Why does Newtonian dynamics break down at the speed of light

[DrStupid]

According to SR, a constant number of water molecules (amount of matter) will increase in mass when heated due to increased kinetic energy. According to Newton's mechanics the mass is fixed.

That does not result from definition 1.

According to Newton's mechanics, the mass of all particles together ("condensed" or other) equals the sum of all particles separately.

By replacement of Galilean transformation by Lorentz transformation Newton's quantity of matter turns into relativistic mass and relativistic mass is additive.

The fact that this is not exactly the case is therefore called mass "defect".

That's another topic. Mass defect is the difference of the total rest mass of a system (including binding energy and kinetic energies) and the sum of the rest masses of its sub systems (excluding binding energy between them). That doesn't contradict Newton because he didn't make corresponding claims.

 

[zoki85]

There's no "rest mass" becouse there's no "relaivistic mass". Mass doesn't depend on velocity. Therefore, there is just mass .

 

[harrylin]

That does not result from definition 1.

It is stated that mass equals "amount of matter" and it is implied that it is not a function of temperature or speed. You will search in vain for any such a relationship in classical mechanics.

By replacement of Galilean transformation by Lorentz transformation Newton's quantity of matter turns into relativistic mass and relativistic mass is additive. [..]

We disagree about how to present the same facts; I'm afraid that we will have to agree to disagree. Newton's quantity of matter is not a function of speed. The Newtonian definitions and laws resulted in (or gave an explanation for) the "Galilean transformations" which Newton's mechanics assumed to be correct. The "relativistic mass" and "invariant mass" concepts came about because Newton's mass concept - as well as his time and length concepts - could not be maintained in relativity theory.

In order to stay within the bounds of this forum, I won't comment on claims about relativity theory in this thread. However, if you can show mass increase due to temperature increase in Newton's mechanics, I'll be happily corrected!

 

[brainpushups]

Even Newton's (well, Newton's and Euler's) definitions of mass are a little mixed up. Indeed, Newton defines mass as the amount of matter, but the operational definition of mass (in terms of the second law) is that mass is a measure of inertia.

Also the definition of mass is often used differently in relativity. Most authors now prefer to define the mass of an object the invariant mass while others use variable mass.

 

[DrStupid]

It is stated that mass equals "amount of matter" and it is implied that it is not a function of temperature or speed.

Quantity of matter is Newton's name for his concept of mass but not its definition. You must not confuse it with amount of substance or similar modern concepts. I totally agree with brainpushup that quantity of matter is a measure for inertia.

Newton's quantity of matter is not a function of speed.

Not in classical mechanics, but in special relativity.

The Newtonian definitions and laws resulted in (or gave an explanation for) the "Galilean transformations"

That does not apply to definition 1-2 and lex 1-3. They work with Lorentz transformation as well.

The "relativistic mass" and "invariant mass" concepts came about because Newton's mass concept - as well as his time and length concepts - could not be maintained in relativity theory.

In special relativity the relativistic mass directly results from Newton's quantity of matter (as defined by definition 2, lex 2 and lex 3).

In order to stay within the bounds of this forum, I won't comment on claims about relativity theory in this thread.

Than you must not post in this thread at all. The break down of Newtonian dynamics at the speed of light is well outside classical mechanics.

However, if you can show mass increase due to temperature increase in Newton's mechanics, I'll be happily corrected!

Why should I do that? It is sufficient that Newton's mechanics does not exclude an increase of quantity of matter due to temperature increase. In addition it is in agreement with historical concepts of heat (e.g. phlogiston).

Also the definition of mass is often used differently in relativity. Most authors now prefer to define the mass of an object the invariant mass while others use variable mass.

That's why it is better to use Newton's term quantity of matter to avoid confusions with mass (zoki85 already got caught in that trap).

 

[Vanadium 50]

DrStupid, are you just arguing for the sake of arguing?