Force and special relativity.

In summary, the conversation discusses the change in magnitude of force when one frame is moving with respect to another at a high speed in the context of Special Relativity. It is mentioned that the magnitude of 4-acceleration and 4-force remain invariant, but 3-acceleration and 3-force are affected by the Lorenz transform. It is also noted that the magnitude of force is measured differently along the direction of motion compared to perpendicularly. The need for a specific example is emphasized.
  • #1
bgq
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Hi,

Does the magnitude of the force change when the frame moves with a high speed with respect to another frame at rest? If yes, How?

Thanks for any replies.
 
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  • #2
Are you familiar with four-vectors? If so, the easiest way to understand force in relativity is to look at how the four-force transforms:

http://en.wikipedia.org/wiki/Four-force

If not, let me know and I will try to find a different reference, but it won't be as easy to understand.
 
  • #3
DaleSpam said:
Are you familiar with four-vectors? If so, the easiest way to understand force in relativity is to look at how the four-force transforms:

http://en.wikipedia.org/wiki/Four-force

If not, let me know and I will try to find a different reference, but it won't be as easy to understand.

Actually I am sorry, I am not familiar with four-vectors; however, I am not looking for a detailed derivation, I am just looking for a simple equation that allows me to calculate the magnitude of a force in an inertial frame if the magnitude is known in an other inertial frame - something like Lorentz transformation.
 
  • #4
In Special Relativity the force acting on a particle is not always parallel to its acceleration. It is parallel only when the acceleration is either parallel or perpendicular to the velocity. Also, force can be defined in more than one way. If you define it as the change of the particle's momentum with respect to coordinate time, then

f = γ ma + γ3 mv dv/dt v/c2

On the other hand, if you want to define it as the change of momentum with respect to the particle's proper time, multiply the above by γ:

F = γ2 ma + γ4 mv dv/dt v/c2
 
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  • #5
bgq said:
Hi,

Does the magnitude of the force change when the frame moves with a high speed with respect to another frame at rest? If yes, How?

Thanks for any replies.
First what do you mean by "the force"? What force are you talking about? We know, since Galileo, that force is proportional to acceleration. As long as one frame is moving at a constant speed, with respect to another, acceleration, and so "force" should remain the same.
 
  • #6
HallsofIvy said:
First what do you mean by "the force"? What force are you talking about? We know, since Galileo, that force is proportional to acceleration. As long as one frame is moving at a constant speed, with respect to another, acceleration, and so "force" should remain the same.

Well, the magnitude of 4-acceleration is invariant, thus also magnitude of 4-force. However, 3-acceleration (either coordinate or by proper time) is not a vector under the Lorenz transform, and its magnitude is not a scalar invariant.

Trivial example: a world line with constant coordinate acceleration in one IRF transforms to a world line with time varying coordinate acceleration in another IRF.
 
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  • #7
bgq said:
Hi,

Does the magnitude of the force change when the frame moves with a high speed with respect to another frame at rest? If yes, How?

Thanks for any replies.
I take that you mean if the magnitude of a force is measured differently with systems in relative motion. It depends on the direction of the force: along the direction of motion the force is measured the same.
Fx'= Fx

However, perpendicularly it is not the same. For an object that is at rest in the moving system:
Fy'= γ Fy

It's more complex if the object is also moving in the moving system.

In order to avoid confusion (in view of the different answers here), it may be useful if you give an example of what you have in mind exactly.
 
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1. What is force?

Force is a physical quantity that describes the interaction between two objects. It is typically measured in units of Newtons (N) and can be represented as a vector quantity with both magnitude and direction.

2. How does force affect motion?

According to Newton's Second Law of Motion, force is directly proportional to an object's acceleration. This means that the greater the force applied to an object, the greater its acceleration will be. Additionally, if there is no net force acting on an object, it will remain in a state of constant motion (either at rest or moving at a constant velocity).

3. What is special relativity?

Special relativity is a theory developed by Albert Einstein that describes the relationship between space and time. It states that the laws of physics are the same for all observers in uniform motion, and the speed of light is constant regardless of the observer's frame of reference.

4. How does special relativity impact our understanding of force?

Special relativity introduces the concept of relativistic mass, which states that an object's mass increases as its velocity approaches the speed of light. This means that the force required to accelerate an object also increases as its velocity approaches the speed of light.

5. Can special relativity be applied to everyday situations?

Yes, special relativity has been proven to be accurate and is used in various technologies, such as GPS systems and particle accelerators. However, the effects of special relativity are only noticeable at very high speeds or in extreme scenarios, so it may not be directly applicable to everyday situations.

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