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kaleidoscope
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Why is the vertical axis time multiplied by the speed of ligth? And, what is the purpose of using Minkowski space?
Minkowski space, and the Lorentz transformations, tell us how space and time look different to different observers.kaleidoscope said:And, what is the purpose of using Minkowski space?
The Lorentz transformations mix x and t in a way that's loosely analogous to the way a rotation in the x-y plane mixes x and y. The existence of rotations shows that it would be silly to measure x in meters and y in feet. Similarly, the existence of Lorentz transformations shows that it would be silly to measure x in meters and t in seconds.kaleidoscope said:Why is the vertical axis time multiplied by the speed of ligth?
If you're asking because you've seen a diagram with x and ct on the axes, and are wondering why they put ct there instead of t, the answer is just that this is a convenient choice. It's convenient because it ensures that the world line of a light ray has slope 1 in the diagram. An alternative, which I prefer, is to take the axes to be x and t, and choose units such that c=1. This convention gives us the same diagrams, the same physics, and easier calculations.kaleidoscope said:Why is the vertical axis time multiplied by the speed of ligth?
kaleidoscope said:And, what is the purpose of using Minkowski space?
Minkowski space is a mathematical model used in the study of special relativity and spacetime. It is a four-dimensional space that combines three dimensions of space and one dimension of time.
In Minkowski space, time is considered to be the fourth dimension and is treated on equal footing with the three dimensions of space. This allows for the concept of spacetime, where time and space are interconnected and can affect each other.
The speed of light in Minkowski space is a constant value, denoted by c, which is approximately 299,792,458 meters per second. It is considered to be the maximum speed at which all objects and information can travel in the universe.
Minkowski space is used in physics to study the behavior of objects and events in the universe, particularly in relation to special relativity and spacetime. It allows for the formulation of mathematical equations and models that accurately describe the motion and interactions of particles and objects.
The study of Minkowski space is essential for understanding the fundamental principles of special relativity and the interconnected nature of space and time. It also has practical applications in fields such as physics, astronomy, and engineering.