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Comment by vecter | Hacker News Reader

Could anyone explain to me why there's such a dramatic change in the incidence of extra-solar high energy cosmic rays or the incidence of solar particles? Without reading this article, I would have guessed that those graphs should've tailed off "smoothly" as distance from the sun increases, but what we're seeing instead is more of a "phase change". What about the underlying physics at a certain distance causes this very discontinuos behavior, and why this distance specifically? I imagine this cutoff distance must be a function of properties of our sun like luminosity, magnetic field strength, etc.

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Well the data looks close enough to these theories http://en.wikipedia.org/wiki/Heliosphere

Thanks. I think this part describes why: http://en.wikipedia.org/wiki/Heliosphere#Heliopause

    The heliopause is the theoretical boundary where
    the Sun's solar wind is stopped by the interstellar 
    medium; where the solar wind's strength is no longer 
    great enough to push back the stellar winds of the 
    surrounding stars.

It is curious that the wiki mentions Voyager I data for some claims and we use those to verify Voyager I data?

1) When you have a hypothesis, you conduct an experiment.

2) When your experiment yields results that match your hypothesis, you consider that evidence.

3) When you have sufficient evidence, you upgrade your hypothesis to a theorem.

According to the Wikipedia article, we've got at least two probes that are producing results in line with our hypotheses. The bar for wikipedia is "sourced", not proven theorem with scientific rigor. In this case, we're in some nebulous area between 2 and 3. I think that meets the bar for an encyclopedia, which is intended to serve as a summary for these types of things.

Hit the sources and the transitive closure of references for more details.

> 3) When you have sufficient evidence, you upgrade your hypothesis to a theorem.

A theorem is a mathematical result: something proved logically from (possibly physical) assumptions.

Such as the four colour theorem? en.wikipedia.org/wiki/Four_colour_theorem

Especially the four colour theorem - the first mathematical theorem to be proved with software. That said, I believe this discussion pertains to the hypothesis -> theory "upgrade", not to theorems.

The point I was hinting at was that some theorems can be proven by a sufficient body of evidence rather than requiring logical deduction - the four colour theorem being a good example as it was proven by 'brute force' rather than analytically.

Doesn't a logical proof count as evidence? To my mind, these two methods are demonstrating the same thing: considering all the possible inputs, we can show [using logic|by testing them all] that the output meets our criteria.

To my mind, in this context, the difference between maths and physics is that maths is exhaustive while in physics we don't usually have exhaustive evidence so we have to work with what we've got.

Interesting question - to me, the distinction is that 'evidence' of the validity of something is expected output(s) given known input(s), whereas 'proof' (at least in the mathematical sense) is a logical transformation that is applied to make it obvious that the theorem must be true. I'm not sure you could call a proof 'evidence' because it's not an output of the theorem - it is the theorem.

I'm less certain than I was before I read your post, though - so I stand to be corrected :-)

I meant to say "theory", as in gravity.

There are two things: The strength (energy) of the particles, and the number of them.

The particles slow down because they press against the electric field of interstellar particles. So the energy will smoothly go down as Voyager gets farther.

But the number of particles won't change. The number will reach zero once the particles slow down so much they turn around and go the other way but until that point the number of particles won't change.

It would be interesting to see a graph of the energy levels, but I don't know if Voyager carries such a device.

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