Differences between Lorentz scalars and Lorentz invariants

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Discussion Overview

The discussion revolves around the differences between Lorentz scalars and Lorentz invariants, exploring their definitions and implications in the context of physics, particularly in relation to the power radiated by an accelerated charge as described by the Larmor formula.

Discussion Character

  • Debate/contested

Main Points Raised

  • Some participants question whether there is a difference between Lorentz scalar quantities and Lorentz invariant quantities, citing the example of power radiated by an accelerated charge, which has different expressions in different frames but yields the same value.
  • One participant proposes that scalars are a subset of invariants, defining scalars as invariants that are neither vectors nor tensors.
  • Another participant emphasizes that the term "invariant" can have multiple definitions, suggesting that both "invariant" and "scalar" refer to quantities that do not change value under coordinate transformations.
  • There is a reiteration of the idea that if two formulas yield the same value, it raises questions about how they can be considered "different."

Areas of Agreement / Disagreement

Participants express differing views on the relationship between scalars and invariants, with some agreeing on the definitions while others highlight the complexity and potential overlap in terminology. The discussion remains unresolved regarding the distinctions between the two concepts.

Contextual Notes

The discussion does not clarify certain assumptions about the definitions of scalars and invariants, nor does it resolve the implications of different expressions yielding the same value in different frames.

Llewlyn
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Are there any differences between a Lorentz scalar quantity or a Lorentz invariant quantity?
That sound be stupid but we dindt find anything exaustive about that.
Take as example the power irradiate by an accelerated charge (Larmor formula, relativistic one). The expression for evaluating in two frames (rest and lab) are different but they refer to same value (if 10W is in one frame, 10 W is in the other).

Is it a scalar or an invariant?

We really appreciate your help,

Ll.
 
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As I understand it, scalars are a subset of invariants. So a scalar is an invariant that is not a vector or tensor. No doubt someone will correct this if it's wrong.
 
The word "invariant" is used in many different ways. The appropriate definition here is "does not change value if we change to a new coordinate system". Of course that is also the definition of "scalar". There is no difference between "invariant" and "scalar" here.

I'm trying to figure out how two formulas could be "different" if the always give the same value!
 
Mentz114 said:
As I understand it, scalars are a subset of invariants. So a scalar is an invariant that is not a vector or tensor. No doubt someone will correct this if it's wrong.

I think you point out correctly.
I find it too this is the most logical way.

Ll.
 

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