# Definition of Space

1. Aug 25, 2011

### rasp

Can someone provide for a layman a positive definition of space? I am looking for a definition of what space is, rather than a definition of what space relations to. So far I can only perceive space as "the distance between 2 non spatial entities" or "'the absense of a non-spatial (i.e. physical) entity". Obviously, at least the second of these definitions is circular and unsatisfying.

As a second question , but without complicating the above primary question, would someone try to give a positive (rather than a relationship or functional) definition of time?

Thirdly, as a bonus, could anyone perceive of a logic that included action but was not limited to a progression in the sequence of time?

2. Aug 25, 2011

### HallsofIvy

Two problems with that. How do define "non spatial entity" without defining "space" first, and that definition makes "space" a single number.

Physics deals with "events" which refers to what happens at a specific place and specific time. "space" is "where" things happen as opposed to "when". That's about as specific as you can be. To "define" something means to explain in in terms of simpler concepts. "Space" is itself so simple, I suspect the only way to define it is to "point" at it.

Why? The best way to define something in physics is a functional definition.

3. Aug 26, 2011

### Naty1

Go with what you have. I don't like like the ideas posted above, but they are the best we've got.

Nobody knows what space nor time "is".

We use operational definitions and have some mathematics to describe what we observe...we haven't defined either entity to it's essential character yet.

We don't even have a singular precise and unambiguous definition for a particle.... nor matter....

I think of space, time, matter, energy, forces, and so forth as apparently different manifestations which were previously unified in a single entity at the moment of the big bang. Now they appear so different to us in this low energy hopefully stable universe; In the extremely unstable and high energy start, they were indistinguishable from each other.

A rough analogy might be the very high energy quantum foam at Planck scale where time, space and so forth all become mixed together...indistinguishable from one another.....or inside a black hole horizon where time seems to morph into space....and eventually at the singularity even matter seems to cease to exist.

Last edited: Aug 26, 2011
4. Aug 26, 2011

### rasp

Here is a more specific example: We can observe the path of light around a heavy object and conclude that the space the light passes through is curved. So for that region we know SPACE IS CURVED. We know therefore that space has properties that respond to gravity. What are those properties?

My understanding is that the light wave itself is not bending around the heavy object, but the space (i.e. the medium) through which the light travels is bending. The question than poses itself WHAT is actually bending. The old definition of space as simply the distance or the emptiness between two physical bodies won't work if Something actually bends.

5. Aug 26, 2011

### Staff: Mentor

Space is the thing that we measure with rods. It is typically represented by x in physics formulas. As Naty1 mentioned, the fundamental things in physics are defined operationally.

6. Aug 26, 2011

### RayYates

In simple terms, space is the medium in which all matter exists, its measure is always taken relative to physical objects. (an inch -- the length af the kings thumb). Time is the motion of matter or energy through space and is measured by the amount of motion. (Rotations of a clock hand, a light year - miles traveled by light)

In this way, space and time are fundamentally linked and in the end are always measured relative to matter.

Near the event horizon of a black hole space becomes compressed and time slows. In a cingularity time stops, space becomes zero, mass no longer has a "size".

Space and time are plastic so they ultimately they can not be "defined" but are always described "relative" to something else. (matter or motion)

7. Aug 26, 2011

### pervect

Staff Emeritus
I'd suggest taking a look at http://www.eftaylor.com/pub/chapter2.pdf, "curving", a section of one of Taylor's books (coauthored with Wheeler) that he's made available online.

It's not really any more mysterious than that, when it comes down to actualy doing it. Probably the handiest tool is a radar and a clock for measuring both space and time intervals. By sending out a radar signal, and timing how long it takes to return, you can find the shortest distance between two points, assuming you have a static spatial geometry. You can use the same radar method to investigate space-time even if it's not static, but it requires a bit more sophisticated methods to analyze the results.

Curvature effects become noticable via effects such as 'gravitational time dilation", which is really just another way that space-time curvature manifests itself.

8. Aug 27, 2011

### Naty1

"The old definition of space as simply the distance or the emptiness between two physical bodies won't work if Something actually bends."

That's where I come out.

Except realizing that the stress never disappears..it ha stayed with me for every subsequent contact with curved spacetime.....!!! If it were so common place, simple, we would not have constant disagreements in these forums about whether space is "something" or just a mathematical construct.

For me space is just as real as matter or force or time...not that we really know what each of those is either.

9. Aug 27, 2011

### Naty1

10. Aug 27, 2011

### pervect

Staff Emeritus
Well, as long as we are not being philosophers, we can make space simple.

The only parts of space we are interested in in the context of science is what we actually measure with a ruler - or some more portable equivalent, like a radar set and a clock.

If you put on a philosophers hat, I'm sure you can waste - errr, I mean spend - a lot of time, as much time as you like (once you've decided what time is, of course - or perhaps not, perhaps you'll spend the time without knowing ever knowing what time is) talking about it.

Preferably in the philosophy forum, where you'll find likeminded people :-)

But all we need to know about space to do science, including GR, is how to measure distances with a ruler (or a radar set).

And all we need to do to define how space curves is to take a bunch of measurements with our rulers (like we did with the hypothetical rowboat).

It Really Is That Simple. You don't need to do anything else but be able to measure distances with a ruler in order to define and measure curvature.

Furthermore, once you have a standard ruler (like the SI ruler), it's an empirical question (and not a philosophical one) as to whether or not space is curved or flat. You go out, and do the measurements, and analyze them and report back.

Like the rowboat case, you need to measure the distances between a bunch of events in space-time (or nails, in the case of the rowboat) in order to come up with some idea of whether or not it's curved or not. Putting in two nails and mesuring the distance between them won't tell you anything about curvature, for instance.

For starters, it might be productive to imagine that you are a flatlander, http://en.wikipedia.org/wiki/Flatland, living on the curved surface of a sphere, trying to figure out the geometry of said surface.

You'll see that as a flatlander, you'll need to measure the distances between at least four points to be able to measure curvature, a total of six measurements. Three points and three measurements won't tell you anything about curvature, you can always draw a triangle on any curved surface.

If you arrange your four points so they determine a square, whether or not the diagonal is sqrt(2) times the sides will give you a Big Clue as to whether or not you, as a flatlander, are living on a flat surface or a curved one.

Last edited: Aug 27, 2011
11. Aug 27, 2011

### Naty1

All I would add is "....all we need to know about space to do CURRENT science....."

I always try to remember that NEW (original) thinking is usually required for new science.....break throughs.

12. Aug 27, 2011

### pervect

Staff Emeritus
Well, probably the manifold structure will break down at some point, and we'll need something completely different.

However, for doing GR, and understanding curvature, all you need in the way of philosophy is to be able to use a ruler.

That, and a boatload of math :-)

13. Aug 28, 2011

### Phrak

Is spacetime "curved" or are the imposed coordinate systems, or what they measure, distorted?

14. Aug 28, 2011

### pervect

Staff Emeritus
Because curvature is expressed by tensor formula, the coordinates aren't relevant to determining whether or not space-time is curved.

You can make a flat geometry mimic a curved one by having the rulers shrink and expand - Einstein used a heated disk as an example. All we can say definitely is that using the rulers and clocks that we usually use (and not some funky "tweaked" ones), space-time appears to be curved.

15. Aug 29, 2011

### Phrak

Interesting. Thanks, pervect.

16. Aug 29, 2011

### rasp

Pervect, I'll stay out of philisophical discussions here, but I will say many scientists would reject your idea that the ability to measure something is equivalent to knowing how it works.

At best your statement is only accurate if you equate science to engineering.

My question was not to define "how space curves" but rather why space curves. In other words does the current state of science have a theory as to what properties space has that cause it to curve or stretch or compress?

To describe space simply as a geometry is to sidestep the issue. For it begs the question a geometry of what?

17. Aug 29, 2011

### Staff: Mentor

That is not what pervect said, but what he said is generally accepted by the mainstream scientific community.

You always have to be careful with "why" questions, particularly if you expressly do not want "how" answers. Such questions are generally non-scientific in nature and not appropriate for this forum. The only way to answer questions in science is with a theory and its equations (but I think you would consider that a "how" answer), the relevant theory for your question is GR and the relevant equations are the Einstein Field Equations. If you do not wish to admit those as possible answers then science currently has no answer for you.