6 Special Relativity
115
end. Why? The reason is that the back end of the carriage is moving towards
the flash, and thus the light has a shorter distance to travel, compared with
the light travelling towards the front end, which is moving away. So, the two
events (when the light impacts on each end of the carriage) appear to be
simultaneous to Mary, but not to Peter, who sees light arrive at the rear end
first.
The implications arising from the dependence of the simultaneity of events
on the state of motion of the observer are profound. Will someone watching
a murder from a speeding carriage see the victim die before the trigger of the
revolver is pulled? Relativity protects us from such absurdities. Events that are
causally connected , i.e. where one event is a direct consequence of the other,
cannot have their order reversed by Lorentz transformations. All observers,
irrespective of their motion, see these events in the correct sequence.
However, we saw in the last Chapter when discussing Entanglement, that
Quantum Mechanics plays free and easy with the concept of simultaneity.
When an observation specifies the state of one of a pair of entangled particles,
the state of the other is simultaneously specified, no matter how far away that
particle is located. There is a disagreement here with the Theory of Relativity,
and it cannot be swept under the carpet. We shall discuss this point further
in Chap. 12, Part 3.
Let us now move on to the final topic in our brave new world . It is so
momentous, not just to physics, but to the history and future of humankind,
that we break the rule we have set ourselves for this book: we allow ourselves
just one mathematical formula.
6.9 The Only Formula in This Book
In fact, it is such an important formula, and it looks so elementary that it
can be found everywhere, even on the T-shirts of people who have no idea of
what it means. We refer, of course, to:
E = mc
2
,
where E stands for energy, m for mass and c is, as usual, the velocity of
light. The formula states the equivalence between mass and energy, with a
coefficient c 2 in the transformation from the latter to the former.
Before Einstein, there existed two separate conservation laws in chemistry
and physics; i.e. the Law of Conservation of Mass, and the Law of Conservation of Energy. In chemical reactions, the total mass of the reactants had to
be equal to the total mass of the reaction products. In physics, it had long
115
end. Why? The reason is that the back end of the carriage is moving towards
the flash, and thus the light has a shorter distance to travel, compared with
the light travelling towards the front end, which is moving away. So, the two
events (when the light impacts on each end of the carriage) appear to be
simultaneous to Mary, but not to Peter, who sees light arrive at the rear end
first.
The implications arising from the dependence of the simultaneity of events
on the state of motion of the observer are profound. Will someone watching
a murder from a speeding carriage see the victim die before the trigger of the
revolver is pulled? Relativity protects us from such absurdities. Events that are
causally connected , i.e. where one event is a direct consequence of the other,
cannot have their order reversed by Lorentz transformations. All observers,
irrespective of their motion, see these events in the correct sequence.
However, we saw in the last Chapter when discussing Entanglement, that
Quantum Mechanics plays free and easy with the concept of simultaneity.
When an observation specifies the state of one of a pair of entangled particles,
the state of the other is simultaneously specified, no matter how far away that
particle is located. There is a disagreement here with the Theory of Relativity,
and it cannot be swept under the carpet. We shall discuss this point further
in Chap. 12, Part 3.
Let us now move on to the final topic in our brave new world . It is so
momentous, not just to physics, but to the history and future of humankind,
that we break the rule we have set ourselves for this book: we allow ourselves
just one mathematical formula.
6.9 The Only Formula in This Book
In fact, it is such an important formula, and it looks so elementary that it
can be found everywhere, even on the T-shirts of people who have no idea of
what it means. We refer, of course, to:
E = mc
2
,
where E stands for energy, m for mass and c is, as usual, the velocity of
light. The formula states the equivalence between mass and energy, with a
coefficient c 2 in the transformation from the latter to the former.
Before Einstein, there existed two separate conservation laws in chemistry
and physics; i.e. the Law of Conservation of Mass, and the Law of Conservation of Energy. In chemical reactions, the total mass of the reactants had to
be equal to the total mass of the reaction products. In physics, it had long