E=mc^2

Your statment is incorrect. Mass is a Lorentz relativistic invariant. This mean that mass is not dependent on the speed. What increase to infinity when a massive particle approches the speed of light is not its mass but its energy.

(p. 40)
      REAL SACRIFICES

The faculty, upon occasion, of converting energy into matter
and matter into energy, constitutes one of the most wonderful
characteristics of chess, and reveals, perhaps, the innermost
secret of its fascination.
   The question: "How can I favorably turn matter into
energy?" occurs as a rule in the early part of the game; the
converse is more likely to obtain for the later phase. We are
now concerned with the transformation of matter into energy
--the sacrifice of material for the sake of dynamic advantages.

Spielmann, Rudolf. 1995. The Art of Sacrifice in Chess. New York: Dover Publications, Inc.

You're defining mass as the resting mass.  It's true that objects have a non-relativistic mass that never changes with velocity, but it's kind of pointless to worry about that, because nothing in the universe is actually at rest ;)...

If you prefer it can be stated this way:

with an increase of the speed of an object you need more and more energy in order to make it move faster.

An increase in energy is an increase in mass. This is precisely the meaning of 

In other words, this equation relates both rest mass to rest energy, and total energy to relativistic mass.

Well, for a massive particle you can defined a refence frame where the particle is at rest.

Ernegy (or more preciselsy the energy squared) can be written as

E^2 = m^2 *c^4 + p^2*c^2

For mass less particles, like photons, we get

E = pc

and for massive particle we get

when at rest

E^2 = m^2 *c^4

and when it is moving we get

E^2 = m^2 *c^4 + p^2*c^2

The increase in energy is purely due to the second part ( p^2*c^2).

There is no increase in the mass m of the particle.

You should review your physics textbook again. You'll see that the equation is actually

The subscript on the m means that this equation only applies to the rest mass. Relativistic mass increases with velocity, given precisely by 

Both sides vary implicitly with velocity such that the equation always holds true. The explicit variation of energy with velocity is given by

Thanks Ticklish !....sorry this's 9 months delayed........

Not that Tickler's right....just that he tried.

....and BTW, I always thought mass is a universe invariable.

Signed:

Somewhat Left Confused

The third option is that you don't comprehend in the slightest what you are being told. The velocity dependence is present via the momentum term.

You seem to expect an entire course on relativity to be condensed for you, and instantly abuse anyone who match the explanation to your level of ignorance. Indeed, you are even too lazy to realize that the obvious "punch you in the face" equation has already been given 9 months ago.

I suggest you check your attitude at the door.

(#57) Do any of the nascent physicists out there know where the idea of increasing mass as proportional to an increase in velocity comes from?

****

Uhhh, No....not me.

Signed:

Sheepishly Left Wondering

A critique of my reading comprehension? Oh the irony. You do realize that 'to check at the door' actually means to offload said thing at entrance? The expression comes from checking your coat at the door.

You know, I am usually quite happy to have long discussions on interesting physical concepts, and elaborate in great depth. But not when I am blithely accused of incompetence based on nothing but ignorance.

There is no need for a subscipt because the only meaningful mass is the rest mass.

As Einstein worte in 1948:

"It is not good to introduce the concept of the mass of a moving body for which no clear definition can be given. It is better to introduce no other mass concept 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."

Since you seem to be a bit confused, please, let me recomend you a good text book: "The classical theory of fields" by L.D. Landau and E.M. Lifschitz.

http://www.amazon.com/Classical-Theory-Fields-Fourth-Edition/dp/0750627689

You are presenting a point of view as if it were fact. Einstein actually prefered to work in terms of the relativistic mass in his original papers, before changing his mind later.

There is no doubt that momentum is given by

But whether or not a relativistic mass is introduced on the right hand side is a matter of taste. It gives mathematically equivalent results and certainly is not wrong, which by being blind to the existence of a relativistic mass up to now, you implied in all your posts.

 There are several issues with the use of relativistic mass:

• The notion of relativistic mass can, and usually does, lead to misunderstanding and wrong representation of physical phenomena.
• The concept of relativistic mass does not give you any new insight in the physics.
• Theory of special relativity can be explained without the introduction of the concept of relativistic mass. So, when you consider also my first two remarks, then what is the point of introducing the concept in the first place?
• The concept of relativistic mass can’t be extended to more general cases and actually has to be discarded by people who want to dwell deeper in the subject.
• The theory of relativity is often described as the most beautiful theory in physics. It is indeed beautiful and elegant, but the introduction of the concept of relativistic mass destroys the elegance of the theory.

Therefore, as we are now in the 21st century, it is not wise to talk about relativistic mass.