How Does Einstein's Theory Explain the Nature of Space?

[omin]

In terms of the said theory Special or General Theory, What is this thing called Space?

(Please discuss this in terms of the said Forum, because the last one was removed because of this violation.)

 

[Gerinski]

I'm just an amateur with no real knowledge of theoretical physics, so don't take my answer as the right one, but as far as I can say:

Energy making up our universe, whenever "slowed down" from the speed of light (because transformed into matter or because it slowed down its speed due to traveling through matter), causes the 4 dimensions (space + time) to grow (emerge to a measurable quantity).
Energy "moving" at the speed of light (energy without rest mass) does not take any space (nor time) as distance (and time) become shrinked to zero-size at the speed of light.
In this sense, space is the extension of dimensions (let alone the time one) occupied by the sub-light-speed-energy of the universe.
We only perceive radiation "moving" at the speed of light because we (matter) have caused the extension of space-time dimensions against which we may measure any speed. For radiation itself, the term speed is meaningless.

 

[omin]

...Energy making up our universe, whenever "slowed down" from the speed of light...

I have to stop you there, because I'm unsure what your terms represent.

I only know energy as an equation that represents the movement of mass. KE = 1/2 m * v^2. That's how I see it. Do you mean to represent mass and it's movement? Or not?

The speed of light. I know you don't mean just the property of speed. You atleast mean the light itself. I heard light is not mass.

Now, I try to see them interact by your assertion. I'm not getting an meaningful image. Could you explain the properties relevant to energy and light so the physical interaction "slowed down" may make more sense to me?

 

[Gerinski]

As I said I'm afraid of being just confusing you with wrong comments, we better wait for the reply from some more competent member.

What I meant is, I heard the combination of the movement through space + the movement through time is always c (speed of light). The more you move through space, the slower you travel through time and viceversa.
So it seems space (distance measured between points or objects) is just a kind of perspective which unfolds more or less depending on the relative speed of objects

 

[pmb_phy]

In terms of the said theory Special or General Theory, What is this thing called Space?

(Please discuss this in terms of the said Forum, because the last one was removed because of this violation.)

Space is just one of those things which people know what it is without a definition. Its so basic of a term that definitions usually require another, similar, term to define. Space is a collection of places is about the best I can do. This reminds me of something I once read

My own pet notion is that in the world of human thought generally , and in physical science particularly, the most important and most fruitful concepts are those to which it is impossible to attach a well-defined meaning - H.A.Kramers

 

[jcsd]

Yep, space is prtty much axiomatic in all physical theories, that is to say it's existence is so obvious that we just assume it exists.

I suppose we could talk about the mathematical models we have of the physical phenoumena called space, but that's beside the point as it really doesn't tell us what space is, just some of it's properties.

 

[russ_watters]

I suppose we could talk about the mathematical models we have of the physical phenoumena called space, but that's beside the point as it really doesn't tell us what space is, just some of it's properties.

On the other hand, to a scientist, what something is is simply the sum of all of its properties.

 

[jcsd]

On the other hand, to a scientist, what something is is simply the sum of all of its properties.

I disagree, it's like the chicken and the egg; the mathematical models were forumlated to describe space, so they don't offer any insite into what space 'is'. Space is space is space.

 

[Gerinski]

I only know energy as an equation that represents the movement of mass. KE = 1/2 m * v^2. That's how I see it. Do you mean to represent mass and it's movement? Or not?
The speed of light. I know you don't mean just the property of speed. You atleast mean the light itself. I heard light is not mass.

I believe your formula is for kinetic energy, indeed the energy associated with a mass due to it's velocity (relative to the measurement frame).

Even light has no rest mass, it surely conveys energy, how would otherwise solar panels (photovoltaic cells) heat up your house water ?
Light (electromagnetic -EM- radiation, including heat) is just another type of energy.

I meant the faster you travel, the space in the direction of your movement shrinks. If you travel at the speed of light c (which matter can't but EM radiation does -in the vacuum-), you don't travel through space (or more accurately, space in front of you has shrinked to zero size). If you travel at sub-luminal speed (the fate of all matter), the space in front of you "expands again", getting bigger the slower you travel. The combination of how much you move through space and through time is always c.
The transition pictured here from light-speed to sub-luminal or viceversa -by which space grows from zero-size to some size and viceversa- is not possible for matter (which can never attain c speed) but it's routine for EM which in the vacuum travels at c but is slowed down when passing through matter (i.e. out atmosphere or water).

Once again, some expert correct me if I'm saying bull****. i posted a similar issue in this same forum with the title 1-dimension

 

[turin]

jcsd,
Can you give an example of some essence/object that is described by science in a different way than simply by demonstrating all of its relevant properties?

 

[jcsd]

jcsd,
Can you give an example of some essence/object that is described by science in a different way than simply by demonstrating all of its relevant properties?

point taken, but the point still is that space is an axiom not a result of physical theories.

 

[turin]

Isn't Einstein's general theory of relativity an attempt to remedy this problem with space-time.

 

[russ_watters]

I disagree, it's like the chicken and the egg; the mathematical models were forumlated to describe space, so they don't offer any insite into what space 'is'. Space is space is space.

I'm not following - what does that have to do with the chicken/egg thing?

 

[jcsd]

Isn't Einstein's general theory of relativity an attempt to remedy this problem with space-time.

hmm, but isn't space still axiomatic in general relativity even if we no longer assume it's Euclidean.

Oh well perhaps I was too rash, but still we really can't such else about space than what we observe of it.

 

[turin]

It's not the non-Euclidean feature (the curvature itself), but the dynamical feature (of the curvature), that has given me the impression of something substantial. I guess that, in a sense, I would say that the existence of space-time is axiomatic, but so is the existence of anything fundamental. In some ways, I agree that the description of a fundamental object does not offer any insight into what that object really is. But I also hold that this is the way of the entire science, and the best one can do in science is suppose that something happens to consist of a nontrivial arrangement of these fundamental objects. All this does is hide the issue of what a tree is by displaying hundreds of them in an invented arrangement that we happen to call a forrest.

 

[omin]

If you travel at the speed of light c (which matter can't but EM radiation does -in the vacuum-), you don't travel through space (or more accurately, space in front of you has shrinked to zero size).

Would space light up from distance objects of mass reflecting light no matter what speed you traveled in relation to them? Would these rays of light convey space?

 

[Gerinski]

When we say that space-time is curved (warps under the presence of matter), is it not licit to ask "where does it curve into ?".

I mean, in the classic analogy of euclidean geometry in 2 dimensions that becomes non-euclidean when the surface curves, it's clear that the 2-dimensional surface curves in a 3rd dimension (even if the surface itself stays 2-dimensional of course. Inhabitants could infere the existence of the 3rd dimension from the fact that their 2-dimensional universe is curved). Apparently "there must be a 3rd dimension for the 2-dimensional surface to curve on".

The fact that our 3-dimensional space curves, would it not imply that there must be a 4th spatial dimension for it to curve on ? (that we can not occupy but we can only infere its existence). Otherwise into what / where can it curve on ?

 

[jcsd]

When we say that space-time is curved (warps under the presence of matter), is it not licit to ask "where does it curve into ?".

I mean, in the classic analogy of euclidean geometry in 2 dimensions that becomes non-euclidean when the surface curves, it's clear that the 2-dimensional surface curves in a 3rd dimension (even if the surface itself stays 2-dimensional of course. Inhabitants could infere the existence of the 3rd dimension from the fact that their 2-dimensional universe is curved). Apparently "there must be a 3rd dimension for the 2-dimensional surface to curve on".

The fact that our 3-dimensional space curves, would it not imply that there must be a 4th spatial dimension for it to curve on ? (that we can not occupy but we can only infere its existence). Otherwise into what / where can it curve on ?

Actually no, it doesn't really make any sense to ask "where does it curve into?" as the tacit assumption of the question is that all geometry is somehow Euclidean/Minkowskian and there's no reason to believe this is so.

There does not need to be a 3rd dimension for a 2 dimensional surface to show intrinsic curvature, it's just what we take for granted from our everyday experince of inhabiting a 3 dimensional space that is very close to Euclidean.

Infact in gerneral relativity, though space is curved, spacetime is also curved

 

[Gerinski]

Would space light up from distance objects of mass reflecting light no matter what speed you traveled in relation to them? Would these rays of light convey space?

Sorry I didn't fully understand the question (and if I did I'm not expert enough to answer it!), but as far as I understand, light does not "convey space", I believe what we call space is only experienced by matter.

 

[turin]

Would space light up from distance objects of mass reflecting light no matter what speed you traveled in relation to them? Would these rays of light convey space?

Only if you travel below c wrt all the rest of the matter in space. At a speed c, all light rays from all the matter in front of and behind you arive and are experienced at the exact same time, indicating that they are all equidistant (that dimension is gone).

 

[robphy]

In terms of the said theory Special or General Theory, What is this thing called Space?

Naively, "[three-dimensional] space" is an instant of time.

Consider the case of Galilean Relativity ("Galilean Spacetime") or Special Relativity ("Minkowski Spacetime").
Given an observer and a given event on his worldline, "space [for that observer, at that instant]" is the set of all events that are simultaneous with that event.
In Galilean Relativity, it turns out that: all observers will agree on the set of events constituting space at that instant. In Special Relativity, of course, there is disagreement. This is the relativity of simultaneity.

This following picture is helpful. Imagine a cube [representing spacetime] and a vertical or slightly-tilted-off-vertical thread [representing the worldline of an inertial observer] running through that cube. Now imagine slicing up that cube into parallel slices [described below], each slice containing a point of that thread. [This is a "foliation".]

In Galilean relativity, those slices are horizontal slices, independent of the tilting of the thread. (Geometrically, those slices are [Galilean-]orthogonal to the thread.)
In special relativity, those slices are [Minkowski]-orthogonal to the thread, and do depend of the tilting of the thread. Pictorially speaking: when the thread is tilted by an angle Q to the right off the vertical, the slices are tilted by an angle Q up off the horizontal.

In general relativity, this notion is captured by the idea of a foliation of a spacetime manifold into "spacelike slices" (fancy form: "spacelike hypersurfaces").

(for some definitions, you might want to google the quoted phrases)

 

[Gerinski]

Actually no, it doesn't really make any sense to ask "where does it curve into?" as the tacit assumption of the question is that all geometry is somehow Euclidean/Minkowskian and there's no reason to believe this is so.

I get the point, sure there's no reason to believe that space(time) geometry should be euclidean/minkowskian, but shouldn't we expect that either it is or it is not? The strange thing is that it is neither yes or not, but it switches from yes (as it apperars when there's no matter around) to not (under the presence of matter).
Doesn't it seem even stranger to assume that geometry itself has no intrinsic property but is 'flexible' ? The only mechanism we know by which a euclidean behaviour can turn into non-euclidean is the existence of an additional space dimension, isn't it ? (besides the assumpion that the presence of matter is by itself another such mechanism).

 

[selfAdjoint]

The only mechanism we know by which a euclidean behaviour can turn into non-euclidean is the existence of an additional space dimension, isn't it ?

Not the only mechanism we know, just the only mechanism we can visualize. As to mechanisms, Einstein's field theory is a mechanism for curving spacetime! And it doesn't require any reference to an embedding space.

Once you get past three dimensions, visualization is no guide at all.