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Thread: Question on Matter and Energy Equivalence

  1. #1 Question on Matter and Energy Equivalence 
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    Alright, if 2 particles of known initial mass are accelerated to an incredibly high speed (a relativistic speed) in opposite directions, and then collide in an inelastic collision, the final mass of the 2 collided particles is greater than the sum of their initial masses, right?

    Am I understanding that correctly?


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  3. #2  
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    In order to have such an inelastic collision between two particles, you would have to meet some conditions. For one they would have to be particles that would naturally merge to form a new particle.

    So if you collide a Proton and Electron, you could form an neutron if the kinetic energy of the pair before the collision was 780 Kev. In which case you would have your more massive particle. If their KE was greater than that, you would produce a neutron and and anti-neutrino which would carry away the excess energy.

    You can't just collide any two particles together and form a new particle which has the equivalent mass of the combined mass of the two plus their KE.


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  4. #3 Re: Question on Matter and Energy Equivalence 
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    Quote Originally Posted by kojax
    Alright, if 2 particles of known initial mass are accelerated to an incredibly high speed (a relativistic speed) in opposite directions, and then collide in an inelastic collision, the final mass of the 2 collided particles is greater than the sum of their initial masses, right?

    Am I understanding that correctly?
    An inelastic collision is a notion that does not apply to elementary particles. It is an indealization used at the macroscopic level in which kinetic energy is not conserved, but momentumis conserved. In reality energy is conserved in that some of the initial kinetic energy of the colliding bodies is realized as heat.

    At the level of elementary particles all collisions demonstrate explicit conservation of both momentum and energy.

    The mass-energy of the particles (all of them) following a collison is equal to the mass-energy of the particles prior to the collision. Momentum is also conserved. There may be other quantum numbers that are conserved as well, depending on the particles involved.
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  5. #4 Re: Question on Matter and Energy Equivalence 
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    An inelastic collision is a notion that does not apply to elementary particles. It is an indealization used at the macroscopic level in which kinetic energy is not conserved, but momentumis conserved. In reality energy is conserved in that some of the initial kinetic energy of the colliding bodies is realized as heat.

    At the level of elementary particles all collisions demonstrate explicit conservation of both momentum and energy.
    Although energy is always conserved, there is a distinction between collisions which result simply in a change of direction (elastic) and those where some of the energy is absorbed internally by one or the other particles (inelastic). This is quite common in neutron-nuclei collisions.
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  6. #5 Re: Question on Matter and Energy Equivalence 
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    Quote Originally Posted by mathman
    An inelastic collision is a notion that does not apply to elementary particles. It is an indealization used at the macroscopic level in which kinetic energy is not conserved, but momentumis conserved. In reality energy is conserved in that some of the initial kinetic energy of the colliding bodies is realized as heat.

    At the level of elementary particles all collisions demonstrate explicit conservation of both momentum and energy.
    Although energy is always conserved, there is a distinction between collisions which result simply in a change of direction (elastic) and those where some of the energy is absorbed internally by one or the other particles (inelastic). This is quite common in neutron-nuclei collisions.
    Yes, but nuclei are not elementary particles. Technically, neither are neutrons.

    On the other hand, I stand appropriately corrected in that they are hardly macroscopic either

    The key ingredient is the ability to absorb some of the energy internally -- in a form not being directly considered in the model at hand.

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  7. #6 Re: Question on Matter and Energy Equivalence 
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    Quote Originally Posted by DrRocket
    Quote Originally Posted by kojax
    Alright, if 2 particles of known initial mass are accelerated to an incredibly high speed (a relativistic speed) in opposite directions, and then collide in an inelastic collision, the final mass of the 2 collided particles is greater than the sum of their initial masses, right?

    Am I understanding that correctly?
    An inelastic collision is a notion that does not apply to elementary particles. It is an indealization used at the macroscopic level in which kinetic energy is not conserved, but momentumis conserved. In reality energy is conserved in that some of the initial kinetic energy of the colliding bodies is realized as heat.
    Is there any form of the experiment that can be carried out on the macroscopic level, maybe for slightly lower speeds? Would all the excess energy simply become heat, or would some small, yet observable increase in mass still occur?
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  8. #7 Re: Question on Matter and Energy Equivalence 
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    Quote Originally Posted by kojax
    Quote Originally Posted by DrRocket
    Quote Originally Posted by kojax
    Alright, if 2 particles of known initial mass are accelerated to an incredibly high speed (a relativistic speed) in opposite directions, and then collide in an inelastic collision, the final mass of the 2 collided particles is greater than the sum of their initial masses, right?

    Am I understanding that correctly?
    An inelastic collision is a notion that does not apply to elementary particles. It is an idealization used at the macroscopic level in which kinetic energy is not conserved, but momentum is conserved. In reality energy is conserved in that some of the initial kinetic energy of the colliding bodies is realized as heat.
    Is there any form of the experiment that can be carried out on the macroscopic level, maybe for slightly lower speeds? Would all the excess energy simply become heat, or would some small, yet observable increase in mass still occur?
    As mathman noted there are good models in terms of collisions with nuclei.

    The equivalence of mass and energy is confirmed in experiments in colliders daily.

    When we say that excess energy becomes heat, that simply means that some of the kinetic energy in the initial particles is, after the collision, realized as kinetic energy of the particles that comprise one or more of the bodies involved. That kinetic energy also contributes to the mass of the body, so there is an increase in mass that goes along with the heat.

    Now you have opened a can of worms, and someone is certain to chime in with the philosophy that "mass" should only be interpreted as "rest mass". But that is a red herring. A hot body will weigh more, on a scale, than a cold body and the relationship is precisely quantified using the equation .

    Mass and energy are the same thing, and at a deeper level they also identified with momentum. To emphasize these points Misner, Thorne and Wheeler in their book Gravitation which is now one of the classics use the terms mass-energy and momenergy to get across the idea that the ideas are not really separable.
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  9. #8 Re: Question on Matter and Energy Equivalence 
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    Quote Originally Posted by kojax
    Quote Originally Posted by DrRocket
    Quote Originally Posted by kojax
    Alright, if 2 particles of known initial mass are accelerated to an incredibly high speed (a relativistic speed) in opposite directions, and then collide in an inelastic collision, the final mass of the 2 collided particles is greater than the sum of their initial masses, right?

    Am I understanding that correctly?
    An inelastic collision is a notion that does not apply to elementary particles. It is an indealization used at the macroscopic level in which kinetic energy is not conserved, but momentumis conserved. In reality energy is conserved in that some of the initial kinetic energy of the colliding bodies is realized as heat.
    Is there any form of the experiment that can be carried out on the macroscopic level, maybe for slightly lower speeds? Would all the excess energy simply become heat, or would some small, yet observable increase in mass still occur?
    Would two bodies of macroscopic scale, properly accelerated, result in an increase in mass or energy? I know that heat increases the mas, and so does compression, but what about just the relativistic mass increase? You may have answered that but i missed it.
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  10. #9 Re: Question on Matter and Energy Equivalence 
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    Quote Originally Posted by Wildstar
    Would two bodies of macroscopic scale, properly accelerated, result in an increase in mass or energy? I know that heat increases the mas, and so does compression, but what about just the relativistic mass increase? You may have answered that but i missed it.
    Technically, yes. But they would need to be approaching lightspeed for the change in mass to be noticable, I suspect.
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  11. #10 Re: Question on Matter and Energy Equivalence 
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    Quote Originally Posted by DrRocket
    Now you have opened a can of worms, and someone is certain to chime in with the philosophy that "mass" should only be interpreted as "rest mass". But that is a red herring. A hot body will weigh more, on a scale, than a cold body and the relationship is precisely quantified using the equation .

    Mass and energy are the same thing, and at a deeper level they also identified with momentum. To emphasize these points Misner, Thorne and Wheeler in their book Gravitation which is now one of the classics use the terms mass-energy and momenergy to get across the idea that the ideas are not really separable.
    Maybe you're thinking of me when you refer to someone chiming in. Let me clarify--I don't dispute that one can make sense of "relativistic mass". I just personally find it more natural and less confusing to use the word mass to refer to "rest mass", and otherwise confine myself to speaking in terms of 4-momentum, etc.

    For me, this perspective is easier because I'm more comfortable dealing with tensors and scalars (like 4-momentum and rest mass) than with frame-dependent quantities like relativistic mass. Chalk that up to my background in manifold-theory.
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  12. #11  
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    So if you collide a Proton and Electron, you could form an neutron if the kinetic energy of the pair before the collision was 780 Kev.
    Wait....will an actual neutron be formed or an atom that has a total charge of a neutron?
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  13. #12 Re: Question on Matter and Energy Equivalence 
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    Quote Originally Posted by salsaonline
    Quote Originally Posted by DrRocket
    Now you have opened a can of worms, and someone is certain to chime in with the philosophy that "mass" should only be interpreted as "rest mass". But that is a red herring. A hot body will weigh more, on a scale, than a cold body and the relationship is precisely quantified using the equation .

    Mass and energy are the same thing, and at a deeper level they also identified with momentum. To emphasize these points Misner, Thorne and Wheeler in their book Gravitation which is now one of the classics use the terms mass-energy and momenergy to get across the idea that the ideas are not really separable.
    Maybe you're thinking of me when you refer to someone chiming in. Let me clarify--I don't dispute that one can make sense of "relativistic mass". I just personally find it more natural and less confusing to use the word mass to refer to "rest mass", and otherwise confine myself to speaking in terms of 4-momentum, etc.

    For me, this perspective is easier because I'm more comfortable dealing with tensors and scalars (like 4-momentum and rest mass) than with frame-dependent quantities like relativistic mass. Chalk that up to my background in manifold-theory.
    Actually I was thinking of someone a bit more dogmatic, and less perceptive.

    There is nothing whatever wrong with thinking of mass and energy in terms of the 4-vector which includes both of them. That is probably the best way to do it. That perspective actually does away with the need to talk about "mass" per se, and that is ultimately the right way, since mass, ordinary energy, and ordinary momentum are observer-dependent. The "norm" of the 4-vector for mass-energy is always mc (where m is rest mass), independent of the observer and therefore you an invariant quantity.

    The only real problem that I know of arises when you are talking about real macroscopic matter -- an ensemble of particles jiggling around. And there you don't have any clear reference frame in which to talkie about rest mass of each of them simultaneously (whatever simultaneous means), and when you weigh that blob on a scale you unavoidably get the relativistic mass which includes thermal kinetic energy.

    There is a bit of a conflict between the elegance of the Minkowski formulation and the exigencies of instruments and experiment, because to do experiments in the laboratory you must ultimates coordinatize things and work with 3 spatial dimensions and 1 separate time dimension, rather than directly with Minkowski space-time with its inherent metric.

    The tenor of the discussion becomes quite different when one is permitted to conduct it using the unadulterated languate of manifolds. But it is also limited to those who are confortable in the language.
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  14. #13  
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    When dealing with ensembles of particles, if the Lagrangian of the entire ensemble is symmetric under boosts, then the "center of energy" will be conserved. So, at least in low gravity situations, this seems like a good way to deal with that situation.
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  15. #14  
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    Quote Originally Posted by salsaonline
    When dealing with ensembles of particles, if the Lagrangian of the entire ensemble is symmetric under boosts, then the "center of energy" will be conserved. So, at least in low gravity situations, this seems like a good way to deal with that situation.
    How does that address the issue of increasesd mass-energy with temperature ?
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  16. #15  
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    Now you're asking me how to do relativistic thermodynamics. I have enough trouble with regular thermodynamics. I imagine someone can answer your question, but that someone unfortunately isn't me.
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