Pairs that cancel to zero ...

[TaoRich]

Greetz,

 

What is the correct term for "pairs of opposites" that "cancel to zero".

 

For example:

• 7 and -7 cancel to zero if added
• identical rising and falling waves cancel to zero if they interfere at a point where their amplitude is precisely the same
• a particle and an antiparticle cancel each other out if they interact

The word complementary seems to describe the relationship quite well, but there are (many) very specific uses in Maths & Physics.

 

In set theory, a complement of a set A refers to things not in (that is, things outside of), A.

In physics, complementarity is a basic principle of quantum theory proposed by Niels Bohr, closely identified with the Copenhagen interpretation, and refers to effects such as the wave–particle duality.

So we'd hit some confusion there.

 

The word symmetry also seems to describe the relationship quite well since we could say:

• 7 and -7 lie symmetrically opposite from each other in equal distance from (the reflection plane) 0
• identical rising and falling waves lie symmetrically opposite from each other in equal distance from (the reflection plane) 0 amplitude
• a particle and an antiparticle are symmetrical and opposite

But again, symmetry has formal specific meaning in various Maths & Physics contexts.

 

I've been hunting around for a term in common usage - but not much luck thus far.

 

Can anybody help with a reference or some suggestions ?

 

I'd like to use it in the context:

• 7 is the ________ of -7
• a rising wave is the ________ of a falling waves with identical amplitude
• a particle is the ________ of an antiparticle

I'm inclined to lean towards:

A particle is the

symmetric complement

of an antiparticle

But I'm acutely aware that inventing a new language, or using established formal terms in a sloppy fashion is not a good way to earn respect or be taken seriously.

 

Cheers

Rich

Edited February 22, 2011 by TaoRich

[Schrödinger's hat]

Greetz,

 

What is the correct term for "pairs of opposites" that "cancel to zero".

 

For example:

• 7 and -7 cancel to zero if added
• identical rising and falling waves cancel to zero if they interfere at a point where their amplitude is precisely the same
• a particle and an antiparticle cancel each other out if they interact

The word complementary seems to describe the relationship quite well, but there are (many) very specific uses in Maths & Physics.

 

 

 

So we'd hit some confusion there.

 

The word symmetry also seems to describe the relationship quite well since we could say:

• 7 and -7 lie symmetrically opposite from each other in equal distance from (the reflection plane) 0
• identical rising and falling waves lie symmetrically opposite from each other in equal distance from (the reflection plane) 0 amplitude
• a particle and an antiparticle are symmetrical and opposite

But again, symmetry has formal specific meaning in various Maths & Physics contexts.

 

I've been hunting around for a term in common usage - but not much luck thus far.

 

Can anybody help with a reference or some suggestions ?

 

I'd like to use it in the context:

• 7 is the ________ of -7
• a rising wave is the ________ of a falling waves with identical amplitude
• a particle is the ________ of an antiparticle

I'm inclined to lean towards:

A particle is the

symmetric complement

of an antiparticle

But I'm acutely aware that inventing a new language, or using established formal terms in a sloppy fashion is not a good way to earn respect or be taken seriously.

 

Cheers

Rich

 

 

 

Inverse is the often used term.

7 and -7 are additive inverses. They add to give the identity 0.

A slightly different version of your waves: A sine wave and one 180 degrees out are also additive inverses. They add to give the identity in their space (a 0 function)

5 and 0.2 are multiplicative inverses.

 

I guess you could use the same word for a particle/antiparticle pair. I haven't seen it done very often. The particles are time-reversed counterparts (or compliments). So are a the rising and falling wave.

 

 

[TaoRich]

Inverse is the often used term.

Thanks.

 

Again however with the term inverse, we've got:

• additive inverses which adds to zero
• multiplicative inverses which multiply to one

Here's a quotation which may help focus my query and the discussion:

 

 

Where did the substance of the universe come from ?

 

If 0 equals ( + 1) + (-1), then something which is 0 might just as well become + 1 and -1.

 

Perhaps in an infinite sea of nothingness, globs of positive and negative energy in equal-sized pairs are constantly forming, and after passing through evolutionary changes, combining once more and vanishing. We are in one of these globs between nothing and nothing and wondering about it.

 

~ Isaac Asimov

So when we "cleave zero into symmetrical complementary pairs" what do we call those pairs ?

Edited February 22, 2011 by TaoRich

[ajb]

So when we "cleave zero into symmetrical complementary pairs" what do we call those pairs ?

 

Clearly such a decomposition is is far from unique. Other than a pair of mutually additive inverses, I am unaware of any special name attached.

 

You may also be interested in the notion of characteristic. In short, given a ring it is the minimum number of times you must sum the multiplicative identity 1, to get the rings additive identity 0.