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The difference between the terms "space" and "spacetime"


geordief

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When I come across the term "space" and the term "spacetime" am I right that they refer to different things ?

 

Can they ever mean the same thing ? (I would not be surprised that ,if the user of the term did not understand the subject then that confusion would be expected)

 

Would there be a generally accepted distinction between the two terms or would it depend on the context in which they are used?

 

My inclination would be that "spacetime" would refer to the "spacetime" model that Einstein theorized and which has so far held up to scrutiny.

 

"Space" on the other hand I would associate with a layman's appreciate of what apparently exists between "things" (not events)

 

Is my understanding more or less correct? Or does "space" also have a well defined meaning within Relativity Theory that would be distinct from "spacetime"

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So a

 

Space (to my mind) is just three of the dimensions in space-time.

So a( incomplete part of a ) model rather than an attempt to describe an aspect of reality?

 

Is that fair?

 

To my mind you cannot disentangle space and time but does there need to be a term that describes separation between "objects" or do we just accept that (in layman's terms) " empty space" is "full" ?

Edited by geordief
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I think there are two different things there. "Space", when compared to space-time, can mean just the 3 spatial dimensions. And that is the "separation between objects".

 

But if you start talking about the volume of space between objects, then that is full of all sorts of things: gas, dust, neutrinos, fields, photons, virtual particles, dark matter, dark energy, ... But I think of them as what is in space, rather then being space. So there is no such thing as "empty space" (although you can often treat it as that, for practical purposes).

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Space is the three spatial dimensions. Which can be equated to volume.

 

Spacetime adds a 4th dimension.

 

One definition of spacetime is any geometry of space that includes time.

 

In a real sense your defining the number of coordinate dimensions by the use of space or spacetime. 3d for space 4d for spacetime.

 

So when you hear the term curved spacetime your referring to a curved coordinate system where each coordinate is 1 unit.

 

Curved spacetime doesn't suggest that space or spacetime is made of some mysterious fabric. Thats a common misunderstanding.

Edited by Mordred
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The way that I understand it, which I admit is still a bit fuzzy in spots is that special relativity linked space and time together by virtue of the speed of light being constant and the fact that nothing can go faster than the speed of light.

 

The most obvious example of this is that when we look at any celestial body that is n light years away, we are looking at it as it existed n years in the past because that's how long the light took to arrive here.

 

Other examples that they are linked has to do with the relativistic effects when traveling near the speed of light, e.g. Time dilation and length contraction, seem to go hand in hand.

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Is it correct to say that the 3 dimensional model is less accurate than the 4 dimensional model or is it possible to say that each is equally accurate depending on their area of applicability?

 

I would have assumed that the 4-D model included the 3-D model (Russian doll style) whereas the 3-D model was inherently incomplete.

 

Is this just semantics(?) or fundamentally important?


The way that I understand it, which I admit is still a bit fuzzy in spots is that special relativity linked space and time together by virtue of the speed of light being constant and the fact that nothing can go faster than the speed of light.

The most obvious example of this is that when we look at any celestial body that is n light years away, we are looking at it as it existed n years in the past because that's how long the light took to arrive here.

Other examples that they are linked has to do with the relativistic effects when traveling near the speed of light, e.g. Time dilation and length contraction, seem to go hand in hand.

Even if light had not been constant would space and time not have still been linked together? Does not any measurement presuppose a time taken to make it?

 

If light did not exist as a method of communication then would we not rely upon some other method?

Edited by geordief
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The 3 dimensional model is accurate in everyday applications. Its only when you need to model relativistic effects when the 4d becomes necessary.

 

For example the average person doesnt need to know the time dilation between your feet and head in everyday use. So even though the 4d is more accurate. Its unnecessary for everyday applications such as the age of your individual body parts

Even if light had not been constant would space and time not have still been linked together? Does not any measurement presuppose a time taken to make it?

 

If light did not exist as a method of communication then would we not rely upon some other method?

The way it would be linked would be different as you probably wouldnt need to alter the spatial components. Ie no curvature

If you model spacetime as coordinate points. 4d.

Time dilation and length contraction both occur. ( Time being the fourth coordinate.)

So when you involve length contraction, from coordinate to coordinate the velocity doesn't change. What changes is the number of coordinates from a to b. (Sort of)

Lorentz transformation.

First two postulates.

1) the results of movement in different frames must be identical

2) light travels by a constant speed c in a vacuum in all frames.

Consider 2 linear axes x (moving with constant velocity and [latex]\acute{x}[/latex] (at rest) with x moving in constant velocity v in the positive [latex]\acute{x}[/latex] direction.

Time increments measured as a coordinate as dt and [latex]d\acute{t}[/latex] using two identical clocks. Neither [latex]dt,d\acute{t}[/latex] or [latex]dx,d\acute{x}[/latex] are invariant. They do not obey postulate 1.

A linear transformation between primed and unprimed coordinates above

in space time ds between two events is

[latex]ds^2=c^2t^2=c^2dt-dx^2=c^2\acute{t}^2-d\acute{x}^2[/latex]

Invoking speed of light postulate 2.

[latex]d\acute{x}=\gamma(dx-vdt), cd\acute{t}=\gamma cdt-\frac{dx}{c}[/latex]

Where [latex]\gamma=\frac{1}{\sqrt{1-(\frac{v}{c})^2}}[/latex]

Time dilation

dt=proper time ds=line element

since [latex]d\acute{t}^2=dt^2[/latex] is invariant.

an observer at rest records consecutive clock ticks seperated by space time interval [latex]dt=d\acute{t}[/latex] she receives clock ticks from the x direction separated by the time interval dt and the space interval dx=vdt.

[latex]dt=d\acute{t}^2=\sqrt{dt^2-\frac{dx^2}{c^2}}=\sqrt{1-(\frac{v}{c})^2}dt[/latex]

so the two inertial coordinate systems are related by the lorentz transformation

[latex]dt=\frac{d\acute{t}}{\sqrt{1-(\frac{v}{c})^2}}=\gamma d\acute{t}[/latex]

So the time interval dt is longer than interval [latex]d\acute{t}[/latex]

 

 

Here are the Lorentz transformations

[latex]\acute{t}=\frac{t-vx/c^2}{\sqrt{1-v^2/c^2}}[/latex]

[latex]\acute{x}=\frac{x-vt}{\sqrt{1-v^2/c^2}}[/latex]

[latex]\acute{y}=y[/latex]

[latex]\acute{z}=z[/latex]

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The way it would be linked would be different as you probably wouldnt need to alter the spatial components. Ie no curvature

You are talking about curvature caused by mass/energy , are you ? So you are not talking about Special Relativity where as I understand it curvature is not a feature ?

 

Is my point a valid one ,then ?You would still have to have had a (different) theory of Relativity even if the speed of light had not been observed to be constant in all frames of reference?

 

By the way ,is it true that Maxwell had actually predicted in his equations for electro-magnetism that the speed of light would be the same in all FoRs ?

 

If so should/could Michelson and Morley not have realized they were wasting their time?

 

EDIT:We cross posted . I will look at your post now.

Edited by geordief
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The Lorentz transformation I posted above work for SR as well as GR. The main difference between SR and GR is that one observer is assumed to be at rest. Though there are corrections to SR for a moving observer. The coordinate system of an observer at rest is the Euclidean (flat) coordinate system which is in Cartesian coordinates (Minkowskii).

 

Though whats not often mentioned is GR use of tensors do not rely on any coordinate system. They work in all coordinate systems.

 

An oversimplification is SR shows us how to transform from Cartesian to polar coordinates. The polar coordinate representing the relativistic object.

(Fundamentally this is whats meant behind curved spacetime) as polar coordinates are essentailly curved Euclidean coordinates.

 

Take a flat map and fold it onto a ball. The curvature is the curvature of the ball which will change by the amount of Lorentz factor

Edited by Mordred
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Even if light had not been constant would space and time not have still been linked together? Does not any measurement presuppose a time taken to make it?

I'm not sure this question makes sense.

 

If any theory is in fact true speculating what would happen if it wasn't true means the universe doesn't exist.

 

However, we may have doubts about a theories correctness and speculate what would happen if such and such was not true when looking for an alternative theory that may make more sense. If that is the way you intended the question than I don't know, but what Mordred said is probably a pretty good bet before I've had a chance to fully digest his response.

 

If light did not exist as a method of communication then would we not rely upon some other method?

(aside from sound) we mostly communicate using signal waves in electromagnetic fields through substrate materials, in which light plays only one role, i.e. Fiber optics, but there are plenty of other examples of communication that does not involve light, such as any of the Ethernet protocols or wireless communications. Though they all still propagate at the speed of light and are fundamentally based on Maxwells equations. Edited by TakenItSeriously
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Even if light had not been constant would space and time not have still been linked together? Does not any measurement presuppose a time taken to make it?

 

 

I don't think they would be linked in the same way - where changes in one are tied to changes in the other.

 

So in a non-relativistic universe, everyone would agree on the meaning of "now" so there would be no problem synchronising distant measurements. You would just agree to do them at 1 o'clock. In relativity (and the real world) you can't easily do that.

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