What's so special about C?

[IIRichard]

Not to throw too much confusion in here, but physicists no longer use the term "relativistic mass", nor do they talk about "mass increasing", nor do they use E = mc^2. The term "mass" is reserved for the invariant mass, or rest mass. So it is true that it takes infinite energy for an object with mass to achieve the speed of light, but not that the "mass" becomes infinite. For particles with nonzero mass, the modern version of Einstein's famous equation is E = gamma*mc^2.

Even Einstein himself was trying to get away from the whole "relativistic mass" usage, since he said it created more confusion than it resolved.

Thanks

 

[drkitten]

I share many of the questions that Pragmatist brought up. Why would your mass go to INFINITE when you get closer to light? I can understand that your mass could increase as you accelerate but can't understand how your mass would become infinite.

Your mass-energy becomes closer to infinite as your speed becomes closer to that of light. Mathematically, this can be expressed as as a formula in which the term (c - v) appears in the denominator of a fraction. When c > v, then the term is finite, but gets smaller and smaller as v gets closer to c. Dividing by a smaller and smaller number results in a larger and larger overall energy -- if v actually were equal to c, you would be dividing by zero, which gives an "infinite" overall energy.

For a physical intuition about how it happens, you can think about the amount of work it takes to accelerate a heavy object compared to a light object. Trucks don't accelerate as fast as cars, which don't accelerate as fast as motorcycles. But since adding energy makes something heavier, the faster it is going, the harder it is to accelerate further -- and, like Zeno's hare, you never actually catch up to the speed of light.

Alternatively, you can think of it in terms of length contraction and time dialation. As you get closer and closer to the speed of light, your meters get shorter and your seconds get longer. So an acceleration of 10 m/s is "really" (to an outside observer) 10 millimeters per hour, or 10 nanometers per month. Again, you will never actually catch up, because the faster you go, the smaller your "real" acceleration is.

 

[bigred]

When?



His genius.



When?



He didn't.

Don't you love it when someone gives pointless non-answers to questions in a (failed) attempt to look clever and witty OMG LMAO

 

[Darat]

Don't you love it when someone gives pointless non-answers to questions in a (failed) attempt to look clever and witty OMG LMAO

You forget your question mark.

 

[SkepticalScience]

Oh - interesting post new drkitten.

So if (c-v) is in the denominator of the fraction - isn't that just a result of how the equation was set up?


A zero as a denominator is Undefined, not infinite. Meaning, that

1/0 does not equal 5/0. It just invalid. . .not infinite.

So maybe it's an urban legend that your mass approaches infinity. Because I still haven't heard, what happens at the molecular level that causes your mass to increase.

I mean, do your protons get larger or something? And if so - why?

 

[drkitten]

Oh - interesting post new drkitten.

So if (c-v) is in the denominator of the fraction - isn't that just a result of how the equation was set up?

A zero as a denominator is Undefined, not infinite. Meaning, that

1/0 does not equal 5/0. It just invalid. . .not infinite.

You're not treating the math properly. The expression 1/0 is undefined, but the limit of the quanitity 1/x, as x approaches 0, is well-defined as being infinite. Or if your analysis teacher didn't permit you to regard infinity as an actual limit value, then you can express that the value 1/x increases without limit as x approaches zero.

So as the difference (c-v) approaches zero, your mass-energy increases without limit.

So maybe it's an urban legend that your mass approaches infinity. Because I still haven't heard, what happens at the molecular level that causes your mass to increase.

I mean, do your protons get larger or something? And if so - why?

They get more energetic, and since energy and (relativistic) mass are equivalent (sorry, rppa), they are therefore more massive. And it's not just your protons, but everything about you. Again, a more formal statement is that you are gaining energy (by accelerating).

 

[rppa]

They get more energetic, and since energy and (relativistic) mass are equivalent (sorry, rppa), they are therefore more massive. And it's not just your protons, but everything about you. Again, a more formal statement is that you are gaining energy (by accelerating).

Two good summaries from the sci.physics FAQ:


If you go too fast, do you become a Black Hole?

In part the misunderstanding arises because of the use of the concept of relativistic mass in the equation E = mc2. Relativistic mass, which increases with the velocity and kinetic energy of an object, cannot be blindly substituted into formulae such as the one that gives the radius for a black hole in terms of its mass. One way to avoid this is to not speak about relativistic mass and think only in terms of invariant rest mass.

and
Does mass change with velocity?

Despite the general usage of invariant mass in the scientific literature, the use of the word mass to mean relativistic mass is still found in many popular science books. For example, Stephen Hawking in A Brief History of Time writes "Because of the equivalence of energy and mass, the energy which an object has due to its motion will add to its mass." and Richard Feynman in The Character of Physical Law wrote "The energy associated with motion appears as an extra mass, so things get heavier when they move." Evidently, Hawking and Feynman and many others use this terminology because it is intuitive and useful when you want to explain things without using too much mathematics. The standard convention followed by some physicists seems to be: use invariant mass when doing research and writing papers for other physicists but use relativistic mass when writing for non-physicists. It is a curious dichotomy of terminology which inevitably leads to confusion.

In a 1948 letter to Lincoln Barnett, Einstein wrote
"It is not good to introduce the concept of the mass M = m/(1-v^2/c^2)^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."

 

[phildonnia]

Well, it's high enough level to be somewhat portable, but close enough to the machine to do system programming.

Oh, not the programming language? never mind...


--Terry.

That was my first thought. Anyway the correct answer is:

1) It's a powerful antioxidant, and was endorsed by Linus Pauling for prevention of the common cold
2) The natural tones of the key contain no sharps or flats, so it's easiest to learn on a keyboard instrument
3) It's for "cookie", that's good enough for me.