# What is k-Minkowski spacetime, and is it a tool in a theory of quantum gravity?

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What is k-Minkowski spacetime, and...

In http://www.physorg.com/news157203574.html, k-Minkowski spacetime, which decreases down towards zero at small scales, is mentioned as a possible tool in a theory of quantum gravity and spacetime. But it is very, very vague. First, how is k-Minkowski space-time defined, and where precisely would it enter? Is the "k" here the same as the "q" in the description of the quantum group given in http://en.wikipedia.org/wiki/Quantum_group#Drinfel.27d-Jimbo_type_quantum_groups? Roughly what role would such fractional spacetime play? An explanation for a non-physicist (but with a mathematical background) would be greatly appreciated.

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K-Minkowski spacetime is a generalization of Minkowski spacetime in which the signature of the metric tensor is changed from the standard signature of Minkowski spacetime to the signature of the Lorentzian metric. It is often sufficient to use this model for background geometry when working with curved spacetimes.

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Thanks, Greg Bernhardt!

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the signature of the metric tensor is changed from the standard signature of Minkowski spacetime to the signature of the Lorentzian metric.
What's the difference between Minkowski and Lorentzian signature?

A bonus question, is k-Minkowski the same as kappa-Minkowski?

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the standard signature of Minkowski spacetime to the signature of the Lorentzian metric.
From https://mathworld.wolfram.com/MetricSignature.html
"For n-dimensional Lorentzian space Rn-1,n , the metric signature is (n-1,n) , e.g., (3,1) (as above) for the Minkowski space of special relativity."
So if I understand correctly (wishing to be corrected), perhaps by "changing" the signature one means that in generalizing the Minkowski to more dimensions than 4, one generalizes the signature as well to the Lorentzian.

A bonus question, is k-Minkowski the same as kappa-Minkowski?
I am presuming that the author of the article (first link in my original post) used k instead of κ (kappa) out of typographical reasons. (Which may or may not be a euphemism...)

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What's the difference between Minkowski and Lorentzian signature?

A bonus question, is k-Minkowski the same as kappa-Minkowski?
For your first question, I am not sure there's even such a thing as a Lorentzian metric.
There's a Lorentz transformation and Minkowski metric or space-time.
Before I learned GR from Schutz's book I didn't think to myself that the global spacetime metric may be flat, i.e. Minkowski.