Sum over histories implies no definite history?

[Happiness]

What does Feynman's sum over histories mean to the interpretation of our world? Does it mean that we (or a particle) do not have a definite history, but only the most probable one?

 

[AlexCaledin]

According to Feynman, Nature seems analogous to chess game... So, then, the Histories work as the game organizer, a sort of Chessboard.

https://www.ling.upenn.edu/~kroch/courses/lx550/readings/feynman1-4.pdf
(scanned page 59)

 

[EPR]

There is a big difference between an electron and a chair or a table.
The electron may have many histories(within coarse graininess).
The chair, for what we know, has only a single history due to the fact that it obeys approximate classical laws.
With many degrees of freedom and big objects, quantum effects become quite negligible so much so that you can exclude them for all practical purposes.

 

[atyy]

What does Feynman's sum over histories mean to the interpretation of our world? Does it mean that we (or a particle) do not have a definite history, but only the most probable one?

Feynman's sum over histories is not a separate interpretation of quantum mechanics. It is a wonderful and very effective mathematical trick for calculating the probabilities of measurement outcomes, but Feynman's calculation method fits well within the orthodox, Copenhagen-style interpretation.

 

[Demystifier]

What does Feynman's sum over histories mean to the interpretation of our world?

Nothing, absolutely nothing. As @atyy said, it's just a mathematical method of computation. In the case of fermionic fields, the method does not even involve a sum over histories.

 

[Happiness]

Feynman's sum over histories is not a separate interpretation of quantum mechanics. It is a wonderful and very effective mathematical trick for calculating the probabilities of measurement outcomes, but Feynman's calculation method fits well within the orthodox, Copenhagen-style interpretation.

Nothing, absolutely nothing. As @atyy said, it's just a mathematical method of computation. In the case of fermionic fields, the method does not even involve a sum over histories.

This, at best, says Feynman's sum over histories is consistent with the orthodox, one-history Copenhagen-style interpretation? But Feynman's sum over histories could also be consistent with a multi-histories interpretation?

Before Feynman's sum over histories, most of us were oblivious to or ignorant of the possibility of a multi-histories interpretation. So Feynman's sum over histories at least opened up our horizon, gave us the awareness needed before we could question what we heretofore have taken for granted, the awareness needed to review our epistemology? How do you know what we think is true, is true? What makes you so confident?

 

[Happiness]

The electron may have many histories(within coarse graininess).

Feynman's method shows that the historical path of a particle is not encrypted into the present state of the particle, so this is also true for a collection of particles, this implies that our history is also not encrypted into our present state?

 

[PeterDonis]

What does Feynman's sum over histories mean to the interpretation of our world?

Nothing. The term "sum over histories" is unfortunate given that the word "histories" has come to be associated with certain interpretations of QM. That's not how Feynman was using the word (those interpretations hadn't even been invented yet when he coined the term). He was just describing the path integral formulation of QM: a "history" is just one of the paths that goes into the integral. The path integral formulation is just a different way of computing amplitudes, mathematically equivalent to the Schrodinger Equation; it only applies when no measurement is being made, and has nothing whatever to say about what happens when a measurement is being made.

 

[AlexCaledin]

___________________________________________________________________

In 1948 Feynman, building on the work of Dirac, introduced his sum-over-histories formulation of quantum mechanics and with it the path integral that has proved a powerful tool in many branches of physics. It is possible to see the sum-over-histories as merely a technical tool - a useful device for computing certain amplitudes within the usual Schrödinger-Heisenberg formulation of quantum mechanics in terms of states on spacelike surfaces. That is not, however, how I think Feynman saw it. Rather, the sum-over-histories formulation of quantum mechanics can be regarded as an independent formulation of quantum theory.
Its equivalence with the usual formulations is not automatic but rather a question whose answer may be different in different theories and for different physical systems. In this talk I shall review the current status of the sum-over-histories formulation as an independent statement of quantum theory. I shall argue that, viewed most fundamentally, it is different from the Schrödinger-Heisenberg formulations because the totality of alternatives to which it potentially assigns probabilities is different from that of Schrödinger-Heisenberg quantum mechanics. Sum-over-histories alternatives at definite moments of time are more restricted than in usual quantum mechanics because they refer only to the coordinates of the configuration space in which the paths are defined. By contrast, at a moment of time, Schrödinger-Heisenberg quantum mechanics has all the alternatives provided by transformation theory. However, even in non-relativistic quantum mechanics, the sum-over-histories formulation allows a generalization of the alternatives at definite moments of time to genuine spacetime alternatives that are not considered in usual Schrödinger-Heisenberg formulations.
This generalization allows a more realistic description of everyday experiments. But, more importantly, it may be central for the construction of a quantum theory of gravity in which there is no well-defined notion of time. There, alternatives "at a moment of time" may be difficult to find, while spacetime alternatives may be the natural "observables" for which the theory makes predictions.
___________________________________________________________________

James B Hartle
Introduction to "THE SPACETIME APPROACH TO QUANTUM MECHANICS"

 

[EPR]

The contribution of quantum uncertainty to the world of chairs and tables is almost zero.
There is only one history in the macro world.
People seem to have conceptual issues what relates to what and how everything is being determined.
Quantum mechanics rules apply IN the quantum world. There, no single history exists.
On the other hand, there are no multiple histories in the macro world. Why? Because the contribution of quantum effects IN the macro world is negligible. With all things taken together, a collection of atoms has VERY little uncertainty. The bigger it gets, the less uncertain the object is. For something as big as a giraffe, the uncertainty of position is practically zero.
Not so with a single atom.
We shouldn't even be talking of histories in the plural.

 

[Happiness]

I realize it's not easy to get neutral, impartial responses. Most of us have our own perspectives, beliefs and biases, and we allow these biases to influence our response, knowingly or unknowingly.

My attempt of an impartial, fair response would be:

"Feynman's sum over histories is a mathematical tool. In that respect, it is neutral to the various interpretations. It neither supports nor rejects the orthodox one-history interpretation. It also neither supports nor rejects the multi-histories interpretation. The multi-histories interpretation could turn out to be false; it could also turn out to be true. The same is true for the orthodox one-history interpretation. At best, you could say that the sum over histories may have stimulated ideas in the exploration and investigation of the multi-histories interpretation."

There is only one history in the macro world.

This is what we observe, or more rigorously speaking, this is what we think we observe. I understand why you make that statement, but that statement has not been proven scientifically rigourously. Until then, other alternatives cannot be excluded.

We shouldn't even be talking of histories in the plural.

An overwhelming majority of people may be of the opinion that this is true, but in the true scientific spirit, rigour and exploration, science would response: "Don't be too overconfident. Be open to different perspectives. It is still too early to tell now." Science is humble, for it only says what has been proven to be true, is true, for the remaining, it says: "I do not know, at least not so, as for now."

 

[EPR]

The MWI is a very extravagant idea... But we are not even talking about the MWI but the fundamentals of quantum systems - their indeterminacy(which fapp is limited in scope and fapp coincides with... Hang on - yes, with classicality).

You don't need a new Universe to explain the fuzziness of the hydrogen atom.
What evidence is there of many histories in the macro world?
There is none.
It's not an opinion. It's an observational fact.

 

[Happiness]

What evidence is there of many histories in the macro world?
There is none.
It's not an opinion. It's an observational fact.

Similarly, someone could say:
"Currently, what conclusive evidence is there of a one-and-only history in the macro world?
There is none.
It's not an opinion. It's a scientific fact."

So an impartial, fair response would be:
"There is currently neither conclusive evidence for the multi-histories interpretation nor for the single-history interpretation. We simply do not know which is true at this point in time."

When we view the world from our own perspective, we often exclude and forget the existence of other perspectives. But the true scientific attitude is to keep all options open until their possibility is excluded by the rigourous process of science. And fair, impartial responses help to inform and remind us what options are still open for consideration, for the progress of science and for uncovering the truth.

 

[PeterDonis]

"There is currently neither conclusive evidence for the multi-histories interpretation nor for the single-history interpretation. We simply do not know which is true at this point in time."

The Feynman "sum over histories" is not an interpretation of QM; it certainly is not the same as the MWI. It's just a different mathematical formulation, and is compatible with multiple interpretations just as the usual mathematical formulation is.

 

[PeterDonis]

Everyone, please bear in mind that asking about the implications of the sum over histories is not the same as asking whether the MWI is true. This thread is not about the MWI.

 

[Happiness]

The Feynman "sum over histories" is not an interpretation of QM; it certainly is not the same as the MWI. It's just a different mathematical formulation, and is compatible with multiple interpretations just as the usual mathematical formulation is.

Yes I meant the response

"There is currently neither conclusive evidence for the multi-histories interpretation nor for the single-history interpretation. We simply do not know which is true at this point in time."

is an impartial, fair response in relation to EPR's response

"What evidence is there of many histories in the macro world?
There is none.
It's not an opinion. It's an observational fact."

a "history" is just one of the paths that goes into the integral.

I wonder why Feynman used the word "histories" instead of "paths".

 

[PeterDonis]

I wonder why Feynman used the word "histories" instead of "paths".

When he used the word "histories", he probably didn't anticipate that that word would later be used in a much more general class of QM interpretations (since those wouldn't be invented for several more decades). It's a natural enough word to use for the spacetime paths, although it is somewhat weird that many of those paths are very, very different from classical paths (i.e., they violate the classical equations of motion by very large amounts), whereas the term "histories" does have at least somewhat of a connotation of classical paths.