Relativistic Vectors: Find Transformation Between A & B

[Niles]

Homework Statement

Two 4-vectors are given by A = (5,4,3,0) and B = (5,5,0,0). I have to find out, which type of transformation comes out when transforming A over in B.

The Attempt at a Solution

I don't even think I understand the question. Can you give me a hint?

 

[George Jones]

Homework Statement

Two 4-vectors are given by A = (5,4,3,0) and B = (5,5,0,0). I have to find out, which type of transformation comes out when transforming A over in B.

The Attempt at a Solution

I don't even think I understand the question. Can you give me a hint?

1) The time coordinates of the two 4-vectors are the same.

2) The lengths of the spatial 3-vectors are the same.

This means that you're looking for a spatial transformation that preserves spatial length.

 

[ogb p]

As a scientist, it is important to have a clear understanding of the problem before attempting to solve it. Let's start by defining what a 4-vector is. A 4-vector is a mathematical object that consists of four components, similar to a 3-dimensional vector that has three components. In this case, the components represent different physical quantities, such as time, position, and momentum.

Now, the given 4-vectors A and B have different components, but they are related to each other through a transformation. This transformation can be described by a mathematical equation that relates the components of A to the components of B. In this problem, we are looking for the specific type of transformation that relates A to B.

To find this transformation, we need to use the principles of special relativity, which is a theory that explains the relationship between space and time. In special relativity, there are two important concepts that are relevant to this problem: time dilation and length contraction. Time dilation refers to the idea that time appears to pass slower for an object moving at a high speed, while length contraction refers to the idea that an object appears to be shorter in the direction of its motion.

Using these concepts, we can determine that the transformation between A and B involves a change in velocity or a change in the reference frame. This means that the components of A and B are measured in different frames of reference, and the transformation relates these two frames.

To find the specific type of transformation, we can use the Lorentz transformation equations, which are the mathematical equations that describe the relationship between two frames of reference in special relativity. By plugging in the components of A and B into these equations, we can determine the type of transformation between them.

In summary, the transformation between A and B involves a change in velocity or a change in the reference frame, and can be described by the Lorentz transformation equations. By solving these equations, we can find the specific type of transformation that relates A to B.