# Questions tagged [invariants]

This tag is for questions relating to invariant, a property of a system which remains unchanged under some transformation. In physics, invariance is related to conservation laws.

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### Why is it necessary that different observers agree on the value of the spacetime interval $ds^2$?

What's the physical reason that all (inertial) observers agree on the value of the spacetime interval $$ds^2 = (c dt)^2 - dx^2 - dy^2 -dz^2 \, ?$$ What would be the physical implications if different ...
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### How could 'rest mass' and 'invariant mass' be the same?

The terms rest mass and invariant mass are often interchanged, however i cannot reconcile these concepts: Consider a photon ...
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### time invariance for “Translations” versus “Galilean transformations”

Why would the time coordinate (t) be NOT invariant under translations, but invariant under Galilean transformations? I thought it should be invariant under both Here is what I'm tying to understand:
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### Can GR be reformulated in terms of invariant observables?

Question So recently I was thinking about this: How many scalars are available in $4$ dimensions in General Relativity (without being redundant)? For example, with metric we can construct the ...
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### Physical meaning of the Casimir operators of Poincarè algebra

If one considers the algebra $su(2)$, it is well known that the Casimir Operator is $$C=L_1^2+L_2^2+L_3^2.$$ It corresponds to the total angular momentum and correctly is a conserved quantity. ...
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### Value of the invariant $R_{\mu \nu}F^{\mu \nu}$

Is there a simple way to find the value of $R_{\mu \nu}F^{\mu \nu}$ (where $R_{\mu \nu}$ is the Ricci tensor and $F^{\mu \nu}$ is the electromagnetic tensor), knowing that it is an invariant? ...
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### Can anyone provide a simple, inuitive explanation for Noether's Theorem? [duplicate]

I recently came across this theorem for the first time. As I understand it, what she showed was that conservation 'laws' are often simply an artifact of symmetry or invariance. For example, the ...
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### How is Einstein's postulate about the invariance of the laws of physics justified? [duplicate]

According to one of Einstein's postulates related to special relativity, > "the laws of physics remain invariant in their form and nature in all inertial frames". But global inertial frames don't ...
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### Restrictions on the form of a scalar-valued function imposed by Lorentz invariance

Let $f(p,q)$ be a smooth Lorentz-invariant function of 4-vectors $p$ and $q$. Should $f$ necessarily be of the form $f(p,q) = g(p^2, q^2, p_\mu q^\mu)$, where $g(x,y,z)$ is some scalar-valued ...
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### Scalar versus invariant in Newtonian mechanics

I looking up coriolis transport theorem for rotating refrence frames and while reading through this derivation he wrote: In Newtonian mechanics, scalar quantities must be invariant for any given ...
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### Gauge invariant scalar which is not Lorentz-invariant

I'm looking for examples of the following descriptions: A gauge invariant scalar which is not Lorentz-invariant A Lorentz covariant scalar For 1. I was thinking about the scalar potential $A$ (for ...
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### What is the physical meaning of the third invariant of the strain deviatoric?

In continuum mechanics of materials with zero volumetric change, the material condition can be expressed by the strain deviatoric tensor instead of the strain tensor itself. To express the plasticity ...
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### Are there Galilean scalars?

In special relativity there are scalar quantities which are invariant under any Lorentz transformation, called Lorentz scalars. For example, the magnitude of the four-velocity is a Lorentz scalar. If ...
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### Formal Term for an invariant constant to all observers

I was thinking of the speed of light and realized I don't know how to quickly name the concept of "physical quantity that is measured to be the same in all reference frames". Are there examples of ...
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### Using the energy-momentum invariant for a decay process

For a decay process in which particle A ----> particle B + a photon in which particle A has mass $m_A$, particle of mass $m_B$ and energy and momentum are conserved. Show that in the frame in ...
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### Quantities invariant by Lorentz transform

If I rotate a triangle lying on the two-dimensional plane both the lengths of the sides and the angles formed are invariant (ie, they are the same before and after the rotation). In a 2D Lorentz ...
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### Why should an action in SR be a lorentz scalar? [duplicate]

I have taken it granted that an action in the special relativity must be a lorentz scalar. However is there a fundamental reason for this requirement? I cannot think of a plausible reason for this ...
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### What Lorentz covariance has to do with Lorentz invariance? [duplicate]

Does saying that the Dirac equation is invariant under Lorentz transformations is the same as saying that it is Lorentz covariant?