# Spec Rel: Changes in gradient between frames

• Totoro Recall
In summary, the gradient of the rod in the S' frame would be the same as in the S frame, as per the Lorentz transformations.
Totoro Recall

## Homework Statement

Suppose a rod measured in the S frame has a gradient of M.

The S' frame travels at v (along x-axis) relative to S. What is the gradient of the rod in the S' frame?

## Homework Equations

Lorentz tranformations

## The Attempt at a Solution

y'=y

x' = $\gamma$(x-vt)

so that m = y'/$\gamma$(x-vt)

This seems straightforward enough, which is why I'm worried. I'm not used to problems in relativity being this easy. Have I missed anything?

I can confirm that your solution is correct. The Lorentz transformations allow us to calculate the measurements of an object in one frame of reference from measurements in another frame of reference. In this case, the gradient of the rod in the S' frame would be the same as in the S frame, as the length of the rod would not change due to its orientation being perpendicular to the direction of motion. This is a fundamental concept in relativity and is a key part of understanding the effects of time and space in different frames of reference. Keep up the good work!

## 1. What is "Spec Rel" in relation to changes in gradient between frames?

"Spec Rel" stands for "spectral relationship". It refers to the relationship between the spectral properties of an object and the changes in those properties between different frames or time points.

## 2. How is the gradient between frames calculated in spectral analysis?

The gradient between frames is calculated by comparing the spectral properties (e.g. intensity, wavelength) of an object in two or more frames and determining the change in those properties over time.

## 3. Why is it important to study changes in gradient between frames in scientific research?

Studying changes in gradient between frames allows scientists to track and understand how the spectral properties of an object change over time. This can provide valuable insights into the behavior and characteristics of the object, and can also be used to detect and monitor any changes or abnormalities.

## 4. What are some examples of research fields that utilize "Spec Rel" in their studies?

Some examples of research fields that utilize "Spec Rel" include astronomy, remote sensing, medical imaging, and environmental monitoring. In each of these fields, scientists use spectral analysis to study changes in gradient between frames to gain a better understanding of their subject of study.

## 5. How can changes in gradient between frames be visualized and interpreted?

Changes in gradient between frames can be visualized through plots, graphs, and images that show the changes in spectral properties over time. These visualizations can be interpreted by analyzing the patterns and trends in the data, and comparing them to known information about the object being studied.

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