Sum of Histories Simultaneous Paths

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In summary, Feynman claims that particles (photons, electrons, carbon molecules), when traveling from A to B, take every possible path to get there...simultaneously. This does not mean that a photon, traveling at lightspeed from A to B in a 'straight' line (shortest path), would travel faster than the speed of light when taking another path, because it takes a longer path in the same time. If you calculate expressions for physical processes then you will find that photons always travel with speed = c.
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PhanthomJay
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OK I'm just starting to read Hawking new book, and am confused already. I'll never get through the book if I don't understand this:

Feynman apparently claims that particles (photons, electrons, carbon molecules), when traveling from A to B, take every possible path to get there...simultaneously.

I've probably misunderstood this, because would this not imply that a photon, traveling at lightspeed from A to B in a 'straight' line (shortest path), would travel faster than the speed of light when taking another path, because it takes a longer path in the same time? I know this is not something new, but can someone clear this up for me?

Thanks.
 
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Bump? I'm just trying to find out if a photon violates its own finite speed when it simultaneously probablistically takes all possible paths to reach its destination, paths that are longer than the geodesic path. Thanks.
 
  • #3
What Feynman did (and what Hawking repeats) is to translate (his own) rigorous mathematical formulation into colloquial language. But that does not mean that one can invert this procedure and translate blindly eveything back b/c this is somehow like playing Chinese whispers.

In your case I would say that in the exact quantum mechanical formulation the "speed" of the photon is not defined. If you try to play Chinese whispers then 'yes', the photon would "move" with speed unequal c", but again "moving" is not defined as well.

If you calculate expressions for physical processes then you will find that photons always travel with speed = c.

For a better understanding I recommend Feynmans books:
"QED: The Strange Theory of Light and Matter": http://en.wikipedia.org/wiki/The_Feynman_Lectures_on_Physics
"The Feynman Lectures on Physics": http://en.wikipedia.org/wiki/QED:_The_Strange_Theory_of_Light_and_Matter

(it is not my place to criticize Hawking but I am not a fan of his popular writings; I miss statements like "one has to be careful taking this too literally ..." - which would be not a good advertisement, of course :-)
 
  • #4
Tom..thank you for the response. I'll have to agree that sometimes Hawking does take a lot of liberties in his writings, without qualifying his statements.

Thanks again.
 

Related to Sum of Histories Simultaneous Paths

1. What is the Sum of Histories Simultaneous Paths (SHSP) theory?

The SHSP theory is a concept in quantum mechanics that suggests that all possible paths that a particle can take in a given system are equally valid and contribute to the final outcome. This means that the particle can take multiple paths simultaneously, and the final result is a sum of all these paths.

2. How does the SHSP theory differ from the traditional view of quantum mechanics?

In traditional quantum mechanics, particles are described as having a single definite path or trajectory. However, the SHSP theory suggests that particles can take all possible paths simultaneously, which is a departure from the traditional view.

3. What evidence supports the SHSP theory?

The SHSP theory is supported by various experiments, such as the double-slit experiment, which has shown that particles can exhibit wave-like behavior and take multiple paths simultaneously. Additionally, the theory is also supported by mathematical models and calculations.

4. How does the SHSP theory explain the phenomenon of interference?

Interference occurs when two or more waves interact with each other, resulting in either constructive or destructive interference. In the SHSP theory, the interference pattern is explained by the superposition of all possible paths that the particle can take, which can either reinforce or cancel each other out.

5. What implications does the SHSP theory have in the field of quantum computing?

The SHSP theory has sparked interest in the development of quantum computers, as it suggests that particles can process information through multiple paths simultaneously, potentially leading to faster and more efficient computing. However, the practical application of this theory in quantum computing is still being researched and developed.

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