Additions:
Additions:
For [[http://en.wikipedia.org/wiki/Identical_particles identical particles]], there is no way of telling which is which in a measurement. Switching identical particles makes no difference to the physical situation. We extend the language to cover this situation.
For a two particle system ""
"", and we require that ""
"" and ""
"" are both ""TRUE"",
Deletions:
For [[http://en.wikipedia.org/wiki/Identical_particles identical particles]], there is no way of telling which is which in a measurement. Switching identical particles makes no difference to the physical situation. We extend the language to cover this situation. For a two particle system """", and we require that """" and """" are both ""TRUE"",
Additions:
For [[http://en.wikipedia.org/wiki/Identical_particles identical particles]], there is no way of telling which is which in a measurement. Switching identical particles makes no difference to the physical situation. We extend the language to cover this situation. For a two particle system """", and we require that """" and """" are both ""TRUE"",
Deletions:
For [[http://en.wikipedia.org/wiki/Identical_particles identical particles]], there is no way of telling which is which in a measurement. Switching identical particles makes no difference to the physical situation. We extend the language to cover this situation. For a two particle system, """", """" and we require that """" are both ""TRUE"",
Additions:
For [[http://en.wikipedia.org/wiki/Identical_particles identical particles]], there is no way of telling which is which in a measurement. Switching identical particles makes no difference to the physical situation. We extend the language to cover this situation. For a two particle system, """", """" and we require that """" are both ""TRUE"",
Deletions:
For [[http://en.wikipedia.org/wiki/Identical_particles identical particles]], there is no way of telling which is which in a measurement. Switching identical particles makes no difference to the physical situation. We extend the language to cover this situation. For a two particle system
""""
"""" and """" are both ""TRUE"",
Additions:
In practice we may not know how many particles there are, and the number of particles may be subject to change. To accommodate this within the structure of vector space we form a [[http://en.wikipedia.org/wiki/Direct_sum direct sum]]. A direct sum means that we take a set of all the basis elements of all the spaces, ""Hn"", and use it as a basis for a new vector space by introducing new operations of addition and multiplication space, while maintaining compatibility with existing addition and multiplication by scalars. In terms of the formal language this means we can make statements about an uncertain number of particles, using weighted logical ""OR"", ""“If, for each of n or m particles, but more likely n than m, …”"", etc.
Deletions:
In practice we may not know how many particles there are, and the number of particles may be subject to change. To accommodate this within the structure of vector space we form a [[http://en.wikipedia.org/wiki/Direct_sum direct sum]]. A direct sum means that we take a set of all the basis elements of all the spaces, ""Hn"", and use it as a basis for a new vector space by introducing new operations of addition and multiplication space, while maintaining compatibility with existing addition and multiplication by scalars. In terms of the formal language this means we can make statements about an uncertain number of particles, using weighted logical """OR"", ""“If, for each of n or m particles, but more likely n than m, …”"", etc.
