Is Energy-Mass Equivalence the Same in Pair Creation and Direct Conversion?

[carl fischbach]

It seems rather odd to me energy mass equivalancy
of pair creation would be the same as for the
the energy mass equivalancy of direct conversion of
energy to mass with increased velocity.
In the first case you are not only creating
mass but you are also creating particles.In the
the second case you are only losing or gaining
mass and not creating particles, any thoughts on
this.

 

[Tron3k]

Well Einstein sort of make an intellectual leap when he proposed that mass was simply a form of energy. He had found the equation:

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

And he saw that when momentum is 0, the energy is $mc^2$. So it shows that rest mass is also a part of the energy. So mass and energy must be equivalent.

Anyway, I know I haven't really answered your question. It is rather odd that the same formula is used. However, keep in mind that this formula has been verified in particle accelerators over and over, including for pair creation. So it's true

 

[HallsofIvy]

Are you asserting that there exist mass that is not connected with particles? What, exactly, are your definitions of "particle" and "mass"?

 

[carl fischbach]

particles and mass

What I am saying is the energy of creating a
particle exactly equivalent to it's mass or is
the energy of bringing a particle into existence with
it's properties different,no matter how small,
than the mass it posesses?

 

[Creator]

Originally posted by carl fischbach
It seems rather odd to me energy mass equivalancy
of pair creation would be the same as for the
the energy mass equivalancy of direct conversion of
energy to mass with increased velocity.

Why does it seem odd to you when Conservation of Energy requires it?

In the first case you are not only creating
mass but you are also creating particles.In the
the second case you are only losing or gaining
mass and not creating particles, any thoughts on
this. [/B]

Carl-
I think you if you use the most fundamental definition of mass you will avoid such conundrums.

Mass is most simply defined as "resistance to acceleration".
Thus in the first case (pair creation), you are creating particles that have the property of 'resisting acceleration'. In the second case, by increasing velocity you are merely increasing the 'resistance to acceleration'. The origin of mass (resistance to acceleration) has never been specified. As such mass becomes quite independent of the particles themselves.

Creator

 

[mathfeel]

Originally posted by carl fischbach
It seems rather odd to me energy mass equivalancy
of pair creation would be the same as for the
the energy mass equivalancy of direct conversion of
energy to mass with increased velocity.
In the first case you are not only creating
mass but you are also creating particles.In the
the second case you are only losing or gaining
mass and not creating particles, any thoughts on
this.

I think what you are confused about is that when a particle travels at high speed, its energy is:
$$E=\gamma m c^2$$
and when it's at rest, it's
$$E=mc^2$$
So, it seems as if when a particle travel at high speed, energy is now in some form of mass. I always think this interpreation is not appropriate. Mass is mass. Like proper length, you can only measure it realistically if you are in the particle's rest frame (i.e. there is only such thing as rest mass, no so call relativistic mass). As you gain speed, you don't gain mass, you gain kinetic energy. And the total energy is given by:
$$E^2=m^2c^4+p^2c^2$$
Where the second term is the kinetic energy term with:
$$p=\gamma m v$$
So we should just say that the theory of Special Relativity gives a different definition of momentum as a function of velocity as does the old Newtonian theory (p=mv).

I think the reason they defined relativistic mass $$m'=\gamma m$$ is that the new relativistic formula for total energy E as a function of v goes to infinity as v goes to the speed of light. So as your speed become closer and closer to the speed of light, you need more energy to increase your speed (in order to conserver energy). And this is perceived as a gain in mass (the ability of resist change in motion). I don't think I have a well-sounded argument again this, but I just don't like this interpretation. Because it makes it sound as if you can gain mass by simply gaining speed. Mass is a scalar and should be invariant under frame transformation.

I think the short answer to your question is: when a massive particle travel at high speed, it DOES NOT gain mass. It gain kinetic energy just like it does classically (though the formula is different). However we also find that energy and mass are equivalent, in the sense that such reaction as $$\gamma+\gamma \arrow e^++e^-$$happens and creates two particle out of two...shall we say...pockets of energy. So energy-mass equivalent is no more than conservation of energy. Where as the other kind of "mass", the so call relativistic mass you are talking about is not mass at all.