E3 Mass and Energy – Observations in a Closed System
For the following considerations we must introduce the concept of a ‘closed system'. One imagines an arbitrarily large, clearly limited space (e.g. a cube, a box, or the inside of an enormous thermos bottle etc.). One postulates that the enclosed area has no exchange with the surrounding space: Neither matter nor charge, neither energy nor momenta flow through the walls. No fields on the outside have influence on the inside nor vice-versa, nor do any forces from the outside act on the inside, nor any from the inside on the outside. We imagine such a perfectly isolated region of space and we immediately admit that no such thing really exists. We also know that no Einstein trains exist, no ideal clocks and no rigid yardsticks! That cannot prevent from imagining such things.
Let such a closed system contain only two lead clumps of equivalent mass, which race toward each other with equal velocities. After the collision they form one large clump of lead at rest (diagram and argument from [15-117]):
Where does the increased mass go, which, due to their speed, the two clumps possess before the collision? It must be somewhere in our closed system. Students usually hit upon a good answer: The large resting clump is warmer due to the deformation of the collision. The individual particles of matter have an increased velocity. The dynamic mass is thus still available, but no longer macroscopically visible. Okay, but that means that we add mass to a stone, whenever we warm it up - no matter how ! Energy input is thus connected to an increase in mass. If we use a car battery and a radiating heater, in order to warm up a stone, the stone will have more mass afterwards than before - and the battery less! With the flow of energy from the battery into the stone we have also moved mass into the stone!
We can easily avoid using thermodynamics in our thought experiment, if we reverse the process: A spring is wedged between two small clumps with the assistance of a thread. The thread is strained to its limit and is about to break. The spring relaxes, remains where it was and the two clumps race in opposite directions from it. They both have a large speed now and their mass thus has increased. Where does this mass come from? The spring got warmer when relaxing, so the extra mass cannot this time be from the temperature. If afterwards the clumps have more mass - what did we have before? Before elastic energy was in the tensed spring, and the additional mass must have come from it.
Epstein provides in [15-117f] a similar example:
Before, the flywheel is at rest and the spiral spring is tensed. After, we have a relaxed spiral spring and a rotating flywheel. The rotating flywheel must have more mass than the one standing still. This additional mass can only come from the energy in the tensed spring. Yes, we must say that this additional mass of the flywheel was previously in the tensed spring, if we assume the entire mass in a closed system must be constant.
We must get accustomed to the idea that an energy input always implies an increase of mass. A spring has more mass after stretching than before, and a loaded condenser must have more mass than one unloaded, although only some electrons were shifted from one condenser plate to the other. The question then arises, how much additional mass does a Joule of additional energy bring? The Scottish brewer and ‘amateur physicist’ James Prescott Joule answered in 1843 the question, how many Joules of mechanical energy correspond to a calorie of heat energy. We must now clarify, how many Joules of energy correspond to a kilogram of mass!
James Prescott Joule (1818-1889)
Joule at the age of 16 to 18 enjoyed together with his brother two years of private instruction with the great John Dalton. He was not allowed to study at a university and had to take over the direction of the family brewery at an early age. It is very informative to see how hesitantly the distinguished Royal Society in London and other established gentlemen took notice of Joule’s elegant experiments. Commendable exceptions were James Clerk Maxwell, whom we have already met and John Davis, promoter also of another great autodidact Faraday.
Read the Wikipedia contribution to Joule or that at www.bhak-bludenz.ac.at/physik/geschichte/physiker/joule.shtml