| Chronology | Current Month | Current Thread | Current Date |
| [Year List] [Month List (current year)] | [Date Index] [Thread Index] | [Thread Prev] [Thread Next] | [Date Prev] [Date Next] |
-----Original Message-----The energy of a particle is its rest mass. That's all there is too it. If, in some reference frame, the particle is moving, the kinetic energy associated with that motion is part of the total energy of a larger system, it isn't part of the total energy of the particle.
From: Phys-l [mailto:phys-l-bounces@www.phys-l.org] On Behalf Of John
Denker
Sent: Tuesday, September 29, 2015 4:09 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] let's define energy
On 09/29/2015 12:52 PM, Jeffrey Schnick wrote:
/Physics/ energy is just mass.
I wouldn't have said that. The equation E=mc^2 is perhaps the most famous
equation in the history of equations ... but it is widely misinterpreted. The E
on the LHS is the rest energy, not the total energy.
This is the meaning that Einstein intended in his original paper, and remains
the only reasonable interpretation.
No. A particle can have no kinetic energy. To assign the kinetic energy of a system to a particle is convenient--I do it all the time. But to think of it as an actual characteristic of the particle is going too far. Unless the particle interacts with something else, the kinetic energy has no relevance. When it does interact with something else it is the energy in the rest frame of the system consisting of the particle and that something else that matters. Observers in all reference frames would all agree on what happens in the interaction and they would all agree that any kinetic energy that the participants in the interaction might be said to have because the center of mass of the system is moving relative to them (the observers) is irrelevant. Having the outcome of the interaction depend on that kinetic energy would be a violation of Galilean relativity. That energy would indeed be relevant to the interaction of the participants with a third party, but it would then be a contribution to the mass/energy of the system of all three parties, it would not belong to the first two.
Energy is conserved. Mass is not. [1]
The usual objection to that is that the kinetic energy of a particle
is not its mass.
Indeed. That is a fatal objection ... perhaps not quite as fatal as [1], but fatal
enough.
With each system there is a reference frame. There are an infinite number of systems to choose from, in an infinite number of reference frames. Physics survives.
In interactions, what matters is the kinetic energy of the system in
the reference frame in which the center of mass is at rest.
That is not a viable way of getting around the fatal objection. In particular,
when watching a baseball game, I can define "the system" to be bat+ball ...
or define it as bat+ball+earth. If you insist that there's only one reference
frame in which the energy can be correctly calculated, all of physics comes to
an end.
Not to mention the fact that it violates Galileo's principle of relativity.
In special relativity, energy is one component of the [energy, momentum] 4-
vector. In any particular frame, each component of this 4-vector is separately
conserved.
Mass is the invariant norm of this 4-vector. Oddly enough, even though it is
intimately related to some conserved quantities, and even though it is
Lorentz invariant, it is not conserved.
https://www.av8n.com/physics/spacetime-welcome.htm#sec-invariance-
conservation
or equivalently
http://www.av8n.com/physics/spacetime-welcome.htm#sec-invariance-
conservation
_______________________________________________
Forum for Physics Educators
Phys-l@www.phys-l.org
http://www.phys-l.org/mailman/listinfo/phys-l