<p>Gravity is, in the model as described in General Relativity (GR) is caused by Stress-energy.  The extract isn't about the cause of gravity.  Stress-energy is the distribution of energy (including mass) and stress in space-time and is represented as a tensor (a 4x4 matrix in this case).</p>
<p>The extract says you can get a geometric interpretation of the model in GR as a curvature of space-time. This is the usual way to interpret GR.</p>
<p>You can get a geometric interpretation of the model of Newtonian Gravity as a curvature of time in flat space.</p>
<p>Normally this is not how Newtonian gravity is presented. Normally one interprets the equations of Newtonian gravity as being a force that acts instantly between any two bodies with mass.  But the &quot;curvature of time&quot; description gives the same maths. It is a matter of didactics which interpretation is taught.</p>
<p>Gravitational time dilation is a phenomenon that can be deduced from the principle of equivalence. If you include equivalence in your model of Newtonian mechanics then you must get time dilation. It is a property of gravity, not a cause of gravity.</p>

CC BY-SA 4.0
2024-12-17T00:39:22.477Z
Curvature is not caused by stress-energy. See the Schwarzschild and Kerr metrics which describe black holes and whose corresponding stress-energy-momentum tensors are zero everywhere, along with the various other curved spacetimes whose SEM tensors are also vanishing. (Much more minor note: I would stress against describing a tensor as simply a 4x4 matrix. You can represent all the components in one, but they are not the same.)
controlgroup
CC BY-SA 4.0
2024-12-17T01:00:40.573Z
@controlgroup "The [Einstein field equations](https://en.wikipedia.org/wiki/Einstein_field_equations) determine the metric tensor of spacetime for a given arrangement of stress–energy–momentum in the spacetime. [...] The expression on the left represents the curvature of spacetime as determined by the metric; the expression on the right represents the stress–energy–momentum content of spacetime".
PM 2Ring
CC BY-SA 4.0
2024-12-17T01:03:03.613Z
@PM2Ring Where did you get that? It's necessarily the reverse, given that there exist multiple metrics with the same SEM tensor (i.e. Schwarzschild vacuum and Minkowski vacuum and Kerr vacuum). If it were as you say, it would be impossible to differentiate on the basis of the SEM tensor alone between flat spacetime and curved spacetime.
controlgroup
CC BY-SA 4.0
2024-12-17T01:09:10.230Z
(I see where you found that on the wiki article. I will correct that, along with another couple things, soon.)
controlgroup
CC BY-SA 4.0
2024-12-17T04:55:28.670Z
@James K Yes I agree, and I thought I understood gravity, until this (crazy?) claim started popping up all over the place, and not just in Youtube, but in "Ask a Mathematician / Ask a Physicist" and even Brian Greene's 2011 book "The Hidden Reality"?!
Blankety Blank
CC BY-SA 4.0
2024-12-17T23:14:55.797Z
@controlgroup I'm going to magic away black holes by saying something like "non-singular solutions".  I do recall a theorem along these lines, that the only vacuum metric that doesn't have a singularity is the Minoski metric, and that this generalises to other SEM tensors. Astrophysically, black holes are considered to be limits produced by collapse, with a definite time of collapse, not eternal.
James K
CC BY-SA 4.0
2024-12-17T23:41:49.627Z
You are then forgetting various other vacua, including the Oszváth–Schücking (describes a gravitational wave), Khan-Penrose (colliding plane waves), Taub-NUT (gravitating object), and Kasner (cosmological vacuum model), among many others. I know of no such theorem, though I would be very interested to see a reference to it; I find it hard to believe given that any Ricci-flat manifold is necessarily a vacuum solution to the EFEs, and that there exist plenty of non-singular Ricci-flat manifolds.
controlgroup
CC BY-SA 4.0
2024-12-24T14:01:13.457Z
@James K So U are saying that since Newton's space is flat, the only curvature left is time?
Blankety Blank
CC BY-SA 4.0
2024-12-15T16:59:52.633Z
2024-12-15T16:59:52.633Z
James K
<p>Relativity (GR/SR) predicts many things, including both relativistic and kinetic time dilation and gravity. You can derive all of those effects solely from GR. That doesn't mean that time dilation <em>causes</em> gravity. Gravity and kinematic/gravitational time dilation are both caused by the geometry of spacetime, but that doesn't draw a causal arrow between the two.</p>

CC BY-SA 4.0
2024-12-17T04:39:03.263Z
Yes I agree, and I thought I understood gravity, until this (crazy?) claim started popping up all over the place, and not just in Youtube, but in "Ask a Mathematician / Ask a Physicist" and even Brian Greene's 2011 book "The Hidden Reality"?!
Blankety Blank
CC BY-SA 4.0
2024-12-17T21:52:43.427Z
All things considered, you shouldn't get your physics info from YouTube.
controlgroup
CC BY-SA 4.0
2024-12-18T04:39:25.360Z
Oh, here we go again. The lecture. I knew you were gonna say that! Soon as one mentions Youtube, you guys get on your blinkered high horse. Maybe if you guys took the time to explain things like this in plain English properly, lay/people wouldn't have to. I am still not 100% sure how they can make such a claim! Even though I sort of understand JK's answer.
Blankety Blank
CC BY-SA 4.0
2024-12-18T13:27:57.297Z
They *can’t* make such a claim because it’s false (but pop-sci authors have less of a problem saying wrong things than actual physicists). GTD and gravity are predicted by the same framework but neither causes the other. This is evidence for YouTube and other pop-sci media being a bad source of information. That’s all I’m saying.
controlgroup
CC BY-SA 4.0
2024-12-18T15:38:23.927Z
I wish that was so, because I thought I understood GR/gravity, and I thought it was entirely due to space curvature! You just called Brain Greene a pop-sci physicist, because I think he made just such a claim in his 2011 (pop-physics?) book "The Hidden Reality", in a footnote on P14, I think. I can try to get the exact quote, if you like, because this is important, to me. And the same with Matt O'Dowd, who is the presenter of the Youtube PBS Space Time channel and an astrophysicist! And didn't this Wikipedia article make just such a claim?!
Blankety Blank
CC BY-SA 4.0
2024-12-18T15:39:48.153Z
If he claimed that, then he was misunderstanding general relativity. It’s just a fact that GTD and gravity don’t directly cause one another - they are *effects* of a bigger theory.
controlgroup
CC BY-SA 4.0
2024-12-18T15:49:31.383Z
I wish it was so but I have heard it so often now that I have come to suspect that there must be some truth to it. And is not the deflection of the grazing starlight by the Sun half due to time curvature and half due to space curvature?
Blankety Blank
CC BY-SA 4.0
2024-12-18T15:53:24.103Z
Deflection of light from the sun is partially due to both, yes - calculate the geodesic equation for a light moving near the Sun and see for yourself. But there is no truth to the idea of GTD *causing* gravity. They are certainly related but there is no causal link between them.
controlgroup
CC BY-SA 4.0
2024-12-18T16:57:13.913Z
But isn't GTD just the measure of the gravitational time curvature?!
Blankety Blank
CC BY-SA 4.0
2024-12-18T17:00:52.843Z
GTD is an *effect* of what I guess you could call time curvature. Gravity is also an effect of that. But it’s very important not to then draw the arrow from GTD to gravity.
controlgroup
CC BY-SA 4.0
2024-12-18T18:47:45.710Z
No, BG did not say GTD but GTC. I know that g/ravity and GTD do not decrease in the same way, with radius/distance, and I don't know how to calculate GTC.
Blankety Blank
CC BY-SA 4.0
2024-12-18T19:12:07.370Z
OK, if you like, but I am/have actually finished, for now, and I don't know how to do it/that.
Blankety Blank
CC BY-SA 4.0
2024-12-19T07:17:55.333Z
@BlanketyBlank The slogan "time dilation causes gravity" is a simplification of the following, from https://physics.stackexchange.com/a/837585/123208 "In the weak field approximation, the overwhelming majority of the gravitation we experience is due to the $g_{00}(x,y,z)$ component of the spacetime metric. This controls time dilation as a function of location, rather than spatial curvature".
PM 2Ring
CC BY-SA 4.0
2024-12-17T00:39:30.067Z
2024-12-17T00:39:30.067Z
controlgroup
<p>As this extract from Wikipedia's &quot;Curved spacetime&quot; article seems to be saying:</p>
<blockquote>
<p>Clocks in a gravitational field do not all run at the same rate. Experiments such as the Pound–Rebka experiment have firmly established curvature of the time component of spacetime. The Pound–Rebka experiment says nothing about curvature of the space component of spacetime. But the theoretical arguments predicting gravitational time dilation do not depend on the details of general relativity at all. Any theory of gravity will predict gravitational time dilation if it respects the principle of equivalence.[6]: 16  This includes Newtonian gravitation. A standard demonstration in general relativity is to show how, in the &quot;Newtonian limit&quot; (i.e. the particles are moving slowly, the gravitational field is weak, and the field is static), curvature of time alone is sufficient to derive Newton's law of gravity.[7]: 101–106</p>
</blockquote>
<blockquote>
<p>Newtonian gravitation is a theory of curved time. General relativity is a theory of curved time and curved space. Given G as the gravitational constant, M as the mass of a Newtonian star, and orbiting bodies of insignificant mass at distance r from the star, the spacetime interval for Newtonian gravitation is one for which only the time coefficient is variable:[6]: 229–232</p>
</blockquote>
<blockquote>
<p><span class="math-container">$ Δ s ^ 2 = ( 1 − 2 G M / c ^ 2 r ) ( c Δ t ) ^ 2 − ( Δ x ) ^ 2 − ( Δ y ) ^ 2 − ( Δ z ) ^ 2 $</span></p>
</blockquote>
<blockquote>
<p>Curvature of space</p>
</blockquote>
<blockquote>
<p>The <span class="math-container">$ ( 1 − 2 G M / ( c ^ 2 r ) ) $</span> coefficient in front of <span class="math-container">$ ( c Δ t ) ^ 2  $</span>  describes the curvature of time in Newtonian gravitation, and this curvature completely accounts for all Newtonian gravitational effects. As expected, this correction factor is directly proportional to <span class="math-container">$ G $</span> and <span class="math-container">$ M $</span>, and because of the <span class="math-container">$ r $</span> in the denominator, the correction factor increases as one approaches the gravitating body, meaning that time is curved.</p>
</blockquote>
<blockquote>
<p>But general relativity is a theory of curved space and curved time, so if there are terms modifying the spatial components of the spacetime interval presented above, should not their effects be seen on, say, planetary and satellite orbits due to curvature correction factors applied to the spatial terms?</p>
</blockquote>
<blockquote>
<p>The answer is that they are seen, but the effects are tiny. The reason is that planetary velocities are extremely small compared to the speed of light, so that for planets and satellites of the solar system, the <span class="math-container">$ ( c Δ t ) ^ 2 $</span> term dwarfs the spatial terms.[6]: 234–238</p>
</blockquote>
<blockquote>
<p>Despite the minuteness of the spatial terms, the first indications that something was wrong with Newtonian gravitation were discovered over a century-and-a-half ago. In 1859, Urbain Le Verrier, in an analysis of available timed observations of transits of Mercury over the Sun's disk from 1697 to 1848, reported that known physics could not explain the orbit of Mercury, unless there possibly existed a planet or asteroid belt within the orbit of Mercury. The perihelion of Mercury's orbit exhibited an excess rate of precession over that which could be explained by the tugs of the other planets.[8] The ability to detect and accurately measure the minute value of this anomalous precession (only 43 arc seconds per tropical century) is testimony to the sophistication of 19th century astrometry.</p>
</blockquote>
<p>The cause of gravity in the model of gravity called General Relativity is the stress-energy distribution, expressed as a tensor, and in which energy includes mass.  But, is it true that in Newtonian gravity, i.e. weak field gravity that we experience in the solar system, the forces felt arise completely from the stress tensor curving time? And is this time distortion the same as what we call time dilation?</p>

CC BY-SA 4.0
2024-12-15T13:34:34.923Z
Some formatting help: https://astronomy.stackexchange.com/help/formatting Math notation: https://physics.stackexchange.com/help/notation
PM 2Ring
CC BY-SA 4.0
2024-12-15T13:42:02.150Z
The question in the title is a matter for the philosophers, not astronomers.  The "cause" of gravity in the model of gravity called "Relativity" is the stress-energy distribution, expressed as a tensor, and in which "energy" includes "mass".  The theory doesn't provide a reason why stress-energy should curve spacetime, it just says "if it does, then these are the predictions" and those predictions match observations very very well.
James K
CC BY-SA 4.0
2024-12-15T14:55:27.700Z
What would philosophers know, about it?! And don't you have a PhD? I have changed the title. The joining page said this was also a space for astrophysicists! I didn't ask why?how matter warps space/time.
Blankety Blank
<solar-system><gravity><general-relativity>
Is gravity really caused by gravitational time dilation?
Blankety Blank
# Is gravity really caused by gravitational time dilation?

(Asked by: username_0 on 2024-12-15)

As this extract from Wikipedia's "Curved spacetime" article seems to be saying:

> Clocks in a gravitational field do not all run at the same rate. Experiments such as the Pound–Rebka experiment have firmly established curvature of the time component of spacetime. The Pound–Rebka experiment says nothing about curvature of the space component of spacetime. But the theoretical arguments predicting gravitational time dilation do not depend on the details of general relativity at all. Any theory of gravity will predict gravitational time dilation if it respects the principle of equivalence.[6]: 16  This includes Newtonian gravitation. A standard demonstration in general relativity is to show how, in the "Newtonian limit" (i.e. the particles are moving slowly, the gravitational field is weak, and the field is static), curvature of time alone is sufficient to derive Newton's law of gravity.[7]: 101–106

> Newtonian gravitation is a theory of curved time. General relativity is a theory of curved time and curved space. Given G as the gravitational constant, M as the mass of a Newtonian star, and orbiting bodies of insignificant mass at distance r from the star, the spacetime interval for Newtonian gravitation is one for which only the time coefficient is variable:[6]: 229–232

> $ Δ s ^ 2 = ( 1 − 2 G M / c ^ 2 r ) ( c Δ t ) ^ 2 − ( Δ x ) ^ 2 − ( Δ y ) ^ 2 − ( Δ z ) ^ 2 $

> Curvature of space

> The $ ( 1 − 2 G M / ( c ^ 2 r ) ) $ coefficient in front of $ ( c Δ t ) ^ 2 $ describes the curvature of time in Newtonian gravitation, and this curvature completely accounts for all Newtonian gravitational effects. As expected, this correction factor is directly proportional to $ G $ and $ M $, and because of the $ r $ in the denominator, the correction factor increases as one approaches the gravitating body, meaning that time is curved.

> But general relativity is a theory of curved space and curved time, so if there are terms modifying the spatial components of the spacetime interval presented above, should not their effects be seen on, say, planetary and satellite orbits due to curvature correction factors applied to the spatial terms?

> The answer is that they are seen, but the effects are tiny. The reason is that planetary velocities are extremely small compared to the speed of light, so that for planets and satellites of the solar system, the $ ( c Δ t ) ^ 2 $ term dwarfs the spatial terms.[6]: 234–238

> Despite the minuteness of the spatial terms, the first indications that something was wrong with Newtonian gravitation were discovered over a century-and-a-half ago. In 1859, Urbain Le Verrier, in an analysis of available timed observations of transits of Mercury over the Sun's disk from 1697 to 1848, reported that known physics could not explain the orbit of Mercury, unless there possibly existed a planet or asteroid belt within the orbit of Mercury. The perihelion of Mercury's orbit exhibited an excess rate of precession over that which could be explained by the tugs of the other planets.[8] The ability to detect and accurately measure the minute value of this anomalous precession (only 43 arc seconds per tropical century) is testimony to the sophistication of 19th century astrometry.

The cause of gravity in the model of gravity called General Relativity is the stress-energy distribution, expressed as a tensor, and in which energy includes mass. But, is it true that in Newtonian gravity, i.e. weak field gravity that we experience in the solar system, the forces felt arise completely from the stress tensor curving time? And is this time distortion the same as what we call time dilation?

**Tags:** solar-system, gravity, general-relativity
> **Comments:**
> **username_1**: Some formatting help: https://astronomy.stackexchange.com/help/formatting Math notation: https://physics.stackexchange.com/help/notation  
> **username_2**: The question in the title is a matter for the philosophers, not astronomers.  The "cause" of gravity in the model of gravity called "Relativity" is the stress-energy distribution, expressed as a tensor, and in which "energy" includes "mass".  The theory doesn't provide a reason why stress-energy should curve spacetime, it just says "if it does, then these are the predictions" and those predictions match observations very very well.  
> **username_0**: What would philosophers know, about it?! And don't you have a PhD? I have changed the title. The joining page said this was also a space for astrophysicists! I didn't ask why?how matter warps space/time.  

---

## 2 answers

### Answer by username_2 on 2024-12-15. Score: 3 | Accepted answer

Gravity is, in the model as described in General Relativity (GR) is caused by Stress-energy. The extract isn't about the cause of gravity. Stress-energy is the distribution of energy (including mass) and stress in space-time and is represented as a tensor (a 4x4 matrix in this case).

The extract says you can get a geometric interpretation of the model in GR as a curvature of space-time. This is the usual way to interpret GR.

You can get a geometric interpretation of the model of Newtonian Gravity as a curvature of time in flat space.

Normally this is not how Newtonian gravity is presented. Normally one interprets the equations of Newtonian gravity as being a force that acts instantly between any two bodies with mass. But the "curvature of time" description gives the same maths. It is a matter of didactics which interpretation is taught.

Gravitational time dilation is a phenomenon that can be deduced from the principle of equivalence. If you include equivalence in your model of Newtonian mechanics then you must get time dilation. It is a property of gravity, not a cause of gravity.

> **Comments:**
> **username_3**: Curvature is not caused by stress-energy. See the Schwarzschild and Kerr metrics which describe black holes and whose corresponding stress-energy-momentum tensors are zero everywhere, along with the various other curved spacetimes whose SEM tensors are also vanishing. (Much more minor note: I would stress against describing a tensor as simply a 4x4 matrix. You can represent all the components in one, but they are not the same.)  
> **username_1**: @controlgroup "The [Einstein field equations](https://en.wikipedia.org/wiki/Einstein_field_equations) determine the metric tensor of spacetime for a given arrangement of stress–energy–momentum in the spacetime. [...] The expression on the left represents the curvature of spacetime as determined by the metric; the expression on the right represents the stress–energy–momentum content of spacetime".  
> **username_3**: @PM2Ring Where did you get that? It's necessarily the reverse, given that there exist multiple metrics with the same SEM tensor (i.e. Schwarzschild vacuum and Minkowski vacuum and Kerr vacuum). If it were as you say, it would be impossible to differentiate on the basis of the SEM tensor alone between flat spacetime and curved spacetime.  
> **username_3**: (I see where you found that on the wiki article. I will correct that, along with another couple things, soon.)  
> **username_0**: @James K Yes I agree, and I thought I understood gravity, until this (crazy?) claim started popping up all over the place, and not just in Youtube, but in "Ask a Mathematician / Ask a Physicist" and even Brian Greene's 2011 book "The Hidden Reality"?!  
> **username_2**: @controlgroup I'm going to magic away black holes by saying something like "non-singular solutions".  I do recall a theorem along these lines, that the only vacuum metric that doesn't have a singularity is the Minoski metric, and that this generalises to other SEM tensors. Astrophysically, black holes are considered to be limits produced by collapse, with a definite time of collapse, not eternal.  
> **username_3**: You are then forgetting various other vacua, including the Oszváth–Schücking (describes a gravitational wave), Khan-Penrose (colliding plane waves), Taub-NUT (gravitating object), and Kasner (cosmological vacuum model), among many others. I know of no such theorem, though I would be very interested to see a reference to it; I find it hard to believe given that any Ricci-flat manifold is necessarily a vacuum solution to the EFEs, and that there exist plenty of non-singular Ricci-flat manifolds.  
> **username_0**: @James K So U are saying that since Newton's space is flat, the only curvature left is time?  

---

### Answer by username_3 on 2024-12-17. Score: 3

Relativity (GR/SR) predicts many things, including both relativistic and kinetic time dilation and gravity. You can derive all of those effects solely from GR. That doesn't mean that time dilation *causes* gravity. Gravity and kinematic/gravitational time dilation are both caused by the geometry of spacetime, but that doesn't draw a causal arrow between the two.

> **Comments:**
> **username_0**: Yes I agree, and I thought I understood gravity, until this (crazy?) claim started popping up all over the place, and not just in Youtube, but in "Ask a Mathematician / Ask a Physicist" and even Brian Greene's 2011 book "The Hidden Reality"?!  
> **username_3**: All things considered, you shouldn't get your physics info from YouTube.  
> **username_0**: Oh, here we go again. The lecture. I knew you were gonna say that! Soon as one mentions Youtube, you guys get on your blinkered high horse. Maybe if you guys took the time to explain things like this in plain English properly, lay/people wouldn't have to. I am still not 100% sure how they can make such a claim! Even though I sort of understand JK's answer.  
> **username_3**: They *can’t* make such a claim because it’s false (but pop-sci authors have less of a problem saying wrong things than actual physicists). GTD and gravity are predicted by the same framework but neither causes the other. This is evidence for YouTube and other pop-sci media being a bad source of information. That’s all I’m saying.  
> **username_0**: I wish that was so, because I thought I understood GR/gravity, and I thought it was entirely due to space curvature! You just called Brain Greene a pop-sci physicist, because I think he made just such a claim in his 2011 (pop-physics?) book "The Hidden Reality", in a footnote on P14, I think. I can try to get the exact quote, if you like, because this is important, to me. And the same with Matt O'Dowd, who is the presenter of the Youtube PBS Space Time channel and an astrophysicist! And didn't this Wikipedia article make just such a claim?!  
> **username_3**: If he claimed that, then he was misunderstanding general relativity. It’s just a fact that GTD and gravity don’t directly cause one another - they are *effects* of a bigger theory.  
> **username_0**: I wish it was so but I have heard it so often now that I have come to suspect that there must be some truth to it. And is not the deflection of the grazing starlight by the Sun half due to time curvature and half due to space curvature?  
> **username_3**: Deflection of light from the sun is partially due to both, yes - calculate the geodesic equation for a light moving near the Sun and see for yourself. But there is no truth to the idea of GTD *causing* gravity. They are certainly related but there is no causal link between them.  
> **username_0**: But isn't GTD just the measure of the gravitational time curvature?!  
> **username_3**: GTD is an *effect* of what I guess you could call time curvature. Gravity is also an effect of that. But it’s very important not to then draw the arrow from GTD to gravity.  
> **username_0**: No, BG did not say GTD but GTC. I know that g/ravity and GTD do not decrease in the same way, with radius/distance, and I don't know how to calculate GTC.  
> **username_0**: OK, if you like, but I am/have actually finished, for now, and I don't know how to do it/that.  
> **username_1**: @BlanketyBlank The slogan "time dilation causes gravity" is a simplification of the following, from https://physics.stackexchange.com/a/837585/123208 "In the weak field approximation, the overwhelming majority of the gravitation we experience is due to the $g_{00}(x,y,z)$ component of the spacetime metric. This controls time dilation as a function of location, rather than spatial curvature".  

---

