Gravity comes from Hyperspace ??

[Widdekind]

Standard Relativity texts describe the fabric of Space-Time as being like a proverbial rubber-sheet, which stretches under the weight of masses put upon it.

 

Now, that analogy requires that the rubber sheet (2D "Flatland") exist in an external Gravity field, pointing perpendicular to the rubber sheet (3D "Hyperspace"). It is that Gravity field that drives the masses down into the rubber sheet.

 

To wit, in the rubber sheet analogy:

• Gravity from 3D interacts w/ mass embedded in 2D "Flatland", telling it how much to warp the rubber sheet
  
• The warp of the rubber sheet tells the masses how to move
  

This compares with the oft-said phrase, from basic textbooks, that:

• Mass tells Spacetime how to curve
  
• Spacetime tells Mass how to move
  

 

For further emphasis, the rubber sheet analogy wouldn't work in Zero-G (!!). The rubber sheet analogy requires that the rubber sheet, representing 2D Flatland, be embedded in a 3D "Hyperspace" containing a perpendicular Gravity field — which gives Flatland masses "weight", which drives them "down" through the Hyperspace dimension, causing Flatland to curve, bend, stretch, and warp.

QUESTION: Could there be something analogous for our SpaceTime ??

 

Perhaps our Space-Time is embedded in a higher dimensional Hyperspace, which exerts some sort of "Hyperspace Push", from Hyperspace, "perpendicular" to Space. That "Hyperspace Push" affects Mass, driving it "down", and causing curvature in Space. Then, that induced curvature in Space tells Mass, embedded in Space, how to move.

 

In J.A.Wheeler's Journey into Gravity & Spacetime, Wheeler shows that the curvatures of Space, outside of an ideal mass (ie., in the Schwarzschild Solution), offset, leaving no "net force" acting on Space. He makes an analogy to a film of soap, stretched taught between two hoops, as they're dipped into the soapy water, pulled out, and pulled apart. Although only a 2D analogy, it shows how the 2 perpendicular radii of curvature offset, leaving the soap film in static equilibrium.

 

But, inside a star, the curvature of Space is "contractile", and has a net curvature "upwards". To use the rubber sheet analogy, it is this net curvature that offsets the weight of the ball put on the sheet !

 

Thus, this net curvature, pointing "up" into Hyperspace, proves the presence of a "Hyperspace Push" force...

 

at least for the rubber sheet Flatland analogy.

 

Could something similar be true for real Space ??

[ajb]

QUESTION:[/b] Could there be something analogous for our SpaceTime ?

 

Classical gravity in the form of general relativity does not require that our spacetime be embedded in a higher dimensional space. Also, it does not say that it cannot be.

 

Attempts at quantum gravity, an in particular string theory suggest that our world is embedded in a higher dimensional space called the "bulk". The idea is that we are confined to exist on a 3-brane. That is some " three dimensional sheet" in a higher dimensional space.

 

So, really we do not know if the universe requires more than 4 dimensions (1 time 3 space). Many scientists are thinking about this. Maybe we will know soon when the results of the LHC are in.

[Widdekind]

"Hyperspace Directionality" to mass-induced Curvature of Spacetime

 

Basic geometric arguments seemingly suggest, that there is a "directionality" to the Curvature of Spacetime, "through Hyperspace", caused by mass.

 

Consider the Flamm Paraboloids of two nearby masses — the two "dimples" in the "rubber sheet" of Spacetime.

 

Mathematically, it makes no differenece, whether you visualize those Flamm Paraboloids as "pointing upwards" — looking like "mountains" jutting up above Flatland — or as "pointing downwards" — looking like "valleys" sinking down below Flatland. Equivalently, you can look at Flatland from above, or below, seeing mountains, or valleys (respectively), but you'll always see the same motions.

 

But — imagine that, on the "rubber sheet" of Flatland, one mass produced a "mountain", but the other mass produced a "valley". That is, imagine that two equal masses (say) produced "equal but opposite pointing" dimples on the rubber sheet.

 

Locally, their Gravitational effects work out fine. But, now, imagine those masses move towards each other, and collide & combine. The "mountain" from the first mass will — purely Geometrically speaking — exactly cancel out the "valley" from the second mass...

 

leaving a perfectly flat "rubber sheet"...

 

w/ no more Gravity (!!).

 

 

____/\____ + _____..._____ = ______________

............................\/

 

 

 

But, this is clearly unphysical — two equal masses cannot collide & combine to produce perfectly flat Space(time). (More generally, two masses cannot collide & combine to amount to less mass (but what about Matter vs. Anti-Matter ??).)

 

 

CONCLUSION: The "Hyperspace directions" of the Flamm Paraboloids produced by masses — their "dimples" in the "rubber sheet" — are not arbitrary: they all point in the same sense "through Hyperspace" (they all create "valleys", or they all create "mountains", but not a random mix of both).

 

Whether you look at Spacetime "from above", or "from below" — to see either "mountains" or "valleys" — may be arbitrary. But every mass "dimples" Spacetime in the same "Hyperspace direction".

 

 

QUESTION: How does mass know "which way to go" ?? How does mass know to "dimple down", or "mountain up" ?? How is it, that every mass "pushes into" Spacetime in the same Hyperspace direction ?? (What about Matter vs. Anti-Matter — would their "dimples" in Space "point in opposite directions" ??)

 

 

 

---

Merged post follows:

Consecutive posts merged

Classical gravity in the form of general relativity does not require that our spacetime be embedded in a higher dimensional space. Also, it does not say that it cannot be.

 

Attempts at quantum gravity, an in particular string theory suggest that our world is embedded in a higher dimensional space called the "bulk". The idea is that we are confined to exist on a 3-brane. That is some " three dimensional sheet" in a higher dimensional space.

 

So, really we do not know if the universe requires more than 4 dimensions (1 time 3 space). Many scientists are thinking about this. Maybe we will know soon when the results of the LHC are in.

 

Thanks for this succinct summary !!

 

 

 

 

---

Merged post follows:

Consecutive posts merged

 

 

Rudolf v.B. Rucker (Geometry, Relativity, and the Fourth Dimension, pg. 107) depicts a (1+0)D slice through the curved space of a (vaguely (Hyper-)Spherical) Closed Universe. Note that all of the masses "bulge outwards", away from the Center of Curvature. This satisfies our requirement of "directionality", for the Hyperspace curvature, caused by mass, in Space(time).

 

 

Returning to the rubber sheet analogy, we now have a big "rubber balloon" — and whenever we put masses onto said rubber balloon, the balloon bulges outwards. Confining ourselves strictly to the analogy, this situation requires that there be some sort of "expansion pressure" inside the balloon, that "pushes out" masses placed onto the rubber balloon... as if there was some "reverse radial gravity field". (For (1+0)D, you could create this effect by rapidly rotating a rubber band upon a Carousel. Then, whenever you put masses up against that rubber band, Centrifugal Forces would push them outwards, precisely as in R.v.B.Rucker's picture.)

 

Could such an "expansion Pressure", originating from the "interior Hyperspace" inside of a curved, Closed, Cosmos, cause, perhaps, both the expansion of that Space, as well as pushing all masses "outwards", towards "exterior Hyperspace", away from the Center of Curvature ???

 

Could this explain, perhaps, the Cosmological Constant [math]\Lambda[/math] ???

Edited August 29, 2009 by Widdekind
Consecutive posts merged.

[ajb]

With your adding "peaks and troughs" of curvature what you are really doing is adding two metrics on the manifold of space-time to get to a flat one. I think this is ok from the point of view that the collection of all metric on a manifold is a space, but I am worried that as the field equations of general relativity are highly non-linear that in general adding two perfectly good solutions is not gong to be a solution. In general there is no known composition law. (One could linearise and then you would have a superposition principle.)

 

I think that for asymptomatically flat metric you could imagine bringing two objects from infinity to close proximity. I would have to do some reading to understand how this works. (Maybe this is only well understood for specific solutions or just the linearised case).

 

It is not something I have thought much about.

Edited August 31, 2009 by ajb

[sananda]

how many times has the rubber sheet been analogy been used on this forum...

 

i wish people would think for themselves.

[swansont]

how many times has the rubber sheet been analogy been used on this forum...

 

i wish people would think for themselves.

 

Please refrain from this. Your objections to relativity and its descriptions MUST NOT drag other discussions off topic — they should be kept within their own thread, and in the Speculations forum

[sananda]

come on, you have to admit the rubber sheet must be sagging it's so overused at this stage...

 

I am a 100% supporter of relativity.

[mooeypoo]

come on, you have to admit the rubber sheet must be sagging it's so overused at this stage...

 

I am a 100% supporter of relativity.

We have to admit nothing other than scientific evidence, sananda.

 

If an analogy fits, it will be used to make a point. You should be thankful that people take the time to try and explain complex physics to show you where you might be wrong, as opposed to just sending you along to read some basic (and not so basic) physics.

 

I recommend you give some respect to the people who take the time to answer you and actually care enough to help you understand.

 

~moo

[ajb]

come on, you have to admit the rubber sheet must be sagging it's so overused at this stage...

 

The rubber sheet analogy is great for basic illustrations. The main point it fails on is that it is presented as embedded in 3 dimensions. This is what often leads to mush confusion, general relativity says nothing about if our universe is embedded in higher dimensions or not.

[Widdekind]

The rubber sheet analogy is great for basic illustrations. The main point it fails on is that it is presented as embedded in 3 dimensions. This is what often leads to mush confusion, general relativity says nothing about if our universe is embedded in higher dimensions or not.

 

Thanks for the clarifications about the non-linearities of GR.

 

 

 

Would you please posit some speculations, about such "Hyperspace" (aka "The Bulk") ??

 

In particular, is there any likelihood, that light travels faster in Hyperspace — to wit, even if you could "jump out" of the "3-Brane" of standard Spacetime (and if you could "jump back in" some place else), could you use such "Hyperspace travel" to voyage faster than light ??

 

And, also, if you could "jump out" of the "3-Brane"...

what force keeps particles back inside it ??

 

To make a crude QM analogy, could there be some sort of "energy barrier", acting along the "Hyperspace dimension / axis" (the "W" direction on a Flamm Paraboloid), that "squeezes" particles "back into" the 3-Brane ?? Could such an "energy barrier skin" around the 3-Brane explain the tiny sizes of String Theory's extra dimensions (they're not "curled up", but "energy bounded") ???

[ajb]

It seems that, based on string theory only closed strings can travel in the bulk. These correspond to gravity.

[Widdekind]

Thanks again for the info