# Need to remember something

1. Dec 14, 2003

### MathematicalPhysicist

with the increase of a body's velocity to the speed of light (v->c) so does the body's mass increase m->infinity.
does this means that light has infinite mass? i know that light doesnt have rest mass because it never rests .

hope that my layman terms wont affect the answer.

2. Dec 14, 2003

### DW

Mass doesn't increase with speed. According to modern relativity it is invariant. And a photon has zero mass. The relation between energy and mass according to special relativity is
E^2 = (pc)^2 + (mc^2)^2
For a photon E = hf and p = h/lamda = hf/c.
This gives:
(hf)^2 = (hf)^2 + (mc^2)^2
m = 0.
It is only when the momentum of a massive particle is zero, p = 0 that it gives the popular result
E = mc^2.

3. Dec 15, 2003

### MathematicalPhysicist

i was under the impression that when you acclerate a matter up to the speed of light the mass of the body increases, thanks for correcting me.

4. Dec 15, 2003

### DW

Thats an old paradigm introduced by Tolman, Lewis, and Plank, not Einstein who came to oppose it, that has no place in modern relativity. The modern definition of mass is such that it does not depend on speed. It is invariant.

5. Dec 16, 2003

### Janus

Staff Emeritus
This thread has been edited in order to get it back on topic.

6. Dec 18, 2003

### MathematicalPhysicist

so the mass of a body stays constant all the time? (i derived that from ivariant- doesnt change).

7. Dec 18, 2003

### DW

Invariant and conserved mean two different things. An invariant thing does not change value with respect to velocity changes or in general in coordinate transformations. A conserved thing keeps the same value over time. The mass of an object is defined as its center of momentum frame energy divided by the square of the speed c. You can change the mass of an object over time simply by adding energy too it. Of course if you include the matter where that energy came from as a part of the system center of momentum frame energy and therefor mass will be conserved so whether the objects mass is conserved over time really depends on what you want to include as a part of the system defining the object.

8. Dec 18, 2003

### MathematicalPhysicist

"You can change the mass of an object over time simply by adding energy too it." -two questions: 1. the adding of energy will it increase the mass or decrease it? 2. the other way around of is substracting from the object energy and you can do so by freazing it then object looses energy but it doesnt affect the mass (so this is a bad example of substracting mass that will change the mass) can you give example of substraction of energy from object and as a consequence a change in the mass?

9. Dec 19, 2003

### DW

By adding energy I do mean center of momentum frame energy. So, yes heating it up adds a minute amount of mass. Cooling it down subtracts mass from it. You may also remove mass simply by cutting a chunk off. It may also absord or emit latent energy in a phase change. You might also change the pressure at constant temperature.

10. Dec 19, 2003

### marcus

welcome DW

IIRC an atomic mass unit is about 930 MeV and
boltzmann k is about 8.6E-5 eV per kelvin
so we can even do an example
and see by how much the weight of an iron cannonball increases if it is heated by 10 degrees.

by what percentage, or ppm, or parts per billion, do I guess the weight would increase?

it would be so much nicer if an atomic mass unit were 1000 MeV
and boltzmann k were a tenthousandth of an eV per kelvin,
a flat E-4 eV/K.

Then an iron atom of 56 mass units would be 56 GeV
and, since the heat capacity of a solid chunk of metal is about 3k per atom, raising temp by 10 kelvin would mean putting in about 30E-4 eV per atom

the fractional weight gain is whatever fraction 3E-3 eV is of 56GeV.
it looks like less than one tenth of a part per trillion.

So if Loop can supply a set of scales that can weigh accurate to one part in ten trillion, then we can demonstrate to him that heating an iron ball makes it heavier. and cooling it makes it lighter

this was meant as a friendly intrusion, you said everything necessary but I just felt sociable and chimed in