Bending of space and time, is it true?

[AshUchiha]

I've heard many theories like object with mass bends the space-time and causes object to fall for it. If that's true then the Earth should end up being colliding with the Sun right? , because the Earth's mass is 1/1 million of that of Sun according to my knowledge.

If we take Earth's mass as m then Sun would be 1mil m, so would m's gravity really matter to 1mil m? I don't guess so, I don't think the theory explains quite of it. There is also another question I would like to put up, I'm sorry its not in the heading but, can this statement be true "Gravity can neither be created nor be destroyed". I've tried searching it in google and everywhere else but I wasn't able to get a satisfactory answer.

 

[FactChecker]

The distortion of space and time is another way of looking at gravity. The Sun bends space and time in such a way that the Earth is really traveling in a straight line as it orbits the Sun.

 

[Cruz Martinez]

I've heard many theories like object with mass bends the space-time and causes object to fall for it. If that's true then the Earth should end up being colliding with the Sun right? , because the Earth's mass is 1/1 million of that of Sun according to my knowledge.

If we take Earth's mass as m then Sun would be 1mil m, so would m's gravity really matter to 1mil m? I don't guess so, I don't think the theory explains quite of it. There is also another question I would like to put up, I'm sorry its not in the heading but, can this statement be true "Gravity can neither be created nor be destroyed". I've tried searching it in google and everywhere else but I wasn't able to get a satisfactory answer.

You can't conclude that the Earth should be falling and eventually colliding with the sun just because space-time has non-zero curvature. Freely falling particles follow inertial paths through space-time, one possible inertial trajectory is to move straight towards the massive object. Another possible inertial path is the one Earth follows.
Which particular inertial path is followed by a freely falling particle is determined from initial conditions.

 

[pvk21]

I don't think Earth will fall into sun because space-time bending.if that was the case it would have fallen way before.instead due to sun's space-time bending Earth rotate around the sun in elliptical path.

 

[Drakkith]

I've heard many theories like object with mass bends the space-time and causes object to fall for it. If that's true then the Earth should end up being colliding with the Sun right? , because the Earth's mass is 1/1 million of that of Sun according to my knowledge.

There is only one theory that posits this. It's called Einstein's General Theory of Relativity, or General Relativity for short. GR explains that space and time are joined together into space-time and that gravity is a geometrical effect of mass and energy. In other words, mass and energy 'bend' space-time in a way that is (slightly) analogous to putting a bowling ball on a trampoline or rubber sheet. The weight of the bowling ball bends the surface, and if you roll a smaller ball you will see that this bending of the surface causes its path to curved instead of continue on straight. Of course, the rubber sheet analogy is just that. An analogy. Space-time is a 4-dimensional construct and the way it 'bends' is much, MUCH more complicated and difficult to grasp.

If you perform the analogy above you will notice that you can roll the smaller ball in such a way as to make it 'orbit' the larger ball a few times before it loses enough speed to fall into the larger ball. This happens because there is friction slowing the ball down. The Earth orbits the Sun in a near-vacuum so there is practically no friction. This allows the Earth to continue to orbit the Sun without falling in. In order to fall into the Sun the Earth would have to slow down by a significant amount.

There is also another question I would like to put up, I'm sorry its not in the heading but, can this statement be true "Gravity can neither be created nor be destroyed".

Eh, I don't really like the question to begin with. Gravity, as a general term, simply refers to the fundamental interaction known as Gravitation. This interaction, as a whole, cannot be destroyed and it already exists, so it cannot be created again. Also, in simple terms gravity can be understood as a value at any point in space representing the strength of the gravitational force at that point. In other words, if we measure the gravitational force at a point in space that is 10,000 km directly above the north pole of the Sun, we will get some value that represents the strength of the force felt at that point. If we move away from the Sun this value gets smaller, and if we move closer this value increases. This value can change without you moving if other objects move by, but it is a smooth process. You can't have a value of, say 100, and then have it instantly jump to 200 or 0 or anything else. It increases gradually in response to the movement of other objects. So in that sense you can't destroy or create gravity. You can only change the value at any point in space by moving objects around. More

So I guess the short answer is no, gravity cannot be created or destroyed.

 

[Bandersnatch]

So I guess the short answer is no, gravity cannot be created or destroyed.

Have you got Guth's Inflationary Universe on hand? He's got a neat thought experiment there that shows how it can happen. In short - imagine an empty, spherical shell of matter collapsing under its own gravity. What is the gravitational acceleration outside and inside the original shell radius before and after the collapse?

 

[Drakkith]

Have you got Guth's Inflationary Universe on hand?

I do not.

What is the gravitational acceleration outside and inside the original shell radius before and after the collapse?

Offhand I'd guess that the acceleration is the same outside the original shell radius, and a lot more inside since it was zero originally. That's why I don't like the question "can gravity be created or destroyed". The answer kind of depends on what you mean by 'created' and 'destroyed' in this context.

 

[Bandersnatch]

I understood it as going from zero to any positive value. Which, as you said, is what happens inside the shell.

 

[Drakkith]

I understood it as going from zero to any positive value. Which, as you said, is what happens inside the shell.

That's they way I understand it too.

 

[AshUchiha]

Drakkith, Actually "Gravity can neither be created nor be destroyed". What I really meant was, you see Mass can neither be created nor be destroyed right? And we know that each object with mass would have its own gravity, so as mass cannot be destroyed or created. Their gravities can neither be created nor be destroyed too right? And Bandersnatch, that spherical thing you are saying can you explain it a bit less complicated?, atleast so that an Highschool kid can understand it

 

[Bandersnatch]

I'm going to assume you have learned about Newton's Law of Gravity already.

This thought experiment relies on something that Newton first proved a while back, and what you might have been told in school without much explaining - that gravity far away from a spherically-symmetric mass is the same as if all the mass were concentrated in its centre. That's why you can calculate the acceleration due to gravity on the surface of Earth as if all its mass were in its centre, 6700-odd km away.
It's what is called the 'shell theorem', and it can be understood if you know some calculus, or purely on geometrical terms - look it up on Wikipedia.
The other thing the theorem shows is that the gravitational field inside a spherically symmetric, empty shell of matter is always 0.

Imagine a set-up like this:

You've got a hollow shell of mass M represented by the grey circle. The shell contracts under its own gravity until it is smaller - here represented by the black circle. It doesn't matter how far it had actually contracted when we look at it again. The point is, it's smaller than before.

The gravity field (i.e., acceleration due to gravity, or $F/m$) outside this shell (at point A) is the same as if all the mass were concentrated in the centre of the circle and given by $g=\frac{GM}{R^2}$.

The field inside the grey circle before it contracted is zero throughout the volume, including points B and C.

Now let's look at it after it contracted:
-the field outside the original radius (outside the grey circle, point A) is still the same, because we can still treat it as if the mass were concentrated in the centre;
-the field inside the new radius (inside the black circle, point C) is still zero, because this volume is still surrounded on all sides by spherically-symmetric shell of matter;
-the field between the two radii (point B) is now equal to $g=\frac{GM}{R_B^2}$, whereas before the shell contracted, it was zero.

So what you've got, is gravity appearing in a volume of space where once it wasn't there.This works the other way around as well. Imagine a star exploding (for simplicity, let's say it doesn't leave anything behind - like a supernova type Ia explosion).
Before it explodes, a planet can be in orbit around it due to the gravity it feels from all that mass.
After it explodes, the gravity that held the planet in orbit disappears as soon as the 'shrapnel', i.e. the envelope of matter ejected by explosion, passes the planet's orbit. Now the planet is inside an expanding, spherically symmetric and hollow shell of matter, and the value of the gravitational field it experiences is zero.

 

[pvk21]

I'm going to assume you have learned about Newton's Law of Gravity already.

This thought experiment relies on something that Newton first proved a while back, and what you might have been told in school without much explaining - that gravity far away from a spherically-symmetric mass is the same as if all the mass were concentrated in its centre. That's why you can calculate the acceleration due to gravity on the surface of Earth as if all its mass were in its centre, 6700-odd km away.
It's what is called the 'shell theorem', and it can be understood if you know some calculus, or purely on geometrical terms - look it up on Wikipedia.
The other thing the theorem shows is that the gravitational field inside a spherically symmetric, empty shell of matter is always 0.

Imagine a set-up like this:
View attachment 81178
You've got a hollow shell of mass M represented by the grey circle. The shell contracts under its own gravity until it is smaller - here represented by the black circle. It doesn't matter how far it had actually contracted when we look at it again. The point is, it's smaller than before.

The gravity field (i.e., acceleration due to gravity, or $F/m$) outside this shell (at point A) is the same as if all the mass were concentrated in the centre of the circle and given by $g=\frac{GM}{R^2}$.

The field inside the grey circle before it contracted is zero throughout the volume, including points B and C.

Now let's look at it after it contracted:
-the field outside the original radius (outside the grey circle, point A) is still the same, because we can still treat it as if the mass were concentrated in the centre;
-the field inside the new radius (inside the black circle, point C) is still zero, because this volume is still surrounded on all sides by spherically-symmetric shell of matter;
-the field between the two radii (point B) is now equal to $g=\frac{GM}{R_B^2}$, whereas before the shell contracted, it was zero.

So what you've got, is gravity appearing in a volume of space where once it wasn't there.This works the other way around as well. Imagine a star exploding (for simplicity, let's say it doesn't leave anything behind - like a supernova type Ia explosion).
Before it explodes, a planet can be in orbit around it due to the gravity it feels from all that mass.
After it explodes, the gravity that held the planet in orbit disappears as soon as the 'shrapnel', i.e. the envelope of matter ejected by explosion, passes the planet's orbit. Now the planet is inside an expanding, spherically symmetric and hollow shell of matter, and the value of the gravitational field it experiences is zero.

So you mean to say that gravity can be created or destroyed

 

[Bandersnatch]

Like Drakkith, I dislike such words, as they suggest agency.
I mean what I said - you change the arrangement of some mass, and you get a positive value of the field where it used to be zero (and vice versa).

 

[Drakkith]

Things are even more complicated than they seem. In GR the curvature of space-time is not zero inside the shell, so even though you won't accelerate in any direction if you were inside the shell, you would be experiencing time dilation compared to an observer outside and far away from the shell.

 

[phinds]

Drakkith, Actually "Gravity can neither be created nor be destroyed". What I really meant was, you see Mass can neither be created nor be destroyed right? And we know that each object with mass would have its own gravity, so as mass cannot be destroyed or created. Their gravities can neither be created nor be destroyed too right? And Bandersnatch, that spherical thing you are saying can you explain it a bit less complicated?, atleast so that an Highschool kid can understand it

Mass cannot be destroyed?

What do you think goes on at CERN every day? Mass is converted to energy.

What do you think goes on in an atom bomb? Mass is converted to energy.

How about the interior of the sun? Mass is converted to energy.

 

[Drakkith]

Mass cannot be destroyed?

What do you think goes on at CERN every day? Mass is converted to energy.

What do you think goes on in an atom bomb? Mass is converted to energy.

How about the interior of the sun? Mass is converted to energy.

Mass is not destroyed in any of those situations. Matter is converted into energy, but this energy has mass.

In other words, if you measure the mass of the system prior to this conversion, and then measure the mass of the system after the conversion but before any energy leaves the system, you will find that the mass of the system is identical in both cases. Once this energy leaves the system, perhaps by being radiated away, the mass of the system is reduced according to Einstein's equation.

Einstein's equation doesn't really tell us that mass can be 'converted' to energy, it tells us that if you track where Y amount of energy goes, you will find that X amount of mass accompanied it, and if you move X amount of mass around, it took Y amount of energy to do so. That's how I understand it at least.

 

[phinds]

Mass is not destroyed in any of those situations. Matter is converted into energy, but this energy has mass.

Yeah, I know the mass/energy total remains the same but the matter that goes into the energy is no more.

 

[Drakkith]

Yeah, I know the mass/energy total remains the same but the matter that goes into the energy is no more.

Your posts confuse me, good sir.

 

[phinds]

Your posts confuse me, good sir.

Hm ... seems clear to me so I must be missing something. My understanding is that although mass/energy total is conserved in a closed system, the matter being converted to energy means less matter (less mass) and more energy.

 

[Drakkith]

Hm ... seems clear to me so I must be missing something. My understanding is that although mass/energy total is conserved in a closed system, the matter being converted to energy means less matter (less mass) and more energy.

You replied to my earlier post while I was editing it. Have you reread post 16 since I edited it? If not, that may make it a little clearer what I mean.

 

[phinds]

You replied to my earlier post while I was editing it. Have you reread post 16 since I edited it? If not, that may make it a little clearer what I mean.

Einstein's equation doesn't really tell us that mass can be 'converted' to energy,

OK, that's not what I thought was the case, so assuming you got that right, then my post was wrong. I'm still puzzled though because where does the energy come from if the matter is not "converted"?

I'm accustomed to seeing statements like this one from Wikipedia:

In nuclear physics, nuclear fusion is a nuclear reaction in which two or more atomic nuclei collide at a very high speed and join to form a new type of atomic nucleus. During this process, matter is not conserved because some of the matter of the fusing nuclei is converted to photons (energy).

Seeing it in Wikipedia doesn't make it right, of course, but I've been reading that kind of statement in various places for decades.[/quote]

 

[Drakkith]

I'm still puzzled though because where does the energy come from if the matter is not "converted"?

The matter IS converted. As I understand it, the matter contained binding energy that was transformed into another type of energy. But the total mass and the total energy of the particles is conserved both before and after the reaction. In other words, the mass of the particles (reactants) is equal to the mass of the products, and the total energy of the reactants is equal to the total energy of the products.

 

[phinds]

The matter IS converted. As I understand it, the matter contained binding energy that was transformed into another type of energy. But the total mass and the total energy of the particles is conserved both before and after the reaction. In other words, the mass of the particles (reactants) is equal to the mass of the products, and the total energy of the reactants is equal to the total energy of the products.

I hear what you're saying but am having trouble digesting it. I'm well aware that the universe doesn't care what I find likely or unlikely, but still ...

 

[Drakkith]

You're not confusing mass with matter, are you?

 

[phinds]

You're not confusing mass with matter, are you?

Yes, I guess I am. Layman's mistake?

 

[Drakkith]

Let's just blame it on Greg somehow.

 

[phinds]

Let's just blame it on Greg somehow.

Sounds right to me.

 

[wabbit]

I don't think "mass is converted to energy" is wrong, though it depends on what we call mass. For instance, the sum of the rest masses of a colliding electron and positron is not conserved in the collision since the result is essentially massless photons. Not sure which definition of mass is conserved - as far as I can tell, only the length of the energy-momentum 4-vector is.

 

[AshUchiha]

Ummm..., so how does our Earth manages not colliding with the sun when taking space-time as a rubber sheet and our Earth as a very small ball compared to the Sun. It will eventually fall into it, and now, how Inertia is helping it not to fall to Sun, I mean so Inertia helps the Earth move forward? So Earth's state of rest was and is straight motion but the Sun is disturbing its motion by pulling it? If that's so, why can't we see the bending of the space-time?

 

[Bandersnatch]

Ummm..., so how does our Earth manages not colliding with the sun when taking space-time as a rubber sheet and our Earth as a very small ball compared to the Sun. It will eventually fall into it, and now, how Inertia is helping it not to fall to Sun, I mean so Inertia helps the Earth move forward? So Earth's state of rest was and is straight motion but the Sun is disturbing its motion by pulling it? If that's so, why can't we see the bending of the space-time?

When you say 'space-time as a rubber sheet' you're probably thinking of something like this:


Which is NOT a visualisation of space-time. Of a few things it shows, one is objects moving in gravitational potential of other objects. The depth of the indentation in the sheet represent the depth of the gravitational well.

In this analogy, the planets stay in 'orbits' as a result of their tangential velocity (how strong you push a ball sideways). If velocity is low, a 'planet' will follow an elliptic orbit, falling towards the centre and then getting back to where it started. If the velocity is just right, it will move in circles in the gravitational well of the central body.

Another good analogy that shows the same thing, is a ball in a roulette game - it goes in circles in a 'gravity well'. It only falls down towards the centre due to friction, which is not present in space, so the motion (circular or elliptical) is eternal (barring interactions with other bodies).

These are both Newtonian representations of gravity, though. There is no time dimension being curved anywhere in there.
Here, you can indeed say that the 'natural state' of a planet is to move in a straight line, and the star is pulling it towards itself.

Gravity as bending of space-time is different. The following video shows how it's supposed to work in in one spatial dimension (plus time of course):

(all credits to @A.T.)

Here, the Sun's gravity changes what it means to move in a straight line. In this space-time curving model of General Relativity the 'natural state of a planet is to follow the 'straight' lines in curved space-time, and it takes some other force to change this natural state.

 

[AshUchiha]

Wow, thanks it helped a lot. So the in the examples shown in the second video, I find Newton's theory more reasonable, as gravity acts on all objects with mass and energy at all times right?. Just one last question, is gravity a relative quantity??, for example let's assume a very big (such that all other celestial bodies are negligible in mass to that), is on the space. So all the objects would fall to it ? As that objects velocity and gravity is much higher compared to those. Really bugs me...

 

[phinds]

Wow, thanks it helped a lot. So the in the examples shown in the second video, I find Newton's theory more reasonable, as gravity acts on all objects with mass and energy at all times right?. Just one last question, is gravity a relative quantity??

Only in the sense that bigger masses have a stronger gravitation attraction, but "relative" is NOT a good description for gravity.

, for example let's assume a very big (such that all other celestial bodies are negligible in mass to that), is on the space. So all the objects would fall to it ? As that objects velocity and gravity is much higher compared to those. Really bugs me...

You can have a stable orbit around any size mass so things will not necessarily fall in.

Velocity is relative, so your statement about velocity doesn't make sense since you have not specified what it is that the large object has a high velocity relative to.

 

[wabbit]

Velocity is relative, so your statement about velocity doesn't make sense since you have not specified what it is that the large object has a high velocity relative to.

Actually if that big mass has a very high velocity compared to everything else, it will capture less: this means that other objects are likely to be above escape velocity relative to that big mass, so they do not fall in unless their path directly crosses that body.

 

[phinds]

Actually if that big mass has a very high velocity compared to everything else, it will capture less: this means that other objects are likely to be above escape velocity relative to that big mass, sobthey do not fall in unless their path ditectly crosses that body.

Good point.

 

[AshUchiha]

Wait phinds, Gravitation is equal to every object no matter their mass I guess (Ignoring Drag).Can you explain me how gravity isn't a "good" example for being relative quantity..? Also assuming that any object with minimum required mass would have it's own orbit , is wrong? just reference...And it's velocity is higher than any other object available in space