# Distance is undefined for "nothing"

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This is a digression of the "ontology" thread...

I think it is fair to say that you cannot have time without space and matter. Einstein said also, "People before me believed that if all the matter in the universe were removed, only space and time would exist. My theory proves that space and time would disappear along with matter"

Can anyone think of a philosophical reasoning that this wouldn't be true, specifically by describing some definition of distance that has meaning without the presence of matter?

How could you possibly measure (or express) distance of nothingness? Isn't 1m between nothing the same as a billion light years between nothing?

How can you measure distance without using matter? If you stick a tape measure in it, the matter of the tape measure defines distance. If you shine a light into it, you receive no information back (unless spacetime is closed). Is there any example of distance that is defined without requiring some form of matter at its extremities?

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You are on to something. I think your thinking is correct.

I just made a posting in the "What is space" thread started in 94. What I said there is what I will say here to you and I think not different from what you assert. Space can properly be defined as the volume that matter occupies. Linear space can be defined as the distance between matter, where matter is the yardstick. As Rene Descartes put it, space is an extension of matter.

"People before me believed that if all the matter in the universe were removed, only space and time would exist. My theory proves that space and time would disappear along with matter" Einstein. Einstein had a lot of great quotes and this is one of them. What would be the meaning of space or time without matter. Space requires extension and time is simply an interval of change in matter. Any other meanings for either seemingly would make no sense.

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This is a digression of the "ontology" thread...

Can anyone think of a philosophical reasoning that this wouldn't be true, specifically by describing some definition of distance that has meaning without the presence of matter?

How could you possibly measure (or express) distance of nothingness? Isn't 1m between nothing the same as a billion light years between nothing?

How can you measure distance without using matter? If you stick a tape measure in it, the matter of the tape measure defines distance. If you shine a light into it, you receive no information back (unless spacetime is closed). Is there any example of distance that is defined without requiring some form of matter at its extremities?

You could define space as: that which is confined within some arbitrary co-ordinates ie it's observer-dependent.

If something has the potential to be occupied and therefore measured, it exists. Nothing, by it's very definition, can't be measured as it doesn't exist but it's one of those words that has a meaning very much dependent on context. For the sake of discussive clarity I don't think Space and Nothing should be seen as synonymous...they are two totally different concepts...one exists and the other doesn't.

To summarise:

Space is that which is not occupied and Nothing is that idea which suggests an absent of all things. IMO.

Edited by StringJunky
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Distance can be defined abstractly, so that the distance between imaginary points is still defined, and this doesn't depend on what space is defined as (because we can always (maybe???) define an abstract space as well that is infinite and covers any "nothing" we want to consider).

It seems that if space is flat (infinite) and homogeneous and isotropic then an abstract definition of distance would match a real definition of distance?

Then, even if we couldn't measure distance in nothing without putting something into it, we could extrapolate it. This relies on the assumption that spacetime curvature is homogeneous to an infinite distance in any direction, which kinda implies that infinite distance is defined. I'm confusing myself now, but there must be something in this statement. Matter causes spacetime curvature at a distance. That curvature can be measured or extrapolated. Or is spacetime curvature the same as distance, and could be argued to have no meaning except between given reference points?

Without figuring out the meaning of nothingness or space, I would guess that the calculable effect of spacetime curvature caused by mass would allow for a definition of distance, and this curvature is defined within the light cone of that mass.

So I think that on the "real" end of the spectrum, distance is measurable between points of matter,

and on the "abstract" end of the spectrum, distance is defined abstractly in an infinite flat geometric space,

and somewhere in between, there is spacetime, which is defined only within the union of all light cones of all matter, and that distance is defined throughout and only throughout all of spacetime. But then, I don't know whether or not nothing would be defined to be exclusive to spacetime, or within spacetime, or both.

I think you would have to allow nothing within spacetime, or spacetime would have to be considered "something" and there's no good reason to do that.

Alright I've talked myself in circles but it comes back to the original idea: Even if distance is only defined between things, doesn't all matter "radiate information" (for example in the form of gravity waves) that define distance within that matter's light cone, all around it? Or does information only exist if it causes an effect -- only if there is something out there to receive it?

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Md65536,

".....It seems that if space is flat (infinite) and homogeneous and isotropic then an abstract definition of distance would match a real definition of distance?

Then, even if we couldn't measure distance in nothing without putting something into it, we could extrapolate it. This relies on the assumption that spacetime curvature is homogeneous to an infinite distance in any direction, which kinda implies that infinite distance is defined. I'm confusing myself now, but there must be something in this statement. Matter causes spacetime curvature at a distance. That curvature can be measured or extrapolated. Or is spacetime curvature the same as distance, and could be argued to have no meaning except between given reference points?

Without figuring out the meaning of nothingness or space, I would guess that the calculable effect of spacetime curvature caused by mass would allow for a definition of distance, and this curvature is defined within the light cone of that mass......"

IMHO you are definitely thinking logically concerning these quotes.

your quotes: "...I'm confusing myself now..." ..."I've talked myself in circles.."

The problem you are confronting I believe is. If space is totally flat (or spacetime if you prefer) then it does not warp; there is is a contradiction. Einstein proposed that space "warps" (bends) but based upon the Hubble space telescope, space appears to be flat. Most of those who continue to adhere to the warped space concept believe that in the grand scheme and outside the observable universe, that there is a curve (a small angle of warp) to the universe that we presently cannot observe. This is required by General Relativity (GR) based upon Einstein's explanation for using Riemann geometry in his equations. It could also be that his equations are right or partly right but that space does not warp or bend.

You also mentioned gravity waves. Of course it has not been proven that gravity waves exist but there is evidence that they might, and a Nobel Prize given for the evidence to suggest them. If they exist then, the question becomes, "what do they do." Some think that they are the cause of gravity but in GR, gravity is caused by warped space. Others including myself believe that gravity waves are simply waves produced by very massive objects and are unrelated to gravitational effects. They are more like De Broglie waves IMO.

So my point is that if you take warped space out of your thinking then it will make more sense to you IMO, at least as far as this thread is concerned. Another point concerns your idea of infinite space. If space is defined by matter as in the BB model or other finite universe models and Einstein (according to his quote in the O.P.), then space is not infinite by definition.

You could define space as: that which is confined within some arbitrary co-ordinates ie it's observer-dependent.

If something has the potential to be occupied and therefore measured, it exists. Nothing, by it's very definition, can't be measured as it doesn't exist but it's one of those words that has a meaning very much dependent on context. For the sake of discussive clarity I don't think Space and Nothing should be seen as synonymous...they are two totally different concepts...one exists and the other doesn't.

To summarise:

Space is that which is not occupied and Nothing is that idea which suggests an absent of all things. IMO.

I agree.

Edited by pantheory
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The problem you are confronting I believe is. If space is totally flat (or spacetime if you prefer) then it does not warp; there is is a contradiction.

[...]

You also mentioned gravity waves. Of course it has not been proven that gravity waves exist but there is evidence that they might, and a Nobel Prize given for the evidence to suggest them. If they exist then, the question becomes, "what do they do." Some think that they are the cause of gravity but in GR, gravity is caused by warped space. Others including myself believe that gravity waves are simply waves produced by very massive objects and are unrelated to gravitational effects. They are more like De Broglie waves IMO.

Well, my reasoning is as follows:

- Distance seems to be defined between any 2 points in space.

- Distance also seems to be defined "around" matter, since mass curves spacetime. But to what extent? There seems to be no intrinsic limit based only on length (distance from the mass). I don't have a firm handle on curvature but I think curvature due to mass approaches 0 (flat) as distance approaches infinity, but it is still non-zero at any arbitrary distance???

- However, there is an intrinsic limit to distance based on time. A mass cannot have any effect on anything outside its light cone, ie. no information can travel faster than c. This is the law of causality. To me it means that a mass cannot define the curvature of space at a distance farther than where light (or eg. gravity waves) could be able to travel in the time that the mass has been around. In other words, space could not be defined farther than c * age of the universe away from any matter (even if inflation allows the matter to escape other matter's "causal horizon", which might allow for "gaps in space").

That spacetime warps (consistent with SR and GR) is a fact of reality that I accept. The universe appears (to the limit of our measurement) to be flat*; these are not mutually inconsistent statements. I don't understand it enough to say why.

If there is infinite matter in the universe (which I don't believe is true) and it's evenly distributed, then distance would be defined to infinity in any direction.

* Admittedly, this is pretty meaningless, because it's like saying "To the limit of my vision, the Earth appears to be flat."

Another point concerns your idea of infinite space. If space is defined by matter as in the BB model or other finite universe models and Einstein (according to his quote in the O.P.), then space is not infinite by definition.

I agree.

I believe that there's a finite amount of mass, all within some distance (related to the big bang), and that spacetime and distance is not defined beyond some limit (the union of all causal horizons of all matter and energy in the universe, I guess), and that spacetime is probably flat instead of closed. I don't think that all these beliefs are mutually consistent, and I'm missing some understanding of the meaning or implications of curvature, or mixing up the meanings of a flat universe and flat spacetime.

Edited by md65536
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Md65536,

"I don't have a firm handle on curvature but I think curvature due to mass approaches 0 (flat) as distance approaches infinity, but it is still non-zero at any arbitrary distance???"

Yeah, that sounds right to me according to the warped space model, that matter warps the space surrounding it and is the cause of gravity.

" ... there is an intrinsic limit to distance based on time (concerning gravity). A mass cannot have any effect on anything outside its light cone."

This is also valid but indirectly there is a gravitational effect of everything on everything else. The idea is that although it is outside your light cone now, for instance, it does and did effect its neighbors, which effected its neighbors, and so on, all the way back to you. If something is outside your light cone but could somehow disappear, then according to GR it could never effect you because its effects could not travel faster than the speed of light.

"That spacetime warps (consistent with SR and GR) is a fact of reality that I accept."

The warping of space (space-time) is unrelated to SR which says nothing about this. It is strictly a GR proposal. But of course the concept does not violate SR.

"...I don't think that all these beliefs are mutually consistent, and I'm missing some understanding of the meaning or implications of curvature..."

As to the meaning of flat space: it is what we see in the everyday world. It's the way other animals see the world. It is simply a three dimensional structure of reality which is the natural way that it appears to be to the unaided eye. It was the reality of physics up until Einstein proposed it differently. Remember, there is no evidence of any kind that I know of, that space is curved.

There is evidential support that gravity works in a non-linear fashion, not strictly according to the inverse square law of Newton. As to curved space: In Riemann geometry which is the geometry of GR, two parallel lines can eventually cross. There is no forth dimension involved (other than time) so that it is a type of non-linear geometry which Riemann said did not apply to the natural world, yet Einstein found an application of it in the equations of GR, whether right or wrong. If space is entirely flat at the largest scales of the universe, then at least the warped space/ curved space idea of Einstein is wrong. All observations so far seem to indicate that at least the observable universe appears to be flat.

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You could define space as: that which is confined within some arbitrary co-ordinates ie it's observer-dependent.

It should be more like observer independent. One has coordinate transformations to take care of this.

Classical spaces exist independent of the coordinates as a collection of points and a topology.

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Eek, I thought I lost a posting. But no, my mistake.

Edited by pantheory
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It should be more like observer independent. One has coordinate transformations to take care of this.

Classical spaces exist independent of the coordinates as a collection of points and a topology.

You are taking it here a different way and to a higher level to that which I intended. I just meant in simple terms of a space, the volume and position of which can be observer defined; expressed as some co-ordinates ie the observer chooses what the size and position of the space is.

I was trying to come up with a simple and broad definition of 'space'.

It's good to read your more qualified take on it though because I want to learn and understand the convention.

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I was trying to come up with a simple and broad definition of 'space'.

That is quite a deep subject in reality. One approach is basically as something that has "coordinates", in a rather general sense. One can lose the notion of a point almost completely in this way.

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I must conclude that my initial idea was wrong.

We can define space in such a way that it is defined for nothing, simply by having the definition not depend on things like matter.

More practically, we can consider distance in terms of curvature, and discuss what curvature is like away from matter.

I think that GR might not define curvature in the absence of all matter, but it does define curvature remote from matter, to any distance (since spacetime is homogeneous). ?

I still "believe" that spacetime might not be homogeneous and there is some way to express some kind of curvature where distance "ends" or something, but this belief is based on ignorance.

But I think there may be some insights into the topic in the question of "How would you measure a distance of nothing without sticking any matter into it?"

(I think it's an interesting question, because if space curves due to matter, then measuring it with matter changes it, and then the real answer might be the answer to another question: "Do we assume that measuring space changes it very little, due to assumptions, or due to extrapolation?")

So back to the question of how might we measure distance where there is no matter?

If you beam photons into it, you will never get information back from them?

Is there a way to beam energy into a void, and have it change direction without interacting with anything? Perhaps you can have something photon-like that decays into other photon-like energy that is emitted in different directions, at least one of which can be intercepted? Or perhaps shooting 2 converging beams into nothingness... would you be able to detect information from the point of convergence?

And is putting energy into nothing the same as putting matter into it?

Edited by md65536
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I think that GR might not define curvature in the absence of all matter, but it does define curvature remote from matter, to any distance (since spacetime is homogeneous). ?

What about dS and AdS space? These are vacuum solutions of the Einstein field equations with an non-zero cosmological constant without any reference to matter at all. These spaces have constant curvature as defined in differential geometry.

The Schwarzschild solution is itself a vacuum solution and describes the space-time around a star. It is a bit like the electric field around a point charge, you have a source of the field. So this you say "includes matter" as the "total space-time" requires a smooth matching of the interior stellar solution and the exterior vacuum one.

In a practical astronomy one would observe the light rays to deduce the curvature of the space-time. For instance via gravitational lensing. Without some kind of test particle I cannot imagine how one could examine space-time. The same goes for electromagnetic fields, you need to throw in some small charges to observe the force.

Edited by ajb
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StringJunky, on 19 June 2011 - 01:01 AM, said:

I was trying to come up with a simple and broad definition of 'space'.

This is my idea of the proper definition of space.

I agree with those theorists who assert that both time and space were created from the beginning of the universe, and that there is no such thing as before that. In the same way the meaning of space could be defined as the volume that is occupied by the field (ZPF), which can include matter within its extension. Distance can be defined as a two dimensional extension of space which can be defined as a distance between points within a field which might include matter. This I think explains the question. Space extends as far as the field extends and not beyond. Similarly as Decarte proposed, space is an extension of matter, or you might say matter and field. Hypothetical space vacant of field or matter I believe is only imaginary or science fiction. At such a boundary space would end and the potential for extending space would begin.

.

Edited by pantheory
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This is a digression of the "ontology" thread...

Can anyone think of a philosophical reasoning that this wouldn't be true, specifically by describing some definition of distance that has meaning without the presence of matter?

How could you possibly measure (or express) distance of nothingness? Isn't 1m between nothing the same as a billion light years between nothing?

How can you measure distance without using matter? If you stick a tape measure in it, the matter of the tape measure defines distance. If you shine a light into it, you receive no information back (unless spacetime is closed). Is there any example of distance that is defined without requiring some form of matter at its extremities?

Philsophically, It seems reasonable that virtual particles should be able to exist in a virtual distance within a vitual time frame.

I actually think about these kinds of things way to much, but I'm no expert.

Still, here's my thoughts on the subject for what ever they're worth:

Let's say your observing an electron quantum jumping around in it's field of probability. And let's say you measure the distance and the time between one appearence, and a next. The measurement you take is only relative to your own distance and time frame reference within your own space/scale model. From the electron's point of view it was probably you, and the atom's nucleous that you were observing, that moved. Within it's space/scale model you and the atom's nucleous are vibrating while it's just sitting still, there at home in it's own infinte space/scale feild.

Both you and the atom's nucleous is affected by the momentum of the expanding universe. Things with mass vibrate and they vibrate according the lattice work of the vibrational frequencies that defined the notes and octives of our reality. The periodic table of elements. The electron has no mass. Therefore the so called "sphere of electron probability" is actually the sphere of atomic nuclei probability. Everything in the universe is in perfect logical and geomtrical position all the time, but the universe is expanding and the expansion is not always one of perfect symetry. Wherefore perfect position must be defined and redefined instant to instant. So where the x,y, and z, axis' intersect in three dimensional space there is imperfection on very small scales. This leads to the harmonic vibrations of things that occupy and exist in it's field ie. mass.

So, if you had a glass jar and sucked all the air and everything out of it until there was nothing in it at all, you would more than likely be able to encounter a pocket of vacuum energy. And let's say find two pockets at the same time. You could measure the distance of the two pockets on the outside of the glass and say they were this distance apart. but relative to the inside of the glass they were both everywhere and nowhere at the same time, or perhaps, to that which is relative in their own frame of virtual space/distance/time.

Edited by 36grit
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This is a digression of the "ontology" thread...

I think it is fair to say that you cannot have time without space and matter. Einstein said also, "People before me believed that if all the matter in the universe were removed, only space and time would exist. My theory proves that space and time would disappear along with matter"

Can anyone think of a philosophical reasoning that this wouldn't be true, specifically by describing some definition of distance that has meaning without the presence of matter?

Here is where I pulled that quote. I think it explains the context of his reasoning.

Einstein's resolution

In 1915, Einstein realized that the hole argument makes an assumption about the nature of spacetime: it presumes that the gravitational field as a function of the coordinate labels is physically meaningful by itself. By dropping this assumption general covariance became compatible with determinism, but now the gravitational field is only physically meaningful to the extent that it alters the trajectories of material particles. While two fields that differ by a coordinate transformation look different mathematically, after the trajectories of all the particles are relabeled in the new coordinates, their interactions are manifestly unchanged. This was the first clear statement of the principle of gauge invariance in physical law.

Einstein believed that the hole argument implies that the only meaningful definition of location and time is through matter. A point in spacetime is meaningless in itself, because the label which one gives to such a point is undetermined. Spacetime points only acquire their physical significance because matter is moving through them. In his words:

"All our spacetime verifications invariably amount to a determination of spacetime coincidences. If, for example, events consisted merely in the motion of material points, then ultimately nothing would be observable but the meeting of two or more of these points." (Einstein, 1916, p.117)

He considered this the deepest insight of general relativity. When asked by reporters to summarize his theory, he said:

"People before me believed that if all the matter in the universe were removed, only space and time would exist. My theory proves that space and time would disappear along with matter."

If coordinates are not real but just an arbitrary means of labeling matter... then without matter there really would be nothing left.

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Here is where I pulled that quote. I think it explains the context of his reasoning.

If coordinates are not real but just an arbitrary means of labeling matter... then without matter there really would be nothing left.

Thanks. A lot of that is beyond my understanding, but it seems to clear things up, for me.

What I gleaned from it: Distance is meaningless or undetermined (not undefined) for "nothing".

You can define distance with respect to nothing, but you can do so in many different ways, each equally valid with nothing to determine the metric.

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I think that the important thing is to define nothing as something relative to humans. What we call nothing could be something to another entity other than a human.Therefore time would exist for a different entity, which would then lead to our Universe existing.

Edited by Pincho Paxton

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