect from the circumference.

The analogy of a bowling ball on a trampoline is imperfect. If you roll a marble on a trampoline it moves toward the bowling ball more because of the Earth's REAL gravity than because of the curvature of the trampoline.

To be more precise, think of a two dimensional graph. The vertical axis is height (space) and the horizontal axis is time. If you graph a ball falling, you'll get a parabolic curve. But if you were to take the GRAPH and warp IT into a parabolic shape, then you could make it so that the graph of the ball was actually the shortest distance between two points on the graph. Furthermore, anytime you drew a line that was the shortest distance between two points on this graph, it would look like a parabola if you were to again flatten the graph. So what you have is a warp in the relationship between space and time so that objects behave differently than if they were in a flat spacetime. This is what causes the phantom "force" of gravity.

Now that is still an oversimplification, because it is two dimensional, not four dimensional. It also ignores the fact that gravity changes with distance from the earth. But it really gets more to the root of what is meant by saying it is warped spacetime that causes gravity.

 

[shalayka]

As I understand it, any moving matter will create gravitational wave ( although motion is relative and this sounds suspect).

You are correct in being suspicious.

http://en.wikipedia.org/wiki/Gravitational_wave

"Sources of gravitational waves: In general terms, gravitational waves are radiated by objects whose motion involves acceleration..."

So, a spherically symmetric body undergoing rectilinear motion will not radiate gravitational waves. Of course, a spherically symmetric body undergoing rectilinear motion only truly exists in theory, since nothing's that perfect.

 

[Mentz114]

shalayka:

thanks for the heads up.

M

 

[pmb_phy]

In GR there are no forces.

Not quite. In GR the gravitational force is an inertial force, just like the centrifugal force or the Coriolis force. In Newtonian mechanics people often refer to such forces as "fictitious" (aka inertial forces) whereas Einstein, considering the gravitational field to be very real and since the gravitational force was of the same type as an inertial force then he viewed the inertial forces as "real." Some people view this in the opposite way, i.e. since inertial forces are fake then so is gravity.

Therefore the only debate in GR is not whether there is a gravitational force, but whether one considers inertial forces, like gravitation and the Coriolis force, as real.

Pete

 

[A.T.]

I've heard of gravity likened to a bowling ball sitting on a spring mattress. The mattress is deformed or warped around the bowling ball, creating an indentation. The explanation discusses that this is analogous to a massive object, e.g. a star, warping the fabric of spacetime around itself. Is this understanding of gravity correct?

No, it is a misleading analogy. The mattress represents curved space only. But the cause of gravity is curved spacetime. Here a much better visualization:
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html
more links to curved spacetime visualizations:
https://www.physicsforums.com/showpost.php?p=1557122

 

[GRB 080319B]

...bodies follow worldlines dictated by space-time, and the energy and momentum of the body.

Are worldlines the same as light cones, and if they are can you define what a light cone is?

...So if you imagine that the time between waves was one second when it was emitted, it will be more than that when it arrives higher up in the gravitational field. That causes clocks to tick slower lower down in a gravitational field. This causes a distortion in the measurement of time.

So all clocks, not only light clocks, have their measurements distorted? I'm having trouble visualizing how gravity effects mechanical clocks and other time measuring devices that don't use light directly. Do GPS satellites constantly have to sync up their clocks with clocks on Earth to maintain a consistent time?

...If you graph a ball falling, you'll get a parabolic curve. But if you were to take the GRAPH and warp IT into a parabolic shape, then you could make it so that the graph of the ball was actually the shortest distance between two points on the graph. Furthermore, anytime you drew a line that was the shortest distance between two points on this graph, it would look like a parabola if you were to again flatten the graph. So what you have is a warp in the relationship between space and time so that objects behave differently than if they were in a flat spacetime.

Are the clocks slowing down because they have to move through curved spacetime, which is a longer distance/more space than non-curved spacetime ,e.g. going around the circumference of a circle as opposed to traveling across the diameter?

I am not well versed in physics jargon, so if there is any way to explain this in lay mans terms I would greatly appreciate that. If that is impossible or too arduous a task, I understand. Thank you.

 

[A.T.]

Are worldlines the same as light cones

Worldlines are the paths of all objects in a spacetime.

I'm having trouble visualizing how gravity effects mechanical clocks and other time measuring devices that don't use light directly.

The speed of all physical processes is affected in the same way. Light propagation is just a basic example.

Do GPS satellites constantly have to sync up their clocks with clocks on Earth to maintain a consistent time?

I guess, but you could also use a constant multiplier.

Are the clocks slowing down because they have to move through curved spacetime, which is a longer distance/more space than non-curved spacetime ,e.g. going around the circumference of a circle as opposed to traveling across the diameter?

Yes, the distances between coordinate ticks along the time dimension are changed. This is visualized quite well in resources the I gave in the https://www.physicsforums.com/showpost.php?p=1666415&postcount=7".

 

[Mentz114]

GRB 080319B asks,

Are worldlines the same as light cones, and if they are can you define what a light cone is?

Please look at this -

en.wikipedia.org/wiki/Minkowski_diagram

Light cones and worldlines are both plotted on space-time diagrams. At any point on a worldline one can plot a lightcone that defines what the observer at that point can and can't see, because of the finite speed of light. Curved space-time causes light cones to 'tilt' with respect to each other.

 

[CJames]

So all clocks, not only light clocks, have their measurements distorted? I'm having trouble visualizing how gravity effects mechanical clocks and other time measuring devices that don't use light directly. Do GPS satellites constantly have to sync up their clocks with clocks on Earth to maintain a consistent time?

It will effect all physical processes the same. But it is all related to the redshift. Say you were in orbit looking down on an ordinary mechanical clock. Now on the ground, that clock will be reflecting light. The light reflected from that clock will have a certain number of waves each second. So each time the clock ticks, there will be that many waves in between. Now when you view the clock from space, those waves will arrive spaced out. This means there will be more time between each tick of the clock.

You might be tempted to think of this as an optical illusion, but it doesn't change the fact that it has a real effect on the clocks when we compare them later.

The effect is small on earth, but large enough that, yes, GPS satellites in fact do have to compensate for this effect in order to remain accurate.

Are the clocks slowing down because they have to move through curved spacetime, which is a longer distance/more space than non-curved spacetime ,e.g. going around the circumference of a circle as opposed to traveling across the diameter?

Well, distance divided by speed is time. So if the distance traveled is shorter, so is the time. The distance of the circumference is in fact shorter than one would expect from the radius. This means that fewer seconds would pass and you get the same result. So in a way that is another way you could look at it. For me it is much more intuitive to start with the redshift to discover the warp in time which you can use to find the warp in space.

 

[CJames]

3.) Is there any correlation between a gravitational field and a electromagnetic field? Do electric and magnetic fields create the same kind of warping in spacetime as gravity does? If so, is the geometry of spacetime warped in different ways for opposite charges and is this why opposite charges attract? In reference to the force of gravity acting like the bowling ball on a mattress, would like charges be similar to two depression meeting or two anti-depression meeting and repelling one-another? Do gravitational waves behave like or share any properties with electromagnetic waves? Do gravitational waves lose energy as they propagate through spacetime and are they absorbed and re-emmited like electromagnetic waves? Is gravity in any way similar to the property of electric charge and if so would the opposite charge of gravity be that of dark matter? If dark energy is expanding spacetime, which I assume to be true, does gravity contract spacetime between two massive objects or does it just create an attractive force between the particles and decrease the distance between them? Do electromagnetic fields expand or contract their local spacetime? Is light slowed down or does it lose energy when it interacts with a gravitational field, e.g. a car slowed down by speed bumps or pot holes in a road? Does the speed of light have anything to do with gravitational fields?

I might be wrong about this but I'm fairly sure this is essentially what the Kaluza-Klein theory was about. They found that by adding a fifth dimension they could get maxwell's equations for electromagnetism out of general relativity. But the theory was abandoned because it created more problems than it solved, I'm told.

At this time gravity is the only force explained using a warp in spacetime. The strong, weak, and electromagnetic forces are all explained most accurately by the quantum field theories of the standard model of particle physics. The problem is all those theories are unable to make predictions outside of a flat spacetime, which has left physics in a pickle for over thirty years.