Quantum physics uses a parameter space that is curved. It is possible to cure this situation by converting the quantum state functions to distributions that have a flat parameter space.
Let ψ(q) be a quaternionic probability amplitude distribution (QPAD). ψ(q) can be used as a quantum state function of a particle. It can affect its own parameter space. It does that when it couples to a second QPAD. That is why its parameter space is curved.
All quantum state functions share the affine versions of their parameter space. In the HBM this space is called "Palestra". The curvature of the Palestra is defined by a continuous quaternionic distribution ℘(x), which has a flat parameter space that is spanned by the quaternions. It connects a location in the Palestra to each location in its own (flat) parameter space.
Let Φ(x)= ψ(℘(x)) define the flat quaternionic probability amplitude distribution (FQPAD) that corresponds to ψ(q).
Φ(x) is also a quantum state function, but it has a flat parameter space. It is no longer a QPAD. It does not affect its parameter space like ψ(q) can do.
Φ(x)= ψ(℘(x)) unifies regular quantum physics with gravitation theory.
It converts "curved" quantum physics to "flat" quantum physics.
The distance function ℘(x) enables the specification of a "quaternionic GR". Its (full) derivative defines a quaternionic metric.
Note: the existence of black holes indicates that the distance function has no inverse. However, outside these singular locations it can have a local inverse.
It appears that quantum physics uses a flat kind of derivative in which partial derivatives that concern the functions values that belong to other quaternionic dimensions are ignored. This makes that in quantum mechanics the quaternionic nabla ∇ makes sense and the differential ∇f can be written as a product of two quaternionic objects ∇ and f of which the nabla ∇ is the operator.
In gravitation theory the full quaternionic differential df must be used. This differential concerns all sixteen partial derivatives of the quaternionic distribution f. In the HBM the full differential is used in the definition of the quaternionic metric d℘(x).
For more details see:
- PHYSICAL SCIENCES
- EARTH SCIENCES
- LIFE SCIENCES
- SOCIAL SCIENCES
Subscribe to the newsletter
Stay in touch with the scientific world!
Know Science And Want To Write?
- Part I: Bee Deaths Mystery Solved? Neonicotinoids (Neonics) May Actually Help Bee Health
- Is The Micropower Revolution Here?
- On integrating out short-distance physics
- Chronic Pain Isn't All In The Brain
- Big Data Could Be A Big Problem For Workplace Discrimination Law
- You Are Not Alone, Shows Hacked Webcam Site
- Like Collaboration And Intelligence In Humans? Thank War
- "Chimpanzees go to war with each other and yet they did not evolve into a similarly intelligent..."
- "I have always thought that that formulas like (1) are not clear . If G(u) is a primitive of f(u)..."
- "I am indeed checking with vanEnglesdorp even though the matter seems quite clear cut to me: showing..."
- "Hi, the comics linked below seems to deal with a similar stuff. http://www.smbc-comics.com/?id=3554#comi..."
- "they don't see how it damages the economic system that made America great in the past. Huh? Empirical..."
- Study reveals significantly increased risk of stillbirth in males
- Moderate coffee consumption may lower the risk of Alzheimer's disease by up to 20 percent
- New research supporting stroke rehabilitation
- The artificial pancreas shown to improve the treatment of type 1 diabetes
- The Lancet: Leading medical experts call for an end to UK postcode lottery for liver disease treatment and detection