Vectors in Minkowski Space & Parity: Checking the Effect

In summary, the conversation discusses the effect of parity reversal on vectors in different spaces, specifically in Minkowski space. It is known that under parity reversal, vectors change sign, but it is unclear if this applies to Minkowski space as well. The action of parity reversal is the same for space components, but time reversal changes the sign of the T bits. The conversation ends with a request to continue the discussion in a thread about pseudotensors in different dimensions.
  • #1
illuminates
26
0
It is known that vectors change them sing under the influence of parity when ##(x,z,y)## change into ##(-x,-z,-y)##
$$P: y_{i} \rightarrow -y_{i}$$
where ##i=1,2,3##
But what about vectors in Minkowski space? Is it true that
$$P: y_{\mu} \rightarrow -y_{\mu}$$
where ##\mu=0,1,2,3##.
If yes how one can check it?
 
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  • #2
The action of parity reversal is the same for the space components. Time reversal changes the sign of the T bits.
 
  • #3
illuminates said:
But what about vectors in Minkowski space? Is it true that
Just to be clear, no.
 
  • #5
Thread closed as it is a duplicate thread on the same topic.
 

1. What is a vector in Minkowski space?

A vector in Minkowski space is a mathematical object that represents both magnitude and direction in a four-dimensional space-time. It is used to describe the position, velocity, and acceleration of objects in the special theory of relativity.

2. How is parity defined in Minkowski space?

Parity is a symmetry operation in Minkowski space that changes the sign of all spatial coordinates while leaving the time coordinate unchanged. This operation is also known as spatial inversion or mirror symmetry.

3. What is the effect of parity on a vector in Minkowski space?

The effect of parity on a vector in Minkowski space is to change the direction of the vector while keeping its magnitude unchanged. This means that if a vector points in the positive x-direction, after a parity transformation, it will point in the negative x-direction.

4. How can we check the effect of parity on a vector in Minkowski space?

To check the effect of parity on a vector in Minkowski space, we can apply the parity transformation to the vector and observe the resulting changes in its components. If the sign of all spatial components is flipped, then the parity transformation has been successful.

5. Why is understanding vectors in Minkowski space and parity important in science?

Understanding vectors in Minkowski space and parity is important in science, particularly in the field of physics, as it allows us to accurately describe and predict the behavior of objects moving at high speeds. It also helps us understand the fundamental symmetries of the universe and the laws of physics that govern them.

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