How to Visualize a 4 vector (e.g. a velocity)?

In summary, a velocity 4-vector has 3 space dimensions and 1 time dimension. Its space parts are directed at the 3 space directions while its time part is directed at the time dimension. It can be visualized in a Minkowski diagram, with a Minkowski normalized tangent to the particle's worldline in a (1+1)d representation, and in (2+1)d with a more complex diagram. However, there is no known way to draw a (3+1)d representation of a velocity 4-vector.
  • #1
Ashshahril
4
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Homework Statement
How to Visualize a 4 vector(e.g. velocity)?
Relevant Equations
Velocity = distance/time
Velocity is a 4-vector which has 3 space dimensions and 1 time dimension. It's space parts will be directed at the 3 space directions and time parts will be directed at the time dimension (But it is inverse. So, will it point at the inverse direction?). How can someone Visualize it? How they arrange themselves in a 4d grid line?

Can you show all the 4-vectors at once?
 
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  • #2
Ashshahril said:
Velocity is a 4-vector which has 3 space dimensions and 1 time dimension. It's space parts will be directed at the 3 space directions and time parts will be directed at the time dimension
A vector is just a magnitude and a direction. Don't think of it in terms of components - just think of it as an arrow at a point, pointing in some direction.
Ashshahril said:
But it is inverse.
I don't know what you mean by "inverse".
Ashshahril said:
How can someone Visualize it?
In (1+1)d, draw a Minkowski diagram. This is a Euclidean representation of a Minkowski plane, but that's as good as it gets. The four velocity is the Minkowski normalised tangent to the particle's worldline.

In (2+1)d you can also draw Minkowski diagrams but they're harder to understand.

I don't know any way to draw (3+1)d diagrams.
 
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FAQ: How to Visualize a 4 vector (e.g. a velocity)?

1. What is a 4 vector?

A 4 vector is a mathematical representation of a physical quantity in four-dimensional spacetime. It includes three spatial components and one time component.

2. How do you visualize a 4 vector?

To visualize a 4 vector, you can use a spacetime diagram, which shows the four components of the vector on a graph with time on the vertical axis and space on the horizontal axis.

3. What do the four components of a 4 vector represent?

The three spatial components represent the direction and magnitude of the vector in three-dimensional space, while the time component represents the time component of the vector.

4. How do you interpret the length of a 4 vector?

The length of a 4 vector, also known as its magnitude, represents the speed of the object in spacetime. A longer vector indicates a faster speed, while a shorter vector indicates a slower speed.

5. Can a 4 vector be used to represent any physical quantity?

No, a 4 vector is specifically used to represent quantities in four-dimensional spacetime, such as velocity, momentum, and energy. It cannot be used to represent quantities in other dimensions, such as temperature or mass.

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