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<title>Albert van der Sel : Intro Interpretations in Quantum Mechanics</title>਍㰀洀攀琀愀 栀琀琀瀀ⴀ攀焀甀椀瘀㴀∀䌀漀渀琀攀渀琀ⴀ吀礀瀀攀∀ 挀漀渀琀攀渀琀㴀∀琀攀砀琀⼀栀琀洀氀㬀 挀栀愀爀猀攀琀㴀椀猀漀ⴀ㠀㠀㔀㤀ⴀ㄀∀㸀ഀഀ
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<h1>A few notes on Entanglement, Decoherence, and other aspects of Quantum Mechanics (QM).</h1>਍ഀഀ
Version	    : 0.8 <br>਍䐀愀琀攀ऀऀ㨀 ㈀㔀⼀　㄀⼀㈀　㄀㈀㰀戀爀㸀ഀഀ
By		    : Albert van der Sel<br>਍吀礀瀀攀 漀昀 搀漀挀ऀ㨀 䨀甀猀琀 愀渀 愀琀琀攀洀瀀琀 琀漀 搀攀挀爀椀戀攀 琀栀攀 猀甀戀樀攀挀琀 椀渀 愀 昀攀眀 猀椀洀瀀氀攀 眀漀爀搀猀⸀ 䠀漀瀀攀昀甀氀氀礀Ⰰ 椀琀✀猀 愀渀礀 最漀漀搀⸀㰀戀爀㸀ഀഀ
For who		: For anyone interested. <br>਍㰀栀爀⼀㸀ഀഀ
<br>਍ഀഀ
The sole purpose of this doc, is to quickly introduce some concepts, that hopefully "clarifies"<br>਍愀 昀攀眀 椀洀瀀漀爀琀愀渀琀 挀漀渀挀攀瀀琀猀 氀椀欀攀 ∀攀渀琀愀渀最氀攀洀攀渀琀∀Ⰰ ∀搀攀挀漀栀攀爀攀渀挀攀∀Ⰰ ∀䴀圀䤀∀Ⰰ ∀倀圀䤀∀Ⰰ 愀渀搀 椀渀琀攀爀瀀爀攀琀愀琀椀漀渀猀 漀昀 儀䴀 椀渀 最攀渀攀爀愀氀⸀㰀戀爀㸀ഀഀ
਍㰀戀爀㸀ഀഀ
<font face="arial" size=2 color="blue">਍䌀漀渀琀攀渀琀猀㨀㰀戀爀㸀ഀഀ
<br>਍㄀⸀ 䄀 昀攀眀 眀漀爀搀猀 漀渀 ∀攀渀琀愀渀最氀攀洀攀渀琀㰀戀爀㸀ഀഀ
2. A few words on "non-locality"<br>਍㌀⸀ 䄀 昀攀眀 眀漀爀搀猀 漀渀 ⠀挀氀愀猀猀椀挀愀氀⤀ ∀䌀漀瀀攀渀栀愀最攀渀 椀渀琀攀爀瀀爀攀琀愀琀椀漀渀∀㰀戀爀㸀ഀഀ
4. A few words on "Decoherence"<br>਍㔀⸀ 䄀 昀攀眀 眀漀爀搀猀 漀渀 䔀瘀攀爀攀琀琀✀猀 ∀䴀愀渀礀 圀漀爀氀搀猀∀ 䤀渀琀攀爀瀀爀攀琀愀琀椀漀渀 ⠀䴀圀䤀⤀㰀戀爀㸀ഀഀ
6. A few words on Porier's "Waveless" Classical Interpretation<br>਍㜀⸀ 䄀 昀攀眀 眀漀爀搀猀 漀渀 搀攀 䈀爀漀最氀椀攀 ⴀ 䈀漀栀洀 ∀倀椀氀漀琀 圀愀瘀攀∀ 䤀渀琀攀爀瀀爀攀琀愀琀椀漀渀 ⠀倀圀䤀⤀㰀戀爀㸀ഀഀ
8. A few words on Weak Measurements and TSVF<br>਍ഀഀ
<font face="arial" size=2 color="black">਍㰀戀爀㸀ഀഀ
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਍㰀昀漀渀琀 昀愀挀攀㴀∀愀爀椀愀氀∀ 猀椀稀攀㴀㈀ 挀漀氀漀爀㴀∀戀氀甀攀∀㸀ഀഀ
<h3>1. A few words on "entanglement":</h3>਍㰀昀漀渀琀 昀愀挀攀㴀∀愀爀椀愀氀∀ 猀椀稀攀㴀㈀ 挀漀氀漀爀㴀∀戀氀愀挀欀∀㸀ഀഀ
਍倀爀漀戀愀戀氀礀 琀栀攀 搀椀猀挀甀猀猀椀漀渀 椀渀 琀栀椀猀 猀攀挀琀椀漀渀 椀猀 愀 戀椀琀 琀漀漀 ∀䌀漀瀀攀渀栀愀最攀渀ⴀ猀琀礀氀攀∀ 漀爀椀攀渀琀攀搀Ⰰ 戀甀琀 琀栀愀琀 椀猀 栀漀眀 攀渀琀愀渀最氀攀洀攀渀琀㰀戀爀㸀ഀഀ
usually is introduced, in most literature.<br>਍㰀戀爀㸀ഀഀ
਍ഀഀ
Erwin Schrödinger came up with the expression “entanglement”, and called it <I>“the"</I> characteristic trait of quantum mechanics.<br>਍ഀഀ
<br>਍䴀愀渀礀 漀昀 甀猀 瀀爀漀戀愀戀氀礀 栀愀瘀攀 栀攀愀爀搀 漀昀 椀琀Ⰰ 戀甀琀 漀昀琀攀渀 椀琀 椀猀 昀攀氀琀 愀猀 愀 爀愀琀栀攀爀 ∀猀琀爀愀渀最攀∀ 攀昀昀攀挀琀⸀㰀戀爀㸀 ഀഀ
<br>਍䤀渀搀攀攀搀Ⰰ 眀栀愀琀 椀猀 椀琀 㼀 䰀攀琀✀猀 挀漀渀猀椀搀攀爀 愀 琀眀漀 ∀瀀愀爀琀椀挀氀攀猀∀ 猀礀猀琀攀洀⸀ 䤀渀 愀 猀瀀攀挀椀愀氀 挀愀猀攀Ⰰ 琀栀攀椀爀 挀漀洀洀漀渀 猀琀愀琀攀 挀愀渀 戀攀 椀渀 猀甀挀栀 愀 眀愀礀Ⰰ㰀戀爀㸀ഀഀ
that we may only describe it effectively as being two parts of <I>the same entity</I>.<br>਍䰀椀欀攀 琀栀攀 眀漀爀搀 ∀攀渀琀愀渀最氀攀洀攀渀琀∀ 愀氀爀攀愀搀礀 猀甀最最攀猀琀猀Ⰰ 椀琀✀猀 愀 猀漀爀琀 漀昀 ∀挀漀爀爀攀氀愀琀椀漀渀∀⸀ 䤀渀 戀攀琀琀攀爀 眀漀爀搀猀㨀㰀戀爀㸀ഀഀ
you need both particles in order to fully 'describe' the state of the system.<br>਍㰀戀爀㸀ഀഀ
਍ഀഀ
Fig 1.<br>਍㰀椀洀最 猀爀挀㴀∀攀渀琀愀渀最氀攀洀攀渀琀㄀⸀樀瀀最∀ 愀氀椀最渀㴀∀挀攀渀琀爀攀∀⼀㸀ഀഀ
<br>਍吀栀攀 ☀倀猀椀㬀⠀爀Ⰰ琀⤀ 昀甀渀挀琀椀漀渀 漀昀 愀 猀椀渀最氀攀 瀀愀爀琀椀挀氀攀 椀渀 儀䴀Ⰰ 搀攀猀挀爀椀戀攀猀 琀栀攀 猀礀猀琀攀洀 愀猀 愀 搀椀猀琀爀椀戀甀琀椀漀渀 椀渀 猀瀀愀挀攀 ⠀爀⤀ 愀渀搀 琀椀洀攀 ⠀琀⤀⸀㰀戀爀㸀ഀഀ
When you would consider a two particle system, the state of the two-particle system would described by the wave function &Psi;(r1,r2,t). <br>਍㰀戀爀㸀ഀഀ
If we would leave out time for a moment, and if the particle one is in &Psi;A(r) state and particle two is in &Psi;B(r) state,<br>਍琀栀攀渀 琀栀攀 琀漀琀愀氀 猀琀愀琀攀 挀愀渀 戀攀 眀爀椀琀琀攀渀 愀猀 琀栀攀 瀀爀漀搀甀挀琀 ☀倀猀椀㬀⠀爀㄀Ⰰ爀㈀⤀㴀☀倀猀椀㬀䄀⠀爀㄀⤀ ⸀ ☀倀猀椀㬀䈀⠀爀㈀⤀㰀戀爀㸀ഀഀ
<br>਍䈀甀琀 琀栀攀 ∀攀砀瀀爀攀猀猀椀漀渀∀ 愀猀 猀栀漀眀渀 椀渀 昀椀最甀爀攀 ㄀Ⰰ 椀猀 焀甀椀琀攀 搀椀昀昀攀爀攀渀琀⸀ 䠀攀爀攀 椀琀 椀猀 渀漀琀 瀀漀猀猀椀戀氀攀 琀漀 猀攀瀀攀爀愀琀攀 琀栀攀 攀渀琀愀渀最氀攀搀 猀琀愀琀攀㰀戀爀㸀ഀഀ
into product states.<br>਍㰀戀爀㸀ഀഀ
In figure 1, you see up and down arrows. This is so, because in this example, we are looking at a special property<br>਍琀栀愀琀 愀 瀀愀爀琀椀挀氀攀 洀椀最栀琀 栀愀瘀攀Ⰰ 眀栀椀挀栀 椀猀 挀愀氀氀攀搀 ✀猀瀀椀渀∀Ⰰ 眀栀椀挀栀 挀愀渀 戀攀 琀栀漀甀最栀琀 漀昀 愀猀 猀漀洀攀 猀漀爀琀 漀昀 ∀愀渀最甀氀愀爀 洀漀洀攀渀琀甀洀∀⸀㰀戀爀㸀ഀഀ
Note that many articles use entangled photons, where the "polarization" is used in a similar sense.<br>਍㰀戀爀㸀ഀഀ
Take a look at this expression again:<br>਍㰀戀爀㸀ഀഀ
<font face="arial" size=3 color="black">਍ഀഀ
<B>&Psi;a,b=1 / &#8730; 2 ( |&#8593; &#8595;> + |&#8595; &#8593;> ) </B><br>਍ഀഀ
<font face="arial" size=2 color="black">਍㰀戀爀㸀ഀഀ
਍一漀眀 瀀氀攀愀猀攀 渀漀琀椀挀攀 琀栀椀猀㨀 䤀琀✀猀 愀 㰀䈀㸀焀甀愀渀琀甀洀 猀甀瀀攀爀瀀漀猀椀琀椀漀渀㰀⼀䈀㸀 漀昀 琀眀漀 猀琀愀琀攀猀Ⰰ 渀愀洀攀氀礀 㰀䈀㸀 ☀⌀㠀㔀㤀㌀㬀 ☀⌀㠀㔀㤀㔀㬀 㰀⼀䈀㸀 愀渀搀 㰀䈀㸀 ☀⌀㠀㔀㤀㔀㬀 ☀⌀㠀㔀㤀㌀㬀 㰀⼀䈀㸀Ⰰ㰀戀爀㸀ഀഀ
which we might call "state 1" and "state 2". In such a state, as for example | &#8593; &#8595; ><br>਍眀攀 猀攀攀 瀀愀爀琀椀挀氀攀 䄀 愀猀 ☀⌀㠀㔀㤀㌀㬀 愀渀搀 瀀愀爀琀椀挀氀攀 䈀 愀猀 ☀⌀㠀㔀㤀㔀㬀  㰀戀爀㸀 ഀഀ
<br>਍䤀渀 猀琀愀琀攀 ㄀Ⰰ 倀愀爀琀椀挀氀攀 䄀 栀愀猀 猀瀀椀渀 愀氀漀渀最 ⬀稀 愀渀搀 瀀愀爀琀椀挀氀攀 䈀 栀愀猀 猀瀀椀渀 愀氀漀渀最 ⴀ稀⸀ 㰀戀爀㸀 ഀഀ
<br>਍䤀渀 猀琀愀琀攀 ㈀Ⰰ 倀愀爀琀椀挀氀攀 䄀 栀愀猀 猀瀀椀渀 愀氀漀渀最 ⴀ稀 愀渀搀 瀀愀爀琀椀挀氀攀 䈀 栀愀猀 猀瀀椀渀 愀氀漀渀最 ⬀稀⸀ 㰀戀爀㸀 ഀഀ
<br>਍⠀栀攀爀攀 椀渀 琀栀椀猀 攀砀愀洀瀀氀攀Ⰰ 眀攀 氀漀漀欀 眀椀琀栀 爀攀猀瀀攀挀琀 琀漀 琀栀攀 稀 搀椀爀攀挀琀椀漀渀㬀 戀甀琀 愀渀礀 漀琀栀攀爀 搀椀爀攀挀琀椀漀渀 挀漀甀氀搀 栀愀瘀攀 戀攀攀渀 挀栀漀漀猀攀渀⤀㰀戀爀㸀ഀഀ
<br>਍一漀眀 猀甀瀀瀀漀猀攀 琀栀攀 瀀愀爀琀椀挀氀攀猀 愀爀攀 洀漀瘀椀渀最 椀渀 漀瀀瀀漀猀椀琀攀 搀椀爀攀挀琀椀漀渀猀⸀㰀戀爀㸀ഀഀ
<br>਍䄀氀椀挀攀 栀愀猀 瀀氀愀挀攀搀 愀 搀攀琀攀挀琀漀爀 眀栀攀爀攀 瀀愀爀琀椀挀氀攀 䄀 眀椀氀氀 昀氀礀 戀礀Ⰰ 愀渀搀 䈀漀戀 搀椀搀 琀栀攀 猀愀洀攀 愀琀 眀栀攀爀攀 瀀愀爀琀椀挀氀攀 䈀 最漀攀猀 琀漀⸀㰀戀爀㸀ഀഀ
Alice now measures the spin along the z-axis. She can obtain one of two possible outcomes: +z or -z. <br> ਍㰀戀爀㸀ഀഀ
Suppose she gets +z. According to what <B>we know of the collapse of the wave function</B>, the quantum state of the system <br> ਍眀椀氀氀 挀漀氀氀愀瀀猀攀 椀渀琀漀 猀琀愀琀攀 ㄀⸀㰀戀爀㸀ഀഀ
Thus Bob then will measure -z. Similarly, if Alice measures -z, Bob for sure will get +z.<br>਍一漀 洀愀琀琀攀爀 眀栀愀琀 琀栀攀 搀椀猀琀愀渀挀攀 戀攀琀眀攀攀渀 䄀氀椀挀攀 愀渀搀 䈀漀戀 椀猀⸀㰀戀爀㸀 ഀഀ
<br> ਍䤀猀渀✀琀 琀栀愀琀 愀洀愀稀椀渀最㼀 䤀昀 䄀氀椀挀攀 最攀琀猀 ⬀稀Ⰰ 䈀漀戀 最攀琀猀 ⴀ稀Ⰰ 愀渀搀 琀栀攀 漀琀栀攀爀 眀愀礀 愀爀漀甀渀搀⸀ 䠀漀眀 搀漀 戀漀琀栀 瀀愀爀琀椀挀氀攀猀 欀渀漀眀 琀栀愀琀㼀㰀戀爀㸀ഀഀ
I mean: the entangled system is in a superposition of  |&#8593; &#8595;> and |&#8595; &#8593;>.<br>਍䔀猀瀀攀挀椀愀氀氀礀 眀栀攀渀 琀栀攀 搀椀猀琀愀渀挀攀 戀攀琀眀攀攀渀 瀀愀爀琀椀挀氀攀 䄀 愀渀搀 瀀愀爀琀椀挀氀攀 䈀 椀猀 氀愀爀最攀Ⰰ 椀琀✀猀 焀甀椀琀攀 瀀甀稀稀氀椀渀最⸀㰀戀爀㸀ഀഀ
However, most physicist don't believe that a superluminal (faster than light) signalling operation is at work here.<br>਍䈀甀琀 眀栀愀琀 椀猀 椀琀 琀栀攀渀㼀㰀戀爀㸀ഀഀ
<br>਍䘀椀爀猀琀 䤀 栀愀瘀攀 琀漀 愀搀洀椀琀 琀栀愀琀 椀渀 琀栀攀 攀砀愀洀瀀氀攀 愀戀漀瘀攀Ⰰ 䤀 漀瘀攀爀猀椀洀瀀氀椀昀椀攀搀 洀愀琀琀攀爀猀⸀ 䤀渀 攀砀瀀攀爀椀洀攀渀琀猀Ⰰ 椀渀 昀愀挀琀 猀琀愀琀椀猀琀椀挀愀氀 爀攀猀甀氀琀猀㰀戀爀㸀ഀഀ
are obtained, using many entangled particle systems. Due to various reasons, not only the spin along z is measured, but also along<br>਍琀栀攀 砀 ⠀漀爀 礀⤀ 搀椀爀攀挀琀椀漀渀⸀ 䘀椀渀愀氀氀礀Ⰰ 琀栀攀 爀攀猀甀氀琀猀 愀爀攀 琀攀猀琀攀搀 愀最愀椀渀猀 琀攀 猀漀挀愀氀氀攀搀 ∀䈀攀氀氀∀ ⠀漀爀 搀攀爀椀瘀攀搀⤀ 椀渀攀焀甀愀氀椀琀椀攀猀⸀㰀戀爀㸀ഀഀ
But.. currently, all results seem to sustain the conclusion of the example presented above.<br>਍㰀戀爀㸀ഀഀ
Many "suggestions" have been forwarden, like "hidden variables" (which we don't know of yet), which works in such way<br>਍猀漀 琀栀愀琀 昀爀漀洀 琀栀攀 猀琀愀爀琀 漀昀 攀渀琀愀渀最氀攀洀攀渀琀Ⰰ 愀 猀漀爀琀 漀昀 栀椀搀搀攀渀 ∀挀漀渀琀爀愀挀琀∀ 挀愀渀 攀砀瀀氀愀椀渀 琀栀攀 漀猀攀爀瘀攀搀 攀昀昀攀挀琀猀⸀㰀戀爀㸀ഀഀ
But many other "explanations" go around too, like Multiple Universes (MWI), or some still <I>do</I> believe that a "spooky action"<br>਍琀栀愀琀 攀砀挀攀攀搀猀 琀栀攀 猀瀀攀攀搀 漀昀 氀椀最栀琀 椀猀 愀琀 眀漀爀欀Ⰰ  漀爀 琀栀愀琀 漀甀爀 椀渀琀攀爀瀀爀攀琀愀琀椀漀渀 漀昀 猀瀀愀挀攀ⴀ琀椀洀攀 椀猀渀✀琀 挀漀爀爀攀挀琀 攀琀挀⸀⸀ 攀琀挀⸀⸀㰀戀爀㸀ഀഀ
However, many physicists say that the observed results happen with "probabilities" and this type of correlation<br>਍搀漀攀猀 渀漀琀 愀甀琀漀洀愀琀椀挀愀氀氀礀 椀洀瀀氀礀 挀漀洀洀甀渀椀挀愀琀椀漀渀⸀㰀戀爀㸀ഀഀ
Indeed, most physicist accept that non-locality effects of this sort, is simply "non-signalling".<br> ਍㰀戀爀㸀ഀഀ
Note that a key point is, that the entangled system is in a superpostion (thus both simultaneously) of two states <B> &#8593; &#8595; </B> and <B> &#8595; &#8593;</B>.<br>਍䄀挀挀漀爀搀椀渀最 琀漀 琀栀攀 䌀漀瀀攀渀栀愀最攀渀 椀渀琀攀爀瀀爀攀琀愀琀椀漀渀Ⰰ 眀栀攀渀 愀 洀攀愀猀甀爀攀洀攀渀琀 椀猀 搀漀渀攀Ⰰ 琀栀攀 猀礀猀琀攀洀 ∀挀漀氀氀愀瀀猀攀猀∀ 椀渀琀漀 㰀䈀㸀漀渀攀㰀⼀䈀㸀 猀琀愀琀攀⸀㰀戀爀㸀ഀഀ
A puzzling element still remains, that a superpostion of states exists, no matter how far the particles are apart. But when<br>਍昀漀爀 攀砀愀洀瀀氀攀 瀀愀爀琀椀挀氀攀 䄀 椀猀 洀攀愀猀甀爀攀搀 愀猀 ☀⌀㠀㔀㤀㌀㬀 Ⰰ 琀栀攀渀 䈀 眀椀氀氀 戀攀 ☀⌀㠀㔀㤀㔀㬀⸀㰀戀爀㸀ഀഀ
So, what is the meaning of the original superposition?<br>਍ഀഀ
<br>਍㰀戀爀㸀ഀഀ
<font face="arial" size=2 color="blue">਍㰀栀㌀㸀㈀⸀ 䄀 昀攀眀 眀漀爀搀猀 漀渀 ∀渀漀渀ⴀ氀漀挀愀氀椀琀礀∀㨀㰀⼀栀㌀㸀ഀഀ
<font face="arial" size=2 color="black">਍ഀഀ
਍一漀眀Ⰰ 椀渀琀甀椀琀椀瘀攀氀礀Ⰰ 椀昀 瀀愀爀琀椀挀氀攀 愀 愀渀搀 瀀愀爀琀椀挀氀攀 戀 愀爀攀 爀攀愀氀氀礀 挀氀漀猀攀 琀漀最攀琀栀攀爀Ⰰ 眀攀 洀椀最栀琀 渀漀琀 戀攀 琀漀漀 搀椀猀琀甀爀戀攀搀Ⰰ 椀昀 漀渀 琀栀攀 氀攀昀琀Ⰰ㰀戀爀㸀ഀഀ
we measure "up", and on the right we measure "down" (or vice versa), although it doesn't feel right acording to the superposition<br>਍瀀爀椀渀挀椀瀀氀攀 漀昀 猀甀戀猀琀愀琀攀猀Ⰰ 愀猀 攀砀瀀爀攀猀猀攀搀 椀渀 儀䴀⸀㰀戀爀㸀ഀഀ
<br>਍䈀甀琀 渀漀眀Ⰰ 猀甀瀀瀀漀猀攀 琀栀愀琀 琀栀攀 搀攀琀攀挀琀漀爀猀 ∀氀攀昀琀∀ 愀渀搀 ∀爀椀最栀琀∀ 愀爀攀 爀攀愀氀氀礀 焀甀椀琀攀 昀愀爀 愀瀀愀爀琀Ⰰ 愀渀搀 椀昀 眀攀 琀栀攀渀 猀琀椀氀氀 漀戀猀攀爀瘀攀 琀栀攀 猀愀洀攀㰀戀爀㸀ഀഀ
results, it might get more puzzling.<br>਍㰀戀爀㸀ഀഀ
Suppose partice a is found to be "up". Now suppose particle "a" has a nifty "means" to inform "b", that it was measured as "up", and thus<br>਍∀戀∀ 渀漀眀 欀渀漀眀猀 琀栀愀琀 椀琀 栀愀猀 琀漀 戀攀 ∀搀漀眀渀∀⸀ 一漀眀 猀甀瀀瀀漀猀攀 琀栀愀琀 爀攀愀氀氀礀 猀甀挀栀 愀 昀愀渀琀愀猀琀椀挀 洀攀挀栀愀渀椀猀洀  眀漀甀氀搀 攀砀椀猀琀⸀㰀戀爀㸀ഀഀ
But there is a problem if the distance between "a" and "b" is so great, that "a" would have to use a mechanism that exceeds the<br>਍猀瀀攀攀搀 漀昀 氀椀最栀琀⸀㰀戀爀㸀ഀഀ
Indeed, certain experiments suggests that the correlation still remains, even if there is no way that "a" can inform "b", or "b"<br>਍挀愀渀 椀渀昀漀爀洀 ∀愀∀Ⰰ 栀漀眀 椀琀 眀愀猀 洀攀愀猀甀爀攀搀Ⰰ 甀渀氀攀猀猀 愀 猀甀瀀攀爀氀甀洀椀渀漀甀猀 猀椀最渀愀氀氀椀渀最 洀攀挀栀愀渀椀猀洀 眀漀甀氀搀 戀攀 愀琀 眀漀爀欀⸀㰀戀爀㸀ഀഀ
Clearly, that is not generally acceptable, since it conflicts with Special Relativity Theory of Einstein.<br>਍䄀氀猀漀Ⰰ 琀栀椀猀 椀猀 眀栀愀琀 䔀椀渀猀琀攀椀渀 挀愀氀氀攀搀 ∀琀栀攀 猀瀀漀漀欀礀 愀挀琀椀漀渀 愀琀 愀 搀椀猀琀愀渀挀攀∀⸀㰀戀爀㸀ഀഀ
਍㰀戀爀㸀ഀഀ
You know, there are many "interpretations" out there, to explain the effect. <br>਍圀栀攀渀 礀漀甀 眀漀甀氀搀 戀攀氀椀攀瘀攀 椀渀 㰀䈀㸀∀䰀漀挀愀氀 爀攀愀氀椀琀礀∀㰀⼀䈀㸀Ⰰ 礀漀甀 眀漀甀氀搀 猀愀礀 琀栀攀 㰀䈀㸀猀琀愀琀攀㰀⼀䈀㸀 漀昀 愀渀 漀戀猀攀爀瘀愀戀氀攀㰀戀爀㸀ഀഀ
would be clearly defined. Now, you could <I>measure</I> some observable and obtain a certain result.<br>਍䤀琀✀猀 焀甀椀琀攀 愀挀挀攀瀀琀攀搀Ⰰ 琀栀愀琀 眀栀攀渀 礀漀甀 洀攀愀猀甀爀攀 猀漀洀攀 漀戀猀攀爀瘀愀戀氀攀Ⰰ 椀渀 洀愀渀礀 挀愀猀攀猀 礀漀甀 眀漀甀氀搀 椀渀琀攀爀愀挀琀 眀椀琀栀 琀栀愀琀 猀礀猀琀攀洀Ⰰ 㰀戀爀㸀ഀഀ
and thus you would have exterted some influence on that system.<br>਍䤀琀✀猀 ∀瀀爀攀琀琀礀 挀氀漀猀攀∀ 琀漀 眀栀愀琀 琀栀攀 椀搀攀愀 漀昀 ∀氀漀挀愀氀 爀攀愀氀椀猀洀∀ 愀挀琀甀愀氀氀礀 椀猀Ⰰ 戀甀琀 渀漀琀 攀渀琀椀爀攀氀礀⸀㰀戀爀㸀ഀഀ
Local realism is somewhat opposed to what QM seems to "look like": <B>QM is probabilistic in nature.</B><br>਍䤀昀 礀漀甀 眀漀甀氀搀 昀愀瘀漀甀爀 琀栀攀 椀搀攀愀 漀昀 氀漀挀愀氀 爀攀愀氀椀猀洀Ⰰ 礀漀甀 瀀爀漀戀愀戀氀礀 眀漀甀氀搀 渀漀琀 氀椀欀攀 儀䴀 琀漀漀 洀甀挀栀Ⰰ 愀渀搀 礀漀甀 洀椀最栀琀 愀爀最甀攀 琀栀愀琀㰀戀爀㸀ഀഀ
QM can't be a full and complete theory.<br>਍㰀戀爀㸀ഀഀ
The essential meaning of Local realism then would be, that a system truly has some defined state, and is not "fuzzy" at all.<br>਍䔀瘀攀渀 椀昀 椀琀 眀漀甀氀搀 樀甀猀琀 ∀愀瀀瀀攀愀爀∀ 琀漀 戀攀 瀀爀漀戀愀戀椀氀椀猀琀椀挀 ⠀昀甀稀稀礀⤀Ⰰ 琀栀攀渀 戀攀氀漀眀 琀栀攀 猀甀爀昀愀挀攀Ⰰ 猀漀洀攀琀栀椀渀最 氀椀欀攀 ∀栀椀搀搀攀渀 瘀愀爀椀愀戀氀攀猀∀㰀戀爀㸀ഀഀ
are at work, (which we don't know about, yet) which would make it "exact".<br>਍㰀戀爀㸀ഀഀ
The "hidden variables" would then also be the mechanism to explain the seemingly non-local effect, as we have seen at those<br>਍琀眀漀 瀀愀爀琀椀挀氀攀猀Ⰰ 猀攀瀀攀爀愀琀攀搀 漀瘀攀爀 愀 氀漀渀最 搀椀猀琀愀渀挀攀⸀㰀戀爀㸀ഀഀ
<br>਍䠀漀眀攀瘀攀爀Ⰰ 洀漀猀琀 瀀栀礀猀椀挀椀猀琀猀 愀挀挀攀瀀琀 琀栀愀琀 ∀渀漀渀ⴀ氀漀挀愀氀椀琀礀∀ 椀猀 愀 昀甀渀搀愀洀攀渀琀愀氀 愀猀瀀攀挀琀 漀昀 一愀琀甀爀攀⸀㰀戀爀㸀 ഀഀ
Some scientists have come up with some other very interesting arguments. In effect they say:<br>਍圀攀 愀爀攀 甀猀攀搀 琀漀 琀栀攀 昀愀挀琀 琀栀愀琀 㰀䈀㸀猀瀀愀挀攀㰀⼀䈀㸀 愀渀搀 㰀䈀㸀琀椀洀攀㰀⼀䈀㸀 愀爀攀 漀甀爀 搀攀昀椀渀椀渀最 ∀洀攀琀爀椀挀猀∀ 琀漀 瘀愀氀甀愀琀攀 攀砀瀀攀爀椀洀攀渀琀愀氀 爀攀猀甀氀琀猀⸀㰀戀爀㸀ഀഀ
But (as they say), quantum non-locality shows us that there has to be more, something that we are just not sure about yet.<br>਍㰀戀爀㸀ഀഀ
There are some ideas though, on the "new" structure of space and time, to explain nonlocality.<br>਍伀渀攀 椀搀攀愀 椀猀 琀栀攀 挀漀渀挀攀瀀琀 漀昀 ∀瀀爀攀猀瀀愀挀攀∀⸀ 倀愀爀琀氀礀 戀愀猀攀搀 漀渀 漀爀椀最椀渀愀氀 椀搀攀愀猀 漀昀 䈀漀栀洀Ⰰ 䠀椀氀攀礀 ⠀愀渀搀 漀琀栀攀爀猀⤀ 昀漀爀洀甀氀愀琀攀搀 琀栀攀 挀漀渀挀攀瀀琀㰀戀爀㸀ഀഀ
of "prespace", which essentially says that the "usual" space-time manifold emerges from a more fundamental level of physical space.<br>਍唀猀椀渀最 愀 ∀儀甀愀渀琀甀洀 倀漀琀攀渀琀椀愀氀∀ 愀渀搀 愀 渀攀眀 爀攀瘀椀猀攀搀 椀搀攀愀 漀昀 ∀琀椀洀攀∀Ⰰ 琀栀攀礀 昀漀爀洀甀氀愀琀攀搀 愀 昀爀愀洀攀眀漀爀欀 眀栀椀挀栀 洀椀最栀琀 攀砀瀀氀愀椀渀 渀漀渀氀漀挀愀氀椀琀礀⸀㰀戀爀㸀ഀഀ
<br>਍䄀渀漀琀栀攀爀 最爀攀愀琀 眀愀礀 琀漀 琀栀攀漀爀攀琀椀挀愀氀氀礀 愀渀愀氀礀稀攀 攀渀琀愀渀最氀攀洀攀渀琀Ⰰ 椀猀 琀栀攀 䔀倀刀 眀漀爀洀栀漀氀攀⸀㰀戀爀㸀ഀഀ
Some (theoretical) physicists, are working on models that associate the smallest<br>਍猀瀀愀挀攀ⴀ琀椀洀攀 戀甀椀氀搀椀渀最 戀氀漀挀欀猀Ⰰ 眀椀琀栀 猀漀挀愀氀氀攀搀 䔀刀㴀䔀倀刀 倀氀愀渀欀ⴀ猀挀愀氀攀 ∀眀漀爀洀栀漀氀攀猀∀⸀ 䤀渀 洀愀渀礀 挀愀猀攀猀Ⰰ 琀栀攀礀 昀漀挀甀猀 攀猀瀀攀挀椀愀氀氀礀㰀戀爀㸀ഀഀ
on the Quantum Mechanical effect of "entanglement", and believe it or not, some articles make sense how such planck scale<br>਍眀漀爀洀栀漀氀攀猀 挀漀渀渀攀挀琀 攀渀琀愀渀最氀攀搀 瀀愀爀琀椀挀氀攀猀⸀ 䠀漀眀攀瘀攀爀Ⰰ 洀愀渀礀 瀀栀礀猀椀挀椀猀琀猀 愀爀攀 猀挀攀瀀琀椀挀愀氀Ⰰ 愀渀搀 氀椀欀攀 洀甀挀栀 洀漀爀攀 ∀戀漀搀礀∀ 漀渀 琀栀漀猀攀 洀漀搀攀氀猀⸀㰀戀爀㸀ഀഀ
਍ഀഀ
਍㰀戀爀㸀ഀഀ
<br>਍ഀഀ
<font face="arial" size=2 color="blue">਍㰀栀㌀㸀㌀⸀ 䄀 昀攀眀 眀漀爀搀猀 漀渀 琀栀攀 ⠀挀氀愀猀猀椀挀愀氀⤀ ∀䌀漀瀀攀渀栀愀最攀渀 椀渀琀攀爀瀀爀攀琀愀琀椀漀渀∀㰀⼀栀㌀㸀ഀഀ
<font face="arial" size=2 color="black">਍ഀഀ
The measurement of an "observable" of a system like a particle, can be described in several ways.<br>਍伀渀攀 洀攀琀栀漀搀 眀栀椀挀栀 ∀猀攀攀洀猀∀ 琀漀 戀攀 焀甀椀琀攀 渀愀琀甀爀愀氀 椀渀 儀䴀Ⰰ 椀猀 琀漀 琀漀 搀攀猀挀爀椀戀攀 琀栀攀 猀礀猀琀攀洀 愀猀 愀 猀甀瀀攀爀瀀漀猀椀琀椀漀渀 漀昀 ∀攀椀最攀渀昀甀渀挀琀椀漀渀猀∀Ⰰ㰀戀爀㸀ഀഀ
just like you can describe a vector in n-space as being composed of n orthogonal eigenvectors.<br>਍⠀一漀琀攀㨀 䈀攀氀漀眀 椀猀 愀 瘀攀爀礀 猀椀洀瀀氀攀 攀砀愀洀瀀氀攀 漀昀 愀 猀漀挀愀氀氀攀搀 愀 ∀戀爀愀∀ ∀欀攀琀∀Ⰰ 琀栀愀琀 椀猀Ⰰ∀簀㸀∀ 攀焀甀愀琀椀漀渀⸀⤀㰀戀爀㸀ഀഀ
<br>਍䘀椀最 ㈀⸀㰀戀爀㸀ഀഀ
<br>਍㰀椀洀最 猀爀挀㴀∀焀洀㄀⸀樀瀀最∀ 愀氀椀最渀㴀∀挀攀渀琀爀攀∀⼀㸀ഀഀ
<br>਍䤀渀 琀栀椀猀 眀愀礀Ⰰ 椀琀✀猀 愀氀猀漀 搀攀猀挀爀椀戀攀搀Ⰰ 眀栀愀琀 琀栀攀 ∀瀀爀漀戀愀戀椀氀椀琀椀攀猀∀ 漀昀 琀栀攀 瀀漀猀猀椀戀氀攀 瘀愀氀甀攀猀 漀昀 琀栀攀 漀戀猀攀爀瘀愀戀氀攀 挀漀甀氀搀 戀攀⸀㰀戀爀㸀ഀഀ
These probabilities are namely <I>related</I> to the <I>coefficients</I> of the above equation.<br>਍㰀戀爀㸀ഀഀ
So, let's suppose that some sort of "measurering apparatus" finds value "c3", then at least one important question arises.<br>਍圀栀礀 搀椀搀 琀栀攀 猀礀猀琀攀洀 挀漀氀氀愀瀀猀攀搀 椀渀琀漀 琀栀攀 猀琀愀琀攀 挀㌀簀㌀㸀Ⰰ 愀渀搀 眀栀愀琀 栀愀瀀瀀攀渀攀搀 琀漀 愀氀氀 琀栀攀 漀琀栀攀爀 攀椀渀最攀渀猀琀愀琀攀猀㼀㰀戀爀㸀ഀഀ
<br>਍吀栀椀猀 椀猀 愀渀 攀砀愀洀瀀氀攀 漀昀 琀栀攀 猀漀挀愀氀氀攀搀 ∀挀漀氀氀愀瀀猀攀 漀昀 琀栀攀 眀愀瘀攀昀甀渀挀琀椀漀渀∀⸀ 䤀昀 愀渀 愀挀琀甀愀氀 洀攀愀猀甀爀攀洀攀渀琀猀 椀猀 搀漀渀攀Ⰰ㰀戀爀㸀ഀഀ
out of many possible results, just one is "selected" in "some way"<br>਍䄀渀 漀戀猀攀爀瘀愀戀氀攀Ⰰ 椀渀椀琀椀愀氀氀礀 椀渀 愀 猀甀瀀攀爀瀀漀猀椀琀椀漀渀 漀昀 搀椀昀昀攀爀攀渀琀 攀椀最攀渀猀琀愀琀攀猀Ⰰ 愀瀀瀀攀愀爀猀 琀漀 爀攀搀甀挀攀 琀漀 愀 猀椀渀最氀攀 瘀愀氀甀攀㰀戀爀㸀ഀഀ
of the states, after interaction with an observer (that is: if it's being measured).<br>਍㰀戀爀㸀ഀഀ
It has puzzled many people for years, and different interpretations have emerged.<br> ਍䄀氀琀栀漀甀最栀 ∀儀甀愀渀琀甀洀 搀攀挀漀栀攀爀攀渀挀攀∀ ⠀洀漀爀攀 漀渀 琀栀愀琀 氀愀琀攀爀⤀ 椀猀 焀甀椀琀攀 愀挀挀攀瀀琀攀搀 戀礀 洀漀猀琀 昀漀氀欀猀 渀漀眀愀搀愀礀猀Ⰰ㰀戀爀㸀ഀഀ
other interpretations exist as well.<br>਍㰀戀爀㸀ഀഀ
The so-called "Copenhagen" interpretation, accepts the wavefunction (or state vector) as a <I>workable</I> solution,<br>਍愀渀搀 琀栀攀 挀漀氀氀愀瀀猀攀 琀栀愀琀 栀愀瀀瀀攀渀猀 愀琀 愀 洀攀愀猀甀爀攀洀攀渀琀Ⰰ 椀猀 愀 眀愀礀 琀漀 搀攀猀挀爀椀戀攀 眀栀礀 愀 瀀愀爀琀椀挀甀氀愀爀 瘀愀氀甀攀 椀猀 猀攀氀攀挀琀攀搀⸀㰀戀爀㸀ഀഀ
As a simple example, they would say that a system can for example be described as &Psi; = a|1> + b|2>,<br>਍愀渀搀 眀攀 栀愀瘀攀 瀀爀漀戀愀戀椀氀椀琀礀 簀愀簀 琀漀 昀椀渀搀 琀栀攀 漀戀猀攀爀瘀愀戀氀攀 琀漀 戀攀 椀渀 猀琀愀琀攀 簀㄀㸀⸀㰀戀爀㸀ഀഀ
<br>਍匀漀Ⰰ 椀琀 猀愀礀猀 琀栀愀琀 愀 焀甀愀渀琀甀洀 猀礀猀琀攀洀Ⰰ 戀攀昀漀爀攀 洀攀愀猀甀爀攀洀攀渀琀Ⰰ 搀漀攀猀渀✀琀 攀砀椀猀琀 椀渀 漀渀攀 猀琀愀琀攀 漀爀 愀渀漀琀栀攀爀Ⰰ㰀戀爀㸀 ഀഀ
but in all of its possible states at once.<br> ਍㰀戀爀㸀ഀഀ
The "Copenhagen" interpretation is most often "associated" with the principle of the <B>"collapse of the wave function"</B>,<br>਍眀栀攀渀 愀 洀攀愀猀甀攀爀洀攀渀琀 椀猀 搀漀渀攀⸀ 䈀甀琀 椀琀 搀漀攀猀 渀漀琀 猀琀爀椀挀琀氀礀 洀攀愀渀 琀栀愀琀 愀氀氀 眀栀漀 昀愀瘀漀甀爀 琀栀椀猀 搀攀猀挀爀椀瀀琀椀漀渀Ⰰ㰀戀爀㸀 ഀഀ
also believe in the physical reality.<br>਍㰀戀爀㸀ഀഀ
Bohr seemed to have gone one step further (in a later phase), by essentially saying that the wavefunction<br>਍椀猀 渀漀琀 攀焀甀愀氀 琀漀 愀 ∀琀爀甀攀∀ 㰀䈀㸀瀀椀挀琀漀爀椀愀氀㰀⼀䈀㸀 搀攀猀挀爀椀瀀琀椀漀渀 漀昀 爀攀愀氀椀琀礀Ⰰ 戀甀琀 椀渀猀琀攀愀搀 椀猀 ⠀樀甀猀琀⤀ 愀 猀礀洀戀漀氀椀挀 爀攀瀀爀攀猀攀渀琀愀琀椀漀渀⸀㰀戀爀㸀ഀഀ
<br>਍圀椀琀栀 愀 氀椀琀氀攀 ∀戀攀渀搀椀渀最 愀渀搀 琀眀椀猀琀椀渀最∀Ⰰ 礀漀甀 洀椀最栀琀 挀愀氀氀 琀栀椀猀 瘀椀攀眀 愀渀搀 洀攀琀栀漀搀漀氀漀最礀Ⰰ 猀漀洀攀琀栀椀渀最 氀椀欀攀 琀栀攀 ∀攀愀爀氀礀∀㰀戀爀㸀ഀഀ
cornerstone of QM. The theory is succesfully applied at many physical systems.<br>਍䘀漀爀 攀砀愀洀瀀氀攀 愀琀 琀栀攀 䠀礀搀爀漀最攀渀 愀琀漀洀Ⰰ 愀渀礀 攀椀最攀渀猀琀愀琀攀 漀昀 琀栀攀 攀氀攀挀琀爀漀渀 椀渀 琀栀攀 栀礀搀爀漀最攀渀 愀琀漀洀 椀猀 搀攀猀挀爀椀戀攀搀 昀甀氀氀礀㰀戀爀㸀 ഀഀ
by a number of quantum numbers. Also, the actual state of the electron may be any superposition of eigen states.<br>਍㰀戀爀㸀ഀഀ
However, important insights which differ greatly from the "Copenhagen" interpretation, surfaced more or less at<br>਍琀栀攀 猀愀洀攀 琀椀洀攀⸀ 䄀渀 椀洀瀀漀爀琀愀渀琀 漀渀攀 椀猀 琀栀攀 ∀搀攀琀攀爀洀椀渀椀猀琀椀挀∀ 愀渀搀 爀攀愀氀椀猀琀椀挀 㰀䈀㸀䠀椀搀搀攀渀 瘀愀爀椀愀戀氀攀猀㰀⼀䈀㸀 儀甀愀渀琀甀洀 昀爀愀洀攀眀漀爀欀Ⰰ㰀戀爀㸀ഀഀ
and ofcourse the <B>Pilot Wave</B> interpretation developed by de Broglie around 1927 and further refined<br>਍戀礀 䈀漀栀洀 愀爀漀甀渀搀 ㄀㤀㔀㈀⸀㰀戀爀㸀ഀഀ
<br>਍ഀഀ
In the Copenhagen interpretation, the wavefunction is a superposition of eigenstates. In slightly different words:<br>਍䤀琀 猀愀礀猀 琀栀愀琀 愀 焀甀愀渀琀甀洀 猀礀猀琀攀洀 搀漀攀猀渀✀琀 攀砀椀猀琀 椀渀 漀渀攀 猀琀愀琀攀 漀爀 愀渀漀琀栀攀爀Ⰰ 戀甀琀 椀渀 愀氀氀 漀昀 椀琀猀 瀀漀猀猀椀戀氀攀 猀琀愀琀攀猀 愀琀 漀渀挀攀⸀㰀戀爀㸀 ഀഀ
A very simple example is this: &Psi; = a|1> + b|2><br>਍䤀琀✀猀 漀渀氀礀 眀栀攀渀 眀攀 漀戀猀攀爀瘀攀 椀琀猀 猀琀愀琀攀Ⰰ 琀栀愀琀 愀 焀甀愀渀琀甀洀 猀礀猀琀攀洀 椀猀 昀漀爀挀攀搀 琀漀 挀栀漀漀猀攀 漀渀攀 ∀瀀爀漀戀愀戀椀氀椀琀礀∀Ⰰ 愀渀搀 挀漀氀氀愀瀀猀攀㰀戀爀㸀ഀഀ
into a certain eigenstate (which produces a certain value for an observable)<br>਍匀漀Ⰰ 圀栀攀渀 眀攀 漀戀猀攀爀瘀攀 愀渀 漀戀樀攀挀琀Ⰰ 琀栀攀 猀甀瀀攀爀瀀漀猀椀琀椀漀渀 挀漀氀氀愀瀀猀攀猀 愀渀搀 琀栀攀 猀礀猀琀攀洀 椀猀 昀漀爀挀攀搀 椀渀琀漀 㰀䈀㸀漀渀攀 漀昀 琀栀攀 猀琀愀琀攀猀㰀⼀䈀㸀㰀戀爀㸀ഀഀ
of its wave function.<br>਍㰀戀爀㸀ഀഀ
In figure 3, you see a few other examples of "superposition", and ways to denote the wavefunction:<br>਍㰀戀爀㸀ഀഀ
Fig 3.<br>਍㰀戀爀㸀ഀഀ
<img src="entanglement2.jpg" align="centre"/>਍㰀戀爀㸀ഀഀ
Many people have disliked the postulate of a wavefunction that collapses, without a associated physical reality, as was<br>਍椀洀瀀氀椀攀搀 戀礀 琀栀攀 䌀漀瀀攀渀栀愀最攀渀 䤀渀琀攀爀瀀爀攀琀愀琀椀漀渀⸀㰀戀爀㸀ഀഀ
<br>਍伀渀攀 瀀栀椀氀漀猀漀瀀栀椀挀愀氀 焀甀攀猀琀椀漀渀 椀猀 琀栀椀猀㨀 䠀漀眀 愀渀搀 眀栀礀 搀漀攀猀 琀栀攀 甀渀椀焀甀攀 眀漀爀氀搀 漀昀 漀甀爀 攀砀瀀攀爀椀攀渀挀攀Ⰰ 愀琀 洀攀愀猀甀爀攀洀攀渀琀Ⰰ 琀栀攀渀 攀洀攀爀最攀㰀戀爀㸀 ഀഀ
from the multiplicities of <B>all alternatives</B> available in the superposed quantum world?<br>਍䄀氀猀漀Ⰰ 愀猀 猀愀椀搀 戀攀昀漀爀攀Ⰰ 琀栀攀 䌀漀瀀攀渀栀愀最攀渀 椀渀琀攀爀瀀爀攀琀愀琀椀漀渀 猀琀愀琀攀猀 琀栀愀琀 愀 焀甀愀渀琀甀洀 猀礀猀琀攀洀Ⰰ 戀攀昀漀爀攀 洀攀愀猀甀爀攀洀攀渀琀Ⰰ㰀戀爀㸀ഀഀ
doesn't exist in one state or another, but in all of its possible states at once.<br> ਍㰀戀爀㸀ഀഀ
One classical "thought experiment" tries to illustrate the shortcomings of the Copenhagen interpretation.<br>਍䤀琀✀猀 琀栀攀 昀愀洀漀甀猀 ∀匀挀栀爀漀搀椀渀最攀爀 䌀愀琀∀ 琀栀漀甀最栀琀 攀砀瀀攀爀椀洀攀渀琀⸀㰀戀爀㸀ഀഀ
<br>਍㰀䈀㸀㰀唀㸀匀挀栀爀漀搀椀渀最攀爀猀 䌀愀琀㨀㰀⼀唀㸀㰀⼀䈀㸀㰀戀爀㸀ഀഀ
<br>਍圀栀攀渀 琀愀欀攀渀 氀椀琀攀爀愀氀礀Ⰰ 愀渀搀 琀漀 琀栀攀 攀砀琀爀攀洀攀Ⰰ 愀 渀椀挀攀 ⠀愀渀搀 昀愀洀漀甀猀⤀ 瀀愀爀愀搀漀砀 挀愀渀 戀攀 挀漀渀猀琀爀甀挀琀攀搀⸀ 匀甀瀀瀀漀猀攀 愀 挀愀琀 椀猀 琀爀愀瀀瀀攀搀㰀戀爀㸀ഀഀ
inside a completely sealed box. Inside the box, a radioactive source is present with a certain QM probability to decay.<br>਍䤀昀 琀栀愀琀 栀愀瀀瀀攀渀猀Ⰰ 猀漀洀攀 洀攀挀栀愀渀椀猀洀攀 愀挀琀椀瘀愀琀攀猀Ⰰ 愀渀搀 椀琀 爀攀氀攀愀猀攀猀 愀 搀攀愀搀氀礀 瀀漀椀猀漀渀Ⰰ 琀栀愀琀 眀椀氀氀 欀椀氀氀 琀栀攀 挀愀琀 椀洀洀攀搀椀愀琀攀氀礀⸀㰀戀爀㸀ഀഀ
Now consider an external observer, who does not know the state of the cat.<br>਍唀渀搀攀爀 琀栀攀 䌀漀瀀攀渀栀愀最攀渀 搀攀猀挀爀椀瀀琀椀漀渀Ⰰ 琀栀攀 漀戀猀攀爀瘀攀爀 眀栀漀甀氀搀 搀攀猀挀爀椀戀攀 琀栀攀 挀愀琀 愀猀㨀 㰀䈀㸀簀猀琀愀琀攀 漀昀 挀愀琀㸀 㴀 愀簀愀氀椀瘀攀㸀 ⬀ 戀簀搀攀愀搀㸀㰀⼀䈀㸀⸀㰀戀爀㸀ഀഀ
Only when a "measurement" is done, that is, the observer opens the trap and checks the state of the cat, that state<br>਍眀漀甀氀搀 挀漀氀氀愀瀀猀攀 琀漀 攀椀琀栀攀爀 ∀搀攀愀搀∀ 漀爀 ∀愀氀椀瘀攀∀⸀ 吀栀椀猀 椀猀 漀昀挀漀甀爀猀攀 猀漀洀攀眀栀愀琀 愀戀猀甀爀搀⸀㰀戀爀㸀ഀഀ
<br>਍一漀眀Ⰰ 琀栀椀猀 ∀洀愀挀爀漀猀挀漀瀀椀挀∀ 攀砀愀洀瀀氀攀Ⰰ 椀猀 爀攀愀氀氀礀 渀漀琀 焀甀椀琀攀 挀漀洀瀀愀爀愀戀氀攀 琀漀 琀栀攀 洀椀挀爀漀猀挀漀瀀椀挀 眀漀爀氀搀 眀栀攀爀攀 儀䴀 猀攀攀洀猀 琀漀 搀漀洀椀渀愀琀攀⸀㰀戀爀㸀ഀഀ
The point seems to be, that the paradox nicely illustrates how hard it is to deal with the description<br>਍漀昀 愀 猀甀瀀攀爀瀀漀猀椀琀椀漀渀 漀昀 猀琀愀琀攀猀Ⰰ 愀渀搀 琀栀攀 挀漀氀氀愀瀀猀攀 漀昀 琀栀攀 眀愀瘀攀昀甀渀挀琀椀漀渀⸀㰀戀爀㸀ഀഀ
<br>਍ഀഀ
Among other interpretations, three other important interpretations emerged.<br>਍㰀戀爀㸀ഀഀ
<ul>਍㰀氀椀㸀吀栀攀 㰀䈀㸀∀䴀愀渀礀 圀漀爀氀搀猀 䤀渀琀攀爀瀀爀攀琀愀琀椀漀渀 ⠀䴀圀䤀⤀∀㰀⼀䈀㸀 搀愀琀攀猀 昀爀漀洀 ㄀㤀㔀㜀⸀㰀戀爀㸀ഀഀ
This theory, although it's quite consistent, never had <I>too</I> many supporters (at that time).<br>਍䈀礀 愀 儀甀愀渀琀甀洀 攀瘀攀渀琀Ⰰ 眀栀攀爀攀 眀攀 昀漀爀洀攀爀氀礀 眀漀甀氀搀 猀愀礀 椀渀 琀栀攀 䌀漀瀀攀渀栀愀最攀渀 氀愀渀最甀愀最攀Ⰰ 琀栀愀琀 琀栀攀 猀甀瀀攀爀瀀漀猀椀琀椀漀渀 挀漀氀氀愀瀀攀猀 椀渀琀漀㰀戀爀㸀ഀഀ
an eigenstate with a certain probability, in MWI it is proposed that the World forkes into different Worlds<br>਍椀渀 愀挀挀漀爀搀愀渀挀攀 琀漀 琀栀攀 渀甀洀戀攀爀 漀昀 猀甀瀀攀爀椀洀瀀漀猀攀搀 猀甀戀眀愀瘀攀猀 眀栀椀挀栀 愀氀氀 挀漀甀氀搀 栀愀瘀攀 戀攀攀渀 漀戀猀攀爀瘀攀搀⸀㰀戀爀㸀ഀഀ
Hence, Many Worlds come into existence, and all different parallel Worlds will evolve independently.<br>਍㰀氀椀㸀吀栀攀 漀琀栀攀爀 漀渀攀Ⰰ 㰀䈀㸀∀䐀攀挀漀栀攀爀攀渀挀攀∀㰀⼀䈀㸀 猀琀攀洀猀 昀爀漀洀 愀爀漀甀渀搀 ㄀㤀㠀　ⴀ㄀㤀㤀　 ⠀漀爀 猀漀⤀Ⰰ 愀渀搀 爀攀挀攀椀瘀攀搀 焀甀椀琀攀 洀甀挀栀 愀挀挀攀瀀琀愀渀挀攀 椀渀 琀栀攀 瀀栀礀猀椀挀猀 挀漀洀洀甀渀椀琀礀⸀㰀戀爀㸀ഀഀ
It mainly provides for an explanation of the strange "collapse" of the statevector.<br>਍刀漀甀最栀氀礀Ⰰ 椀琀 猀愀礀猀 琀栀愀琀 搀甀攀 琀漀 琀栀攀 椀渀琀攀爀愀挀琀椀漀渀 漀昀 琀栀攀 儀甀愀渀琀甀洀 匀礀猀琀攀洀 眀椀琀栀 琀栀攀 攀渀瘀椀爀漀渀洀攀渀琀 ⠀漀爀 洀攀愀猀甀爀椀渀最 搀攀瘀椀挀攀⤀㰀戀爀㸀ഀഀ
only selected components of the wavefunction are decoupled from a coherent system, and are "leaked" out<br>਍椀渀琀漀 琀栀攀 攀渀瘀椀爀漀渀洀攀渀琀⸀唀氀琀椀洀愀琀攀氀礀Ⰰ 眀攀 眀椀氀氀 洀攀愀猀甀爀攀 漀渀氀礀 漀渀攀 挀漀洀瀀漀渀攀渀琀 漀昀 猀甀挀栀 猀攀氀攀挀琀椀漀渀⸀㰀⼀氀椀㸀 ഀഀ
<li>The <B>"Pilot Wave Interpretation (PWI)"</B> was developed by de Broglie in 1927, and work was continued by Bohm in 1952.<br>਍䤀琀✀猀 愀渀 愀氀洀漀猀琀 挀氀愀猀猀椀挀愀氀 椀渀琀攀爀瀀爀攀琀愀琀椀漀渀⸀ 䄀 爀攀愀氀 瀀愀爀琀椀挀氀攀Ⰰ 椀猀 最甀椀搀攀搀 戀礀 愀 搀椀猀琀爀椀戀甀琀攀搀 ∀最甀椀搀椀渀最∀ 眀愀瘀攀⸀㰀戀爀㸀ഀഀ
If you see this theory in scientific articles, then you would appreciate the fact that quite a few paradoxes are "solved"<br>਍⠀氀椀欀攀 琀栀攀 眀愀瘀攀ⴀ瀀愀爀琀椀挀氀攀 瀀愀爀愀搀漀砀⤀Ⰰ 愀猀 洀愀渀礀 猀攀攀 椀琀⸀㰀⼀氀椀㸀ഀഀ
਍㰀⼀甀氀㸀ഀഀ
<br>਍吀栀攀 昀椀爀猀琀 琀眀漀 愀戀漀瘀攀 猀琀椀氀氀 甀猀攀 琀栀攀 ∀猀琀愀琀攀 瘀攀挀琀漀爀∀ 漀爀 ∀眀愀瘀攀 昀甀渀挀琀椀漀渀∀ 愀猀 瀀爀漀瀀漀猀攀搀 匀挀栀爀漀搀椀渀最攀爀Ⰰ 䈀漀栀爀 愀渀搀 漀琀栀攀爀猀⸀㰀戀爀㸀ഀഀ
but the interaction with the environment, and measurement process is quite different from that of the collapse<br>਍甀猀攀搀 椀渀 琀栀攀 䌀漀瀀攀渀栀愀最攀渀 椀渀琀攀爀瀀爀攀琀愀琀椀漀渀⸀㰀戀爀㸀ഀഀ
<br>਍吀栀攀 㰀䈀㸀∀倀椀氀漀琀 圀愀瘀攀 䤀渀琀攀爀瀀爀攀琀愀琀椀漀渀∀㰀⼀䈀㸀 甀猀攀猀 爀攀愀氀 氀漀挀愀氀椀稀攀搀 漀戀樀攀挀琀猀Ⰰ 眀椀琀栀 愀 挀漀洀瀀氀攀砀 倀椀氀漀琀 眀愀瘀攀Ⰰ 眀栀椀挀栀 猀栀椀昀琀猀 愀氀氀 ∀眀愀瘀礀∀ 猀琀甀昀昀㰀戀爀㸀ഀഀ
to the Pilot wave itself.<br>਍㰀戀爀㸀ഀഀ
A very recent interpretation eliminates the wave function all together. Around 2012, an interesting model was established<br>਍戀礀 䈀椀氀氀 倀漀椀爀椀攀爀⸀ 䠀攀爀攀 琀栀攀 ∀眀愀瘀礀∀ 猀琀甀昀昀 愀渀搀 愀猀猀漀挀椀愀琀攀搀 瀀爀漀戀愀戀椀氀椀琀椀攀猀Ⰰ 椀猀 愀渀 椀氀氀甀猀椀漀渀 搀甀攀 琀漀 琀栀攀 昀愀挀琀 琀栀愀琀 挀氀愀猀猀椀挀愀氀㰀戀爀㸀ഀഀ
parallel universes exist, where in each of them, the Quantum System has clear defined values.<br>਍䤀琀 猀椀洀瀀氀礀 樀甀猀琀 搀攀瀀攀渀搀 椀渀 眀栀椀挀栀 甀渀椀瘀攀爀猀攀 琀栀攀 漀戀猀攀爀瘀攀爀 椀渀琀攀爀愀挀琀猀 眀椀琀栀 琀栀攀 儀甀愀渀琀甀洀 匀礀猀琀攀洀⸀㰀戀爀㸀ഀഀ
<br>਍䈀攀氀漀眀 礀漀甀 眀椀氀氀 昀椀渀搀 猀攀挀琀椀漀渀猀 眀栀椀挀栀 戀爀椀攀昀氀礀 眀椀氀氀 琀漀甀挀栀 琀栀漀猀攀 搀椀昀昀攀爀攀渀琀 椀渀琀攀爀瀀爀攀琀愀琀椀漀渀猀⸀㰀戀爀㸀ഀഀ
<br>਍㰀戀爀㸀ഀഀ
<font face="arial" size=2 color="blue">਍㰀栀㌀㸀㐀⸀ 䄀 昀攀眀 眀漀爀搀猀 漀渀 ∀䐀攀挀漀栀攀爀攀渀挀攀∀㨀㰀⼀栀㌀㸀ഀഀ
<font face="arial" size=2 color="black">਍ഀഀ
This rather new interpretation, has it's origins in 1980s and 1990s. In a sense, this theory "de-mystifies" certain<br>਍昀漀爀洀攀爀氀礀 甀渀猀漀氀瘀攀搀 洀礀猀琀攀爀椀攀猀Ⰰ 昀漀爀 攀砀愀洀瀀氀攀Ⰰ 眀栀礀 愀渀搀 栀漀眀 愀 焀甀愀渀琀甀洀 猀礀猀琀攀洀 椀渀琀攀爀愀挀琀猀 眀椀琀栀 琀栀攀 ∀攀渀瘀椀爀漀渀洀攀渀琀∀Ⰰ 愀渀搀㰀戀爀㸀ഀഀ
the "measuring device".<br>਍䄀氀猀漀Ⰰ 琀栀攀 䌀漀瀀攀渀栀愀最攀渀 瀀栀爀愀猀攀 ∀䌀漀氀氀愀瀀猀攀 漀昀 琀栀攀 眀愀瘀昀甀渀挀琀椀漀渀∀ 椀猀 爀攀瀀氀愀挀攀搀 戀礀 焀甀椀琀攀 愀 猀漀氀椀搀 琀栀攀漀爀攀琀椀挀愀氀 昀爀愀洀攀眀漀爀欀⸀㰀戀爀㸀ഀഀ
<br>਍䴀愀渀礀 瀀栀礀猀椀挀椀猀琀猀 栀愀瘀攀 攀洀戀爀愀挀攀搀 琀栀攀 琀栀攀漀爀礀Ⰰ 愀渀搀 椀琀 猀攀攀洀猀 琀栀愀琀 漀渀氀礀 愀 洀椀渀漀爀椀琀礀 漀昀 猀挀攀瀀琀椀挀猀 爀攀洀愀椀渀⸀㰀戀爀㸀ഀഀ
Especially technical and experimental oriented physicst, for example working on the field Quantum Computing,<br>਍猀攀攀 琀栀攀 琀栀攀漀爀礀 愀猀 漀渀攀 漀昀 琀栀攀椀爀 瀀爀椀洀愀爀礀 眀漀爀欀椀渀最 琀漀漀氀猀⸀㰀戀爀㸀ഀഀ
(For example, sometimes they want to preserve a qubit or nqubit for some time, <I>before it de-coheres</I>).<br>਍㰀戀爀㸀ഀഀ
However, in general, we all must be carefull in associating "truth" to any theory at all. It's just characteristic<br>਍漀昀 猀挀椀攀渀挀攀Ⰰ 琀栀愀琀 琀栀攀漀爀椀攀猀 攀瘀攀爀 攀瘀漀氀瘀攀Ⰰ 愀渀搀 漀渀挀攀 椀渀 愀 眀栀椀氀攀Ⰰ 攀瘀攀渀 最攀琀 挀漀洀瀀氀攀琀攀氀礀 爀攀瀀氀愀挀攀搀 戀礀 戀攀琀琀攀爀 漀渀攀猀⸀㰀戀爀㸀ഀഀ
But the "decoherence" framework, is might well be, the best interpretation of QM we have right now.<br>਍㰀戀爀㸀ഀഀ
Decoherence is important in the area of "the measurement problem", possibly also to "the flow of time", and<br>਍愀戀漀瘀攀 愀氀氀 椀琀✀猀 瘀攀爀礀 愀瀀瀀攀愀氀椀渀最 昀漀爀 洀漀猀琀 瀀栀礀猀椀挀椀猀琀猀 戀攀挀愀甀猀攀 椀琀 猀攀攀洀猀 琀漀 猀漀氀瘀攀 琀栀攀 焀甀攀猀琀椀漀渀 漀渀 栀漀眀 琀栀攀 ∀挀氀愀猀猀椀挀愀氀 眀漀爀氀搀∀㰀戀爀㸀ഀഀ
emerges from quantum mechanics.<br>਍㰀戀爀㸀 ഀഀ
Key to the "Decoherence" interpretation, is that it was realized that the "environment" and the quantum system (like a particle)<br>਍愀爀攀 爀攀愀氀氀礀 琀椀攀搀 椀渀琀漀 愀 琀攀洀瀀漀爀愀爀礀 ∀攀渀琀愀渀最氀攀搀∀ 猀礀猀琀攀洀Ⰰ 昀漀爀 愀 挀攀爀琀愀椀渀 搀甀爀愀琀椀漀渀⸀㰀戀爀㸀ഀഀ
Ofcourse, it was already long known that a measurement will influence any system, but this time, a whole framework<br>਍攀洀攀爀最攀搀 昀爀漀洀 ∀琀栀攀 搀攀攀瀀 椀渀琀攀爀琀眀椀渀攀洀攀渀琀∀ 漀昀 琀栀攀 焀甀愀渀琀甀洀 猀礀猀琀攀洀 愀渀搀 琀栀攀 攀渀瘀椀爀漀渀洀攀渀琀⸀㰀戀爀㸀ഀഀ
<br>਍䤀渀 愀 渀甀琀猀栀攀氀氀Ⰰ 琀栀攀 挀攀渀琀爀愀氀 椀搀攀愀 漀昀 琀栀攀 琀栀攀漀爀礀 最漀攀猀 ⠀洀漀爀攀 漀爀 氀攀猀猀⤀ 氀椀欀攀 琀栀椀猀㨀㰀戀爀㸀ഀഀ
<br>਍䄀猀 甀猀甀愀氀Ⰰ 椀渀椀琀椀愀氀氀礀Ⰰ 愀渀 甀渀搀椀猀琀甀爀戀攀搀 焀甀愀渀琀甀洀 猀礀猀琀攀洀Ⰰ 椀猀 愀 猀甀瀀攀爀瀀漀猀椀琀椀漀渀 漀昀 挀漀栀攀爀攀渀琀 猀琀愀琀攀猀⸀㰀戀爀㸀ഀഀ
When the quantum system and the environment (the environment as a whole, or a measuring device) starts<br>਍琀漀 椀渀琀攀爀愀挀琀Ⰰ 琀栀攀 挀漀栀攀爀攀渀琀 猀琀愀琀攀猀 眀椀氀氀 㰀䈀㸀∀搀攀挀漀栀攀爀攀∀㰀⼀䈀㸀 椀渀琀漀 猀漀挀愀氀氀攀搀 ∀瀀漀椀渀琀攀爀猀琀愀琀攀猀∀ 眀栀椀挀栀 愀爀攀 爀攀愀氀氀礀㰀戀爀㸀ഀഀ
determined by the environment.  It means the loss of coherence or ordering of the phase angles between the components<br>਍漀昀 琀栀攀 焀甀愀渀琀甀洀 猀甀瀀攀爀瀀漀猀椀琀椀漀渀⸀ 䔀昀昀攀挀琀椀瘀攀氀礀Ⰰ 琀栀攀 䌀漀瀀攀渀栀愀最攀渀 ∀瀀栀爀愀猀攀∀ 㰀䤀㸀∀挀漀氀氀愀瀀猀攀 漀昀 琀栀攀 猀琀愀琀攀 瘀攀挀琀漀爀∀㰀⼀䤀㸀Ⰰ㰀戀爀㸀ഀഀ
this time has a real physical basis or "explanation".<br>਍䄀昀琀攀爀 琀栀攀 猀礀猀琀攀洀 栀愀猀 搀攀挀漀栀攀爀攀搀Ⰰ 琀栀攀猀攀 ∀瀀漀椀渀琀攀爀猀琀愀琀攀猀∀ 挀漀爀爀攀猀瀀漀渀搀猀 琀漀 琀栀攀 攀椀最攀渀猀琀愀琀攀猀 漀昀 琀栀攀 漀戀猀攀爀瘀愀戀氀攀猀⸀㰀戀爀㸀ഀഀ
In other words, only selected components of the wavefunction are decoupled from a coherent system, and are "leaked" out<br>਍椀渀琀漀 琀栀攀 攀渀瘀椀爀漀渀洀攀渀琀⸀㰀戀爀㸀 ഀഀ
This selection of pointerstates is also called "einselection" in various articles describing decoherence.<br>਍㰀戀爀㸀ഀഀ
Again rephrased in slightly other words: the wavefuctions of the environment and the quantum system, will interact<br>਍椀渀 猀甀挀栀 愀 眀愀礀Ⰰ 琀栀愀琀 琀栀攀 挀漀栀攀爀攀渀琀 猀甀瀀攀爀瀀漀猀椀琀椀漀渀 漀昀 琀栀攀 焀甀愀渀琀甀洀 猀礀猀琀攀洀 眀椀氀氀 㰀䈀㸀搀攀ⴀ挀漀栀攀爀攀㰀⼀䈀㸀 愀渀搀 ∀攀椀渀ⴀ猀攀氀攀挀琀攀搀∀ 猀琀愀琀攀猀㰀戀爀㸀ഀഀ
remain, which resembles a classical system again.<br>਍吀栀椀猀 琀漀漀 椀猀 焀甀椀琀攀 椀洀瀀漀爀琀愀渀琀㨀 戀攀昀漀爀攀 琀栀攀 搀攀挀漀栀攀爀攀渀挀攀 瀀栀愀猀攀Ⰰ 琀栀攀 猀礀猀琀攀洀 椀猀 琀爀甀氀礀 愀 儀甀愀渀琀甀洀 猀礀琀攀洀Ⰰ 琀栀愀琀 椀猀Ⰰ 愀 猀甀瀀攀爀瀀漀猀椀琀椀漀渀⸀㰀戀爀㸀ഀഀ
Then, after the "perturbation", or de-coherence phase, the system behaves much like a classical system.<br>਍匀漀Ⰰ 昀漀爀 琀栀攀 昀椀爀猀琀 琀椀洀攀Ⰰ 愀 挀氀攀愀爀 戀漀甀渀搀愀爀礀 栀愀猀 攀洀攀爀最攀搀 戀攀琀眀攀攀渀 愀 瀀甀爀攀 儀甀愀渀琀甀洀 猀琀愀琀攀Ⰰ 愀渀搀 眀栀愀琀 椀猀 戀攀氀椀攀瘀攀搀 琀漀 戀攀 ∀挀氀愀猀猀椀挀愀氀∀⸀㰀戀爀㸀ഀഀ
<br>਍一漀琀攀 琀栀愀琀 琀栀攀 琀栀攀漀爀礀 瀀爀漀瘀椀搀攀猀 昀漀爀 愀 戀攀琀琀攀爀 攀砀瀀氀愀渀愀琀椀漀渀 昀漀爀 眀栀愀琀 栀愀瀀瀀攀渀猀 愀琀 愀 洀攀愀猀甀爀攀洀攀渀琀Ⰰ 漀爀 椀渀琀攀爀愀挀琀椀漀渀Ⰰ㰀戀爀㸀ഀഀ
with the environment, compared to the Copenhagen interpretation.<br>  ਍㰀戀爀㸀ഀഀ
For example, do you notice that "Quantum decoherence" only gives the <B>appearance</B><br> ਍漀昀 眀愀瘀攀 昀甀渀挀琀椀漀渀 挀漀氀氀愀瀀猀攀㼀㰀戀爀㸀ഀഀ
<br>਍䤀渀 琀栀攀 椀渀琀攀爀瀀爀攀琀愀琀椀漀渀 甀猀椀渀最 琀栀攀 瀀爀椀渀挀椀瀀氀攀 漀昀 ∀搀攀挀漀栀攀爀攀渀挀攀∀Ⰰ 椀猀 渀漀琀 瀀漀猀猀椀戀氀攀 琀漀 猀攀瀀愀爀愀琀攀 愀渀 漀戀樀攀挀琀 戀攀椀渀最 洀攀愀猀甀爀攀搀Ⰰ㰀戀爀㸀ഀഀ
from the apparatus performing the measurement. Or, to seperate the object from the "environment".<br>਍䤀渀 琀栀椀猀 椀渀琀攀爀瀀爀攀琀愀琀椀漀渀Ⰰ 椀渀 愀渀礀 椀渀琀攀爀愀挀琀椀漀渀 戀攀琀眀攀攀渀 琀栀攀 猀礀猀琀攀洀 愀渀搀 琀栀攀 攀渀瘀椀爀漀渀洀攀渀琀Ⰰ 搀攀挀漀栀攀爀攀渀挀攀 琀愀欀攀猀 瀀氀愀挀攀Ⰰ㰀戀爀㸀ഀഀ
and not just when you use some measurement device. <br>਍䜀攀渀攀爀愀氀氀礀 猀瀀攀愀欀椀渀最Ⰰ 琀栀攀 攀渀瘀椀爀漀渀洀攀渀琀 愀渀搀 琀栀攀 瀀愀爀琀椀挀氀攀 愀爀攀 戀漀甀渀搀Ⰰ 漀爀 攀渀琀愀渀最氀攀搀Ⰰ 椀渀 猀甀挀栀 愀 眀愀礀Ⰰ 琀栀愀琀 漀渀氀礀 愀 猀甀戀猀攀琀 㰀戀爀㸀ഀഀ
of superimposed waves (the "pointerstates) is "selected". <br>਍䄀昀琀攀爀 琀栀攀 搀攀ⴀ挀漀栀攀爀攀渀挀攀 瀀栀愀猀攀Ⰰ 琀栀攀 愀挀琀甀愀氀 瘀愀氀甀攀 漀昀 愀渀 漀戀猀攀爀瘀愀戀氀攀 椀猀 猀攀氀攀挀琀攀搀 昀爀漀洀 琀栀攀 瀀漀椀渀琀攀爀猀琀愀琀攀猀⸀㰀戀爀㸀ഀഀ
<br>਍吀栀椀猀 渀攀眀 椀渀琀攀爀瀀爀攀琀愀琀椀漀渀 栀愀猀 焀甀椀琀攀 猀漀洀攀 瀀栀椀氀漀猀漀瀀栀椀挀愀氀 椀洀瀀愀挀琀 愀猀 眀攀氀氀⸀ 吀栀攀 琀栀攀漀爀礀 昀甀爀琀栀攀爀 搀攀猀挀爀椀戀攀猀 栀漀眀 琀栀攀 攀渀瘀椀爀漀渀洀攀渀琀㰀戀爀㸀ഀഀ
sort of "monitors" the de-cohered systems, and it affects our human perception as well.<br>਍吀栀攀爀攀 椀猀 愀 猀漀爀琀 漀昀 爀攀搀甀渀搀愀渀挀礀 漀昀 琀栀攀 瀀漀椀渀琀攀爀 猀琀愀琀攀猀 椀渀 琀栀攀 攀渀瘀椀爀漀渀洀攀渀琀Ⰰ 猀椀洀瀀氀礀 戀攀挀愀甀猀攀 琀栀攀爀攀 椀猀 ∀愀 氀漀琀∀ 漀昀 攀渀瘀椀爀漀渀洀攀渀琀㰀戀爀㸀ഀഀ
out there. So to speak, the environment "bans" arbitrary quantum superpositions.<br>਍伀渀挀攀 愀 猀礀猀琀攀洀 栀愀猀 搀攀挀漀栀攀爀攀搀Ⰰ 愀渀搀 漀渀氀礀 瀀漀椀渀琀攀爀猀琀愀琀攀猀 爀攀洀愀椀渀 ⠀搀攀琀攀爀洀椀渀攀搀 戀礀 琀栀攀 攀渀瘀椀爀漀渀洀攀渀琀⤀Ⰰ 愀渀搀 眀攀 愀猀 漀戀猀攀爀瘀攀爀猀㰀戀爀㸀ഀഀ
come on the second place. The environment "observes" the system, and determines what "we get to see" from the system.<br>਍伀昀挀漀甀爀猀攀Ⰰ 愀渀礀 愀瀀瀀愀爀愀琀甀猀 椀猀 瀀愀爀琀 漀昀 琀栀攀 攀渀瘀椀爀漀渀洀攀渀琀 琀漀漀Ⰰ 猀漀 椀琀 洀愀欀攀猀 猀攀渀猀攀⸀㰀戀爀㸀ഀഀ
<br>਍圀栀愀琀 洀椀最栀琀 戀攀 渀椀挀攀 琀漀 渀漀琀椀挀攀Ⰰ 椀猀 琀栀愀琀 琀栀攀 ∀搀攀挀漀栀攀爀攀渀挀攀∀ 琀栀攀漀爀礀 椀洀瀀氀椀攀猀 琀栀愀琀 琀栀攀 焀甀愀渀琀甀洀 眀愀瘀攀昀甀渀挀琀椀漀渀 椀猀 愀 瀀栀礀猀椀挀愀氀 爀攀愀氀椀琀礀㰀戀爀㸀ഀഀ
rather than a mere abstraction, or postulate, as in many other interpretations.<br>਍㰀戀爀㸀ഀഀ
<B><U>Non-locality and Decoherence:</U></B><br>਍㰀戀爀㸀ഀഀ
਍一漀渀氀漀挀愀氀椀琀礀 椀猀 栀愀爀搀氀礀 猀攀攀渀 愀琀 洀愀挀爀漀猀挀漀瀀椀挀 氀攀瘀攀氀 戀攀挀愀甀猀攀 漀昀 ∀栀愀爀搀∀ 搀攀挀漀栀攀爀攀渀挀攀Ⰰ 挀愀甀猀攀搀 戀礀 猀漀 洀愀渀礀 椀渀琀攀爀愀挀琀椀漀渀猀㰀戀爀㸀ഀഀ
with the environment.<br>਍䈀甀琀 眀栀愀琀 栀愀瀀瀀攀渀猀 眀椀琀栀 琀眀漀 攀渀琀愀渀最氀攀搀 洀椀挀爀漀猀挀漀瀀椀挀 瀀愀爀琀椀挀氀攀猀Ⰰ 昀氀礀椀渀最 愀眀愀礀 椀渀 搀椀昀昀攀爀攀渀琀 搀椀爀攀挀琀椀漀渀猀Ⰰ 愀渀搀 欀攀攀瀀椀渀最 琀栀攀椀爀 ∀挀漀爀爀攀氀愀琀椀漀渀∀㼀㰀戀爀㸀ഀഀ
In section 2, we touched on that subject. First of all, non-locality still seems to be a fundamental feature of QM.<br>਍一漀渀ⴀ氀漀挀愀氀椀琀礀 椀猀 漀昀挀漀甀爀猀攀 洀漀爀攀 琀栀愀渀 樀甀猀琀 琀栀攀 攀砀愀洀瀀氀攀 漀昀 琀栀攀 琀眀漀 攀渀琀愀渀最氀攀搀 瀀愀爀琀椀挀氀攀猀 漀昀 猀攀挀琀椀漀渀 ㈀⸀㰀戀爀㸀ഀഀ
However, it's still a "strong" example of nonlocality, that is, the absence of a local agent (see section 2).<br>਍㰀戀爀㸀ഀഀ
But decoherence is a "powerfull mechanism" to destroy quantum features, so what about "non-locality"?<br>਍䤀琀✀猀 渀漀琀 攀愀猀礀 琀漀 愀渀猀眀攀爀 琀栀椀猀 漀渀攀⸀ 䴀甀挀栀 攀砀瀀攀爀椀洀攀渀琀愀氀 眀漀爀欀Ⰰ 愀渀搀 琀栀攀漀爀攀琀椀挀愀氀 猀琀甀搀椀攀猀 栀愀瘀攀 戀攀攀渀 搀漀渀攀Ⰰ 愀渀搀 椀琀✀猀㰀戀爀㸀ഀഀ
probably fair to say that a <B>very conclusive</B> answer is not reached yet.<br>਍䄀琀 昀椀爀猀琀 猀椀最栀琀Ⰰ 搀攀挀漀栀攀爀攀渀挀攀 洀椀最栀琀 氀漀漀欀 氀椀欀攀 愀 氀漀挀愀氀 洀攀挀栀愀渀椀猀洀 ⠀氀椀欀攀 愀 焀甀愀渀琀甀洀 猀礀猀琀攀洀 琀栀愀琀 椀渀琀攀爀愀挀琀猀 眀椀琀栀 琀栀攀 氀漀挀愀氀 攀渀瘀椀爀漀渀洀攀渀琀⤀Ⰰ㰀戀爀㸀ഀഀ
but probably it is not, according to some studies.<br>਍㰀戀爀㸀ഀഀ
However, other studies have shown that non-locality seems to be very "robust".<br>਍ഀഀ
਍㰀戀爀㸀ഀഀ
<br>਍ഀഀ
<font face="arial" size=2 color="blue">਍㰀栀㌀㸀㔀⸀ 䄀 昀攀眀 眀漀爀搀猀 漀渀 ∀䴀愀渀礀 圀漀爀氀搀猀∀ 愀渀搀 ∀䴀愀渀礀 䴀椀渀搀猀∀ 䤀渀琀攀爀瀀爀攀琀愀琀椀漀渀猀㨀 㰀⼀栀㌀㸀ഀഀ
<font face="arial" size=2 color="black">਍ഀഀ
QM is absolutely astonishing by itself, but when we go to the Many Worlds interpretation, the excitement-level "shifts gear"...<br>਍㰀戀爀㸀ഀഀ
਍圀攀 欀渀漀眀 眀栀愀琀 琀栀攀 䌀漀瀀攀渀栀愀最攀渀 䤀渀琀攀爀瀀爀攀琀愀琀椀漀渀 最氀漀戀愀氀氀礀 洀攀愀渀猀㨀㰀戀爀㸀ഀഀ
<br>਍䄀渀 愀 焀甀愀渀琀甀洀 猀礀猀琀攀洀Ⰰ 椀渀椀琀椀愀氀氀礀 椀渀 愀 猀甀瀀攀爀瀀漀猀椀琀椀漀渀 漀昀 瀀漀猀猀椀戀氀礀 洀愀渀礀 猀琀愀琀攀猀Ⰰ 愀瀀瀀攀愀爀猀 琀漀 爀攀搀甀挀攀 琀漀 愀 猀椀渀最氀攀 瘀愀氀甀攀㰀戀爀㸀ഀഀ
of the states, after interaction with an observer (that is: if it's being measured).<br>਍㰀戀爀㸀ഀഀ
So, at the moment of measurement, the wave function describing the superposition of states,<br>਍愀瀀瀀攀愀爀猀 琀漀 挀漀氀氀愀瀀猀攀 椀渀琀漀 樀甀猀琀 漀渀攀 洀攀洀戀攀爀 漀昀 琀栀攀 猀甀瀀攀爀瀀漀猀椀琀椀漀渀⸀㰀戀爀㸀ഀഀ
<br>਍䤀渀 昀椀最甀爀攀 ㌀ 愀戀漀瘀攀Ⰰ 眀攀 愀氀爀攀愀搀礀 栀愀瘀攀 猀攀攀渀 愀 昀攀眀 猀椀洀瀀氀攀 昀漀爀洀猀 漀昀 愀 猀甀瀀攀爀瀀漀猀椀琀椀漀渀 漀昀 猀琀愀琀攀猀⸀㰀戀爀㸀ഀഀ
<br>਍吀愀欀攀 愀 氀漀漀欀 愀琀 昀椀最甀爀攀 ㌀Ⰰ 攀砀愀洀瀀氀攀㄀Ⰰ 愀最愀椀渀⸀ 一漀眀Ⰰ 猀甀瀀瀀漀猀攀Ⰰ 琀栀愀琀 椀渀 愀 猀甀戀琀氀攀 洀愀渀渀攀爀Ⰰ 眀攀 爀攀瀀栀爀愀猀攀 琀栀攀 昀漀爀洀攀爀 猀琀愀琀攀洀攀渀琀猀 氀椀欀攀 猀漀㨀㰀戀爀㸀ഀഀ
<br>਍㰀䈀㸀䄀 猀甀瀀攀爀瀀漀猀椀琀椀漀渀 攀砀瀀爀攀猀猀攀猀 愀氀氀 瀀漀猀猀椀戀氀攀 㰀唀㸀∀愀氀琀攀爀渀愀琀椀瘀攀猀∀㰀⼀唀㸀 昀漀爀 昀椀渀搀椀渀最 琀栀攀 瘀愀氀甀攀 漀昀 愀 挀攀爀琀愀椀渀 漀戀猀攀爀瘀愀戀氀攀⸀㰀⼀䈀㸀㰀戀爀㸀ഀഀ
<br>਍䔀砀瀀爀攀猀猀攀搀 椀渀 㰀䤀㸀琀栀椀猀 眀愀礀㰀⼀䤀㸀 椀琀 最攀琀✀猀 猀漀洀攀眀栀愀琀 洀漀爀攀 瀀氀愀甀猀椀戀氀攀Ⰰ 琀栀愀琀 㰀䤀㸀愀氀氀 琀栀攀 漀琀栀攀爀㰀⼀䤀㸀 ∀愀氀琀攀爀渀愀琀椀瘀攀猀∀ 洀愀礀 栀愀瘀攀 爀攀愀氀椀稀攀搀㰀戀爀㸀ഀഀ
in other "branched off" Universes.<br>਍㰀戀爀㸀ഀഀ
Above is not exactly the way that Everett originally formulated it.<br>਍䠀椀猀 琀栀攀漀爀礀 最漀攀猀 ∀洀漀爀攀 漀爀 氀攀猀猀∀ 氀椀欀攀 搀攀猀挀爀椀戀攀搀 戀攀氀漀眀⸀ ഀഀ
But whatever your opinion will be of the MWI, it really <I>does</I> resolve some paradoxes in QM,<br>਍氀椀欀攀 琀栀攀 猀琀爀愀渀最攀 ∀挀漀氀氀愀瀀猀攀 漀昀 琀栀攀 眀愀瘀攀 昀甀渀挀琀椀漀渀∀Ⰰ 愀渀搀 攀瘀攀渀 瀀爀漀瘀椀搀攀猀 愀 猀漀氀甀琀椀漀渀 昀漀爀 琀栀攀 渀漀渀ⴀ氀漀挀愀氀椀琀礀 瀀甀稀稀氀攀 ⠀猀攀挀琀椀漀渀 ㈀⤀⸀㰀戀爀㸀ഀഀ
And..., some core aspects of the "Decoherence interpretation" (section 4), looks remarkably to the central statement of MWI.<br>਍㰀戀爀㸀ഀഀ
In MWI, there is no "collapse of the state vector". Suppose you do a measurement on a quantum system.<br>਍䈀攀昀漀爀攀 礀漀甀 愀挀琀甀愀氀氀礀 瀀攀爀昀漀爀洀 琀栀攀 攀砀瀀攀爀椀洀攀渀琀Ⰰ 琀栀攀 猀礀猀琀攀洀 爀攀猀椀搀攀猀 椀渀 猀甀瀀攀爀瀀漀猀椀琀椀漀渀Ⰰ 洀攀愀渀椀渀最 椀渀 愀氀氀 瀀漀猀猀椀戀氀攀 猀琀愀琀攀猀 愀琀 漀渀挀攀⸀㰀戀爀㸀ഀഀ
This is what we already new from an undisturbed quantum system.<br>਍㰀戀爀㸀ഀഀ
Now you perform the measurement, and you find a certain value. In MWI, different versions of you will have found<br>਍愀氀氀 琀栀攀 漀琀栀攀爀 瀀漀猀猀椀戀氀攀 瘀愀氀甀攀猀 漀昀 琀栀攀 漀戀猀攀爀瘀愀戀氀攀⸀ 䤀琀 椀猀 愀猀 椀昀 琀栀攀 挀甀爀爀攀渀琀 唀渀椀瘀攀爀猀攀 栀愀猀 ∀戀爀愀渀挀栀攀搀∀Ⰰ 漀爀 ∀昀漀爀欀攀搀∀Ⰰ 椀渀琀漀㰀戀爀㸀ഀഀ
multiple Universes where each version of you, is happy with it's own private value.<br>਍㰀戀爀㸀ഀഀ
I hear you think.. <I>"Will then the Universe be rebuild N times, at each ocurrence of such an event and so on and so on..?</I><br>਍一漀⸀ 吀栀攀 琀爀椀挀欀 椀猀 椀渀 琀栀攀 猀甀瀀攀爀瀀漀猀椀琀椀漀渀⸀ 吀栀攀 愀氀琀攀爀渀愀琀椀瘀攀猀 ∀愀爀攀 愀氀爀攀愀搀礀 琀栀攀爀攀∀Ⰰ 猀漀 琀漀 猀瀀攀愀欀⸀㰀戀爀㸀ഀഀ
<br>਍䔀瘀攀爀攀琀琀 爀攀愀氀椀稀攀搀Ⰰ 琀栀愀琀 琀栀攀 漀戀猀攀爀瘀攀爀 ⠀眀椀琀栀 洀攀愀猀甀爀攀洀攀渀琀 搀攀瘀椀挀攀⤀Ⰰ 愀渀搀 琀栀攀 猀礀猀琀攀洀Ⰰ 昀漀爀洀猀 愀 搀攀攀瀀 椀渀琀攀爀琀眀椀渀攀搀 猀礀猀琀攀洀⸀㰀戀爀㸀ഀഀ
<B>Each</B> "wave" of the superposition will "sort of interact" with the observer-measurement device.<br>਍䘀爀漀洀 愀 洀愀琀栀攀洀愀琀椀挀愀氀 瀀攀爀猀瀀攀挀琀椀瘀攀Ⰰ 琀栀椀猀 瀀愀椀爀 眀椀氀氀 猀瀀氀椀琀 漀昀昀Ⰰ 愀渀搀 昀甀爀琀栀攀爀 攀瘀漀氀瘀攀 椀渀搀攀瀀攀渀搀攀渀琀氀礀 昀爀漀洀 愀氀氀 琀栀攀 漀琀栀攀爀 瀀漀猀猀椀戀氀攀 ∀瀀愀椀爀猀∀ 漀昀㰀戀爀㸀ഀഀ
the {wave elements of superposition - observer}.<br>਍䠀攀渀挀攀Ⰰ 愀 渀甀洀戀攀爀 漀昀 椀渀搀攀瀀攀渀搀琀氀礀 昀漀爀欀攀搀 唀渀椀瘀攀爀猀攀猀 眀椀氀氀 漀挀挀甀爀⸀㰀戀爀㸀ഀഀ
<br>਍䐀漀 礀漀甀 猀攀攀 琀栀攀 爀攀猀攀洀戀氀攀渀挀攀 眀椀琀栀 琀栀攀 䐀攀挀漀栀攀爀攀渀挀攀 琀栀攀漀爀礀㼀 伀渀氀礀 琀栀椀猀 琀椀洀攀Ⰰ 渀漀 攀渀瘀椀爀漀渀洀攀渀琀 搀爀椀瘀攀渀 瀀漀椀渀琀攀爀猀琀愀琀攀猀 愀爀攀 挀爀攀愀琀攀搀Ⰰ㰀戀爀㸀ഀഀ
but contrary all "relative states" will "start an existence of their own".<br>਍㰀戀爀㸀ഀഀ
But, intuitively, you might say, as I do, "this can't be the way the Universe operates..."<br>਍䤀渀搀攀攀搀Ⰰ 洀愀渀礀 瀀栀礀猀椀挀椀猀琀猀 渀漀眀愀搀愀礀猀 猀愀礀 琀栀愀琀 琀栀攀 䴀圀䤀 琀栀攀漀爀礀 搀漀攀猀 渀漀琀 瀀爀漀瘀椀搀攀 愀渀 愀搀攀焀甀愀琀攀 昀爀愀洀攀眀漀爀欀 漀渀 栀漀眀 愀㰀戀爀㸀ഀഀ
many-branched tree of Worlds comes into existence.<br>਍㰀戀爀㸀ഀഀ
<br>਍㰀昀漀渀琀 昀愀挀攀㴀∀愀爀椀愀氀∀ 猀椀稀攀㴀㈀ 挀漀氀漀爀㴀∀戀氀甀攀∀㸀ഀഀ
<h3>6. Parallel Universes and the "Wavefunction-less" model of Poirier. </h3>਍㰀昀漀渀琀 昀愀挀攀㴀∀愀爀椀愀氀∀ 猀椀稀攀㴀㈀ 挀漀氀漀爀㴀∀戀氀愀挀欀∀㸀ഀഀ
਍䄀爀漀甀渀搀 ㈀　㄀㈀Ⰰ 愀渀 椀渀琀攀爀攀猀琀椀渀最 洀漀搀攀氀 眀愀猀 攀猀琀愀戀氀椀猀栀攀搀 戀礀 䈀椀氀氀 倀漀椀爀椀攀爀⸀㰀戀爀㸀ഀഀ
<br>਍䠀攀 猀漀爀琀 漀昀 ∀猀挀爀愀瀀瀀攀搀∀ 琀栀攀 ∀眀愀瘀攀 昀甀渀挀琀椀漀渀∀ 漀爀 ∀猀琀愀琀攀 瘀攀挀琀漀爀∀ 挀漀洀瀀氀攀琀攀氀礀Ⰰ 愀渀搀 愀猀猀甀洀攀搀 瀀愀爀愀氀氀攀氀 ⠀琀栀甀猀 洀甀氀琀椀瀀氀攀⤀Ⰰ 挀氀愀猀猀椀挀愀氀ⴀ氀椀欀攀 甀渀椀瘀攀爀猀攀猀Ⰰ㰀戀爀㸀ഀഀ
where observables of entities (like particles) have well-defined classical values.<br>਍䠀椀猀 琀栀攀漀爀礀 琀爀攀愀琀猀 琀栀攀 挀漀氀氀攀挀琀椀漀渀 漀昀 甀渀椀瘀攀爀猀攀猀 愀猀 愀渀 攀渀猀攀洀戀氀攀Ⰰ 愀渀搀 琀栀椀猀 漀渀氀礀 挀爀攀愀琀攀猀 琀栀攀 ∀椀氀氀甀猀椀漀渀∀ 琀栀愀琀㰀戀爀㸀ഀഀ
a particle might be non-localized in position or momentum (or any other observable).<br>਍匀漀Ⰰ 眀栀椀氀攀 愀 瀀愀爀琀椀挀氀攀 洀椀最栀琀 漀渀氀礀 愀瀀瀀攀愀爀 琀漀 栀愀瘀攀 愀 猀琀漀挀栀愀琀椀挀 挀栀愀爀愀挀琀攀爀 ⠀瀀爀漀戀愀戀椀氀椀琀礀⤀ 椀渀 猀漀洀攀 漀戀猀攀爀瘀愀戀氀攀Ⰰ 椀琀✀猀 愀挀琀甀愀氀氀礀 漀渀氀礀㰀戀爀㸀ഀഀ
due to some "indifference" in which universe the oberver resides.<br>਍㰀戀爀㸀ഀഀ
This supposedly explains why QM might "just look" as intrinsical stochastic, but it's actually the interactions between those universa,<br>਍琀栀愀琀 猀椀琀猀 戀攀栀椀渀搀 琀栀攀 漀戀猀攀爀瘀攀搀 攀昀昀攀挀琀猀⸀㰀戀爀㸀ഀഀ
<br>਍倀漀椀爀椀攀爀猀 洀愀琀栀攀洀愀琀椀挀愀氀 昀爀愀洀攀眀漀爀欀Ⰰ 椀猀 漀昀琀攀渀 挀愀氀氀攀搀 愀 ∀琀爀愀樀攀挀琀漀爀礀ⴀ戀愀猀攀搀∀ 吀栀攀漀爀礀 漀昀 ⠀刀攀氀愀琀椀瘀椀猀琀椀挀⤀ ∀儀甀愀渀琀甀洀∀ 倀愀爀琀椀挀氀攀猀⸀㰀戀爀㸀ഀഀ
<br>਍䤀渀猀琀攀愀搀 漀昀 栀椀猀 漀爀椀最椀渀愀氀 愀爀琀椀挀氀攀Ⰰ 䤀 瀀攀爀猀漀渀愀氀氀礀 昀椀渀搀 琀栀攀 昀漀氀氀漀眀椀渀最 ✀昀漀氀氀漀眀 甀瀀✀ 愀爀琀椀挀氀攀 漀昀 洀甀挀栀 洀漀爀攀 椀渀琀攀爀攀猀琀Ⰰ 猀椀渀挀攀 琀栀攀 愀甀琀栀漀爀猀㰀戀爀㸀ഀഀ
provide for explanations for (for example) the double split experiment, quantum tunneling and that sort of typical QM manifestations.<br>਍䤀昀 礀漀甀 氀椀欀攀 琀漀 猀攀攀 琀栀愀琀 愀爀琀椀挀氀攀Ⰰ 礀漀甀 洀椀最栀琀 甀猀攀 㰀愀 栀爀攀昀㴀∀栀琀琀瀀㨀⼀⼀愀爀砀椀瘀⸀漀爀最⼀愀戀猀⼀㄀㐀　㈀⸀㘀㄀㐀㐀∀㸀琀栀椀猀 氀椀渀欀⸀㰀⼀愀㸀㰀戀爀㸀ഀഀ
<br>਍㰀戀爀㸀ഀഀ
<font face="arial" size=2 color="blue">਍㰀栀㌀㸀㜀⸀ 䄀 昀攀眀 眀漀爀搀猀 漀渀 搀攀 䈀爀漀最氀椀攀 ⴀ 䈀漀栀洀 ∀倀椀氀漀琀 圀愀瘀攀∀ 䤀渀琀攀爀瀀爀攀琀愀琀椀漀渀㰀⼀栀㌀㸀ഀഀ
<font face="arial" size=2 color="black">਍ഀഀ
This rather peculiar view was first developed by de Broglie in the late twenties of the former century. Then, later on<br>਍愀爀漀甀渀搀 ㄀㤀㔀㈀Ⰰ 椀琀 眀愀猀 瀀椀挀欀攀搀 甀瀀 愀最愀椀渀 戀礀 䈀漀栀洀 眀栀漀 洀愀搀攀 焀甀椀琀攀 猀漀洀攀 昀甀爀琀栀攀爀 瀀爀漀最爀攀猀猀 漀渀 琀栀椀猀 琀栀攀漀爀礀⸀㰀戀爀㸀ഀഀ
<br>਍匀琀爀愀渀最攀氀礀Ⰰ 椀琀 戀攀挀愀洀攀 渀攀瘀攀爀 猀漀 瀀漀瀀甀氀愀爀 搀甀爀椀渀最 琀栀攀 ㈀　琀栀 挀攀渀琀甀爀礀Ⰰ 挀漀洀瀀愀爀攀搀 琀漀 琀栀攀 䌀漀瀀攀渀栀愀最攀渀 椀渀琀攀爀瀀爀攀琀愀琀椀漀渀Ⰰ 愀渀搀 氀愀琀攀爀Ⰰ 搀攀挀漀栀攀爀攀渀挀攀⸀㰀戀爀㸀ഀഀ
However, I seem to notice some gaining in interest (by simply scouting articles), since 2000 or so.<br>਍㰀戀爀㸀ഀഀ
Note that it was de Broglie who first attained a wave-length to a typical corpusculair entity like an electron.<br>਍㰀戀爀㸀ഀഀ
While the Copenhagen interpretation, and it's "collapse", is quite hard to link to reality, the "Pilot Wave" Interpretation<br>਍爀攀ⴀ椀渀琀爀漀搀甀挀攀猀 愀最愀椀渀 猀漀洀攀 挀氀愀猀猀椀挀愀氀 昀攀愀琀甀爀攀猀 愀最愀椀渀⸀ 一漀琀 氀椀琀攀爀愀氀氀礀Ⰰ 戀甀琀 攀猀猀攀渀琀椀愀氀 琀栀攀 琀栀攀漀爀礀 猀琀愀琀攀猀 琀栀愀琀 眀攀 栀愀瘀攀 愀 爀攀愀氀 瀀愀爀琀椀挀氀攀Ⰰ㰀戀爀㸀ഀഀ
with an accompanying pilot wave, which can be regarded as a "velocity field" guiding the particle.<br>਍䈀漀栀洀 昀甀爀琀栀攀爀 搀攀昀椀渀攀搀 愀渀 ∀漀渀挀漀氀漀最礀∀ 漀爀 昀爀愀洀攀眀漀爀欀 漀渀 琀栀攀 攀猀猀攀渀琀椀愀氀 椀搀攀愀猀Ⰰ 眀栀椀挀栀 洀愀搀攀 琀栀攀 眀愀瘀攀 琀漀 戀攀 挀漀洀瀀愀琀椀戀氀攀 眀椀琀栀㰀戀爀㸀ഀഀ
Schrodingers equation, and thus further is deterministic (in the sense of given initial conditions, the further evolution<br>਍挀愀渀 戀攀 挀愀氀挀甀氀愀琀攀搀⤀⸀㰀戀爀㸀ഀഀ
<br>਍䤀昀 礀漀甀 愀爀攀 椀渀琀攀爀攀猀琀攀搀 椀渀 愀 洀愀琀栀攀洀愀琀椀挀愀氀 昀爀愀洀攀眀漀爀欀 漀昀 琀栀椀猀 琀栀攀漀爀礀Ⰰ 䤀 愀搀瘀椀猀攀 琀漀 䜀漀漀最氀攀 漀渀 ∀倀椀氀漀琀 眀愀瘀攀 愀爀砀椀瘀∀Ⰰ㰀戀爀㸀ഀഀ
which should return many scientific articles.<br>਍㰀戀爀㸀ഀഀ
Amazingly, since the early 2000s, it was discovered that small oildrops in a bath of oil, show striking<br>਍猀椀洀椀氀愀爀椀琀攀猀 眀椀琀栀 琀栀攀 挀漀爀攀 椀搀攀愀 漀昀 琀栀攀 倀椀氀漀琀 眀愀瘀攀 最甀椀搀愀渀挀攀⸀㰀戀爀㸀ഀഀ
Maybe you like to see the following YouTube clip:<br>਍㰀戀爀㸀ഀഀ
<a href="https://www.youtube.com/watch?v=nmC0ygr08tE">The pilot-wave dynamics of walking droplets</a><br>਍㰀戀爀㸀ഀഀ
If you have viewed this clip, then you saw a great pictorial "emulation" of the key concept of this theory.<br>਍ഀഀ
਍㰀戀爀㸀ഀഀ
<br>਍㰀昀漀渀琀 昀愀挀攀㴀∀愀爀椀愀氀∀ 猀椀稀攀㴀㈀ 挀漀氀漀爀㴀∀戀氀甀攀∀㸀ഀഀ
<h3>8. A few words about Weak Measurements and the Two State Vector Formalism: </h3>਍㰀昀漀渀琀 昀愀挀攀㴀∀愀爀椀愀氀∀ 猀椀稀攀㴀㈀ 挀漀氀漀爀㴀∀戀氀愀挀欀∀㸀ഀഀ
਍䤀昀 琀栀攀爀攀 椀猀 猀漀洀攀琀栀椀渀最 攀氀猀攀 焀甀椀琀攀 猀琀甀渀渀椀渀最 椀渀 爀攀挀攀渀琀 昀椀渀搀椀渀最猀 椀渀 儀䴀Ⰰ 椀琀 洀甀猀琀 戀攀 琀栀攀 椀洀瀀氀椀挀愀琀椀漀渀猀 漀昀 琀栀攀 猀漀挀愀氀氀攀搀㰀戀爀㸀ഀഀ
"Weak Measurements" and the Two State Vector Formalism.<br>਍㰀戀爀㸀ഀഀ
Ofcourse, again different <I>interpretations</I> are possible, but one implication seems to be that<br>਍椀昀 礀漀甀 洀攀愀猀甀爀攀 愀渀 漀戀猀攀爀瘀愀戀氀攀 眀椀琀栀漀甀琀 ⠀栀愀爀搀氀礀⤀ 搀椀猀琀甀爀戀椀渀最 椀琀 ⠀愀渀搀 琀栀攀渀 漀昀挀漀甀爀猀攀 礀漀甀 渀攀攀搀 琀漀 爀攀瀀攀愀琀 琀栀愀琀 洀愀渀礀 琀椀洀攀猀㰀戀爀㸀ഀഀ
to get any significant result to standout above the noise), then it seems that;<br>਍㰀戀爀㸀ഀഀ
Pre-selected results (in the past), <U>and</U> post-selected results (in the future), may have impact<br>਍漀渀 眀栀愀琀 礀漀甀 洀攀愀猀甀爀攀 瀀爀攀猀攀渀琀氀礀⸀㰀戀爀㸀ഀഀ
<br>਍吀愀欀攀 愀 挀氀漀猀攀爀 氀漀漀欀 愀琀 琀栀漀猀攀 氀愀猀琀 昀攀眀 眀漀爀搀猀㨀 椀琀✀猀 渀漀琀 琀栀攀 渀漀爀洀愀氀 挀愀甀猀愀氀椀琀礀 琀栀愀琀 眀攀 愀爀攀 甀猀攀搀 琀漀⸀㰀戀爀㸀ഀഀ
<br>਍吀栀攀猀攀 渀攀眀 昀漀爀洀愀氀椀猀洀猀 甀猀攀 愀 琀椀洀攀ⴀ猀礀洀洀攀琀爀椀挀 洀漀搀攀氀Ⰰ 椀渀猀琀攀愀搀 漀昀 琀栀攀 甀猀甀愀氀 ∀猀琀愀渀搀愀爀搀∀ 愀瀀瀀爀漀愀挀栀 甀猀攀搀 椀渀 儀䴀⸀㰀戀爀㸀ഀഀ
<br>਍䤀昀 礀漀甀 眀愀渀琀 琀漀 爀攀愀搀 洀漀爀攀Ⰰ 琀愀欀攀 愀 氀漀漀欀 愀琀㨀㰀戀爀㸀ഀഀ
<br>਍㰀愀 栀爀攀昀㴀∀眀攀愀欀开洀攀愀猀甀爀攀洀攀渀琀猀⸀栀琀洀∀㸀愀 昀攀眀 渀漀琀攀猀 漀渀 ∀眀攀愀欀 洀攀愀猀甀爀攀洀攀渀琀猀∀ 愀渀搀 儀䴀 瀀愀爀愀搀漀砀攀猀⸀㰀⼀愀㸀㰀戀爀㸀ഀഀ
਍㰀戀爀㸀ഀഀ
<br>਍㰀戀爀㸀ഀഀ
<br>਍㰀戀爀㸀ഀഀ
</body>਍㰀⼀栀琀洀氀㸀�