Imagine a one ton solid metal sphere hurtling through space at thousands of miles per second. Classic physics tells us that unless affected by external forces the total linear momentum of the sphere cannot change. Damn. We need to stop that sphere dead in its tracks but we have no way of physically interacting with it.
Well I guess we will just have to increase the velocity of all other matter in the universe to match the velocity of our sphere along its vecter effectively making its velocity zero in relationship to the rest of the universe.
Where did its momentum go?
:O A riddle...
The sphere still has its momentum. You're just capable of space magic, moving everything else at the same rate.
...So, here's another one. What if faster than light travel is not possible?
I can assure you that it is possible.
How is faster than light travel possible?
Also, how is the speed of light measured?
The point behind the example was to force people to take step back from classical physics and take a fresh look at inertia. The goal being to figure out a way to redirect inertia and or to seperate the force from the physical body.
So, the riddle was basically not a riddle. If something is moving, then you get everything around it moving at the same rate, it no longer appears to be moving, or appears to have energy. In fact, it does - along with everything else.
This is kind of like sitting on earth. I don't feel like I'm moving thousands of miles per hour.
well, problem is that there would be no way to change the momentum of a thing without changing the momentum of something else in the opposite direction. Newton's 3rd Law.
I realized that I may have taken this discussion to far too fast. There is an advanced concept of momentum towards which I was heading, but that can wait.
There in fact does exist a modification of Newton's law wherein it remains true that for every action there is an equal and opposit reaction, but recognizes that the two do not have to occur simultaneously. The principal of non-simultaneity.
There is an example of this principal put into practice. It is called the Dean's Space Drive.
If we could track the trajectories of all other matter in the universe. It might then be possible to arrange collisions between individual atoms and masses of atoms so that the resulting changes in velocity and vectors would bring them into alignment with our sphere. Never mind all the heat those collisions would create.
I don't think the mathematics could work. Consider accelerating a ship in which you were riding, so that instead of the sphere zipping by you at "thousands of miles per second", the ship, you and the sphere were all moving in the same direction and the same speed, so that the sphere appeared stationary from your prospective. The only way to accelerate you and the ship in this way would be to throw out mass in the opposite direction. Gravity sling-shotting works in the same way, you move faster along a chosen vector, and as a result, some large body is slowed down (or accelerated in the opposite direction).
If you are looking for an example of momentum disappearing, consider two sticky balls of goo, moving toward each other and colliding. The balls hit and if they have the same mass, the resulting two-ball stuck-together system will have zero momentum.
The momentum of the sticky balls just gets converted to heat. The idea is to create a condition where the momentum of the sphere simply ceases to exist since there would no longer be any reference point for its original momentum. Suppose we convert all other matter into energy. This should not violate any Laws. Without the reference point created when the sphere was initially accelerated is there any way to prove what it's true velocity is or for that matter that it has any velocity at all.
Velocity is a speed and direction, and requires a frame of reference to make any sense or have any meaning. In your example, there could be no observer, and therefore no frame of reference. In universe, comprised of a lot of empty space and a single large object, there would be no concept of momentum.
If that object were split in two (or you started with two). Both objects would have, or gain momentum toward each other due to gravity.
I get your idea. One expends a large amount of energy imparting a large momentum to an object in some frame of reference. You then propose that anything which could provide a frame of reference were removed, what would happen to the momentum imparted. It wouldn't be zero, but would cease to have any meaning. Any and all frames of references could be used. No useful work could be extracted from such an object. Calculations or predictions of future could be done in whatever coordinate system you wanted. Some would be much easier than others.