Can someone explain superposition?

[Syntho-sis]

Maybe in the form of an analogy. I'm attempting to understand this concept...

[Mr Skeptic]

Flip a coin with your eyes closed. It could either be heads or tails, but you won't know until you look. Superposition is like that, except that they say that both states exist superimposed until you look, not just that you don't know.

[granpa]

Flip a coin with your eyes closed. It could either be heads or tails, but you won't know until you look. Superposition is like that, except that they say that both states exist superimposed until you look, not just that you don't know.

when an electron in an atom transitions from one shell to another does it do it instantly or is there a time when it is partially in one and partially in the other. in other words in a superposition of both states.

 

edit:http://209.85.173.132/search?q=cache:q9tx8VVznEMJ:www.physicsforums.com/archive/index.php/t-151024.html+atom+electron+energy+levels+superposition

Edited April 12, 2009 by granpa

[Syntho-sis]

Flip a coin with your eyes closed. It could either be heads or tails, but you won't know until you look. Superposition is like that, except that they say that both states exist superimposed until you look, not just that you don't know.

 

 

Ok makes sense, and how does this apply to waves?

[Mr Skeptic]

It doesn't so much apply to waves. The thing with quantum mechanics is that you are dealing with a wave-particle duality. Basically, things move like a wave and interact like a particle. But a wave is diffuse, and a particle is a point. When you poke a wave-particle, it looks like a particle. But when you pass a wave-particle through a pair of slits, it moves through them like a wave and produces an interference pattern like a wave would. In a sense, it must have passed through both slits at once. Edited April 13, 2009 by Mr Skeptic
Thanks DH

[D H]

It most certainly does apply to waves. The superposition principle applies to forces, potential energy, water waves, ... It applies to any linear system, of which Schrödinger's wave equation is but one example.

[Logica]

The following link is a satirical article on Superposition:

 

http://www.thespoof.com/news/spoof.cfm?headline=s5i24833

 

I have devised an logical format that encapsulates the dynamics of superposition

 

Let X = The cat is alive

 

Therefore

X = The cat is alive

or

-X = The cat is not alive (dead)

 

Opening the box would prove which is true X or -X

So without proof we must say:

 

It is not the case that the cat is alive (no proof)

But it's not the case either that the cat is dead (no proof)

 

This is often awkwardly expressed as "Both Dead and Alive". But better expressed would be 'its indeterminate at this stage whether the cat is dead or alive'

 

-(X) + -(-X)

= -X + X

= 0

 

 

With 0/neutrality (not + or -) I have attempted to encapsulate superposition.

[swansont]

The following link is a satirical article on Superposition:

 

http://www.thespoof.com/news/spoof.cfm?headline=s5i24833

 

I have devised an logical format that encapsulates the dynamics of superposition

 

Let X = The cat is alive

 

Therefore

X = The cat is alive

or

-X = The cat is not alive (dead)

 

Opening the box would prove which is true X or -X

So without proof we must say:

 

It is not the case that the cat is alive (no proof)

But it's not the case either that the cat is dead (no proof)

 

This is often awkwardly expressed as "Both Dead and Alive". But better expressed would be 'its indeterminate at this stage whether the cat is dead or alive'

 

-(X) + -(-X)

= -X + X

= 0

 

 

With 0/neutrality (not + or -) I have attempted to encapsulate superposition.

 

With the cat, we are used to alive and dead as a binary condition. A quantum mechanical superposition of states is more than not knowing which state the system is in — it's in both states at once.

[fredrik]

My favourite way to try make sense out of all possibilities beeing realised at the same time is a game theoretic analogy.

 

First acknowledge, that a system is characterized in the way it behaves. In other world, in the way it interacts with it's environment.

 

This means for superposition that the system actually behaves sort of as if it realized all possibilities at once.

 

Where have we seen that before?

 

Interaction is something mutual. If you are in an environment, a rational player will ideally act consistently with his own expectations of the environment he is in.

 

Similarly, the environment will backreact upon him as per the expectations(read information and subjective relative information state) it has of this system.

 

So a rational player does not choose what to do, from randomly choosing one possibility of the unknown premises. He acts upong all of them, calculating the risks based on all available info. The action based on such total risk analysis can intuively be seen to be different, than a randomly chose action, based on random premises.

 

Roughly speaking one can conceptualize this from an intuitive point.

 

This means that the information interpretation of QM, makes sense. A system interacts with it's environment as if the mutual information is lacking, which is exactly the case. This will persist until there is a mutual information exchange; an interaction; a measurement. Then the behaviour changes, just like we would expect from a rational player.

 

I personally think that the single best abstraction to try to understand the logic of QM is this. All of the mechanical or visual analogies are inadeqaute. Instead, try to think in terms of players actions, based upon incomplete information. And how a set of such players behave in interaction. Each player is an obsever, observing the others.

 

In the particles, one observer is not on par with the others. One observer constitutes an earth based lab, which is massive compared to the particles beeing studied. In this sene, the state of the observer is largely that of an outside obserer, since it's not much influence by the game going on.

 

/Fredirk

[Logica]

With the cat, we are used to alive and dead as a binary condition. A quantum mechanical superposition of states is more than not knowing which state the system is in — it's in both states at once.

 

Thank you for moderator input....maybe my expression was a bit clumsy because I was more focusing on the conceptual case of the Quantum Cat.

 

 

But I have shown the "both states at once" at (2)

 

1) -(X) + -(-X)

2) = -X + X

3) = 0

 

I call (3) Neutral because the TRUE relationship to X or -X is one of Quantum Indeterminacy or neutrality....it is not committed to a single position as we see in the Double-Split Experiment when one slit is covered.

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Merged post follows:

Consecutive posts merged

First acknowledge, that a system is characterized in the way it behaves. In other words, in the way it interacts with it's environment...

 

Fredirk

 

QM will maybe discover the dynamics of these otherwise undetected and unacknowledged interactions (s.a. the presence of an observer:cool:) that perpetually impact on the way reality unfolds.

[swansont]

Thank you for moderator input....maybe my expression was a bit clumsy because I was more focusing on the conceptual case of the Quantum Cat.

 

 

But I have shown the "both states at once" at (2)

 

1) -(X) + -(-X)

2) = -X + X

3) = 0

 

I call (3) Neutral because the TRUE relationship to X or -X is one of Quantum Indeterminacy or neutrality....it is not committed to a single position as we see in the Double-Split Experiment when one slit is covered.

 

 

But the problem is that you have assumed that an OR operator is appropriate, making it a binary condition. Why not an AND function?

[samtheflash82]

Flip a coin with your eyes closed. It could either be heads or tails, but you won't know until you look. Superposition is like that, except that they say that both states exist superimposed until you look, not just that you don't know.

 

that reminded me of the whole; "if a tree falls in a forest..." thing.

[WhataBohr]

Superposition in physics is used in linear systems and in Fourier analysis. If input A outputs X and input B outputs y then Sum of a,b outputs x+y

[Logica]

But the problem is that you have assumed that an OR operator is appropriate, making it a binary condition. Why not an AND function?

 

 

The implication of a binary condition was unintentional.

Simply look at the problem like this:

 

Let X = Within Positive amplitude of a wave

-X = Not within positive amplitude of a wave

p = position of particle

 

We say in superposition that a case of both X and -X exists. In formal logic this is a contradiction. The same applies for binary conditions - only one can be TRUE: Either X or -X is True/1 but not both.

 

Two value logic does not help us here.

So we must assume the need for a third value of (0) Neutral to indicate this state of both true and not true simultaneously shown as.

 

p = -(-X) + -(X) (we have to say this because unobserved position)

p = X + -X (add)

p = 0 (Neutral/Indeterminate etc)

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Merged post follows:

Consecutive posts merged

But the problem is that you have assumed that an OR operator is appropriate, making it a binary condition. Why not an AND function?

 

 

The implication of a binary condition was unintentional.

Simply look at the problem like this:

 

Let X = Positive amplitude of a wave

-X = Negative amplitude of a wave

p = position of particle

 

We say in superposition that a case of both X and -X exists. In formal logic this is a contradiction. The same applies for binary conditions - only one can be TRUE: Either X or -X is True/1 but not both.

 

Two value logic does not help us here.

So we must assume the need for a third value of (0) Neutral to indicate this state of both true and not true simultaneously shown as.

 

p = -(-X) + -(X) (we have to say this because unobserved position)

p = X + -X (add)

p = 0 (Neutral/Indeterminate etc)

[swansont]

We say in superposition that a case of both X and -X exists. In formal logic this is a contradiction. The same applies for binary conditions - only one can be TRUE: Either X or -X is True/1 but not both.

 

Quantum mechanics is not formal logic. As I said before, you have assumed a binary condition — that only one thing can be true. QM doesn't work that way.

[Logica]

Quantum mechanics is not formal logic. As I said before, you have assumed a binary condition — that only one thing can be true. QM doesn't work that way.

 

We all start with the assumption of 1/0

but have to prove otherwise.

Can you see that my solution is eqivalent to

 

x = {0, -1.118033989, 1.118033989}. and goes beyond 1/0 or T/F

 

It goes beyond 1/0 (which binary or formal logic does not do)

I have rendered

1 = T

-1 = -T

0 = -T + T

 

(x/-x/0)

 

3x + -8x + 4(x^3) = 0

 

Simplifying

3x + -8x + 4(x3) = 0

 

Combine like terms: 3x + -8x = -5x

-5x + 4x3 = 0

 

Solving

-5x + 4x3 = 0

 

Factor out the Greatest Common Factor (GCF), 'x'.

x(-5 + 4x2) = 0

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve:

 

Simplifying

x = 0

 

Solving

x = 0

 

Move all terms containing x to the left, all other terms to the right.

 

Simplifying

x = 0

 

Subproblem 2

Set the factor '(-5 + 4x2)' equal to zero and attempt to solve:

 

Simplifying

-5 + 4x2 = 0

 

Solving

-5 + 4x2 = 0

 

Move all terms containing x to the left, all other terms to the right.

 

Add '5' to each side of the equation.

-5 + 5 + 4x2 = 0 + 5

 

Combine like terms: -5 + 5 = 0

0 + 4x2 = 0 + 5

4x2 = 0 + 5

 

Combine like terms: 0 + 5 = 5

4x2 = 5

 

Divide each side by '4'.

x2 = 1.25

 

Simplifying

x2 = 1.25

 

Take the square root of each side:

x = {-1.118033989, 1.118033989}

 

Solution

x = {0, -1.118033989, 1.118033989}

Edited April 28, 2009 by Logica

[Bob_for_short]

With the cat, we are used to alive and dead as a binary condition. A quantum mechanical superposition of states is more than not knowing which state the system is in — it's in both states at once.

 

Classical mechanics says where the cat center of inertia is and what the relative coordinates (of tail, paws, head) are. "Dead" or "alive" are not CM notions.

 

In Quantum Mechanics we must be careful and keep in mind the Heisenberg uncertainty principle. In the cat is in a box, the box sizes are involved in HUP

 

The rest is not physics.

 

Bob.

[Logica]

 

 

The rest is not physics.

 

Bob.

 

Bob - can you please review my arguments regarding expressing the state of superposition? I would like you opinion.

[Bob_for_short]

According to my experience, cats are always alive and funny. I never observed a dead cat in nature.

 

As cats are unpredictable, there is no science describing them.

 

Bob.

 

P.S. They often hide in boxes and other places. Have cat experience from YouTube.

 

Edited April 29, 2009 by Bob_for_short

[Logica]

Have cat experience from YouTube.

 

 

Thanks Bob that was very cute and funny!

[GDG]

According to my experience, cats are always alive and funny. I never observed a dead cat in nature.

 

I've burried a couple...

 

As cats are unpredictable, there is no science describing them.

 

Sure there is: it's called "chaos theory"

[Bob_for_short]

I've burried a couple...

 

For me a dead cat does not exist as does not exist a decayed mu-meson.

 

By the way, what does happen to the mu-meson proper reference frame (watch and three space axis X,Y, and Z)? Do they explode together with the mu-meson while decaying?

 

Bob.

[MustKnow]

how do they know this is true? If it changes on observation? and how does it know its being observed?

[illinglsu]

You know I never really got into the "tree falling in the forest" analogy. I mean, if a tree falls and no one is there to hear it did it fall? Of course it fell. It made a sound, period. Just because humans are not around to record every little thing doesn't mean that things don't happen. So the double slit experiment is sort of the same thing.