Can an electron be in two places at the same time?

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Offline PmbPhy

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Re: Can an electron be in two places at the same time?
« Reply #100 on: 17/02/2015 15:10:28 »
Quote from: Pete
Simple, huh? :)

If you say so!

I was puzzled by the vertical lines which seem to be used as though they were brackets.  I understand that they imply the absolute value of the figure they enclose.  The nearest I could come to understanding the absolute value of a number was that it signifies the distance of that number from zero.  Iím hard pressed to think of a calculation in which this distinction between value and absolute value might be significant.

3 = 1+1+1

|3| = 0+1+1+1 ?????
It's important when the numbers are complex like the wave function. E.g. try as an example

z = 1 + i

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Offline evan_au

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Re: Can an electron be in two places at the same time?
« Reply #101 on: 17/02/2015 20:42:42 »
One domain where an electron seems to be in multiple places at the same time is in photosynthesis.

Physicists explain the very high efficiency of photon capture and electron processing by suggesting that the chlorophyl molecule offers multiple paths for electron transfer, and the photoelectron effectively explores all of them as a delocalised coherent wavicle. This led to the (serious) field of quantum biology.

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Offline yor_on

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Re: Can an electron be in two places at the same time?
« Reply #102 on: 17/02/2015 21:34:51 »
I don't agree John. Without mathematics to back it up nobody would have taken Einstein seriously, neither would people believe QM. The mathematics are telling us some pretty implausible things both ways, especially since we're newly arrivals from a more Newtonian society. And it changes the way we think, we don't have a choice. Sometimes the mathematics has to be invented though, but there will be a consistency to new mathematics too. Take a look at Perelman's work for example, it's all mathematics, and those few able to follow his thinking there https://en.wikipedia.org/wiki/Grigori_Perelman . Mathematics are several languages it seems, although still one and the same, I think of it as logic.
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Offline jeffreyH

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Re: Can an electron be in two places at the same time?
« Reply #103 on: 17/02/2015 23:26:54 »
Mathematics in its most useful form takes something very complex and creates something concise that sums up the situation succinctly.

Think of e=mc^2 or [tex]\lambda[/tex] = h/p.
Fixation on the Einstein papers is a good definition of OCD.

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Offline PmbPhy

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Re: Can an electron be in two places at the same time?
« Reply #104 on: 18/02/2015 08:08:37 »
One domain where an electron seems to be in multiple places at the same time is in photosynthesis.

Physicists explain the very high efficiency of photon capture and electron processing by suggesting that the chlorophyl molecule offers multiple paths for electron transfer, and the photoelectron effectively explores all of them as a delocalised coherent wavicle. This led to the (serious) field of quantum biology.
That's not the same thing as being in two places at once since at no time does any photon ever measured to be at more than one place. What you're talking about is Feynman's Explore all paths approach to the path integral formulation of quantum mechanics.

http://en.wikipedia.org/wiki/Path_integral_formulation#Feynman.27s_interpretation

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Offline Bill S

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Re: Can an electron be in two places at the same time?
« Reply #105 on: 18/02/2015 11:59:57 »
Quote from: Pete
That's not the same thing as being in two places at once since at no time does any photon ever measured to be at more than one place.

Would it be right to say that the Path Integral Formulation maintains that the quon explores all paths, but a measurement would have to be made to establish the position of the quon at any given time? 
There never was nothing.

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Offline Bill S

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Re: Can an electron be in two places at the same time?
« Reply #106 on: 18/02/2015 12:07:24 »
Quote from: Pete
try as an example

z = 1 + i

I would, if I had any idea what could be done with it.   [:-\]
There never was nothing.

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Offline JohnDuffield

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Re: Can an electron be in two places at the same time?
« Reply #107 on: 18/02/2015 14:08:04 »
Would it be right to say that the Path Integral Formulation maintains that the quon explores all paths, but a measurement would have to be made to establish the position of the quon at any given time?
No. That's old hat. A photon has its E=hc/λ wavelength, it doesn't have a localised pointlike position, just like a seismic wave doesn't have a localised pointlike position. See the physicsworld article In Praise of Weakness. This describes how Aephraim Steinberg et al used "weak measurement" to map the path of a photon going though both slits of Young's double slit experiment:



Its path is not some line, just as the path of a seismic wave isn't some line. However when you use strong measurement to detect the photon, it's like detecting a seismic wave with a pointy stick the size of a mountain range. It gets totally absorbed by the stick, and you think the location of the photon was at the point of the stick. Check out the optical Fourier transform, it's maybe something like. Something that isn't pointlike, looks pointlike:



http://cns-alumni.bu.edu/~slehar/fourier/fourier.html
« Last Edit: 18/02/2015 14:10:04 by JohnDuffield »

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Offline jeffreyH

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Re: Can an electron be in two places at the same time?
« Reply #108 on: 19/02/2015 00:02:54 »
Ahem, John! That's an energy equation and not a wavelength equation.  You in fact need the equation [tex]\lambda = \frac {h}{p}[/tex].

NOTE: You need linear momentum here since de Broglie substituted velocity for c in deriving the general wave equation.
« Last Edit: 19/02/2015 18:52:22 by evan_au »
Fixation on the Einstein papers is a good definition of OCD.

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Offline PmbPhy

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Re: Can an electron be in two places at the same time?
« Reply #109 on: 19/02/2015 16:52:40 »
Quote from: Pete
try as an example

z = 1 + i

I would, if I had any idea what could be done with it.   [:-\]
Find the magnitude. That's done by using the expression

[tex]e^{i\theta} = cos \theta  + i sin \theta[/tex]

Then any complex number C can be represented as

[tex]C = Ae^{i\theta} = A(cos \theta  + isin \theta) = x + iy[/tex]

where

[tex]x = A cos \theta[/tex]
[tex]y = A sin \theta[/tex]

The magnitude of C is defined by

[tex]|C| = \sqrt{x^2 + y^2}[/tex]

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Offline PmbPhy

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Re: Can an electron be in two places at the same time?
« Reply #110 on: 19/02/2015 16:56:42 »
Quote from: Bill S
Would it be right to say that the Path Integral Formulation maintains that the quon explores all paths, but a measurement would have to be made to establish the position of the quon at any given time?
What's a "quon"? If you're talking about a particle then yes, that's true.

Quote from: JohnDuffield
No. That's old hat.
In no way is the Path Integral Formulation of quantum mechanics "old hat."
« Last Edit: 19/02/2015 18:50:02 by evan_au »

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Offline Bill S

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Re: Can an electron be in two places at the same time?
« Reply #111 on: 19/02/2015 17:40:21 »
Quote from: Pete
What's a "quon"?

http://en.wikipedia.org/wiki/Quon

Sensu Nick Herbert.
There never was nothing.

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Offline PmbPhy

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Re: Can an electron be in two places at the same time?
« Reply #112 on: 19/02/2015 20:17:04 »
Quote from: Pete
What's a "quon"?

http://en.wikipedia.org/wiki/Quon

Sensu Nick Herbert.
Interesting. I call them particles myself.

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Offline JohnDuffield

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Re: Can an electron be in two places at the same time?
« Reply #113 on: 19/02/2015 22:21:18 »
In no way is the Path Integral Formulation of quantum mechanics "old hat".
OK, let me restate: the notion that a photon is some point-particle thing with a discrete location is garbage.

Jeffrey: your point noted.

Bill: if you've read that book I recommend you also watch this program