Can someone explain the 4-force to me.

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In summary: The energy-momentum four-vector, p, combines the concepts of energy and momentum into a single mathematical object, making calculations and understanding relativistic systems easier. The fourth component, time, allows for the inclusion of time dilation and other relativistic effects in the calculations. Overall, using four-vectors simplifies the equations and makes them more elegant and concise. And yes, it is possible to solve problems using only three-vectors, but using four-vectors can often provide a more complete and accurate understanding of the system.
  • #1
ozone
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I understand that we can write the 4-force in terms of the vector force based on velocity, and the energy of the system in general.

What I don't understand is what this gains for us, and why we use it. Also correct me if I am incorrect in my definition above.. I don't have my book infront of me.
 
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  • #2
Knowing [itex]dp/d\tau = f[/itex] isn't useful?
 
  • #3
no that's very useful. I don't understand though why we have a vector we call the energy-momentum four-vector,

defined as
[itex]p = (E, p) [/itex]

Where the vector p is just our ordinary momentum.

Also we have a 4-vector force defined as
[itex]f = (\gamma F \cdot V, \gamma \text{ }F)[/itex]

Obviously both terms contain standard 3-vector, but I'm not sure what physical good the fourth piece is.

This is out of James Hartle's Intro to relativity.
 
  • #4
I'm not sure I understand what "fourth" piece you're referring to.

At any rate, I find the formulas for converting between ordinary force and four-force (and the same for acceleration) to be very annoying and tedious. I personally try to avoid dealing in ordinary force and acceleration precisely for this reason. It's just much easier to deal only with four-vectors or only with three-vectors and not constantly convert back and forth between them.
 
  • #5
The fourth piece (the time piece) is just confusing to me.. I understand having momentum in terms of velocity but my book doesn't really explain why/what the 4th piece of the vector is.

Also I solved a relativistic energy conservation problem (in the lab frame) and I am pretty sure I only needed to use the 3-vector but I want to make sure that I did that correctly.
 
  • #6
The time component of the four-force is basically the power the force applies to the object in question.
 

1. What is the 4-force?

The 4-force is a concept used in physics and is a combination of the 3-dimensional force and the force of time. It is represented as a 4-dimensional vector with components of 3-dimensional force and the force of time.

2. How is the 4-force different from regular force?

The 4-force takes into account the force of time and incorporates it into the traditional 3-dimensional force. This allows for a more comprehensive understanding of the effects of force on objects in the universe.

3. Can you give an example of how the 4-force is used?

One example of the 4-force in action is in the study of relativity. In this theory, the 4-force is used to describe the force that an object experiences due to the curvature of spacetime caused by the presence of massive objects.

4. How is the 4-force calculated?

The 4-force is calculated using a mathematical equation known as the 4-force equation. It involves multiplying the 3-dimensional force vector by the 4-velocity vector, which represents the movement of an object through spacetime.

5. What is the significance of the 4-force in physics?

The 4-force is significant because it allows for a more complete understanding of the forces at play in the universe. It helps to explain phenomena that cannot be fully understood using traditional 3-dimensional force equations, such as the effects of gravity and the behavior of particles at high speeds.

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