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The weak force is the force that violates CP symmetry as the way it effects a particle depends on that particles handedness. Particles have a property known as spin although it is different from classical spin as it does not involve actual rotation and it is impossible to change the magnitude of a particles spin. Unlike classical spin there are only two spin states a particle can have known as up or down and which spin state a particle has tends to be probabilistic. The helicity of a particle depends on rather the direction of spin is the same as the direction of motion or rather it is in the opposite direction. In three spatial dimensions if a particle is massless and moves at the speed of light then its direction of motion is the same from all reference frames and so its helicity is the same from all reference frames. If a particle is massive then its direction of motion depends on the reference frame and so its helicity depends on the reference frame however its handedness is the same from all reference frames because its handedness depends on its chirality instead of its helicity. Without the higgs boson every particle would be massless and move at the speed of light so that the direction of motion would be the same in all reference frames so that the helicity would be the same in all reference frames. With the higgs boson some particles have mass from interacting with the higgs field which prevents them from moving at the speed of light so that what would otherwise be the particles kinetic energy is instead the mass of the particle.

In four spatial dimensions an object with simple rotation rotates around a plane instead of around an axis and so it is impossible to use a vector for an objects rotation in four spatial dimensions. Without being able to assign a vector for spin in four spatial dimensions it would be impossible to define helicity even for a particle moving at the speed of light even though the direction of motion is the same from all reference frames.

So my questions are

1: Would particles have handedness in a universe with four spatial dimensions? 2: Would CP Violation take place in a universe with four spatial dimensions? 3: Would there be an imbalance between the amount of matter and antimatter in a universe with four spatial dimensions?

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    $\begingroup$ 1. There might be some quantity that looks like handedness, but the specific term "helicity" or "handedness" is rather by definition only used in 3D. 2. is an interesting question (but you should clarify in which model you're asking that - it's not that straightforward to generalize the Standard Model to 4+1D) 3. is unanswerable since we don't even know the full reason for that imbalance in our universe (CP violation is widely thought to be too weak to explain the effect fully). $\endgroup$ – ACuriousMind Dec 2 '15 at 15:34

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