# General Relativity

#### RuroumiKenshin

Gravity is a curvature of space. Agree?
Thhe Sun for example causes space to curve.
Hence it creates a gravitational pull.
What does the sun weigh?
Do you understand what I am getting at?
How can the sun or anyother mass curve space with their wieght without something pulling it? We weigh differently on other planets because of different gravitational pulls.

I am confused here.

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#### ahrkron

Staff Emeritus
Gold Member
Originally posted by RuroumiKenshin
How can the sun or anyother mass curve space with their wieght without something pulling it?
The reason you are confused is that you are confusing mass and weight.

Some objects have mass.
Mass "interacts" with spacetime by curving it.
Other objects travel with the curved spacetime,
We measure this second interaction and call it "weight".

#### RuroumiKenshin

I see:
How does mass interact with space?

#### marcus

Gold Member
Dearly Missed
Originally posted by RuroumiKenshin
Gravity is a curvature of space. Agree?
Thhe Sun for example causes space to curve.
Hence it creates a gravitational pull.
What does the sun weigh?
Do you understand what I am getting at?
How can the sun or anyother mass curve space with their wieght without something pulling it? We weigh differently on other planets because of different gravitational pulls.

I am confused here.
to understand this, don't you need a way to measure curvature?

in General Relativity (often abbreviated GR) it is measured in units 1/square meter----units of reciprocal area

In GR it is the energy density of the sun----joules per cubic meter----that causes curvature-----1/square meter.

It is not the "weight" of the sun but the concentration of mass-energy----the fact that the sun represents a huge energy packed into a rather small space. this is a big "joules per cubic meter" and it causes the curvature around the sun.

The Einstein equation, the main equation of GR, says:

Gm,n = 8pi Tm,n

and the lefthandside is curvature (number per sq. meter) and the righthandside is energy density (joule per cub. meter)

How can those two kinds of quantities be related? By a constant universal force. This force multiplied by curvature gives energy density. A newton, the metric unit of force, would work except for the fact that it is not the right size.

newton x (1/sq.meter) = newton/sq meter = joule/cubic meter

So multiplying newton by curvature gives energy density.

It would work except it is too weak. The right force---the one that actually connects the sun energy density to the resulting curvature, is 12E43 newtons. Also written "c4/G."

You do not cause gravity by your weight.
You cause gravity by your concentrated energy. That is what pulls other things. If only people would just take the equations seriously and read what they actually say, there would be a wider understanding of this.

the best window on this I know are the Friedmann equations, the simplified Einstein equation used by cosmologists. There the energy density is shown explicitly and it is obvious that it is what causes the bending (and as a result the "pull" on other things which you talked about)

#### RuroumiKenshin

What causes the energy to be focused into a certain area in space?

#### marcus

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Originally posted by RuroumiKenshin
I see:
How does mass interact with space?
mass has energy
energy interacts with space thru this force constant
light has zero mass (according to the way most physicists use the term mass) but it has energy
so concentrations of light bend space just as matter would

the only thing that matters is the energy density---the joules per volume.

it does not matter if the energy is matter or light, or some other form of energy we dont know about (like dark energy)

arkhon side-tracked you by bringing up the concept of mass
(which in modern physics means rest mass and is not directly relevant)

you should be asking "How does energy interact with space?"-----that is a really interesting question and fits well into the context of GR

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#### marcus

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Originally posted by RuroumiKenshin
What causes the energy to be focused into a certain area in space?
Yes yes now you are talking to good purpose! Think about all the energy in the sun and what keeps it concentrated there. meditate on it a little.

There is all that nuclear energy---and the heat energy at 15 million degrees in the core----where matter is being converted to heat. And all the E=mc^2 energy which is invested in the sheer EXISTENCE of the atom that make up the sun. energy that would appear in a flash if they were annihilated. And the sun is soaked full of light. Light is percolating from deep inside towards the surface. When it gets to the surface it gets loose and flies out in all directions.

You say: what keeps energy concentrated? Well in the case of the sun it is mostly the suns own gravity that keeps it concentrated.

So there is a feedback-----energy density causes gravity and its gravity keeps it together so it doesnt spread out all over the place.

But some does get loose, little by little, and does spread out. Light has a tendency to do this.

So the universe is full of spread out energy as well as concentrated-into-stars-and-planets energy.

I have to go----I'm sort of talked out now. But another time we can have another try at this. Roroumi. Be well

#### RuroumiKenshin

How does density create gravity?

#### planetology

Originally posted by RuroumiKenshin
How does density create gravity?
The answer to this question is unknown. Einstein concluded that space-time must be curved by matter/energy (strictly speaking momentum and energy fluxes also contribute to curvature), and he described exactly how much it is curved by a given amount of matter/energy. But his equations give no insight at all as to why matter/engergy causes space-time to be curved. In this way it is a bit like Newton's law of gravity, which describes how much force given masses experience due to gravity, but says nothing about why. Einstein's theory gives a bit more information as to why (curvature) but still does not solve the mystery of how curvature is generated.

#### marcus

Gold Member
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Originally posted by RuroumiKenshin
How does density create gravity?
He says we do not know WHY energy density creates gravity.

Look at the emphasis on the word WHY in his post.

If why is the same as how
then your question "how does density create gravity?" cannot
be answered on this forum and you will have to go to
a church or somewhere to find someone with an idea about it.

But how is just slightly different from why.

I will repeat. There is a force and there is Einstein's equation
between curvature and energy-density.

G_m,n = 8pi T_m,n

Each G term is curvature and each T term is energy density, there are several terms on each side labeled with subscripts m,n which are a nuisance to type. By G_m,n what I mean is Gm,n

what is always there linking the two is this universal constant force---which is about 1040 tons.
whatever the curvature is on the lefthand side, if you multiply it by this force then you get the energy density causing it on the righthand side.

This is HOW the two things are related.
Who made this force? You tell me. Why did
they put it there? For what purpose? What was the idea? Who knows? But that is how curvature and energy-density are related.

#### einsteinian77

how can energy be concentrated?

#### marcus

Gold Member
Dearly Missed
Originally posted by einsteinian77
how can energy be concentrated?
the usual unit of energy density is joules per cubic meter

all the energy I can think of has some degree of concentration in space

for sunlight, for example, one can say how much energy is in a cubic kilometer of space near the earth

for the core of the sun, for example, one can say what the density (or in more colloquial language the concentration) of X-ray energy is

and matter has mass-energy invested in its existence (which is released when/if the matter is annihilated) so ordinary matter represents a concentration of energy also

do you have questions about this? it is an interesting topic of conversation and can lead to calculating the densities of various kinds and occurrences of energy

#### einsteinian77

General Relativity still seems to me an incomplete theory of gravitation.I think that there is something fundamentally missing between the curvature of space and energy density.

#### marcus

Gold Member
Dearly Missed
Originally posted by einsteinian77
General Relativity still seems to me an incomplete theory of gravitation.I think that there is something fundamentally missing between the curvature of space and energy density.
Good, you are pointing to where there is a missing piece to the puzzle, I think. Actually I am thankfull that nature has these mysteries---questions for which no one currently has an answer.

I visualize the missing piece as the force which connects curvature to the energy density causing it----as a kind of universal built in proportion. Why this particular force? Where does it come from? How does it get the job done? A sense of total (but unembarrassed) ignorance. Part of one's job is simply to wonder.

There is a certain force which in metric is 12E43 newtons or roughly 10^40 tons force and it always turns out that

this 12E43 newtons multiplied by the curvature equals the energy density-----and as far as I know no one has a clue why.

cheers, einsteinian,

marcus

#### jeff

RuroumiKenshin,

I think maybe you want to know about how current physics characterizes the actual mechanism underlying gravitational interactions.

Let's begin by representing the connection between spacetime curvature and energy density in general relativity schematically by the relation

(spacetime curvature) = G x (mass-energy density)

where G is the gravitational constant which thus characterizes how much spacetime curvature would be created in the presence of some given mass-energy density. We can understand why mass-energy density, rather than just mass-energy, appears in the above relation by noting the basic inverse square law behaviour (as marcus pointed out, curvature has units of inverse distance squared) of gravitational force it implies, and then observing that if a planet's density were increased by gradually shrinking it, it's inhabitants would feel themselves growing heavier as they approached the planet's centre of mass.

Can we take this further to describe in some way how gravity operates in the sense that I think you meant? No, not directly, because quantum theory is needed to understand the current picture of fundamental interactions. But the main idea can be understood by observing that two people on roller skates throwing a ball back and forth will roll away from each other (as a result of momentum conservation). Somewhat similarly, electrons are mutually repelled as a result of exchanging photons, and likewise, gravity is the result of graviton exchange.

However, the analogy doesn't work as well in this latter case because gravity is attractive, the explanation of which is unfortunately not intuitive because of it's quantum theoretic origin. Briefly, elementary particles are classified in terms of spin, mass and charge, and only massless even-spin particles can mediate attractive forces between like charged bodies: suffice it to say that gravitons are spin-2 and, like photons (which are spin-1, consistent with electromagnetic repulsion between like charged bodies), are massless.

The reason that gravitational and electromagnetic fields - whose quanta we've learned are the graviton and photon respectively - grow stronger as their sources are approached is also quantum theoretic. Again, briefly, because of the time-energy uncertainty principle, the distance from a source that field quanta can travel decreases with their energy. So, for example, the strength of the gravitational field grows stronger as a gravitating body - like a planet say - is approached because gravitons of progressively higher energies are encountered (analogous statements hold for the electromagnetic field).

So what's the connection between the classical notion of spacetime curvature, and the quantum view of the gravitational field as a continuum of gravitons? The answer is that because gravitons - unlike photons - interact with each other, they assemble themselves in a way that's in fact governed at lower energies by general relativity, so spacetime curvature is merely a large-scale structural quality of the resulting gravitational matrix.

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