Solving a Relativity Problem: Two MAsses in Motion

[trichop]

I am wondering about this:

1)Firtly, is it "reasonable" considering and studing the behaviour
of two masses only, as if they were the only in the whole
universe?

2) Suppose we can. Let as think we have two masses.
A very big one, and a second times smaller than the first.These
two masses are moving steadily against each other on the same
line. Firtly we stand on the small mass and look towards the other.
If we stand each time on a different mass, in both cases
we want be able to tell the truth about the kinetic energy of the system.
And if we try to do, we will conlclude in two different values for the
kinetic energy.

I think something must be wrong with one of the above statements
or both of them.Has anyone a clue?

 

[HallsofIvy]

I don't see what this has to do with relativity. I interpret "moving steadily against each other on the same line" to mean that they are moving at the same speed- one is pushing the other? The kinetic energy is (1/2)M v² where v is there joint speed and M is their total mass. If they are moving at the same speed, then it is purely a Newtonian problem- relativity only comes into play if you have two objects with distinctively different speeds.

 

[mezarashi]

Firtly we stand on the small mass and look towards the other.
If we stand each time on a different mass, in both cases
we want be able to tell the truth about the kinetic energy of the system.
And if we try to do, we will conlclude in two different values for the
kinetic energy.

Nothing to do with relativity at all. It's one of the fundamental laws of mechanics. The laws of variance and invariance. See a car speed by you? It's kinetic energy is 1/2mv^2. Now go sit on that car and what do you have? The car having zero kinetic energy. The difference in energy due to arbitrary frames of reference will not invalid any laws of physics. Even after relativity, only a few laws of variance and invariance changed.

To sum up (in classical mechanics):
Invariant - same to all observers in all frames
mass
charge

Variant - depends on selected frame of reference
velocity
energy
momentum

Another property, laws of conservation
Conserved
energy
mass
charge
momentum

Not Conserved
velocity

 

[trichop]

No, the masses are not pushing each other, just moving towards each other in constant speed (the same or not). But let's make it more clear. We stand on the big mass (M). At first M is moving towards the small mass (m). So we think we stand still and m is moving against us, kinetic energy (KE) = (1/2)m v^2, which is wrong. If now m is comming towards us with the same speed u, KE = (1/2)m u^2, which is right.
So what's wrong?

 

[trichop]

Although I haven't heart of "The laws of variance and invariance",
I think now of this:
If mass is invariant and energy variant, according to the energy-mass
equation , isn't this contradictory?

 

[JesseM]

No, the masses are not pushing each other, just moving towards each other in constant speed (the same or not). But let's make it more clear. We stand on the big mass (M). At first M is moving towards the small mass (m). So we think we stand still and m is moving against us, kinetic energy (KE) = (1/2)m v^2, which is wrong. If now m is comming towards us with the same speed u, KE = (1/2)m u^2, which is right.
So what's wrong?

First of all, that's not the correct formula for kinetic energy in relativity. In SR, kinetic energy is given by $$(\gamma - 1)mc^2$$, where m is the rest mass and $$\gamma = 1/\sqrt{1 - v^2/c^2}$$. Second of all, the total kinetic energy (and total energy in general) of a system can be different in different reference frames, this is true in Newtonian mechanics too (as your example shows).

 

[pervect]

Although I haven't heart of "The laws of variance and invariance",
I think now of this:
If mass is invariant and energy variant, according to the energy-mass
equation , isn't this contradictory?

Here's how it works. If you use a system of units such that c=1, you have

E^2 - p^2 = m^2.

E is the energy
p is the momentum
m is the invariant mass.

The more general formula when c is not 1 is

E^2 - (p*c)^2 = (m*c^2)^2

So when an object is at rest relative to you, it has a momentum of zeo, and it's energy is equal to its rest mass (when c=1), or its energy is equal to it's rest mass * c^2 (when c is not 1).

When an object is moving relative to you, it has a higher energy, a non-zero momentum, however its rest mass (aka invariant mass) remains the same.

I have the feeling that you are groping your way towards the concept of energy in genreal relativity. This is unfortunately harder than it first appears. The sci.physics.faq is probably one of the few good acessible sources of information on this that isn't too technical.

http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html

But you need to understand energy and mass, first.

You might try therfore

http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

which addresses this topic. Note that we have a few enthusiastic fans of the concept of relativistic mass (discussed in this FAQ and contrasted to invariant mass) here on the board - however, I'm not one of them :-).

 

[quantumdude]

If we stand each time on a different mass, in both cases
we want be able to tell the truth about the kinetic energy of the system.

That statement right there seems to sum up your problem. You expect that there is some value of the KE that is more true than any of the others, when it is not so. KE is relative.

 

[jcsd]

I am wondering about this:

1)Firtly, is it "reasonable" considering and studing the behaviour
of two masses only, as if they were the only in the whole
universe?

Well it certainly seems reasonable as there are many situations in which we can predict to a level that conforms highly to experimental results the behaviour of two masses by using models that ignore any othe rmass in the universe. However this is not the first time that someone has asked this question, you might wnat to investigate Machian relativty.

2) Suppose we can. Let as think we have two masses.
A very big one, and a second times smaller than the first.These
two masses are moving steadily against each other on the same
line. Firtly we stand on the small mass and look towards the other.
If we stand each time on a different mass, in both cases
we want be able to tell the truth about the kinetic energy of the system.
And if we try to do, we will conlclude in two different values for the
kinetic energy.

I think something must be wrong with one of the above statements
or both of them.Has anyone a clue?

As pointed out kinetic energy is relative i.e. it's value is dependent on who is observing it.