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What is "lorentz invariant" ? Please explain with few examples.

Physics
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Something that does not change with Lorentz transformations (that is, is the same no matter what the relative velocity of the observer). The speed of light is Lorentz invariant, and because of this \[t^2-x^2\] is also Lorentz invariant (if same units are used for t as for x)
Things like electron charge, mass (yes, mass does NOT increase with relative velocity) and other things are also Loretnz invariant.
Is Mode of \[\left| B ^{2} - E ^{2} \right|\] is Lorentz invariant?

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No idea, I don't know anything about electrodynamics.

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