[Armad (OP)]

In the diagram there is two volumes of space , one is labelled volume one that has x amount of energy and one is labelled volume two that has no  energy . Between the volumes is a void that is also absense of all energy .

In this thought experiment we are going to transfer energy from volume one to volume two as labelled with the arrow of direction .

My question is , will the wave function collapse because any energy passing through the void , may be conserved by the void ?


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Usefull note : ''The name comes from Zeno's arrow paradox, which states that because an arrow in flight is not seen to move during any single instant, it cannot possibly be moving at all.[note 1] The first rigorous and general derivation of the quantum Zeno effect was presented in 1974 by Degasperis, Fonda, and Ghirardi,[5] although it had previously been described by Alan Turing.[6] The comparison with Zeno's paradox is due to a 1977 article by George Sudarshan and Baidyanath Misra.[1]

According to the reduction postulate, each measurement causes the wavefunction to collapse to an eigenstate of the measurement basis. In the context of this effect, an observation can simply be the absorption of a particle, without the need of an observer in any conventional sense.''

[Colin2B]

My question is , will the wave function collapse because any energy passing through the void , may be conserved by the void ?

What wave function, please specify. Also specify what measurement is being made.
If volume 2 is a void, why bother with a void between the 2 volumes.

[Armad (OP)]

My question is , will the wave function collapse because any energy passing through the void , may be conserved by the void ?

What wave function, please specify. Also specify what measurement is being made.
If volume 2 is a void, why bother with a void between the 2 volumes.

The wave function can be any carrier signal or natural wave function of electromagnetic radiation  . The measurements of volume one can be viewed as an Eigenstate or the vacuum physical constants . The measure of volume two is absolute 0 . A void between the volumes just made it easier to show the question , allowing a vector x for discussion purposes if required .

Useful notes: ''In mathematics, Hilbert spaces (named after David Hilbert) allow generalizing the methods of linear algebra and calculus from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. A Hilbert space is a vector space equipped with an inner product which defines a distance function for which it is a complete metric space. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as function spaces.''

[Colin2B]

The wave function can be any carrier signal or natural wave function of electromagnetic radiation  . The measurements of volume one can be viewed as an Eigenstate or the vacuum physical constants . The measure of volume two is absolute 0 . A void between the volumes just made it easier to show the question , allowing a vector x for discussion purposes if required .

We all know what Hilbert spaces are, but your “useful note” does not help understand the quote above.
What are you actually measuring and what is the vector x.
Try to be specific rather than making up meaningless phrases, otherwise I’ll start calling you Steve!

[Armad (OP)]

The wave function can be any carrier signal or natural wave function of electromagnetic radiation  . The measurements of volume one can be viewed as an Eigenstate or the vacuum physical constants . The measure of volume two is absolute 0 . A void between the volumes just made it easier to show the question , allowing a vector x for discussion purposes if required .

We all know what Hilbert spaces are, but your “useful note” does not help understand the quote above.
What are you actually measuring and what is the vector x.
Try to be specific rather than making up meaningless phrases, otherwise I’ll start calling you Steve!

   

I have no idea why you would move a thought experiment with a question to new theories when it isn't a new theory ?  You have assumed I am trying to measure something when the title of the thread asks a question , ''In this thought experiment would the wave function ''collapse'' ? 
I then provided useful notes to help discuss the question in which you mocked !
Not everyone knows what a Hilbert space is ,  that is not very educational Colin . Can I call you Collin ? My name is Armad , pleased to make your acquaintance .
I am not impressed Colin because if I had presented a new theory , it would have a title , an abstract, an introduction , several title chapters and citations . I would never present a question as a new theory .

[Armad (OP)]

My conclusion to my own question was that when unbounded electromagnetic radiation travels from within the Hilbert space , arriving at the ''border'' between Hilbert space and spaces that may be infinite-dimensional, that the wave function collapses based on the attached equation . Also the ''border'' could be viewed as a physical boundary , where quantum mechanics breaks down . In deeper thoughts , a photon travelling at c to the ''border'' could be viewed as stoppable on the ''border'' .
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The wave function Ψ collapsing at the ''border'' before being  transformed into zero point energy ,  that contributes to the Hilbert spaces expansion of measure and physical constant .

[Origin]

I have no idea why you would move a thought experiment with a question to new theories when it isn't a new theory ?

It certainly seems like a new theory.

title of the thread asks a question , ''In this thought experiment would the wave function ''collapse'' ?

OK, the answer is no, mainly because there is no wave function specified so there is nothing to collapse.

[Origin]

My conclusion to my own question was that when unbounded electromagnetic radiation travels from within the Hilbert space , arriving at the ''border'' between Hilbert space and spaces that may be infinite-dimensional, that the wave function collapses based on the attached equation .

There's no such thing as an infinite-dimensional space, so there is no border so the question is moot.

[Armad (OP)]

I have no idea why you would move a thought experiment with a question to new theories when it isn't a new theory ?

It certainly seems like a new theory.

title of the thread asks a question , ''In this thought experiment would the wave function ''collapse'' ?

OK, the answer is no, mainly because there is no wave function specified so there is nothing to collapse.

I do not see your argument , wave function in general can be specified  Ψ without a specific value . This question would apply to all energies that have motion . A particle travelling outwards from within the Hilbert space frame of reference would also be stoppable at the ''border'' of Hilbert space . The ''border'' of Hilbert space could be viewed as an impenetrable wall that isn't constructed of matter or energy .

[Armad (OP)]

My conclusion to my own question was that when unbounded electromagnetic radiation travels from within the Hilbert space , arriving at the ''border'' between Hilbert space and spaces that may be infinite-dimensional, that the wave function collapses based on the attached equation .

There's no such thing as an infinite-dimensional space, so there is no border so the question is moot.

How do you know there is no border to Hilbert space if you are unable to travel the distance to observe whether there is a border or not ?
Also Hilbert space can be viewed as having a border because that is what the theory is about .

''In mathematics, Hilbert spaces (named after David Hilbert) allow generalizing the methods of linear algebra and calculus from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. A Hilbert space is a vector space equipped with an inner product which defines a distance function for which it is a complete metric space. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as function spaces.''

Are you saying this information is incorrect ?

[Origin]

I do not see your argument , wave function in general can be specified  Ψ without a specific value .

That is not the problem, you stated, "would the wave function collapse?"  What wave function?

This question would apply to all energies that have motion .

This is difficult to answer since that really doesn't make sense as stated.  I assume you are talking about a photon for instance, which is not energy but carries energy.

A particle travelling outwards from within the Hilbert space frame of reference would also be stoppable at the ''border'' of Hilbert space . The ''border'' of Hilbert space could be viewed as an impenetrable wall that isn't constructed of matter or energy .

Well obviously if the wall was impenetrable the particle would stop.  This 'border' however, is not something that would occur in the real world it is more in the realm of science fiction.

[Origin]

''In mathematics, Hilbert spaces (named after David Hilbert) allow generalizing the methods of linear algebra and calculus from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. A Hilbert space is a vector space equipped with an inner product which defines a distance function for which it is a complete metric space. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as function spaces.''

No, I am saying you do not understand this.  You need to understand the basics of physics before trying to tackle more complicated topics. 

[Armad (OP)]

I do not see your argument , wave function in general can be specified  Ψ without a specific value .

That is not the problem, you stated, "would the wave function collapse?"  What wave function?

This question would apply to all energies that have motion .

This is difficult to answer since that really doesn't make sense as stated.  I assume you are talking about a photon for instance, which is not energy but carries energy.

A particle travelling outwards from within the Hilbert space frame of reference would also be stoppable at the ''border'' of Hilbert space . The ''border'' of Hilbert space could be viewed as an impenetrable wall that isn't constructed of matter or energy .

Well obviously if the wall was impenetrable the particle would stop.  This 'border' however, is not something that would occur in the real world it is more in the realm of science fiction.

Is the conservation of energy science fiction ?

When a photon travels at the speed of light and reaches the Hilbert spaces '''border'' , the wave-function collapse could be viewed as : E=mc²


When the process of the wave-function collapses , this can be  precisely measured .

''The CMB has a thermal black body spectrum at a temperature of 2.72548±0.00057 K.[9] The spectral radiance dEν/dν peaks at 160.23 GHz, in the microwave range of frequencies, corresponding to a photon energy of about 6.626 ⋅ 10−4 eV. Alternatively, if spectral radiance is defined as dEλ/dλ, then the peak wavelength is 1.063 mm (282 GHz, 1.168 ⋅ 10−3 eV photons). The glow is very nearly uniform in all directions,''

Thanks

[Origin]

Is the conservation of energy science fiction ?

No.

When a photon travels at the speed of light and reaches the Hilbert spaces '''border'' , the wave-function collapse could be viewed as : E=mc²

You keep talking about this border between a mathematical concept and spacetime, how does that make any sense?

[Armad (OP)]

''In mathematics, Hilbert spaces (named after David Hilbert) allow generalizing the methods of linear algebra and calculus from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. A Hilbert space is a vector space equipped with an inner product which defines a distance function for which it is a complete metric space. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as function spaces.''

No, I am saying you do not understand this.  You need to understand the basics of physics before trying to tackle more complicated topics.

I think it is you that doesn't understand a Hilbert space , which could be viewed as a volume with a conserved energy constant . An energy that exists in all of the Hilbert space vacuum that is conserved by the space uniformly .

[Eternal Student]

Hi.

   1.    I would have asked a similar question to Colin2B about your original post:

    Usually we don't consider there to be one wave function to describe everything.     Typically each particle has its own wave function and depending on the set up of your experiment or theoretical situation, it can be possible to make an observation that will collapse one wave function but not the other.
    In Quantum Field Theory you get a bit closer to there being one wave function for everything.   Every particle of the same type shares one field,  for example an electron is always an oscillation in the same electron field.   However, there are are still many fields,  one for each particle in the standard model.
     So, when you asked about "the" wave function as if there is only one to describe everything, then that has moved the discussion to the edge of currently established and mainstream science.   There may be one wave function to describe everything but that's not well established at the moment.

2.   

The wave function can be any carrier signal or natural wave function of electromagnetic radiation  .

    That's also not a conventional description of what a wave function is.

I have no idea why you would move a thought experiment with a question to new theories when it isn't a new theory ?

    Maybe @Colin2B  made a mistake but you can see why they weren't sure.


3.     About Hilbert Spaces:

In mathematics, Hilbert spaces (named after David Hilbert) allow generalizing the methods of linear algebra and calculus from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. A Hilbert space is a vector space equipped with an inner product which defines a distance function for which it is a complete metric space. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as function spaces.''

    That quote seems OK.   However, I think the problem is that the word  "space" appears in the title   "Hilbert Space" and you are assuming it must have something to do with real physical space out in the universe.
     A Hilbert space is a very general algebraic object and the elements in this space are not usually points (or vectors) in our physical space.    In conventional Quantum Mechanics, the elements of our Hilbert space are the wave functions.    This is complicated and not worth trying to explain in a forum post.  There are texts written on the subject but they aren't short.   The main point is that Hilbert Space isn't used to describe a location in actual physical space, or even to describe the behaviour and properties of a region of actual space.   Instead it usefully describes how we can combine and manipulate wave functions.
    So things don't move "out of the Hilbert Space" and into some other space,  it's just not a description of location or of space.

Can I answer the question?
   Not really and I'm sorry about that.  I can't easily connect what is being asked with what little Physics is known to me.   I don't think I can help much.

Best Wishes.

[Armad (OP)]

Is the conservation of energy science fiction ?

No.

When a photon travels at the speed of light and reaches the Hilbert spaces '''border'' , the wave-function collapse could be viewed as : E=mc²

You keep talking about this border between a mathematical concept and spacetime, how does that make any sense?

A mathematical concept that represents a physical concept . Space-time is a mathematical model , you could measure a Hilbert space using space-time .
My question is a question about the physics rather than any sort of measure , although I have provided suitable equations that fit the physical process of a Hilbert space .

[Armad (OP)]

Hi.

   1.    I would have asked a similar question to Colin2B about your original post:

    Usually we don't consider there to be one wave function to describe everything.     Typically each particle has its own wave function and depending on the set up of your experiment or theoretical situation, it can be possible to make an observation that will collapse one wave function but not the other.
    In Quantum Field Theory you get a bit closer to there being one wave function for everything.   Every particle of the same type shares one field,  for example an electron is always an oscillation in the same electron field.   However, there are are still many fields,  one for each particle in the standard model.
     So, when you asked about "the" wave function as if there is only one to describe everything, then that has moved the discussion to the edge of currently established and mainstream science.   There may be one wave function to describe everything but that's not well established at the moment.

2.   

The wave function can be any carrier signal or natural wave function of electromagnetic radiation  .

    That's also not a conventional description of what a wave function is.

I have no idea why you would move a thought experiment with a question to new theories when it isn't a new theory ?

    Maybe @Colin2B  made a mistake but you can see why they weren't sure.


3.     About Hilbert Spaces:

In mathematics, Hilbert spaces (named after David Hilbert) allow generalizing the methods of linear algebra and calculus from (finite-dimensional) Euclidean vector spaces to spaces that may be infinite-dimensional. A Hilbert space is a vector space equipped with an inner product which defines a distance function for which it is a complete metric space. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as function spaces.''

    That quote seems OK.   However, I think the problem is that the word  "space" appears in the title   "Hilbert Space" and you are assuming it must have something to do with real physical space out in the universe.
     A Hilbert space is a very general algebraic object and the elements in this space are not usually points (or vectors) in our physical space.    In conventional Quantum Mechanics, the elements of our Hilbert space are the wave functions.    This is complicated and not worth trying to explain in a forum post.  There are texts written on the subject but they aren't short.   The main point is that Hilbert Space isn't used to describe a location in actual physical space, or even to describe the behaviour and properties of a region of actual space.   Instead it usefully describes how we can combine and manipulate wave functions.
    So things don't move "out of the Hilbert Space" and into some other space,  it's just not a description of location or of space.

Can I answer the question?
   Not really and I'm sorry about that.  I can't easily connect what is being asked with what little Physics is known to me.   I don't think I can help much.

Best Wishes.

Thank you for your considerate reply, I have now drifted into new theory because the subject was moved , no bother .

I understand that a Hilbert space is a mathematical concept but there is no laws in physics that states we can't give mathematical concepts a physical concept .  A Hilbert space can be viewed as any volume of a portion of space and can be viewed to conserve an amount of bounded energy proportional to the volume xyz .

Suppose you have a box that is 1m³ and you remove all the atmosphere from within the box , this inner space could be viewed as a physical Hilbert space that has a conserved energy vacuum constant .

Anyway that is what a physical Hilbert space is to me , I just thought I'd explain . Also in a physical Hilbert space , any vector can curve and/or wave .

[Origin]

A mathematical concept that represents a physical concept . Space-time is a mathematical model , you could measure a Hilbert space using space-time .

You're not getting this.  In mathematics we set up boundary condition.  Lets say I want to know the number of gamma rays in a cubic meter that is 10 meters from a gamma ray source.  If I know the dimensions of the source and the radioactive isotope I can calculate the number of gamma rays passing through that enclosed boundary per second.  You are asking the question, "what happens to the gamma rays when they hit the boundary?"  The answer is, they never hit the boundary because it is a mathematical concept not an actual boundary!

[Armad (OP)]

A mathematical concept that represents a physical concept . Space-time is a mathematical model , you could measure a Hilbert space using space-time .

You're not getting this.  In mathematics we set up boundary condition.  Lets say I want to know the number of gamma rays in a cubic meter that is 10 meters from a gamma ray source.  If I know the dimensions of the source and the radioactive isotope I can calculate the number of gamma rays passing through that enclosed boundary per second.  You are asking the question, "what happens to the gamma rays when they hit the boundary?"  The answer is, they never hit the boundary because it is a mathematical concept not an actual boundary!

I already explained that a physical Hilbert space doesn't have a boundary that is constructed of energy or matter , the physics does not require it .
If the space that ''borders'' the physical Hilbert space is absence of all energy and matter , when a gamma ray hits the  physical Hilbert space boundary , it is stopped in an instant E=mc² . Relative to the gamma ray , the conservation of energy of the empty space acts like an instant ''glue'' .