# Differences between Lorentz scalars and Lorentz invariants

• Llewlyn
In summary, the conversation discusses the differences between a Lorentz scalar quantity and a Lorentz invariant quantity. The example of power irradiated by an accelerated charge is used as an illustration, where the expression for evaluation in two frames may be different but they refer to the same value. The concept of scalars and invariants is also clarified, with the understanding that scalars are a subset of invariants. It is noted that there may be different definitions of "invariant" but in this case, it refers to a quantity that does not change value when changing to a new coordinate system, which is also the definition of a scalar.
Llewlyn
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?

Ll.

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.

## 1. What is the difference between Lorentz scalars and Lorentz invariants?

Lorentz scalars are quantities that remain the same under Lorentz transformations, while Lorentz invariants are quantities that are independent of the reference frame in which they are measured. This means that Lorentz scalars have the same value for all observers in different reference frames, while Lorentz invariants have the same value for all observers in the same reference frame.

## 2. How are Lorentz scalars and Lorentz invariants used in physics?

Lorentz scalars and Lorentz invariants are used to describe physical quantities in special relativity. They are important in calculating physical phenomena, such as time dilation and length contraction, that occur at high speeds.

## 3. Can you give an example of a Lorentz scalar and a Lorentz invariant?

One example of a Lorentz scalar is the speed of light, which has the same value for all observers regardless of their reference frame. An example of a Lorentz invariant is the spacetime interval, which is the difference in space and time coordinates between two events and remains the same for all observers in different reference frames.

## 4. What is the significance of Lorentz scalars and Lorentz invariants in the theory of relativity?

Lorentz scalars and Lorentz invariants are crucial in the theory of relativity as they provide a way to understand and calculate physical quantities in different reference frames. They also play a key role in showing that the laws of physics are the same for all inertial observers, regardless of their relative motion.

## 5. Are there any other types of Lorentz invariants?

Yes, there are other types of Lorentz invariants, such as the energy-momentum tensor, which describes the distribution of energy and momentum in a system, and the electromagnetic field tensor, which describes the electromagnetic field in special relativity. These invariants are important in understanding and predicting physical phenomena in different reference frames.

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