# Does Weight Change with Reference Frame? A Question Explored

• lightarrow
In summary, the conversation discusses the effects of acceleration on weight and the use of 4-forces to calculate the weight of an object in different reference frames. It is possible for the reading on a scale to change depending on the observer's frame of reference due to the concept of 4-forces and the transformation of 4-vectors according to the Lorentz transform.
lightarrow
Sorry for the trivial (and certainly already covered) question.
Does a body's weight change with the ref. frame? If I had a very long scale on which the body can move without friction, would I observe the scale to sign different values according if I am stationary with the scale or with the object?

Basically, yes. If you assume that the scale is in an accelerating rocketship (to provide the acceleration needed to impart weight) the reading on the scale (assumed to be oriented so the pans are perpendicular to the direction of acceleration) will increase by a factor of gamma = sqrt(1-v^2/c^2).

Note that if the scale isn't oriented perpendicular to the direction of acceleration, the problem becomes a lot more complex.

pervect said:
Basically, yes. If you assume that the scale is in an accelerating rocketship (to provide the acceleration needed to impart weight) the reading on the scale (assumed to be oriented so the pans are perpendicular to the direction of acceleration) will increase by a factor of gamma = sqrt(1-v^2/c^2).

Note that if the scale isn't oriented perpendicular to the direction of acceleration, the problem becomes a lot more complex.
First of all, thanks for the answer.
Can you explain how this is possible? Which is the meaning of "reading the body's weight on the scale" for any observer? Shouldn't it be independent of the fact the observer moves or not with respect to the body?

The scale has its own frame - the main point of interest is the force on the scale in its frame, but it is possible to define the notion of force relativistically for any observer.

Relativistically, this is most conveniently handled by the concept of a 4-force. If we assume our mass is pointlike (or at least very small), we can find the 4-force by multiplying the mass m of our weight by the 4-acceleration.

The 4-acceleration is just the rate of change of the 4-velocity with respect to proper time.

See for instance http://en.wikipedia.org/wiki/Special_relativity#Force

Another way of saying this - the three-force is the rate of change of the momentum of the mass m with respect to coordinate time. The four-force is the rate of change of the energy-momentum 4-vector with respect to proper time. So the 4-force has one additional component (the rate of change of energy with respect to proper time), and is computed with respect to proper time rather than coordinate time.

The reason to use 4-forces rather than 3-forces is that they transform via the Lorentz transform. In fact, this is a property of any of the various 4-vectors that I've mentioned - all 4 vectors transform in an identical manner (that's their defining characteristic) - i.e. they transform via the Lorentz transform.

Thank you very much.
lightarrow

## 1. How does weight change with reference frame?

Weight is a measurement of the force of gravity on an object. Therefore, weight does not change with reference frame because gravity remains constant regardless of the reference frame being used.

## 2. Can weight appear to change with different reference frames?

Yes, weight can appear to change with different reference frames because the perception of weight can be influenced by factors such as acceleration and motion. However, the actual weight of an object remains constant.

## 3. Does weight change when an object is in motion?

No, weight does not change when an object is in motion. The perception of weight may change due to the effects of acceleration and motion, but the actual weight of the object remains the same.

## 4. How does the theory of relativity relate to weight and reference frames?

The theory of relativity states that the laws of physics are the same for all observers, regardless of their reference frame. This means that weight remains constant in all reference frames, as gravity is a fundamental force that is not affected by the observer's perspective.

## 5. Can weight change in a weightless environment?

In a weightless environment, such as in space, the perception of weight may change due to the absence of gravity. However, the actual weight of an object remains the same, as weight is a measure of the force of gravity on an object.

• Special and General Relativity
Replies
51
Views
2K
• Special and General Relativity
Replies
11
Views
986
• Special and General Relativity
Replies
26
Views
2K
• Special and General Relativity
Replies
144
Views
6K
• Special and General Relativity
Replies
24
Views
1K
• Special and General Relativity
Replies
5
Views
1K
• Special and General Relativity
Replies
5
Views
1K
• Special and General Relativity
Replies
7
Views
844
• Special and General Relativity
Replies
35
Views
3K
• Special and General Relativity
Replies
2
Views
983