Is Space-Time a Physical Entity or a Mathematical Model?

[swansont]

So ,to use my terminology the "modeled" is not so much a thing as a set of events of differing properties?

 

Can we talk of an event having a property?

 

If not what do "Position, speed, acceleration, energy, momentum" describe?

 

Relationships between events?

 

 

They describe whatever is being observed. A rock, for example. It could be a rock striking another rock — you would consider some or all of those observables, and other measurable properties, like mass.

[Tim88]

As far as I know there are some Physicists who consider Space-Time to be an actual physical thing whereas others regard it as merely an abstract concept - Brian Greene expressed his belief that the results from Gravity Probe B confirm this. What is the general consensus of this?

 

I came late to this thread; but after scrolling through it, it turns out that there is still some more that can be added.

 

The general consensus among physicists is perhaps "shut up and calculate"; the discussion has been redirected to philosophy journals.

 

Nevertheless there are strong arguments that the "vacuum" is more than just emptiness.

At first SR and GR were interpreted as relating to a physical space (a relativistic ether), as argued first by Langevin, based on SR [1] and next by Einstein, based on GR [2]. And although Einstein originally considered Minkowski spacetime as nothing more than a mathematical model to describe phenomena [3], it appears that he later adopted Minkowski's concept of a block universe [4].

 

I think that there is convincing evidence for either physical space or physical spacetime; there seems to be no reasonable alternative to one of those two concepts [edit: although it is always possible that someone will come up with another alternative].

It should be realized that these two physical models or interpretations correspond to very different, even opposing views of time: the one implies presentism, the other suggests eternalism. The choice of which model one prefers depends on what one thinks makes most sense.

 

 

[1] p.47 of https://en.wikisource.org/wiki/Translation:The_Evolution_of_Space_and_Time

[2] https://en.wikisource.org/wiki/Ether_and_the_Theory_of_Relativity

[3] https://en.wikisource.org/wiki/Relativity:_The_Special_and_General_Theory/Part_I#Section_17_-_Minkowski.27s_Four-Dimensional_Space

[4] http://quotingeinstein.blogspot.ch/2013/06/einstein-and-michele-besso.html

Edited September 12, 2016 by Tim88

[swansont]

The vacuum and spacetime are concepts that are distinct from each other.

[Tim88]

The vacuum and spacetime are concepts that are distinct from each other.

 

Yes, exactly.

[Memammal]

It should be realized that these two physical models or interpretations correspond to very different, even opposing views of time: the one implies presentism, the other suggests eternalism. The choice of which model one prefers depends on what one thinks makes most sense.

For information:

In a scientific paper entitled “Is there An Alternative To The Block Universe View?” Vesselin Petkov shows that the eternal block universe view, regarding the universe as a timelessly existing four-dimensional world, is the only one that is consistent with special relativity. The paper concludes: In this sense special relativity alone appears to provide a definite proof of the block universe view. One may argue that the arguments discussed here are insufficient for rejecting the presentist view since those arguments demonstrated that presentism contradicts only special relativity, not the other established theories (quantum mechanics, for instance). Such a position could hardly be defended because if a view contradicts the experimental evidence it is definitely wrong. There is just one way to prove that the presentist view does not contradict the relativistic effects – to demonstrate that the experiments which confirm the kinematic consequences of special relativity can be explained if it is assumed that the world is three-dimensional.

[studiot]

For information:

In a scientific paper entitled “Is there An Alternative To The Block Universe View?” Vesselin Petkov shows that the eternal block universe view, regarding the universe as a timelessly existing four-dimensional world, is the only one that is consistent with special relativity. The paper concludes: In this sense special relativity alone appears to provide a definite proof of the block universe view. One may argue that the arguments discussed here are insufficient for rejecting the presentist view since those arguments demonstrated that presentism contradicts only special relativity, not the other established theories (quantum mechanics, for instance). Such a position could hardly be defended because if a view contradicts the experimental evidence it is definitely wrong. There is just one way to prove that the presentist view does not contradict the relativistic effects – to demonstrate that the experiments which confirm the kinematic consequences of special relativity can be explained if it is assumed that the world is three-dimensional.

 

Another good reference is a refutation by John Polkinghorne

 

'On Space and Time' page 279

 

The book oS&T is a recent collection of papers from several famous physicists and mathematicians, published by Cambridge University Press.

[Tim88]

For information:

In a scientific paper entitled “Is there An Alternative To The Block Universe View?” Vesselin Petkov shows that the eternal block universe view, regarding the universe as a timelessly existing four-dimensional world, is the only one that is consistent with special relativity. The paper concludes: In this sense special relativity alone appears to provide a definite proof of the block universe view. One may argue that the arguments discussed here are insufficient for rejecting the presentist view since those arguments demonstrated that presentism contradicts only special relativity, not the other established theories (quantum mechanics, for instance). Such a position could hardly be defended because if a view contradicts the experimental evidence it is definitely wrong. There is just one way to prove that the presentist view does not contradict the relativistic effects – to demonstrate that the experiments which confirm the kinematic consequences of special relativity can be explained if it is assumed that the world is three-dimensional.

Do you use Google or DuckDuckGo? I read that paper a week ago as I was looking for the technical terms about concepts of time. It is useful for understanding how very different "space" and "spacetime" concepts are, and I found there the term "presentism" that I was looking for, and which I also mentioned here.

 

Apart of that, it seems that Petkov understands the block universe concept which he advocates - but regretfully, he has not understood a thing of what Langevin and Einstein explained. Was that paper peer reviewed?

 

[edit:] as a matter of fact, anyone who knows SR and the history of SR, also knows that his conclusion is definitely wrong.

 

 

Another good reference is a refutation by John Polkinghorne

 

'On Space and Time' page 279

 

The book oS&T is a recent collection of papers from several famous physicists and mathematicians, published by Cambridge University Press.

 

Difficult to access, perhaps you can summarize?

It will be similarly interesting to read the refutations of the block universe which incited Petkov to write his paper.

Edited September 13, 2016 by Tim88

[Memammal]

@ Tim88: Let me quote that same paragraph from your previous post again:

I think that there is convincing evidence for either physical space or physical spacetime; there seems to be no reasonable alternative to one of those two concepts [edit: although it is always possible that someone will come up with another alternative].

It should be realized that these two physical models or interpretations correspond to very different, even opposing views of time: the one implies presentism, the other suggests eternalism. The choice of which model one prefers depends on what one thinks makes most sense.

 

First of all this entire thread so far has been dealing with the question about whether there is an actual, physical, tangible space-time. Are you implying that there is convincing evidence that space-time is "tangible"? Secondly the reason why I provided the quote from the Petkov paper was to point towards your very last sentence that I quoted above. You gave the impression that the choice between eternalism and presentism is based on personal preference (what makes the most sense to any individual). Surely that cannot be right..? Petkov (among others) argued against presentism...and so does this paper:

 

Relativity of Simultaneity and Eternalism: In Defense of the Block Universe

Abstract: Ever since Hermann Minkowski’s now infamous comments in 1908 concerning the proper way to view space-time, the debate has raged as to whether or not the universe should be viewed as a four-dimensional, unified whole wherein the past, present, and future are regarded as equally real or whether the views espoused by the possibilists, historicists, and presentists regarding the unreality of the future (and, for presentists, the past) are more accurate. Now, a century after Minkowski’s proposed block universe first sparked debate, we present a new, more conclusive argument in favor of the eternalism. Utilizing an argument based on the relativity of simultaneity in the tradition of Putnam and Rietdijk and explicit novel but reasonable assumptions as to the nature of reality, we argue that the past, present, and future should be treated as equally real, thus ruling that presentism and other theories of time that bestow special ontological status to the past, present, or future are untenable. Finally, we respond to our critics who suggest that: (1) there is no metaphysical difference between the positions of eternalism and presentism, (2) the present must be defined as the “here” as well as the “now”, or (3) presentism is correct and physicists’ current understanding of relativity is incomplete because it does not incorporate a preferred frame. We call response 1 deflationary since it purports to dissolve or deconstruct the age-old debate between the two views and response 2 compatibilist because it does nothing to alter special relativity (SR), arguing instead that SR unadorned has the resources to save presentism. Response 3 we will call incompatibilist because it adorns SR in some way in order to save presentism a la some sort of preferred frame. We show that neither 1 nor 2 can save presentism and 3 is not well motivated at this juncture except as an ad hoc device to refute eternalism.

 

PS. But perhaps we should first consider whether discussing the merits of eternalism vs presentism will add value to the topic under discussion..?

Edited September 14, 2016 by Memammal

[Tim88]

@ Tim88: Let me quote that same paragraph from your previous post again:

 

First of all this entire thread so far has been dealing with the question about whether there is an actual, physical, tangible space-time. Are you implying that there is convincing evidence that space-time is "tangible"? Secondly the reason why I provided the quote from the Petkov paper was to point towards your very last sentence that I quoted above. You gave the impression that the choice between eternalism and presentism is based on personal preference (what makes the most sense to any individual). Surely that cannot be right..?

 

I'm not sure what you mean with "tangible"... I agree with the physical arguments by Langevin and Einstein in the references I gave.

 

Those arguments support the existence of the Lorentz ether which originally served, together with the relativity postulate, as the basis on which the Lorentz transformations were derived (note that that simple fact debunks Petkov, except if the derivations of SR by both Lorentz and Einstein were faulty). For a somewhat inaccurate discussion see https://en.wikipedia.org/wiki/History_of_Lorentz_transformations

 

Einstein explained how GR has more need for it than SR, and he enhanced the properties of the Lorentz ether accordingly. However, those arguments can just as well be used in favour of Minkowski's block universe concept (which was similarly enhanced for GR), so that there is a choice of at least two physical models that have not been disproved by measurements.

Petkov (among others) argued against presentism...and so does this paper:

 

Relativity of Simultaneity and Eternalism: In Defense of the Block Universe

Abstract: Ever since Hermann Minkowski’s now infamous comments in 1908 concerning the proper way to view space-time, the debate has raged as to whether or not the universe should be viewed as a four-dimensional, unified whole wherein the past, present, and future are regarded as equally real or whether the views espoused by the possibilists, historicists, and presentists regarding the unreality of the future (and, for presentists, the past) are more accurate. Now, a century after Minkowski’s proposed block universe first sparked debate, we present a new, more conclusive argument in favor of the eternalism. Utilizing an argument based on the relativity of simultaneity in the tradition of Putnam and Rietdijk and explicit novel but reasonable assumptions as to the nature of reality, we argue that the past, present, and future should be treated as equally real, thus ruling that presentism and other theories of time that bestow special ontological status to the past, present, or future are untenable. [..]

 

PS. But perhaps we should first consider whether discussing the merits of eternalism vs presentism will add value to the topic under discussion..?

 

I think that it can be useful and interesting to discuss arguments for and against both concepts, as well as other issues such as what block universe implies about time as physically different from length, or not.

 

But before that, it would be appropriate, I think, to first consider the arguments that SR and GR (and perhaps QFT) imply something more than only mathematical space, in other words, the arguments that physical space (and by extension, spacetime) must contain more than nothingness. It seems to me that that main point of this thread has not yet sufficiently been addressed here.

Only if several of us think that space or space-time implies more than math, is it useful to consider if we should next distinguish between space and time as substantial entities or as a single physical entity (if those are the right terms!), and in what way.

Edited September 14, 2016 by Tim88

[Memammal]

I suggest that the presentism vs eternalism part of the discussion be moved to another similar thread: http://www.scienceforums.net/topic/97604-is-a-deterministic-universe-as-profoundly-counter-intuitive-for-you-too/

 

I am not too sure about the protocol for doing this...may I proceed copying the relevant parts of the posts from this thread to the other, should the OP first OK it, or should the moderators do it?

[Tim88]

I suggest that the presentism vs eternalism part of the discussion be moved to another similar thread: http://www.scienceforums.net/topic/97604-is-a-deterministic-universe-as-profoundly-counter-intuitive-for-you-too/

 

I am not too sure about the protocol for doing this...may I proceed copying the relevant parts of the posts from this thread to the other, should the OP first OK it, or should the moderators do it?

 

I don't think so, a deterministic universe is in my opinion a totally different topic, as a 3D universe can be deterministic.

 

PS. It may be useful to spin the discussion about the space vs spacetime debate off to a dedicated thread though.

Edited September 16, 2016 by Tim88

[Tim88]

 

I came late to this thread; but after scrolling through it, it turns out that there is still some more that can be added.

 

The general consensus among physicists is perhaps "shut up and calculate"; the discussion has been redirected to philosophy journals.

 

Nevertheless there are strong arguments that the "vacuum" is more than just emptiness.

At first SR and GR were interpreted as relating to a physical space (a relativistic ether), as argued first by Langevin, based on SR [1] and next by Einstein, based on GR [2]. And although Einstein originally considered Minkowski spacetime as nothing more than a mathematical model to describe phenomena [3], it appears that he later adopted Minkowski's concept of a block universe [4].

 

I think that there is convincing evidence for either physical space or physical spacetime; there seems to be no reasonable alternative to one of those two concepts [edit: although it is always possible that someone will come up with another alternative].

It should be realized that these two physical models or interpretations correspond to very different, even opposing views of time: the one implies presentism, the other suggests eternalism. The choice of which model one prefers depends on what one thinks makes most sense.

 

 

[1] p.47 of https://en.wikisource.org/wiki/Translation:The_Evolution_of_Space_and_Time

[2] https://en.wikisource.org/wiki/Ether_and_the_Theory_of_Relativity

[3] https://en.wikisource.org/wiki/Relativity:_The_Special_and_General_Theory/Part_I#Section_17_-_Minkowski.27s_Four-Dimensional_Space

[4] http://quotingeinstein.blogspot.ch/2013/06/einstein-and-michele-besso.html

 

Is there anyone here who wants to argue that there is only mathematical space-time, and thus argue against the presented arguments that space or space-time should be "substantial", or at least, contain something physical?

[koti]

 

Is there anyone here who wants to argue that there is only mathematical space-time, and thus argue against the presented arguments that space or space-time should be "substantial", or at least, contain something physical?

The whole discussion here is people arguing about that very issue. I agree with you on the your view that space-time should be "substancial" but undortunately it doesnt seem that easy to prove that and eliminate that "should be"

[Tim88]

The whole discussion here is people arguing about that very issue. I agree with you on the your view that space-time should be "substancial" but undortunately it doesnt seem that easy to prove that and eliminate that "should be"

 

I didn't express my opinion about the debate opposing physical space to physical space-time; but in my opinion the conclusion that there's more than just mathematical space-time is about as provable as the physical existence of for example magnetic fields. I guess that such fields are considered part of modern physics because they play a clearly identified, active role in equations.

 

I'm curious to hear what counterarguments exist against the presented arguments. Although I don't follow all of Einstein's reasoning, and he mixes up his own reasoning with that of others, I think that he gives a good overview. If we go through the list that Einstein presented, https://en.wikisource.org/wiki/Ether_and_the_Theory_of_Relativity

 

1. He starts with gravity's action at a distance, which we know to be not immediate. This implies that far away from the original cause, locally an influence acts on objects. For such a local action to occur, something physical must be "there".

However I would counter that one usually describes that as a gravitational field which can be imagined as something physical in itself, and not, as "field" originally meant, a property of space.

 

2. Next he gets to the topic of light propagation. In a nutshell, the second postulate is based on ether theory: the speed of light in vacuum is a constant, independent of the motion of the source (and also independent of the motion of the detector). And it seems to me that my counter argument about self existing fields does not apply for this case: far away from heavy masses the speed of light is effectively the same as very far from heavy masses. If I'm not mistaken, the argument that maybe the gravitational fields of far away stars impose the speed of light in interstellar space is not compatible with GR, and probably also not with observation.

Thus I consider light propagation the first strong argument in the list for the conclusion that physical space itself has properties. Is there any other plausible explanation?

[Tim88]

 

I didn't express my opinion about the debate opposing physical space to physical space-time; but in my opinion the conclusion that there's more than just mathematical space-time is about as provable as the physical existence of for example magnetic fields. I guess that such fields are considered part of modern physics because they play a clearly identified, active role in equations.

 

I'm curious to hear what counterarguments exist against the presented arguments. Although I don't follow all of Einstein's reasoning, and he mixes up his own reasoning with that of others, I think that he gives a good overview. If we go through the list that Einstein presented, https://en.wikisource.org/wiki/Ether_and_the_Theory_of_Relativity

 

1. He starts with gravity's action at a distance, which we know to be not immediate. This implies that far away from the original cause, locally an influence acts on objects. For such a local action to occur, something physical must be "there".

However I would counter that one usually describes that as a gravitational field which can be imagined as something physical in itself, and not, as "field" originally meant, a property of space.

 

2. Next he gets to the topic of light propagation. In a nutshell, the second postulate is based on ether theory: the speed of light in vacuum is a constant, independent of the motion of the source (and also independent of the motion of the detector). And it seems to me that my counter argument about self existing fields does not apply for this case: far away from heavy masses the speed of light is effectively the same as very far from heavy masses. If I'm not mistaken, the argument that maybe the gravitational fields of far away stars impose the speed of light in interstellar space is not compatible with GR, and probably also not with observation.

Thus I consider light propagation the first strong argument in the list for the conclusion that physical space itself has properties. Is there any other plausible explanation?

 

I do think that the topic of this thread is a matter of contention, so that I'm surprised to hear no counter arguments!

 

By way illustration, we can think of a road with a strongly enforced speed limit. We see the cars on that road passing at varying speed, but (ideally) none surpassing a certain speed. Effectively that speed is not a property of the cars, but of the road.

Similarly there is good reason to regard the maximum speed in nature c as a property, not of particles and radiation, but of the space through which they pass.

 

For latecomers to this thread I'll now complete the list.

 

3. Einstein next discusses the fact that rotation affects the mechanical properties of rotating objects; again one should conclude that this is a characteristic, not of the object, but of the space in which it rotates - as Newton did. He omits there the reference to Newton's illustration (or experiment), which I'll add here for those who are not familiar with it: https://en.wikipedia.org/wiki/Bucket_argument#The_argument

Then Einstein goes on to refer to Mach, as he included (somewhat) Mach's principle in GR; and Mach intended a purely relational theory, in which rotation is purely relative. However, in GR the effect of distant stars acts locally and not instantly at a distance; thus one arrives again at the concept of an ether. However, this GR ether is itself conditioned by masses.

 

I also referred to Langevin:

 

4. First he mentioned the fact that acceleration is responsible for the creation of electromagnetic waves; if there is no physical space that corresponds to mathematical space, then there is nothing with respect to which such waves can be created.

I can think of for example Brehmstrahlung as a good example.

 

5. As we know, the clock retardation in Langevin's "twin" example is absolute; it is a function of relative velocity, caused by the changes in velocity due to the non-inertial motion of the traveler. Thus he argued that in order to make physical sense of it, we should admit that these velocity changes must be happening with respect to something physical (the "ether").

 

I consider all of these good arguments for the claim that spacetime implies more than only mathematical space.

 

However, probably most participants will agree with that generic conclusion, and the main contention is then what feasible physical interpretations are available. The main contenders that I know are the Lorentz ether (as enhanced by GR) and Minkowski block universe (again as enhanced by GR). The title of this thread doesn't give visibility to that subtopic, so I will later start the discussion of that topic in its own thread.

[Tim88]

[..] probably most participants will agree with that generic conclusion, and the main contention is then what feasible physical interpretations are available. The main contenders that I know are the Lorentz ether (as enhanced by GR) and Minkowski block universe (again as enhanced by GR). The title of this thread doesn't give visibility to that subtopic, so I will later start the discussion of that topic in its own thread.

 

I now started that spin-off topic here:

http://www.scienceforums.net/topic/98845-models-for-making-sense-of-relativity-physical-space-vs-physical-spacetime/

[Logic and Theory]

Hello.

 

I have recently opened a post that touches on this topic."The existence of tangible space". I was pro aether, however, after a period of research and reflection I have come to agree with GR.

 

Space does not need to be made of a tangible measurable substance or anti substance. We live in a 3 dimensional reality. we. have the length, highth, and depth of things to measure. space provides the convienient ability to distinguish between a 2d and 3d existance. A 4'th dimension of time may be observed that is relative to the speed of light. Our perception of time, and perhapse, Our manipulation of time, when the ability to generate such speeds progresses, is all thanks to our ability to understand and observe the properties of space time. So space time IS more than a mathematical model but less than a tangible substance you can physically measure.

 

Space Time may also be warped by gravity, causing effectus such as gravitational lensing. This phenomena has been observed, and tested. The ability of gravity to warp space time, and our ability to observe and mathematically theorize about it's behavior basically captures the essence of what physics is right?

Edited September 27, 2016 by Logic and Theory

[Tim88]

Hello.

 

I have recently opened a post that touches on this topic."The existence of tangible space". I was pro aether, however, after a period of research and reflection I have come to agree with GR. [..] We live in a 3 dimensional reality. [..]

 

"The existence of tangible space": "No such thread found" [edit:] do you mean that it was a comment hidden inside another topic? However I just started a thread related to the debate between 3D+1 and 4D, as linked in the post just before yours. And what follows sounds rather inconsistent to me: I just summarized Einstein's explanations of why GR implies some kind of ether, see my preceding posts # 212-215.

[..] space time IS more than a mathematical model but less than a tangible substance you can physically measure. [..]

 

I agree that it's not "tangible" in the sense of "material", indeed it cannot be measured like that. But there are other physical measurements of space, some of which already mentioned.

Edited September 27, 2016 by Tim88

[Memammal]

Space Time may also be warped by gravity, causing effectus such as gravitational lensing. This phenomena has been observed, and tested. The ability of gravity to warp space time, and our ability to observe and mathematically theorize about it's behavior basically captures the essence of what physics is right?

Gravitational lensing might have already been raised earlier in this thread, but I think it remains to be a valid point. Another phenomena that is directly associated with spacetime (and that was also mentioned earlier) is gravitational waves. Used to be theory only, now these ripples of spacetime have been observed.

Edited September 27, 2016 by Memammal

[koti]

I think this will be relevant here... I found this lecture by Nima Arkani-Hamed, at 48th minute he states that space and time are an aproximation because we can't measure them to perfect accuracy. He later asserts that space-time is an aproximation:

Edited October 4, 2016 by koti

[Tim88]

Funny enough (in view #214, 215 [edit: and #219], the following comments were posted in the spin-off thread for those who want to compare the usefulness of the two models of reality (which makes them rather off topic there and very much on topic here):

 

 

Well, it's unclear to Einstein why you need presentism/aether/preferred frame of reference/etc to make more sense of the equations.

And

 

lol I don't know about Einstein but I never needed it. Even when I first started learning GR.

 

In other words, some people don't have understanding for those arguments for more than mathematical space, or even deny them.

Edited October 19, 2016 by Tim88

[VandD]

 

5. As we know, the clock retardation in Langevin's "twin" example is absolute; it is a function of relative velocity, caused by the changes in velocity due to the non-inertial motion of the traveler. Thus he argued that in order to make physical sense of it, we should admit that these velocity changes must be happening with respect to something physical (the "ether").

I.o.w. there can be no non-inertial motion without the existence of an ether?

[Strange]

I.o.w. there can be no non-inertial motion without the existence of an ether?

 

 

No.

[Mordred]

You still haven't defined reality Tim.

 

Quite frankly nothing is solid, everything is nothing more than attractive/repulsive field excitations to field interactions and interferance.

 

GR simply maps this under the umbrella spacetime. That is reality, nothing more than a collection of excitations and field interactions. Massless particles have no binding field interactions. Simple

 

 

You keep looking for a medium but even matter is nothing more than the above. A medium is simply a macroscopic view of reality. At the quantum level this disappears.

 

Tim what makes you think that arguments based on an understanding over a 100 years ago defines reality? Why are ignoring moderm physics? The particles known at their time period is the electron and proton. The Neutron wasn't even discovered. So naturally they thought the electromagnetic force could possibly account for gravity.

 

You will probably declare the above off topic. Seems to be your pattern whenever physics or math is involved. However it us related as how one views reality depends on perspective.

 

Please stop misquoting my posts by the way. You obviously refuse to see my arguments as you never address them. In particular adherence to basic math and definitions when discussing mathematical models such as Lorentz ether. Your agument is two faced. You refer to a math model of reality but at the same time call that very mathematical model off topic when the math itself is being addressed.

 

Lorentz Ether is a mathematical model, discussing the implications of the math within that model is on topic

 

Yet you place your faith in a mathematical model as being the best descriptive of reality. Yet ignore the physics and math behind it as "Off topic"

 

How does that make any sense?

 

Quite frankly I don't think of the universe in 3d or even 4d. It has far more inherent degrees of freedom. Yet these degrees of freedom can be described by action. Action correlates to vector paths (Worldlines) so I can further reduce these degrees of freedom to 4d.

 

I cannot however reduce it to 3d, as the time component is independent (variable).

 

Right back to GR. Not SR its too limitted.

Edited December 18, 2016 by Mordred

[studiot]

 

Mordred

......................................I don't think of the universe in 3D or even 4D..............

 

The whole question of how many D is one of mathematical convenience, rather than physical reality.

 

Peano et al showed that it is perfectly possible to catalogue every point in the plane with what are now known as Peano curves and every point in 3D 'solid' space by what are known as space filling curves.

 

These curves are one dimensional objects.

 

The problem is they do not have usable metrics or neighbourhoods so this makes maths on them very tricky.