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1. √(-1) = √(-1)
√(-1/1) = √(1/-1)
√(-1)/√(1) = √(1)/√(-1)
√(-1)√(-1) = √(1)√(1)
-1 = 1

The error here is the ambiguity of √(-1). This is not equal to j, but is equal to +/- j. Because +j^2 = -1, and (-j)^2 = -1. The flaw in the argument is that at one stage √(-1) = +j, and that at another moment it equals -j.
2. (Original post by Willla2)
√(-1) = √(-1)
√(-1/1) = √(1/-1)
√(-1)/√(1) = √(1)/√(-1)
√(-1)√(-1) = √(1)√(1)
-1 = 1

The error here is the ambiguity of √(-1). This is not equal to j, but is equal to +/- j. Because +j^2 = -1, and (-j)^2 = -1. The flaw in the argument is that at one stage √(-1) = +j, and that at another moment it equals -j.
I think it's "i" from what I remember all those years ago... (but lets not argue over some letters which are interchangeable in Latin anyway!)

I don't quite understand... Are you saying Squishy is or might be right? I don't see how you can arbitarially say root minus one is i in one case, -i in another and then multiply them together to give you 1. If you do that I could say (root one) squared is -1 and that (cube root one) cubed can be either one or either of the complex conjugate roots, depending on what value I give to (cube root one) on each occassion.

It doesn't hold water for me (which is a ***** as I'm very hot and thirsty! )

PS - I think you are right on the negative mass thing... My mate Dave (a masochist - both used to go to a dodgy club called the Dungeon in Soton and chose to do a theoretical physics PhD!) said that my question was based on a fallacy. Negative mass does not exist, the neutrons formed in beta positive decay simply have less mass/energy than the protons they come from..
3. i used it as 'i' but from what i can recall my teacher said that 'j' is used by some people too.
4. but no, neutrons have MORE mass/energy than protons - they are more unstable! The additional mass comes from the surrounding unstable nucleus.

And i use j's because that's what we use now-a-days

and i'm working on a better explanation for the problem with that maths thingum. It's definitely wrong, and it's definitely due to an ambiguity of root of -1.

i've just thought of something you might get though.

√(-1) = √(-1)
√(-1/1) = √(1/-1)

Agreed on that, that is true
but the next stage makes a mistake:

√(-1)/√(1) = √(1)/√(-1)

Here, we must make it clear that the square roots are +/- (especially the root of 1)

so for simplicity sake I will say √(-1) = j again, therefore:

(+- j)/(+- 1) = (+- 1)/(+- j)

so (+- j)(+- j) = (+- 1)(+- 1)

and the sequence assumes all the values are +, when in fact either one of the 1's is a -, or one of the j's is a minus.

argh that's not very clear, but i'm not thinking that straight today.
5. (Original post by Willla2)
but no, neutrons have MORE mass/energy than protons - they are more unstable! The additional mass comes from the surrounding unstable nucleus.
Are you claiming that all independant protons/neutrons have the same mass. I don't buy that.

If you are firing "high energy" neutrons at some nucleus or other, these neutrons must have more mass than another neutron relaxing down at the beach with a nice drink with lots of ice in it.

I believe that there is probably a normal distribution of energies and that at the extremes a heavy proton can have more mass than a light neutron...

Maybe we should wait until one of the MSc dudes comes along to help us out on this! (I acknowledge that you may be right)
6. dude, i dont need their help. Protons have a lower REST MASS than neutrons. That is a fact. Protons only B+ decay when it is energetically favourable (i.e. when the nucleus is so unstable that it is better that a single proton become more unstable in exchange for the overall nucleus stablity to increase)
7. (Original post by rockindemon)
i used it as 'i' but from what i can recall my teacher said that 'j' is used by some people too.
i = maths, j = engineering
8. (Original post by polthegael)
Are you claiming that all independant protons/neutrons have the same mass. I don't buy that.

If you are firing "high energy" neutrons at some nucleus or other, these neutrons must have more mass than another neutron relaxing down at the beach with a nice drink with lots of ice in it.

I believe that there is probably a normal distribution of energies and that at the extremes a heavy proton can have more mass than a light neutron...

Maybe we should wait until one of the MSc dudes comes along to help us out on this! (I acknowledge that you may be right)
Hmmmm...seems to be the scientific debate has now moved onto this thread

G
9. (Original post by Willla2)
Protons have a lower REST MASS than neutrons.
I agree. Now you show me a stationary neutron or proton...
10. you can sure as hell make a proton stationary...just slap it in an electric field and increase the filed strength until all the kinetic energy disappears!
11. (Original post by Willla2)
you can sure as hell make a proton stationary...just slap it in an electric field and increase the filed strength until all the kinetic energy disappears!
Work your fields to a tee, and you have a variety of same energy/mass protons... Well done!

Now place them in the confines of a nucleus with loads of topless neutrons playing gluon-volleyball with them and their energies will change significantly...

Or just let them buzz around the universe and they will also have various energies/masses.

In such, they will have a normal distribution of energies, I'd guess. I'd also postulate that the heaviest protons would be more massive than the lightest neutron...
12. of course the heaviest protons are heavier than the lightest neutrons, but that doesnt necessarily have anything to do with their stability. I'm pretty sure that if you accelerate a neutron it doesn't increase it's probability of decay.
13. (Original post by Willla2)
of course the heaviest protons are heavier than the lightest neutrons, but that doesnt necessarily have anything to do with their stability. I'm pretty sure that if you accelerate a neutron it doesn't increase it's probability of decay.
I'd possibly even argue the opposite. Faster travelling neutrons travel slower through time, so they will probably have a longer lifetime...

I do agree though that stability is probably more to do with quarks throwing weak force carrying bosons at each other or something ike that.

The only point I ever made was that negative mass is without definition...

Maybe we agreed all along..!
14. negative mass does have a definition. Anti-mass is matter that repels normal matter with normal mass. That is it's definition. But it's just theoretical stuff, because of course, we havent actually seen anything that repels matter itself. We live in a mass univerise, so anti-mass would go all over the place (and in fact, so would mass)
15. The confusion arising from proton and neutron decay is because people are simply taking into account their rest mass. When a particle is moving it has kinetic energy as well, and this extra energy means they have more mass. So even though a proton does not have enough rest mass to decay into a neutron, when it has enough extra energy from moving at a fast enough speed, it is perfectly welcome to decay into a neutron and a positron (and don't forget a neutrino ).

Updated: August 1, 2004
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