# What is spacetime? [duplicate]

What is space time? Is it like a material or a theoretical substance? Is it made up of chemicals? Is there a way to interact with it?

I know that gravity can deform it but other than that. Can some one give me a good explanation? I am only 15 :)

Spacetime is something physical which has a deep mathematical meaning.

The General (intuitive) Idea

Intuitively and roughly speaking, spacetime is the "place" of all events, or the set of all events. An event is something that "happens in a time $$\tau$$ and takes place somewhere". You can grasp the main concept with a simple example: You have a physics test, Friday 11:00 AM, at the Physics Departament building, on floor 5. Well, if you go to the right place but wrong time you will miss the test. To access the event "test" you have to be in the right place at right time. So, you necessarily must to deal with four numbers: one for time and three for space.

Because of relativity, the time are not just a parameter, but a coordinate! In Lorentz transformations you transform time as a usual coordinate. You must consider time as just another coordinate as the usual spatial ones.

The idea of Gravity and "Deformation"

Well, I would like to present to you an equation:

$$\textbf{G} = \frac{8\pi G}{c^{4}}\textbf{T} \tag{1}$$

This equation is called Einstein Field Equation. This equation tells us about how bodies moves in that "place of all events" (the Spacetime) due to a matter-energy distribuition. The quantity $$\textbf{G}$$ is called Einstein Tensor. This quantity encodes the curvature of this "place of all events", and because of that, other bodies have their trajectories changed due to this curved "place of all events", like Earth around the Sun. And this sounds familiar, no? Well, this is just the fingerprint of a gravitational system; gravity is a consequence of curved spacetime.

On the right hand side we have the information of which body performs the curvature; could be a planet, star, other fields... The quantity $$\textbf{T}$$ is called Matter Tensor and this quantity encondes all of the information about which type of matter are curving spacetime.

A Very Nice Phrase

There's a nice phrase said by a physicist called John Wheeler which is:

"Spacetime tells matter how to move$$^{*}$$ and Matter tells spacetime how to curve$$^{**}$$"

$$^{*}$$ This is just the intuitive idea of what physical meaning the Einstein Tensor carries: here this quantity is just a "pure mathematical thing", which tells curvature. But this curvature modifies the trajectories of particles, and this is just gravity.

$$^{**}$$ And this is the intuitive idea behind the Matter Tensor: a planet (for instance) curves spacetime and then this curvature modifies trajectories of particles, and this is just gravity....and so on.

$$* * *$$

I recommend a nice book: Relativity: The Special and General Theory by Einstein himself.

A "self motivation" disclaimer: Special and General Relativity aren't difficult to understand when you have the basic pre-requisites, so don't be afraid.

• I think General Relativity is difficult to understand, because (1) the equations are hard to solve; (2) the energy issues are subtle; (3) it is very hard to tell whether two apparently different metrics describe the same manifold; (4) you get things like coordinate singularities which need careful handling, etc. It took the physics community many years to understand the Schwarzschild metric, and this was not because people were slow or less intelligent than us. – Andrew Steane Oct 29 '19 at 1:30
• Would it be fair to translate the John Wheeler quote to "Spacetime tells matter how to move and Matter tells spacetime how to [tell matter how to move]"? – Chechy Levas Oct 29 '19 at 13:04

There is no quick or easy answer to the question 'what is spacetime'? But I will have a go.

Spacetime is a beautifully subtle but mathematically precise arena.

Mathematically speaking, spacetime can be accurately described as a 4-dimensional manifold, which is just a technical name for a type of multi-dimensional space which is smooth. It is furthermore a type of space in which nearby points (called events) can be said to have definite separations (called intervals), with a particular quadratic function specifying these intervals.

Physically speaking, spacetime is a collection of quantum fields that extend everywhere and everywhen. When someone talks about spacetime, as opposed to stuff occupying spacetime, they usually have in mind the case where these fields are in their joint ground state (their lowest energy state). And the ground state of this collection of quantum fields has a wonderful property: it is Lorentz-invariant. This means that the state shows no change whatsoever if an observer or measuring device inspecting it changes from one state of inertial motion to another. So nothing you can do can possibly show you spacetime 'moving by'. Spacetime is not like that: not like something you can put your finger in and detect.

Yet you can disturb spacetime. You can disturb it by shaking massive objects. Even shaking your hands will disturb it a little, and send out tiny gravitational waves. But how do these gravitational waves manifest themselves? They manifest themselves by influencing all those quantum fields I mentioned just now: they change the shape of the arena in which the fields are situated. And what is really strange is that you can never detect this influence at any single point. You can only detect it only by comparing different points, and finding out time and space intervals between them.

So in one sense spacetime is not made of anything, because it is the arena where stuff lives, and it is not the stuff. And yet on the other hand spacetime is made of everything, in the sense that all the quantum fields are present at every event.

• How does one calculate the disturbance of the quantum fields caused by gravitational waves and how can one mathematically proof that it is not possible to detect this disturbance at a single point? – undefined Oct 29 '19 at 8:05
• @undefined At the moment we calculate this by treating the quantum fields as located in a classical spacetime described by GR. In the classical limit one ends up with ordinary clocks and rods responding to the gravitational stress tensor. The fact that one cannot detect gravity at a point follows from the Equivalence Principle. This can in turn be seen as owing to the fact that the metric is Minkowskian in the vicinity of any event. – Andrew Steane Oct 29 '19 at 9:04
• I don't like this answer because spacetime and quantum fields arises from completely different and incompatible theories. We have no idea how the two of them interact precisely, and this answer just assume space time is made up by quantum fields because that is an intuitive feeling. – lvella Oct 29 '19 at 11:58
• @Ivella The question asked what is spacetime. The physical picture of quantum fields everywhere is likely to remain broadly correct as a more complete understanding is developed. Also, the difficulty with QFT and GR is not quite corrrectly described as straight incompatibility. QFT is compatible with special relativity, and in a similar way it is compatible with general relativity except in extremes of curvature or when there is entanglement involving significantly different metrics. – Andrew Steane Oct 29 '19 at 13:05

The rubberband sheet is just a popsci metaphor, and can confuse you.

In mainstream physics, spacetime is the events, that happen at a particular space at a particular time.

Spacetime is a mathematical model that fuses the spatial and temporal dimensions into a four dimensional manifold.

Until the 20th century, they assumed that the spatial geometry of space was independent of the temporal dimension.

With the introduction of SR, some nontrivial consequences appeared:

1. temporal ordering of events change in different inertial frames

2. the linear additivity of speed no longer holds true

Mathematically, spacetime is a manifold, which is to say, it appears locally "flat" near each point in the same way that, at small enough scales, a globe appears flat.[4] An extremely large scale factor, $$c$$ (conventionally called the speed-of-light) relates distances measured in space with distances measured in time. The magnitude of this scale factor (nearly 300,000 kilometres or 190,000 miles in space being equivalent to one second in time), along with the fact that spacetime is a manifold, implies that at ordinary, non-relativistic speeds and at ordinary, human-scale distances, there is little that humans might observe which is noticeably different from what they might observe if the world were Euclidean.

https://en.wikipedia.org/wiki/Spacetime

You say gravity curves spacetime, and this is an expression we use, but this just means that its geometry is non-Eucledian.

So basically the spatial and temporal dimensions are no longer independent. As per GR, the curvature of spacetime in your case affects the relative passage of time, this is called time dilation.

Time dilation is a difference in the elapsed time measured by two clocks, either due to them having a velocity relative to each other, or by there being a gravitational potential difference between their locations.

https://en.wikipedia.org/wiki/Time_dilation

As of today this is a question that cannot be answered. To know exactly what spacetime is we would have to understand gravity at a fundamental level. This is the field of quantum gravity which is still a topic of debate between theoretical physicists (none of the theories have been proven yet).

The idea of spacetime dates to the work of A. Einstein and his theory of relativity. It can be thought of as the set of all of the events in the universe. By event we mean a "point" that can be specified with a position and a time (you have 3 dimensions in space, adding time gives you the 4 dimensions of spacetime).

To get to the modern notion of spacetime there are two distinct ideas:

1. Time and space can "mix" with one another (a moving observer will see that space contracts and time dilates). They play a kind of similar role with the exception that you can only travel in one direction in time. This is one of the key ideas in Special Relativity (1905).

2. Gravity is not a force, it is a consequence of the curvature in spacetime caused by the presence of energy in it (mass is also a form of energy by the famous equation $$E=mc^2$$). This is the core idea in General Relativity (1915).

Idea #1 has been adopted successfully at a fundamental level (in Quantum Field Theory). The problem lies with idea #2, which is why one has to consider quantum gravity.

Two the most accepted ideas (there are many, many more) are the following,

We can go along with the ideas of Loop Quantum Gravity. In this theory you "quantize" space and time (a quantum is a unit or block of a physical quantity), and in this picture you actually know what spacetime is like: "an extremely fine fabric or network woven of finite loops". In this scenario gravity is not really a force and a fundamental particle (graviton) does not exist. This aligns better to Einstein's idea of spacetime.

But there is another way to go. String Theory suggests that all particles are a consequence of the vibration of tiny strings (different modes of vibration result in different particles). If this picture is true then gravity is actually force (just like electromagnetism and the weak and strong nuclear forces) and it has its own associated particle, the graviton. In this scenario spacetime is just a macroscopic approximation to a more fundamental interaction.

The problem is that currently no one knows which is the right way to do quantum gravity. We cannot even say if it is fundamental or not, so it wouldn't make sense to talk about its properties. What we can do is use it as a tool to understand and model astrophysical and cosmological processes.

NOTE: This is not by any means a comprehensive answer and I may have (willingly or unwittingly) omitted some important details. I am not an expert in ST or LQG so if I said something wrong let me know in the comments.

• Can some one give me a good explanation? 'No.' +1 – Mazura Oct 29 '19 at 3:50

Spacetime is a "4D space" that surrounds everything in the universe. It is the space and time that we exist in. It's not "made of anything" in the sense of a perceivable material, but mass and energy make it bend. Essentially, imagine a blanket held tight, it's flat right now, but if you put a bowling ball on it, it will deform. That's like the sun, in the depression. Then if you add a golf ball, it will roll towards the bowling ball. This is the earth. If you roll the "earth" alongside the sun, it will begin to "orbit" (eventually it will fall in because of friction with the blanket). This is a conceptual idea of what "spacetime" is, but spacetime is actual a 4d space, so take this with a grain of salt.

What is space, you know.
What is time, you know, too.
If you are in the place $$X$$ in the space at time $$t$$, you may tell that you are in position $$(X, t)$$ in spacetime.

So spacetime is something artificially invented for comfortable work with math.
Somehow similar to “heightmass” of a man (which I just now invented for you) to simultaneously express the two characteristics of a man.

It's just enough for your age (and an assumed math/phys skill).

Spacetime is the 4d place where everything "happens", where 'happens' might just mean simply existing. Objects move through spacetime along their world-lines and features of the world lines and features of space dictate how things move even in the absence of an applied force.

Think of a place on the surface of the earth. It has a longitude, a latitude, and an elevation. Events can happen at that location at some point in time.

Now, if you walk from that place to another along the surface of the earth, you will not be walking on a straight line path in the euclidean sense. You have to stay on the curved surface of the earth.

Forced to walk along the surface of the earth, the shortest distance between two points is not the euclidean straight line, but a great circle, the circle having the same radius as the earth and which passes through the starting and ending point of the path.

A euclidean straight line path would require digging through the earth, extra effort and energy to maintain that path.

Imagine graphing the earth moving around the sun, but replace the z axis with time. The sun stays roughly in place just moving 'up' in a straight line, while the earth moves up and around that line in a spiral. This is a representation of 3 of the 4 dimensions of space time. In this depiction, time is treated as a coordinate on the same footing as the other dimensions. An "event" in spacetime is just a point in 4d space time. A world line is a continuous set of such events.

World lines also give us information of the kinematics of a particle. The the world line has x,y,and z positions varying with time. The derivative of the x coordinate with respect to time is the speed in the x direction. The second derivative with respect to time is acceleration, closely related to the curvature of the world line.

All this can be brought together. Einstein discovered that Newton's first law is not generally correct. Objects don't move in straight (euclidean) lines in the absence of an applied external force. They move along "geodesics" in space time. Geodesics are length minimizing paths in space time which are straight lines only in flat, euclidean space. They are "curved" outside of flat space time, like curved paths on the surface of the earth.

Mass/energy/momentum causes space time to curve so force-free paths are no longer straight euclidean lines. Just as objects are constrained to move in curved paths on the surface of a sphere, there are constraints in the motion of objects in spacetime. Force-free paths are now curved, almost like following invisible grooves, hence the frequent depiction of small objects moving in different ways on a rubber sheet spread by a bowling ball.