Mass vs. Energy

[LegionOnomaMoi]

Yes it's the celebrity death match of the millennium! Ok, no. It isn't. But I remembered not long ago that as a child I was told there are 4 quarters in a dollar. I was very confused because I couldn't feel 4 quarters in any dollar. I didn't understand that saying 4 quarters are in a dollar meant the value of a dollar is equal to that of 4 quarters.

Enter Einstein's Energy-correspondence. Too frequently people get amazed by the fact that energy equals mass (times a constant)! And we get all these statements about how mass and energy are the same and how everything is really one thing and so on all because the famous e= mc^2 equation is so misunderstood. I have tried to explain it by illustrating that energy is also mathematically related to the momentum of massless particles, by talking about what the equation means in terms of systems, by saying we don't equate work and matter or momentum and speed, and so on.

Then I thought of something simpler. Are four quarters the same as one dollar? No. Metal and cloth-like paper are very different and nobody is going to cut a dollar in to four equal pieces and claim they have quarters. But 4 quarters equal a dollar

$.25 * 4 = $1.00

What does this mean!? It means that the value of four quarters is equal to that of a dollars. There's no mystical property about physical quarters that makes them equivalent to a dollar. Just because we can relate things mathematically doesn't mean we are making any ontological equivalences. Mass isn't energy.

 

[lewisnotmiller]

Yes it's the celebrity death match of the millennium! Ok, no. It isn't. But I remembered not long ago that as a child I was told there are 4 quarters in a dollar. I was very confused because I couldn't feel 4 quarters in any dollar. I didn't understand that saying 4 quarters are in a dollar meant the value of a dollar is equal to that of 4 quarters.

Enter Einstein's Energy-correspondence. To frequently people get amazed by the fact that energy equals mass (times a constant)! And we get all these statements about how mass and energy are the same and how everything is really one thing and so on all because the famous e= mc^2 equation is so misunderstood. I have tried to explain it by illustrating that energy is also mathematically related to the momentum of massless particles, by talking about what the equation means in terms of systems, by saying we don't equate work and matter or momentum and speed, and so on.

Then I thought of something simpler. Are four quarters the same as one dollar? No. Metal and cloth-like paper are very different and nobody is going to cut a dollar in to four equal pieces and claim they have quarters. But 4 quarters equal a dollar

$.25 * 4 = $1.00

What does this mean!? It means that the value of four quarters is equal to that of a dollars. There's no mystical property about physical quarters that makes them equivalent to a dollar. Just because we can relate things mathematically doesn't mean we are making any ontological equivalences. Mass isn't energy.

When you start dumbing this stuff down to the point that it makes sense to me, I automatically assume you've dumbed it down too much, and are doing the old 'lies to children' thing.
(Lie-to-children - Wikipedia, the free encyclopedia)

So c'mon...fess up. What's the single largest fact here that you're glossing over.

 

[Sunstone]

When you start dumbing this stuff down to the point that it makes sense to me, I automatically assume you've dumbed it down too much, and are doing the old 'lies to children' thing.
(Lie-to-children - Wikipedia, the free encyclopedia)

So c'mon...fess up. What's the single largest fact here that you're glossing over.

Apparently, Legion is glossing over the fact that -- as everyone knows -- mass is a religious ritual which requires energy to perform. In fact, his omission of that fact in his OP is nothing less than glaring.

 

[LegionOnomaMoi]

What's the single largest fact here that you're glossing over.

That the analogy is imperfect because the correspondence in the quarter/dollar instance is due to the value each has abstractly whereas in physical systems both energy and matter are properties ascribed to the system. Probably that's the biggest. There's also the fact that mathematical relations frequently do entail ontological commitments and actually do so in this case it's simply that the relations between the properties can really only be understood as equivalent in that properties of a physical system change in related ways through things like motion and position.

 

[LegionOnomaMoi]

Apparently, Legion is glossing over the fact that -- as everyone knows -- mass is a religious ritual which requires energy to perform. In fact, his omission of that fact in his OP is nothing less than glaring.

I'm such an idiot! You got me. I'm totally wrong. Energy is equal to church.

 

[Mr Spinkles]

That's a very simple and helpful analogy. Nice!

 

[Enai de a lukal]

Apparently, Legion is glossing over the fact that -- as everyone knows -- mass is a religious ritual which requires energy to perform.

Very nice...

 

[Quagmire]

Yes it's the celebrity death match of the millennium! Ok, no. It isn't. But I remembered not long ago that as a child I was told there are 4 quarters in a dollar.

There are four quarters in everything.

(this is what I usually tell panhandlers when they hit me up for change).

 

[ScottySatan]

In the real world, do energy and mass interconvert with complete efficiency, or is some energy or material lost to something else?

I'm thinking of fluorescence as I ask this. Even though it's quantum, the emitted photon has less energy than the exciting photon: energy was lost to something else.

Or maybe here's a bad analogy... it takes some work to get change for a dollar?

 

[LegionOnomaMoi]

Do energy and mass interconvert perfecty

They don't at all. They don't convert. But systems that gain or lose energy can gain or lose mass.

More specifically, it's taking the equation of energy expressed in units of the mass of some physical system evolving in time (kilograms & meters, with time being a displacement of distance): Erest = m or the equivalence of a system at rest expressed in terms of the systems total energy (not unlike various potential energies of systems in classical physics) and expressing it in terms of energy units (joules). The real derivation doesn't involve either equation but rather is a consequence of the relativistic equation for energy:

The equation expressed in terms of units of mass is, like the equation of energy in terms mass units, even simpler:

The above is energy expressed in terms of mass units in motion. To get the famous equation

, we simply remove the velocity conversion factor which gives us the energy in terms of kilograms of a system at rest: the mass.

Without getting into the mathematics, this is basically just taking Newtonian mechanics and realizing that in relativistic physics, gravitation as a force doesn't exist and momentum as classically defined cannot be correct. The difficult part is using Lorentz transformations to get a value for a relativistic scaling factor to put in place of the 1/2 of the Newtonian K = 1/2 (mv^2)

If we did this, we'd get K = (γ-1)mc^2
So relativistic kinetic energy replaces the velocity of Newtonian kinetic energy with the one constant velocity (the speed of light) and the 1/2 scaling factor with (γ-1). However, a system at rest has no kinetic energy, so we just remove the factor (γ-1) and get K = mc^2. To convert this into mass units, we simply remove the conversion factor as well and we get that E-naught = m.



This is also true of gasoline in a car engine or when you shine a light on a thin metal surface. It's just usually pretty pointless to use relativistic physics when the conservation of energy holds without it such that the difference is so close we can barely measure it. Knocking electrons out of metals using light (massless particles) creates a change in the total mass conserving total energy, but even if you ask very politely the electrons will not group together in an orderly fashion and land gently on a measuring device suitable for weighing things that are practically weightless.

Thankfully, the energy of photons even with very short wavelengths (high frequency) is not enough to break nuclear bonds. So you don't have to worry about nuclear fission when you turn on a flashlight. This would be very inconvenient. Almost as bad as total protonic reversal:

Dr. Egon Spengler: Don't cross the streams.
Dr. Peter Venkman: Why?
Dr. Egon Spengler: It would be bad.
Dr. Peter Venkman: I'm fuzzy on the whole good/bad thing. What do you mean, "bad"?
Dr. Egon Spengler: Try to imagine all life as you know it stopping instantaneously and every molecule in your body exploding at the speed of light.
Dr Ray Stantz: Total protonic reversal.
Dr. Peter Venkman: Right. That's bad. Okay. All right. Important safety tip. Thanks, Egon.

The required equation for the total energy of a particle is E=

. That bottom part is usually expressed by the Greek letter gamma (just take out the mc^2 and keep the denominator as a denominator only written under the numerator 1). A simpler equation is E= mc^2 + pc.
The point is that the equation doesn't define energy as mass. It tells you that some physical system with x amount of energy travelling at y speed must have z mass, or that a physical system with z mass and x energy must be going at y speed, or that a physical system with z mass going at y speed must have x energy. These are all properties of physical systems in relativistic physics, but they do not define energy, mass, or speed. These are defined already as properties of physical systems (including those which aren't intuitively physical such as massless particles).

 

[Curious George]

Apparently, Legion is glossing over the fact that -- as everyone knows -- mass is a religious ritual which requires energy to perform. In fact, his omission of that fact in his OP is nothing less than glaring.

I am just happy he put away his Ricci tensor. I am always thinking "legion! What are you doing? You can't just waltz around with that thing dangling about!"

 

[LegionOnomaMoi]

"You can't just waltz around with that thing dangling about!"

You know, that's exactly what she said!

 

[ScottySatan]

The point is that the equation doesn't define energy as mass. It tells you that some physical system with x amount of energy travelling at y speed must have z mass, or that a physical system with z mass and x energy must be going at y speed, or that a physical system with z mass going at y speed must have x energy.

I think I get it, you mean it's kind of a state equation like the ideal gas law? you can use known values to calculate other ones, but the gas law does not define pressure to be the same thing as temperature?

Are you sure matter and energy never, ever interconvert? not in a star? not in a matter and antimatter collision? were we lied to? we totally were, weren't we?

 

[LegionOnomaMoi]

I think I get it, you mean it's kind of a state equation like the ideal gas law? you can use known values to calculate other ones, but the gas law does not define pressure to be the same thing as temperature?

Pretty much, yes.

Are you sure matter and energy never, ever interconvert?

They are defined as distinct.

 

[Curious George]

You know, that's exactly what she said!

Honestly though, one should be embarrassed of such curvature.

 

[LegionOnomaMoi]

Honestly though, one should be embarrassed of such curvature.

Hey. It's for her pleasure.

 

[Curious George]

Hey. It's for her pleasure.

I really anticipated you saying "it's natural" but your reply works as well.

 

[ScottySatan]

Pretty much, yes.

They are defined as distinct.

Holy hell, we have a real physicist here! Thanks.

 

[LegionOnomaMoi]

Holy hell, we have a real physicist here!

We do! But that would be Mr. Sprinkles and Meow Mix. I'm a neuroscientist.

 

[Slapstick]

We do! But that would be Mr. Sprinkles and Meow Mix. I'm a neuroscientist.

Ya right! You are a mystic. Only mystics would know stuff like that. :sarcastic