Frequently Asked Questions

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1—How is the wave function (ψ) different in tri-space from quantum mechanics?

In tri-space the driving metric, corresponding to external space and time, connects to and drives oscillations in the other metric spaces (according to the GEC). Each such discrete connection is a particle, with total energy equal to the driving frequency (times the Planck constant). The wave function in tri-space corresponds to the amplitude of this inter-metric connection, so it must involve coordinates in multiple metric spaces.

The wave function in quantum mechanics represents the system of particles being studied, at a single level of description in the local space and time coordinates, by an oscillatory amplitude describing the local energy and momentum density. The wave function is defined operationally.

For non-relativistic systems, described in centre-of-mass coordinates, the two wave functions correspond; but the tri-space wave function includes factors describing the environment, providing a logically complete description of the system, including heat energy for example. The wave function in quantum mechanics includes only the amplitudes corresponding to the items and properties being studied, in the local coordinates.

In practice, these differences become significant only when the system exchanges energy with the environment, causing the tri-space multi-metric structure to re-arrange. Then the external multi-metric description also becomes involved; but in quantum mechanics, the wave function simply vanishes, requiring a classical description of the results. Tri-space can also describe hybrid multi-metric structures, including liquids, which defy description in quantum mechanics.

2—What are elementary particles in tri-space?

An elementary particle is a disctrete inter-connection of the metric spaces of tri-space. Mass arises from an unseen metric space(s) of oscillators ('Modal space'). Elementary particles correspond to the various, discrete topologies of modal space that can be connected and driven separately by tempospace. They may have no mass, but they must still connect each of the metric spaces. Some are multi-point particles, comprising two or three distinct (un-symmetric) modal configurations that cannot be driven and projected into real space independently.

Less elementary are particles corresponding to oscillations in the spatial projections of composites of other particles, eg lattice phonons. These do not involve modal space.

3—What are the differences between space-time in relativity and the metric spaces in tri-space?

Special relativity relates space and time intervals on a single, unsigned metric involving the universal speed of light, so that co-moving frames of reference are related by Lorentz transformations. It does not relate to any theory of matter, but the single metric necessarily mixes up length and time intervals, making it inconsistent with quantum mechanics, for example.

The local, unsigned metric described in special relativity is decomposed, in the tri-space theory, into separate, signed, temporal and real spatial metrics, with shared Lorentz transformation symmetry. Massive particles are described by inter-connections of the metric spaces, including unseen, oscillation spaces. The reduction of material objects into co-moving point masses is completely invalid, in this theory.

The external, driving metric ('tempospace') is global, corresponding to time and empty space, and all driven objects obey the Planck quantisation law. This space is curved in proportion to the total driven frequency, corresponding to the Einstein gravitation law. Each wave function is projected into a local 'real space', with 3 real dimensions and one 'virtual time'. When and where they are connected, real spaces are mapped on to empty tempospace, allowing particles to interact.

Where particles are bound into composites, relative real spaces of projection define physical length intervals, which are mapped directly into tempospace, in the common rest frame, by 'tempodrivers'. Rotations in real space are discrete, corresponding to the quantisation of angular momentum, which is required to keep the driving phases consistent.

Interactions that change the energy of isolated systems (physical measurements for example), are non-local in tri-space. The local metric spaces are re-arranged instantaneously, and with them the local wave functions, simultaneously resolving every connected metric into a state of definite energy. No signals can be transmitted by this process.

The description of gravitation by general relativity involves only time-like material vectors and tensors. This description is carried over to tempospace only, in the tri-space theory, so that the classical description is the only description of gravitation. However, where gravity becomes very strong, it may affect the wider multi-metric structure of tri-space.

4—What does tri-space have to offer as opposed to other theories?

Tri-space is the only logically complete theory of space, time and matter (provided all of the metrics are fully understood). It includes all of the known laws of physics (and many new laws) in a single, logically-consistent framework. No other theory in history has this property.

Provided physicists can work on real problems, using tri-space theory directly, they will never again meet a problem that cannot be fully understood.

Your comments and other questions about this theory are very welcome (to robertherrod@tri-space-lab.com).