01 Jul 10
Other than using the word principle when it should be theorem, or inequality,or proposition this article is really a great one from Terry Tao (as usual!). If you are interested in these things and want to get a more technical perspective of a subject that catches the attention of a lotta people just give this article a read cause it will be worth your time.
http://terrytao.wordpress.com/2010/06/25/the-uncertainty-principle/
01 Jul 10
Originally posted by adam warlockWhy is the word 'principle' inappropriate?
Other than using the word principle when it should be theorem, or inequality,or proposition this article is really a great one from Terry Tao (as usual!). If you are interested in these things and want to get a more technical perspective of a subject that catches the attention of a lotta people just give this article a read cause it will be worth your time.
http://terrytao.wordpress.com/2010/06/25/the-uncertainty-principle/
01 Jul 10
1 edit
Originally posted by adam warlockHe's the basturd who kept showing me the physics of long sticks flying through the air ending on my arm......
I'll answer in the form of a question: What is the meaning of the word principle in Physics?
Seriously, I didn't know there was a connection to UP and the fourier series, but it makes sense, fourier transforms of waves meaning an infinitely high frequency as the position smearing out the momentum, the higher the position is known, the less the momentum is known. Nice. Learn something new every day. I didn't see any gripe with using the word 'principle' though.
02 Jul 10
Originally posted by adam warlockSimilar to the meaning in English.
I'll answer in the form of a question: What is the meaning of the word principle in Physics?
Its not a Law, or Theorem. The Law, would be something like the Second Law of Thermodynamics. A Theorem would be something like a specific provable case showing exactly what the relationship is between say the velocity and the position of a particle.
The principle, is simple a statement that we cannot know both velocity and position simultaneously. ie we are doomed to be uncertain.
In English we would say 'Its not that its difficult to find out both velocity and position simultaneously, its that you cannot find them on principle'.
02 Jul 10
1 edit
Originally posted by twhiteheadActually the usage of the word Law in Physics is also incoherent. But you're almost right: a theorem is something you can prove (the second part of your statement is wrong the result of theorem doesn't have to be exact: there are plenty of theorems that are approximations and inequilities), since this "principle" is something we can prove using the axioms of QM and results from Linear Algebra (there are other ways to prove it) it isn't a principle in any way: it is a theorem, or any equivalent designation, and principle isn't to theorem.
Similar to the meaning in English.
Its not a Law, or Theorem. The Law, would be something like the Second Law of Thermodynamics. A Theorem would be something like a specific provable case showing exactly what the relationship is between say the velocity and the position of a particle.
The principle, is simple a statement that we cannot know both velocit nd out both velocity and position simultaneously, its that you cannot find them on principle'.
A principle is something akin to a postulate. but it normally has a metaphysical connotation.
But tradition has its weight and almost everybody uses the word principle.
02 Jul 10
Originally posted by adam warlockWhat do you understand by the word 'principle'.
.... it isn't a principle in any way: it is a theorem, or any equivalent designation, and principle isn't to theorem.
A principle is something akin to a postulate. but it normally has a metaphysical connotation.
What do you think of:
http://en.wikipedia.org/wiki/Principle
I think 'principle' can be used in place of 'Law' or even 'Theorem', but it has its own connotations that suit some situations better.
For example, I might ask "What is the principle that applies when lifting weights with a double pulley?". Sure there is a provable theorem involved, or possibly a 'Law of Pulleys', but 'principle' just fits better.
But tradition has its weight and almost everybody uses the word theorem.
Not sure what you mean here. I thought everybody uses the word 'principle'.
Look up 'Uncertainty theorem' on Google and the first hit is 'Uncertainty Principle'.
02 Jul 10
3 edits
Originally posted by twhiteheadThis wikipedia page is defining principle with too much generality. I was only talking about the word principle in the context of Physics. But I'd go with this section: http://en.wikipedia.org/wiki/Principle#Principle_as_axiom_or_logical_fundament
What do you understand by the word 'principle'.
What do you think of:
http://en.wikipedia.org/wiki/Principle
I think 'principle' can be used in place of 'Law' or even 'Theorem', but it has its own connotations that suit some situations better.
For example, I might ask "What is the principle that applies when lifting weights with a double pulley?". Uncertainty theorem' on Google and the first hit is 'Uncertainty Principle'.
Thanks for the tip I have made a mistake on my last sentence but now I've corrected it.
The thing is that I like to use coherent language and the incoherent usage of Law and Principle in Physics rubs the wrong way.
edit: I've googled it too and on the first page only one hit uses the uncertaintity theorem expression. 😵
http://planetmath.org/encyclopedia/UncertaintyTheorem.html and it has a proof too.
edit2: This guys also has its problems with the Uncertainty principle denomination, even though they are different from mine. He does say that it is a theorem, but calls it a principle nevertheless and you can see what he has to say here: http://lesswrong.com/lw/pq/the_socalled_heisenberg_uncertainty_principle/ 😵😵😵
02 Jul 10
1 edit
Originally posted by adam warlockI look at it this way:
I was only talking about the word principle in the context of Physics.
The thing is that I like to use coherent language and the incoherent usage of Law and Principle in Physics rubs the wrong way.
An Uncertainty Theorem would apply to a given situation, and can be proved.
From your original link I take these two quotes:
"A recurring theme in mathematics is that of duality:"
"....thanks to various mathematical manifestations of the uncertainty principle."
One could almost call 'duality' a principle, but it is not a general rule, hence the weaker 'theme'.
A principle is not a single instance of a law, but a more general rule that seems to apply to more than one situation - but can't necessarily be stated exactly.
Lets think about the principle "opposites attract". It can be applied to magnetism, electricity, and even boys and girls. It is not a Theorem.
So you may find the 'uncertainty principle' manifesting itself in different situations, and for each situation, you could have an 'uncertainty Theorem'.
From:
http://en.wikipedia.org/wiki/Uncertainty_principle
We find:
"In quantum mechanics, the Heisenberg uncertainty principle states by precise inequalities that certain pairs of physical properties, like position and momentum, cannot simultaneously be known to arbitrary precision."
Notice the generality of the statement. "Certain pairs of physical properties".
If you go down the page you will find various 'uncertainty principles' in maths and physics, and finally some 'uncertainty theorems'.
Is it just tradition, or a subtle difference in the meanings of 'principle', 'law' and 'Theorem'?
02 Jul 10
Originally posted by twhiteheadIt's just incoherent usage.
Is it just tradition, or a subtle difference in the meanings of 'principle', 'law' and 'Theorem'?
At first the uncertainty principle was indeed a principle since Heisenberg's "proof" was highly schematic and particular.
But this result is proven with fool generality using some basic results. So it should be called a theorem, an inequality, a proposition, but it certainly isn't a principle no more.
02 Jul 10
Originally posted by adam warlockNice typo.
.... fool generality ....
So it should be called a theorem, an inequality, a proposition, but it certainly isn't a principle no more.
You are probably right, especially when talking of a specific case. I still think it sounds better when talking of the general concept.
So do you think the word 'principle' ever has a place in science?
How about this sentence:
"What principle would you use to explain what happens to light when it goes through a prism?"
Should I have used 'theorem'?
02 Jul 10
Originally posted by twhiteheadIn that case it is a principle since you can't derive that result from more basic assumptions.
Nice typo.
[b]So it should be called a theorem, an inequality, a proposition, but it certainly isn't a principle no more.
You are probably right, especially when talking of a specific case. I still think it sounds better when talking of the general concept.
So do you think the word 'principle' ever has a place in science?
How about this sente ...[text shortened]... plain what happens to light when it goes through a prism?"
Should I have used 'theorem'?[/b]
The difference between a principle and axiom (or postulate) are murky, but usually principle have a metaphysical quality.