Description
The violation of the discrete symmetries of charge conjugation, parity inversion, and time reversal (T) observed in high energy physics are fundamental aspects of nature. A new quantum theory [1,2] based on sums over paths has been introduced to explore the possibility of their large-scale physical consequences. Within the theory, time evolution and conservation laws are phenomenological repercussions of T violation. The relative scale for clock time is determined by the effective strength $\lambda={\rm i}\langle\big[\hat{H}_F,\hat{H}_B\big]\rangle$ of the T violation, where $\hat{H}_F$ and $\hat{H}_B=\hat{T}\hat{H}_F\hat{T}^{-1}$ are the Hamiltonians for forward and backward time evolution, respectively, and $\hat{T}$ is the time reversal operator. It follows that two identical clocks lose synchronicity if they are in spatial regions with differing values of $\lambda$, and this time-dilation effect is accompanied by a corressponding change (contraction) in lengths measured by observers in each region. Moreover, if the T violation is due to a field which has velocity dependent Hamiltonians in a particular form, the time-dilation and length-contraction effects become equivalent to those in special relativity. Importantly, these effects are manifested as differences in relative quantum states rather than differences in coordinates.
My latest work takes a step back and begins with 4D space where 'protoparticles' are defined in terms of sums over paths. The generator of translations is identified as an operator representation of the Fourier transform. A break in the 4D isotropy affecting the Fourier transform of one of the dimensions leads to it having time-like behaviour and further, if the broken symmetry is velocity dependent, the protoparticles behave as regular point particles with mass, kinetic energy and momemtum on a spacetime background.
[1] J.A.Vaccaro, Quantum asymmetry between time and space, Proc.R.Soc.A 472 (2016) 20150670.
https://dx.doi.org/10.1098/rspa.2015.0670
[2] J.A.Vaccaro, The quantum theory of time, the block universe, and human experience, Phil.Trans.R.Soc.Lond.A 376, 20170316 (2018). https://dx.doi.org/10.1098/rsta.2017.0316
| I am the presenting author | Yes |
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