The "x'=x-vt" in Galilean/Lorentz transformation

In summary: Lorentz/Galilean transformation. There are two coordinate systems involved, one acting as a reference point and the other representing a system in motion. The x' component, which describes motion in the x-axis, is given by x'=x-vt. The negative sign in front of vt represents the direction of motion relative to the reference frame. If the prime system is moving in the opposite direction of the x-axis, then it will be -vt. This can be visualized by drawing a displacement-time graph or an x' vs t graph.
  • #1
JohnTitor
1
0
Hello people,
I have a question regarding the x' component in the Lorentz/Galilean transformation.
So from what i understand is that there are 2 coordinate systems used in the transformations. One is used as a reference point and one is used for moving away from this point. The moving away in x-axis is described with x'=x-vt but where does the "-vt" come from and why is it "minus vt" and not "positive vt"?

Is the sign determined by how the prime(')-coordinate system moves relative to the other system? (So it's -vt when you move against the direction of the x-axis?)
 
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  • #2
You can work out the direction of motion by checking if x' increases or decreases with t.
 
  • #3
You can draw a displacement-time graph for a pair of objects moving at speed v. What is the equation of the line in terms of x and t? Can you relate x' to this? Drawing an x' vs t graph may help with the latter.
 
  • #4
JohnTitor said:
Hello people,
I have a question regarding the x' component in the Lorentz/Galilean transformation.
So from what i understand is that there are 2 coordinate systems used in the transformations. One is used as a reference point and one is used for moving away from this point. The moving away in x-axis is described with x'=x-vt but where does the "-vt" come from and why is it "minus vt" and not "positive vt"?

Is the sign determined by how the prime(')-coordinate system moves relative to the other system? (So it's -vt when you move against the direction of the x-axis?)
It's geometric. The S' frame is moving with positive velocity v relative to the S frame. Draw a picture showing the location of the S' frame relative to the S frame at two different times, and you will see visually how this plays out.

Chet
 

Related to The "x'=x-vt" in Galilean/Lorentz transformation

1. What is the meaning of "x'=x-vt" in Galilean/Lorentz transformation?

In Galilean/Lorentz transformation, "x'=x-vt" represents the transformation of position (x) from one reference frame to another, where v is the relative velocity between the two frames and t is the time elapsed. It is also known as the Galilean transformation equation.

2. How is "x'=x-vt" derived?

The Galilean/Lorentz transformation equations were first derived by Galileo Galilei and later refined by Hendrik Lorentz. The equation "x'=x-vt" is derived from the principle of relativity, which states that the laws of physics are the same in all inertial reference frames.

3. What is the difference between Galilean and Lorentz transformations?

Galilean transformations are based on classical mechanics and assume that space and time are absolute. Lorentz transformations, on the other hand, take into account the effects of special relativity, which states that the laws of physics are the same for all observers in uniform motion.

4. Can "x'=x-vt" be applied to all types of motion?

The equation "x'=x-vt" is valid for objects moving at constant velocities in a straight line. It cannot be applied to objects undergoing acceleration or moving in curved paths, as these situations require more complex mathematical equations.

5. What are the practical applications of "x'=x-vt"?

The Galilean/Lorentz transformation equations, including "x'=x-vt", have many practical applications in physics and engineering. They are used in the study of special relativity, electromagnetism, and the design of electronic devices such as GPS systems. They also have applications in fields such as astronomy, where the positions of celestial objects are measured from different reference frames.

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