# Wave Function Property

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When Heisenberg stated the following, I assume he was talking about the quantum wave function as massless:

Quote

"The atoms or elementary particles themselves are not real; they form a world of potentialities or possibilities rather than one of things or facts."

The same goes for Bohr with this statement:

Quote

"Everything we call real is made of things that cannot be regarded as real."

So my question is:

Are there still physicists who support that concept of a massless wave function? Or has it been abandoned totally?

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Neither quote refers to 'massless' anything.
They relate the wave function to a probability ( or potentiality ) distribution rather than a physical object, such that it cannot be 'regarded as real'

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12 minutes ago, MigL said:

Neither quote refers to 'massless' anything.
They relate the wave function to a probability ( or potentiality ) distribution rather than a physical object, such that it cannot be 'regarded as real'

Is that your interpretation, or do you have sources to back it up?

We both know that when Einstein visited Bohr in Copenhagen, and they talked about it, Einstein mentioned the moon as an example, and Bohr replied: Can you prove that it's there, when you don't look?

Clearly he's talking about things "being", and not about chances. At least that's my opinion of it.

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My 'source' is any introductory QM textbook.
Th square of the magnitude ( of the wavefunction ) at any given point corresponds to the probability of finding the particle at that point.

The Bohr/Einstein exchange relates to observational collapse of the wave function ( and taking it to silly extremes ).

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36 minutes ago, MigL said:

My 'source' is any introductory QM textbook.
Th square of the magnitude ( of the wavefunction ) at any given point corresponds to the probability of finding the particle at that point.

I know and I agree! But this thread is not about the collapse.

36 minutes ago, MigL said:

The Bohr/Einstein exchange relates to observational collapse of the wave function ( and taking it to silly extremes ).

Maybe it was silly. The measurement always shows particles. We can't measure the wave as a wave. If you add a detector closer to the source, the wave vanishes.

From my perspective it seems like you are presuming more than knowing. But I'd like to hear other opinions (if there are any?).

Edited by QuantumT

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1 hour ago, QuantumT said:

When Heisenberg stated the following, I assume he was talking about the quantum wave function as massless:

Quote

"The atoms or elementary particles themselves are not real; they form a world of potentialities or possibilities rather than one of things or facts."

Since neither Heisenberg nor Bohr were responsible for the quantum wave funtion why do you ask this?

The Schrodinger wave function,  has units of metres -3/2, since

The units of ${\Psi ^2}$ are those of volume the units of Psi are the square root of volume.

Mass in not mentioned and so Psi is independent of volume.

What more do you want?

Edited by studiot

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3 minutes ago, studiot said:

What more do you want?

Well, now that you ask, I really want to know why the wave (function) vanishes, when you add a detector closer to the source?

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1 minute ago, QuantumT said:

Well, now that you ask, I really want to know why the wave (function) vanishes, when you add a detector closer to the source?

Um, what? What is your source for this assertion?

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1 minute ago, QuantumT said:

Well, now that you ask, I really want to know why the wave (function) vanishes, when you add a detector closer to the source?

You should ask a magician , not a mathematician such a wide open question.

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2 minutes ago, swansont said:

Um, what? What is your source for this assertion?

The double slit experiment?

Bare in mind, I'm here to learn, contribute, and to be corrected, if I'm wrong. But don't correct me based on assumptions, no matter how much consensus they have.

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Just now, QuantumT said:

The double slit experiment?

Are you fishing, hoping that this answer explains anything?

Just now, QuantumT said:

Bare in mind, I'm here to learn, contribute, and to be corrected, if I'm wrong. But don't correct me based on assumptions, no matter how much consensus they have.

I asked for clarification precisely because I was not assuming anything.

I’m still asking. Explain how the double slit is an example of

10 minutes ago, QuantumT said:

the wave (function) vanishes, when you add a detector closer to the source?

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2 minutes ago, swansont said:

I asked for clarification precisely because I was not assuming anything.

I’m still asking. Explain how the double slit is an example of

The collapse of the wave function happens in the DSE when a detector is added to see actions at the slits.

I thought that was an axiom, since it has been proven countless times.

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13 minutes ago, QuantumT said:

Bare in mind, I'm here to learn, contribute, and to be corrected, if I'm wrong. But don't correct me based on assumptions, no matter how much consensus they have.

How can anyone tell if you are right or wrong when your posts are so lacking in specificity.

There have been many different double slit experiments, studying many different properties and phenomena.

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2 minutes ago, studiot said:

How can anyone tell if you are right or wrong when your posts are so lacking in specificity.

There have been many different double slit experiments, studying many different properties and phenomena.

I'm just trying to understand the wave function. Can it be more basic? The collapse is another thing that I'm also curious about, but in this thread, it's the wave.

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2 hours ago, QuantumT said:

Are there still physicists who support that concept of a massless wave function? Or has it been abandoned totally?

Has this question now been answered?

Do you understand what a function is?

Here are a couple of images

Edited by studiot

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11 minutes ago, studiot said:

Has this question now been answered?

Do you understand what a function is?

Here are a couple of images

A function is a mathematical concept to the best of my knowledge.

Do those images show particles with and without a Higgs field?

My fear now is that I sound completely ignorant, so please be gentle.

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38 minutes ago, QuantumT said:

The collapse of the wave function happens in the DSE when a detector is added to see actions at the slits.

I thought that was an axiom, since it has been proven countless times.

That’s not what you said, though. You said the wave function disappears when you add a detector closer to the source. That’s not the same thing. Closer to the source could be a micron closer. I wondered why you think that would matter.

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1 minute ago, swansont said:

That’s not what you said, though. You said the wave function disappears when you add a detector closer to the source. That’s not the same thing. Closer to the source could be a micron closer. I wondered why you think that would matter.

I chose to simplify it, assuming everybody would know what I meant.

I was wrong.

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32 minutes ago, QuantumT said:

A function is a mathematical concept to the best of my knowledge.

Yes indeed so to look into it further:

A function uses a mathematical rule to process values of one or more input variables (perhaps in combination) to generate values of an output variable.
The collection or set of all the possible values the input variables may take on is called the domain.
This rule applies to every value in the domain, even if the result is a null (zero) value of output.

The function itself includes every input and output value and may be plotted as a graph.

The foregoing images are graphs of functions chosen to illustrate particular points.

In the the first one the domain is the whole of the positive x axis (although only part is shown).

The image shows a whole family of functions called 'Bessel functions' shown in different colours and labelled J0(x), J1(x) etc.
Each one is different and the difference depends upon circumstances.
These circumstances are reflected in the form of the rule for calculating the output.

So the Bessel function J0(x) is the red curve.

And the function is the whole of the red curve.

I cannot stress enough how important this is.

These are one dimensional functions.

The second plot are also Bessel functions but are two dimensional because there are two input variables.
And the 'curve' is now a surface.

A wave function (Schrodinger or classical wave) is essentially no different.

The wave function extends over the whole domain.

But there is not one wave function it is a whole family of curves, each different depending upon circumstances.

Armed with this  knowledge it is possible to proceed to examine them and their properties.

Edited by studiot

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16 minutes ago, studiot said:

Yes indeed so to look into it further:

A function uses a mathematical rule to process values of one or more input variables (perhaps in combination) to generate values of an output variable.
The collection or set of all the possible values the input variables may take on is called the domain.
This rule applies to every value in the domain, even if the result is a null (zero) value of output.

The function itself includes every input and output value and may be plotted as a graph.

The foregoing images are graphs of functions chosen to illustrate particular points.

In the the first one the domain is the whole of the positive x axis (although only part is shown).

The image shows a whole family of functions called 'Bessel functions' shown in different colours and labelled J0(x), J1(x) etc.
Each one is different and the difference depends upon circumstances.
These circumstances are reflected in the form of the rule for calculating the output.

So the Bessel function J0(x) is the red curve.

And the function is the whole of the red curve.

I cannot stress enough how important this is.

These are one dimensional functions.

The second plot are also Bessel functions but are two dimensional because there are two input variables.

A wave function (Schrodinger or classical wave) is essentially no different.

The wave function extends over the whole domain.

Armed with this  knowledge it is possible to proceed to examine them and their properties.

It makes sense. Thank you.

I still have questions, but I need to leave now. I'll be back tomorrow or next week.

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Goodnight then.

Perhaps tomorrow we can see what it means that the Schrodinger wave function "extends over the whole domain".

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The wave function itself is not a probability; calling the square of the wave function  a probability is an interpretation.

So the next important thing to understand is this.

So the probability of heads plus the probability of tails for a coin toss is 0.5 + 0.5 = 1.

So when we interpret the square of the wave function as the sum of all the probabilities about it must add up to 1.

For a wave function, interpreted as a probability plot, this means that we take add up all the values of the raw calculated wave function (squared) from Schrodinger over the whole domain and scale the total to 1 to make this so.

This process is called normalisation.

The value of the normalised wave function (squared) in any small region within the domain is then the probability of finding the energy or particle in that small space in any one measurement.

I do not know if you understand this adding up process - it is called integration?

Edited by studiot

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2 hours ago, studiot said:

I do not know if you understand this adding up process - it is called integration?

I'll have to read that many times before I fully comprehend it. Learning stuff is much easier in your native language.
If what you have written is covering the following questions, I apologize in advance.

You have shown me a model of the wave pattern (the image above) - I assume.
What I want to know is your opinion if those "waves" are particles or energy before they hit the detector?

I assume you will say that the wave is particles, but can we know for sure that the wave consists of particles? Or is it a logic presumption?

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3 minutes ago, QuantumT said:

I'll have to read that many times before I fully comprehend it. Learning stuff is much easier in your native language.
If what you have written is covering the following questions, I apologize in advance.

You have shown me a model of the wave pattern (the image above) - I assume.
What I want to know is your opinion if those "waves" are particles or energy before they hit the detector?

I assume you will say that the wave is particles, but can we know for sure that the wave consists of particles? Or is it a logic presumption?

They are wavicles.

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2 hours ago, QuantumT said:

I'll have to read that many times before I fully comprehend it. Learning stuff is much easier in your native language.
If what you have written is covering the following questions, I apologize in advance.

You have shown me a model of the wave pattern (the image above) - I assume.
What I want to know is your opinion if those "waves" are particles or energy before they hit the detector?

I assume you will say that the wave is particles, but can we know for sure that the wave consists of particles? Or is it a logic presumption?

Of  course learning is easier in your native language. I will try to remember that English is not yours.

I have said that the images are plots or graphs of functions.

You said, quite forcefully, that you wanted to discuss the wave function.

I do not know why it is so important to you to classify phenomena as waves or particles. Can you tell me?

To be so definite you have to know what a wave is and what a particle is.

How would I know if I met something in the street whether it was a wave or a particle or something else entirely?