Lorentz invariance of wave eqn.

In summary, the conversation discusses using the chain rule to show that the classical wave equation is Lorentz invariant. The attempt at a solution involves substituting in transformed coordinates and using Lorentz transformation, but it is unclear where the error occurs. The suggested solution is to use the chain rule implicitly and simplify the equation back to its original form.
  • #1
Hymne
89
1
Hello! Hopefully somebody could give me a push from behind on this one :)

Homework Statement



Show that the classical wave equation is lorentz invariant.

The Attempt at a Solution


I tried to exchange all derivatives by the chain rule:

[tex] (c^2 \frac{d^2 }{dt^2} + \frac{d^2 }{dx^2} + \frac{d^2 }{dy^2} + \frac{d^2 }{dz^2}) \phi = 0 ; \quad

\frac{d}{dx} \rightarrow \frac{d}{dx}\frac{dx}{dx'}[/tex]
And the same for the time derivative and use lorentz transformation. But somewhere it goes wrong..
 
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  • #2
I'd just substitute in the transformed coordinates and boil it all back down to what it started as. Not sure I'd use the chain rule explicitly.

Adrian.
 

FAQ: Lorentz invariance of wave eqn.

What is Lorentz invariance of wave equations?

Lorentz invariance of wave equations refers to the property that the mathematical equations that describe the behavior of waves do not change under transformations between different reference frames in special relativity. This means that the equations remain the same regardless of the observer's position or velocity.

Why is Lorentz invariance important in physics?

Lorentz invariance is a fundamental principle in physics that is necessary to maintain consistency with the laws of special relativity. It ensures that the laws of physics are the same for all observers, regardless of their relative motion. This is essential for the development of accurate and consistent theories in modern physics.

How is Lorentz invariance related to the speed of light?

The speed of light, denoted by c, is a fundamental constant in physics and is invariant in all reference frames. This means that the speed of light is the same for all observers, regardless of their motion. The Lorentz invariance of wave equations is closely related to this fundamental property of light.

Can Lorentz invariance be violated?

There have been various theories proposed in physics that suggest possible violations of Lorentz invariance, such as some theories of quantum gravity. However, experimental evidence has consistently supported the principle of Lorentz invariance, and it remains a fundamental concept in modern physics.

How is Lorentz invariance tested?

Lorentz invariance can be tested through high-precision experiments, such as measurements of the speed of light in different reference frames or tests of special relativity predictions. These tests have consistently shown that Lorentz invariance holds true, providing strong evidence for its validity in the laws of physics.

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