# How do space and time fuse together to form “spacetime?”

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• Wiredcerebellum
Wiredcerebellum
TL;DR Summary
If neither space nor time have any physical properties of matter underlying them, how can space and time merge to form spacetime?
Here is the definition of spacetime?

“In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum.”

But if space is literally the absence of matter or physical properties, and time has no physical properties, how do the two merge to form the 4-dimensional structure called spacetime?

Spacetime can bend and ripple like a physical object so it seems like spacetime should have physical properties of matter underlying it that allow for the bending and rippling, but it doesn’t. So how do space and time “fuse” to form spacetime if neither have physical properties?

Wiredcerebellum said:
TL;DR Summary: If neither space nor time have any physical properties of matter underlying them, how can space and time merge to form spacetime?

So how do space and time “fuse” to form spacetime if neither have physical properties?
Who says they don’t have physical properties? You can measure them quite accurately.

Dale said:
Who says they don’t have physical properties? You can measure them quite accurately.
What are the physical properties of matter? That’s where I’m lost. Thanks for your help in advance.

Wiredcerebellum said:
What are the physical properties of matter? That’s where I’m lost. Thanks for your help in advance.
Well, notably, length, width and height.
In the absence of matter we can measure distances using 3 coordinates, such as x, y and z.

Wiredcerebellum said:
What are the physical properties of matter? That’s where I’m lost.
Spscetime has geometrical properties. Lengths, widths, heights, durations, angles, etc.

Matter also has charge, spin, etc.

DaveC426913 said:
Well, notably, length, width and height.
But what is the length, width, and height measuring? What are the properties of matter underlying it that allow spacetime to bend and ripple? That’s where I’m lost.

Wiredcerebellum said:
What are the physical properties of matter? That’s where I’m lost. Thanks for your help in advance.
What do you think matter even is to ask that question?

DaveC426913 said:
Well, notably, length, width and height.
In the absence of matter we can measure distances using 3 coordinates, such as x, y and z.
ProfuselyQuarky said:
What do you think matter even is to ask that question?
I’m wondering what is bending and rippling when we say spacetime can bend and ripple? Is there matter underlying spacetime that allows it to bend and ripple? When I say matter I’m referring to atoms.

Wiredcerebellum said:
What are the properties of matter underlying it that allow spacetime to bend and ripple?
To be clear, spacetime is not really a 'thing', in the sense that it does not actually bend and ripple.

DaveC426913 said:
To be clear, spacetime is not really a 'thing', in the sense that it does not actually bend and ripple.
Then how are gravitational waves formed if spacetime cannot literally bend and ripple?

DanMP
Wiredcerebellum said:
So how do space and time “fuse” to form spacetime if neither have physical properties?
How do up/down, left/right and forward/backward "fuse together" to make the 3d space you see around you? I don't think that question really makes sense, and it doesn't get clearer if you add time as a fourth dimension to the mix.

Note that the paragraph you quote is specifically talking about the mathematical model. Historically we have tended to view space as "where stuff happens" and time as some separate thing that kerps everything from happening at once. But relativity turns out to be easier to understand if you think of time as just another dimension, albeit with some slightly different properties. We aren't "fusing" anything in reality - just fitting two parts of our models together more closely than we used to.

You are reading too much into popsci descriptions of physics, in other words.
Wiredcerebellum said:
Spacetime can bend and ripple like a physical object
No it can't, although you do see that kind of thing written. The curvature of spacetime is about how the rules of geometry vary through space and time. It's not really anything like a distorted rubber sheet.

Unfortunately it's really hard to talk about this stuff precisely without post-grad maths. So some physicists try to talk in more casual allegorical terms to try to get their ideas across. But that often just ends up confusing people in new ways...

dextercioby, phinds, Dale and 1 other person
Wiredcerebellum said:
Then how are gravitational waves formed if spacetime cannot literally bend and ripple?
That's why we're looking for the existence of gravitons.

DanMP
DaveC426913 said:
That's why wer'e looking for the existence of gravitons.
Ok I understand. So currently there is no matter underlying the rippling and bending of spacetime that we know of? It’s all theoretical?

Wiredcerebellum said:
Ok I understand. So currently there is no matter underlying the rippling and bending of spacetime that we know of? It’s all theoretical?
Not 'theoretical'; it's an analogy. It is really the behavior of the geometry of things that move through spacetime. Their paths bend due to applied forces (such as encountering the Earth's surface)

phinds
DaveC426913 said:
Not 'theoretical'; it's an analogy. It is really the behavior of the geometry of things that move through spacetime. Their paths bend.
Ok then…

Wiredcerebellum said:
Then how are gravitational waves formed if spacetime cannot literally bend and ripple?
Time is a part of spacetime, so talking about spacetime changing is already a mistake. All that changes is which "slice" of spacetime you currently think of as "now" - the gravitational waves are already baked in.

As Ibix said:
Ibix said:
Unfortunately it's really hard to talk about this stuff precisely without post-grad maths. So some physicists try to talk in more casual allegorical terms to try to get their ideas across. But that often just ends up confusing people in new ways...

The nature of things IS the math that describes them. To try to frame fundamental things in terms of what we intuitively know means inevitably that we use simplified, flawed analogies.

PhDeezNutz
Ibix said:
Time is a part of spacetime, so talking about spacetime changing is already a mistake. All that changes is which "slice" of spacetime you currently think of as "now" - the gravitational waves are already baked in.
Well alright then.

Law o
DaveC426913 said:
As Ibix said:The nature of things IS the math that describes them. To try to frame fundamental things in terms of what we intuitively know means inevitably that we use simplified, flawed analogies.
What about the law of parsimony?

Dale
Ibix said:
Time is a part of spacetime, so talking about spacetime changing is already a mistake. All that changes is which "slice" of spacetime you currently think of as "now" - the gravitational waves are already baked in.
Alright.

DaveC426913 said:
You shouldn’t need advanced math to explain how spacetime works.

PeroK
Wiredcerebellum said:
What about the law of parsimony?
GR is pretty parsimonious. At its core is literally one equation plus a couple of "energy conditions" that help to define what we call reasonable solutions.

Unfortunately it doesn't map very well into everyday language, and you can write very long textbooks on the topic.

Wiredcerebellum said:
You shouldn’t need advanced math to explain how spacetime works.
The entire history of modern physics was kicked off by Newton developing calculus. I'm afraid that the maths has done nothing but get harder to learn since then. We can do analogies and hand-waving all day long, but the only working models of any physical system are mathematical ones.

Spacetime is the background on which physics happens. General relativity makes the geometry of that background depend on what's in it, whereas most other theories just assume there's a background there and don't interact with it. That's really all there is to know at the high level. It isn't really anything except whatever aspect of reality that furnishes notions of dustance, angle,and speed.

phinds
Wiredcerebellum said:
You shouldn’t need advanced math to explain how spacetime works.
Why not?

PeroK and jbriggs444
Wiredcerebellum said:
I’m wondering what is bending and rippling when we say spacetime can bend and ripple? I
Nothing. That "bending and rippling" description isn't right, it's just the best that we can do to describe the theory without using the math needed for a complete and accurate description.

PhDeezNutz
Wiredcerebellum said:
You shouldn’t need advanced math to explain how spacetime works.

PhDeezNutz
Wiredcerebellum said:
if space is literally the absence of matter or physical properties
It isn't.

Wiredcerebellum said:
and time has no physical properties
It does.

Reasoning from false assumptions never works out well.

Wiredcerebellum said:
What are the physical properties of matter?
Why is that relevant? You asked about spacetime, not matter. In John Wheeler's famous statement, spacetime tells matter how to move. That is the key physical property that spacetime has.

@Wiredcerebellum A table top is physically flat, and the legs are physically perpendicular to the surface. Those words “flat” and “perpendicular” are geometrical words, but they describe a physical object. So geometry is part of physics.

The geometry that most people are used to is called Euclidean geometry. It is captured in this equation, which comes from the Pythagorean theorem: $$ds^2=dx^2+dy^2+dz^2$$ Everything from Euclidean geometry comes from this equation, including things like the interior angles of a triangle sum to 180 degrees. This is the geometry we use to say that the table top is flat and that the legs are perpendicular.

When we say that spacetime is space and time together, what we mean is simply that the geometry of physics is given by $$ds^2=-dt^2+dx^2+dy^2+dz^2$$ You cannot accurately describe the geometry of physics without including time as well as space.

This in no way implies that spacetime is matter. Nor does it imply that spacetime has no properties. That is a false dichotomy.

PhDeezNutz, agnick5, Vanadium 50 and 2 others
Dale said:
$$ds^2=-dt^2+dx^2+dy^2+dz^2$$
Am I over-interpreting, or is this (almost) the pythagorean formula for a 4-dimensional cube?
And as long as t is very small, it degenerates to a 3D cube....

DaveC426913 said:
Am I over-interpreting, or is this (almost) the pythagorean formula for a 4-dimensional cube?
And as long as t is very small, it degenerates to a 3D cube....
It is the spacetime version of the arc length formula. So it could be considered the “length” of the line segment across the diagonal of an infinitesimal 4D cube. Just like in the Pythagorean theorem ##A^2+B^2=C^2## you can consider ##C## to be the length of the diagonal across a rectangle of sides ##A## and ##B##.

Wiredcerebellum said:
Then how are gravitational waves formed if spacetime cannot literally bend and ripple?
I used to have a book of physics essays. In the early days of GR, some physicist made this point and criticised the theory of GR on the basis that it contradicted SR and in his view implied an ether. It was the same idea that in order to have geometric properties spacetime must have a physical substance.

But, an alternative approach, is to be guided by nature. We don't assume a priori that geometric properties demand physical susbstance. Instead, we keep an open mind and, as far as GR is concerned, we find spacetime has geometric properties without the need for spacetime to have physical substance.

If you don't accept that, then essentially you are deaf to what nature is telling you and preferring your own a priori reasoning.

The history of modern physics, from Newton to Maxwell to Einstein to Quantum Mechanics is a lesson in looking at nature first before drawing conclusions about how nature must be. If we didn't do that we would still be laboring under the misapprehensions of Aristotle and there would be no modern physics.

ersmith
Wiredcerebellum said:
You shouldn’t need advanced math to explain how spacetime works.
If it takes you two hours to drive to grandma's house, a distance of 150 km, then you drive at an average speed of 75 km/h. You've combined space and time in a calculation. That's an example of how spacetime works.

For a full explanation of how spacetime works you do indeed need advanced graduate-level math.

Wiredcerebellum said:
But if space is literally the absence of matter or physical properties
This is not what space is. First, space is not the same thing as empty space, so it does not need to be without matter. Second, which seems to be the main source of your confusion, even if there is no matter, why do you think that space does not have physical properties? In fact, what exactly do you mean by physical properties?

If you try to find precise answers to such questions, you might realize that the notion of "physical property" can me much more general than you thought. Any property that has some role in the science called "physics" deserves a title of "physical property". Physical does not need to mean tangible, or even measurable. Physics to a large extent is a theoretical science working with mental concepts. Space, time, and spacetime are such theoretical mental concepts. You cannot measure space directly, but you can think of space directly. The fusion of space and time into spacetime should be understood as a mental fusion, not as a material fusion.

Dale

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