General Lorentz Transformation Explained: Visualize and Grasp It!

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• Sang-Hyeon Han
In summary, the author explains in chapter 1.3 of his book "The Theoretical Minimum: Special Relativity and Classical Field Theory" that the general Lorentz transformation, which relates two frames in relative motion along an oblique direction, can be achieved by performing a sequence of rotations and a simple Lorentz transformation along the new x axis. This allows for uniform motion in the x direction. If the desired velocity is not in the x direction, the axes can be rotated to align with the desired direction before performing the Lorentz transformation. This process can be visualized as rotating a set of axes before and after the transformation.
Sang-Hyeon Han
Hi guys, I'm reading a book 'the theoretical minimum: special relativity and classical field theory'. In chapter 1.3, author explains the general Lorentz transformation.

He said "Suppose you have two frames in relative motion along some oblique direction, not along any of the coordinate axes. It would be easy to make the primed axes line up with the unprimed axes by performing a sequence of rotations. After doing those rotations, you would again have uniform motion in the x direction. The general Lorentz transformation—where two frames are related to each other by an arbitrary angle in space, and are moving relative to each other in some arbitrary direction—is equivalent to:

1. A rotation of space to align the primed axes with the unprimed axes.
2. A simple Lorentz transformation along the new x axis.
3. A second rotation of space to restore the original orientation of the
unprimed axes relative to the primed axes. "

My head is stuck with that paragraph and I can't understand how he can do that. I can't visualize it in my head. Could anyone make me grasp it?

If the velocity you want to boost in isn't the x direction, then you rotate your axes (you can imagine a little construction of rods pointing in three directions that you imagine rotating) so that the new x direction does point in the direction you want to boost. Then you boost. Then you rotate your axes back to how they were before.

1. What is the Lorentz Transformation?

The Lorentz Transformation is a mathematical equation that describes how measurements of space and time change between different frames of reference in special relativity. It was developed by Dutch physicist Hendrik Lorentz in the late 19th century and later refined by Albert Einstein.

2. Why is the Lorentz Transformation important?

The Lorentz Transformation is important because it is a fundamental concept in special relativity, which is a cornerstone of modern physics. It helps us understand how measurements of space and time are relative to the observer and how they change at high speeds.

3. How does the Lorentz Transformation work?

The Lorentz Transformation uses a set of equations to relate measurements of space and time between two inertial frames of reference that are moving at a constant velocity relative to each other. It takes into account the effects of time dilation and length contraction at high speeds.

4. What is the visual representation of the Lorentz Transformation?

The Lorentz Transformation can be visualized using a spacetime diagram, which shows how measurements of space and time change between two frames of reference. It also includes the concept of a light cone, which represents the maximum speed at which information can travel.

5. How can I grasp the concept of the Lorentz Transformation?

The best way to grasp the concept of the Lorentz Transformation is to study its equations and visualize it using diagrams and animations. It may also be helpful to understand the principles of special relativity and the implications of the speed of light being constant for all observers.

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