## Main Question or Discussion Point

If an electron can be at two places at one time, why can't Santa be in multiple houses simultaneously?

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Simon Bridge
Homework Helper
An electron cannot be in two places at the same time.

Or - to put it another way - Santa can be at all houses at the same time, but only if he does not deliver any presents, drink the brandy, or collect the mince pie. Any of these things would collapse his wave-function to one location just like detection of the electron does.

I suppose Norad could be slowing Santa down by constantly localizing him ;)

An electron cannot be in two places at the same time.
Perhaps the question may be asked, "If the wave passes through 2 slits at the same time, then why blah blah blah...???"

Or - to put it another way - Santa can be at all houses at the same time, but only if he does not deliver any presents, drink the brandy, or collect the mince pie. Any of these things would collapse his wave-function to one location just like detection of the electron does.

I suppose Norad could be slowing Santa down by constantly localizing him ;)
Was National Aeronautics and Space Administration (NASA) lying to us?

Drakkith
Staff Emeritus
As objects get larger and more massive their wavefunctions describing position shrink down to absolutely miniscule sizes. Because Santa is made up of almost countless atoms, quantum effects only take place over a distance so small as to make it totally irrelevant. (Fractions of the diameter of an atom)

Simon Bridge
Homework Helper
@dipungal:
1. what wave?
As a lay representation of what I'm talking about - I really like Feynman's lectures on youtube.

2. of course they are - the trouble is: about what?

@Drakkith: spoilsport :)
Doesn't quite work though does it? In principle we could set up an arbitrarily wide potential (say: the width of the lab) and confine an alpha to it... let it settle to it's ground state... then it's wavefunction has a wavelength roughly twice the potential's width right? Same if we confined an electron to the same volume?

You mean the deBroglie wavelength - which is important for diffraction experiments on particles.

The bits of the alphas interact with each other - so the alpha is well localized with respect to it's center of mass (kinda the Penrose description iirc)... however the whole particles position may be highly uncertain. My point? Is it not the interaction that localizes something?

In Santa's case it is his interaction with The Rest Of The Universe. Of course his bits interact with more than just NORAD installations... thus we can locate macroscopic objects with nanometer precision.

@dipungal:
1. what wave?
The wave aspect of electrons, a single electron can pass through 2 different slits at the same time.

http://www.hitachi.com/rd/research/em/doubleslit.html" [Broken]

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Simon Bridge
Homework Helper
The wave aspect of electrons, a single electron can pass through 2 different slits at the same time.
Yes I know: did you see the Feynman lectures before replying?

note - your [hitachi.com] reference only describes the electron diffraction experiment.

The experimenters have no direct knowledge of the electron's wave travelling around both sides of the biprism at the same time. They are just asserting that this is what happened. You realize of course that in the setup, electrons are not all fired vertically downwards, they scatter somewhat so it is not surprising that some get around the barrier. See Lichte [e-J. Surf. Sci. Nanotech. Vol. 2 (2004) 52-55 Conference - ALC ’03]
http://amser.org/index.php?P=AMSER--ResourceFrame&resourceId=12348 [pdf]

So what is the wave-aspect of the electron a wave of?

See this Richard Feynman Lecture Series:
[video]
... that's the first one, watch the whole series, and the questions.
... it's a more rigorous description than your reference and more accessible than Lichte (above).

Executive Summary:
The wave is of probability amplitudes, the square of which is a probability density function. A probability is an expression of odds - it is not a physical object. What we are saying is that the process that ends up correctly describing the resulting diffraction pattern is mathematically equivalent to that of a wave. That does not mean it is physically the same thing as a wave.

Technically speaking, every object that has a volume greater than zero is in more than one place at one time.

For example, we call the object we live IN...Earth. The "earth" object has a volume and size greater than zero. So if you ask, can the earth be in two places at the same time,,I say yes, because earth is in more than one point in space at the same time. Likewise for the electron.

Simon Bridge
Homework Helper
What is the volume of an electron?

Drakkith
Staff Emeritus
What is the volume of an electron?
From wikipedia on Electron:
The electron has no known substructure.[2][72] Hence, it is defined or assumed to be a point particle with a point charge and no spatial extent.[9] Observation of a single electron in a Penning trap shows the upper limit of the particle's radius is 10−22 meters.[73] There is a physical constant called the "classical electron radius", with the much larger value of 2.8179×10−15 m. However, the terminology comes from a simplistic calculation that ignores the effects of quantum mechanics; in reality, the so-called classical electron radius has little to do with the true fundamental structure of the electron.[74][note 5]

Simon Bridge
Homework Helper
Thanks Drakkith, I was hoping @dipungal would find that out for himself.
Concepts like "size" get tricky at quantum scales... we can talk about a cross-section for particular interactions but that's not the same thing.

I recall a lecture where the class was asked to figure which of a group of objects was the smallest. There were cubes, pyramids, balls, rubber ducks, and a really long thin pole. After the results were in the lecturer showed us a garden sieve as the standard for smallness - the only shape to fit through the sieve was the long pole. Nobody had picked the pole.

Electrons can have an extent in terms of it's position wavefunction in different situations. My thesis involved treating conduction-band electrons and holes as if they were smeared out across 6-7nm in a crystal. I was wondering if dipungal would claim the volume of a minimum uncertainty wavepacket as the volume of the electron, or something else.

Of course, the other approach would be to ask if an object has more than one place inside it is the same as the object existing in more than two places at the same time. But that's too easy.

What is the volume of an electron?
Greater than zero, and that's all that matters.

Simon Bridge
Homework Helper
Greater than zero.
evidence?
afaik, nobody treats the electron as having a non-zero volume.

What about the other objection? That containing more than one location is not the same thing as being in more than one location...? A small point in semantics perhaps, but I feel this may be an important one.

Whatever - even if we accept that Santa, containing more than one location within his considerable volume, can be said to exist in more than one place at the same time ... it seems unlikely that his girth is bigger than, say, the distance between two chimneys and also be less than the inside diameter of the smaller of them (soas to fit down it, naturally).

So - to the extent that Santa can be said to be in two places at once - this still does not extend to letting him visit every chimney in the World in one night.

Isn't philosophy fun?!

Gold Member
... Isn't philosophy fun?!
Philosophy?? We’re talking about the empirical truth here! :grumpy:

:rofl:

Dale
Mentor
Or - to put it another way - Santa can be at all houses at the same time, but only if he does not deliver any presents, drink the brandy, or collect the mince pie. Any of these things would collapse his wave-function to one location just like detection of the electron does.
The presents wavefunction is highly entangled with the naughty-nice field via the preparation process known as "Santa's list". As soon as the first present is opened and observed the whole wavefunction collapses resulting in the delivery of all presents.

Gold Member

... and what happens if you get a decohered wavefunction that you never wished for ...

Dale
Mentor

... and what happens if you get a decohered wavefunction that you never wished for ...
Then the probability of Santa decreases, but Bayesians and frequentists disagree on the interpretation.

Gold Member
Then the probability of Santa decreases, but Bayesians and frequentists disagree on the interpretation.
:rofl:

I was just thinking... sure, it’s the wrong (mono?)pole... but if there’s (Feynman) http://en.wikipedia.org/wiki/Penguin_diagram" [Broken], surely there must also be "Santa diagrams"...?

Has anyone seen it? It would probably help us to visualize the problem... :uhh:

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Drakkith
Staff Emeritus
Hah! Love the pic!

Gold Member

... and what happens if you get a decohered wavefunction that you never wished for ...
Well, "it's the thought that counts". More evidence that conciousness is required to collapse the wavefunction ...

... and what happens if you get a decohered wavefunction that you never wished for ...
Ugh, as long as it's not another particle in a box.

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As objects get larger and more massive their wavefunctions describing position shrink down to absolutely miniscule sizes. Because Santa is made up of almost countless atoms, quantum effects only take place over a distance so small as to make it totally irrelevant. (Fractions of the diameter of an atom)
Santa Claus is a virtual object, and his particles have no real mass, and neither does he. His wavelength is much greater than the distance between any two houses.

Or more parsimoniously, it cannot be proven that Santa Claus does not exist in any given chimbley. And if that isn't proof enough, I can't help you.