Question about gravity

[Zeuzzz]

Einstein already did, nearly a century ago.

How does matter 'bend' space-time then?

 

[Southwind17]

How does matter 'bend' space-time then?

I'm sure that when Sol imparts his understanding, which surely must be simple and easily conveyed, given that it usurps the degree of understanding of almost anything else in the World, then we'll all ... well ... simply understand, I guess!

 

[Ziggurat]

How does matter 'bend' space-time then?

The foundations of any physical theory cannot have a "how" answer. They just are. If you ever come up with an answer to a "how" question about the foundations, that just means you've pushed the foundations of your theory to a new location, which will have new unanswered "how"s. So there is no "how" answer, and there never was. There is only an answer to the "what", and that answer is
[latex]$G_{ab} = \kappa T_{ab}$[/latex]

 

[Southwind17]

The foundations of any physical theory cannot have a "how" answer. They just are. If you ever come up with an answer to a "how" question about the foundations, that just means you've pushed the foundations of your theory to a new location, which will have new unanswered "how"s. So there is no "how" answer, and there never was. There is only an answer to the "what", and that answer is
[latex]$G_{ab} = \kappa T_{ab}$[/latex]

Excuse me; what's the question?

 

[Yllanes]

Really? Please go ahead and explain it, then, and satisfy the majority of the Earth's collective unfulfilled wonderment!

What Ziggurat and sol invictus said. But why don't you or Robinson explain why you feel gravitation is not understood, while the other three forces are?

 

[Southwind17]

What Ziggurat and sol invictus said. But why don't you or Robinson explain why you feel gravitation is not understood, while the other three forces are?

Why don't you just go ahead and explain it, simply, if it's so well understood?

 

[Yllanes]

How does matter 'bend' space-time then?

Exactly like this:

[latex]
\[
R_{ab} - \frac12 R g_{ab} = 8\pi G T_{ab}
\]
[/latex]

If what you are asking is why this happens, then the same question can be posed for any other force. As in: why do electrons exchange virtual photons?

 

[Southwind17]

Exactly like this:

[latex]
\[
R_{ab} - \frac12 R g_{ab} = 8\pi G T_{ab}
\]
[/latex]

If what you are asking is why this happens, then the same question can be posed for any other force. As in: why do electrons exchange virtual photons?

I don't see how citing a formula satisfactorily addresses either the "how" or the "why". As such it helps little in promoting understanding.

 

[Southwind17]

Incidentally, not wishing to plagiarize Einstein, but are we talking "general" gravity here or "specific" gravity? If the latter then my father held an inimitable understanding, but then he was pretty adept in the home-brew department!

 

[sol invictus]

All I said was that we understand gravity better than just about anything else in the world. If you don't agree, why not give some examples of things you think we understand better?

 

[Yllanes]

I don't see how citing a formula satisfactorily addresses either the "how" or the "why". As such it helps little in promoting understanding.

That formula explains exactly how energy bends spacetime. If you don't understand it, that's your problem, not the theory's.

When we say that gravity is understood just as well if not better than the other interactions, we mean exactly that. We don't mean it can be explained in a forum post.

 

[Zeuzzz]

Simplistically:

Q1 - None of those. The effects of gravity would be more apparent on the surface of the Earth.
Q2 - None of those. The effects of gravity would decrease.

Technically, if ur being pedantic, your answer of 'none of those', is correct, i should have worded it better

The answer is not what i expected,

Well, the way I figured:

For a homogenouos sphere it can be determined that g(r)=GM(r)/r2. M(r) being the mass within of the sphere with radius r. - G gravitational constant and rho density

The total mass outside that radius is cancelling each other. Since M(r)=4/3 * rho * pi *r^3 it follows that g(r)=4/3 * G * rho * pi * r. In other words the gravity inside a homogenouos sphere is directly proportional to the distance to the centre.

Now assuming that the density rho is linear decreasing from value a with increment b, we replace rho with rho(r)=a-br. Substitute it in the first formula to get only a simple square formula, so intergrating is basic.

However we have five discontinuing layers: inner core, outer core, lower mantle, upper mantle, lithosphere. Each with their own numbers r-min, r-max, rho-a and b. I used 100 km increments for each shell.

Now, the answers are clear albeit a bit surprising. Gravity remains more or less constant initially. Why? We still can neglect the mass outside the radius when heading for the centre - this is decreasing the gravity. But we also come closer and closer to the very dense core - this is increasing the gravity. Both are of about the same magnitude initially, cancelling each other. (note that in the initial stage, entering the (relatively very light) crust the gravity increases sharply from 9.81 to 9.96 ms-2)

Coming closer to the the core however, the increasing factor wins and my model indicates a maximum value of 10,62 ms-2 at the core mantle boundary versus 9,81 at the Earth surface.

Inside the cores the behaviour is more or less approaching the homogeneous sphere - lineair proportional to the radius. Now isns't that a nice to know for discussions. So concluding:

Q1 Where is gravity of the Earth the strongest?

A - On the surface of the Earth
B - In the centre of the Earth
x C – SOMEWHERE ABOUT HALFWAY DOWN TO THE CENTRE OF THE EARTH. 10,62 ms-2 at a depth of approximately 2890 km


Q2 If you dig yourself about one thousand of miles into the Earth, what happens to gravity?

A. - Increases definitely.
X B. - STAYS MORE OR LESS CONSTANT. (fluctuates actually between 9.96 and 10.04 ms-2)
C. - Decreases definitely.

There is more to it than the eye meets.

 

[portlandatheist]

Just for some fun;

Q1 Where is gravity of the Earth the strongest?

A - On the surface of the Earth
B - In the centre of the Earth
C – Somewhere about halfway down to the centre of the Earth


Q2 If you dig yourself about one thousand of miles into the Earth, what happens to gravity?

A. - Increases definitely.
B. - Stays more or less constant.
C. - Decreases definitely.

There is more to it than you might think.

Q1: C
Q2: A (at some point after a thousand miles, it would begin to decrease)

If you dug a hole all the way through the earth, and took away the atmosphere, you could drop an object and it would bounce back and forth, essentially being a highly elliptical orbit.

ETA: missed your latest post

 

[Southwind17]

That formula explains exactly how energy bends spacetime. If you don't understand it, that's your problem, not the theory's.

So, when my kids become old enough to start to try to assimilate this wonderful formula what do you suggest, that they persist in staring at it until it makes sense, or might it help if somebody really "explains" it to them?

When we say that gravity is understood just as well if not better than the other interactions, we mean exactly that. We don't mean it can be explained in a forum post.

"We" being who, exactly? If one properly understands something then one should be able to explain it to others in a comprehensible way. If you can't explain gravity here than I posit your understanding is not as complete as you clearly seem to think it is.

 

[Southwind17]

All I said was that we understand gravity better than just about anything else in the world. If you don't agree, why not give some examples of things you think we understand better?

Wouldn't it be more sensible for you simply to posit your understanding? If you insist, however, I believe our understanding of how and why rain falls, for example, is pretty much complete. Or how and why the plasma screen I'm looking at works.

 

[shadron]

Describing gravity is easy, and was understood long ago. Describing something is not the same as understanding how, or why.

I'm not really sure I should stick my oar in this water, but the question about how, and particularly why, gravity is like it is is at least philosophical and metaphysical, and perhaps downright theological (pardon my French). *How* does gravity "suck"? Who knows? No one likely to answer on this forum, certainly. If you had the answer, I predict that it will be at least an order of magnitude harder to understand than gravity. *Why* does it suck? Perhaps because if it didn't we couldn't have asked the question? Ask the creator, if you can find him.

Sometimes *why* is a valid scientific question: why does almost all the mass in the universe seem to be matter as opposed to anti-matter? Good question - it might lead to a new discovery. But why does gravity vary directly with mass and inversely with distance squared? It just does. The difference, as was pointed out above, is that you can ask why when there is some basic, underlying principle that can be measured and observed. With gravity, there is none such, so asking why is scientifically futile.

In most basic science description is the best we have. With a suitable description you can predict what gravity will do to Jupiter next Wednesday, or where it was on Dec 25, 1BC. Sol reminds us that we can do that to within a whisker's width. The description is as complete as we can make it without any new discrepancies to explain away, and that is why Sol says we understand it.

There is no theory for gravity like there is for the other fundamental forces. Saying there is, is dumb.

Oh? Please explain the electromagnetic force, then. Why does it expel, as well as attract, unlike gravity? How does the strong force overcome electromagnetic repulsion only out to about the radius of a Uranium nucleus? Why that far and no farther? What theory have we got to cover these sorts of questions? None.

Again, the question isn't about understanding, it is about explaining.

Some basic things have to be simply accepted as observed. Sorry - no deeper scientific explanation is currently possible. Perhaps it will be so forever.

 

[Cold one]

If you insist, however, I believe our understanding of how and why rain falls, for example, is pretty much complete.

The way I understand it rain falls due to gravity and since you dont understand gravity then your understanding of water falling from the sky is therefore incomplete.

 

[Fredrik]

I agree with the claim that gravity is at least as well understood as anything else. It's not at all correct to say that there's no theory of gravity as there is for the other interactions. There's no quantum theory of gravity yet, but that's another matter. (See my comments at the end of this post).

It isn't possible to really understand Einstein's equation (the one posted by several people earlier in this thread) without studying differential geometry, but you can get a rough idea.

The right-hand side represents all the matter and energy in the universe. The two indices go from 0 to 3, so it has 16 components, but it is symmetric (T_ab=T_ba), so only 10 of the components are independent. One of those components is the density of matter/energy as a function of position. The others are stuff like the pressure, and internal stresses. (Take a piece of rubber and hold on to one end while twisting the other end. You don't change the density much, but you introduce forces between different parts of the rubber, and that changes its contribution to those "other" components of the stress-energy tensor).

The left hand side represents the geometric properties of space-time. The quantities on the left (the G, or equivalently the Rs) can be constructed from another symmetric tensor with two indices called the metric tensor. The metric tensor tells us the "distance" between any two points in space-time, and it also tells us which lines are to be considered "straight". I put "distance" in quotes because it's defined in a way that means it can be negative, and I put "straight" in quotes because it's not what we're used to either. The path through space-time that a planet takes when it's orbiting a star is straight in this geometry. The distance between the event where a laser beam is emitted and the event where it hits its target is always zero in this geometry (and this path is straight too).

If there had been no matter or energy in the universe whatsoever, the components of the metric tensor would have been

[latex]$$\begin{pmatrix}-1 & 0 & 0 & 0\\0 & 1 & 0 & 0\\0 & 0 & 1 & 0\\0 & 0 & 0 & 1\end{pmatrix}$$[/latex]

The space-time with this metric tensor is called Minkowski space. This is the space-time of special relativity, the theory that Einstein came up with in 1905. Special relativity is nothing more than the claim that space and time can be represented mathematically by Minkowski space. This means it doesn't describe gravity, but it's a suitable framework for e.g. both classical and quantum mechanical theories of electromagnetism. General relativity is the claim that the relationship between the metric tensor and the matter/energy content of the universe is described by Einstein's equation.

Famous quote by John Wheeler: "Matter tells space how to curve. Space tells matter how to move".

It might seem that we understand gravity less than the other interactions since we've been able to find quantum theories describing those, but that conclusion would be incorrect. The piece of information that you would need to understand why, is that all of those quantum theories are formulated in the framework of special relativity, which we already know is a much less accurate representation of space-time than general relativity.

 

[Southwind17]

The way I understand it rain falls due to gravity and since you dont understand gravity then your understanding of water falling from the sky is therefore incomplete.

That's why I wrote "pretty much complete" and not "entirely complete". The gravity aspect of rain physically "falling" is essentially incidental to the wider question of why rain "happens". I didn't think "rain happens" sounded very eloquent, though. I'm sure you got all that, though, the first time around!

 

[Yllanes]

So, when my kids become old enough to start to try to assimilate this wonderful formula what do you suggest, that they persist in staring at it until it makes sense, or might it help if somebody really "explains" it to them?

It was claimed in this thread that our knowledge of gravity was more imperfect than our knowledge of the other interactions. Someone said we lack a theory for it such as we have for the other fundamental forces. And that is incorrect because we do have a theory, based on a couple of postulates (one of which is the equation I posted earlier), which lets us predict the physics of gravitation with astonishing precision.

To really understand gravitation one must be able to carry out such calculations. You can't understand it at that level with just a couple of paragraphs in English. What you can do with a couple of paragraphs is to say something such as Fedrik's post. But the same thing is true for the other interactions. You cannot explain the Standard Model in a forum post so that you audience can then go and compute, say, the half life of the Higgs boson at tree level.

So, my question to you is: do you believe gravity is less understood than, say, the strong nuclear force? If you don't then we agree and there's nothing else to say. If you do, please tell us why.