Differences between Lorentz scalars and Lorentz invariants

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Lorentz scalars and Lorentz invariants are closely related concepts in physics, with scalars being a specific type of invariant that does not include vectors or tensors. Both terms refer to quantities that remain unchanged across different coordinate systems. The discussion highlights the example of power radiated by an accelerated charge, where different formulas yield the same value in different frames, illustrating the concept of invariance. Ultimately, there is no significant distinction between a Lorentz scalar and a Lorentz invariant in this context. Understanding these terms is crucial for grasping the principles of relativity and their applications.
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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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