Can quantum mechanics explain the relationship between mass and energy?

[Algren]

E=mc^2 , defines mass energy "Equivalence", but after some surfing, I don't guess that Mass can be straight converted into pure energy.

Is there any place which defines mass in terms of energy?

 

[Antiphon]

Matter+antimatter=photon.

 

[maverick_starstrider]

E=mc^2 , defines mass energy "Equivalence", but after some surfing, I don't guess that Mass can be straight converted into pure energy.

Is there any place which defines mass in terms of energy?

You can't simply "make" mass convert to energy, it's more the other way around. If you have enough energy (say 2m_e c^2 worth, where m_e is the mass of an electron) the system will spontaneously convert that energy into the mass of a particle (rather two particles since the amount of charge must also be conserved so you get a positively charge positron and a negatively charge electron). No "mass energy" power stations are allowed I'm afraid.

 

[atyy]

Yes, mass can be converted to energy.

http://www.colorado.edu/physics/2000/periodic_table/amu.html
http://www.dummies.com/how-to/content/nuclear-fission-basics.html

 

[DrStupid]

E=mc^2 , defines mass energy "Equivalence", but after some surfing, I don't guess that Mass can be straight converted into pure energy.

Yes, mass and energy are equivalent and yes, mass can not be converted into energy and vice versa. There is not "but".

 

[DrStupid]

Yes, mass can be converted to energy.

That would be a violation of energy conservation.

 

[atyy]

That would be a violation of energy conservation.

Ok, to be more precise:

Rest mass can be converted to energy.

Relativistic mass is by definition, the same as energy, and is conserved.

 

[DrGreg]

Energy comes in many forms, kinetic, potential, heat, sound, etc. I wouldn't say mass can be converted into energy, I would say mass is one form of energy. And, yes, you can convert mass-energy into other forms of energy. atyy gave some examples in post #4. The total energy, including mass-energy, is conserved. (In special relativity: always; in general relativity: always locally and sometimes globally.)

 

[Antiphon]

Yes, mass and energy are equivalent and yes, mass can not be converted into energy and vice versa. There is not "but".

Mass can (and is routinely) converted directly into energy. Electron-positron anhiliation.

Energy can and is routinely converted into mass. Gamma rays of the right energy can turn into electron-positron pairs.

This is not confined to rest mass. Nuclear binding energy manifests as increased mass. Or nuclear mass is released as energy in fission. It's all the same thing.

Mass and energy are directly transformable into one another.

 

[DrStupid]

Mass and energy are directly transformable into one another.

No, they aren't. Mass and energy are equivalent. It is similar to radius and circumference of a circle.

 

[Passionflower]

I think that rest mass at the quantum level cannot possibly exist as nothing can be at rest, this would violate the uncertainty principle.

Perhaps elementary particles have (theoretical) rest mass but even that I doubt, even charged particles for that matter. Furthermore it would be hard to reconcile the existence of uncharged point particles with mass as I think one cannot have a stress-energy at a point.

 

[Antiphon]

No, they aren't. Mass and energy are equivalent. It is similar to radius and circumference of a circle.

How do you explain Positron-Electron anhiliation?

 

[jtbell]

How do you explain Positron-Electron anhiliation?

To keep things simple, suppose the positron and electron have zero kinetic energy. They're simply sitting right next to each other, about to annihilate. The mass of this system is 2 x 511 keV/c^2 = 1022 keV/c^2. The total energy is 1022 keV, consisting of the rest-energies of the two particles. The total momentum is zero.

They annihilate, and you have two photons going off in opposite directions, each with energy 511 keV, so the total energy is still 1022 keV (energy is conserved). They each have momentum with magnitude 511 keV/c, but in opposite directions, so the total momentum is still zero (momentum is conserved).

Each photon has mass zero (using the "invariant mass" as physicists normally do), so the sum of the masses is also zero. Does that mean that the mass has been converted to energy? No, because the total energy before is the same as the total energy afterwards! If mass had been converted to energy, then the total energy afterwards would be greater than the total energy before, because new energy would have been created, right?

One way to look at this is to say that energy is conserved, but mass isn't. What we often call "conversion of mass to energy" is actually conversion of energy from one form to another (from rest-energy to kinetic energy). The masses of the electron and positron simply disappear.

There's another way to look at this. The energy, mass and momentum of a single particle are related by

$$E^2 = (pc)^2 + (mc^2)^2$$

For a system of particles, we can define the "mass of the system" using

$$E_{total}^2 = (p_{total}c)^2 + (m_{system}c^2)^2$$

The mass of the system must be conserved, because both the total momentum and total energy are conserved. In our example, the mass of the system of two photons is 1022 keV/c^2, equal to the total mass of the electron and positron. In this view, the mass of a system of particles does not generally equal the sum of the masses of the component particles.

Either way of looking at it, you can't say (strictly speaking) that "mass is converted to energy" because this implies that "new" energy is created, which contradicts the principle that total energy is always conserved.

 

[Antiphon]

Sorry, but you're torturing the terminology. Though your math is spot on.

Here's the basic convention you're laboring to reject. Electrons and positrons are particles of matter. Photons are quanta of energy. When the matter disappears and is replaced by the energy, it can be called "conversion."

This is what the terms have meant for over a hundred years.

 

[maverick_starstrider]

I think that rest mass at the quantum level cannot possibly exist as nothing can be at rest, this would violate the uncertainty principle.

Perhaps elementary particles have (theoretical) rest mass but even that I doubt, even charged particles for that matter. Furthermore it would be hard to reconcile the existence of uncharged point particles with mass as I think one cannot have a stress-energy at a point.

You cannot talk about quantum mechanics and rest mass, quantum mechanics is, by design, non-relativistic. If you want to merge the two you get quantum field theory, in which case mass is due to the Higgs mechanism.

 

[maverick_starstrider]

Mass can (and is routinely) converted directly into energy. Electron-positron anhiliation.

Energy can and is routinely converted into mass. Gamma rays of the right energy can turn into electron-positron pairs.

This is not confined to rest mass. Nuclear binding energy manifests as increased mass. Or nuclear mass is released as energy in fission. It's all the same thing.

Mass and energy are directly transformable into one another.

Let's be clear here, protons and electrons are BY FAR the most common type of matter we find in everyday life. Neither decays and cannot simply be "directly transformed into energy". Yes you can annihilate them with their anti-matter particle but you would first have to create that anti-matter. Pure mass energy is not a directly accessible form of energy. "Mass" held in bonding can of course be accessed (this is nuclear fission/fusion) but all decay pathways end at the proton or electron.

 

[ghwellsjr]

Let's be clear here, protons and electrons are BY FAR the most common type of matter we find in everyday life. Neither decays and cannot simply be "directly transformed into energy". Yes you can annihilate them with their anti-matter particle but you would first have to create that anti-matter. Pure mass energy is not a directly accessible form of energy. "Mass" held in bonding can of course be accessed (this is nuclear fission/fusion) but all decay pathways end at the proton or electron.

A neutron will decay into an electron and a proton giving off an energy equivalent to the difference in its rest mass and the sum of the rest masses of a proton and an electron.

 

[Passionflower]

You cannot talk about quantum mechanics and rest mass, quantum mechanics is, by design, non-relativistic. If you want to merge the two you get quantum field theory, in which case mass is due to the Higgs mechanism.

I cannot what?

You either agree or disagree with what I say. If you disagree please use physics not "you can't say because you are wearing your quantum hat while talking relativity".

 

[Passionflower]

They annihilate, and you have two photons going off in opposite directions, each with energy 511 keV, so the total energy is still 1022 keV (energy is conserved). They each have momentum with magnitude 511 keV/c, but in opposite directions, so the total momentum is still zero (momentum is conserved).

Each photon has mass zero (using the "invariant mass" as physicists normally do), so the sum of the masses is also zero.

A system of two photons going in opposite direction does have mass.

 

[DrStupid]

How do you explain Positron-Electron anhiliation?

Parities and electric charges of both particles cancel each other out. Mass and energy remain unchanged (see jtbell's post for details).

When the matter disappears and is replaced by the energy, it can be called "conversion."

There is no replacement of matter by energy. Matter has energy. If the matter disappears the energy remains (e.g. in the form of radiation).

 

[maverick_starstrider]

A neutron will decay into an electron and a proton giving off an energy equivalent to the difference in its rest mass and the sum of the rest masses of a proton and an electron.

I'm not quite sure what your point is... I am well aware that neutrons decay, which is why I didn't include it in saying that decay paths ends at protons and electrons. Which you can't get energy out of without creating anti-particles... Again I don't really see what you're trying to say. I explicitly said that "mass" held in bonding CAN be accessed and then you give an example of exactly such a case (neutron decay).

 

[maverick_starstrider]

I cannot what?

You either agree or disagree with what I say. If you disagree please use physics not "you can't say because you are wearing your quantum hat while talking relativity".

Um again, quantum mechanics is non-relativistic BY DESIGN. Take a look at the Schrödinger's equation, first derivative in time, second derivative in space, does that look compatible with relativity to you? So no, you can't talk about relativity and quantum mechanics regardless your hat, by design you will be wrong. A concept of rest mass vs. relativistic mass has no meaning in QM. If you want to talk about both relativity and quantum in the same sentence you have to take BOTH your quantum mechanics hat off AND your relativity hat off and put on your QUANTUM FIELD THEORY hat. I'm afraid that is the "physics" as you say.

 

[ghwellsjr]

I'm not quite sure what your point is... I am well aware that neutrons decay, which is why I didn't include it in saying that decay paths ends at protons and electrons. Which you can't get energy out of without creating anti-particles... Again I don't really see what you're trying to say. I explicitly said that "mass" held in bonding CAN be accessed and then you give an example of exactly such a case (neutron decay).

You just made it sound like the common types of matter don't decay.
.

 

[Passionflower]

Um again, quantum mechanics is non-relativistic BY DESIGN. Take a look at the Schrödinger's equation, first derivative in time, second derivative in space, does that look compatible with relativity to you? So no, you can't talk about relativity and quantum mechanics regardless your hat, by design you will be wrong. A concept of rest mass vs. relativistic mass has no meaning in QM. If you want to talk about both relativity and quantum in the same sentence you have to take BOTH your quantum mechanics hat off AND your relativity hat off and put on your QUANTUM FIELD THEORY hat. I'm afraid that is the "physics" as you say.

All what you are doing avoiding the issue by cubbyholing things.

All I wrote was "at the quantum level" and refer to the uncertainty principle.