How Do You Calculate the Magnitude of a 4-Vector?

In summary, the conversation is about computing the magnitude of a 4-vector, specifically the four-momentum of a photon traveling in the positive x-direction. The individual attempting the computation is questioning why their calculation resulted in a magnitude of 0 and is seeking clarification on their error.
  • #1
Jonsson
79
0
Hello there,

Given any 4-vector ##x = (x_0,x_1,x_2,x_3)##, hvor do I compute its magnitude? I couldn't find a simple explanation online.

For example I want to compute the magnitute of the momenergy 4-vector of a photon traveling in the positive x-direction where ##E## is the energy of the photon and ##P_\mu = (E,E,0,0)##. What is incorrect in the following computation of its magnitude?
$$
(P_\mu\,P^\mu)^{1/2} = (E^2-E^2)^{1/2} = 0
$$

Surely the magnitude of the vector should not be ##0##? Can you help? Thank you for your time.

Kind regards,
Marius
 
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  • #2
It is 0. You did it correctly. The magnitude of the four momentum is the mass and light is massless.
 

Related to How Do You Calculate the Magnitude of a 4-Vector?

1. What is a 4-vector in physics?

A 4-vector is a mathematical object that contains four components and is often used in physics to describe the properties of a physical system in spacetime. It combines the three components of space (x, y, z) with the time component (t) into a single mathematical entity.

2. Why is it important to compute the magnitude of a 4-vector?

The magnitude of a 4-vector is an important quantity in physics as it represents the overall magnitude or length of the vector in spacetime. It can provide information about the energy and momentum of a physical system, which are crucial in understanding the behavior of particles and their interactions.

3. How do you compute the magnitude of a 4-vector?

To compute the magnitude of a 4-vector, you need to use the Minkowski metric, which is a mathematical tool used to measure distances in spacetime. The formula for calculating the magnitude is the square root of the dot product of the vector with itself, taking into account the sign and units of the metric.

4. What are the steps involved in computing the magnitude of a 4-vector?

The steps involved in computing the magnitude of a 4-vector include identifying the components of the vector in spacetime, converting the units to the appropriate system, applying the Minkowski metric, and finally taking the square root of the dot product to find the magnitude. It is also important to correctly identify the sign of the metric in the calculation.

5. Can you provide an example of computing the magnitude of a 4-vector?

Yes, for example, if we have a 4-vector with components (2, 3, 4, 5) in units of meters, and we use a Minkowski metric with the signature (-1, 1, 1, 1), the magnitude would be calculated as follows:
Magnitude = √((-2)^2 + 3^2 + 4^2 - 5^2) = √(4 + 9 + 16 - 25) = √(4) = 2 meters.

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