<p>I think "Twisted" is a bad choice of description in your question. Suppose we used "curved" instead. Now you say you read that</p>

<blockquote>
  <p>space is the totality of geometric relations (distance, angle, etc) between things.</p>
</blockquote>

<p>and it makes sense to say that collection of geometric relation is curved or flat. Consider three points in space and connected them by the "straight" (ie as short as possible) lines to make a triangle. Now measure the angles between those lines and add them up. If you always get 180 degrees then your space is flat -- it is "the same shape as" the standard space with real coordinates <span class="math-container">$(x,y,z)$</span> and distance given be <span class="math-container">$\sqrt{x^2 + y^2 + z^2}$</span>.  But that is not the only possibility. You might find that the angles always add up to <em>more than</em> 180 degrees, with the "excess" angle proportional to the area of the triangle. This is called a positively curved space, and can be modelled by the surface of a four dimensional ball with lines being "great circles". Or it might be <em>less than</em> 180 degrees (again with the "missing" angle proportional to the area) which is called negatively curved. </p>

<p>This all gets a little more complicated when time is also involved, but essentially Einstein's theory describes how the curvature of space-time (those geometrical relations again) have to match up with the amount of mass and energy in that space-time and how that mass and energy moves. </p>

CC BY-SA 4.0
2019-02-23T18:02:53.047Z
2019-02-23T18:02:53.047Z
Steve Linton
<p>Einstein thought of space as a thing. See his 1920 <a href="https://einsteinpapers.press.princeton.edu/vol7-trans/192?highlightText=%22neither%20homogeneous%22" rel="nofollow noreferrer">Leyden Address</a> where he said this:</p>

<blockquote>
  <p><em>“According to this theory the metrical qualities of the continuum of space-time differ in the environment of different points of
  space-time, and are partly conditioned by the matter existing outside
  of the territory under consideration. This space-time variability of
  the reciprocal relations of the standards of space and time, or,
  perhaps, the recognition of the fact that 'empty space' in its
  physical relation is neither homogeneous nor isotropic, compelling us
  to describe its state by ten functions (the gravitation potentials
  g<sub>μν</sub>), has, I think, finally disposed of the view that space
  is physically empty”.</em></p>
</blockquote>

<p>He ended by saying <a href="https://einsteinpapers.press.princeton.edu/vol7-trans/197" rel="nofollow noreferrer">this</a>: </p>

<blockquote>
  <p><em>"Recapitulating, we may say that according to the general theory of relativity space is endowed with physical qualities; in this sense,
  therefore, there exists an ether"</em>.</p>
</blockquote>

<p>Also see the Wikipedia <a href="https://en.wikipedia.org/w/index.php?title=Aether_theories&amp;oldid=780870304#General_relativity" rel="nofollow noreferrer">aether theories</a> article and note the quote by Robert B Laughlin: </p>

<blockquote>
  <p><em>"It is ironic that Einstein’s most creative work, the general theory of relativity, should boil down to conceptualizing space as a medium
  when his original premise [in special relativity] was that no such
  medium existed".</em></p>
</blockquote>

<p>Laughlin also said space is more like a piece of window glass than ideal Newtonian emptiness. He finished up saying this: </p>

<blockquote>
  <p><em>"the modern concept of the vacuum of space, confirmed every day by experiment, is a relativistic ether. But we do not call it this
  because it is taboo".</em></p>
</blockquote>

<p>Einstein is supposed to have done away with the aether in 1905 but in the end, he didn’t. He thought of space as a something rather than a nothing. In his 1929 essay on <a href="http://www.rain.org/~karpeles/einsteindis.html" rel="nofollow noreferrer">the history of field theory</a>, he described a field as a state of space. He was talking about gravitational fields and electromagnetic fields, and said this: </p>

<blockquote>
  <p><em>"it can, however, scarcely be imagined that empty space has conditions or states of two essentially different kinds".</em></p>
</blockquote>

<p>The point to appreciate is that according to Einstein a field isn’t something that exists in space, it’s a state of space. So yes, space is a thing.  </p>

CC BY-SA 4.0
2019-02-23T13:13:39.383Z
John, shouldn't be meticulously repeat soace-*time* a crucial point in this kind of discussions?
Alchimista
CC BY-SA 4.0
2019-02-23T16:59:59.457Z
@Alchimista : space isn't the same as spacetime. Space is a real thing, but spacetime is an abstract mathematical model of space "at all times". Hence there's no motion in spacetime. Our world is not like that. So if Aung Satt  had asked if spacetime is a thing, I would have said no.
John Duffield
CC BY-SA 4.0
2019-02-23T17:54:50.287Z
How do not understand your answer anymore then. What is then " According to this theory the metrical qualities of the continuum of space-time differ in the environment of different points of space-time, and are partly conditioned by the matter existing outside of the territory under consideration. This space-time variability of the reciprocal re...... , ,,," ? Note that I am just asking.
Alchimista
CC BY-SA 4.0
2019-02-23T18:38:49.033Z
@Alchimista : I took that to mean Einstein was talking about space and time together, such that you measure time at various points in space with clocks, then model it using spacetime. Then because spacetime is the map and the map is not the territory, he started talking about space, which is the territory.
John Duffield
CC BY-SA 4.0
2019-02-23T18:40:20.607Z
@Alchimista : Imagine you could place a 15 x 15 array of optical clocks throughout a horizontal slice of space around the Earth. Then you plot all the clock rates, such that the lower slower clock rates generate data points lower down in a 3D image, and the higher faster clock rates generate data points higher up in the 3D image. When you join the dots, your plot looks like [this](https://commons.wikimedia.org/wiki/File:Spacetime_curvature.png).
John Duffield
CC BY-SA 4.0
2019-02-23T18:48:33.637Z
Thanks.  The map territory is quite a good analogy except that I can roll a map without affecting the territory. I am not a specialist as you can see. I always took it as geodetic are the straight trajectory in space time. It is quite philosophical at the end. I certainly agree that it depends on what one define as a thing.
Alchimista
CC BY-SA 4.0
2019-02-24T13:48:41.393Z
@Alchimista : re _"I always took it as geodetic are the straight trajectory in space time"_. I'd say that's what's generally taught. But I'd also say that when you read the [Einstein digital papers](https://einsteinpapers.press.princeton.edu/), you get a different understanding.
John Duffield
CC BY-SA 4.0
2019-02-23T12:50:58.707Z
2019-02-23T12:50:58.707Z
John Duffield
<p>Much depends on what you mean by thing.  But first lets think about space, or space-time.</p>

<p>If you have a flat sheet of paper, and you draw a triangle on it, you will find that the angles add up to 180 degrees (I hope you are familiar with this fact). However, if you have curved surface and draw lines that are "straight" in the sense that they are the shortest distances between points, then you will find that the angles don't add up to 180 degrees. This is one of the rules of geometry on a curved surface.</p>

<p>Now if you make a triangle in deep space the 180 degree rule works. But if you make a triangle in a gravitational field you will find that the angles don't add up to 180 degrees. (It is actually nearly impossible to measure this, but observations of gravity are exactly consistent with this).  We say that "spacetime is curved" to mean "Geometry done in a gravitational field doesn't obey the rules for flat geometry, but for curved geometry."</p>

<p>What do people mean by "thing" - If you mean "an object made of some material" then space is not a thing. If you mean "the description of the location and geometric relationships between objects" then space is a thing.</p>

<p>The final insight is that it is not space that is curved, but four-dimensional "spacetime" and the geometric relationships between objects is described by a block of 16 numbers for each point in spacetime, that depend on the distribution and motion of mass, energy and charge. These 16 numbers can describe with incredible accuracy how objects in space will interact gravitationally, as they just follow straight lines in curved spacetime.</p>

CC BY-SA 4.0
2019-02-23T13:15:30.070Z
2019-02-23T13:15:30.070Z
James K
<p>Based on my extent of knowledge relating to astrophysics, I once thought space is a thing, which can be twisted a long side with Time regarding masses of objects(According to relativity theory).</p>

<p>But I found out in this comment session of the following thread (I put the link following to this paragraph), I was pointed out as Space is not a thing, but space is the totality of geometric relations (distance, angle, etc) between things. And my confusion started. </p>

<p><a href="https://astronomy.stackexchange.com/questions/29665/do-interstellar-asteroids-decelerate-and-eventually-stop">Do interstellar asteroids decelerate and eventually stop?</a></p>

<p>How is it possible that the space can be twisted, if the space is not a thing? or is it? </p>

CC BY-SA 4.0
2019-02-23T09:55:41.943Z
I think it depends on the meaning of "thing". I might be wrong but some "physicality" of spacetime is conveyed by gravitational waves as possibility, and even more by their recent detection. But already I am not sure if I could write the same using space instead of spacetime. Looking at the interferometer might be "yes".
Alchimista
CC BY-SA 4.0
2019-02-24T18:28:05.617Z
Space is filled with virtual particle pairs. Can't call that nothing.
Wayfaring Stranger
CC BY-SA 4.0
2019-02-25T20:10:47.080Z
This is a philosophical question, not a scientific one.
Carl Witthoft
<astrophysics><space-time><space><general-relativity>
Is space a thing?
Aung Satt
# Is space a thing?

(Asked by: username_0 on 2019-02-23)

Based on my extent of knowledge relating to astrophysics, I once thought space is a thing, which can be twisted a long side with Time regarding masses of objects(According to relativity theory).

But I found out in this comment session of the following thread (I put the link following to this paragraph), I was pointed out as Space is not a thing, but space is the totality of geometric relations (distance, angle, etc) between things. And my confusion started.

[Do interstellar asteroids decelerate and eventually stop?](https://astronomy.stackexchange.com/questions/29665/do-interstellar-asteroids-decelerate-and-eventually-stop)

How is it possible that the space can be twisted, if the space is not a thing? or is it?

**Tags:** astrophysics, space-time, space, general-relativity
> **Comments:**
> **username_1**: I think it depends on the meaning of "thing". I might be wrong but some "physicality" of spacetime is conveyed by gravitational waves as possibility, and even more by their recent detection. But already I am not sure if I could write the same using space instead of spacetime. Looking at the interferometer might be "yes".  
> **username_2**: Space is filled with virtual particle pairs. Can't call that nothing.  
> **username_3**: This is a philosophical question, not a scientific one.  

---

## 3 answers

### Answer by username_6 on 2019-02-23. Score: 4 | Accepted answer

Much depends on what you mean by thing. But first lets think about space, or space-time.

If you have a flat sheet of paper, and you draw a triangle on it, you will find that the angles add up to 180 degrees (I hope you are familiar with this fact). However, if you have curved surface and draw lines that are "straight" in the sense that they are the shortest distances between points, then you will find that the angles don't add up to 180 degrees. This is one of the rules of geometry on a curved surface.

Now if you make a triangle in deep space the 180 degree rule works. But if you make a triangle in a gravitational field you will find that the angles don't add up to 180 degrees. (It is actually nearly impossible to measure this, but observations of gravity are exactly consistent with this). We say that "spacetime is curved" to mean "Geometry done in a gravitational field doesn't obey the rules for flat geometry, but for curved geometry."

What do people mean by "thing" - If you mean "an object made of some material" then space is not a thing. If you mean "the description of the location and geometric relationships between objects" then space is a thing.

The final insight is that it is not space that is curved, but four-dimensional "spacetime" and the geometric relationships between objects is described by a block of 16 numbers for each point in spacetime, that depend on the distribution and motion of mass, energy and charge. These 16 numbers can describe with incredible accuracy how objects in space will interact gravitationally, as they just follow straight lines in curved spacetime.


---

### Answer by username_4 on 2019-02-23. Score: 3

I think "Twisted" is a bad choice of description in your question. Suppose we used "curved" instead. Now you say you read that

> space is the totality of geometric relations (distance, angle, etc) between things.

and it makes sense to say that collection of geometric relation is curved or flat. Consider three points in space and connected them by the "straight" (ie as short as possible) lines to make a triangle. Now measure the angles between those lines and add them up. If you always get 180 degrees then your space is flat -- it is "the same shape as" the standard space with real coordinates $(x,y,z)$ and distance given be $\sqrt{x^2 + y^2 + z^2}$. But that is not the only possibility. You might find that the angles always add up to *more than* 180 degrees, with the "excess" angle proportional to the area of the triangle. This is called a positively curved space, and can be modelled by the surface of a four dimensional ball with lines being "great circles". Or it might be *less than* 180 degrees (again with the "missing" angle proportional to the area) which is called negatively curved.

This all gets a little more complicated when time is also involved, but essentially Einstein's theory describes how the curvature of space-time (those geometrical relations again) have to match up with the amount of mass and energy in that space-time and how that mass and energy moves.


---

### Answer by username_5 on 2019-02-23. Score: 3

Einstein thought of space as a thing. See his 1920 [Leyden Address](https://einsteinpapers.press.princeton.edu/vol7-trans/192?highlightText=%22neither%20homogeneous%22) where he said this:

> *“According to this theory the metrical qualities of the continuum of space-time differ in the environment of different points of
> space-time, and are partly conditioned by the matter existing outside
> of the territory under consideration. This space-time variability of
> the reciprocal relations of the standards of space and time, or,
> perhaps, the recognition of the fact that 'empty space' in its
> physical relation is neither homogeneous nor isotropic, compelling us
> to describe its state by ten functions (the gravitation potentials
> gμν), has, I think, finally disposed of the view that space
> is physically empty”.*

He ended by saying [this](https://einsteinpapers.press.princeton.edu/vol7-trans/197):

> *"Recapitulating, we may say that according to the general theory of relativity space is endowed with physical qualities; in this sense,
> therefore, there exists an ether"*.

Also see the Wikipedia [aether theories](https://en.wikipedia.org/w/index.php?title=Aether_theories&oldid=780870304#General_relativity) article and note the quote by Robert B Laughlin:

> *"It is ironic that Einstein’s most creative work, the general theory of relativity, should boil down to conceptualizing space as a medium
> when his original premise [in special relativity] was that no such
> medium existed".*

Laughlin also said space is more like a piece of window glass than ideal Newtonian emptiness. He finished up saying this:

> *"the modern concept of the vacuum of space, confirmed every day by experiment, is a relativistic ether. But we do not call it this
> because it is taboo".*

Einstein is supposed to have done away with the aether in 1905 but in the end, he didn’t. He thought of space as a something rather than a nothing. In his 1929 essay on [the history of field theory](http://www.rain.org/~karpeles/einsteindis.html), he described a field as a state of space. He was talking about gravitational fields and electromagnetic fields, and said this:

> *"it can, however, scarcely be imagined that empty space has conditions or states of two essentially different kinds".*

The point to appreciate is that according to Einstein a field isn’t something that exists in space, it’s a state of space. So yes, space is a thing.

> **Comments:**
> **username_1**: John, shouldn't be meticulously repeat soace-*time* a crucial point in this kind of discussions?  
> **username_5**: @Alchimista : space isn't the same as spacetime. Space is a real thing, but spacetime is an abstract mathematical model of space "at all times". Hence there's no motion in spacetime. Our world is not like that. So if Aung Satt  had asked if spacetime is a thing, I would have said no.  
> **username_1**: How do not understand your answer anymore then. What is then " According to this theory the metrical qualities of the continuum of space-time differ in the environment of different points of space-time, and are partly conditioned by the matter existing outside of the territory under consideration. This space-time variability of the reciprocal re...... , ,,," ? Note that I am just asking.  
> **username_5**: @Alchimista : I took that to mean Einstein was talking about space and time together, such that you measure time at various points in space with clocks, then model it using spacetime. Then because spacetime is the map and the map is not the territory, he started talking about space, which is the territory.  
> **username_5**: @Alchimista : Imagine you could place a 15 x 15 array of optical clocks throughout a horizontal slice of space around the Earth. Then you plot all the clock rates, such that the lower slower clock rates generate data points lower down in a 3D image, and the higher faster clock rates generate data points higher up in the 3D image. When you join the dots, your plot looks like [this](https://commons.wikimedia.org/wiki/File:Spacetime_curvature.png).  
> **username_1**: Thanks.  The map territory is quite a good analogy except that I can roll a map without affecting the territory. I am not a specialist as you can see. I always took it as geodetic are the straight trajectory in space time. It is quite philosophical at the end. I certainly agree that it depends on what one define as a thing.  
> **username_5**: @Alchimista : re _"I always took it as geodetic are the straight trajectory in space time"_. I'd say that's what's generally taught. But I'd also say that when you read the [Einstein digital papers](https://einsteinpapers.press.princeton.edu/), you get a different understanding.  

---

