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General relativity is often explained as saying spacetime is curved by gravity, what does this mean? How could we perceive a curve in spacetime when there is no external "straight" reference frame for instance?

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  • $\begingroup$ Dimensions. Think about dimensions. $\endgroup$ – Nico Feb 4 '16 at 10:51
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    $\begingroup$ I think your title and your question are two quite different topics, albeit related. I assume you mean "What (not where) is spacetime made of". The answer to that is somewhat philosophical, but a physical discussion is probably better fit in the physics.SE forum. The answer to "What are gravitational waves and how do they work" is more tangible (although not super-easy to understand), but should also be asked in the physics forum, I think. $\endgroup$ – pela Feb 4 '16 at 11:20
  • $\begingroup$ If an area of space that was devoid of any matter and devoid of any energy can be said to have some residual characteristic, it must in some sense be composed of something. Otherwise it would have no zero point energy or quantum foam. IM undeducated O. $\endgroup$ – Howard Miller Feb 4 '16 at 22:40
  • $\begingroup$ Very hypothetical, but some scientists are actually trying to figure out whether this is true or not: quantamagazine.org/20160119-time-entanglement $\endgroup$ – Florin Andrei Feb 5 '16 at 2:46
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    $\begingroup$ Quantum vacuum and Higgs field $\endgroup$ – 0tyranny 0poverty Jul 6 '17 at 14:16
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Space-time is not "made" of anything, it is merely a medium or coordinate system. Think about the grid lines on a map, they aren't "made" of anything, they're just a representation of the geometry of the Earth. Space-time is a concept envisaged by Einstein when he wrote his theory of Special Relativity that the properties of space and time become intrinsically linked at relativistic speeds. One of the consequences of this is that you cannot go forward in space without going forward in time, this can be visualized in a light cone:

This is by no means a representation of what space-time looks like, only how it behaves in 2 dimensions of space and one of time. Gravitational waves are caused when two massive objects (binary stars) orbit each other, and they cause "ripples" in space-time. Again another 2D visualization is needed: enter image description here This shows how the gravitational potentials of two stars interact in the fabric of space-time as they orbit, causing the radiation of gravitational waves.

Both of these are only visual guides, we will never be able to "see" gravitational waves or space-time itself with our own eyes, that is why we need detectors such as LIGO or VIRGO to infer their existence.

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  • $\begingroup$ So when I say space is nothing real but just an theoretical instrument of analysing than it is ok? $\endgroup$ – Marijn Feb 4 '16 at 13:57
  • $\begingroup$ Space is real, otherwise we simply wouldn't exist, yhere is nothing theoretical about it. Gravitational waves on the other hand are still a theory because they haven't been detected yet. I dont understand what you mean by a "theoretical instrument of analysing"? $\endgroup$ – Dean Feb 4 '16 at 14:30
  • $\begingroup$ I thought that the current dogma was that everything is made out of something else. Kicking the can down the road. $\endgroup$ – LocalFluff Feb 4 '16 at 14:32
  • $\begingroup$ By '"theoretical instrument of analysing" I mean that this is just the theater everything is going on. Imagine that next week it appear that gravitywaves exist, What is the necessity of space while the interactions between planets are arranged by just gravitons, do we than really need space as a real thing? $\endgroup$ – Marijn Feb 4 '16 at 14:36
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    $\begingroup$ This answer is rather misleading because it suggests that curving a coordinate system is what spacetime curvature means. That would be very wrong, e.g. taking curvilinear coordinate system in flat spacetime in some sense represents a nontrivial change in gravitational field (specifically, in the sense of changing the connection coefficients), but it definitely isn't physically significant, nor it does not introduce any curvature. Coordinates just aren't physically important; they're labels we give events. $\endgroup$ – Stan Liou Feb 4 '16 at 23:08
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General relativity is often explained as saying spacetime is curved by gravity, what does this mean?

It means that general relativity can be formulated in a way in which its mathematics have a very direct analogue to differential geometry on a curved four-dimensional manifold. In other words, the way test particles would behave under the influence of only gravitational forces is exactly how they would behave if moving freely on a curved four-dimensional manifold. The mathematics have a direct correspondence: nothing more, nothing less.

Electromagnetism has a description in which the electromagnetic field strength is the curvature of a connection on a line bundle. I realize that this statement is very cryptic to someone who hasn't studied gauge theory, but it's important to realize that an essentially geometric description is not special to gravity. What's special to gravity is that it couples to all stress-energy-momentum equally, and gravitational freefall of a test particle is completely independently of composition.

Because of this universality, it is possible to interpret the properties of the gravitational field as properties of spacetime, i.e. as property of the arena on which everything else happens. We don't have to do so, and indeed there are some presentations of general relativity (e.g., Weinberg's) in which the geometric interpretation is relegated to an unimportant side note, but we can--and geometry is how general relativity was originally developed.

How could we perceive a curve in spacetime when there is no external "straight" reference frame for instance?

We could measure it.

As a conceptually (but not practically) simple way to do so, we could set up a small ball consisting of initially comoving test particles. With no curvature of the gravitational field, every such ball would keep the same shape and volume because they're all the test particles are moving in the same direction with the same speed. But if the gravitational field has Ricci curvature, the volume of the ball would either start shrinking or expanding. Similarly, changes in the shape of the ball would give information about Weyl curvature.

This is the same kind of answer as in the case of electromagnetism: the field strength is also a kind of curvature (though not of spacetime), but how do we perceive it? Well, we could measure it by seeing how test charges behave.

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A mathematicial primer.

A triangle on a flat surface has three angles, and these three angles add up to 180degrees - This is a well known theorem from geometry. It is also well known that if you draw a triangle on a ball, then the angles will add up to more than 180 degrees, due to the curvature of the ball. (and if you draw on a pringles crisp, the angle sum will be less than 180).

An creature crawling on the ball could, by observing only the angles, discover that the surface of the ball was curved. So curvature can be observed by a creature inspecting only local parts of the ball, the creature doesn't need to be able to move away from the ball to observe its curvature. Curvature is an intrinsic property.

Similarly we don't need to be outside of spacetime to observe that spacetime is curved. It is actually the case that the angles in triangles don't add up to 180 due to the gravitational curvature of space (but this effect is too small to be noticeable). We can perceive a curvature in space-time without space-time having to be "in" anything else.

The most obvious consequence of spacetime being curved is that things fall down towards the centre of the Earth.

At some level you should remember that general relativity describes a theoretical model of how gravitational mechanics functions. That model includes coordinates for time and space, and in this model space-time is a mathematical construct, which allows us to predict with extreme accuracy the behaviour of objects under gravitational influence.

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  • $\begingroup$ "space-time is a mathematical construct": So it doesn't have to exist, like the theorema of Pythagoras is not necessary to have a triangle? $\endgroup$ – Marijn Feb 4 '16 at 20:24
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    $\begingroup$ @Marijn That's not a good analogy, because the second part of your statement is a reflection of the fact that the Pythagorean theorem is only valid for right triangles. $\endgroup$ – HDE 226868 Feb 5 '16 at 0:34
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General relativity is often explained as saying spacetime is curved by gravity, what does this mean?

This sounds dodgey.

Gravity is a manifestation of spacetime curvature which is caused by, among other things, massive objects like stars, planets etc. In other words gravity is a consequence of spacetime curvature.

How could we perceive a curve in spacetime when there is no external "straight" reference frame for instance?

Like the answers above, this is achieved through experimental observations or measurements. For e.g. Eddington measured the bending of light around the limb of the Sun which would not have been possible where it not for curvature.

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General relativity is often explained as saying spacetime is curved by gravity, what does this mean?

This OP's comment narrowed the question down:

So [the spacetime] doesn't have to exist, like the theorema of Pythagoras is not necessary to have a triangle? – Marijn Feb 4 '16 at 20:24

The spacetime is a map and not a territory. Spacetime is a model. In other words it is something that exists in human brain, to help that brain exactly predict the future experiences out of previous experiences. For example, the concept of spacetime (in context of the General Theory of Relativity) helps you to predict that the gravitational lensing exists. Your brain is better equipped to process on that level, rather than calculating the same picture by taking a bunch of individual photons and applying the equations to each photon.

Gravitational lens example

A "model" inside a brain is made by imagining something very close to reality and then by deliberately removing the details until you got something so simple that is becomes computable. You forget all the attributes of a star (color, alien civilizations around it, its prehistory, its internal dynamics) and you only think of the star as the mass, etc. This way you turn "enlightening imagination" into a "primitive mechanism usable for predicting experiences".

Marjin, I'd like to say I love the style of your questioning, and I've signed up especially to attempt to answer this one question.

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  • $\begingroup$ I cant decide whether to disagree with what your saying about "spacetime just exists in the human brain", I can see what your trying to say but I think its a bad choice of words, if you remove the human brain spacetime will still exist, just that it wont have any human beings to give it the name "spacetime" $\endgroup$ – Dean Feb 4 '16 at 21:15
  • $\begingroup$ No @Dean. You seem to mix the map with the territory. Let me ask you: does your additional assertion "spacetime exists outside of my brain" let you predict any additional experiences? As a scientific theory, is it experimentally falsifiable? $\endgroup$ – kubanczyk Feb 4 '16 at 21:24
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    $\begingroup$ I know what your saying about the map and the territory, I just think its a poor choice of words that could be misinterpreted that spacetime is just a fabrication of the human brain. Its like most mathematics, we didnt invent it we just discovered it. I dont understand your question of experiences, do you mean like the force of gravity? I have a question for you though, if spacetime is the map then what is the territory? $\endgroup$ – Dean Feb 4 '16 at 21:34
  • $\begingroup$ Experiences, especially experiments, are the signals that come into your brain like for example "oh I see these galaxies seem to curve around in that picture". You use math to try and predict future experiences. You do that inside your brain. Predicting future experiences is good for you, because it lets you kill that great mammoth and have a lot of fat meat for the winter. Arguing that math also exists outside the brain is pointless because it doesn't help to catch the meat - they also call it Occam's razor. $\endgroup$ – kubanczyk Feb 4 '16 at 21:44
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    $\begingroup$ @Dean whether mathematics is discovered or invented is a philosophical matter that's certainly questionable in either direction, but neither claim has any scientific content. Let's just say your position on that is far from universally shared. $\endgroup$ – Stan Liou Feb 4 '16 at 22:34

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