# Quantum mechanics is easy



## HAL9000 (Oct 24, 2011)

Quantum mechanics is easy (understanding is hard )

http://news.bbc.co.uk/today/hi/today/newsid_9622000/9622751.stm


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## stuff_it (Oct 25, 2011)

HAL9000 said:


> Quantum mechanics is easy (understanding is hard )
> 
> http://news.bbc.co.uk/today/hi/today/newsid_9622000/9622751.stm


I found it fairly easy to get a basic understanding, but tbf it's not that people can't understand but that like with so many other things they can't be bothered to learn.


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## gentlegreen (Oct 25, 2011)

Would it be useful enough to me to make the effort worth it ?

I'll settle for old fashioned electrons and amps, volts and watts.


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## stuff_it (Oct 25, 2011)

gentlegreen said:


> Would it be useful enough to me to make the effort worth it ?
> 
> I'll settle for old fashioned electrons and amps, volts and watts.


Surely learning is it's own reward?


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## Greebo (Oct 25, 2011)

gentlegreen said:


> Would it be useful enough to me to make the effort worth it ?<snip>


Maybe not, but IMHO quantum physics has a beauty of its own, even if you never make practical use of it.


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## gentlegreen (Oct 25, 2011)

Physicists are often barking  - not surprised really.

A while back there was a programme on TV where electrons were described as an occasional random flash on the roof of the cathedral that was modelling the atom.

A couple of days ago on QI, Brian Cox brought up someone's theory that there might actually only be one electron in the whole universe ...


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## stuff_it (Oct 25, 2011)

gentlegreen said:


> Physicists are often barking - not surprised really.
> 
> A while back there was a programme on TV where electrons were described as an occasional random flash on the roof of the cathedral that was modelling the atom.
> 
> A couple of days ago on QI, Brian Cox brought up someone's theory that there might actually only be one electron in the whole universe ...


Now that's just silly, everyone knows that there are 42


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## wayward bob (Oct 25, 2011)

it's not rocket science


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## dilute micro (Oct 25, 2011)

Learning is easier with cartoons.


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## Dr Jon (Oct 25, 2011)

gentlegreen said:


> ...
> 
> A couple of days ago on QI, Brian Cox brought up someone's theory that there might actually only be one electron in the whole universe ...


wot?
like one mighty time-share electron?


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## 8ball (Oct 25, 2011)

It doesn't make sense to number the electrons.

(or electron)


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## ericjarvis (Oct 26, 2011)

It's really easy to understand. First get really really stoned. Then get to grips with the idea that everything you think you know about the basic nature of stuff is wrong. Now you are ready to learn and understand quantum physics. The other important point is that under no circumstances should you ever, no matter what, perform the famous twin slit experiment after taking LSD. Unless, of course, you want to know what is REALLY going on.


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## DotCommunist (Oct 26, 2011)

I have tried to understand quantum computers. Rather than the on-off of binary there is on-off or probably on- probably not on. A four switch system where the 'probablies' only concrete into on or off if they are looked at or observed etc but in the meantime are potentially one or the other.

makes my brain ache


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## TruXta (Oct 26, 2011)

Never quite got the hang of quantum computational logics meself. Q-bits? No thanks.


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## danny la rouge (Oct 26, 2011)

stuff_it said:


> I found it fairly easy to get a basic understanding, but tbf it's not that people can't understand but that like with so many other things they can't be bothered to learn.


It's not so much understanding that's the problem, but liking what you find out.  It makes me angry.


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## DotCommunist (Oct 26, 2011)

TruXta said:


> Never quite got the hang of quantum computational logics meself. Q-bits? No thanks.


 
well I sort of get it through the schrodingers cat thing- it might be on or it might be off but untill you look you don't know. But that wold be three states, on-off-dunno have a look.


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## TruXta (Oct 26, 2011)

danny la rouge said:


> It's not so much understanding that's the problem, but liking what you find out. It makes me angry.



QM makes you angry? Why?


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## danny la rouge (Oct 26, 2011)

TruXta said:


> QM makes you angry? Why?


It offends my sense of logic and reason.


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## TruXta (Oct 26, 2011)

DotCommunist said:


> well I sort of get it through the schrodingers cat thing- it might be on or it might be off but untill you look you don't know. But that wold be three states, on-off-dunno have a look.



I think that's how it is, 1, 0 or superposition. It makes my brain ache too.


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## TruXta (Oct 26, 2011)

danny la rouge said:


> It offends my sense of logic and reason.



Mine too, but I feel deeply amused by QM. God had a sense of humour after all.


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## Greebo (Oct 26, 2011)

danny la rouge said:


> It offends my sense of logic and reason.


It doesn't offend mine, but then again, I didn't expect all the scientific theory which is currently known to be perfect.


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## danny la rouge (Oct 26, 2011)

Greebo said:


> It doesn't offend mine, but then again, I didn't expect all the scientific theory which is currently known to be perfect.


I'm an old fashioned modernist.


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## Greebo (Oct 26, 2011)

Yes, but wouldn't it be boring if there was nothing more to work out or discover?


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## TruXta (Oct 26, 2011)

Greebo said:


> Yes, but wouldn't it be boring if there was nothing more to work out or discover?



This here.


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## DotCommunist (Oct 26, 2011)

tbf I still get moon eyed with wonder about the time dilation effect of near c travel and that isn't even quantum, it is just mental.


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## TruXta (Oct 26, 2011)

DotCommunist said:


> tbf I still get moon eyed with wonder about the time dilation effect of near c travel and that isn't even quantum, it is just mental.



Dunno why, but that always made immediate sense to me.


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## danny la rouge (Oct 26, 2011)

Greebo said:


> Yes, but wouldn't it be boring if there was nothing more to work out or discover?


Yes.

Oh, I don't want QM banned or anything.  I just feel the same way about it that my guitar students do when I tell them about double flats! (But _why_ is it even a diminished 7th?  That's a 6th!  Look!  Look! <counts from the tonic> And double flattened b is *A*!!!).


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## Greebo (Oct 26, 2011)

danny la rouge said:


> <snip>I don't want QM banned or anything. I just feel the same way about it that my guitar students do when I tell them about double flats! (But _why_ is it even a diminished 7th? That's a 6th! Look! Look! <counts from the tonic> And double flattened b is *A*!!!).


  but IMHO it's the headfuck thing which makes it interesting instead of just boring stuff to learn by rote combined with a bit of maths.


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## Orang Utan (Oct 26, 2011)

don't people use it to explain all sorts of pseudoscience?


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## TruXta (Oct 26, 2011)

Orang Utan said:


> don't people use it to explain all sorts of pseudoscience?



"Explain" you mean? Yeah, it's a right load of cock.


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## danny la rouge (Oct 26, 2011)

Orang Utan said:


> don't people use it to explain all sorts of pseudoscience?


No, they just sprinkle their prose with the word itself.  No explanation needed.


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## Orang Utan (Oct 26, 2011)

can anyone explain it to me as if they were explaining it to a 10 year old? i looked it up on wiki and couldn't get into it.


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## TruXta (Oct 26, 2011)

Orang Utan said:


> can anyone explain it to me as if they were explaining it to a 10 year old? i looked it up on wiki and couldn't get into it.





> The central idea of quantum mechanics is that a particle can exist in a state where it doesn't have a well defined value for properties like position, momentum, and energy that we normally think of as being properties of objects we observe on a daily basis.
> 
> Rather, our best possible description of the particle involves a mathematical object called a "wavefunction." The basic idea behind the wavefunction is that it tells that, if we were to measure say the position, we would get certain values with certain probabilities. It tells how the dice are loaded. Quantum mechanics tells how those probabilities change over time. But when we make those measurements, even if we know the probabilities, quantum mechanics says that it's truly random what outcome we're going to get.
> 
> What's really interesting is that certain pairs of properties of a particle cannot both be measured at the same time. Most famously, position and momentum are one such pair. If I know really well where a particle is, there's a limit to how well I can know how fast its moving. This is the basis behind Heisenberg's Uncertainty Principle.



source http://www.reddit.com/r/askscience/comments/j2qo9/can_someone_please_explain_quantum_physics_to_me/


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## Kuso (Oct 26, 2011)

DotCommunist said:


> well I sort of get it through the schrodingers cat thing- it might be on or it might be off but untill you look you don't know. But that wold be three states, on-off-dunno have a look.



it's not three states, it's just that it exists in both until you do look, then it's one or the other


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## stuff_it (Oct 26, 2011)

danny la rouge said:


> It's not so much understanding that's the problem, but liking what you find out. It makes me angry.


Don't try to spot the gaps when you're off you r tits for starters....


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## 8ball (Oct 26, 2011)

Orang Utan said:


> don't people use it to explain all sorts of pseudoscience?



Yeah, fuckin' "laptops".

I've never seen a fuckin' "laptop" and I don't know anyone else who has either (though they all seem to have a 'friend of a friend' who's seen one ).


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## Greebo (Oct 26, 2011)

8ball said:


> Yeah, fuckin' "laptops".
> 
> I've never seen a fuckin' "laptop" and I don't know anyone else who has either (though they all seem to have a 'friend of a friend' who's seen one ).


Good analogy.  Now, can anyone pass me a teaspoonful of quarks, please?


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## DotCommunist (Oct 26, 2011)

the entanglement one really does my nut. A pair of particles entangled on a quantum level (check mah gcse science) can show the effect of something on the one, on the other instantly despite vast gulfs of physical space between them.

I swear they are making it up to fuck with me.


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## 8ball (Oct 26, 2011)

Greebo said:


> Good analogy. Now, can anyone pass me a teaspoonful of quarks, please?



You can never _fill _a tablespoon with quarks, silly.


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## Greebo (Oct 26, 2011)

8ball said:


> You can never _fill _a tablespoon with quarks, silly.


That's why I only asked for a teaspoonful.


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## 8ball (Oct 26, 2011)

Greebo said:


> That's why I only asked for a teaspoonful.



Size means nothing to a quark.

That's what she said, anyway.


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## Greebo (Oct 26, 2011)

8ball said:


> Size means nothing to a quark.
> 
> That's what she said, anyway.


Unless she said it to you, she was probably lying.


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## Ich bin ein Mod (Oct 26, 2011)

Quantum tunnelling is what got me when I was studying. "Borrowing" energy from the "future" then instantly paying it back.

It's not too difficult though, it just needs a bit of thinking. My favourite part of the course to teach.


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## dylanredefined (Oct 26, 2011)

Ich bin ein Mod said:


> Quantum tunnelling is what got me when I was studying. "Borrowing" energy from the "future" then instantly paying it back.
> 
> It's not too difficult though, it just needs a bit of thinking. My favourite part of the course to teach.


  Sounds more like some sort of dodgy city scheme than physics.


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## stuff_it (Oct 26, 2011)

dylanredefined said:


> Sounds more like some sort of dodgy city scheme than physics.


You're saying it's the M6 Toll of Physics?


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## dylanredefined (Oct 26, 2011)

stuff_it said:


> You're saying it's the M6 Toll of Physics?


  NO more like some one in a suit telling you we borrowing a million from the future and then paying back  instantly  and somehow their going to make a profit out of it.


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## stuff_it (Oct 26, 2011)

dylanredefined said:


> NO more like some one in a suit telling you we borrowing a million from the future and then paying back instantly and somehow their going to make a profit out of it.


That's what I just said.


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## dylanredefined (Oct 26, 2011)

Ah right


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## ericjarvis (Oct 27, 2011)

danny la rouge said:


> Yes.
> 
> Oh, I don't want QM banned or anything.  I just feel the same way about it that my guitar students do when I tell them about double flats! (But _why_ is it even a diminished 7th?  That's a 6th!  Look!  Look! <counts from the tonic> And double flattened b is *A*!!!).



Actually QM is very amenable to guitar logic. The key is that we don't observe the actual complete "note". We can only observe harmonics and from that we have to work out what's actually being played.


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## ericjarvis (Oct 27, 2011)

Orang Utan said:


> don't people use it to explain all sorts of pseudoscience?



To be fair people generally use all sorts of shit to "explain" pseudoscience.


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## ericjarvis (Oct 27, 2011)

The first thing you have to do is ditch your preconceptions of what a particle is. If you don't do that then quantum effects won't ever make any sense. Admittedly a lot of physicists don't manage that, which is why they say they don't understand it except through the maths, it's because they won't let go of a classical physics concept of a particle. I found it was really helpful to think in terms of "stuff" rather than trying to keep matter, energy, and space time as separate distinct things.


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## WouldBe (Oct 27, 2011)

HAL9000 said:


> Quantum mechanics is easy



Yeah right. Have you seen how small the spanners are?


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## stuff_it (Oct 27, 2011)

WouldBe said:


> Yeah right. Have you seen how small the spanners are?


That's if you can find them in the first place. Damned things could be just about anywhere.


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## ericjarvis (Oct 27, 2011)

WouldBe said:


> Yeah right. Have you seen how small the spanners are?



I have no idea how small they are, because I'm able to tell how fast the little buggers are moving.


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## HAL9000 (Oct 27, 2011)

ericjarvis said:


> The first thing you have to do is ditch your preconceptions of what a particle is. If you don't do that then quantum effects won't ever make any sense. Admittedly a lot of physicists don't manage that, which is why they say they don't understand it except through the maths, it's because they won't let go of a classical physics concept of a particle. I found it was really helpful to think in terms of "stuff" rather than trying to keep matter, energy, and space time as separate distinct things.



The bit in the audio clip at the start of this thread.   Not just uncertain about the particle position in a room but the whole universe. 

What about quantum entanglement?   Is there's somthing linking the particles or is it just two bits of "stuff" joined together and stretched any distance without light speed limitation.

What about qubits?   Couple of qubits linked together can go through all number combinations instantly and come out with the correct answer. 

Quantum foam.   Anti mater and mater appearing in the universe at random, then annihilating each other.


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## Guineveretoo (Oct 27, 2011)

I had a boyfriend once who was a physicist and who tried to get me to understand quantum physics.  He even co-wrote a book about it, which he got me to read to check that it was understandable by non-physicists. It wasn't. I never did understand.


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## Guineveretoo (Oct 27, 2011)

I remember when I was young and thought I was clever, I had a friend who is now a lecturer in the Philosophy of Science, who explained quantum mechanics and Schrodingers Cat and all that stuff, to me on many occasions.  Always after we had been drinking.

Every time, I was quite sure I had understood, and felt very pleased with myself, and a bit smug at being able to understand something which was so Intellectual, but promptly forgot it when I woke up in the morning. Every time!


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## ericjarvis (Oct 28, 2011)

HAL9000 said:


> The bit in the audio clip at the start of this thread.   Not just uncertain about the particle position in a room but the whole universe.
> 
> What about quantum entanglement?   Is there's somthing linking the particles or is it just two bits of "stuff" joined together and stretched any distance without light speed limitation.
> 
> ...



Right. This is all about ditching the idea of a particle as a discrete solid object with a clear position and precise boundaries. At a quantum level they don't exist. Seriously. Looking at the quantum level a particle isn't a thing. It is a pattern of "vibrations" in stuff. Stuff being the space-time-energy that the universe is composed of. Now look at it all again, and remember the old physicist's joke "I remember when it was all fields".


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## ericjarvis (Oct 28, 2011)

It's not uncommon to understand quantum physics far better when in a state of extreme psychoenlargement than when stone cold sober. This is because to understand it requires forgetting a hell of a lot of things you think you know.


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## ferrelhadley (Oct 29, 2011)

Ich bin ein Mod said:


> Quantum tunnelling is what got me when I was studying. "Borrowing" energy from the "future" then instantly paying it back.
> 
> It's not too difficult though, it just needs a bit of thinking. My favourite part of the course to teach.


When I was about 15 I read "In Search of Schrodengers Cat". A whole host of idea like virtual particle (quantum fluctuations), particle wave duality problem, the collapse of the de broglie wave function.... I could not absorb it all in one swallow but it was mind blowing stuff.

Impossible to ever see the world the same.


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## jannerboyuk (Nov 5, 2011)

DotCommunist said:


> tbf I still get moon eyed with wonder about the time dilation effect of near c travel and that isn't even quantum, it is just mental.


i love that too. but every time i try to explain it to people (admittedly very badly) they look at me with either boredom or like i'm mental.


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## jcsd (Nov 7, 2011)

To have a decent understanding of the basics of quantum mechanics, you need a decent understanding of linear algebra (i.e. vector spaces and operators in particular), plus the abilty to deal with a physical theory which has a very abstract setting.

For example mathematically quantum entanglement straightforwardly follows from the basic postulates of quantum mechanics and the trivial fact that the tensor product of two vector spaces with more than two dimensions is of higher dimension than their direct product.


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## Guineveretoo (Nov 9, 2011)

jcsd said:


> To have a decent understanding of the basics of quantum mechanics, you need a decent understanding of linear algebra (i.e. vector spaces and operators in particular), plus the abilty to deal with a physical theory which has a very abstract setting.
> 
> For example mathematically quantum entanglement straightforwardly follows from the basic postulates of quantum mechanics and the trivial fact that the tensor product of two vector spaces with more than two dimensions is of higher dimension than their direct product.



See - that is why I will never understand quantum mechanics. I understand most of the words in there (although I have just spotted a spelling mistake, so it is possible that there are others!), but I get no meaning at all from those two paragraphs.


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## stuff_it (Nov 9, 2011)

jcsd said:


> To have a decent understanding of the basics of quantum mechanics, you need a decent understanding of linear algebra (i.e. vector spaces and operators in particular), plus the abilty to deal with a physical theory which has _*a very abstract setting.*_
> 
> For example mathematically quantum entanglement straightforwardly follows from the basic postulates of quantum mechanics and the trivial fact that the tensor product of two vector spaces with more than two dimensions is of higher dimension than their direct product.


Especially if you are going to go along with current thinking on the Standard model with several of the dimensions being 'rolled up very small'.


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## jcsd (Nov 9, 2011)

Guineveretoo said:


> See - that is why I will never understand quantum mechanics. I understand most of the words in there (although I have just spotted a spelling mistake, so it is possible that there are others!), but I get no meaning at all from those two paragraphs.


It isn't too complex a statement (though some of its a bit hand-wavey, nto sure I should've mentioned the direct product or dimensions).

I assume you know what a vector is (a vector quantity is informally one which has magnitude and direction, though the concept is actually quite abstract). A vector space is a set of vectors that can be added together and multiplied by scalars. For example the set of all vectors in the plane whose origin is the same point, is a vector space. The tensor product of two vector spaces is just a way of taking two vector spaces to generate a third. E.g. for two vector spaces V and W their tensor product will be denoted V⊗W (note the order of V and W does matter technically, but as if you change the order you still get what is basically the same thing, it doesn't matter that much)

In quantum mechanics the state of a system is described by a state vector (or technicaally an equivalence class of state vectors called a 'ray'), which is an enitrely abstract concept, which, if you like is a way of keeping tabs on whats going on. All the possible state vectors of a quantum system form a vector space which is called its state space. One of the basic postulates of quantum mechanics is that the state space of a quantum system is the tensor product of the state spaces of its subsystems. For example if you wish to describe a quantum system consisting of two particles, you would describe it in terms of the tensor product of the state spaces of the two particles.

The tensor product can also be defined between individual vectors and the tensor product of two vectors will be a vector in the tensor product space of their respective vector spaces. e.g. for a vector v in V and a vector w in W, their tensor product v⊗w will be in V⊗W. The thing to note though is that generally speaking their are vectors in V⊗W that cannot be decomposed in to the tensor product of two vectors in V and W.

In quantum mechanics this means that in, for example, a two particle system there exists states which are not simply the tensor product of states of the two particles. Such states are said to be entangled, as you cannot describe the behaviour of one particle without referencing the other particle.


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## Orang Utan (Nov 9, 2011)

the above post is unreadable


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## jcsd (Nov 9, 2011)

stuff_it said:


> Especially if you are going to go along with current thinking on the Standard model with several of the dimensions being 'rolled up very small'.


Compactified (a technical term for 'rolled up') dimensions are really the domian of String theory (and related theories such as Kaluza-Klein theory) and thye don't appear in the Standard Model of particle physics.


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## stuff_it (Nov 9, 2011)

jcsd said:


> Compactified (a technical term for 'rolled up') dimensions are really the domian of String theory (and related theories such as Kaluza-Klein theory) and thye don't appear in the Standard Model of particle physics.


We're explaining to five-year-olds, don't go confusing them; clearly sting theory is what I meant, I was in a massive hurry when I posted that.


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## jcsd (Nov 9, 2011)

Orang Utan said:


> the above post is unreadable


Is that due to my laissez-faire approach to sentence structure and grammatical accuracy or the contents?


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## 8ball (Nov 9, 2011)

jcsd said:


> Is that due to my laissez-faire approach to sentence structure and grammatical accuracy or the contents?



Needs diagrams.


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## stuff_it (Nov 9, 2011)




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## Greebo (Nov 9, 2011)

Relax, stop expecting it to make sense, and start visualising, but without trying too hard.  IMHO it's like a magic eye picture, you have to be in the right state of mind to get it.   I couldn't possibly comment on what that says about people who specialise in the subject.


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## Orang Utan (Nov 9, 2011)

jcsd said:


> Is that due to my laissez-faire approach to sentence structure and grammatical accuracy or the contents?


vocabulary mostly. vectors? scalars? wtf?


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## jcsd (Nov 9, 2011)

8ball said:


> Needs diagrams.


Unfortunately as the state spaces of quantum mechanics are usually complex vector spaces (i.e. complex as in the complex numbers) of infinite dimension, you can't really illustarte them with diagrams.


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## jcsd (Nov 9, 2011)

Orang Utan said:


> vocabulary mostly. vectors? scalars? wtf?


As I said, informally speaking, a vector is a quantity that has both magnitude and direction. For example velocity is a vector because it has magnitude (i.e. speed) and it also has a direction. A scalar, again informally speaking, is a quantity which just has magnitude, so for example speed is a scalar and it is also the magnitude of velocity.

I should say though that in quantum mechanics, vectors are used in a very abstract way and the directions and magnitudes of vectors in a state space only relate to real world quantities in an indirect way.


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## stuff_it (Nov 9, 2011)

8ball said:


> Needs diagrams.






















With tits - I hope this has been of help....


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## Orang Utan (Nov 9, 2011)

jcsd said:


> As I said, informally speaking, a vector is a quantity that has both magnitude and direction. For example velocity is a vector because it has magnitude (i.e. speed) and it also has a direction. A scalar, again informally speaking, is a quantity which just has magnitude, so for example speed is a scalar and it is also the magnitude of velocity.
> 
> I should say though that in quantum mechanics, vectors are used in a very abstract way and the directions and magnitudes of vectors in a state space only relate to real world quantities in an indirect way.


i don't even understand that though!


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## 8ball (Nov 9, 2011)

Orang Utan said:


> i don't even understand that though!



If talking about rate of motion:

Scalar = 'speed' - as in 'I am travelling at 25mph' - you can write it down as just a number (so long as you know the units)

Vector = 'velocity' - as in 'winds will be 25mph in a southwesterly direction' - this needs at least one more number or a frame of reference (like compass directions) to give all the relevant information

Often 'velocity' is used to just mean 'speed' but that's not quite right. You can see the need for directionality better when thinking about things like forces (where forces acting in different directions can counteract each other.

(this post brought to you by half-remembered GCSE physics  )


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## jcsd (Nov 9, 2011)

Orang Utan said:


> i don't even understand that though!


Okay, let's say I won't to describe the movement of a car, I need a concept that encompasses both the direction the car is moving and how fast it is moving that direction. That quantity is called velocity and it can be represented by an arrow poitning in the direction of movement, plus a number (the speed that it is moving in that direction). Velocity is a vector quantity. Speed on the other hand doesn't tell me which direction the car is moving in, but it does tell me how fast it is moving and it can be represented by just a number (e.g. 20 mph). Speed is a scalar quantity.


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## Greebo (Nov 9, 2011)

Orang Utan said:


> i don't even understand that though!


Instead of the usual flat arrows going from one point to another on a graph (for the vector), try seeing it with something sticking out of the back which represents the other thing (the scalar). You haven't got a line, you've got a long 3-sided needle, with a width which varies depending on the scalar.


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## Orang Utan (Nov 9, 2011)

I don't think I'll ever understand it tbh. It's all gobbledygook to me


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## fractionMan (Nov 9, 2011)

Orang Utan said:


> I don't think I'll ever understand it tbh. It's all gobbledygook to me



you get post 79 though, right?



jcsd said:


> Okay, let's say I won't to describe the movement of a car, I need a concept that encompasses both the direction the car is moving and how fast it is moving that direction. That quantity is called velocity and it can be represented by an arrow poitning in the direction of movement, plus a number (the speed that it is moving in that direction). Velocity is a vector quantity. Speed on the other hand doesn't tell me which direction the car is moving in, but it does tell me how fast it is moving and it can be represented by just a number (e.g. 20 mph). Speed is a scalar quantity.


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## Orang Utan (Nov 9, 2011)

Not really. I mean, I still wouldn't be able to apply that to the other posts. You can break it up into digestible chunks, but then it's no longer a meaningful whole.


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## jcsd (Nov 9, 2011)

Orang Utan said:


> I don't think I'll ever understand it tbh. It's all gobbledygook to me


I'm of the school of thought that living in a society like the one which we live in you probably already have an intuttive undertsnading of vectors and scalars.

The concept of a vector space is a little more abstarct, but basically it covers all mathematical structures that have certain simlairities to complete* sets of the familiar arrows+numbers we intutively think of when thinking of vectors.

*by complete, I mean exhaustive e.g. all the possible velocities a car could have.


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## Orang Utan (Nov 9, 2011)

Do you really expect laymen to understand that post? Wtf is a mathematical structure?


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## fractionMan (Nov 9, 2011)

Orang Utan said:


> Not really. I mean, I still wouldn't be able to apply that to the other posts. You can break it up into digestible chunks, but then it's no longer a meaningful whole.



Well, speed is a number, right? like 10 miles an hour.

Velocity is a way of measuring speed _and_ direction at the same time. So you could be going 10 miles and hour due east. We call that representation a vector. We could write it down something like this: [10,90] with 90 being 90 degrees, due east.

Recalling my pretty shaky maths, you can add vectors up like normal numbers. So if, say, a UFO is going 10 miles an hour due east then turns on the hoverdrive and starts going 200 miles and hour straight up in the sky _at the same time_ you can add the two vectors together using some magic maths and work out exactly which direction and speed it's going in 3d space.

I think that's where you start needing matricies, which are a bit like vectors but with more dimensions.


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## jcsd (Nov 9, 2011)

Orang Utan said:


> Do you really expect laymen to understand that post? Wtf is a mathematical structure?



A mathematical structure, just means an abstarct 'structure' or 'idea' in mathematics. For example we might say the sets {0,1} (the set containing only 0 and 1) and the sets {3,4} have the same matheamtical structure (as sets) as they are both sets containing two objects.

Thoguh the term 'mathematical structure' doesn't have that precise a definition.


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## Orang Utan (Nov 9, 2011)

Are you a scientist/mathematician, jcsd?


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## fractionMan (Nov 9, 2011)

I was just thinking, that assumes you know what a set is.


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## stuff_it (Nov 9, 2011)

Orang Utan said:


> Do you really expect laymen to understand that post? Wtf is a mathematical structure?


You aren't even trying. How are you at putting up flat pack? Or map reading? Or DIY?

Don't be put off by the term 'mathematics' or 'mathematical', it's nothing to do with being good at mental arithmetic or owt.* 

*And I should know


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## Orang Utan (Nov 9, 2011)

fractionMan said:


> I was just thinking, that assumes you know what a set is.


Yeah jcsd keeps using language that s/he assumes the reader will understand. It's infuriating!


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## Orang Utan (Nov 9, 2011)

stuff_it said:


> You aren't even trying. How are you at putting up flat pack? Or map reading? Or DIY?
> 
> Don't be put off by the term 'mathematics' or 'mathematical', it's nothing to do with being good at mental arithmetic or owt.*
> 
> *And I should know


I'm trying to understand but I don't have the apparatus to, I suspect. Though I can read maps well. I'm just having trouble grasping the abstracts I think


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## fractionMan (Nov 9, 2011)

I think it's really easy to do without even realising (use technical language you're familiar with as if everyone else knows what you're on about)

A set is simply a collection of zero or more things in no particular order. Say a cat, a dog and the colour blue. We'd write that as {cat,dog,blue} We could add that to another set containing cowboys {cowboys} and end up with {cat,dog,blue,cowboys}

I think JCSD was saying that {cowboys,indians} and {red,blue} have the same _mathematical structure_ because they're both sets and they've both got 2 things in them.


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## fractionMan (Nov 9, 2011)

I have now probably confused you further by ditching the numbers and using cowboys


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## Greebo (Nov 9, 2011)

Orang Utan said:


> Are you a scientist/mathematician, jcsd?


Relax, don't panic, you're trying too hard.

Stop thinking in terms of numbers and start thinking in terms of shapes.  If time is left to right, you've got a horizontal line.  Add in distance (going up and down on the page)  and you've got a diagonal line (velocity).  Add in direction by making the line stick out of the paper in whichever compass direction the thing is travelling.  The sticky out bit is your scalar.


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## Orang Utan (Nov 9, 2011)

I have trouble visualising abstract things so that approach is fruitless. Even if I understood vectors and scalars, I would still then have to apply it to the post in which jcsd mentions them.
A friend told me that the best way for a non-mathsy person to understand QP was to read Neal Stephenson's Anathem, so that is what I shall do.


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## Greebo (Nov 9, 2011)

Orang Utan said:


> I'm trying to understand but I don't have the apparatus to, I suspect. Though I can read maps well.<snip>


If you can read a map, you can get your head around this, eventually. No need for perfect understanding of it though IMHO.


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## stuff_it (Nov 9, 2011)

Orang Utan said:


> I have trouble visualising abstract things so that approach is fruitless. Even if I understood vectors and scalars, I would still then have to apply it to the post in which jcsd mentions them.
> A friend told me that the best way for a non-mathsy person to understand QP was to read Neal Stephenson's Anathem, so that is what I shall do.


Well worth a read anyway, then move on to some Greg Egan....


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## jcsd (Nov 9, 2011)

Orang Utan said:


> Are you a scientist/mathematician, jcsd?


Nope, as that would imply I was some sort of professional. I just know a bit about the subject and I hasten to add these aren't my own ideas (for example they're covered briefly on pgs 422-423 of Griffith's _Introduction to Quantum Mechanics_, though he deosn't specifically reference the tensor product).


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## 8ball (Nov 9, 2011)

I think everyone understands abstract stuff, really, but sometimes the half-memory of a hated school subject can bring on a bit of the brain-freeze.

Saying 1 + 1 = 2 is involving abstraction. There's an age where you can get kids 2 understand that 1 apple plus 1 apple is 2 apples, and 1 orange plus 1 orange is 2 oranges, but they can't quite make the leap to 1 + 1 = 2 (and leaving the fruit-based idea-scaffolding behind).

Some people have the same problem when maths moves on from numbers to Greek letters and stuff, but I think it's mostly bad teaching that causes the lockup at that stage, cos the second leap is a lot easier than the first.


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## jcsd (Nov 9, 2011)

Oops didn't see the other posts on this page. FractionMan is quite right about sets, I've just assumed really that everyone is familair concepts like vectors and sets which I learnt at secondary school.

I honestly think that most people who struggle a bit with maths only do so, because they get caught up with the idea of maths being a difficult, esoteric subject and get frustrated with it and feel hopless. I've always found though that, maths is just a subject that take a bit of time to understand. You get eureka moments when suddenly you understand a concept that seemed like complete goobledegook at first, but often its just a matter of chipping away at concepts slowly until you understand them. I think its importnat to remember that every bit of mathematical language and symbolism is meant to mean something precise (though quite often it has an imprecise meaning which is easier to understand, like for example the informal definition of a vector given above) and also that its' not there to confuse you, it's just meant as a shorthand to express abstract and sometimes quite complex ideas.

Key as well is also how well maths is explained. I find that if you don't understand a concept, quite often its simply a case of seeking a better explanation than the one your looking at.

Here's perhaps another simplified way of understanding entanglement:

Say I have two particles A and B. Particle A has 10* possible quantum states and particle B also has 10 possible quantum states.

Classically speaking if I combined the particles in to a single classical system, then the number of possible states of the system would simply be 10*10 = 100, however in the quantum system it is, lets say, 1000**. That means that there must be states in the quantum system which cannot be decomposed in to "particle A is in state ___" and "particle B is in state ___" (otherwise there would be 100 states like in the classicla example), instead any description of particle A, must allude to particle B and vice versa and so even when spatially seperated they will affect each other in some sense.

*I have used 10 just to simplify the situation, in reality as a quantum state space must be something called a "Hilbert space" there will always be infinitely many possible quantum states even when there are only a finite number of possible states than correspond to the result of a measurement.

**1000 is purely a number I've pulled out of my arse, I only use it as it is an order of magnitude bigger than 100 to show that in some sense there are many more entangled than non-entangled states.


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## Orang Utan (Nov 9, 2011)

i got a B in maths at school somehow, but i had trouble keeping what i'd learnt in my head. it's all gone 20 years later of course. but you're dead right about people's attitudes to match. i don't find it at all interesting, so my motivation to learn more about it is almost non-existent.


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## stuff_it (Nov 9, 2011)

Orang Utan said:


> i got a B in maths at school somehow, but i had trouble keeping what i'd learnt in my head. it's all gone 20 years later of course. but you're dead right about people's attitudes to match. i don't find it at all interesting, so my motivation to learn more about it is almost non-existent.


I got a C, I hated it and didn't try very hard. This was back before you got to get the calculators out of the calculator cupboard for anything less than doing Sin and Cos, etc though. Mr _it got to use one of those graphing jobbies, 

I've since gone back to it and managed to pass the applied maths course to get a BEng having not done a stroke of anything more than basic maths since (with liberal use of calculators and Mathcad may I add), so it's not all downhill.


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## fractionMan (Nov 10, 2011)

jcsd said:


> Here's perhaps another simplified way of understanding entanglement:
> 
> Say I have two particles A and B. Particle A has 10* possible quantum states and particle B also has 10 possible quantum states.
> 
> ...



As someone who didn't know what entanglement _is_, I like this explanation.


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## 8ball (Nov 10, 2011)

fractionMan said:


> As someone who didn't know what entanglement _is_, I like this explanation.



Looks more like a description than an explanation to me.


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## fractionMan (Nov 10, 2011)

picky picky


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## jcsd (Nov 10, 2011)

No its meant to be more an explanation. I'm not really describing the physical effects of quantum entanglement, I'm trying to explain why they occur.

I don't think there is a much more basic explanation in quantum mechanics for quantum entanglement than the existance of 'non-seperable states' (and the existance of non-seperable states as tried to explain earlier comes from the basic postulates of QM plus the basic properties of the tensor product) in composite quantum systems.

It might seem a little unsatisfactory to explain what is a physical problem in a way that is quite abstract and maths-heavy, but that's purely the nature of QM.


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## editor (Mar 21, 2019)

Get your noggin around this: 
More Than One Reality Exists (in Quantum Physics)


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