# Where does all this spacetime curvature come from?

#### Atran

Hi,

From what I know, science is the study of the observable world, its theories are supported by evidence.

Now GR is a theory, and it informs that mass curves the 'fabric' of space and time. The thing I don't understand is that there is no evidence of mass curving spacetime, then how is GR a theory? If there is evidence, then what is spacetime, really, since it's something which has the potential to be curved?

From what I know, in GR gravity is not a force, it's a curvature of spacetime. If so, force is needed to curve the spacetime, but where is that force in GR?

Thanks...

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#### Nabeshin

Hi,

From what I know, science is the study of the observable world, its theories are supported by evidence.

Now GR is a theory, and it informs that mass curves the 'fabric' of space and time. The thing I don't understand is that there is no evidence of mass curving spacetime, then how is GR a theory? If there is evidence, then what is spacetime, really, since it's something which has the potential to be curved?
It's like saying you have a theory that the Earth is actually a sphere. Imagine you cannot directly observe this by leaving the earth, and ask what evidence is there for a spherical rather than flat geometry? Surely you can come up with many, but none of them come from the surface itself, but rather its consequences on observable phenomenon. GR is the same. We see einstein's crosses, precession of perihelions, and light being curved all in perfect accord with what we expect if spacetime is curved by mass. The evidence is no less strong.

From what I know, in GR gravity is not a force, it's a curvature of spacetime. If so, force is needed to curve the spacetime, but where is that force in GR?

Thanks...
Why do you assume you need a force to curve spacetime? Simply because a force is required to curve normal objects? Do not take the "rubber sheet" analogy too far! A force is not needed, the presence of mass simply distorts spacetime by the mere fact that it exists.

#### Dale

Mentor
The thing I don't understand is that there is no evidence of mass curving spacetime, then how is GR a theory?
I am surprised at your ignorance on the subject. There is quite a bit of evidence on the subject, some of it is quite famous such as the orbit of Mercury, gravitational lensing, and gravitational time dilation (along with a lot of less-famous evidence).

#### starthaus

I am surprised at your ignorance on the subject. There is quite a bit of evidence on the subject, some of it is quite famous such as the orbit of Mercury, gravitational lensing, and gravitational time dilation (along with a lot of less-famous evidence).
Shapiro delay is one of the "orphans". But the most obvious "orphan" is GPS functionality :-)

#### bcrowell

Staff Emeritus
Gold Member
The thing I don't understand is that there is no evidence of mass curving spacetime, then how is GR a theory?
There is evidence of mass curving spacetime. Of course, it depends somewhat on what you'd consider to be conclusive evidence. It's possible to express GR in a non-geometrical form. In any case, GR is certainly a scientific theory, because it makes a variety of predictions that differ from those of Newtonian gravity, and those predictions have been extensively tested against observations and found to be correct.

#### Atran

I am surprised at your ignorance on the subject. There is quite a bit of evidence on the subject, some of it is quite famous such as the orbit of Mercury, gravitational lensing, and gravitational time dilation (along with a lot of less-famous evidence).
I'm in first year of high school (grade 10). My physics book is very classical.
I didn't mean there are no evidence for GR, I meant why to postulate a curved spacetime.
I'm not against SR stuff, I questioned the curvature.

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#### Atran

...GR is the same. We see einstein's crosses, precession of perihelions, and light being curved all in perfect accord with what we expect if spacetime is curved by mass...
I mean, is spacetime really curved? or an analogy for the consequences?
Why do you assume you need a force to curve spacetime? Simply because a force is required to curve normal objects? Do not take the "rubber sheet" analogy too far! A force is not needed, the presence of mass simply distorts spacetime by the mere fact that it exists.
This still vague for me. Now in the classical sense, mass is the resistance to change object's state. What is mass in GR?

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#### Atran

It's possible to express GR in a non-geometrical form.
That would be better for me.
...light being curved all in perfect accord with what we expect...
Is that because of photon's momentum and the exerted force by it? I'm not sure...

#### bcrowell

Staff Emeritus
Gold Member
I mean, is spacetime really curved? or an analogy for the consequences?
It depends on what you mean by "really." For example, would you accept the following as evidence? You make a triangle out of three laser beams, and the sum of the interior angles is not equal to 180 degrees. Real experiments very similar to this, although not quite as conceptually simple, have been done. If you want to, you can insist that space isn't "really" curved, and that the beams are curving under the influence og a force or something. But IMO insisting that the beams aren't "really" geometrical lines is unreasonable, since there is nothing that makes a *better* standard of a straight line than a ray of light.

I hope you aren't too taken aback by reactions like DaleSpam's. People here generally don't bite the newbies. It's just that we get a lot of kooks here who think they've proved Einstein is wrong, and people get impatient with them; I think your original post may have given people that impression, when in fact you were just asking an honest question.

#### bcrowell

Staff Emeritus
Gold Member
If so, force is needed to curve the spacetime, but where is that force in GR?
There is no need to posit a force that curves spacetime. Force is a concept from Newtonian physics in which one object with mass interacts with another object with mass. Spacetime isn't a material object, so we shouldn't expect a physical force to act *on* spacetime.

#### Nabeshin

This still vague for me. Now in the classical sense, mass is the resistance to change object's state. What is mass in GR?
Like bcrowell says, you're trying to apply Newtonian reasoning to something decidedly non-Newtonian!

Mass, in GR, is still inertia. Or, a property that determines how much spacetime will curve. The two are the same (note: the equivalence principle). You can still apply forces to things in GR, it's just that gravity is not one of them.

For the photon curving, I would definitely advise you to drop the Newtonian picture of the situation alltogether. Some people like to do a derivation in newtonian mechanics of this (it gives the wrong result, but only by a factor of 2), but I think it's more destructive than instructive. Simply put, in a curved spacetime anything follows the shortest line between two points (known as a geodesic). Light is no exception, and when the spacetime isn't flat, light does not move in a straight line.

#### atyy

Now in the classical sense, mass is the resistance to change object's state. What is mass in GR?
In the Newtonian sense, there are two sorts of masses.
There is inertial mass which is the resistance to change in an object's velocity.
But there is also gravitational mass which produces a gravitational field.

In Newtonian gravity, the gravitational mass is one number at every point in space (the number is zero where there is vacuum). In general relativity, the gravitational mass is 10 numbers at every point in spacetime.

In Newtonian gravity, the gravitational field is a number at every point in space. In general relativity the gravitational field is 10 numbers at every point in spacetime, and these 10 numbers can be interpreted as spacetime curvature by a mathematical analogy.

#### Atran

It depends on what you mean by "really."
I mean real, like the screen you're looking at or the chair you're sitting on.
Spacetime isn't a material object
Is it energy or a concept?
Like bcrowell says, you're trying to apply Newtonian reasoning to something decidedly non-Newtonian!
I haven't studied more than Newtonian physics yet.
The two are the same (note: the equivalence principle).
Yea, now I know what the principle means, 'cause I've seen it earlier.
I would definitely advise you to drop the Newtonian picture of the situation alltogether.
Ok, but I don't know yet more than the classics, I need time.
But there is also gravitational mass which produces a gravitational field.
Ok, thnx.

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#### Atran

If gravity is not force and is explained by geometry, then:
How can gravity be written in algebra? What is its unit?
- - - - -
Math can be used for calculating geodesics, but is there a "easy" formula for knowing the deepness/height of an object's curve?

Thanks for all replies.

#### atyy

How can gravity be written in algebra? What is its unit?
Let c be the speed of light.

The gravitational field in Newtonian physics is the gravitational potential U, which has units of (speed of light)2, ie. [ U ]=[c2]

The gravitational field in general relativity is the metric tensor g. If coordinate distances have units of metre and coordinate times have units of seconds, then the metric tensor has no units.

[ g ]=[ U ]/[c2]

But I think we can do it the other way round and have coordinate distances and time have no units, and give units to the metric tensor - after all, isn't that supposed to be the thing that gives us length and time? I think it's usually not done that way, because even though length and time should have the same units, we usually use the metre as the unit of length and the second as the unit of time.

http://arxiv.org/abs/astro-ph/0303376

#### Dale

Mentor
I'm in first year of high school (grade 10). My physics book is very classical.
I didn't mean there are no evidence for GR,
OK, understood. You may want to proof-read your posts more carefully in the future. I hope you can understand how "there is no evidence of mass curving spacetime, then how is GR a theory" sounds exactly like you are asserting that there is no evidence for GR.

I meant why to postulate a curved spacetime.
I'm not against SR stuff, I questioned the curvature.
In SR an inertially moving object is represented geometrically by a straight line (geodesic) in spacetime and determined experimentally by an ideal accelerometer that reads 0. Two inertial objects at rest wrt each other are represented by parallel lines. In extending these simple concepts to GR you find that gravity can cause two straight lines (accelerometer reads 0) to be parallel at one point (at rest wrt each other) and yet intersect at another point. Two straight lines which are parallel cannot intersect in a flat spacetime, so spacetime must be curved in gravitation.

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