# What in the world does E =mc2 mean?

#### learningphysics

Homework Helper
Igor_S said:
How can masses of the particles depend on their velocity ? Mass is a Lorentz-invariant quantity. All that changes is kinetic energy of the particles. Their masses remain the same. If this would not be the case, you would surely have different decays at different temperatures.
The invariant mass of each particle remains the same. The invariant mass of the system of particles changes. Pete's page here explains this well:

http://www.geocities.com/physics_world/sr/invariant_mass.htm

#### pmb_phy

Igor_S said:
How can masses of the particles depend on their velocity ? Mass is a Lorentz-invariant quantity. All that changes is kinetic energy of the particles. Their masses remain the same. If this would not be the case, you would surely have different decays at different temperatures.
It's only the proper mass that is invariant. Not the relativistic mass.

Pete

#### Aer

pmb_phy said:
Take the simple case of a box of particles whose velocity has only an xy-component and no z component. Let the mass of the containment walls be insignificant when compared to the mass of the gas. Then as the gas is heated the particles move faster. The faster they move the greater the weight.
Is this an experimental result or something derived based on certain postulates? If it is the latter, what are the postulates used to derive this result?

#### εllipse

Aer said:
Is this an experimental result or something derived based on certain postulates? If it is the latter, what are the postulates used to derive this result?
It was originally derived from the postulates of the special theory of relativity (that all inertial reference frames are equivalent for the description of the laws of nature and that the speed of light is the same in all inertial reference frames), by Einstein himself. The original publishing was Does the Inertia of a Body Depend Upon its Energy-Content which was a follow-up to On the Electrodynamics of Moving Bodies.

The mass of a body is a measure of its energy-content; if the energy changes by L, the mass changes in the same sense by L/9 × 1020, the energy being measured in ergs, and the mass in grammes.
It has, of course, been proven since by experiment.

#### Aer

εllipse said:
It was originally derived from the postulates of the special theory of relativity (that all inertial reference frames are equivalent for the description of the laws of nature and that the speed of light is the same in all inertial reference frames), by Einstein himself. The original publishing was Does the Inertia of a Body Depend Upon its Energy-Content which was a follow-up to On the Electrodynamics of Moving Bodies.

It has, of course, been proven since by experiment.
You are reiterating the concepts since abandoned by physicists. I am very aware that Einstein proposed relativistic mass long ago. However, regardless of an objects speed relative to some other abitrary reference frame (I could say the Earth is moving at .9c relative to a ship's reference frame) does that neccessarily mean that an object on our fast moving Earth has a larger mass and takes more energy to accelerate? No. Why? Because you measure accelerate with respect to the object which is accelerating. If an object is said to accelerate constantly, it is assumed that the object is accelerating constantly with respect to the instantaneous velocity's inertial reference frame at any given instance. It is not a physical concept to assume that an object is accelerating constantly in a single inertial reference frame because eventually the object will have to reach a speed greater than c. And it is this situation (measuring acceleration in a single inertial reference frame) in which relativistic mass has any relevance. And since the notion itself is not physical, it is not too much to say that relativistic mass is not physical either.

In summary, if you wish to use relativistic mass, you must add extra rules such that you don't lead to a non-physical situation. I believe Occam would have something to say about this.

#### εllipse

Aer said:
You are reiterating the concepts since abandoned by physicists. I am very aware that Einstein proposed relativistic mass long ago.
You asked for a reference; I provided one. No need to be so harsh.

Aer said:
And it is this situation (measuring acceleration in a single inertial reference frame) in which relativistic mass has any relevance.
You seem to be assuming that the only thing we care about is how the world looks to us as we accelerate. But what about how things look to us as we accelerate them, while we remain inertial? For instance, when we get particles moving close to the speed of light in particle accelerators, the concept of relativistic mass does have use to us then because we do have a single inertial reference frame with which to make the measurement. Why can't we put a charged particle in a strong enough magnetic field to accelerate it faster than the speed of light? A very simple explanation is that its relativistic mass increases as we accelerate it, so its inertia/resistance to acceleration increases as well.

#### Aer

εllipse said:
You asked for a reference; I provided one. No need to be so harsh.

You seem to be assuming that the only thing we care about is how the world looks to us as we accelerate. But what about how things look to us as we accelerate them, while we remain inertial? For instance, when we get particles moving close to the speed of light in particle accelerators, the concept of relativistic mass does have use to us then because we do have a single inertial reference frame with which to make the measurement. Why can't we put a charged particle in a strong enough magnetic field to accelerate it faster than the speed of light? A very simple explanation is that its relativistic mass increases as we accelerate it, so its inertia/resistance to acceleration increases as well.
I've never said you cannot do this to obtain a correct result. However, it is not neccessary to use relativistic mass to get the same thing, that is all I am saying. Relativistic mass is mearly a perception in other frames - however, too many people equate this perception to be actual mass accumulation to the object in the objects rest frame. This point of view is very wrong. It is just as easy to not use relativistic mass, but I'm not going to prohibit you from doing so.

#### Aer

pmb_phy said:
Then as the gas is heated the particles move faster. The faster they move the greater the weight.
What is the weight of a particle (you may choose any particle you wish) moving .9999c through the atmosphere?

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving