1. May 23, 2010

### rmshepherd

I'm trying to get my head around an idea that i had and i was wondering if you people here could clarify for me i am sure some of my basic assumptions are wrong so here goes

1 objects cannot go faster than the speed of light, it take more and more energy to accelerate an object as it approaches the speed of light
2 the energy that has been put in to the moving body increases its mass

if these assumptions are correct what happens if 2 object are moving toward each other at very close to the speed of light wouldn't they have a very powerful gravitational field as the objects fall into each others gravity shouldn't they accelerate?
if they do there mass would increase again which in turn would increase the gravitational attraction but then if the mass increases where did that energy actually come from

my brain usually bsods not long after this thought

2. May 23, 2010

### Dmitry67

When object accelerates, it increases its so called 'relativistic' mass, which is depreciated now. Now it is called just 'energy'.

so, relativistic mass does not create gravity so accelerated objects do not create more gravity and they cant convert into black holes. Gravity is created by stress-energy tensor, which contains rest mass, and other components (pressure, flux). In some specific cases the increase of gravity is equivalent to the naive calculation based on the relativistic mass (for example, when object is heated, atoms move faster -> relativistic mass increase -> object becomes heavier -> more gravity).

Interaction of objects moving at relativistic speeds cant be described using that 'naive' model with only relativistic mass.

3. May 23, 2010

### Buckleymanor

If relativistic mass does not create gravity why would it take all the mass of the universe to accelerate a housebrick to the speed of light.

4. May 23, 2010

### Dmitry67

accelerating of an object close to the speed of light requires huge amounts of ENERGY
How does it contradict what I wrote above?

5. May 23, 2010

### Buckleymanor

If it takes all the mass in the universe it would allso take all the gravity.
Energy is mass.

6. May 23, 2010

### Dmitry67

Energy is not mass
Energy is proportional to the RELATIVISTIC mass
Gravity is created by the REST mass (+ other components of the tensor), not by the RELATIVISTICS mass
-> what is repeated in many low quality popular books "when object is accelerated, it becomes heavier so it starts to attract gravitationally everythins" is 100% bull****

7. May 23, 2010

### Buckleymanor

So if energy is not mass what is it.
If you take a spring and compress it, the input of energy by your compression of the spring will make it more massive and will weigh very slightly more than the same spring which is not compressed.
Add energy to mass is equal to more mass.
Take energy away from mass is equal to less mass.

8. May 23, 2010

### yuiop

I think this basically correct. The rest mass of a system of particles is the total energy of the system in a reference frame where the total momentum of the system is zero. A good example is given in this thread: https://www.physicsforums.com/showthread.php?t=403833

In that thread there are two objects of 10kg rest mass each, heading towards each other at 0.5c. The total rest mass of the system before collison is 20kg + kinetic energy = $20/\sqrt(1-0.5^2)$ = 23.1 kgs. After the inelastic collision the rest mass is the same and the two collided 10kgs masses have a total rest mass of 23.1 kgs. The rest mass of the system has not changed and the fact that the two collided masses weigh more than the two masses when they initially stationary is due to the heat generated by the collision. Note that before the collision, part of the rest mass of the system is in the form of kinetic energy and after the collision part of the rerst mass is in the form of heat energy (which is a form of kinetic energy). This is in agreement with your statement that the total rest mass of a system is in fact its total energy (it its zero momentum frame).

Last edited: May 24, 2010
9. May 24, 2010

### Dmitry67

For bound systems with momentum =0
The original question was about '2 flying objects attracting to each other'
That logic is not applicable there.

10. May 24, 2010

### rmshepherd

well thanks for your replies people but I still don’t have a clear picture in my head that would occur in this scenario, so could I get a straight answer on these questions as the seems to be some debate

1 if I accelerate a brick to the 99.9% c will it have a stronger gravitational field than a brick at rest?

As I write that it seems like a stupid question because 99.9% c relative to what and how does the brick know it’s at 99.9%c relative to the earth for example
however I guess as the brick is actually accelerating special relativity does not apply because it is not in uniform motion so I ask anyway (I have no formal scientific education so I apologise if I make a completely false statement and would welcome the feedback)

2 as the mass increases due to acceleration why wouldn’t that new energy/mass exert the same forces as any other energy

as I understand it if 2 subatomic particles collide with each other the kinetic energy they have is converted into new particles at the moment of impact so the energy the particle had from its speed was the same sort of energy that makes up the brick in the first place I know the quantum world and the relative world don’t mix well but it still seems a relevant observation in this question

3 is there something specific in known physics that precludes an objet accelerating to beyond the speed of light due to gravitational attraction