The Weinberg-Witten theorem

[bascule]

Holy shit, the two physicists I have the most respect for in the world, Steven Weinberg (who is intricately tied into the whole Dennett/Dawkins atheist memeplex) and Ed Witten (all my knowledge of which comes from Brian Greene, but I know him as the Einsteinesque genius behind M-theory) collaborated to create a theorem. But lo and behold, as I read about it, it flew right in the face of my beliefs in spiritual evolution, namely that all the complexity of the universe is emergent from a system with extremely simple underlying rules.

 

Sadly, when I look at something like:

 

[math]q\delta^3(\vec{p'}-\vec{p})=\langle p'|Q|p\rangle

= \int d^3x\, \langle p'|J^0(\vec{x},0)|p\rangle

=\int d^3x\, \langle p'|e^{-i\vec{P}\cdot\vec{x}}J^0(0,0)e^{i\vec{P}\cdot\vec{x}}|p\rangle[/math]

[math]=\int d^3x\, e^{i(\vec{p}-\vec{p'})\cdot \vec{x}} \langle p'|J^0(0,0)|p\rangle = (2\pi)^3\delta^3(\vec{p'}-\vec{p})\langle p'|J^0(0,0)|p\rangle [/math]

 

Hell if I can make any sense of it.

 

Can anyone give me a boiled down layman's interpretation of what specifically the Weinberg-Witten theorem says about emergence?

 

I'm specifically interested in this in the context of "universe from scratch" models which depend entirely on emergence to "construct" the laws of physics. Unless I'm horribly confused (which I probably am) isn't this how Seth Lloyd's computational universe model works?

[bascule]

I wanted to add this little bit in from The Ancestor's Tale where Dawkins references Weinberg:

 

We understand that the circumeference and the diameter of a circle are not independent, otherwise we might feel tempted to postulate a plethora of possible universes, each with a different value of [math]\pi[/math]. Perhaps, argue some physicists such as the Nobel Prize-winning theorist Stephen Weinberg, the fundamental constants of the universe, which at present we treat as independent of one another, will in some Grand Unified fullness of time be understood to have fewer degrees of freedom than we now imagine. Maybe there is only one way for a universe to be. That would undermine the appearance of an anthropic coincidence.

[MacroQuantum]

The math is beyond me. But I am willing to take a shot at English.

 

We understand that the circumeference and the diameter of a circle are not independent' date=' otherwise we might feel tempted to postulate a plethora of possible universes, each with a different value of pi. [/quote']

 

Because circumeference and diameters of a circle of dependent upon one another, so to must Pi be a fixed value across the multi-verse.

 

Perhaps' date=' argue some physicists such as the Nobel Prize-winning theorist Stephen Weinberg, the fundamental constants of the universe, which at present we treat as independent of one another, will in some Grand Unified fullness of time be understood to have fewer degrees of freedom than we now imagine. [/quote']

 

Septhen Weinberg argues that there is a Unified Field Theory, in which fundamental constants of the universe are fixed; not truly variable as we now perseve them.

 

Maybe there is only one way for a universe to be. That would undermine the appearance of an anthropic coincidence.

 

If universal constants are truly constants, if there is only one way for life to be, then the universe did not appear by accident.

[[Tycho?]]

If universal constants are truly constants, if there is only one way for life to be, then the universe did not appear by accident.

 

Why do some many people come to these ludicrous conclusions? If contansts are truely constants, HOW does this prove the universe did not appear by "accident"?

[bascule]

'']Why do some many people come to these ludicrous conclusions? If contansts are truely constants, HOW does this prove the universe did not appear by "accident"?

 

I think he's using "accident" to mean non-determinism, i.e. human life is an inevitable consequence of the existence of the universe, because the states that led to it arising are causally linked in a deterministic manner to all the states that came before it (in a discrete time view)

[DV8 2XL]

Weinberg and Witten consider the so-called emergent theories to be misguided. so, they came up with a no-go theorem that excludes, under very general assumptions, the hypothetical composite and emergent theories. Decades later, some condensed matter physicists are proposing theories of emergent gravity and the mainstream high-energy physicists are still using this theorem to "debunk" such theories. However because most of these emergent theories aren't Lorentz covariant, the WW theorem doesn't apply.