What is the role of the path-integral formulation in quantum mechanics?

[I2004]

Thomas Hertog a colleague of Hawking has stated that quantum mechanics implys the universe has many histories. Is this an agreed fact or just his opinon/interpretation?

 

[I2004]

he also states:

This summation of all paths, proposed in the 1960s by physicist Richard Feynman and others, is the only way to explain some of the bizarre properties of quantum particles, such as their apparent ability to be in two places at once. The key point is that not all paths contribute equally to the photon's behaviour: the straight-line trajectory dominates over the indirect ones.

IS THIS TRUE?

 

[I2004]

all I am after is a simple answer, does quantum mechanics forbid a single history universe?

please someone help...

 

[Maui]

Quantum mechanics implies different things to different people. In collapse interpretations there is just 1 single history. The key word is 'imply' which is different from 'is'.

 

[I2004]

and hidden variables also say there is one history along with a number of interpretation?

So hertog is just quoting his opinon of interpretation rather than accepted fact?

 

[Dali]

and hidden variables also say there is one history along with a number of interpretation?

So hertog is just quoting his opinon of interpretation rather than accepted fact?

Yes, and yes.

 

[Greg-ulate]

Even the sum of all histories interpretation agrees that there is only one history. Its just that its the sum of all possible ones...

 

[DrChinese]

Thomas Hertog a colleague of Hawking has stated that quantum mechanics implys the universe has many histories. Is this an agreed fact or just his opinon/interpretation?

Interpretation. The agreed part is that this is an acceptable interpretation, but not the only one. If you look at a closed system, you will realize that entropy is at a local minimum at that point. Going to the past or the future, there are many histories which are possible which will be consistent with the observed system. You could say that entropy and histories are essentially a measure of the same thing.

 

[I2004]

This summation of all paths, proposed in the 1960s by physicist Richard Feynman and others, is the only way to explain some of the bizarre properties of quantum particles, such as their apparent ability to be in two places at once. The key point is that not all paths contribute equally to the photon's behaviour: the straight-line trajectory dominates over the indirect ones.

so this is just his opinon too I take it?

 

[vanhees71]

This is of course nonsense. The path-integral formulation is a (mathematically less well defined) but physically equivalent (whenever one can make sense of it and calculate things with it) way to describe standard quantum theory of Heisenberg, Born, Dirac et al (1926). Often it's a nice tool to express things more elegantly than in the way with Hilbert-space objects (vectors, Statistical Operators, observables, etc.), e.g., the quantization of gauge theories and other functional methods in QFT, some aspects of scattering theory (asymptotic limits etc), and also the (semi-)classical approximation.

However, no matter in which way you express quantum theory mathematically, in quantum theory a particle is not at several places at once but there is a probability distribution for its position depending on the state it is in. The many-worlds "interpretation" is nice to think about in science-fiction story like ways but it doesn't solve anything to the problems some people still have with accepting quantum theory as the way nature works on the most fundamental level because it partially contradicts our "common sense", which however is "trained" by everyday experience with macroscopic objects (i.e., many-body systems with a huge number of microscopic constituents and electromagnetic fields), which behave according to classical physics, because that's the case for the rough "coarse grained" description which is sufficient to understand their behavior. All this can be explained with appropriate approximations for the dynamics of collective (macroscopic) observables of quantum theory, no matter whether you use the path-integral formalism or not.