A question of relativity

[ResidentIdiot]

The energy released in an atomic bomb is equal to the change in mass due to the fission of the deuterium molecules multiplied by the speed of light squared, or E=mc2. Now this mass is a relative quantity therfore it is multiplied by a factor of the square root of one minus the speed of the object squared divided by the speed of light squared. In real world applications this is irrelevant as, for example, when an atomic bomb is dropped from a plane it achieves terminal velocity at about 120kph so the relative difference to a stationary observer is negligable. However from an inertial point of reference outside of our galaxy the bomb could potentially be moving at a considerable proportion of the speed of light and therefore the yeild of the bomb could be increased several times over.

I am asking this question as somone who has taught themselves on this topic and so there is the chance that i have missed somthing blindingly obvious.

How can the yeild of a nuclear bomb be a realtive quantity?

 

[silverpig]

First, it's fission of uranium or plutonium, or, fusion of deuterium and tritium.

Now, when an object gains mass as it speeds up, that mass doesn't necessarily have to be more of whatever the object is made of. For example, protons are made of 3 quarks and some gluons, yet, when they smash them open at .999c or whatever, a whole slew of other particles pop out of the mess. kaons, pions, etc etc.

Basically, when you speed up an object you give it kinetic energy. At slow speeds, most of what you put in results in the object speeding up. As you get closer to c, the energy you put in turns into mass. If you then turn this mass into energy again via a nuclear reaction, you'll just get your input energy back again. The energy just changes into mass, is transported, and then changes back.

 

[Woodchuck2000]

Silverpig - Are you saying that other fundamental particles literally appear in the object to account for the extra mass?
I was under the impression that the reason the particles appear from high-energy collisions is that sufficient energy is produced to break atoms into their tiniest components.

As far as the original question goes: The absolute mass of any object (as modified proportional to it's velocity) is relative to something that is completely still. The reference frame you're looking at it from is irrelevant.

The yield of a bomb is indeed proportional to its absolute velocity since the mass converted to energy increases.

I think...

EDIT:
BTW, welcome to the forums.

 

[Woodchuck2000]

Basically, when you speed up an object you give it kinetic energy. At slow speeds, most of what you put in results in the object speeding up. As you get closer to c, the energy you put in turns into mass. If you then turn this mass into energy again via a nuclear reaction, you'll just get your input energy back again. The energy just changes into mass, is transported, and then changes back. /q]
Thinking about it, That statement isn't technically correct (by my understanding.)

You talk about varying amounts of 'what you put in' going to either energy or mass depending on the absolute velocity.

The fundamental thing is, Mass is fundamentally the same as energy. hence the direct conversion E=MC^2
Even accelerating things by 1M/s^2 is increasing their mass - the change is just so infinitessimal as to be irrelevant and unmeasurable. Because the particular relationship between velocity and mass is exponential, the effects are very much greater at high velocities.

 

[bwanaaa]

as i understand resident idiot's question, i would propose the following corollary- If you have an unlimited supply of identical atomic bombs and detonate each one at succssively greater velocities, then the yield of each would increase because the mass of the bomb is greater. But one has to be a little more precise here i think.

enargy at detonation = mc^2 +mv^2 where
mc^2 is the energy released by the nuclear process and
mv^2 is kinetic energy of the bomb at the time of detonation

As v approaches c, you max out the total detonation energy at double.

now what is this crap about mass increasing as you approach c?

(i wanted to use a stronger 4 letter word but the algorithm of this board is too puritan and would not permit it)

 

[RossGr]

This is a bit more complex then has been so far presented. The energy produced by an atomic explosion (either fission or fusion) is determined by the binding energy of the atoms present. The binding energy is essentialy the change in mass from the original atoms to those produced by the reaction. Is atomic binding energy effected by relativity? It is not clear to me, and I would lean towards no, it is not. If it is not, then the total energy of the explosion, being dependent only on the NUMBER of reacting atoms, will not vary. Since the number of atoms is certianly not effected by relativity.

Now I have even a more basic concern about this entire line of thinking. When we accelerate a body from our rest frame to a higher velocity, we observe and can measure an apparent increase in mass. The theory is that as we accelerate the body a portion of the energy applied is transformed into mass. The higer the relative velocity, the greater the portion of energy transformed to mass. Does this change in mass apply to an object which is initially observed at the higher velocity? We have not supplied any energy so why is the mass increased? My thought is that it would depend upon how you determine that mass. If it is based upon motion relative to other bodies in its frame of reference it seems that we would measure its REST mass and not the relativistic mass. So a fundamental question would have to be, "How do you measure the mass?" This question must be answered before any meaningful answer can be given to this question.

 

[bwanaaa]

I agree that the velocity of a nuclear reaction should not affect its mass and therefore its output. Accelerating a star does not make it brighter.

 

[esun]

I agree that the velocity of a nuclear reaction should not affect its mass and therefore its output. Accelerating a star does not make it brighter.

Well let's say we accelerate the nuclear reaction to c. What then? If we convert the entire mass of the bomb to energy certainly the result will be a much larger explosion that otherwise provided by the tiny amount of mass converted under real velocities.

And while accelerating a star may not increase its brightness, what about its mass? Either way you're increasing its energy.


I believe this question has an obvious answer. If you're increasing the mass of the entire system (bomb and all) by increasing its velocity (and we'll assume the same relative velocity between the bomb and its target), then of course the energy released must increase. Don't think of it as changing the frame of reference of the observer, but of the bomb (we know they will have the same effect, and it's easier to think of it if the bomb is changing speed than if the observer is).

now what is this crap about mass increasing as you approach c?

I wish I could remember the equation, but I can't. There is a relationship between mass and velocity, length and velocity, and time and velocity (aka time dilation). The important thing to know is that the limit of the mass of an object as the velocity of that object approaches c is infinity (which is why Einstein believed nothing can travel at or faster than the speed of light).