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Bill1939's avatar

Planck's universe, cube or sphere?

Asked by Bill1939 (10219points) May 20th, 2012

In trying to understand the universe at a quantum level, I found it difficult to visualize Einstein’s cosmic foam as cubes of one Planck length, imagining instead spheres. However, the area of a cube is greater than that of a sphere of equal volume.

A “Planck Sphere” with the volume one cubic Planck would have a diameter of 1.2407 Planck lengths. If its diameter was one Planck length, its volume would be 0.52360 cubic Plancks (which, I believe is impossible by definition). Any thoughts on this?

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22 Answers

flutherother's avatar

The problem with spheres is they don’t pack tightly together; they leave odd spaces in between which presumably cannot be smaller than the Planck length.

Bill1939's avatar

I understood this, but it seems to me that initially, at the beginning of space and time, that the object (using this word very loosely) emerging from singularity would have to be a sphere. Further more, given Planck time, that sphere would have a radius of one Plank length. Any thoughts on this (besides the fact that I’m crazy)?

ETpro's avatar

We have such an inadequate understanding of the big bang it is impossible to even form meaningful conjectures about it at this time.But you’re certainly not crazy to be thinking about it.

Bill1939's avatar

I agree. However, I do not think that the Big Bang was the beginning of space and time, just the beginning of our physical universe.

ETpro's avatar

@Bill1939 So, do you think the Big Chill entropy we appear to be heading toward with an expanding universe will trigger another big bang? What would be the physics of that?

Rarebear's avatar

A quibble. Einstein didn’t come up with the quantum foam idea. That was John Wheeler at Princeton.

Bill1939's avatar

@Rarebear, thanks for the correction.

hiphiphopflipflapflop's avatar

I think this taking the notion of a “foam” much too literally and makes it static. The NOVA programs hosted by Brian Greene give a good visualization (go to the two minute mark). Compress the three spatial dimensions of spacetime into a two-dimensional plane and mark it off with a grid of light rays that you can adjust the spacing on at will. In vacuum far from massive objects, the grid will be regular and static with the spacing set at reasonable spacings (by that I mean down to a couple orders of magnitude of the Planck length).

What John Wheeler and others who did the first serious work on quantum gravity found was that if you jam quantum theory and general relativity together and lash it up with the mathematical physicists’ equivalents of duct tape (since they don’t fit) the picture you get of spacetime is that this plane that appears smooth and static becomes a boiling dynamic mess at the Planck length. Even in vacuum, even far away from massive objects the metric will twist up and form loops and arbitrarily complicated figures that come and go from moment to moment.

Bill1939's avatar

Thanks for the link to string theory. I have a layman’s understanding of this theory, although I will never be able to grasp it at a mathematical level. I visualize the “foam” as an arbitrary three-dimensional grid (in the sense that the two-dimensional longitude and latitude grid we use to navigate is arbitrary) whose x, y, and z lengths are Planck scaled.

An arm chair cosmologist, I imagined the universe expanding from a point of singularity, which logically produces a sphere. Assuming Planckness to be true, after one Planck time the sphere would be two Planck lengths in diameter. However, when the sphere’s volume was one cubic Planck, only .62 Plank time would have elapsed and the diameter would be 1.24 Planck lengths. This led to my question, Planck’s universe, cube or sphere?

A spherical Planck with one cubic Planck volume placed inside of a Planck cube of the same volume would penetrate the cube at the midpoint of each side by a distance of .12 Planck lengths. If the shape of a Planck volume could vacillate between sphere and cube at different frequencies, might this be an alternate theory to string theory?

agnostikos's avatar

A planck volume or planckon (not my coinage) has only one thing to say, provided it is considered as a unit of a holographic bound (and HBs pervade all of our allegedly illusory 3D space; every planckon is on some HB). That one thing is 0 or 1 (or however one wishes to label binary bits). It must do so with a surface of 4 Planck areas. My favorite candidate is a superfat torus (SFT) where R=r=½Planck length. This is of course a 3D calabicle (my coinage) hence Ricci-smooth etc. It has two spin modes, hence can signify binary bits. As an added bonus the SFT is what happens when a Planck-sized sphere is given spin! And ask yourselves what role the uncertainty principle plays in all this. Assigning an exact size to anything Planckish seems rather foolhardy (and that’s just what I’ve done).

agnostikos's avatar

Further thoughts on my last post. Correction: each planckon would be on as many as 10^183 HBs- and that’s a lot! And we seem to be arguing about what features a planckon may have, when it is in esse featureless and so defined .‘Spherical and overlapping’ makes a lot of sense. Think of the uncertainty principle as a subset of theorems within non-commutative geometry. Cubes are out, though. Edges and corners mean singularities, i.e. infinite curvature of space, which is just what one hopes to avoid with planckons.

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Anna737's avatar

I’m sorry, I’m sure you have probably lost me, but, impossible because it would have to be at LEAST 1.0+? I’m not a mathematician..sorry, can anyone explain?

Anna737's avatar

infinite loop

Anna737's avatar

And why would an object coming from a point of singularity have to be a sphere? Use it as loosely as you like, “object” may be the operative word here. So much math (all?) is based on presumptions, preconceived notions, or are just plain falsely rooted in our “earthly” (physical) “take” or perspective on things.

physitron's avatar

Regarding Anna737’s question. I know of no spontaneously emergent natural phenomena that are square shaped, from smallest to largest, until we get at least to the size scale of molecules, where we find crystals. It is therefore perfectly reasonable that the smallest volume unit of spacetime would be a Planck sphere. Although the Planck volume is listed in CODATA and other sources in terms of the Planck length being the length of one of the sides of a cube with the volume of 4.2 X 10^-105 m^3, other calculations, including those that show the possibility that a Planck sphere has enough mass to be a “black hole” are routinely done with a Planks sphere in mind.

slamatom's avatar

If the universe is made oscillation cube in which opposite sides come together and move out in a phase xyz the cube would become a salient sphere and have spin and counter spin at each of the 8 apexes while the 6 faces would produce electric fields in the aether. The universe has to be a single string of recycled steps xyz one step at a time so that everything in the universe is interconnected and controlled by the past cycle.

JayBe's avatar

This is a good point: cube or sphere. The spheres have the problem, that there are odd spaces in between, and the cubes have the problem that the planck length is not the same in every direction: to pass a planck cube diagonally extendes the original length.

Bill1939's avatar

Whamer’s cosmological conjecture.

Perhaps Einstein’s conception of cosmic foam as cubes of one Planck length is viable when the perceived perspective is only at right angles to Planck cubed foam. If in physical space Planck spheres are relative volumes that can overlap, space would not exist between them. Multi-dimensional information exists in holographic space where at Planck time intervals points having the probability of one can exist on the surface of the expanding (at the speed of light) sphere of cosmic time, each in a field of probabilities less than one that can combine provided their sum does not exceed one; combined probabilities equaling one create virtual points.

slamatom's avatar

Place two bubbles together and watch how the connection is a side or plane between, no reason that a foam of (like sized) bubbles wouldn’t form squares. Both sides at the connections are at equal pressure.

The problem is what is causing the pressure, strings can pull and align together in space in x, y and z directions to form crossed chain sides that slip in between each other to form an oscillating of wall forming an oscillating box of opposite sides coming together and moving out. Reverberation of space would alight crossed chain walls to align up x and y, y and z, and z and x in right angle directions and is necessary to make Planck sized units in space. Also, everything must be recycled like a repeating path or looped universal string..

PuzzleSolver's avatar

I think we are forgetting about locality here. We humans like to define the universe as a grid while Einstein’s relativity tells us it’s not a grid.

A planck volume is a sphere in my opinion coming from a single point, other spheres of a planck volume have their own definition of space because they have a different locality so packing makes no sense. The only thing that does is increasing the sphere in radius with planck length units. Two of these spheres can have the same distance between them and we as humans can come to the conclusion that they are a certain distance away from each other. We would measure this from a 3th sphere. If one of these spheres is moving at a high speed that distance would be different depending on the positions of the sphere and the direction of the speed. Space is fluid.

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