Exploring the Relationship Between Mass and Energy

[JJ]

If mass is energy, then energy is mass. Although the photon has no rest mass, it has energy, thus is liable to gravity.

e=mc^2
hv=mc^2
m=hv/c^2, where m would be the relativistic mass? Damn my high school physics teacher for stopping me from learning this sooner!

This is blowing my mind.

 

[protonman]

The 'E' in E=mc^2 represents the rest-mass energy.

 

[JJ]

I figured m meant relativistic mass and m0 represented rest mass.

 

[protonman]

No this is a misconception that comes about when people who don't understand physics try to popularize it without understanding what they are saying. It is not your fault but the fault of those who are more interested in personal gain than understanding.

In general anytime you see an 'm' in relativity it is the rest mass. When considering the non relativisitic mass they use 'gamma' times m where gamma is the relativistic correction.

The most general expression for relativistic energy is

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

where p is the relativistic momentum. For a photon the rest energy is 0 so this reduces to E=pc for a photon.

 

[JJ]

Yes, I agree with gamma m as relativistic mass, but are you certain it's written that way all the time? For the relativistic kinetic energy expression:

KE = mc^2 - m0c^2, where the first "m" is actually the relativistic mass

I see now that this equation holds true with my supposition of a massive photon, where it receives its energy from relativistic mass, but nothing out of rest mass.

So I guess m0 will always be rest mass and gamma m always relativistic mass, but assuming m is always gamma m is going out on a limb.

 

[DW]

Yes, I agree with gamma m as relativistic mass, but are you certain it's written that way all the time? For the relativistic kinetic energy expression:

KE = mc^2 - m0c^2, where the first "m" is actually the relativistic mass

I see now that this equation holds true with my supposition of a massive photon, where it receives its energy from relativistic mass, but nothing out of rest mass.

So I guess m0 will always be rest mass and gamma m always relativistic mass, but assuming m is always gamma m is going out on a limb.

You may tell your physics teacher that a physicist says he needs to get a modern text. I suggest anything recent from Serway for that level. In modern relativity the expression is
[tex]KE = \gamma mc^{2} - mc^{2}[/tex]
For further detail see http://www.geocities.com/zcphysicsms/chap3.htm

 

[protonman]

The way I explained it is just one convention. In general though it is accepted that anytime the 'm' appears it is the rest mass.

 

[turin]

JJ,
Regardless of the minor quibbling over what "m" really means, I think that the heart of the issue is that, it is not energy as mass but (kinetic) energy and (rest) mass (as well as momentum flux) that gravitates. GR does not need a photon to have a mass to explain the gravitational interaction of a photon. GR says that energy gravitates, and though rest mass is a form of energy, it is not the only form, and thus, not a requisite for gravitation.

 

[JJ]

Ah, makes sense, thanks!

What's the reason for not doing away with the concept of mass?

 

[DrMatrix]

What's the reason for not doing away with the concept of mass?

Because mass is still a valid concept.

 

[protonman]

Ah, makes sense, thanks!

What's the reason for not doing away with the concept of mass?

Because it exists.

 

[pmb_phy]

JJ - It is incorrect to assume that when an author writes "m" in E = mc² that he means rest mass. In almost all circumstances an author who is worth his salt will use a symbol for rest mass and that it is rest mass rather than (relativistic) mass. E.g. some notable examples are texts by Mould, D'Inverno and Rindler. A notable website that uses "m" to mean relativistic mass is the CERN website as well as many other web sites including university sites for relativity courses and online relativity course handouts/lecture notes.

Long short - No! "m" does not always mean rest mass. No! It is not a misconception. This convention is used in more advanced tests such as the well know and authoritaive tests by Rindler etc

For a list of referances to this effect and a list of online notes etc which use "m" to mean relativistic mass please see http://www.geocities.com/physics_world/relativistic_mass.htm

 

[turin]

What's the reason for not doing away with the concept of mass?

Energy causes gravitation, but mass causes inertia. This is somewhat of a traditional slant, but that's the termonology. Perhaps it would have more impact if, instead of, "E = mc²," we said something like,

"the stationary ability of a body to effect a gravitational influence is related ("equivalent") to its resistance to accelerate from the inertial rest frame (moment of inertia)."

This statement is utterly profound because it recognizes that two physically distinct properties (in terms of their physical realization) are essentially the same underlying property. It of course does not contain all that is said by E = mc², though, so, ultimately, once you have gained an appreciation for it, you should stick with E = mc².

 

[JJ]

Is kinetic energy relative? An immobile object has less KE for a relatively stationary object than a moving one, and thus has more gravitational attraction for the former? Just wanting to make sure I havn't missed the boat.

 

[turin]

Is kinetic energy relative?

Most certainly! I will suggest that we refer to the frame dependence of a kinetic energy determination. I believe that you have answered your own question with the following statement:

An immobile object has less KE for a relatively stationary object than a moving one, ...

... and thus has more gravitational attraction for the former?

At this point, you should realize that the source of gravitation is not just a scalar quantity. But, I think you can get away with saying that a moving body gives a stronger gravitational attraction by virtue of its adjunct of kinetic energy. I have never sat down and done any kind of a calculation to determine this, but it does seem reasonable.