# Pair production (Electron, positron)

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How is it possible that the massless photon changes to two particles with mass,

The law of conservation of mass is not obeyed because this means during pair production mass is created

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There is no law of conservation of mass. Quite the contrary: The discovery that mass can be converted to energy, and that very little mass produces a lot of energy, has been a remarkable finding of physics in the early 20th century. The most well-known use is nuclear power plants, where part of the mass of decaying Uranium is converted to heat (and then to electricity). The more modern, but from your perspective even more alien view is that mass literally is a form of energy (I tend to think of it as "frozen energy"). In that view, you can take the famous E=mc^2 literally. There is a law of conservation of energy, but energy can be converted between different forms. In your example, it is converted from kinetic energy of the photons to mass-energy of the electron and the positron (and a bit of kinetic energy for both of them).

Note that the more general form of E=mc^2 is E^2 = (mc^2)^2 + (pc)^2 with p the momentum of the object - it simplifies to the more famous expression for zero momentum. I say this to make the connection to your other question where you asked about this equation.

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Eyshhhhhhhhh!  I get what Timo is saying. This means I'm teaching incorrect staff to high school learners tha the mass cannot be destroyed or created??

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24 minutes ago, Lizwi said:

Eyshhhhhhhhh!  I get what Timo is saying. This means I'm teaching incorrect staff to high school learners tha the mass cannot be destroyed or created??

There is nothing wrong with the law of conservation of mass in the right context.

Certainly it should be taught (in context) to high school students.

In Chemistry (which you seem to do most) it is the basis of chemical stochiometry (the balancing of chemical equations)

It also appears as the Law of Mass Action in Themodynamics,

The Continuity Equation in Fluid Mechanics,

Conservation of Momentum in classical mechanics.

In fact I suspect that a very small percentage of your students will go on to work in disciplines where it does not apply such as sub atomic physics and chemistry, or relativistic physics and chemistry.

For the bulk of Science and Engineering it is just fine.

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You have to keep in mind that mass refers to several different types when thinking of conservation of mass/energy.

Most mass of a particle is given in its rest mass this is $e=m_o c^2$ however this form only refers to in modern terminology the invariant mass.

When you apply The full equation which includes the momentum term that you posted in your other thread you increase its relativistic mass. In modern terms the variant mass. It is this formula that allows the LHS to smash two protons together to create particles larger than their combined rest mass. Example the Higgs boson.

The conservation of mass applies when you use the total mass including the momentum term. The particles  created must cannot exceed the total mass/energy of the incoming particles. In fact the total mass in must equal the total mass/energy out.

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Thanks a lot, I get it

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17 hours ago, Lizwi said:

Eyshhhhhhhhh!  I get what Timo is saying. This means I'm teaching incorrect staff to high school learners tha the mass cannot be destroyed or created??

Don't forget, all theories are limited to domains of applicability. I could be wrong but I can't think of any exceptions.That might be worth getting across to your students: that every theory has limits to where it can be applied.

Edited by StringJunky

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20 hours ago, Lizwi said:

How is it possible that the massless photon changes to two particles with mass,

"massless" means "having no rest-mass"

"mass" means "having rest-mass".

Such shortcuts widely used now.

In Standard Model photon has no rest-mass i.e. has no valid reference frame in which it is at rest.

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Okay, it is clear now, physics is so strange

Edited by Lizwi
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It's so strange that "strangeness" is an actual name of a physics property

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By this standard, physics is not very strange most of the time.

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2 hours ago, timo said:

By this standard, physics is not very strange most of the time.

True...

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