The Universe as a Hologram

Originally posted by black beetle
If a particle is not localized to a specific point in spacetime, how can you claim that it is existent?
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Why would existence require localization?

Originally posted by KazetNagorra
Why would existence require localization?

Because all kinds of physical existence are location dependent
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Originally posted by black beetle
Because all kinds of physical existence are location dependent
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Proof, please. Note lack of smiley.

Richard

Originally posted by Shallow Blue
Proof, please. Note lack of smiley.

Richard

Lack of smiley is irrelevant; I am not aware of any physical existence who is not located at a specific spacetime. Are you?
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Originally posted by black beetle
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Ah. So you do indeed not have any arguments and you do indeed not understand quantum physics at all. Thanks for confirming it.

Richard

Originally posted by Shallow Blue
Ah. So you do indeed not have any arguments and you do indeed not understand quantum physics at all. Thanks for confirming it.

Richard

Have a good time, Richard
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Originally posted by KazetNagorra
Particles are always both localized and a wave, neither of the descriptions, in their pure form, make any sense in a quantum mechanical way. A (pure) wave cannot be normalized and (pure) localization is not a function (it's a so-called generalized distribution, a delta function).

I don't see any value in "ancient texts" as long as they cannot be used in any predictive way. Ad hoc interpretations don't impress me.

I am not using "ancient texts" (records of human thought) as proof, I am indicating the logical and substantial metaphysical attempt within them at interpretation of the phenomenon, and their remarkable coherence with modern scientific findings.
You do not make any interpretation of the phenomenon from a metaphysical viewpoint but give an "ad hoc" blank denial of such arguments.

That is acceptable from a scientific viewpoint if you agree to not go beyond physical data and entering "beyond the physical" interpretation, as most scientists do. But it is not acceptable to seek to discredit those who make such substantial attempts and make statements of blank denial of those attempts without some examination of the inherent paradoxes and departure from the earlier scientific world view.

Labeling and categorization of phenomenon, while important, is not a full attempt at interpreting the ground origins of the phenomenon. You continue to correctly describe and label the phenomenon but do not postulate how it is that such self-contradictory phenomenon is so. You deny any connection of the mental realm at all with the phenomenon, yet there is substantial argumentation of the apparent involvement (not proven) both from within science and beyond it.
You still appear to be interpreting clearly non-Newtonian phenomenon from a Newtonian world view.

At least the early thinkers made a substantial attempt at the metaphysic and came up with remarkable coherence with modern findings (which you do not acknowledge) from an intuitive pathway. The human bi-cameral brain is complementary - one does not fruitfully restrict one self to either left or right-sided thinking. We absolutely need physical science and its critical parameters, but the acceptance of intuitive pathways, particularly in inherently unmeasurable aspects, I and others postulate, is a valid adjunct to achieve a fuller picture of reality.

Nagarjuna was a profound and highly intelligent thinker and logician. Such are not realistically dismissed simply as "ancient texts" any more than was Plato.

Originally posted by KazetNagorra
Particles exist (why describe something that you're not sure, or at least assuming, exists?), they are just not localized to a specific point in spacetime, nor can you describe them using a wave with a single wavelength.

The state of the particle -its temporal behavior- is changing constantly as a result of the constant change of the measured system. Therefore, we would rather talk about the specific (constant, until it is altered by outside intervention) orbit of the particle instead of giving its actual permanently changing coordinates. It is clear that the state of the system will change solely in the case of the occurrence of an interaction with another system.
The particle location is extracted by a spatial probability distribution that can be characterized by its expectation value and its uncertainty, therefore we are not forced to accept, as is the case with a classical system that involves particles, that the location of the particle is time dependent.
Since a trapped undisturbed quantum particle lacks of a defined location, the probability to measure the particle at a certain location remains constant over time but changes throughout space; therefore, the particle seems to act as a point-wave source, forming a standing wave similar to a vibrating piano-string between two fixed ends. Now, a constant probability distribution is typical for particles trapped in a constant potential well.

So, from the classical concept of a well defined particle location, we came into the quantum concept of a statistical expectation value, in a correspondence that is not restricted to space. From Newton’s Third Law we pass to the Schroedinger Equation in order to determine the dynamics of a particle system but, due to the degenerating eigenvalues of the Hamilton operator H, the measurement of the energy in a 3D trap is not sufficient for determining the actual particle distribution.


Now, if the nature of the particle is indeed that of a wave, then the wave’s amplitude represents the probabilistic location of a particle and therefore the particle must not be understood as a particle but as a wave of an indefinite number of point-wave sources. Over here, in my opinion I am justified to claim that the particle is neither existent (because in fact it’s a sum of point-wave sources), nor not existent (because the wave refers solely to the probabilistic location of the particle).

Since the region that these quantum waves inhabit is small, they behave mainly as point-wave sources, therefore the amplitude of the wave does not represent the probable location of a particle but the probable location of a point-wave source. However a single point-wave source is restricted solely to a single point when the location of the wave is detected, therefore the wave does not collapse to give the location of a particle; it collapse always outside of the region where it was detected, therefore the amplitude of the wave represents solely the probability of finding “somewhere” a point-wave source. The point-wave source is located at a given spacetime where there is an amplitude for the wave, and the measurement can be as narrow as it can be allowed by the particle used for the measuring and at any point of the wave, so the smaller the area where that wave is detected, the more that wave acts like a point-wave source. At the same time this point-wave source acts like a particle in many ways, however it is best understood as a wave source and not as a particle. Over here, methinks I am justified to claim that the particle is not both existent (otherwise the point-wave source would be non-existent) and non-existent (because the amplitude of its wave points to an area in which the location of that point-wave source takes place).

Finally, when we check the location of a wave we are detecting the location of a point-wave source at each point of the amplitude that constitutes the wave. The wave source acts almost like a particle because the wave sources have energy and interference type forces. When a wave location is detected in a small region, the behaviour of its point-wave source becomes more apparent. Therefore, since it is better to understand the particle as a 3D point-wave source, methinks I am fully justified to claim that the particle is not neither existent nor non-existent at the same time
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Originally posted by black beetle

Since a trapped undisturbed quantum particle lacks of a defined location, the probability to measure the particle at a certain location remains constant over time

Not necessarily, this depends on the potential. But there is also no reason why the potential cannot depend on time explicitly in which case it is almost always not true that the square of the wavefunction is constant in time.

Originally posted by KazetNagorra
Not necessarily, this depends on the potential. But there is also no reason why the potential cannot depend on time explicitly in which case it is almost always not true that the square of the wavefunction is constant in time.

Still, the probability to measure at a certain location an undisturbed entrapped quantum particle remains constant over time but changes throughout space. A constant probability distribution is typical for particles trapped in a constant potential well, as is the case of an electron in the electric field of a proton
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Originally posted by black beetle
Still, the probability to measure at a certain location an undisturbed entrapped quantum particle remains constant over time but changes throughout space. A constant probability distribution is typical for particles trapped in a constant potential well, as is the case of an electron in the electric field of a proton
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But in a real situation, the potential term will always depend on time, so what are you trying to argue here? Also, I'm not sure that even in the hydrogen atom case, which can be solved analytically, you still get a constant potential if you allow for motion of the proton due to the electron (in the textbook example, the proton is assumed to be stationary due to its much larger mass). Without the assumption you can no longer calculate the solution analytically.

Originally posted by KazetNagorra
But in a real situation, the potential term will always depend on time, so what are you trying to argue here? Also, I'm not sure that even in the hydrogen atom case, which can be solved analytically, you still get a constant potential if you allow for motion of the proton due to the electron (in the textbook example, the proton is assumed to be stationa ...[text shortened]... uch larger mass). Without the assumption you can no longer calculate the solution analytically.

I argue that I explained you in detaild the reason why the tetrallema I mentioned earlier holds, and your reply was that you reject the idea that the probability to measure the entrapped undisturbed in a 3D well particle at a certain location remains constant over time but changes throughout space; so I clarified I was talking about the particle location and the time dependency of the wavefunction in the context of the wave mechanics -and I remind you that we are also talking about the nature of the particle
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Originally posted by black beetle
I argue that I explained you in detaild the reason why the tetrallema I mentioned earlier holds, and your reply was that you reject the idea that the probability to measure the entrapped undisturbed in a 3D well particle at a certain location remains constant over time but changes throughout space; so I clarified I was talking about the particle locatio ...[text shortened]... e wave mechanics -and I remind you that we are also talking about the nature of the particle
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I don't get what you mean, in general the probability density is not constant in time at all, and there are only a few mathematically idealized situations where it does hold. There is no "particle location" apart from the wavefunction being localized around some expectation value. You should not (in my opinion) interpret the wavefunction after measurement as revealing where the particle was prior to measurement; if I'm not mistaken such an interpretation would be in violation of Bell's theorem.

Originally posted by KazetNagorra
I don't get what you mean, in general the probability density is not constant in time at all, and there are only a few mathematically idealized situations where it does hold. There is no "particle location" apart from the wavefunction being localized around some expectation value. You should not (in my opinion) interpret the wavefunction after measureme ...[text shortened]... rement; if I'm not mistaken such an interpretation would be in violation of Bell's theorem.

This simply means that the particles are neither existent, nor not existent, nor both existent and non existent, nor neither
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Originally posted by KazetNagorra
I don't get what you mean, in general the probability density is not constant in time at all, and there are only a few mathematically idealized situations where it does hold. There is no "particle location" apart from the wavefunction being localized around some expectation value. You should not (in my opinion) interpret the wavefunction after measureme ...[text shortened]... rement; if I'm not mistaken such an interpretation would be in violation of Bell's theorem.

Edit: "You should not (in my opinion) interpret the wavefunction after measurement as revealing where the particle was prior to measurement;"

Methinks you read my forth post of the forth page of this thread very quickly. I told you that the wave does not collapse to give the location of a particle: it collapse always outside of the region where it was detected;
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