Theory of Information Could Resolve One of the Great Paradoxes of Cosmology

KentuckyFC writes: When physicists attempt to calculate the energy density of the universe from first principles, the number they come up using quantum mechanics is 10^94 g/cm^3 . And yet the observed energy density is about 10^-27 g/cm^3. In other words, our best theory of reality misses the mark by 120 orders of magnitude. Now one researcher says the paradox can be resolved by considering the information content of the universe. Specifying the location of the 10^25 stars in the visible universe to an accuracy of 10 cubic kilometers requires some 10^93 bits. And using Landauer's principle to calculate the energy associated with all these bits gives an energy density of about 10^-30 g/cm^3. That's not a bad first principles result. But if the location has to be specified to the Planck length, then the energy density is about 117 orders of magnitude larger. In other words, the nature of information should lie at the heart of our best theory of reality, not quantum mechanics.

Comments

Numerology

[PvtVoid]

Why, for instance, 10 cubic-kilometer voxels? Why not 100, or 1, or 0.1? How about 10^{15} cubic kilometers, which is about the volume of the sun? Adjust this number correctly, and you can match any energy density you want.

This is the problem with the science blogosphere: they'll take any press release whatsoever and echo it around regardless of whether or not it makes any fucking sense at all.

Re: Numerology

[funky_vibes]

The idea does actually work if the assumption is that we are living in a simulation, similar to ours. ;)

Re: Numerology

[Wycliffe]

The idea does actually work if the assumption is that we are living in a simulation, similar to ours. ;)

That's actually what I thought too. I've actually pondered this before. If we are in a simulation then stuff at the microscopic
or macroscopic only has to exist when viewed and can be generalized to a much lower resolution the rest of the time which
would greatly reduce the processing power required. This might also help explain some of the observation effects of quantum
physics where it seems that things act differently when observed.

Re:Numerology

[Charliemopps]

Why, for instance, 10 cubic-kilometer voxels? Why not 100, or 1, or 0.1? How about 10^{15} cubic kilometers, which is about the volume of the sun? Adjust this number correctly, and you can match any energy density you want.

This is the problem with the science blogosphere: they'll take any press release whatsoever and echo it around regardless of whether or not it makes any fucking sense at all.

No, they are basing it on Plank Length: http://en.wikipedia.org/wiki/P...
A unit of measure derived specifically from universal constants, the speed of light, the Planck constant, and the gravitational constant.

So it's not some arbitrary unit of measure as you suggest. It's the universes unit of measure. (assuming our current model of the universe holds) It's the smallest unit of measure that has any meaning in the real world.

Re:Numerology

[by (1706743)]

No, I think this information theory "approach" uses 10km^3 voxels:

Specifying the location of the 10^25 stars in the visible universe to an accuracy of 10 cubic kilometers...gives an energy density of about 10^-30 g/cm^3. ...But if the location has to be specified to the Planck length, then the energy density is about 117 orders of magnitude larger.

So they roughly recover the quantum mechanical (apparently incorrect) result if they use Planck length^3 voxels.

Not that I read the article of course, but this seems an odd thing to do, as you should probably be confining them to hbar units of phase-space, not just confining them to voxels.

Re:Numerology

[khallow]

No, they're basing it on an arbitrary volume unit that was made to be 10^120 larger than Planck length cubed. It still doesn't make any sense in that regard.

Another approach is to suppose that relative to a single point of space we try to nail down the position of everything we can see to as accurately as we can. We're going to have more trouble nailing down the position of distant locations because it's harder to build out a sensory network to triangulate positions or launch retroreflectors to everything we can see. That sort of thing.

Re:Numerology

[burtosis]

Not sure if you are describing it correctly. They are not basing it on the plank length. They show that if you do the energy density of the universe is off by 117 orders of magnitude, close to the 120 orders off if you calculate the energy density of dark energy from first principles. The 10^4 km isn't totally at random, it's based on the free energy associated with encoding a center of mass classically in such a way as to make it unambiguous to independent observers.

IANAP but it still smacks of numerology because the paper does not make any basis for why the mass of stars is important in any way. There is plenty of ordinary matter not in stars, black holes etc. what would have caught my attention is if it made a case based on mass and not just stars. Or at least gave a relevant basis for why it is negligible to discard non-star matter.

tl:dr numerology. Though props to the author for saying it can be easily dismissed as numerology in his own paper - that's good scientific method.

Re: Numerology

[LordLimecat]

Fun fact: Everything you know is predicated on some set of assumptions.

Re:Numerology

[rpresser]

It makes a tiny bit of sense to me.

"If we use [unstated first principles] to estimate what energy density should be, it's about 10^94 g/cm^3.
If we use the information content at the Planck scale, it's pretty close -- about 10^90 g/cm^3.

But we actually observe an information density of about 10^-27 g/cm^3.
And if we decrease the resolution from Planck scale voxels to 10 km^3 voxels, we get an information density that equates to 10^-27 g/cm^3.

This is evidence that we are living in a simulation, and the programmers aren't running the universe at Planck scale voxels, but only star sized voxels."

A large mountain of salt needs to be taken with this argument, but it does make sense -- as an argument.

Re: Numerology

[Oligonicella]

A completely bogus concept can be very accurately modeled with math. Reality doesn't care.

Re: Numerology

[BarbaraHudson]

Fun fact: Everything you know is predicated on some set of assumptions.

You're just assuming that's true :-)

Re: Numerology

[BarbaraHudson]

Pi is easily proven to be valid by observation and measurement. It wasn't invented, it's a description of what people had already observed.

Same with the speed of light in a vacuum.

This number has no physical manifestation - it's an unfalsifiable claim. There is absolutely no evidence, nor any way of testing, this "theory." We could just as well say that the dark matter is all magic pixie dust - magic because it can't be detected even though it has mass (an undetectable mass? can't happen).

Re: Numerology

[BarbaraHudson]

Problem is, the universe isn't a conventional computer, and there's nobody outside the system observing it. In other words, no real information. The positions of things could be in any random placement and the "calculations" would be wildly different - but that doesn't "create information" any more than any other random number does.

Re:Numerology

[by (1706743)]

Good point. I think, though, that they approached it completely backwards: they have presented a method for determining the information-theory voxel size of the universe (or whatever you like to call it), NOT the energy density, as TFS claims. That is, I think they should have started with the correct answer (10^-27 g/cm^3) and derived the voxel size from there. Then we could debate on the physical meaning of this voxel, which is a legitimate thing to talk about.

Re:Numerology

[neoritter]

Is it just me, or does all this math wrangling seem like what Geocentric scientists were doing to properly figure out the path of stars in our night sky to align with their theory?

Re: Numerology

[everythingistaken]

Everything you know is predicated by some set of *axioms*; not assumptions. For example: euclidian vs. non-euclidian geometry. Do you accept axiom 5 as part of your axioms? A || B || C => A || C Good science will investigate it's own axioms.

Re:Numerology

[lgw]

Why, for instance, 10 cubic-kilometer voxels? Why not 100, or 1, or 0.1? How about 10^{15} cubic kilometers, which is about the volume of the sun? Adjust this number correctly, and you can match any energy density you want.

Fundamentally, you can't model the universe as voxels in the first place. The Holographic principle, or at least the part about maximum information density, seems quite solid. There's a maximum entropy available in a volume (and thus a maximum amount of information needed to describe that volume) that's proportional to surface area, not volume. The number is absurdly high, well over 10^100 per square meter, but for extremely large volumes the cube/square effect starts making that limit meaningful. And that limit always prevents you from using voxels of the "natural" size of one cubic Planck length - the precision we know can model everything.

Perhaps the 10 cubic-kilometer voxels are reasoned from the limit for the visible universe? Still sounds high, even for that volume, and the visible universe seems like an arbitrary boundary.

Re: Numerology

[PvtVoid]

A collapse is the same as taking a single statistically random sample from a probability distribution given by the wave function.

This is wrong: the complex amplitude collapses, not just the probability (which is the square of the amplitude, and contains less information). This distinction is the heart of what makes quantum mechanics intrinsically different from classical physics.

Re:Numerology

[PvtVoid]

:-) -- My caricature of Muhammad. Please don't kill me.

How about this?

oO:-|>>

Is that enough to be blasphemy?

Re:Numerology

[burtosis]

The visible universe is slightly smaller than the hypothetical light cone originating at the time of the big bang. The last neutrino scattering surface is closer to this hypothetical size. The hypothetical light cone is what defines the surface area of the universe, inflationary models, relativity, etc all show how the shape and size of the visible universe is observer dependent.

that said the 10km cubes come from the free energy associated with representing a classical definate spatial location of all the stars with respect to independent observers. The number of states does scale with temperature but no case is given for discarding other normal warm matter in the universe - making the framework sloppy at best in my opinion.

Re: Numerology

[camperdave]

A constant is significantly interesting in some way. Fractions or multiples of a constant (which, granted, are just as invariable as the constant itself) are not interesting in and of themselves, but only in relation to the base constant from which they are derived. Pi is only interesting because it is half of tau.

A circle is the set of points in a plane equidistant from a fixed point. That distance is called the radius. The perimeter of the circle is the circumference. The circle constant should be the ratio between these two. Using the diameter is one of the biggest blunders in the history of mathematics. You have to have extra definitions. You get the superfluous 2 floating around in all equations. It's sloppy.

Re: Numerology

[khallow]

Like e^(i*pi) = -1? I don't see the 2 in that one.

Re: Numerology

[PvtVoid]

To be clear, I (parent AC) wasn't saying that the probability distribution is the wave function, just that it is given by it (which you confirm, it is the square of the amplitude). Now consider you make an observation and collapse the system to a single state. This state had a certain probability of occurring (again, given by the wave function). If you try to measure again, you will get the same state.

Only if you don't observe any orthogonal characteristics in the meantime. Consider a two-state system, with eigenstates |a> and |b> (for example, z-spin). Now consider an orthogonal basis |1> and |2> (for example, x-spin) which spans the same Hilbert space, such that

|1> = 1/\srqrt{2} |a> + 1/\sqrt{2} |b>
|2> = 1/\sqrt{2} |a> - 1/\sqrt{2} |b>

Now, suppose we observe the system to be in state |a>. Then if we perform an observation in the orthogonal basis, we will have a 50% probability to be in state |1> and 50% in state |2>. Suppose it's in state |2>. Now if we observe the first basis again, it's not in state |a> with certainty any more, despite the fact that we just measured it. It has a 50% chance to be in |a> and 50% to be in |b>.

There is no necessity to "restore coherence": the system is fully coherent throughout. This behavior does not happen with coins.

So the Universe is Shrinking?

[retroworks]

And is false information "anti-matter"? Could be we will witness the end of the universe in a flame war on /.

Need to consider this

[Bruha]

What if the universe is 120 times larger? Maybe our part of the observable universe just looks like it happened from a Big Bang.

Re:...indistinguishable from magic

[ColdWetDog]

Tens of thousands of "Doctors of Philosophy" and just as many historians would disagree with you.

Scientists in the Wonderland

[Anonymous Coward]

"Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality." - Nikola Tesla
"The scientists from Franklin to Morse were clear thinkers and did not produce erroneous theories. The scientists of today think deeply instead of clearly. One must be sane to think clearly, but one can think deeply and be quite insane" - Nikola Tesla
"There is not self containing theory possible aside from practical meaning, for a language is used in its annunciations, which miplys that developed ideas and complex porocesses of thoughts are alrealy in existance beside the general experience associated with there with. We define things in a phrase using words, these words hale to be explained by other words and so on forever in a complicated maze. There is no bottom to anything, we all upside down." - Oliver Heaviside
"They (Scientists) substitute words for realty, and after that talk about the words." - Edwin Armstrong

Re: Scientists in the Wonderland

[iluvcapra]

Sounds like a bunch of philistine engineers to me. Armstrong's quote could easily be applied to Einstein or Maxwell. Heaviside probably would have condemned the Manhattan Project as a bunch of theorists.

It's telling that Tesla draws the line at Morse, who invented Tesla's chosen field of engineering. And Tesla was a brilliant engineer. But later, as an actual scientist and researcher, as someone that had to do experiments and develop new theory, Tesla was a failure. His work was a dead end.

Re:"to an accuracy of 10 cubic kilometers"

[michelcolman]

Exactly. When they plug in an accuracy that makes more sense, all of a sudden they are 117 orders of magnitude off. In other words, they could have gotten any result they wanted by just picking some arbitrary value for the accuracy. "How much do we need the result to be? OK, then let's pick... 10 cubic kilometers. Because the universe really cares about round units based on the circumference of some arbitrary planet in some arbitrary milky way. See, only three orders of magnitude off, our theory is now better than quantum physics!"

Next month, they'l publish a new paper in which they have refined their theory by taking an accuracy of 0.71 cubic km. There, our refined theory now exactly predicts the correct density of the universe, from first principles! Throw away quantum mechanics, information theory is clearly superior!

Plenty of Evidence

[Roger W Moore]

There is no reason or evidence to suggest that the universe operates in any way that correlates directly to our mathematics

Actually there is a lot of evidence that the universe operates in a way that correlates directly with mathematics. Using our mathematical models of fundamental physics we used them to predict the existence of a new particle, the Higgs boson, to solve the flaws in the model. Similarly the same principle applied to the discovery of quarks and the W and Z bosons before.

The fact that we can use mathematical models of the fundamental nature of the universe so incredibly successfully to predict new fundamental phenomena that we have never seen before is clear evidence that the universe does work in a manner that correlates with our mathematics. Indeed I would say that this is one of the truly remarkable things about the fundamental nature of the universe: we can construct mathematical models of it which agree perfectly within our, admittedly limited, ability to test them.