We are a Hologram? Able to probe Planck world? Hocus-pocus or profound discovery?

[JustAnotherGeek]

40 replies in and no one’s mentioned dead pixels?

[Siam_Sam]

I always thought we were one of those paperweight globes?

[Strange_Machine]

@Indistinguishable

Hm… was this it?

From the article:

A device measuring a centimeter across could in principle hold up to 1066 bits–a mind-boggling amount. The visible universe contains at least 10100 bits of entropy, which could in principle be packed inside a sphere a tenth of a light-year across.

Is there a different definition of a bit that is used in thermodynamics? This doesn’t seem like a large amount of information at all.

Thermodynamic entropy is popularly described as the disorder in a physical system. In 1877 Austrian physicist Ludwig Boltzmann characterized it more precisely in terms of the number of distinct microscopic states that the particles composing a chunk of matter could be in while still looking like the same macroscopic chunk of matter. For example, for the air in the room around you, one would count all the ways that the individual gas molecules could be distributed in the room and all the ways they could be moving.

From Wikipedia, Entropy is defined as:
S= kB ln Sigma (kB=Boltzmann constant, Sigma=number of microstates corresponding to observed macrostate)

How do people derive Sigma for any practical use? I can understand measuring the number of molecules in say, one cubic liter of air then using that to get one “microstate” but what about calculating all potential microstates? Or am I off on how people calculate the entropy of a given region?

[Indistinguishable]

Almost certainly, the formatting killed what was originally written as 10[sup]66[/sup] and 10[sup]100[/sup].

[What_Exit]

I read the article today and I search the Dope to see if someone had a thread on it. As expected …

I am trying to understand the Holographic part.

Is this right?
The 2D surface is the surface of the globe that is the universe. For every point in the universe there is a point on the surface. The holographic part of this is that these points on the surface are layered in much the way that a thin sheet of holographic material can so much depth.

Or did I completely misunderstand the article? I am having trouble getting this one at all.

How does the graininess play into this?

[Half_Man_Half_Wit]

@Strange_Machine

Is there a different definition of a bit that is used in thermodynamics? This doesn’t seem like a large amount of information at all.

The formatting’s been lost somewhere due to copypasting, the actual quantities should be 10[sup]66[/sup] resp. 10[sup]100[/sup], which is a rather large amount of information.

How do people derive Sigma for any practical use? I can understand measuring the number of molecules in say, one cubic liter of air then using that to get one “microstate” but what about calculating all potential microstates? Or am I off on how people calculate the entropy of a given region?

The relevant quantity is given by the partition function of the system, which basically gives you the statistical properties of the system you need from considerations involving the quantum mechanically allowed states of the particles within it.

[ZenBeam]

@What_Exit

I am trying to understand the Holographic part.

Is this right?
The 2D surface is the surface of the globe that is the universe. For every point in the universe there is a point on the surface. The holographic part of this is that these points on the surface are layered in much the way that a thin sheet of holographic material can so much depth.
[…]
How does the graininess play into this?

It probably won’t be a direct one-to-one correspondence. More likely it’s analogous to a Fourier transform, where every point in space depends in some way on every point on the surface. If you’ve ever seen a real hologram, the image of some point on something you “see” behind the hologram doesn’t lie on a single point of the hologram’s surface.

The graininess is just because there are many fewer Planck sized pixels on the surface than Planck sized voxels in space, so every Planck sized voxel can’t be independent. You’d instead have large clumps of these voxels, with only as many clumps as pixels on the surface.

[What_Exit]

@ZenBeam

It probably won’t be a direct one-to-one correspondence. More likely it’s analogous to a Fourier transform, where every point in space depends in some way on every point on the surface. If you’ve ever seen a real hologram, the image of some point on something you “see” behind the hologram doesn’t lie on a single point of the hologram’s surface.

The graininess is just because there are many fewer Planck sized pixels on the surface than Planck sized voxels in space, so every Planck sized voxel can’t be independent. You’d instead have large clumps of these voxels, with only as many clumps as pixels on the surface.

Thank you. That really helped. It makes more sense now. Though I did need to look up voxel.