# Mass and spin under acceleration

• metroplex021
In summary, the conversation discusses the preservation of rest mass and spin of a particle under Lorentz transformations and whether it applies to accelerated observers. It is mentioned that for point particles, local Poincare invariance allows for the definition of mass and spin. For extended particles, the situation is more complicated and there is a discussion on defining mass and angular momentum. Finally, the question is raised about the preservation of mass and spin for observers accelerating relative to each other in flat spacetime.
metroplex021
Hi folks,

In his seminal work of 1937, Wigner showed that the rest mass and (absolute) spin of a particle are the same for all observers related by Lorentz transformation. Does anyone know whether these quantities are also preserved under transformations to relatively accelerated observers (including those rotating w/r/t each other)?

Many thanks!

For point particles, we can use general covariance and the properties of a manifold to define mass and spin. Basically, in a small enough neighborhood of a point, we can introduce flat coordinates. So we have local Poincare invariance to allow us to define mass and spin. Since the flat coordinates have to map nicely on intersections of neighborhoods, when we extend this to the rest of the manifold we will find that all observers must agree on the mass and spin of the particle.

For extended particles like the proton, in any experiment that we could actually do, the curvature is constant over the microscopic size of the particle, so we can treat them like point particles. For extended systems (size comparable to the distances over which the curvature is varying), it can be very complicated to define mass and angular momentum. See this wiki for an extensive discussion and references.

1 person
Thanks for that! But can I ask how the situation looks even in flat spacetime? I appreciate that observers related by Poincare transformations will always agree on the proper mass and absolute spin of a particle, but what about observers accelerating w/r/t each other, even in Minkowski spacetime?

Any thoughts much appreciated!

## 1. What is mass under acceleration?

Mass under acceleration refers to the property of an object that determines how much resistance it will have to changes in its motion when a force is applied. It is a measure of the amount of matter an object contains and is directly proportional to its inertia.

## 2. How does mass affect acceleration?

Mass has an inverse relationship with acceleration, meaning that the greater the mass of an object, the less it will accelerate when a given force is applied to it. This is described by Newton's second law of motion, which states that acceleration is equal to the net force acting on an object divided by its mass.

## 3. What is spin under acceleration?

Spin under acceleration refers to the rotation of an object as it moves in a curved path or around an axis. This is caused by the application of a torque or rotational force on the object, which results in a change in its angular momentum.

## 4. How does spin affect acceleration?

Spin can affect acceleration in different ways depending on the situation. In some cases, spin can help stabilize an object and increase its acceleration, such as in the case of a spinning top. However, in other cases, spin can create resistance to acceleration, such as when a spinning object experiences gyroscopic precession.

## 5. How are mass and spin related under acceleration?

Mass and spin are related under acceleration in that both properties affect how an object will respond to a force. The mass of an object determines its inertia, while the spin of an object affects its rotational motion. Together, these factors determine the overall acceleration of an object under the influence of a force.

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