A question about forces in different references of frame

In summary, the conversation discusses the concept of force in relation to special relativity and maxwell's equations. The question is raised about whether an additional force is measured by an observer in motion compared to a stationary observer. It is suggested that the Minkowski force, a 4-vector, can be used to explain this discrepancy. However, it is debated whether force is truly invariant in this case. The conversation concludes with a recommendation to read an intermediate book on electromagnetics or relativity for further understanding.
  • #1
henry_arsenal
1
0
Hello Everyone, I'm new to this forum, I've to say here is one of the greatest physics communities in the net and I'm really glad I have the opportuninty to use the huge amount of information presented here.


By the way, I have a question about Electromagnetics:

Consider two stationary charges, +Q1 and +Q2 and an observer beside them. This observer measures a columbian force on both of the charges and nothing else.

Now, imagine an observer getting close to the charges at a relative speed of V. He should measure an additional force (rather than the former columbian force) produced by the magnetic field which exists due to the fact the the moving observer finds out that the charges are getting close to him at a speed of -V, of course from his point of view.

Both of the observers obey the laws of physics and maxwell's equations correctly, but they measure different forces on the charges. What is the correct answer to this problem?

I guess it should be related to the special relativity transformations, but I don't know how. I'll be thankful if you help me understanding how to solve this problem.

Thanks

Arman.
 
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  • #2
Force can be Lorentz transformed by introducing the "Minkowski force", which is a 4-vector. If you define force as [tex]{\bf F}=\frac{d\bf p}{dt}[/tex],
then the Minkowski force is given by
[tex]{\cal F}^\mu=\left[\gamma\frac{dE}{dt},\gamma{\bf F}\right].[/tex]
Transform this as a 4-vector, and then you can identify F in the new system.
 
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  • #3
Notice that the magnetic force in the moving frame is always in the opposite direction to the electric force. But, the distance between the charges appears less (because of length contraction), so their electric force is a little bit stronger. So everything's fine.

EDIT: I think my above explanation is wrong. If you picture the case where the span between the charges is perpendicular to their motion, then there is no length contraction, but the problem still happens. Does the force really change?

Meir Achuz: I think force is invariant in this case... am I missing something? I have no clue what Minkowski force is.
 
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  • #4
Forget the name, the definition is in the equation I wrote.
"Force" is not a Lorentz invariant.
Read an intermediate EM or relativity book.
 

1. What is the definition of a reference frame in physics?

A reference frame in physics is a coordinate system used to describe the position and motion of an object. It can be fixed or moving, and is used as a point of reference to measure and analyze forces acting on objects.

2. How do forces behave in different reference frames?

Forces behave differently in different reference frames, depending on their relative motion. In an inertial reference frame, where there is no acceleration, Newton's laws of motion apply and forces act in a predictable manner. However, in non-inertial reference frames, such as those that are accelerating or rotating, additional forces such as centrifugal or Coriolis forces may need to be considered.

3. Can forces be added together in different reference frames?

Yes, forces acting on an object can be added together in any reference frame. This is because forces are vectors, meaning they have both magnitude and direction, and can be added using vector addition. However, the resulting acceleration of the object may be different depending on the reference frame used.

4. What is the relationship between reference frames and the laws of physics?

The laws of physics, such as Newton's laws of motion, are true in all reference frames. However, the way these laws are observed and applied may differ in different reference frames. This is why understanding the reference frame of a system is important in accurately analyzing and predicting the behavior of objects.

5. How do you choose the most appropriate reference frame for a given scenario?

The most appropriate reference frame for a given scenario depends on the specific problem being analyzed. In most cases, it is best to choose an inertial reference frame that is most convenient for the problem at hand. However, in some situations, such as when dealing with rotating or accelerating objects, a non-inertial reference frame may be more suitable. It is important to carefully consider the motion and acceleration of objects when choosing a reference frame in order to accurately analyze forces.

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