Post by: Armad on 03/06/2022 13:43:25
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 ?
teleport.jpg (36.42 kB . 1217x605 - viewed 1729 times)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.''
Post by: Colin2B on 03/06/2022 14:06:15
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.
Post by: Armad on 03/06/2022 14:17:08
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 .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.
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.''
Post by: Colin2B on 03/06/2022 14:31:03
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!
Post by: Armad on 03/06/2022 14:52:15
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 .
Post by: Armad on 03/06/2022 15:34:25
teleport1.jpg (1.95 kB . 138x57 - viewed 1881 times)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 .
Post by: Origin on 03/06/2022 15:46:41
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.
Post by: Origin on 03/06/2022 15:51:43
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.
Post by: Armad on 03/06/2022 15:56:41
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 .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.
Post by: Armad on 03/06/2022 15:59:51
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 ?
Post by: Origin on 03/06/2022 16:27:43
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.
Post by: Origin on 03/06/2022 16:32:12
''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.
Post by: Armad on 03/06/2022 16:36:46
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
Post by: Origin on 03/06/2022 16:45:40
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=mc²You keep talking about this border between a mathematical concept and spacetime, how does that make any sense?
Post by: Armad on 03/06/2022 16:46:15
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 .''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.
Post by: Eternal Student on 03/06/2022 16:49:44
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.
Post by: Armad on 03/06/2022 16:51:34
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=mc²You 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 .
Post by: Armad on 03/06/2022 17:09:06
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 .
Post by: Origin on 03/06/2022 17:13:29
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!
Post by: Armad on 03/06/2022 17:26:26
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 .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!
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'' .
Post by: Origin on 03/06/2022 17:36:12
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 .Since there is no such thing as space that is without energy or matter that is an impossible boundary.
That idea makes as much sense as me saying if the area around the Hilbert space had a billion pixies with lead catchers mitts then the gamma rays would be stopped at the boundary.
It is rarely useful to ask a question about an impossible scenario.
Post by: Armad on 03/06/2022 17:44:57
Since there is no such thing as space that is without energy or matter that is an impossible boundary
Actually , there is the possibility of space that is absence of energy and matter . Your impossible is rather subjective and based on a finite closed universe with no external space which I find quite illogical .
Space-time is based on visible bodies and defines the distance between the observer and visible distant bodies . Space-time does not measure how far the space goes because of Olbers Paradox .
Post by: Origin on 03/06/2022 19:33:16
Actually , there is the possibility of space that is absence of energy and matterDo you have a citation for this or is this just your belief?
Your impossible is rather subjective and based on a finite closed universe with no external space which I find quite illogicalNo external space, you mean space 'outside' the universe? I'm sorry that you find physics illogical.
Post by: Origin on 03/06/2022 19:38:07
Space-time does not measure how far the space goes because of Olbers Paradox .No, that is not what Olbers' paradox is about.
Post by: Kryptid on 03/06/2022 19:58:58
Your impossible is rather subjective and based on a finite closed universe with no external space which I find quite illogical .
A finite, closed universe with no external space is very much possible.
Post by: Armad on 03/06/2022 21:13:35
Space-time does not measure how far the space goes because of Olbers Paradox .No, that is not what Olbers' paradox is about.
Olbers paradox is about why the ''night sky'' appears dark . You can't measure darkness because there is nothing to see . The universes volume is based on things we can see , it isn't based on the space . Do you really think that space just ends at the location we see distant bodies ? Please provide some proof of this .
d1.jpg (14.41 kB . 563x333 - viewed 1261 times)Post by: Armad on 03/06/2022 21:19:13
Your impossible is rather subjective and based on a finite closed universe with no external space which I find quite illogical .
A finite, closed universe with no external space is very much possible.
Then why doesn't the energy in the space increase in magnitude from all the energy emitted by stars?
Tit for tat , an infinite universe is also possible . A universe is all of space and all the contents , there is no reason to think that our observable part of the universe is all there is .
Post by: Armad on 03/06/2022 21:25:07
Space beyond our observable portion of a much bigger universe . Space that is absent of matter and energy . There is no citation for this but there is physics such as thermodynamics that can justify the claim .Actually , there is the possibility of space that is absence of energy and matterDo you have a citation for this or is this just your belief?Your impossible is rather subjective and based on a finite closed universe with no external space which I find quite illogicalNo external space, you mean space 'outside' the universe? I'm sorry that you find physics illogical.
Post by: Kryptid on 03/06/2022 22:08:15
Then why doesn't the energy in the space increase in magnitude from all the energy emitted by stars?
On average, energy is leaving a given volume of space about as fast as energy enters it (or at a very slightly higher rate, since the Universe is expanding).
Post by: Armad on 03/06/2022 22:21:23
How can energy leave a finite system when it is claimed there is no external space of the system ? Where could this energy be explained to be going if not external of the system ?Then why doesn't the energy in the space increase in magnitude from all the energy emitted by stars?
On average, energy is leaving a given volume of space about as fast as energy enters it (or at a very slightly higher rate, since the Universe is expanding).
Post by: Kryptid on 03/06/2022 22:24:41
How can energy leave a finite system
I never said that it did.
when it is claimed there is no external space of the system ?
There doesn't have to be.
Where could this energy be explained to be going if not external of the system ?
I never said it was going external to the system.