Gravity Is a Dimension by James R. Akerlund

james akerlund

Essay Abstract

We present four arguments that gravity is the third spacial dimension of spacetime. The first three of these arguments are reinterpretations of "old" science and the fourth argument is "new" science, in that the findings haven't been the subject of one research paper. Along the way, we will show how our understanding of gravity has changed over time and the specific findings that changed our understanding of gravity. This will lead to a contrast between gravity is a force and gravity is a dimension. A summary of the fourth argument is; forces map both positive and negative to spacetime while dimensions map only positive to spacetime, since gravity maps positive to spacetime then gravity is a dimension.

Author Bio

This is the authors second FQXi contest he has entered. Independent researcher currently studying how to communicate with parallel universes without violating the conservation of energy where we assume that each universe is a closed system.

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Joe Fisher

Dear Mr. Akerlund,

I just wanted to tell you that your essay about the possibility of gravity being a dimension is one of the most instructive essays I have ever read. Please believe me, it is not out of envious spite that I wish to throw cold water on your highly fanciful entertaining ideas, but I am a realist and I have to tell you that human eyesight can only immediately detect one dimension at the moment human eyesight is in the act of looking. Because of this, visually, the Universe has only one dimension and everything in the Universe when looked at only has one dimension. You can satisfactorily prove this fact for yourself by looking out of the window at your mailbox. You will note that although you may focus your eyes on the mailbox, it is impossible to completely blot out other material in the scene. The only detectable difference between the materials in the foreground from that of the materials in the background is that the material in the foreground appears to be bigger. If you were to go outside to collect your mail, you would notice as you approached your mailbox that it seemed to be getting larger. It would be physically impossible for your mailbox to alter its size three dimensionally; therefore, all sightings are one dimensional in nature. Gravity alas, is merely a deeply flawed humanly contrived nonsensical invisible abstraction.

james akerlund

Hi Mr. Fisher

I want to thank you for your good comment concerning the "instructiveness" of my essay. In the contest rules 1/3 weight is given to relevancy and 2/3 given to interest. In the subfield of interest is "Well and clearly written, so that it is comprehensible and enjoyable to read." I guess you would give me an "A" for comprehensible then, but an "F" for "Technically correct and rigorously argued, to the degree of a published work or grant proposal."; since the essay didn't convince you.

But, the point you do raise makes me feel like I have entered the dimensional version of "Name That Tune". In the game "Name That Tune", a contestant makes bets with another contestant that they can name a song with fewer notes then their opponent. In the dimensional version you say you can locate your mailbox using just one dimension. Well I am up to that challenge and up the ante and say I can locate your mailbox using zero dimensions. I will define three points in space; 1) you, 2) the handle on your toilet (If you have more then one toilet, you get to decide which one), and 3) your mailbox. The line between you and your toilet handle is the origin line. Now to locate your mailbox from that origin line we need two angles; one rotational about the origin line (with zero being a vertical line from the handle to the floor), and the other rotational about you having a zero point along the origin line towards the toilet handle. With the two angles we can generate a vector towards your mailbox and the distance to your mailbox is the vectors magnitude. Example 34º, 246º, 389 gings (gings is a made up magnitude). Do I win, or is that just more of the "deeply flawed humanly contrived nonsensical invisible abstraction"?

Joe Fisher

Dear Mr. Akerlund,

Had I the power, I would advise the judges of this contest to mark your essay A for interest of content and A for technical efficiency. Writing about abstractions is the most difficult task imaginable (no pun intended) and to hold the reader's attention and cause that reader to think, as your essay effortlessly held my attention and made me think, is clearly an indication of your exceptional literary capability of which I am in deep admiration.

Alas, whereas you now have to create vectors and zero points in space for the abstract mail being placed in your perfectly placed abstract mailbox, all I have to do is go out and pick up my real mail from my real mailbox.

james akerlund

Dear Mr. Fisher

Thank you again for your expressions of admiration. I am humbled. As for the "locating your mailbox" game, you win.

Jim

Vladimir Tamari

Dear James

I have read your essay, and feel you have been rather imprecise in your definitions for example what are the dimensions you refer to of which gravity is the third? As to parrallel universes, I have recently read Brian Greene's The Hidden Reality and he argues for them very well, but I was not convinced. Anyway nice to know there are others in this world exploring all sorts of non-mainstream ideas. Wishing you good luck with this particular universe!

Vladimir

james akerlund

Dear Vladimir,

Thanks for reading my essay. As for your question, it sounds like you are over thinking the issue. You know the three spatial dimensions you are right now using, I'm saying one of them is the gravity dimension not just the up/down dimension.

There is a lot of confusion concerning parallel universes. I'll give you three different forms of paralle universes. 1) Literary parallel universes where every story of fiction creates a parallel uinverse. 2) Cosmological inflation parallel universes where parallel universes are created during cosmological inflation. 3) Different values of π parallel universes, where parallel universes were created during the Big Bang resulting in universes with different values of π. I believe the Brian Greene book is about #2 the argument presented in the paper is about #3. Brian Greene's book shouldn't convince you about #3 or #1. Hope this helps.

Jim

Vladimir Tamari

Jim

You are saying that in an x-y-z space z would be gravity. I understand but do not see how this will work. A room in a house has height (the z dimension) and - oh I see your point its clever - the higher you go the weaker the gravity. Hmm that will work only when when there is one source of gravity in the entire universe, and only if you use spherical coordinates with the radius being the gravity dimension.

In a satellite tumbling in space between the Earth and the moon the z dimension is not necessarily aligned with the line between the centers of the Earth and the Moon...what happens then?

As to multiple Universes you may be right my mind is over thinking about the issue!

Vladimir

james akerlund

Hi Vladimir

The issue that I try to deal with when I say gravity is the third dimension is that my mind is so ingrained with the human made up notion of planar spatial dimensions that I automatically apply it to spacetime. It looks like you are doing the same thing. The satellite creates it's own mass. That mass is inturn affecting other masses around via newton's equation for attraction between two objects or the more exact Einstein equations for two masses. In other words, each mass creates it's own, as you put, z dimension. The equations of Newton and or Eistein simply measure the change in the z dimension based on the masses involved. Hope I have clarified those issues.

Jim Akerlund

Vladimir Tamari

Thanks for the explanation but it does not yet clear up what happens to the third spatial dimension - is it 'replaced' by gravity? What about a box placed at a Lagrangian point where gravity is zero? Does the box have 3 spatial dimensions and a gravity dimension which is zero?

[deleted]

Hi Vladimir,

If gravity didn't exist (going way beyond reality here), then the universe would have only two spatial dimensions. Gravity created the third spatial dimension. Now for my understanding of the Lagrange points, these are points in spacetime where objects orbit them due to the larger masses creating the points. I am unfamiliar with the equations used to find the Lagrange points, but I looked up "Lagrange points" on wikipedia and on the right side of the page it gives a map of the equipotential gravity around a sun/planet system. As you will see in that map only the planet and sun are the zero gravity points and everything else is greater then zero. The Lagrange points are simply the local minimums.

My cat just brought a mouse into the room and the mouse escaped. Having had experience with this before, where the escaped mouse was pregnent and had babies, and then a daugther found mouse and babies and I couldn't remove mouse and babies from house without extreme daughter distress. I need to remove mouse from house, now! I hope I explained enough for you.

Jim Akerlund

Jayakar Joseph

Dear James Akerlund,

We may assume that the third generation of dimensionality is inclusive of gravitation, in that the scenario of dimensionality describes a framework of dimensions and their emergence. First generation of dimensionality includes only spatial dimensions, whereas the second generation includes time also in that dimensionality framework. On evolution of string concepts, gravitation is expressional with the dynamics of closed strings in temporal dimension of space-time, and thus the third generation of dimensionality emerges.

With best wishes,

Jayaker

james akerlund

Hi Jayakar

When Srinivasa Ramanujan sent out his initial letters of math to the math community all of them except one was preceived as not worthy of further investigation. Only Hardy saw something in them. I read your post and I have no idea what you are saying. I tried reading your essay and I got the same thing. In some ways I feel you are onto something, but I can't see my way through your words. I am not Hardy.

Jim Akerlund

James Dwyer

Dear James,

I'm just an unversed pedestrian passerby with some interest in gravity, but I found your essay intriguing. Like Vladimir F.Tamari I found myself wondering what the other two spatial dimensions are. I would have replied to that thread, but I only found disjointed strings...

Your explanation that we are applying "planar spatial dimensions" to spacetime seems inadequate, since it is a plane that is described by two spatial dimensions. I'm wondering with Vladimir which of the three spatial dimensions we perceive is replaced by gravitation. This seems important, since in this scenario gravity can affect only the remaining two spatial dimensions. Personally, I sometimes think that each multiverse lies in the eye of the beholder, but I'll move along...

I don't really grasp your explanation of things mapping to spacetime, but I'm not at all well read and may simply not be able to contextualize.

All I have left are a couple of disjointed thoughts. It seems to me that the notion of gravitational freefall applies only to our human experience on Earth, being dominated by the Earth's superior mass. All things seem to freefall because their own gravitational effects are so insignificant in their interactions with the Earth's gravity. Being unschooled, it seems to me that, for example, that the moon doesn't fall to Earth because the moon produces an opposingly directed flow of spacetime's energy, buffering against its fall.

If gravitation is a physical process imparted by the kinetic interaction between localized potential mass-energy and some energy contained within the malleable dimensions of spacetime, rather than an abstract system of dimensional coordinates upon which effects can described, then gravitation must be considered a force interaction physically imparting acceleration, with directional dimensional effects reflected by changes to time and distance.

OK, I'll quit here while I'm already way ahead of myself... Thanks!

james akerlund

Hi James,

I will try to answer some of your questions. The others I don't answer are because I don't exactly understand them.

First question: "...I found myself wondering what the other two spatial dimensions are." The paper says they are quantum energy that is explained in Penrose's book "The Road To Reality" and in t'Hooft, but I warn you the t'Hooft paper isn't light reading.

Second question: My use of the terms "planar spatial dimensions" is poor. When Cartesian coordinates are described, we imagine the axises extending infinitely along. That extending of the axises infinitely is "the human made up notion" I was referring too.

Third question: "I don't really grasp your explanation of things mapping to spacetime, but I'm not at all well read and may simply not be able to contextualize." Here is an explanation I will try on you, tell me if it works. Where I am living, it is right now summer, one meaning that could be applied to summer is that all the surface temperatures in the state I live in (Colorado) are all positive. If I were to go out right now and measure the surface temperatures in every single location in the state of Colorado, I would find that all of them are positive on the Fahrenheit temperature scale. In other words, one definition of summer in Colorado is, surface temperatue maps positive for all of Colorado. For winter, the surface temperatue might not map positive for all of Colorado. Does that help?

Fourth question: "...for example, that the moon doesn't fall to Earth because the moon produces an opposingly directed flow of spacetime's energy, buffering against its fall." According to Newton this "opposingly directed flow of spacetime's energy" is it's "horizontal" motion relative to the earth. The freefall part occurs where it's difference from tangental horizontal motion is equal to the acceleration do to it's gravitational fall towards the earth, thus the resulting orbit of the moon.

That next paragraph after the moon discussion, left me in the dust of confusion. Anyway, I hope I answered some of your questions with you feeling I said something relavent towards your understanding of the universe.

Jim Akerlund

James Dwyer

Hi Jim,

Thanks for your consideration and additional explanation. My description of myself as a pedestrian is intended to convey that I have no useful formal education in math or physics.

Unfortunately your link to the 't Hooft paper didn't work. A search of arXiv didn't yield a paper I could identify by your link address, but a recent paper entitled "Duality between a deterministic cellular automaton and a bosonic quantum field theory in 1+1 dimensions", http://arxiv.org/abs/1205.4107, stated in its abstract:

"Methods developed in a previous paper are employed to define an exact correspondence between the states of a deterministic cellular automaton in 1+1 dimensions and those of a bosonic quantum field theory."

That made me wonder if you're referring to a two dimensional quantum model of spacetime? I can conceive how two dimensions might be adequate to describe point-like particles...

Otherwise, attempting to incorporate your additional explanations, would it be correct for me to describe (mostly from your Argument #2) your gravitational dimension to be represented by a point along a radial axis extending from a point mass, with the other two dimensions analogous to the longitudinal and latitudinal global coordinates relative to a radial gravitational coordinate?

My point about the moon is that, unlike objects of nearly zero relative mass interacting with a massive object (such as a bowling ball and the Earth) that effectively free fall, the Moon produces its own gravitational field. While Newton only evaluates the gravitational attraction between two objects of mass, doesn't GR describe the local interactions between two fields of spacetimes, each curved by a discrete object of mass? Don't all massive objects effectively accelerate all other objects towards their own center of mass? In this case the curvature of spacetime produced by the Earth accelerates the Moon towards its center of mass, but the Moon is also accelerating the Earth towards its own center of mass - there are two opposingly directed fields of accelerating spacetime that produce Newton's effective attraction force. Sorry if I'm 'making up' my own terminology here - no need for you to respond.

Do please let me know if I've still misunderstood your proposed gravitational mapping of dimensional spacetime.

Thanks again,

Jim

james akerlund

Hi Jim,

Here is a better link to the t'Hooft paper, arXiv:gr-qc/9310026v2 . I believe this is the paper that leads to the papers you cite in the above post.

Your explanation here is exactly what I was thinking. "Otherwise, attempting to incorporate your additional explanations, would it be correct for me to describe (mostly from your Argument #2) your gravitational dimension to be represented by a point along a radial axis extending from a point mass, with the other two dimensions analogous to the longitudinal and latitudinal global coordinates relative to a radial gravitational coordinate?"

As for your point here: "My point about the moon is that, unlike objects of nearly zero relative mass interacting with a massive object (such as a bowling ball and the Earth) that effectively free fall, the Moon produces its own gravitational field. While Newton only evaluates the gravitational attraction between two objects of mass, doesn't GR describe the local interactions between two fields of spacetimes, each curved by a discrete object of mass? Don't all massive objects effectively accelerate all other objects towards their own center of mass? In this case the curvature of spacetime produced by the Earth accelerates the Moon towards its center of mass, but the Moon is also accelerating the Earth towards its own center of mass - there are two opposingly directed fields of accelerating spacetime that produce Newton's effective attraction force. Sorry if I'm 'making up' my own terminology here - no need for you to respond." It looks like your are trying to describe gravitational barycenter. Go to this website for a Wikipedia Barycentric coordinates definition. Let me know if this helps.

Jim Akerlund

[deleted]

Hi Jim,

Very helpful, thanks.

Barycentric coordinates are an interesting adjunct to your, as I understand, proposed mass-centric coordinate system. FYI, not all mass is spherically configured, i.e., condensing clouds of gas and/or dust and, especially at larger scales where innumerable discrete objects of mass are aggregated.

But I'm thinking more of a point in space between two objects of mass where a small body would be equally accelerated in opposing directions. I can't explain this expectation in the context of any theory, but I think there is such a location, although the differential effects may not be very stable. A nudge towards either object of mass would result in the small body being continuously accelerated in the direction of that object.

I have read that there are strong similarities between GR gravitation and fluid dynamics. I'm a relatively simple person who primarily thinks in conceptual terms. As such, I think that ascribing physical actions to dimensional effects is unrealistic. While, as you explain so well, GR very precisely describes the effects of gravitation through an abstract system of dimensional coordinates, as I understand it attributes the cause of those effects to some undescribed property of spacetime.

Perhaps I'm too naive, but I must insist that the effects of gravitation must be the product of some physical process or mechanism acting on physical elements. I am not harping back tho the idea of a material medium (ether) once proposed to have been required for EM wave propagation.

I suggest that spacetime may contain vacuum energy that is manifested in the appearance of virtual particles in space. I envision that this kinetic energy contained within space (with time being an aspect of this energy) is condensed by interaction with the (aggregated) potential mass-energy of matter.

This should be testable by observing the annihilation rate of virtual particles and antiparticles near and far from significantly massive objects - the virtual particle annihilation rate should vary as a function of gravitational field strength (or vice versa).

In this conception, it is the density gradient of vacuum energy in space that produces the directional accelerating effect of gravitation. Gravity is not only equivalent to acceleration, it IS acceleration produced by the interaction between the potential mass-energy of localized matter and the kinetic energy of space. It also is that accelerating energy that produces temporal effects.

Sorry for going off on this tangent, but I cannot accept the idea that actions could be caused caused by dimensional effects - I can accept dimensional changes produced by physical actions...

Thanks again for your help and consideration!

Jim Dwyer

James Dwyer

Note: the preceding comment was intended as a reply to the preceding thread...

[deleted]

Hi Jim,

Your first paragraph seems to be trying to describe a rigid framework and applying it to gravity. The equations of GR are based on where the matter is, not on where the framework is, and then deriving mass motion based on this matter and setting up a framework based on that. The surface of equal gravitational attraction relative to a mass(the other two dimensions) can appear convoluted to an observer not on that surface. I think clarity has just left the building.

As for your second paragraph, it reminds me of a science fiction story by Jules Verne, called "From the Earth to the Moon". In the story, the author describes what life is like while in the spacecraft from the earth to the moon. The spacecraft is launched from the earth by a large cannon, so there are no rockets on the craft to adjust it's flight direction. he describes two very different gravitational effects while in the spacecraft. 1) A dog dies on the trip and he ejects to dog into space. Upon ejecting the dog into space, the passenger observes that the dead dog floats at the same velicity towards the moon as the spacecraft. 2) Meanwhile the passenger in the spacecraft while closest to earth feels gravity towards the earth that is weakening to the point where it is exactly equal to the gravity of the moon, where he floats for a few moments and then remains the rest of the trip walking on the ceiling. To sum that up; 1 dead dog floats with spacecraft and 2 weakening gravity. The weakening gravity sounds a lot like your second paragraph. The weakening gravity has been proven to not exist in reality. All objects in spacetime will follow a freefall path, i.e. the dead dog path. I claim no originality in describing this science fiction story to you. The above example was first cited in the book "Spacetime Physics" by Taylor and Wheeler.

As for the rest of the paragraphs, you seem to be trying to apply an as yet undefined restriction to dimensions that you say can't be applied to gravity. But you are saying that gravity has a property that is unique to gravity that can not be applied to dimensions. Well, in my essay, when I say gravity is a dimension, I'm also saying that whatever property gravity has is also a property of the gravity dimension to distingish it from the other two spatial dimensions. The gravity dimension has properties of a spatial dimension along with the properties of gravity. Instead of taking what appear to be two separate artifacts of spacetime, force of gravity and the third dimension, my essay suggests they are in fact one combined dimension that has the properties of gravity and space. Hope this helps.

Jim Akerlund