Mass And Weight

[mozhigopi]

What are the difference between mass and weight?

[D H]

Depends on what you mean by weight.

 

Legally (at least in the US) and colloquially (in every English-speaking country), weight is a synonym for mass. In the eyes of the law and in the minds of most lay people, there is no difference between the two terms.

 

Physics uses weight to mean force. There are two different meanings even within physics. Most elementary physics texts and most engineering texts teach that the weight of an object is the gravitational force acting on the object. Some elementary physics texts and most advanced general relativity texts teach that the weight of an object is the quantity measured by an ideal spring scale. There is a big difference between these two definitions. Imagine you are in a windowless room and you step on a scale. The scale tells you your scale weight. It does not tell you your gravitational weight. The room might be firmly affixed to the surface of a planet, or it might be a room in an accelerating spacecraft. The scale cannot tell which is which.

[proton]

The scale tells you your scale weight. It does not tell you your gravitational weight.

General relativity holds that the two are identical.

[D H]

General relativity holds that the two are identical.

It would be silly for general relativity to say something that is demonstrably false. Fortunately, general relativity does not say this at all. You are conflating the equivalence principle with weight.

 

Gravitational weight is not even a concept in the framework of general relativity. The quantity registered by a scale most certainly is. A scale measures something real. Gravitational force is a pseudo force in general relativity. In other words, it is not real.

 

Newtonian mechanics struggles with the concept of weight because the simple definition used in most elementary texts represents something that is not measurable. In the context of Newtonian mechanics, gravitational force is not measurable because there is no way to shield gravity. In the context of general relativity, gravitational force is not measurable because it is a pseudo force.

 

In the context of Newtonian mechanics, a scale measures the net sum of all real forces acting on an object except for gravity. In the context of general relativity, a scale measures the net sum of all real forces acting on an object (period).

[proton]

It would be silly for general relativity to say something that is demonstrably false.

What is it that you are claiming that is demonstrably false.?

Fortunately, general relativity does not say this at all.

Not true.

You are conflating the equivalence principle with weight.

Also not true. I was referring to your comment

The room might be firmly affixed to the surface of a planet, or it might be a room in an accelerating spacecraft. The scale cannot tell which is which.

You misunderstood the point I was trying to make. I wasn’t disagreeing with you. All I was saying was that the reason why the scale can’t tell the difference is because general relativity holds that the two are identical in value and in nature. Let me start from scratch for the sake of clarity. Let us start with a definition of weight from a GR point of view. For this reason I will use the terms as defined in the following article

 

The equivalence principle and the question of weight, Kenneth Nordtvedt Jr., Am. J. Phys. 43(3), March 1975

The weight of a body is meant to be the force (e.g., the compression of a spring scale) required to either support the body in a gravitational field (gravitational weight) or to accelerate the body relative to inertial space (inertial weight).

You've probably seen weight defined differently in basic physics texts as being identical to gravitational force. Those texts usually define the term without considerations from general relativity in mind. This is not the best way to define weight. Not all authors define it that way though. One notable example is A.P. French in his text Newtonian Mechanics. French actually wrote up a nice article in AJP on why this was a better way to define weight. The article is On weightlessness, A.P. French, Am. J. Phys. 63 105 (1995). Randall Knight changed the way he defines weight in his basic physics text to be consistent with the definition above.

 

The equivalence principle can be stated as the gravitational forces are identical in nature to inertial forces. Therefore the equivalence principle it is impossible to distinguish whether the scale is measuring inertial weight or gravitational weight.

Gravitational force is a pseudo force in general relativity. In other words, it is not real.

Thank you for your personal opinion on whether the gravitational force is "real" or not. However I don't see how the classification of the gravitational force as being an "apparent" force or a "real" force effects how we make measurements and what the results of those measurements are. I try to stay away from arguements about semantical things like this so I'll state my personal opinion on this point and leave it at that (I hate semantics).

 

What you said is not quite right and it is most certainly not universally accepted. There are two different opinions on this point. One is the position that since the gravitational force is real and since they are identical in nature to inertial forces then inertial forces are also real. The other position is that inertial forces are pseudo-forces and since gravitational forces are identical in nature to inertial forces it follows that gravitational forces are also pseudo-forces. An example of the former can be found in the highly praised text The Variational Principles of Mechanics, by Cornelius Lanczos as well as French’s text mentioned above. Lanczos writes on page 98

Whenever the motion of the reference system generates a force which has to be added to the relative force of inertia I’, measured in that system, we call that force an “apparent force.” The name is well chosen, inasmuch as that force does not exist in the absolute system. The name is misleading, however, if it is interpreted as a force which is not as “real” as any given physical force. In the moving reference system the apparent force is a perfectly real force, which is not distinguishable in its nature from any other impressed force. Let us suppose that the observer is not aware of the fact that his reference system is in accelerated motion. Then purely mechanical observations cannot reveal to him that fact.

And it was Einstein who held that the gravitational force is “real” and for that reason also held that the Coriolis force was also “real.”

 

Have you ever read the book Theory of Relativity, by Wolfgang Pauli? The author notes this very thing on page 148

Gravitation in Einstein’s theory is just as much an apparent force as the Coriolis force and the centrifugal forces are in Newtonian theory. (We would be equally justified in taking the view that neither of the two forces should be called an apparent force in Einstein’s theory.

 

Newtonian mechanics struggles with the concept of weight because the simple definition used in most elementary texts represents something that is not measurable.

I don’t understand what you mean by this!? Are you saying that weight can’t be measured?

In the context of Newtonian mechanics, gravitational force is not measurable because there is no way to shield gravity.

I disagree. There is no reason why gravitational force can’t be measured. Why would you say otherwise?

In the context of general relativity, gravitational force is not measurable because it is a pseudo force.

Just because GR holds that gravitational forces are inertial forces it doesn’t mean that they can’t be measured.

In the context of Newtonian mechanics, a scale measures the net sum of all real forces acting on an object except for gravity. In the context of general relativity, a scale measures the net sum of all real forces acting on an object (period).

That is quite inaccurate. A scale works by requiring the body placed on the scale to be in mechanical equilibrium. This means that the contact force between scale and object must have the same magnitude but opposite direction as the gravitational force.

Edited June 20, 2009 by proton

[D H]

What is it that you are claiming that is demonstrably false.?

That gravitational weight is the same as scale weight.

 

Put a spring scale on your floor and stand on it. What it registers is *not* your gravitational weight. The earth is rotating. If you weigh 180 pounds and are standing at the equator, this corresponds to about 0.6 pounds-force difference between gravitational and scale weight. The Sun and Moon are also attracting you gravitationally, and this too contributes to your gravitational weight. Your scale does not measure this. It measures something different: the tidal gravitational force from the Sun and Moon.

 

Thank you for your personal opinion on whether the gravitational force is "real" or not. However I don't see how the classification of the gravitational force as being an "apparent" force or a "real" force effects how we make measurements and what the results of those measurements are.

A pseudo force is a force that vanishes when the equations of motion are written from the perspective of an inertial frame. The gravitational force vanishes in an inertial frame in general relativity. Gravity is an inertial force. There is no way to construct a device that measures an inertial force because in a very real sense, all inertial forces are not real. Note well: By "real" I mean "if you can't measure it its not real".

 

Inertial forces arise solely as a consequence of the reference frame used to model the system. Choose a different (non-inertial) reference frame and you will need different pseudo forces.

 

An accelerometer is in a sense a three dimensional spring scale. The accelerometers on a spacecraft are activated prior to launch. Those accelerometers had dang well better indicate that the spacecraft is accelerating at about 9.80665 m/s² up even though it is standing still. From the perspective of general relativity, the spacecraft is accelerating upward at about 9.80665 m/s². Accelerometers cannot measure the acceleration due to gravity because the acceleration due to gravity cannot be directly measured -- just as one cannot directly measure any other pseudo force.

 

That is quite inaccurate. A scale works by requiring the body placed on the scale to be in mechanical equilibrium. This means that the contact force between scale and object must have the same magnitude but opposite direction as the gravitational force.

That is inaccurate. One way to look at what a scale measures is from the perspective of an Earth-fixed frame. This is a non-inertial frame no matter how you look at it. You have to ensure you account for all of inertial forces that arise from using this frame.

[proton]

That gravitational weight is the same as scale weight.

 

Put a spring scale on your floor and stand on it. What it registers is *not* your gravitational weight. The earth is rotating.

If this were in the context of Newtonian gravity you'd be correct. But this is in the context of general relativity. In GR the inertial force contribution due to the rotation of the Earth is, by definition, part of the total gravitational force acting on the body.

A pseudo force is a force that vanishes when the equations of motion are written from the perspective of an inertial frame. The gravitational force vanishes in an inertial frame in general relativity.

All that means is that the value of the gravitational force is observer dependant. Just because something is observer dependant it doesn't mean that it doesn't exist. It only means that its existance depends on the observer. E.g. the electric field 4-vector is a vector which is defined in terms of the Faraday tensor and the observer's 4-velocity. For some observers this 4-vector is zero. For other observers its non-zero. In some instances radiation can have an observer dependant existance. For example; Suppose there is a charged particle at rest in a gravitational field. An observer who is at rest with respect to the charge will not detect any radiation. However if there is an observer who is in free-fall in the field then that observer will detect the radiation. That means that the existance of the radiation can be measured by some observers and for other observers it can't be detected.

 

In any case, I'd rather not discuss it in this thread. I'd rather not hijack the thread by going off on a tangent merely to discuss different opinions on metaphysics.

Edited June 20, 2009 by proton

[granpa]

What are the difference between mass and weight?

the same mass weighs more on the earth than it does on the moon