# Proof of three dimensional space

1. Nov 1, 2005

### davstar

I’m was not sure where this topic should be placed but it seemed that General Physics might be the best place. I apologize if I have guessed wrongly.

In a discussion elsewhere on the subject of the world as we experience it through our senses, the point was made that we only receive information in two dimensional form and that there is no direct perception of a third dimension.

The information received by the senses is converted by the brain into a three dimensional image. This is thus an internal process, which has no direct connection to an external reality.

The question then arises as to whether or not there is an absolute scientific proof independent of the observer that this external reality indeed consists of (at least) three dimensions?

If not then the theory of such a space is merely a philosophical one, as are all other theories based upon it and thus may not apply everywhere in the universe.

Best Regards,
Dave

2. Nov 1, 2005

3. Nov 1, 2005

### davstar

Thanks for the reaction.
I'll take a look through these references.
Regards,
Dave

4. Nov 1, 2005

### Bob K

A 3D universe is conceptualizable by starting from a point of origin and extending rigid rods parallel and perpendicular to each other in three directions: North<->South, East<->West, and Up<->Down.

The concept of the proprioceptive sense, the awareness of one's body parts within a 3D space/environment, operates on the principle that there is in fact a 3D universe and there is therefore a necessity for an individual to be aware of his physical existence within that 3D space.

The proprioceptive sense is most noticeably activated in its 3D mode when an individual undertakes activities in three dimensions/directions, as when swimming, diving, flying, etc.

Our stereoscopic vision, our 3D vision, develops from the combination of biology and physics which produces the combination of two images, which appear to be two 2D images, but when an individual uses only one eye and focuses upon the changing dimensions of objects as he changes his space-interval/distance relationships to those objects, and, therefore, his persepctive, he will notice a definite 3D perception while using only one eye, a fact, which is easily observable by anyone with properly functioning eyes, a fact which gives a one-eyed individual a reasonable sense of depth perception, and, therefore, a sense of 3D perception, and, therefore, the physical capability of driving a car, flying an airplane (Wiley Post was a 1920s-30s famed one-eyed airman), and, therefore, what appear to be 2D images/perceptions are in fact 3D images/perceptions.

These facts/examples show that the human mind perceives in 3D.

5. Nov 1, 2005

### davstar

Thanks Bob K for your very lucid description of the theory of proprioceptive cognition.
I would argue that this is just a theory which might explain how a human being perceives three dimensions.
It does not however supply me with a proof that an outer reality of three dimensions really exists, which was what I questioned.

Now going offline until tomorrow
good night all

Last edited: Nov 1, 2005
6. Nov 1, 2005

### -Job-

In your 2D universe if you stand next to a road with two cars going in different directions, then there is a way for you to position yourself such that the two cars must collide even if they're in different lanes.

7. Nov 1, 2005

### ZapperZ

Staff Emeritus
I truly have a lot of trouble understanding this type of questions, and following the logic of the arguments.

It appears that there's some sort of an idea that only WE (human beings) perceive things in 3D, and that there's a possibility that even if the universe is only 2D, we might be "fooled" into seeing it (assuming with our eyes and sensory perception) in 3D.

After I picked myself up from the floor upon realizing the idea that was being presented, and realizing that this is within the PHYSICS section of PF, I decided to present several scenario for consideration.

1. We KNOW what happens when something is confined in lower dimensions. And electron gas, for example behaves VERY differently in 3D, 2D, and 1D. Just look at the density of states in each of the different dimensions. They are DIFFERENT! Do we have any evidence this is so? Damn right! Electrons in high-Tc superconductors are confined to the 2D copper-oxide planes. We also have quantum wells made with semiconductors. 1D? Sure! Quantum wires and the stripe phase in cuprates! Each one of these exhibit CLEAR and characteristic behavior when confined to lower dimensions. These are measureable, reproducible, and don't care who the experimenters are.

2. Try describing a system in 2D and see if you can describe accurately the dynamics of the system. Anyone who had tried solving a Lagrangian can tell you that there is a HUGE difference when the constraints change from 1D to 2D to 3D. If the system is confined to 2D, it doesn't matter in how many degrees you perceive it, it will behave with that kind of constraints. If you incorrectly describe a 2D system using 3D degrees of freedom, you are up the creek stuck without a 2D paddle!

3. Solve Coulomb's law in 2D space and see if you have the 1/r^2 dependence for the electric field of a point charge. Enough said!

Zz.

8. Nov 1, 2005

### -Job-

I actually don't think this is that unlogical a question, even if it hurts my head a little. In fact the changing universe or a subset of it, may be modeled with a binary string, a binary matrix, a binary 3D matrix, or a binary xD matrix with any possible x (matrix only as data structure, not in the linear algebra sense). The reason for this is that you can map an n finite dimensional system to an m finite dimensional system, with m different than n. Looking at the raw data at time t, the number of dimensions seems like an arbitrary parameter. Or am i making things worse?

9. Nov 1, 2005

### Bob K

When we move about in 3D space we note changes in our distances to other objects and references, and these observations of changes generate within us an awareness of the fact that space really is a 3D space.

Let us construct for you a latticework of numbered and painted rigid rods extended in three directions from a common origin.

Let the North<->South direction rigid rods be both numbered and painted red; let the East<->West direction rigid rods be both numbered and painted green; let the Up<->Down direction rigid rods be both numbered and painted yellow.

Let us have you walk, swim, fly, etc., within this latticework and note the distances (length-intervals, space-intervals) which represent your proximity to the rigid rod numbers/paint and the origin as you move about the latticework.

Surely you will note the existence of the 3D space when you continuously note by the rigid rod numbers and paint markings your distance from the origin and from various selected rigid rods.

If this does not satisfy you, then let's toss you into ...

1. a confined pool of water with a very seriously hungry great white shark;
2. a cage with a very seriously hungry lion/tiger/bear/etc.

... or out of ...

3. a high-flying airplane with/without a parachute that works

... and note if you notice that for various reasons including survival you will have a tendency to move about in three different directions.

As a pilot, I am very much aware of the fact that space is 3D; thus, it might be easier on you than the other three possibilities if you were to take flying lessons and see for yourself the fact that space is really 3D.

When I have flown above Boston at 3,000 feet and have observed Provincetown in one direction and Martha's Vineyard in another direction as well as Boston below me, then I have become acutely aware of how the reality of the 3D space in which I am flying is totally different from the 2D aviation maps I use to help me get where I need to go.

Thus, one way or another, because the question is whether or not there is an objective and independent 3D spatial reality outside of your head the best answer is sought by observations of that objective/independent 3D reality.

If that does not convince you of the reality of the 3D spatial reality, then I issue you this Challenge:

Try denying the reality of 3D space by running headfirst at full speed through the space and time coordinates of the Bunker Hill Monument, Boston, MA, and observe if or not there is something 'out there in 3D space' that, independently of your opinion of it, and outside of your body/head, keeps you from traversing the space and time coordinates of the Bunker Hill Monument.

We perceive people/objects/events comprised of matter/energy in the outside/objective reality with our perceptual senses of sight/hearing/touch/smell/taste, and we can use one or more of these perceptual senses to observe/perceive that, yes, there really is a 3D reality, and, therefore, that space really is a 3D reality.

Last edited: Nov 2, 2005
10. Nov 1, 2005

### robphy

Here is the Tegmark reference again
http://arxiv.org/abs/gr-qc/9702052

Additionally, look at the Ehrenfest sections in the latter half of http://www.phys.uu.nl/~boeyink/ehrenfest/images/Nordstrom_Ehrenfest.pdf
(Ehrenfest's paper is
P. Ehrenfest, “In what way does it become manifest in the fundamental laws of physics that space has three dimensions?” Kon. Akad. Wetens. Amsterdam. Proc. Sec. Sci. 20 (1918), 200–209; reprinted in Collected Scientific Papers, ed. Martin J. Klein (Amsterdam: North-Holland, 1959), pp. 400–409. )

I've only read the Ehrenfest 1918 paper.

Last edited by a moderator: May 2, 2017
11. Nov 1, 2005

### pervect

Staff Emeritus
Me too. There have been some high-grade proposals of this sort, though, most notably 'T Hooft's "Holographic principle" (which is really a conjecture, but that's not what it's usually called).

see for instance
http://en.wikipedia.org/wiki/Holographic_principle

As always, demanding experimental results separates the science from the philosphy (much of the current discussion seems to be about philosophy, not experiments with definite results, i.e. science)

12. Nov 2, 2005

### davstar

Bob K
I am not questioning the fact that we as human's experience a 3D-universe. I stated as much in my original post. This is not the point.
What I am trying to discover is whether there is an objective method of proving that the universe around us really is 3D. This means that any experimental proof must be independent of the observer.
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robphy and pervect
I will look at these articles today. Thanks for the pointers.
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Zapper sees what I'm getting at:

It appears that there's some sort of an idea that only WE (human beings) perceive things in 3D, and that there's a possibility that even if the universe is only 2D, we might be "fooled" into seeing it (assuming with our eyes and sensory perception) in 3D.

But then the items that he mentions as "We know" and "Try describing" bring us back to a subjective assessment of the outer reality.

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It is very difficult to keep this purely objective. Quantum Mechanics shows us that it is not possible to independently determine the actual state of reality at the atomic level. The experiment affects the results.
Would this be any different at the macroscopic level?

13. Nov 2, 2005

### ZapperZ

Staff Emeritus
No, it doesn't. If it is "subjective", then the experimental observation will depend on who observes it, what time of the year it is observes, what the observer had for lunch, the observer's religious beliefs, etc. You seem to have ignored the "reproducibility" part of my argument. You simply cannot dismiss such a thing as "subjective". You have to qualitatively AND quantitatively account for the physical evidence to support your argument. This is stil the physics forum.

Do not bastardize QM that way. It is wrong, and misleading at best. If such a thing is highly "subjective", then how are we able to use QM in such a PREDICTIVE fashion for everyone, not just of people of certain beliefs and persuasion? It isn't "subjective".

Zz.

14. Nov 2, 2005

### davstar

Hi ZapperZ,
I used the word subjective when I of course meant human observer. Sorry for the confusion.
regards,
Dave

15. Nov 2, 2005

### ZapperZ

Staff Emeritus
I know what you meant. And I was trying to counter the fact that if ALL we do is misinterpret our observation, we will run into trouble quickly. Howdoes our "subjective human observation" allows us to differentiate the DIFFERENT behavior of electron gas in 1D, 2D, and 3D? In fact, we even have a quantum DOT (zero D) and can tell what its behave is like. These are not "subjective" human observation. Human beings are not THAT smart to make up such things that Nature is giving us.

A valid observation is a valid observation, regardless what our "subjective" human observation is. That is what is meant as "reproducibility". It is what makes Science as science, and not ethics or morals or values.

Zz.

16. Nov 2, 2005

### davstar

Hi ZapperZ,
Ok. Thanks for your response. You've given me something to think about.
I think I'll do some more research on the subject before adding more material.
Best Regards,
Dave

17. Nov 2, 2005

### pervect

Staff Emeritus
These are all philosophical questions, not scientific ones.

As far as science goes, it is sufficient to note that we have a way of measuring distances between objects (rulers), and that we get correct results for these distances when we assume that the universe is represented by a three dimensional manifold, one that has a local chart to $\mathbb{R}^3$ at every point - and that we do NOT get correct results if we assume the universe is represented by a 2-D manifold.

This is science. Questions about whether these measurements represent some underlying "reality" are philosophical questions, not scientific ones. As is the case with most philosophical questions, the argument can go on indefinitely, this is a consequence of the fact that the questions cannot be resolved by any sort of experiment.

So to recap:

Try and think of an experiment to test the idea that the universe is not thrree dimensional. If you cannot find such an experiment, you have a philosophical question. If you do have such an experiment, do it!

Last edited: Nov 2, 2005
18. Nov 2, 2005

### Bob K

The essence of science is observation.

Who/What can observe an objective 3D universe and thereby confirm the existence of a 3D universe/the fact that the universe is a 3D universe?

Humans? Machines?

Humans detect information from the objective environment through their perceptual senses of sight/hearing/touch/smell/taste; machines detect information from the objective environment by through their information detectors which are the light-sensing/sound-sensing/motion-sensing/odor-sensing/etc. sensors which are equivalents of human biological perceptual senses. Humans detect the objective environment/reality by senses; machines detect the objective environment/reality by sensors.

If humans can be deceived by illusions inre their senses is it also possible that machines can also be 'deceived' by illusions inre their sensors?

If so, then perhaps humans can be as reliable as machines in observing/measuring the objective environment/reality.

Humans can choose to use more than one sense to detect information from the objective environment/reality and thereby increase the possibility that what was/is/will be observed/measured is not an illusion; by being alert for the possibility that sesory illusions can occur, humans can use several or all of their senses to effectively, and, in general, accurately detect information inre the objective environment/reality.

If so, when humans via their senses detect information inre the 3D essence/nature of space and therefore the spatial reality of the universe, then they will have the evidence they need to conclude that the universe is a 3D universe.

We can run you through the space + time coordinates of the Bunker Hill Monument, Boston, MA, and observe if or not the universe is a 3D universe either (A) from what we see/hear/etc. of your comments inre what happens if/when your subjective experience becomes aware of the objective existence of the Bunker Hill Monument or (B) from what we see/hear/etc. of what happens when your head/body attempts to traverse the space + time coordinates of the Bunker Hill Monument.

We can also fly a model airplane through the space + time coordinates of the Bunker Hill Monument and observe if or not the universe is a 3D universe from what happens to the model airplane when we attempt to force it to traverse the space + time coordinates of the Bunker Hill Monument.

In philosophy, as described by Professor Dr. Alfred Stenner, Washington University, circa 1961-66, there are facts which he labeled brute facts which I now recognize to be facts which are not analyzable/divisible/reducible/etc. into smaller components/facts, and which are, therefore, to use a favorite expression of Intelligent Design people, of which I am not one, irreducible.

The 3D essence/nature of space, the spatial reality of the universe, is a brute fact of physics.

The universe can be conceptualized as comprised of three realities, (1) space, the spatial reality, (2) time, the temporal reality, and (3) physics (matter/energy), the physical reality. Space exists as the place wherein exist time and physics (m/e).

1. Space is conceptualizable as a volume of infinite radius/diameter, the infinite volume, the i-volume, which surrounds any and all and each and every volume of finite radius/diameter, x, an x-volume. When (A) physical phenomena are conceptualized as occurring as quanta, electrons, photons, gravitons, etc., and (B) each quantum is considered to have a finite volume, an x-volume, and (C) is not contiguous with other quanta, then we note that beyond the finite x-volume of an individual quantum exists, ultimately, the infinite i-volume which is space, and also note that because this space contains no quanta it is a pure vacuum.

2. Time is conceptualizable as the use of durations called time-intervals (TIs) as units of temporal measurement for the measurement of the occurrences of events. Humans and machines who/which need to record or coordinate events use time via TIs to measure the time at which events occurred in the past and the present and to predict/coordinate the occurrences of events of events in the future. The essence of time is the time-interval (TI), the unit of measurement of time, which is a duration, most often modeled from the duration of a regularly recurring periodic or cyclic motion, such as the duration of the yearly orbit of the Earth about the Sun, or the regularly recurring oscillations of a cesium atom. Once chosen, a TI becomes an abstraction which can be manifested/made real/actualized/realized in machines including clocks. A TI as a unit of measurement of the occurrences of events sets the rate of operation (RoO) for machines and the rate of ticking (RoT) for clocks, and describes the occurrences of biological events in humans (and other living organisms), especially the rate at which biological events occur. Because the essence of time is the TI, and a TI is an abstraction until manifested in a machine such as a clock, time is not destroyed when a clock breaks, nor is time dilated when a clock is accelerated/decelerated and thereby, when the accelerative/decelerative forces cease/are terminated, enters into a different inertial reference frame (IRF) wherein its motion in uniform; instead, acceleration/deceleration causes changes in the physical processes which control the rate of operation/RoO of machines including clocks, thus when a clock's RoT/RoO is changed by acceleration/deceleration that change is a physical process and not a temporal process, and that change is caused by a physical process and not by a temporal process, and, thereby, we note that the temporal process is not a causal process. Because the essence of time is the TI, if the duration of a TI is changed by accelerations/decelerations and similar clocks use the same TI and their RoTs are identical, meaning the clocks all "go at the same rate" (Einstein's expression in Relativity), then these clocks can be used for the measurement/coordination of the occurrences of events, and these clocks will thus measure local time (LT), and can be used effectively within an inertial reference frame/IRF; if the duration of a TI is controlled so it is not changed by accelerations/decelerations, because (A) radio signals are sent to a clock to coordinate/synchronize its RoO/RoT with a master clock, as occurs in the US GPS and Russian GLONASS satellite navigation systems, or (B) accelerometers/decelerometers are used to detect accelerations/decelerations and therefore changes of motion and computers are used to maintain the clock's original TI and RoT as occurs in sophisticated inertial guidance systems such as used for the F-117 Stealth Fighter-Bomber and submarines, then this clock and similar clocks can be used for the measurement of events on/in any IRF and these clocks will measure absolute time (AT), and events which occur at a timepoint measured/defined/specified by these clocks will all be simultaneous regardless of being in/on different IRFs.

3. Physics (m/e) is conceptualizable as mass which is conceptualizable as resistance to a change of inertial state/change of motion, for which the unit of measurement is a dimension of mass. From the observations of chemists and thermodynamicists, matter and energy are indestructible while convertible, as matter<->energy, as described by Einstein's e = mc2 and m = e/c2, and, therefore, m/e is eternal in existence, having no beginning/creation/causation/formation/etc., and no ending, which means m/e has existed prior to any Bangs and will exist after any Crunches; the indestructibility of m/e means the universe has always existed, exists now, will always exist. From the extrapolations of the observations of m/e in closed m/e systems, where in a closed m/e system (A) m/e cannot be added (where would the additional m/e come from?), (B) m/e cannot be removed (where would the removed m/e go?), and (C) the sum total of m/e is a constant, the universe is a closed m/e system because (A) m/e cannot be added (where would the additional m/e come from?), (B) m/e cannot be removed (where would the removed m/e go?), and (C) the sum total of m/e is a constant.

We thus note that the physical phenomena which are the three realities which comprise the universe all have specific dimensions which can be used for measurement: (1) space = dimension of length, space-interval; (2) time = dimension of duration, a time-interval; (3) physics = the dimension of mass, resistance to a change of motion/inertial state. Physical phenomena are thus related to each other by the mathematics of their units of measurement/dimensions.

Inre space, the 3D essence/nature of space is measurable by humans/machines in units of length, space-intervals, units of the dimension of length, and when a latticework of rigid rods extending in three directions is created using a dimension of length, space-interval, for the length of a rigid rod, then that latticework will reveal the 3D essence/nature of space.

Because the term universe has been employed/defined/specified to mean all reality, when universe = space/time/physics (m/e), then we are forced to think of all physical phenomena as existing/occurring within this one-and-only universe and we are forced to eliminate from serious conscious thought any possibility of the existence of additional universes, such as parallel universes and multiverses, regardless of any mantras and mathematical 'proofs' claimed by various physics gurus to prove other universes/realities can and do exist.

If a physical phenomena is real, because it can be observed/measured by the dimensions of length (inre space/space-intervals), time (inre durations/time-intervals) and mass (inre resistance to a change motion/inertial state) and is therefore not the content of an idea, then it exists as an objective reality within this one-and-only universe.

19. Dec 14, 2008

### Primitive

The world is 3-d if our best scientific theory say so.

20. Dec 14, 2008

### schroder

There is compelling (mathematical) evidence for a Universe that has exactly three dimensions. Not the least of this evidence is the inverse square law. This law applies not just to gravitation, but to all electromagnetic phenomena, including electric and magnetic fields. The field strengths vary exactly in accordance with radiation in three dimensions. If, for example, bodies in space had four dimensions, we could reasonably expect the radiation to hold to an inverse cube law. It does not seem reasonable to expect a body to have a field or radiate anything in a dimension in which it does not have a spatial extension or vice versa.