Deriving Lorentz Transformation: Wave Eq Invariance & General Relativity

In summary, the Lorentz transformation is obtained by satisfying the requirement of invariance of the wave equation, which can also be achieved through linear transformations by keeping the spacetime interval squared invariant. Other nonlinear transformations, such as conformal transformations, also keep the wave equation invariant, particularly in the case of electromagnetic waves. Solutions of general relativistic problems may involve these transformations, but they do not provide a coordinate transformation.
  • #1
jk22
729
24
I read the Lorentz transformation can be obtained by solving the requirement of invariance of the wave equation. If one considers linear transformations this the same as the spacetime interval squared to be invariant.

What are the other nonlinear transformations keeping the wave equation invariant ?
In particular shall solutions of general relativistic problems give one of those transformations ?
 
Physics news on Phys.org
  • #2
jk22 said:
I read
Where?

the Lorentz transformation can be obtained by solving the requirement of invariance of the wave equation. If one considers linear transformations this the same as the spacetime interval squared to be invariant.

What are the other nonlinear transformations keeping the wave equation invariant?
If you mean electromagnetic waves, the answer is "conformal transformations",
in particular the so-called "special conformal transformations".

This recent thread is partially relevant, and contains links to more info on conformal transformations.

In particular shall solutions of general relativistic problems give one of those transformations?
I failed to any extract sensible meaning from this sentence. A "solution" of the GR field equations gives a metric, not a coordinate transformation.
 

1. What is the significance of deriving Lorentz transformation in the context of general relativity?

The Lorentz transformation is a fundamental mathematical concept in special relativity, which describes the relationship between space and time. In the context of general relativity, it is important because it allows us to understand how the laws of physics remain consistent in different frames of reference, even in the presence of gravity.

2. How does the wave equation invariance relate to the Lorentz transformation?

The wave equation is a mathematical representation of how waves propagate through space and time. Invariance means that the form of the equation remains unchanged under certain transformations. The Lorentz transformation is one such transformation that preserves the form of the wave equation, making it a fundamental principle in the development of special relativity.

3. Can you explain the mathematical derivation of the Lorentz transformation?

The Lorentz transformation can be derived using basic principles of special relativity, such as the constancy of the speed of light and the relativity of simultaneity. It involves solving a set of equations that relate the space and time coordinates in one frame of reference to those in another frame of reference moving at a constant velocity relative to the first.

4. How does the Lorentz transformation differ from Galilean transformation?

The Galilean transformation is a classical transformation that describes the relationship between space and time in non-relativistic physics. It assumes that space and time are absolute and do not depend on the observer's frame of reference. The Lorentz transformation, on the other hand, takes into account the effects of special relativity, such as time dilation and length contraction, which make space and time relative to the observer's frame of reference.

5. What are some practical applications of the Lorentz transformation?

The Lorentz transformation has numerous practical applications in modern physics, including in the development of the theory of special relativity, which has led to many technological advancements in fields such as particle physics and astrophysics. It is also used in the calculation of time and distance in GPS systems, as well as in the design of particle accelerators and other high-speed machines.

Similar threads

I Coord Transform in de Sitter Space: Phys Significance &Linearity?
    • Special and General Relativity
Replies
5
Views
1K
I Lorentz Transformation: Premises + Derivation
    • Special and General Relativity
Replies
5
Views
960
A Lorentz Transformation: Wave Equation vs. Interval Invariance
    • Special and General Relativity
Replies
7
Views
1K
I Does Lorentz invariance imply Einstein's synchronization convention?
    • Special and General Relativity
Replies
32
Views
3K
I Can we choose different functional forms for Lorentz transformation?
    • Special and General Relativity
Replies
10
Views
608
I Explore Spacetimes, Metrics & Symmetries in Relativity Theory
    • Special and General Relativity
Replies
7
Views
1K
I Gravitational Field Transformations Under Boosted Velocity
    • Special and General Relativity
Replies
14
Views
1K
I Deriving Lorentz Transformations: Hyperbolic Functions
    • Special and General Relativity
Replies
33
Views
2K
I Proof of Invariance of Spacetime Interval
    • Special and General Relativity
Replies
6
Views
278
I A Hidden Zero in Einstein's Simple Derivation
    • Special and General Relativity
Replies
22
Views
1K

Hot Threads

Recent Insights

Back
Top