Lorentz covariance

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In physics, Lorentz covariance is a key property of spacetime that follows from the special theory of relativity, where it applies globally. Lorentz covariance has two distinct, but closely related meanings.

1. A physical quantity is said to be Lorentz covariant if it transforms under a given representation of the Lorentz group. According to the representation theory of the Lorentz group, these quantities are built out of scalars, four-vectors, four-tensors, and spinors. In particular, a scalar (e.g. the space-time interval) remains the same under Lorentz transformations and is said to be a Lorentz invariant (i.e. they transform under the trivial representation).
2. An equation is said to be Lorentz covariant if it can be written in terms of Lorentz covariant quantities (confusingly, some use the term invariant here). This condition is a requirement according to the principle of relativity, i.e. all non-gravitational laws must make the same predictions for identical experiments taking place at the same spacetime event in two different inertial frames of reference.

Note: this usage of the term covariant should not be confused with the related concept of a covariant vector. On manifolds, the words covariant and contravariant refer to how objects transform under general coordinate transformations. Confusingly, both covariant and contravariant four-vectors can be Lorentz covariant quantities.

Contents 1 Local Lorentz covariance 2 Lorentz violation 2.1 Constraints 3 See also 4 References 5 External links

[edit] Local Lorentz covariance

Local Lorentz covariance refers to Lorentz covariance applying only locally. This concept is useful in general relativity.

[edit] Lorentz violation

Lorentz violation refers to theories which are approximately relativistic when it comes to experiments that have actually been performed (and there are quite a number of such experimental tests) but yet contain tiny or hidden Lorentz violating corrections.

Such models typically fall into two classes:

• The laws of physics are exactly Lorentz covariant but this symmetry is spontaneously broken. In special relativistic theories, this leads to phonons, which are the Goldstone bosons. The phonons travel at LESS than the speed of light. In general relativistic theories, this leads to a massive graviton (note that this is different from massive gravity, which is Lorentz covariant) which travels at less than the speed of light (because the graviton devours the phonon).
• The laws of physics are NOT Lorentz covariant but Lorentz covariance emerges as an approximate symmetry (at least in the so-called "visible sector"). Models of these sort are typically ether theories.

[edit] Constraints

There are very strict and severe constraints on marginal and relevant Lorentz violating operators within both QED and the Standard Model. Irrelevant Lorentz violating operators may be suppressed by a high cutoff scale, but they typically induce marginal and relevant Lorentz violating operators via radiative corrections. So, we also have very strict and severe constraints on irrelevant Lorentz violating operators.

[edit] See also

• Background independence
• Hendrik Lorentz
• List of mathematical topics in relativity
• Loop quantum gravity
• Lorentz invariance in loop quantum gravity
• Lorentz transformation
• Lorentz violation
• Luminiferous aether
• Relativistic mass
• Rotational symmetry
• Spacetime
• Spin foam
• Symmetry in physics
• Translational symmetry

[edit] References

• http://www.physics.indiana.edu/~kostelec/faq.html
• http://relativity.livingreviews.org/Articles/lrr-2005-5/
• http://www.nature.com/nature/journal/v393/n6687/full/393763a0_fs.html
• http://www.nature.com/nature/journal/v424/n6952/full/nature01882.html
• http://www.nature.com/nature/journal/v424/n6952/full/4241007a.html
• http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PRVDAQ000067000012124011000001

[edit] External links