Physicists Discover Geometry Underlying Particle Physics

New submitter Lee_Dailey sends this news from Quanta Magazine: "Physicists have discovered a jewel-like geometric object that dramatically simplifies calculations of particle interactions and challenges the notion that space and time are fundamental components of reality. 'This is completely new and very much simpler than anything that has been done before,' said Andrew Hodges, a mathematical physicist at Oxford University who has been following the work. The revelation that particle interactions, the most basic events in nature, may be consequences of geometry significantly advances a decades-long effort to reformulate quantum field theory, the body of laws describing elementary particles and their interactions. Interactions that were previously calculated with mathematical formulas thousands of terms long can now be described by computing the volume of the corresponding jewel-like "amplituhedron," which yields an equivalent one-term expression."

Comments

42

[syntheticmemory]

Almost there....

Re:42

[ByteSlicer]

Also, computing proteins folding is probably going to get a serious performance boost too. If this proves to really work genetic engineering is going to enter a new phase.

Probably not.
This just speeds up some mathematical methods used to calculate probability fields in quantum mechanical problems. So it will provide a certain linear speedup of those calculations (for example 1000 times faster).
It will not however help with NP hard problems (like protein folding), because these would need real quantum computations (on a quantum computer) to reduce the exponential order of the problem into a lower order one.
If a problem would take many times the age of the universe to calculate, then dividing that time by a small factor will not help much.

Bejeweled...

[Anonymous Coward]

Is secretly a complex distributed particle physics computation!

Re:Bejeweled...

[gstoddart]

Troi: Captain, I can 'feel' the amplituhedron.

Data: It's become sentient

Q: Foolish humans ... you could never hope to understand this.

Wesley: Oh sure, I made one in science class last week.

ALL: Wesley, STFU.

d20?

[space_jake]

Roll for initiative...

Hold up.

[girlintraining]

Guys, we've been down this road about a million times in physics. Just because a mathematical model simplifies certain calculations, does not mean that the actual underlying physical geometry matches the theoretical model. Mathematicians have been adding extra dimensions to equations and finding they simplify things for years. It doesn't mean we live in a 27 dimension manifold. All direct observations to date point to a 3D universe.

Re:Hold up.

[gstoddart]

It doesn't mean we live in a 27 dimension manifold.

Doesn't mean we don't. ;-)

All direct observations to date point to a 3D universe.

Ummm ... hang on a second. Won't any direct observation we make as 3D critters point to a 3D universe? Isn't that sort of inherent to us being only able to perceive 3D?

I'm not sure how we'd do any direct observations in any other dimensions. (Honestly, not a flame, I'm genuinely puzzled by how we could see anything else and every now and then something like this hurts my head)

Re:Hold up.

[ubermiester]

Check out Richard Feynman's lecture regarding space-time and his analogy of bugs on a sphere. If you tell them that the rule for making a square is to go N units in one direction, then turn 90 degrees and repeat until you complete the square, they would find that they cannot actually make a square. This leads them to conclude that there is "something wrong" with their space.

The point is that while the underlying nature of their universe as a sphere is unavailable to them because they cannot escape it to see the bigger picture, they can still infer that because Euclid's rules of geometry don't work there must be something going on that they can't see. Moreover, they should be able to guess that there is curvature - without knowing for sure - because of exactly how the rules break down.

This is essentially what people talk about when they refer to the difference between larger objects like clumps of atoms and smaller ones like electrons and quarks. For some reason our 3D (technically it's 4D according to Einstein) universe only behaves "normally" until we start measuring it at a small scale. Then we start seeing where our rules about the behavior of "observable" objects - i.e., the stuff we can perceive with our senses - break down and are replaced by the true nature of the subatomic universe. In other words, when we look at quarks do stuff, we can no longer make the square.

Constructs like the one described above are the result of us trying to get our little bug heads around the way in which our every day rules break down when really tiny things are involved. It's a way for the bugs to correct Euclid to account for the spherical nature of things.

Re:the wall of fundamental laws

[meta-monkey]

Given how many insane conspiracy theories are lately turning out to be not completely insane, I'm just waiting for Congress to rip off their masks and reveal their true identities: Lizard Men from the Hollow Earth.

Re:hmmm....

[AliasMarlowe]

Lisi's E_8 conjecture is somewhat more complicated than this one. For a start, the geometry of the E_8 group is richer than that of a mere amplituhedron. Others may note that Lisi's conjecture also includes gravitation in its unification, while TFA appears to be only about particle families.

space & time as emergent properties

[kipsate]

One of the things the article says is that space and time may not be fundamental properties of nature, but properties that emerge (i.e., are the result of) a more fundamental reality.

Warning: IANAP. But with some axioms, it is possible to reach the same conclusion.

Imagine a simple experiment with an electron source and a detector. An electron is emitted in the direction of a detector. The experiment is set up such that while travelling towards the detector, the electron does not interact. More precisely, in between the emitter and the detector, the electron does not exchange any energy. Then, the electron hits the detector and becomes detected (interaction two).

Has the electron physically travelled in the space between the electron source and the detector? May it be assumed that in between the interaction with the emitter and its subsequent interaction with the detector the electron is physically present?

Obviously, it is impossible to establish that the electron is present between the emitter and the detector without actually interacting with the electron. It is therefore herewith observed that any assumptions about physical presence of the electron in between the source and the detector can not be experimentally verified. More generally, it is observed that the assumption of physical presence of any elementary particle in between two interactions can not be falsified.

Equally impossible to falsify is the assumption that in between the emitter and the detector, the electron in the experiment was not physically present. This assumption implies that (in the reference frame of the observer) the electron disappeared at the emitter and reappeared at the detector, and did not take up any physical space at any time in between. In between interactions, the representation of the electron disappeared and became unobservable. For as far as an observer can tell, the electron disappeared from the universe completely in between interactions.

Since obviously, properties about the electron are preserved in between interactions, the electron must still somehow being represented – i.e., the representation of the electron has clearly not disappeared from the universe.

The notion “observable universe” is therefore being introduced to make the distinction between interactions which can be observed, and the herewith theorized part of the universe that is apparently capable of at least holding a representation of an elementary particle and which can not be observed.

Observable universe: The part of the universe in which an interaction manifests itself.

Let us formulate the following two axioms:

Axiom 1: An interaction is instantaneous, i.e., it lasts for an infinitely small amount of time.
Axiom 2: An elementary particle only exists in the observable universe at the moment of its interaction.

Notice that axiom 1 and 2 are unfalsifiable. Consider the reverse of axiom 2:

Reverse of Axiom 2: An elementary particle physically exists in the observable universe in the time that passes (in the reference frame of an observer) between two interactions.

This axiom is equally unfalsifiable, since physical presence of an elementary particle can only be proven by interacting with it. The reverse of axiom 1, which would postulate that an interaction lasts a non-zero amount of time, is equally unfalsifiable.

Elementary particles have no internal structure and are considered point particles. In other words, an elementary particle does not take up any physical space. If we assume that everything in the observable universe consists of elementary particles, then it follows that all particles that exist in the universe do not take up any space. The aggregate volume of all elementary particles is zero.

Combined, axioms 1 and 2 state that in between two interactions, an elementary particle is not present in the observable universe. A particle only manifests itse

simply nonsense

[Browzer]

The Slashdot headline, not the physics.

http://www.math.columbia.edu/~woit/wordpress/

Re:hmmm....

[St.Creed]

This isn't a particle so much as methodology

The important bit here is why? Why does this methodology work so well. Is it because that deep down on a very fundamental level this "Geometry" is hard coded in the way the universe works? If so. What does this tell us about how things really work?

That's a pretty good question. I've been wondering about that too, given the convergence between our definitions of entropy and Kolmogorov complexity, which describes how much information is encoded in a signal (also tied in with Shannon's law). It hits directly into the heart of the question: what is information and how does it relate to reality? At a basic level, our universe may be comprised of "information", or rather: a signal on top of noise.

This new discovery seems to suggest that at the most basic level, particles can be described as a mathematical function on top of some sort of "white noise" as well. I wonder how long it will take to converge the two ideas. If ever.

In any case, exciting times are ahead for so-called computer scientists that deal with things like geometric algorithms. I predict a hot demand for top mathematicians in that field to arise very soon.

Anyway, exciting times to be a theoretical physicist! Everyone expecting breakthroughs coming from the LHC and the experimental boys and girls, and now suddenly, out of left field the theoretical physicists come back with a big right hook out of nowhere :)

Re:Relevance of theory to the real world is unknow

[Guy Harris]

If one assumes that Special Relativity and Quantum Mechanics are correct, and there is no observational evidence that they are not, then Yang-Mills theory, or something very much like it, is inevitable. It arises from the need for conservation of the various charges each force.

A Yang-Mills theory, based on {pick-your-favorite-group}, may be inevitable. Whether it would be the N=4 supersymmetric Yang-Mills theory is another matter; it won't be.