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A Linear combination of Eigenfunctions is itself a valid Quantum state (superposed)

#1
Ostronomos Offline
Suppose an Eigenfunction Ψ1 or Ψ2 or Ψ1 + Ψ2 is defined for a given Quantum state that exists in superposition with another. Does a linear combination of multiple states increase the probability density of the wavefunction if they experience constructive interference? And decrease if they experience destructive interference? Many-worlds was the competing theory to wavefunction collapse within the Copenhagen interpretation if I'm not mistaken. What is said about higher-dimensional string theory? That universes interfere under wavefunction interference? Please help.
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#2
C C Offline
(Dec 23, 2020 04:57 PM)Ostronomos Wrote: [...] Many-worlds was the competing theory to wavefunction collapse within the Copenhagen interpretation if I'm not mistaken. What is said about higher-dimensional string theory? That universes interfere under wavefunction interference?


A "multiverse" also arises in several other background theory scenarios, not just the Everett interpretation.

Refinements and offshoots of string theory produced the idea that our universe is one among many, each confined to a brane, and it's those branes that would potentially collide or interact with, or influence this universe.{1} But string theory is becoming passé, regarded as a fail, apart from the mathematics it introduced. Cosmological inflation (minus string theory), on the other hand, has legs and is widely accepted.{2}

Excerpt from footnote-2:
"The fabric of the multiverse is an inflationary field that's filled with quantum fluctuations. These fluctuations can interfere with each other, creating high inflation at the peaks. The low points of the interference are where stable universes can pop out of the field. Conveniently, the high points continue to inflate, producing more multiverse fabric, which undergoes its own quantum fluctuation, making it an endless producer of universes; Andrei Linde describes it as a fractal process."
- - - - -

Many Interacting Worlds: Physicists Propose Existence, Interaction of Parallel Universes
http://www.sci-news.com/physics/science-...02249.html

EXCERPT: . . . According to the team, their model of such a ‘many interacting worlds’ approach can reproduce some quantum phenomena – such as Ehrenfest’s theorem, wave packet spreading, barrier tunneling, and zero-point energy – as a direct consequence of mutual repulsion between parallel worlds.

“This picture is all that is needed to explain bizarre quantum effects such as particles that tunnel through solid barriers and wave behavior in double-slit experiments.”

Dr Michael Hall of Griffith University, the first author of the paper, said: “the ‘Many-Interacting Worlds’ approach may even create the extraordinary possibility of testing for the existence of other worlds. The beauty of our approach is that if there is just one world our theory reduces to Newtonian mechanics, while if there is a gigantic number of worlds it reproduces quantum mechanics. In between it predicts something new that is neither Newton’s theory nor quantum theory.”

“We also believe that, in providing a new mental picture of quantum effects, it will be useful in planning experiments to test and exploit quantum phenomena.” (MORE - details)

- - - footnotes - - -

{1} The theory of parallel universes is not just maths – it is science that can be tested: ... due to the quantum fluctuations of space-time, some parts of the universe never actually reach the end state of inflation. This means that the universe is, at least according to our current understanding, eternally inflating. Some parts can therefore end up becoming other universes, which could become other universes etc. This mechanism generates a infinite number of universes.

By combining this scenario with string theory [...] the universes predicted by string theory and inflation live in the same physical space (unlike the many universes of quantum mechanics which live in a mathematical space), they can overlap or collide. Indeed, they inevitably must collide, leaving possible signatures in the cosmic sky which we can try to search for... (MORE - details)


{2} Manufacturing universes in a fractal multiverse: To understand the multiverse, you've got to understand inflation, and for that, the panel had Alan Guth, who was instrumental in developing it as a concept. The basic idea of inflation is that, early in the Universe's history, it went through a period where it expanded at a staggering rate...

[...] Another panelist, Andrei Linde of Stanford ... was working on inflation from the perspective of what's called the "graceful exit" problem: how do you get inflation that's just enough to blow up the Universe, but stops before ripping it apart? The answer Linde eventually came up with is that sometimes you do, sometimes you don't. This is where the idea of a multiverse comes in.

The fabric of the multiverse is an inflationary field that's filled with quantum fluctuations. These fluctuations can interfere with each other, creating high inflation at the peaks. The low points of the interference are where stable universes can pop out of the field. Conveniently, the high points continue to inflate, producing more multiverse fabric, which undergoes its own quantum fluctuation, making it an endless producer of universes; Linde describes it as a fractal process.

Festival founder Brian Greene was on hand to mention why, as a string theorist, the multiverse was very satisfying to him. In short, string theory has been suffering from its own inflation, as it looks like there are 10 or 11 extra dimensions beyond the four familiar ones of space-time. How those extra dimensions get compacted away determines the physical properties of our Universe. Over a decade ago, Greene was hoping something would come out of the math that would explain why we have the properties we do, but now he accepts that we're living in a universe with just one out of over 10^500 potential combinations of properties.

The nice thing about the multiverse is that each of the universes it spews out should have its own set of physical rules. So, in short, if the process really is infinite, a universe with our properties was pretty much inevitable. In fact, something with a value for dark energy that's similar to our own universe appears in somewhere around 10^300 of the possible types of physics predicted by string theory.
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#3
confused2 Offline
Ostronomos Wrote:Does a linear combination of multiple states increase the probability density of the wavefunction if they experience constructive interference?
I'm not sure what the question means but the answer might lie in the Double slit experiment which certainly demonstrates constructive and destructive interference. A common misconception about the result (eg wikipedia's account) is that the source needs to be coherent (eg a laser) which is not true.
For example:
https://www.teachspin.com/two-slit
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#4
Ostronomos Offline
(Dec 24, 2020 04:19 AM)C C Wrote:
(Dec 23, 2020 04:57 PM)Ostronomos Wrote: [...] Many-worlds was the competing theory to wavefunction collapse within the Copenhagen interpretation if I'm not mistaken. What is said about higher-dimensional string theory? That universes interfere under wavefunction interference?


A "multiverse" also arises in several other background theory scenarios, not just the Everett interpretation. 

Refinements and offshoots of string theory produced the idea that our universe is one among many, each confined to a brane, and it's those branes that would potentially collide or interact with, or influence this universe.{1} But string theory is becoming passé, regarded as a fail, apart from the mathematics it introduced. Cosmological inflation (minus string theory), on the other hand, has legs and is widely accepted.{2}

Excerpt from footnote-2:
"The fabric of the multiverse is an inflationary field that's filled with quantum fluctuations. These fluctuations can interfere with each other, creating high inflation at the peaks. The low points of the interference are where stable universes can pop out of the field. Conveniently, the high points continue to inflate, producing more multiverse fabric, which undergoes its own quantum fluctuation, making it an endless producer of universes; Andrei Linde describes it as a fractal process."
- - - - -

Many Interacting Worlds: Physicists Propose Existence, Interaction of Parallel Universes
http://www.sci-news.com/physics/science-...02249.html

The nice thing about the multiverse is that each of the universes it spews out should have its own set of physical rules. So, in short, if the process really is infinite, a universe with our properties was pretty much inevitable. In fact, something with a value for dark energy that's similar to our own universe appears in somewhere around 10^300 of the possible types of physics predicted by string theory.

According to my own scientific observations, the interaction between universes does not appear to come from an external source but rather, is indistinguishable from the respective internal universe in which the observer resides. God would be common to every universe but you would experience yourself as an individual existing within a single non-interacting universe with occasional experiences of instantaneous Quantum communication between separate universes. Demons for example can temporarily intersect your universe from theirs in the event that your soul or mind becomes a "signal" or "beacon" for universal consciousness. 

This is why when that fucking imbecile Paddoboy from sciforums says that the universe "doesn't give a rat's ass" I would counter that by saying that from a strictly material perspective that may be the case however from a spiritual perspective the opposite is the case whereby its "reciprocal value" becomes possible and instantaneous communication between a network of spiritual entities is very real, more real than matter.

For example: You are facing both physical and emotional adversity and the television suddenly plays the song "no one" by Alicia Keys (a beautiful song) while being in a completely elevated state of awareness in which you are aware that you have become a "beacon" for the supernatural.
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#5
C C Offline
(Dec 24, 2020 05:17 PM)Ostronomos Wrote: [...] According to my own scientific observations, the interaction between universes does not appear to come from an external source but rather, is indistinguishable from the respective internal universe in which the observer resides. God would be common to every universe but you would experience yourself as an individual existing within a single non-interacting universe with occasional experiences of instantaneous Quantum communication between separate universes. Demons for example can temporarily intersect your universe from theirs in the event that your soul or mind becomes a "signal" or "beacon" for universal consciousness. [...]


Ordinary time-travel itself could be viewed as a journey through a series of parallel universes. Or in other words following an incrementally evolving route among them that is the most coherent in terms of memory holding together and one's slightly changed brain-states being "linked" via such. (We could only be aware of those long sequences of differences that were inter-consistent, lawful like and non-jumbled. Detours and straying into irrational sequences would not be remembered or would be equivalent to the most disorderly of dreams.)

Julian Barbour's version of a multiverse ("Platonia") is depicted as a stratified manifold of all possible configurations of the universe. One's experience or consciousness could seem to follow a gradual, rational developing path through that sea of varying cosmic states (ranging from pre-Big-Bang compactness to an accelerating expansion and heat death or whatever ultimate fate).

Each brain-state is only aware of and confined to the world configuration it exists in -- its personal "now" (cosmic configuration) that it deems alone as real. But because the same memory is replicated in one's body in another universe (along with a slight addition or change), there seems to be a transition from one to the other, as if consciousness is flowing. There's actually no "stuff" teleporting or moving through the equivalent of a 4D nanoscopic pipeline -- phenomenal experience is already instantiated or distributed across those multiple brain-states that have shared and structurally related memories.

Hermann Weyl's quote below only pertains to an ordinary block-universe conception with a single "pathway" (i.e., deterministic). Not the wandering routes and possibilities that a multiverse version or something like Barbour's Platonia could have (in terms of brain-based perspective).

- - - footnote - - -

{*} Hermann Weyl: "The objective world simply IS, it does not HAPPEN. Only to the gaze of my consciousness, crawling upward along the life line [worldline] of my body, does a certain section of this world come to life as a fleeting image in space which continuously changes in time." --Philosophy of Mathematics and Natural Science
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#6
Ostronomos Offline
(Dec 24, 2020 08:15 PM)C C Wrote:
(Dec 24, 2020 05:17 PM)Ostronomos Wrote: [...] According to my own scientific observations, the interaction between universes does not appear to come from an external source but rather, is indistinguishable from the respective internal universe in which the observer resides. God would be common to every universe but you would experience yourself as an individual existing within a single non-interacting universe with occasional experiences of instantaneous Quantum communication between separate universes. Demons for example can temporarily intersect your universe from theirs in the event that your soul or mind becomes a "signal" or "beacon" for universal consciousness. [...]


Ordinary time-travel itself could be viewed as a journey through a series of parallel universes. Or in other words following an incrementally evolving route among them that is the most coherent in terms of memory holding together and one's slightly changed brain-states being "linked" via such. (We could only be aware of those long sequences of differences that were inter-consistent, lawful like and non-jumbled. Detours and straying into irrational sequences would not be remembered or would be equivalent to the most disorderly of dreams.)

Julian Barbour's version of a multiverse ("Platonia") is depicted as a stratified manifold of all possible configurations of the universe. One's experience or consciousness could seem to follow a gradual, rational developing path through that sea of varying cosmic states (ranging from pre-Big-Bang compactness to an accelerating expansion and heat death or whatever ultimate fate).

Each brain-state is only aware of and confined to the world configuration it exists in -- its personal "now" (cosmic configuration) that it deems alone as real. 

(...)

{*} Hermann Weyl: "The objective world simply IS, it does not HAPPEN. Only to the gaze of my consciousness, crawling upward along the life line [worldline] of my body, does a certain section of this world come to life as a fleeting image in space which continuously changes in time." --Philosophy of Mathematics and Natural Science

Fascinating assertion. The moment-by-moment configurations of the universe would seem to suggest that time is quantized (which I believe to be true), and that each moment is frozen in time as in your block universe theory. Whereby the branching of universes according to your reference to a stratified manifold, would lead us to ask, what is the universe if not matter? Which would then lead us to ask, what is matter? Could it merely be the inverse of being?
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