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Stranger
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I was wondering what mass means in a 2 dimensional world...
Originally posted by Stranger
I was wondering what mass means in a 2 dimensional world...
mass is the invariant length of momentum. mass is the coefficient of the "potential" term of the particle field lagrangian. mass is a particle s resistance to acceleration
No. With relativity, mass is most definitely not invariant.Originally posted by lethe
mass is the invariant length of momentum.
uhh...? are you sure? you should double-check your textbook, eh?Originally posted by FZ+
No. With relativity, mass is most definitely not invariant.
Originally posted by FZ+
Ah sorry. Thought you were referencing relativistic mass or matter <-> energy conversions.
Of the two, the definition of invariant mass is much preferred over the definition of relativistic mass. These days, when physicists talk about mass in their research, they always mean invariant mass. The symbol m for invariant mass is used without the subscript 0. Although the idea of relativistic mass is not wrong, it often leads to confusion, and is less useful in advanced applications such as quantum field theory and general relativity. Using the word "mass" unqualified to mean relativistic mass is wrong because the word on its own will usually be taken to mean invariant mass. For example, when physicists quote a value for "the mass of the electron" they mean its invariant mass.
"Ouch! The concept of `relativistic mass' is subject to misunderstanding. That's why we don't use it. First, it applies the name mass--belonging to the magnitude of a four-vector--to a very different concept, the time component of a four-vector. Second, it makes increase of energy of an object with velocity or momentum appear to be connected with some change in internal structure of the object. In reality, the increase of energy with velocity originates not in the object but in the geometric properties of space-time itself."
"It is not good to introduce the concept of the mass M = m/(1-v2/c2)1/2 of a body for which no clear definition can be given. It is better to introduce no other mass than `the rest mass' m. Instead of introducing M, it is better to mention the expression for the momentum and energy of a body in motion."
Originally posted by Stranger
I'm sorry...i know the last one ...and quiet a bit about the 1st one...but the second one...
the attraction from the circle cancels out in every direction.
Originally posted by Stranger
How? Is the thickness a 2 dimensional object equal to that of plank length...
i m still not really sure what you re trying to ask, but i can assure you, the Planck length has nothing to do with geometry, or classical gravitation.
Originally posted by Stranger
No...I was just wondering if there really was no thickness...anyway...its mathematical...so the thought that a 3 dimensional being can rip the two dimensional being or object from its 2 dimensional world doesn't seem to work...because he will have nothing in his hand...if he does then he can tell that it has some thickness...
2D object is only approximately 2D, and actually has some thickness.
Wow, lethe, it looks like you're being particularly patient with this one. I would have thumbed my nose and referenced Halliday and Resnick by now.
Mass in 2D refers to the amount of matter contained within a two-dimensional space. It is a measure of the inertia or resistance to change in motion of an object in a 2D plane.
Mass in 2D only takes into account the amount of matter in a two-dimensional space, while mass in 3D includes the amount of matter in a three-dimensional space. This means that mass in 2D is a simplified version of mass in 3D and is often used in simplified models or calculations.
The formula for calculating mass in 2D is mass = density x area. Density is the measure of how much matter is packed into a given space, while area is the measure of the two-dimensional space. This means that the mass in 2D is directly proportional to both the density and the area.
Some examples of mass in 2D include thin objects like paper, sheets of metal, or flat surfaces such as a tabletop. In these cases, the mass is spread out over a two-dimensional space, rather than being concentrated in a specific volume.
The mass in 2D affects an object's motion by determining its inertia. The greater the mass in 2D, the more inertia an object will have, making it harder to change its motion. This can be seen in objects like frisbees or paper airplanes, where a lighter mass results in easier changes in motion compared to a heavier mass.