The physical world cannot be a single history

[RUTA]

Here is a fun talk by Fay Dowker on a path integral approach to the Greenberger-Horne-Zeilinger (GHZ) correlations. It's a physical instantiation of N. David Mermin's "no instruction sets" for GHZ in his Am. J. Phys. paper "Quantum mysteries revisited," v58, Aug 1990, 731-734.



The talk is titled "Are There Premonitions in Quantum Measure Theory?"

At the 39:36 mark she concludes "The physical world cannot be a single history." So, she proposes that "an interpretational scheme for path integral quantum theory -- is that the physical world is just a set of histories which is as small as it can be ... ."

 

[Jilang]

Thanks RUTA, I started watching it this morning but ran out of time. I have always been a fan of the path integral formulation, but it's amazing how little trod this path is!

 

[Jilang]

I got to the end, but i was pulling my hair out. The Venn diagram bit was fine, but after that she lost me.

 

[Quantumental]

So she's proposing Everett?

 

[RUTA]

I got to the end, but i was pulling my hair out. The Venn diagram bit was fine, but after that she lost me.

I've attached the Mermin article. He makes it easy to understand why there can be no "fact of the matter" concerning unmeasured values of spin for each of the three GHZ particles. That's what he calls "instruction sets" and Fay calls elements of the set for her Venn diagram. That there can be no definite set of spin x and y values for each particle independent of measurement means, in the context of Fay's GHZ device, that the particles cannot have definite paths through the device.

 

[RUTA]

So she's proposing Everett?

No, she's not proposing Many Worlds, she's proposing one world that contains multiple histories. In the reality she's proposing, a single particle can have more than one worldline between the same two spacetime points. Which is to say it can be in more than one place at once.

 

[Quantumental]

No, she's not proposing Many Worlds, she's proposing one world that contains multiple histories. In the reality she's proposing, a single particle can have more than one worldline between the same two spacetime points. Which is to say it can be in more than one place at once.

If every particle that make up an observer takes all different paths between point a and b, then how is this different from many worlds?

 

[RUTA]

If every particle that make up an observer takes all different paths between point a and b, then how is this different from many worlds?

In Many Worlds, there is a different world for each history. In Many Histories, there is just one world with many histories.

 

[bhobba]

Which is to say it can be in more than one place at once.

That's exactly what's going on.

The path integral formalism is actually a hidden variable theory, but of a very non trivial type. The path is the hidden variable, and if you take the formalism as basic then indeed, in that interpretation, its taking many paths and is in many places all at once. Of course since its hidden you can never know what they are.

I rather like the video, and have always believed the path integral approach is more fundamental when I learned that renormalisation of yang-mills theories has only been done with the path integral approach. I even read somewhere, but don't know the truth, that, for some reason, its the only way you can do it.

Thanks
Bill

 

[bhobba]

If every particle that make up an observer takes all different paths between point a and b, then how is this different from many worlds?

Ruta gave the correct answer.

But interestingly, there is Hartle's version using decoherent histories, and its often commented that approach is many worlds without the many worlds - technically in that interpretation QM is a stochastic theory about histories - you don't even have observations. I have always liked that interpretation, but think its a bit more complex than necessary.

Thanks
Bill

 

[Jilang]

In Many Worlds, there is a different world for each history. In Many Histories, there is just one world with many histories.

It makes more sense to me than Many Worlds as I can conceive that histories could interfere when they converge. i have never been clear how the interference happens in Many Worlds if they are all separate.

 

[Jilang]

RUTA, a question if I may? .. I hope it's not too off topic.
Given that the paths/histories must converge at a certain point in time, does that rule out the crazy paths that are often stated in popular texts (like it goes to Alpha Centauri and back) as contributing.
Or putting it alternatively would that mean that only very close paths could add and interfere, as the particle must arrive at the same point in spacetime whichever path it takes?

 

[RUTA]

It makes more sense to me than Many Worlds as I can conceive that histories could interfere when they converge. i have never been clear how the interference happens in Many Worlds if they are all separate.

I'm not an Everettian, maybe someone from that ilk can weigh in. My impression as an outsider is that essentially they're saying configuration space is real (no wave collapse) and it's in configuration space that you get amplitudes canceling, so maybe Worlds do cancel directly?

 

[RUTA]

RUTA, a question if I may? .. I hope it's not too off topic.
Given that the paths/histories must converge at a certain point in time, does that rule out the crazy paths that are often stated in popular texts (like it goes to Alpha Centauri and back) as contributing.
Or putting it alternatively would that mean that only very close paths could add and interfere, as the particle must arrive at the same point in spacetime whichever path it takes?

It does not rule out even the craziest paths. Shankar has a great explanation of interference for different trajectories in the case of one free particle. He even does a nice "back of the envelope" calculation for an electron versus a 1-gram particle on the paths x = t (classical path) and x = t² (non-classical path), so you can see why the non-classical path contributes to the sum over paths for the electron, but likely does not for the 1-gram particle. Hopefully I'll remember to post that when I get to work this afternoon. If not, please remind me :-)

 

[RUTA]

Shankar has a great explanation of interference for different trajectories in the case of one free particle. He even does a nice "back of the envelope" calculation for an electron versus a 1-gram particle on the paths x = t (classical path) and x = t² (non-classical path), so you can see why the non-classical path contributes to the sum over paths for the electron, but likely does not for the 1-gram particle.

I should probably give a proper citation for this :-)

R. Shankar, "Principles of Quantum Mechanics," 2nd ed, Springer, 1994, ISBN 0-306-44790-8. The page numbers are shown on the attachment.

 

[Jilang]

Hi RUTA, thanks for this. I still didn't find anything that would turn my mind though from the idea that the paths must be really close to exhibit quantum effects. I read once ( sorry can't remember where) that an object the size of a person would need move incredibly slowly to exhibit quantum effects. This makes some sense to me in that the larger the object is, the less uncertainly there is to its position in time( and limited paths) In the converging histories the larger object clearly must exhibit less quantum effects as there are fewer paths that will converge at the measured time.

 

[gill1109]

Sascha Vongehr (IMHO) makes a very decent attempt to "save" many worlds/many minds. http://arxiv.org/abs/1311.5419

Against Absolute Actualization: Three "Non-Localities" and Failure of Model-External Randomness made easy with Many-Worlds Models including Stronger Bell-Violation and Correct QM Probability

Sascha Vongehr

Experimental violation of Bell-inequalities proves actualization of many futures (~ many-worlds); I show that this is not mere interpretation. To show this self-contained pedagogically, I resolve the EPR paradox by starting with a visually intuitive non-quantum many-worlds model that already has apparent non-locality. A modification leads to a classical-to-quantum transition model. Model-external randomness (a ghost outside the universe throwing a pebble on state-space) stays unchanged, but the modeled observers witness strong Bell-violation. I derive the quantum probability P from classical-to-quantum consistency. Model-internal probability (~ subjective Bayesianism) is derived as a measure of surprise (~ Deutsch's rational expectation). The model shows how absolute actualization, say by real hidden variables, fails. Models with P and standard Bell-violation are supplied for completeness. The transition model is the first touchable, interactive science-outreach exhibit teaching correct quantum physics. The discussion reinterprets the transition model, defends Einstein-locality, rejects "realism" etc., to the conclusion that the models teach the necessity of "many worlds/minds", rejecting probability concepts with random-randomness regress. The models teach how EPR empirically excludes certain realisms.