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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.Originally posted by Stranger
I was wondering what mass means in a 2 dimensional world....
Can you please elaborate on this....thanksmass 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.
Originally posted by FZ+
No. With relativity, mass is most definitely not invariant.
relativistic massOriginally 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.
-wheeler"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."
-einstein"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."
well, fields act a lot like harmonic oscillators, that is to say, they act like springs. springs obey hookes law, which states that the restoring force is proportional to the displacement. in other words, F=-kx. it s easy enough to see from this definition that the potential energy of a spring is 1/2kx^{2}. the lagrangian is then, by definition, T - V = 1/2mv^{2} - 1/2kx^{2}.Originally posted by Stranger
I'm sorry.....i know the last one ...and quiet a bit about the 1st one...but the second one...
How??? Is the thickness a 2 dimensional object equal to that of plank length....the attraction from the circle cancels out in every direction.
a 2 dimensional object has 2 dimensions. if you call one length and one width, and you want to call thickness the measure in the third or any higher dimension, then the thickness of any 2 dimensional object is 0. 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
How??? Is the thickness a 2 dimensional object equal to that of plank length....
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....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.
i am not really sure how a three dimensional object would interact with a dimensional object.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....
Yes...thats what I was thinking of...Its kinda hard to imagine something without a thickness.....so I think it can also be that our 3D space also has a little extensin in 4D space....every 3 D object....2D object is only approximately 2D, and actually has some thickness.
You mean he is being patient with me....lethe is just helping me out..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.