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Old Jan 4th 2017, 01:34 PM   #1
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Energy, mass and matter

I need some sources to help me understand the relationships... matter to energy and energy to matter, what is the mechanism?
For example, in my search for information I have seen it stated that a photon of great enough frequency would "decay" into an electron? Is this true? What are some good sources for information.

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Old Jan 9th 2017, 06:51 AM   #2
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Originally Posted by ButchBegy View Post
I need some sources to help me understand the relationships... matter to energy and energy to matter, what is the mechanism?
For example, in my search for information I have seen it stated that a photon of great enough frequency would "decay" into an electron? Is this true? What are some good sources for information.

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The relationship is actually between momentum and energy. You know the Einstein equation $\displaystyle E = mc^2$. This relates energy by its rest mass...the mass it has for 0 speed. The more general equation is $\displaystyle E^2 = (mc^2)^2 + (pc)^2$ where p is the momentum of the object in a given frame. (Set p = 0 to get $\displaystyle E = mc^2$.)

That being said there is no "mechanism" to energy-matter exchange. SR works best (IMHO) when dealing with 4-vectors. There is an energy-momentum 4-vector given by $\displaystyle \left ( \frac{E}{c}, p_x, p_y, p_z \right )$. This shows that the energy-momentum transfer really isn't a transfer at all...it merely means that some spatial momentum has transfered itself to the time component of the energy-momentum 4-vector (the E/c part), rather like a rotation of a 3-vector in Classical Physics.

A large energy photon will not create an electron out of the energy. We need to create two particles so that spin can be conserved during the decay. So for this photon to decay we have to create an electron and it's anti-particle the positron for this to occur. The minimum energy that the photon needs to have is $\displaystyle m_e c^2 + m_p c^2 = 2 m_e c^2$. Where $\displaystyle m_e = m_p$ is the mass of the electron and positron (which has the same mass as the electron since they are anti-particles.)

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Old Jan 9th 2017, 02:33 PM   #3
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Do you have math that relates the energy of a photon to its frequency?

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Old Jan 9th 2017, 03:24 PM   #4
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Originally Posted by ButchBegy View Post
Do you have math that relates the energy of a photon to its frequency?

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Sure. Planck's theorem says that $\displaystyle E = h \nu$.

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