Is the Universe a Quantum Computer Algorithm?

[wespe]

In certain respects, physical existence is mathematical. If not, then why does mathematics explain the world so well?

... mathematics isn't used "explain" the world at all. It is used to describe the world.

Sorry for the intrusion. That was once one of my misconceptions (about relativity, but same thing). Best way to make it clear is to think that math was invented to get answers in the physical world. That is, to describe it, not to explain it. Because, things don't happen in physical world because of math says so, it's the other way around. Math is abstract anyway. So when you simplfy or rearrange equations, it may not have a physical meaning, maybe two forces are canceling each other out, but they sill exist, the answer you get is still correct.

 

[PFanalog57]

Incorrect. First, "standing waves" are physical phenomena. And second, even if you mean that they are "standing wave solutions to the wave equation" (which are bona fide mathematical objects), your analysis here by no means proves such a thing. You haven't even specified the parametric equations, nor a dynamical equation that they are supposed to satisfy.



What is so "universal" about this set?

I'm afraid Matt is right: What you have written here is specious nonsense, and has nothing to do with either math or physics.

It is one interpretation of the "Wheeler-Feynman Absorber" theory. I will not give the equations on a silver platter.

 

[quantumdude]

It is one interpretation of the "Wheeler-Feynman Absorber" theory. I will not give the equations on a silver platter.

First of all, you have not presented anything that could be called an interpretation of any physical theory. And second, the Wheeler-Feynman Absorber theory is not a secret.

You keep throwing technical terms around, but you don't seem to have the foggiest idea of what any of them mean.

Has it occurred to you to go into the Math and Physics Forums and ask people for help? This place is loaded with people who can do just that.

 

[PFanalog57]

I can see that my comment went in one ear and out the other.

Here is a quote of Oliver Heaviside, talking about Michael Faraday:

"And it is a noteworthy fact that ignorant men have long been
in advance of the learned about vectors. Ignorant people, like
Faraday, naturally think in vectors. They may know nothing of their
formal manipulation, but if they think about vectors, they think of
them *as* vectors, that is, directed magnitudes. No ignorant man
could or would think about the three components of a vector
separately, and disconnected from one another. That is a device of
learned mathematicians, to enable them to evade vectors. The device
is often useful, especially for calculating purposes, but for general
purposes of reasoning the manipulation of the scalar components
instead of the vector itself is entirely wrong."

First, a question is not a valid argument. Second, mathematics isn't used "explain" the world at all. It is used to describe the world. And third, your position as to the nature of existence is neither a scientific viewpoint nor a mathematical one. It is a philosophical viewpoint, and a rather bad one at that, as it is a form of idealism that mistakes the ideal forms used to describe the physical reality, for the physical reality itself.

Mathematics is a meta-language. Yes, mathematics "describes" the physical universe and it also "explains" :

http://www.m-w.com/cgi-bin/dictionary?book=Dictionary&va=explain&x=15&y=16

EXPLAIN

1 a : to make known b : to make plain or understandable <footnotes that explain the terms>

2 : to give the reason for or cause of

3 : to show the logical development or relationships of

Here is an interesting paper by Max Tegmark that you have probably read before?

http://www.hep.upenn.edu/~max/toe.pdf

Here is a quote about the equivalence of mathematical existence with physical existence:

Our proposed TOE can be summarized as follows:

Physical existence is equivalent to mathematical existence.

What precisely is meant by mathematical existence, or
ME for brevity?

A generally accepted interpretation of
ME is that of David Hilbert:

Mathematical existence is merely freedom from contradiction.
In other words, if the set of axioms that defne a mathematical
structure cannot be used to prove both a statement
and its negation, then the mathematical structure
is said to have ME.

"Mathematical existence is merely freedom from contradiction" The universe must make sense.

Faraday recognized that action at a distance was absurd, and he solved the problem with the "field" concept.

You are saying that fields are not mathematical structures? I disagree. You are saying that Faraday didn't think mathematically? I disagree.

Anyway, the point that led up to this line of discussion was my response to your comment that energy arguments could somehow be invoked in set theory. They can't. Physical arguments are of no use whatsoever in proving mathematical results, because math is not physics, and vice versa.

The laws of physics could be described as laws of geometry. The constants of physics could be described as constants of geometry. That is what Einstein was trying to do, yes?

I have read the Wigner article more than once. Do you know why he calls the effectiveness of mathematics "unreasonable"? It's because no one can explain it. That is precisely why the article is not of any use in proving your assertions.

Then Wigner's paper is also useless for Max Tegmark's writings and I wasn't trying to prove assertions with it.

Incorrect. First, "standing waves" are physical phenomena. And second, even if you mean that they are "standing wave solutions to the wave equation" (which are bona fide mathematical objects), your analysis here by no means proves such a thing. You haven't even specified the parametric equations, nor a dynamical equation that they are supposed to satisfy.

I agree with Michael Faraday and Albert Einstein. Action at a distance is totally absurd. Geometry solves that problem.

What is so "universal" about this set?

Again, I will repeat the first axiom:

If the physical universe includes all that is real and excludes all that is not real, then the physical universe is the universal set.

References for the first axiom:

Chris Langan

www.ctmu.org

Lee Smolin

"Three Roads to Quantum Gravity"


Refute the first axiom. You are a mentor.

I'm afraid Matt is right: What you have written here is specious nonsense, and has nothing to do with either math or physics.

That is your opinion? Refute it mathematically.

First of all, you have not presented anything that could be called an interpretation of any physical theory. And second, the Wheeler-Feynman Absorber theory is not a secret.

You keep throwing technical terms around, but you don't seem to have the foggiest idea of what any of them mean.

Has it occurred to you to go into the Math and Physics Forums and ask people for help? This place is loaded with people who can do just that.

Yes, I will ask for help. One question at a time.

Thank you.

 

[quantumdude]

Here is a quote of Oliver Heaviside, talking about Michael Faraday:

So what? Even if I leave alone the fact that Heaviside and Faraday were not contemporaries[/color], the fact remains that this does not one thing to prove your ridiculous assertion that physics would not exist without mathematics, and neither does it do anything for your equally ridiculous assertions that physical arguments can be used in mathematical proofs. Why won't you just concede that fact, instead of bringing up these silly arguments?

Mathematics is a meta-language. Yes, mathematics "describes" the physical universe and it also "explains" :

Oh does it? Let's look at what you cite as evidence.

EXPLAIN

1 a : to make known b : to make plain or understandable <footnotes that explain the terms>

Mathematical models don't do that. That's what observation does.

2 : to give the reason for or cause of

Nope, mathematical models don't do that either.

3 : to show the logical development or relationships of

OK, mathematical models do that, to a certain extent. But they most definitely don't do that in the most fundamental degrees of freedom, whch is what would be required for an "explanation".

Here is an interesting paper by Max Tegmark that you have probably read before?

http://www.hep.upenn.edu/~max/toe.pdf

Yes, I've read it. Do you really think that a student in theoretical physics hasn't read the articles by Tegmark and Wigner?

Here is a quote about the equivalence of mathematical existence with physical existence:

Here's a novel idea: How about you stop trying to prove your ponits with quotes, and start trying to prove them with arguments. :surprise:

You are saying that fields are not mathematical structures? I disagree. You are saying that Faraday didn't think mathematically? I disagree.

1. I am saying that physical fields, and the mathematical fields used to describe them, are not the same thing.

2. I am not saying that Faraday didn't think mathematically. I am saying that there is no reason to think that your assertion, "Physics would not exist without mathematics", is correct.

The laws of physics could be described as laws of geometry. The constants of physics could be described as constants of geometry. That is what Einstein was trying to do, yes?

That's what he did with GR, and he tried to do it with his attempt at a unified field theory in the 1950's. Still, none of that information lends any credence to the math-o-phille position that mathematical forms acutally exist in nature. That is an unfounded belief.

Then Wigner's paper is also useless for Max Tegmark's writings and I wasn't trying to prove assertions with it.

Then why did you quote it in response to my challenge of your assertion?

I agree with Michael Faraday and Albert Einstein. Action at a distance is totally absurd. Geometry solves that problem.

I agree that action at a distance is absurd. But I would say that geometry describes the problem. I would also be so forward as to say that Faraday and Einstein would agree with that.

Again, I will repeat the first axiom:

If the physical universe includes all that is real and excludes all that is not real, then the physical universe is the universal set.

References for the first axiom:

Chris Langan

www.ctmu.org

Lee Smolin

"Three Roads to Quantum Gravity"

What are you talking about? Axioms don't need references or proofs. They just need logical arguments to flow from them. What you quote here proves nothing.

Refute the first axiom. You are a mentor.

I don't even care about refuting "the first axiom", if nothing can be derived from it.

Tom: I'm afraid Matt is right: What you have written here is specious nonsense, and has nothing to do with either math or physics.

Russell: That is your opinion? Refute it mathematically.

It's not my opinion, it is a fact. You want me to prove mathematically that the gibberish you have posted is wrong? Why should I? Instead why don't you stop screwing around and post something with some actual reasoning behind it?

 

[PFanalog57]

So what? Even if I leave alone the fact that Heaviside and Faraday were not contemporaries[/color], the fact remains that this does not one thing to prove your ridiculous assertion that physics would not exist without mathematics

Nice try.


From the quote of Tegmark and Hilbert: Hilbert defines mathematical existence as "freedom from contradiction"

If mathematical existence equals physical existence:


Physical theories must be free of contradiction.

Physical theories would not exist without mathematics.

Physics must be free of contradiction

Mathematical models don't do that. That's what observation does.

Are you saying that "observation" is not a mathematical process in itself?

eye<-------[photons]------->observed phenomena

Here's a novel idea: How about you stop trying to prove your ponits with quotes, and start trying to prove them with arguments. :surprise:

I am not proving[or trying to prove] points with quotes. This thread started out as a question and was moved to TD. Now I am trying to "develop" the theory. Or more correctly, I am trying to develop a hypothesis

2. I am not saying that Faraday didn't think mathematically. I am saying that there is no reason to think that your assertion, "Physics would not exist without mathematics", is correct.

Earlier, you said this about Faraday:

That's just it: He thought in physical terms.

Now you agree that he thought in mathematical terms also

Thanks.

That's what he did with GR, and he tried to do it with his attempt at a unified field theory in the 1950's. Still, none of that information lends any credence to the math-o-phille position that mathematical forms acutally exist in nature. That is an unfounded belief.

It is not a "belief". It is a hypothesis. Perhaps I should have stated that expilcitly.

I don't even care about refuting "the first axiom", if nothing can be derived from it.

Thanks for the help.

 

[quantumdude]

Nice try.

I have no idea of what you mean by that.

From the quote of Tegmark and Hilbert: Hilbert defines mathematical existence as "freedom from contradiction"

If mathematical existence equals physical existence:


Physical theories must be free of contradiction.

Physical theories would not exist without mathematics.

Physics must be free of contradiction

Was this supposed to be an answer to what I was saying? If so, then I don't see how. All you are doing is starting from your peculiar brand of idealist philosophy, and drawing conclusions from it. I wasn't wondering about the consequences, I was wondering what made you think the statement,

"Mathematical existence equals physical existence,"

was true in the first place.

Are you saying that "observation" is not a mathematical process in itself?

eye<-------[photons]------->observed phenomena

Yes, observation is not a mathematical process.

I am not proving[or trying to prove] points with quotes. This thread started out as a question and was moved to TD. Now I am trying to "develop" the theory. Or more correctly, I am trying to develop a hypothesis

Then why do you respond to comments with quotes and links that have no relevance to the discussion? Why not just post an argument? If you are here to devlop a theory, you don't seem to be trying very hard.

Earlier, you said this about Faraday:

Now you agree that he thought in mathematical terms also

Thanks.

He probably did. So what? It still doesn't mean that physics would not exist without mathematics.

It is not a "belief". It is a hypothesis. Perhaps I should have stated that expilcitly.

A belief is nothing other than a hypothesis that is held to be true, without any evidence.

I feel compelled to echo Matt's earlier thought: When you have figured out what it is you want to prove, let us know.

 

[hello3719]

Mathematics is THE LANGUAGE that express human thoughts in the most logical way. Physics is the study of what exists. You can consider an observation made in an experiment to be part of the mathematical terminology, but in our mathematical system they aren't always included.
Also if you meant to say that "existence" is due to mathematics it isn't true since language isn't by definition the root of existence.

 

[PFanalog57]

I was wondering what made you think the statement,

"Mathematical existence equals physical existence,"

was true in the first place.

Since mathematical existence is defined by David Hilbert as "freedom from contradiction" It holds that, if, mathematical existence is equal to physical existence, then physical existence is also freedom from contradiction. That is to say, physical phenomena[events] are constrained by an intrinsic, logical self-consistency.

Yes, observation is not a mathematical process.

Observation[in the sense of empiricism/scientific method] is NOT self contradictory, if, physical existence is "freedom from contradiction".

Ergo, it follows that your statement: "observation is not a mathematical process" is false.

Then why do you respond to comments with quotes and links that have no relevance to the discussion? Why not just post an argument? If you are here to devlop a theory, you don't seem to be trying very hard.

This appears to be your personal, biased opinion? Elitism? Feigned ignorance? The quotes and links ARE relevant to the discussion.

He probably did. So what? It still doesn't mean that physics would not exist without mathematics.

[1.] Physics would not exist without an ability to describe phenomena.

[2.] The description of phenomena must be logically consistent[free of contradiction].

[3.] Mathematical existence is defined as freedom from contradiction.


[4.] Mathematics describes phenomena.

Therefore

Physics would not exist without mathematics.

A belief is nothing other than a hypothesis that is held to be true, without any evidence.

If the hypothesis cannot be tested, then what good is it?

I feel compelled to echo Matt's earlier thought: When you have figured out what it is you want to prove, let us know.

:zzz: :zzz: :zzz:



If the universe includes all that is real and excludes that which is not real, then the universe is the "universal set".

Background Independence:


The description of any entity inside the real universe can only be
with reference to other things in the universe. Space is then
relational, and the universe, self referential. For example, if an
object has a momentum, that momentum can only be explained with
respect to another object within the universe. Space then becomes an
aspect of the relationships between things in reality.

Physicist Lee Smolin says that space becomes analogous to a sentence, and it is absurd to say that a sentence has no words in it. So the grammatical structure of each sentence[space] is defined by the relationships that hold between the words in it.

For example, relationships like object-subject or adjective-noun. So
there are many different grammatical structures composed of different
arrangements of words, and the varied relationships between them.


If the universe is closed, the "information" or entangled quantum
states cannot leak out of the closed system. So the density of
entangled quantum states, continually increases, as the entropy must
always increase. While to us, it is interpreted as entropy or lost
information, it is actually recombined information, to the universe.

Shannon entropy.

Since entropy can also be defined as the number of states within a
region of space, and the entropy of the universe must always
increase, the next logical step is to realize that the spacetime
density, i.e. the information encoded within a circumscribed region
of space, must be increasing in the thermodynamic direction of time.


The entropy of thermodynamics and entropy of Shannon, are equivalent
concepts, because the number of arrangements that are counted by
Boltzmann entropy reflects the amount of Shannon information needed
to implement any particular combination, or arrangement. The two
entropies also appear to have superficial differences.

Thermodynamic entropy is interpreted in units of energy divided by
temperature, while, the Shannon entropy is interpreted in terms of
dimensionless bits. This seems to point towards a computational/language structure for reality.


The Heisenberg uncertainty principle follows directly from the Cauchy-Schwartz inequality for scalar products. By quantizing spacetime geometry, it seems that the wavefunctions/waveforms aren't based on a background space. The wavefunction space, can be thought of as the space of square-
integrable wavefunctions over classical configuration space. Geometric quantization can be constructed, via fiber bundles.

 

[quantumdude]

Since mathematical existence is defined by David Hilbert as "freedom from contradiction" It holds that, if, mathematical existence is equal to physical existence, then physical existence is also freedom from contradiction. That is to say, physical phenomena[events] are constrained by an intrinsic, logical self-consistency.

OK, fine.

Observation[in the sense of empiricism/scientific method] is NOT self contradictory, if, physical existence is "freedom from contradiction".

Ergo, it follows that your statement: "observation is not a mathematical process" is false.

No, it doesn't follow. You are in dire need of a lesson in elementary logic. It is a simple, obvious fact that denying the statement "physical existence = mathematical existence" and affirming the statement "physical observations must be noncontradictory" are compatible.

Tom: Then why do you respond to comments with quotes and links that have no relevance to the discussion? Why not just post an argument? If you are here to devlop a theory, you don't seem to be trying very hard.

Russell: This appears to be your personal, biased opinion? Elitism? Feigned ignorance? The quotes and links ARE relevant to the discussion.

No, they aren't relevant. You consistently respond to comments with links that have the correct buzzwords, but do not connect to those comments in the slightest. Anyone who knows anything about mathematics or physics can see this.

[1.] Physics would not exist without an ability to describe phenomena.

[2.] The description of phenomena must be logically consistent[free of contradiction].

[3.] Mathematical existence is defined as freedom from contradiction.


[4.] Mathematics describes phenomena.

Therefore

Physics would not exist without mathematics.

Russell, do yourself a huge favor and take a course in logic. This argument is so asinine, I am astounded that a would-be mathematical theorist would even post it.

If the hypothesis cannot be tested, then what good is it?

Exaclty my point: Your belief that physical existence is equivalent to mathematical existence cannot be tested. Ergo, it is no good.

If the universe includes all that is real and excludes that which is not real, then the universe is the "universal set".

Background Independence:

The description of any entity inside the real universe can only be
with reference to other things in the universe. Space is then
relational, and the universe, self referential. For example, if an
object has a momentum, that momentum can only be explained with
respect to another object within the universe. Space then becomes an
aspect of the relationships between things in reality.

Physicist Lee Smolin says that space becomes analogous to a sentence, and it is absurd to say that a sentence has no words in it. So the grammatical structure of each sentence[space] is defined by the relationships that hold between the words in it.

For example, relationships like object-subject or adjective-noun. So
there are many different grammatical structures composed of different
arrangements of words, and the varied relationships between them.


If the universe is closed, the "information" or entangled quantum
states cannot leak out of the closed system. So the density of
entangled quantum states, continually increases, as the entropy must
always increase. While to us, it is interpreted as entropy or lost
information, it is actually recombined information, to the universe.

Shannon entropy.

Since entropy can also be defined as the number of states within a
region of space, and the entropy of the universe must always
increase, the next logical step is to realize that the spacetime
density, i.e. the information encoded within a circumscribed region
of space, must be increasing in the thermodynamic direction of time.


The entropy of thermodynamics and entropy of Shannon, are equivalent
concepts, because the number of arrangements that are counted by
Boltzmann entropy reflects the amount of Shannon information needed
to implement any particular combination, or arrangement. The two
entropies also appear to have superficial differences.

Thermodynamic entropy is interpreted in units of energy divided by
temperature, while, the Shannon entropy is interpreted in terms of
dimensionless bits. This seems to point towards a computational/language structure for reality.


The Heisenberg uncertainty principle follows directly from the Cauchy-Schwartz inequality for scalar products. By quantizing spacetime geometry, it seems that the wavefunctions/waveforms aren't based on a background space. The wavefunction space, can be thought of as the space of square-
integrable wavefunctions over classical configuration space. Geometric quantization can be constructed, via fiber bundles.

Be sure to let me know when you want to present a logical argument for your ideas on geometric set theory.

 

[PFanalog57]

No, it doesn't follow. You are in dire need of a lesson in elementary logic. It is a simple, obvious fact that denying the statement "physical existence = mathematical existence" and affirming the statement "physical observations must be noncontradictory" are compatible.

You agree that physical observations must be non-contradictory.

You must also agree that descriptions of physical existence must be
non-contradictory since observations must be non-contradictory.

We can drop the label "mathematical existence"
if it puts a burr in your saddle.





In other words, you appear to be arguing semantics, not physics.

 

[quantumdude]

It has occurred to me that, just because you use terms such as "modus ponens", it just might not be the case that you understand them. So, I am going to go into more detail on these arguments.

Since mathematical existence is defined by David Hilbert as "freedom from contradiction" It holds that, if, mathematical existence is equal to physical existence, then physical existence is also freedom from contradiction. That is to say, physical phenomena[events] are constrained by an intrinsic, logical self-consistency.




Observation[in the sense of empiricism/scientific method] is NOT self contradictory, if, physical existence is "freedom from contradiction".

Ergo, it follows that your statement: "observation is not a mathematical process" is false.

It does not follow. Let's see why, formally.

The fundamental statements of the argument are these:

p: Mathematical existence is equivalent to physical existence.
q: Physical existence is free from contradiction.
r: Observation is free from contradiction.
s: Observation is not a mathematical process.

Your argument proceeds as follows:

1.) p-->q (Premise)
2.) q-->r (Premise)
3.) Therefore, ~s (Conlcusion)

That this is a non-sequitir is obvious to anyone with any familiarity with logic. The basic statements of the premises do not even appear in the conclusion, which makes the conclusion totally unconnected to the statements cited to support it. Furthermore, it is a simple fact that conclusions of valid arguments cannot contain statements that do not appear in the premises, but this argument does. You can test it for validity yourself by determining the truth table for the compound statement:

[p-->q]^[q-->r]-->(~s)

You will see that the statement is not tautological, and so the argument cannot be valid.

But perhaps you didn't mean to include a new term in the conclusion, and that it only looks like you did due to a poor choice of words?

[1.] Physics would not exist without an ability to describe phenomena.

OK, so formally this is an "if-then" statement:

If physics exists, then it has the ability to describe phenomena.

I'll contract it to:

p: Physics exists.
q: Physics has the ability to describe phenomena.

So we have:

1.) p-->q.

[2.] The description of phenomena must be logically consistent[free of contradiction].

Since this is not a compound statement, it will be denoted by a single logical variable:

2.) r

[3.] Mathematical existence is defined as freedom from contradiction.

Same here.

3.) s

[4.] Mathematics describes phenomena.

And here.

4.) t

Therefore

Physics would not exist without mathematics.

And this is equivalent to the "if-then" statement:

If physics exists, then mathematics exists.

The antecedent was already denoted as "p". Let the consequent be "u". So we have:

p-->u.

And your argument proceeds as follows:

1.) p-->q (Premise)
2.) r (Premise)
3.) s (Premise)
4.) t (Premise)
5.) Therefore, p-->u (Conclusion)

This argument has the same malady as the first one, though to a lesser extent (one logical variable from the premises actually occurs in the conclusion!). But this argument is not valid either, which you can verify using a truth table.

On to your next post:

You agree that physical observations must be non-contradictory.

You must also agree that descriptions of physical existence must be
non-contradictory since observations must be non-contradictory.

Yes.

We can drop the label "mathematical existence"
if it puts a burr in your saddle.

It puts a burr in my saddle because it is irrational.

In other words, you appear to be arguing semantics, not physics.

No, logic is not semantics. Furthermore, you aren't even arguing physics. The position "physical existence is equivalent to mathematical existence" is a philosophical position, not a scientific or mathematical one.

 

[PFanalog57]

That this is a non-sequitir is obvious

Thanks for the help

[1.] Mathematics is a meta language.

[2.] Langauge is descriptive.

[3.] Langauge must be free of contradiction. Mathematics is also defined as a descriptive system that has "freedom from contradiction".

[4.] Mathematics describes physical existence/processes/events.

[5.] Observation is a physical process.

[6.] Mathematics describes observations.

[7.]A description of an observation must be free of contradiction-following from [3.]

[8.] Observation must be free of contradiction.

[8.] A description is an abstract representation of a physical system. The description must be as exact as possible.

[9.] An exact description implies equivalence between abstract structures and physical systems.

[10.] If the exact description exists, then physical existence is a meta-language. A self descriptive entity, free of contradiction. The universe is equivalent to its[exact] description.

 

[matt grime]

9. equivalence?

of course there's then the problem that you cannot prove that any model *exactly* fits the system, so it's all vacuous.

then there's the fact that language needn't be free or contradiction. cleave means to split apart or to stick together...

 

[PFanalog57]

9. equivalence?

of course there's then the problem that you cannot prove that any model *exactly* fits the system, so it's all vacuous.

then there's the fact that language needn't be free or contradiction. cleave means to split apart or to stick together...

A meta language[mathematics] must be "free" of contradiction does it not? Cleave and ...cleave are relativised to the context of the "situation".

The only certainty is uncertainty

X = certainty

The only X is not-X ?

A contradiction. But what we understand about reality, must make sense.

We must assume? that a non-contradictory description [stratified variables]of reality exists.

X = certainty, exists, even if it is an incompletely constructed map by self aware systems within the universe...?

 

[PFanalog57]

I was thinking in terms of nested "hyper-realities" , where the algorithim arises spontaneously, analogously to a quantum fluctuation description.

These nested hyper curves are level-surfaces, analogous to resonating phase spaces:

[<-[-><-]->]

The laws and constants of physics become the laws of geometry. Any measured piece of reality is observed to be constructed of discrete units. The resonating wave functions are the infinite number of possible combinations of position Dx, and momentum Dp.

A quantum computer "algorithm".

Overlapping waves become phase entangled. There are two types of wave "motion", which becomes a mixed wave form. Both transverse and longitudinal wave propagation occurs.

Hypothetically speaking, of course