How to get an inverted (or reversed) tilde on a math symbol?

How can we get a reversed (or inverted) tilde on top of a math symbol, in math-mode? I’m sure that this reversed tilde does exist in LaTeX (I strongly believe I have seen it before), but I’m yet unable to find it back. Maybe I have just dreamed…

I’ve found this answer there: Mirror tilde accent, but it doesn’t work well and I’m pretty sure (I may be wrong) that this mirrored tilde accent exists without the need to create such a macro.

Here’s a MWE code to play with and have fun:

documentclass[11pt,letterpaper,twoside]{book}
usepackage[T1]{fontenc}
usepackage{lmodern}
usepackage[total={6in,10in},left=1.5in,top=0.5in,includehead,includefoot]{geometry}
usepackage{microtype}
usepackage{amsmath}
usepackage{amsfonts}
usepackage{mathtools}
usepackage{accents}
usepackage{tensor}

begin{document}

Blabla:
    begin{equation}
        tilde{t} = t quad text{How to get a reversed tilde ?}
    end{equation}

end{document}

Please, don’t use the sim or backsim symbol, since they’re not very similar to the default tilde accent.

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EDIT: Just to add some context. I need to show two similar (but different) coordinates transformations rules: Galilean transformation and Lorentz transformation. I don’t want to use the same tilde accent for both transformations.