Hilbert Spaces: Cheating at Reality (1219 words)

Disclaimer

These are my opinions.

This is not a beginner friendly piece.

If you are interested but have no physics background, please first check out:

https://churchofentropy.wordpress.com/2015/11/25/quantum-chemistry-teaser/

and

https://churchofentropy.wordpress.com/2015/12/23/why-general-relativity-and-quantum-mechanics-are-incompatible/

Commentary on Modern Physics

According to Wikipedia:

“A Hilbert space is an abstract vector space possessing the structure of an inner product that allows length and angle to be measured. Furthermore, Hilbert spaces are complete: there are enough limits in the space to allow the techniques of calculus to be used.”

https://en.wikipedia.org/wiki/Hilbert_space

What are the techniques of calculus? Calculus is all about measurement: slopes, areas, densities… Calculus is the most accurate way to make these measurements. Calculus says that in the infinitely small spatial limit, the area bounded by a smooth curve is equivalent to the sum of infinitely thin inscribed rectangles.

Is this approach reasonable? It certainly feels true and is perfectly reasonable to use under circumstances where space can be modelled as continuous. That is, it works until we reach the limits set forth by the Uncertainty Principle, at which point spacetime becomes decidedly discrete.

The Rules of Engagement

From: www.web.mit.edu/edbert/GR/gr1.pdf

“[…] the fundamental object in quantum mechanics is the state vector, represented by a ket |ψi in a linear vector space (Hilbert space).”

and

“It is possible to formulate the mathematics of general relativity entirely using the abstract formalism of vectors, forms and tensors. […] To simplify calculations it is helpful to introduce a set of linearly independent basis vector and one-form fields spanning our vector and dual vector spaces. In the same way, practical calculations in quantum mechanics often start by expanding the ket vector in a set of basis kets, e.g., energy eigenstates.

Why is it so important to have a Hilbert Space versus an ordinary Euclidean Space in QM? We can be pretty sure it has to do with measurement: the HS imposes the condition of measurability on all of its lengths and angles (Wikipedia). Measurements must be well-defined for things like the Centre of Mass coordinate system transformation to follow suit.

The only difference between Euclidean and Hilbert spaces is the number of dimensions: the former being a special case of the (potentially) infinite dimensional latter. The Hilbert Space is a way to generalize all that can be known in advance of measurement for a QM system without being limited to 3 spatial coordinates.

Next I will show that although there exist 4 spacetime dimensions on the fine scale, they cannot be basis vectors in a geometric sense because they are maximally dependent.

The Fundamental Spacetime Event

In relativistic mechanics, points are referred to as events, possessing 3 spatial and one temporal coordinate.

The MIT paper says:

  1. “We then need the proper four-volume element, i.e., the physical volume element that is invariant (a scalar) under coordinate transformations.” (for a volume integration).
  2. “By definition, the dimensionality of spacetime (four) equals the number of linearly independent basis vectors and one-forms.”

The existence of such a volume element is central to GR by (1). We also have the condition that the dimensionality of spacetime is equal to the number of l.i. basis vectors by (2). We will next show that the atomic volume cannot possibly satisfy (1), because it contradicts (2). A Hilbert space is not an accurate model of reality on the quantum scale under the coordinate transformations of General Relativity.

The Smear-iodic Table

The Periodic Table is the most extreme demonstration that the 3 physical dimensions are not independent of acts of observation on the fine scale. Below represents the periodic table (two elements per enclosure) as it truly occurs. It starts at the bottom with Hydrogen and Helium. Mass then swirls up through the micro-physical (entangled) dimensions before “running out of room” once it saturates R3 (there are no more elements after the 7p orbital).

postulates of quantum chemistry 3jp

Stylized R’s represent the physical dimensions on the atomic scale

All seven rows of the periodic table are represented here: there is one in R0 and 2 per physical dimension. We can interpret this drawing as mass/energy entering space in an initiating instance (R0). This mass then moves through the 3 dimensions of space, which exist atop this initial instance.

This formulation explains why we observe radioactivity in higher-numbered elements. The Uncertainty Principle indicates that the position and momentum cannot be known to arbitrary precision. As mass saturates the physical dimensions, more becomes known about the atomic system (in this case it is mass-energy that is knowing/observing space), until the limit of what is knowable is breached (by Uncertainty).

The fact that the atomic system is bounded in space and that Uncertainty precludes arbitrary measurement precision forces nuclear decay in higher numbered elements. It is not a coincidence that all elements in the seventh row of the periodic table are radioactive. Stability for these species would imply arbitrary precision to their position and momentum values of their constituent waveforms: precluded by Uncertainty!

th chain
The Thorium Chain (P vs. N)

It is interesting to note that since the atom is a QM system (in potential), that the UP is only violated in a probabilistic sense (decay events aren’t happening all the time).

It is clear that on this fine scale, the physical dimensions are not independent of the mass that is experiencing (observing) them. In fact, on this scale, we can see that the spacetime dimensions are maximally dependent. Every atom vibrates within the same configuration space and so it stands to reason that subsequent dimensions would not be independent of previous ones! R2 is larger than R1 because it is on top of R1. Thus, we can be certain that the proper “four-volume” element cannot be any smaller than the atomic volume, since the latter’s basis vectors are entangled: the opposite of linearly independent, a must-have for a basis vector!

Conclusion

Although the 4 dimensions of spacetime may appear to be connected only by the “event” phenomena of special relativity, they are interconnected on a much deeper level in the atom. Thus the correct four-volume element (necessitated by GR to integrate a scalar field over a 4-dimensional spacetime volume) must be larger than the atomic volume (arguably it must be large enough that the effects of the entaglement of space and time in the atom are negligible).

The GR model is thus incompatible with the QM model.

We model space as continuous when it isn’t, then wonder why we cannot find convergence between quantum mechanics and general relativity. I wish I could say I am surprised, but it’s par for the course in the “land of illusion” 😉 .

Thank you.

Epilogue – Singularities Irritate Me

According to Wikipedia:

“In mathematics, a singularity is in general a point at which a given mathematical object is not defined, or a point of an exceptional set where it fails to be well-behaved in some particular way, such as differentiability.”

https://en.wikipedia.org/wiki/Singularity_(mathematics)

I always found these to be the biggest cop-out of physics. My book will present a model with no singularities. It is nearing completion and I expect to publish before 2017.

In the meantime, I encourage everyone to consider the possibility that mass is everywhere interconnected and that gravitons do not exist. This is permissible if we accept that all mass acts instantaneously at a distance on all other mass and all fields.

This is not a popular viewpoint in physics, but I figured any discipline putting out comics this desperate:

fixion

(http://m.xkcd.com/1621/)

Could probably use a pick-me-up.

Thank you.

 

 

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Why General Relativity and Quantum Mechanics are Incompatible (1721 words)

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All of my knowledge would be impossible without Yoga study

Disclaimer

These are my opinions.

Update 4 – 2016-07-12

The Standard Model is falling apart at the seams and international scientists have come up with a theory that validates my hypothesis in many ways, yet is still not as simple as my full theory…

The so-called “Big Bang” has just been upended. Now apparently it’s a “Big Bounce”.

According to the team – consisting of physicists from the UK and Canada – when the Universe is at its smallest point, it is ruled by quantum mechanics instead of the normal physics of the everyday world around us.”

“Quantum mechanics saves us when things break down,” explains team member Steffen Gielen, from Imperial College London.

“It saves electrons from falling in and destroying atoms, so maybe it could also save the early Universe from such violent beginnings and endings as the Big Bang and Big Crunch.” (Spoiler: The Big Curnch is how scientists predict our Universe might end, and it ain’t pretty.”

Um, ya, I’ll probably not lose any sleep over the “Big Curnch”, given all the psychological subversion tactics simultaneously coming to fruition thanks to Marxist fruitcakes, the civilized world will long since have fallen thanks to your cultural relativism, political correctness and echo chamber ego elation long before we all become one glorious “Curnch”. En passant, there is one application in the Universe for cultural relativism that might be accurate: when all universal mass is concentrated in the same event.

I really don’t know how these people can expect credibility when their fundamental creation hypothesis vacillates between a “bouncing” system and a “banging” system. Shouldn’t the primal cause be worked out by now if we expect our model is correct?

There should never be any “suspension of disbelief” employed at any point during the reasoning process. The only thing I believe could possibly be viewed as the exception to this  (although I certainly do not consider it unreasonable, I know many do) is when a practice has not yet reached the point where it produces tangible benefits, but is still undertaken by instruction of the teacher, who is obeyed by virtue of their superior knowledge. In the meantime, faith is placed in the teacher to deliver the knowledge. Without this essential step, the transfer of knowledge is severely impeded.

In my book, we will have a fourfold action and fourfold scale of magnification model which explains the entire universe with no singularities, predicts the allotropic distribution of elements and enhances structural isomer modelling. My theories also present a Quantum Mind framework which predict the modern psychological afflictions in a “first approximation” way. Looking forward to more science and thanks everyone for taking down the SJW’s with me. It was a real groundswell of cultural libertarianism. We can’t stop now, or ever.

Update 3 – I have expanded this proof here.

What is a Centre of Mass?

  1. Everything massive has gravity. Gravity behaves differently in realized and quantum mechanical systems, but it is universally attractive.
  2. Every massive object exerts gravity on every other massive object, and fields, which in turn can then demonstrate forces on massive objects (although they are not massive themselves).
  3. The centre of mass is the point in an object where the gravity vectors cancel each other out, according to classical mechanics…

Non-Relativistic, Non-Quantum Mechanics

Mechanics is the domain of physics concerning itself with motion. The centre of mass (CoM) coordinate system is central to this discipline. Very often in physics, to simplify the calculations describing complex mechanical systems, we perform a transformation that converts the CoM to the origin. This coordinate transform makes problems that were previously impossible approachable because it reduces the complexity of associated calculations. This operation is a physicist’s best friend. It works well when the shapes in the physical system have a definite shape and volume, (i.e.: a solid).

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The shape and volume of these cheese puffs are realized.

The success of the CoM coordinate transform in classical mechanics has led to its incorrect application to quantum mechanical (QM) systems. The intimate link between the observation and the observed makes this coordinate transformation tricky for QM systems.

QM systems don’t have a localized CoM, only a particular probability distribution of observing the centre of massive energy. This is not equivalent to the macro-scale (CM) 3 dimensional measurements needed to compute the centre of mass: these are not independent of the act of observation in QM systems. Of course this does not matter in non GR circumstances.

 

CoM
The Centre of Mass (C) for 3 blocks

Whereas the calculation of the CoM “C” (above) is trivial (for a practicing physicist), an analogous calculation is not possible without altering the CoM on the QM level for an entangled system. The most obvious demonstration of this is the “spreading” of the spacetime dimensions on the fine scale of the individual atom.

0525151524-00
the potential of the entire Periodic Table exists within every atom

For a more complete explanation of this, see:

https://churchofentropy.wordpress.com/2015/11/25/quantum-chemistry-teaser/

On both the macro and micro scales, there are 3 spatial and one temporal dimension. On the micro-scale, time is a mesh encircling space. On the macro-scale, space is a blob, moving forward in time: a straight line.

On the microscale, the spacetime (energetic) dimensions are smeared out unevenly across the 3 physical dimensions: the 3 dimensions of space are not independent of the act of observation. In the “gross”/realized/day-to-day realm, we have no analogy for this, because we experience the 3 spatial dimensions as equivalent: measuring someone’s height does not affect the measurement of their waist! Strangely, people perceive me as thinner because I am taller. This is permissible of course, and in fact consistent with predictions of the model that the mind is a QM computer (the quantum mind’s measurement of my height is not independent of its measurement of my waist!) 😉 .

PA187966
Quantum Mechanics = So Metal

We shall see here that for complex QM systems under General Relativistic Circumstances, the CoM coordinate transformation is undefined, and thus inapplicable.

The Impossible Coordinate System Transformation

General relativity concerns itself with the general case of coordinate system transformations. It stipulates that space and time curve under the influence of external force fields.

https://en.wikipedia.org/wiki/General_relativity

We must impose the condition of measurability for the CoM, and this is where problems arise. In most systems, this is not an issue because either the centre of mass is fully realized (localized), or the system is not accelerated (so the CoM doesn’t change with time).

The centre of mass coordinate transformation is predicated on the uniqueness of the centre of mass. Since the centre of mass of a complex (entangled) QM entity exists in potential, we cannot know its value at all times, because that would imply the system had been altered irreversibly in the process of determining the time-varying values of the CoM of the system!

This is the quantum mechanical way. It is not possible to know the centre of mass for a system whose state variables are dependent on the act of observation when we need to additionally measure the movement of the coordinate system (in the GR case). The centre of mass, or origin, is in potential for systems with many entangled waveforms under non-uniformly accelerated motion (= under arbitrary external forces).

The GR notion of coordinate system invariance must therefore be given less importance if the QMCS is to remain relevant.

How can we prove our conjecture? Let’s consider the opposite: if General Relativity applies to Quantum Mechanical systems, then we ought to be able to state that the laws of physics apply equivalently in arbitrary systems. Thus all we have to do is choose one in which the CoM is observed and one in which it is not! Since the behaviour of the system with the observed centre of mass will now be different than had it not been, these systems will evolve differently by definition and contradict the precept of General Relativity!

Thus for any system for which measurements are not independent of observation (= QM), there is no way to perform a consistent coordinate transformation into the CoM under GR conditions. General relativity can only be meaningfully applied to systems for which a CoM is uniquely defined and thus for systems for which the classical limit applies (to within a reasonable error margin), not the QMCS.

Quantum Mechanics and General Relativity are thus incompatible.

Conclusion

General relativity is an excellent theory to model systems where the CoM is realized. In the quantum limit, it makes no sense to speak of a CoM which is independent of measurement, a requisite construct for the GR case.

Thank you

Epilogue: Quantum Gravity

The combination of General Relativity with Quantum Mechanics is supposed to herald the much coveted “Quantum Gravity” formulation.

Thought experiment: We are currently held in place along our orbit by the gravity of the Sun. If, (perhaps by some Christmas miracle), the sun suddenly stopped existing, would we feel the change in the gravity field instantly? Or would it take the ~ 8 minutes it takes for the Sun’s rays to reach us?

This question is important: I believe the first answer is correct, while proponents of the “graviton” believe it is the second!

I believe the superior hypothesis is that there are no gravitons because gravity represents instantaneous action at a distance: Mass is everywhere interconnected. I believe we should embrace the interconnected Mass hypothesis because there is no experimental support for gravitons and no reason to believe they exist other than to prop up the attachment our culture has to a Grand Unified Field Theory.

Thank you.

Reddit gave feedback but proved unwilling to abandon Standard Model!

r/physics, thanks for the feedback!

It’s been pointed out to me that there exists an operator to move into the CoM coordinate system for QM systems and that this means what I’ve written is incorrect. I accept that the CoM coordinate transform is necessary for solving most physics problems, and I agree that it is an acceptable shift for systems in which the CoM is independent of the acts of measurement/observation on said system.

That said, in GR circumstances, the CoM changes with time. Thus, we have a problem: the CoM is not independent of the interactions within the system nor of the movement of the system. Since the act of measuring the the CoM in such systems creates a new system (because QM observations change QM systems), such a coordinate transform is not independent of the movement of its coordinate system: the reference frame where the CoM is observed will be different from the one where it isn’t, by the observer effect of QM. I welcome any physicist (amateur or not) to find error with this.