Actually, it's possible to to prove that something doesn't exist. It depends on how well defined it is. For example, you can take the dragon in the garage from Sagan's Demon Haunted World.
If you're not familiar with it, the example is a guy who claims to have a dragon in his garage. When you attempt to look for it, not being able to see it, the guy says 'it's an invisible dragon.' And likewise the story continues, each time, there is a reason provided for why the dragon cannot be found.
The issue here is that it's a very poorly defined dragon.
Let's consider the strongly defined dragon. If I claim that there is an 8ft, red, visible, fire breathing dragon sitting on the ground in my back yard, a simple search will disprove that statement. There is no evidence to be found of that dragon, and it can be safe to say that it doesn't exist.
However, if I then say, 'well, the dragon isn't really visible,' then I've changed what you're looking for, and the search must be conducted with those new parameters.
The case with the higgs is similar. It can be possible to say 'a higgs with these properties does (or does not) exist.' If you say 'well, what if it has these different properties' well, it doesn't invalidate those previous results; it just provides you with something new to do.
The core mistake here is that 'absence of evidence' is not always 'evidence of absence,' but many times it is. In the same way that 'correlation is not causation' but many times it is.
If you're not familiar with it, the example is a guy who claims to have a dragon in his garage. When you attempt to look for it, not being able to see it, the guy says 'it's an invisible dragon.' And likewise the story continues, each time, there is a reason provided for why the dragon cannot be found.
The issue here is that it's a very poorly defined dragon.
Let's consider the strongly defined dragon. If I claim that there is an 8ft, red, visible, fire breathing dragon sitting on the ground in my back yard, a simple search will disprove that statement. There is no evidence to be found of that dragon, and it can be safe to say that it doesn't exist.
However, if I then say, 'well, the dragon isn't really visible,' then I've changed what you're looking for, and the search must be conducted with those new parameters.
The case with the higgs is similar. It can be possible to say 'a higgs with these properties does (or does not) exist.' If you say 'well, what if it has these different properties' well, it doesn't invalidate those previous results; it just provides you with something new to do.
The core mistake here is that 'absence of evidence' is not always 'evidence of absence,' but many times it is. In the same way that 'correlation is not causation' but many times it is.