The jewel found in Quantum mechanics?

[eboy32]

Could someone explain what this crazy new discovery means? Is it the rosetta stone of QM?

 

[bhobba]

I assume you mean this:
https://www.simonsfoundation.org/quanta/20130917-a-jewel-at-the-heart-of-quantum-physics/

Mate, right now, exactly what it means is uncertain. Its without doubt important - but how important remains to be seen. It may be paradigm changing or simply just a better way to calculate.

Thanks
Bill

 

[eboy32]

Right, but I'm trying to grasp what they found, is it just a new equation or is it really some type of jewel. When will we realize that QM is alien intelligence looking at us right in the face.

 

[f95toli]

What they found is a set of equations, that when plotted in a graph LOOKS like a jewel.

It is akin to saying that the equation y=x^2 is shaped like a bowl.

 

[Legaldose]

It says what they found right on the first caption of that link from bhobba. The geometrical properties give rise to probability distributions of the outcomes of particle interactions.

 

[eboy32]

Ah , thank you for that explanation.

 

[bhobba]

When will we realize that QM is alien intelligence looking at us right in the face.

Like I said what it's saying (in the sense of its meaning and significance) at the moment is uncertain.

But as to what QM is that's not quite that mysterious these days:
http://arxiv.org/pdf/quant-ph/0101012.pdf
http://arxiv.org/abs/0911.0695

Basically it would seem that ordinary probability theory and QM are the most reasonable ways to model physical systems as generalized probability models. What singles QM out is it allows entanglement - which ordinary probability theory doesn't.

Thanks
Bill

 

[Zarqon]

There's one thing I don't really get from that article. They keep stating that "locality is a central pillar" in quantum field theory. But what could they possibly mean by that, considering the fact that quantum entanglement (which QFT should be consistent with) is well described by the opposite: non-locality.

 

[bhobba]

FT

There's one thing I don't really get from that article. They keep stating that "locality is a central pillar" in quantum field theory. But what could they possibly mean by that, considering the fact that quantum entanglement (which QFT should be consistent with) is well described by the opposite: non-locality.

QFT has a different foundation than non relativistic QM that respects relativity so must be local. What Bell showed is QM objects can't have well defined properties independent of measurement context and be local. The answer is simple - simply assume QFT doesn't allow well defined properties independent of measurement context.

Also note that non locality of the Bell type can't be used to send information FTL - which is the sense locality is meant - so its probably possible to accommodate non locality in QFT - but the simplest way to handle it is simply say it doesn't have properties independent of context.

Thanks
Bill

 

[Zarqon]

Ahh ok, so there's basically two similar but still different definitions of locality. I'm from the quantum information side, and there locality almost always just mean that an object is local or nonlocal (like in Bell-type experiments).

So just to get what you said, you mean that in QFT locality instead means: An event somewhere in space cannot be caused by something outside the light cone?

 

[San K]

There's one thing I don't really get from that article. They keep stating that "locality is a central pillar" in quantum field theory. But what could they possibly mean by that, considering the fact that quantum entanglement (which QFT should be consistent with) is well described by the opposite: non-locality.

It's local in the sense, I guess, that some properties (but not all of those that are required to send/construct information) could be "connected/joined" via another dimension...as if they were un-affected by space-time.

 

[bhobba]

So just to get what you said, you mean that in QFT locality instead means: An event somewhere in space cannot be caused by something outside the light cone?

In relativity it means information can't be sent FTL. Relativity doesn't strictly rule out non-locality - only the ability to send info FTL to sync clocks.

Non local effects like Bell are allowed if they can't be used to send information. The easiest way to view QFT is it doesn't allow any type of locality violation - but if you want to make life harder, for whatever reason, it's still allowed if it can't be used to sent info FTL.

Thanks
Bill

 

[eloheim]

Please take the quoted material & commentary below as both/either general information for the OP, and/or responses to questions raised farther down the thread. I didn't want to break up the article quotations more than necessary!

All from Natalie Wolchover, for Quanta (same as referenced by bhobba): A Jewel at the Heart of Quantum Physics

The amplituhedron, or a similar geometric object, could help by removing two deeply rooted principles of physics: locality and unitarity.
...
Locality is the notion that particles can interact only from adjoining positions in space and time. And unitarity holds that the probabilities of all possible outcomes of a quantum mechanical interaction must add up to one. The concepts are the central pillars of quantum field theory in its original form, but in certain situations involving gravity, both break down, suggesting neither is a fundamental aspect of nature.
...
Encoded in its volume are the most basic features of reality that can be calculated, “scattering amplitudes,†which represent the likelihood that a certain set of particles will turn into certain other particles upon colliding.

Locality says that particles interact at points in space-time. But suppose you want to inspect space-time very closely. Probing smaller and smaller distance scales requires ever higher energies, but at a certain scale, called the Planck length, the picture gets blurry: So much energy must be concentrated into such a small region that the energy collapses the region into a black hole, making it impossible to inspect. “There’s no way of measuring space and time separations once they are smaller than the Planck length,†said Arkani-Hamed. “So we imagine space-time is a continuous thing, but because it’s impossible to talk sharply about that thing, then that suggests it must not be fundamental — it must be emergent.â€

Unitarity says the quantum mechanical probabilities of all possible outcomes of a particle interaction must sum to one. To prove it, one would have to observe the same interaction over and over and count the frequencies of the different outcomes. Doing this to perfect accuracy would require an infinite number of observations using an infinitely large measuring apparatus, but the latter would again cause gravitational collapse into a black hole. In finite regions of the universe, unitarity can therefore only be approximately known.

Obviously the informal definitions highlighted above may be of use to Zarqon, others here:

So just to get what you said, you mean that in QFT locality instead means: An event somewhere in space cannot be caused by something outside the light cone?

So for some questions of my own: Am I right to think that the disposal of 'locality' proffered in the article is closely related to the Holographic Principles/proposals associated with quantum gravity? I gathered that from language like in the quotations provided--especially the parts about black holes & horizons, and Planck scales. Is this new treatment of 'locality' invoked to avoid the problems (that I've often heard reference to) associated with continuous spacetime and those 'notorious' quantum infinites?? (Hope I'm on the right path here, at least! )

Secondly, I have to admit, I was really surprised to see 'unitarity' (or rather the dispensation, thereof) held up beside 'locality' as a 'problem concept' to be eliminated(!). I would have expected exactly the opposite--I've always considered it (unitarity, that is) to be a pilar of physics beyond the standard model, and one of the key insights of recent times! Am I missing something with this? I'd guess that the reason behind it lies in the 'amplituhedron's' function as a practical tool for real-world calculations (like the rendering of predictions for particle scatterings, and measurements), rather than (e.g.) representing some idealized theoretical formalism.

However, doesn't string theory have a similar picture (of interaction amplitudes), which is infamous for its deafening silence on what's happening 'on the inside' of such a universe (i.e. in time/away from unitarity, etc.)? Is there some key departure on the part of the 'amplituhedron' at this point? Or just, "Why is so much emphasis being put on the implications for our understanding of 'unitarity' exactly?"

 

[stevendaryl]

There's one thing I don't really get from that article. They keep stating that "locality is a central pillar" in quantum field theory. But what could they possibly mean by that, considering the fact that quantum entanglement (which QFT should be consistent with) is well described by the opposite: non-locality.

Well, there are two aspects of quantum mechanics (or quantum field theory): (1) The evolution equations governing the fields, and (2) the interpretation of those fields as representing probability amplitudes for the results of measurements.

Quantum field theory is perfectly local in aspect number 1: The evolution of the quantum fields in one region of spacetime depends only on the values of fields in the backward lightcone.

 

[ddd123]

Secondly, I have to admit, I was really surprised to see 'unitarity' (or rather the dispensation, thereof) held up beside 'locality' as a 'problem concept' to be eliminated(!). I would have expected exactly the opposite--I've always considered it (unitarity, that is) to be a pilar of physics beyond the standard model, and one of the key insights of recent times! Am I missing something with this?

I'd like to know more about this as well. How can we interpret systems in which the total probability isn't one?

Also wasn't there a recent new method, called "the unitarity method" for calculating amplitudes really fast, bypassing the feynman diagram calculations?

 

[eloheim]

I'd like to know more about this as well. How can we interpret systems in which the total probability isn't one?

Good catch. That part interested me very much as well, but somehow it got lost on the way to market when I put together my post.

 

[bhobba]

I'd like to know more about this as well. How can we interpret systems in which the total probability isn't one?

It can't be interpreted as probability - obviously - because one of the axioms of probability is the probability of all possible events must add up to one - see Kolmogorovs axioms.

They will have to find some other way around it like the negative probabilities that plagued relativistic QM in the early days.

Two issues here. First its a populist account bereft of the technical detail - not that I think even if that detail was published more than a few specialists in the area would understand it anyway. And secondly the article is basically saying it needs further investigation.

Thanks
Bill

 

[bhobba]

Am I right to think that the disposal of 'locality' proffered in the article is closely related to the Holographic Principles/proposals associated with quantum gravity?

I think any reading into it beyond its something interesting that needs investigation by specialists in the area is not at this stage warranted.

Secondly, I have to admit, I was really surprised to see 'unitarity' (or rather the dispensation, thereof) held up beside 'locality' as a 'problem concept' to be eliminated(!). I would have expected exactly the opposite--I've always considered it (unitarity, that is) to be a pilar of physics beyond the standard model, and one of the key insights of recent times! Am I missing something with this?

I think any attacks on unitarity will have a hard time contending with Wigners theorem:
http://en.wikipedia.org/wiki/Wigner's_theorem

We need to see exactly what develops.

Thanks
Bill

 

[eloheim]

Two issues here. First its a populist account bereft of the technical detail - not that I think even if that detail was published more than a few specialists in the area would understand it anyway. And secondly the article is basically saying it needs further investigation.

The real paper is finally out, btw. I didn't realize the following was from a different thread: Finally... The Amplituhedron Paper!

http://arxiv.org/abs/1312.2007

The Amplituhedron

Nima Arkani-Hamed, Jaroslav Trnka
(Submitted on 6 Dec 2013)
Perturbative scattering amplitudes in gauge theories have remarkable simplicity and hidden infinite dimensional symmetries that are completely obscured in the conventional formulation of field theory using Feynman diagrams. This suggests the existence of a new understanding for scattering amplitudes where locality and unitarity do not play a central role but are derived consequences from a different starting point. In this note we provide such an understanding for N=4 SYM scattering amplitudes in the planar limit, which we identify as ``the volume" of a new mathematical object--the Amplituhedron--generalizing the positive Grassmannian. Locality and unitarity emerge hand-in-hand from positive geometry.

Also, thanks for the tip on Wigner's theorem. I'll have a look.

 

[bhobba]

Also, thanks for the tip on Wigner's theorem. I'll have a look.

At the math level this is at Wigners theorem would be ho-hum. They would know it backwards up down and sideways. I am pretty sure they have something a bit more subtle in mind.

And no - I have zero idea what it is.

But unless you are into it at that level its pointless really conjecturing - time will tell.

Thanks
Bill