Most difficult to comprehend concept

[mather]

Hello!

Which is the most difficult to comprehend scientific concept you have come across?

How you managed to master it?

Thanks!

 

[Cerlid]

Women. Not exactly a scientific concept, but they sure are mysterious and well who knows? :)

Nah seriously, maths is fairly logical so it's not going to involve something that has an implicit or direct answer; apart from interpretation issues the concepts are sound in physics. But I suppose philosophical issues are generally the hardest to get your head around. So I would suggest that the origins of the universe for me are the hardest to get to grips with. Science gives us a means to explore what is, to explore why is much harder. Is the universe eternal, is there more than one, what caused the universe and does it need a point of origin, ages old questions with no satisfying answers.

 

[mather]

Thanks but i expected something more precise, like a specific quantum mechanics issue

 

[leroyjenkens]

Working with functions in C. Making them, calling them, etc.

 

[Cerlid]

Thanks but i expected something more precise, like a specific quantum mechanics issue

Well the collapse issue is particularly mysterious, but then I think the interpretations have them covered. Pick an interpretation, they're all pretty mysterious, does the moon exist, does anything "exist" before some chimp like us measures them, is there a definable wave function, is it real, is it local is it non local and real, and so on. :)

It's a $64000 question that no one can really answer. Mysterious yes, but it probably just means we are lacking something.

How did I master it, well I don't think I have, I think I have mastered the wave function, in as much as it is capable of being renormalised, but mastered would denote I have an understanding way beyond what I actually have, and if I had I would revolutionise science and not be where I am now.

 

[Darth Frodo]

Probably Self Induction.

I just read the book over and over again from the very beginning of the chapter until the Eureka moment happened. I just didn't have a good enough of a foundation in the earlier material.

 

[Zarqon]

Entanglement.

Quantum superpositions are pretty easy to think about intuitively because of the Bloch sphere representation, but when it's scaled up to include non-local correlations of bigger systems the brain just fails to work it out. It can of course still be calcuated, and it's not so hard (at least conceptually), but intuitively figuring out how entangled states behave under a given operation is just somehow beyond the brains capacity.

 

[lisab]

Entanglement.

Quantum superpositions are pretty easy to think about intuitively because of the Bloch sphere representation, but when it's scaled up to include non-local correlations of bigger systems the brain just fails to work it out. It can of course still be calcuated, and it's not so hard (at least conceptually), but intuitively figuring out how entangled states behave under a given operation is just somehow beyond the brains capacity.

Yeah, I had (and still have) a hard time really getting entanglement. I was sort of OK with it up to learning Bell's inequality, then my head imploded.

 

[physicsboard]

I have a lot of trouble with thermodynamics. My prof wasn't great though and I was too proud to go for extra help so it was my own fault really.

 

[DennisN]

Entanglement.

Quantum superpositions are pretty easy to think about intuitively because of the Bloch sphere representation, but when it's scaled up to include non-local correlations of bigger systems the brain just fails to work it out. It can of course still be calcuated, and it's not so hard (at least conceptually), but intuitively figuring out how entangled states behave under a given operation is just somehow beyond the brains capacity.

Yes, that's probably on the top of my list too, it's a very intellectually challenging topic (and I really hope we will understand it better in the future). But, like Cerlid said, there are other troublesome issues in QM too.

 

[cosmik debris]

The arising of consciousness is second on my list, after women.

 

[Cerlid]

Yeah, I had (and still have) a hard time really getting entanglement. I was sort of OK with it up to learning Bell's inequality, then my head imploded.

Depends if you like maths. If you get why something needs to exhibit a certain functional quantity to be considered non random and another to be considered not, it is straight forward. I like to think of it this way, if something cannot be predicted by spin to be in a position it must be non local and if not random have no exact variable that can explain it.

I suppose a weak analogy would be if you spun something and it never came back to an integer value ie back to the beginning or at another angle that would be congruous with an exact value, or at a point one could predict then it must have some random component, or at least not be explicable by a variable that can be known locally or by a variable hidden as it is. All it says is that the function has to have a certain limit whereby it can no longer be implicitly ascertained by determinism. Say if you spun something around a circle by 45 degrees, then it would always land at a point that is predictable because it is exactly divisible into 360 degrees, all Bell's says is that does not happen. Probably not explaining it all that well but it is just an analogy.

 

[Cerlid]

I have a lot of trouble with thermodynamics. My prof wasn't great though and I was too proud to go for extra help so it was my own fault really.

Frankly everyone has a lot of problems with thermodynamics, entropy at heart is quite a qualitative concept. I don't understand what ordered really means, even given the maths that explains it, at least at some very key fundamental level, I don't think anyone can make it easy or has made it easy. I get the overarching concept, but I don't think anyone has really made entropy a scientific concern at least precisely and in all systems, again QM rears its ugly head with all the problems it has...

 

[Cerlid]

The arising of consciousness is second on my list, after women.

Yeah that would tend to explain women too, I perhaps over exaggerated the mystery of women, if we could work out why and how people consciously think and how such processes arise from the system, women would be easier at least. Not that much easier, but at least logical. We'd have somewhere to start at least!

 

[meldraft]

Schwarz-Christoffel transformations and potential flow. I've been working on it since February and I actually proved a couple of theorems from Milne-Thomson's Theoretical Hydrodynamics before stumbling onto the book (while writting the paper for the theorems... bummer ). Complex analysis is literally making my head spin, and the way I'm trying to master it is simply through sweat, tears, and all nighters.

I've found lately though that if I'm searching for a solution that requires comprehension (not bugs in codes etc.) it's handy to take it slow, spread it over a few days, and sleep on it a lot. One day the answer simply pops up

 

[Dead Boss]

For me, the concept that I find to be my greatest victory to day is understanding of tensors, dual space and related. The concept that I find most difficult and which I don't understand is Lie groups (or Lie algebras, 'cause you know, I have no idea which is which). Of course there are other areas that I have no clue about like string theory, but there I know so little that I don't even know what I don't understand in the first place.