QMechanics

I have some questions to ask about the Uncertainty principle of Quantum Mechanics. First of what exactly is it ? Why does it exist, what is the reasoning behind it ? What are the implications of the principle ? Why is there a conflict between General Relativity and Quantum mechanics ?
I would really appreciate it if someone told me the answers to these questions, as they have been tormenting me for a while.

Sid

May I suggest this thread

www.abovetopsecret.com...

It may have some of the basic answers to your questions, and answers to questions you may not have thought of yet.

Sidd,

I will derive the Uncertainty Principle here for you to see.

I am going to state a mathematical expression that is perfectly general:

[A,B] = iC where A, B, and C are operators

Knowing this, lets solve [x, p] (where I'm talking about operators)

If you don't know, the x operator equals to x itself, and the momentum operator is equal to -i*(h-bar)*partial derivative with respect to x.

Now, [x, p] = xp - px = x*[-i*(h-bar)*partial derivative with respect to x] - [-i*(h-bar)*partial derivative with respect to x]*x

This statement does NOT equal to zero for those of us who are not mathematicians. Operators are not the same as a simple variable. Now, solving this using the chain rule, we get the solution:

[x, p] = i*h-bar

Now, from the perfectly general equation, we have [A, B] = iC, and then

uncertaintyA*uncertaintyB >= 0.5*|| where is the expectation value, and the bars mean take the absolute value. A = x, B = p, C = [A,B]/i

Therefore,

uncertaintyX*uncertaintyP >= 0.5*h-bar

Heisenburg uncertainty principle is there derived. The implications are that you cannot know the exact position and the exact momentum, otherwise, you'd end up with a result that violated this principle.

There is such a thing as relativistic quantum mechanics, but the thing is that classical mechanics does not jive with quantum mechanics, hence why people come up with string theories, etc. It's kind of like Newtonian mechanics breaks down at high velocities...

I want to add that in Quantum Field Theory it is possible to break the uncertainty principle. However, it is something that cannot be observed, so if it is broken, realistically we can't know about it.

Any more questions or clarifications, let me know.

Is brownian motion linked to the uncertainty principle in anyway ?

Originally posted by siddharthsma
Is brownian motion linked to the uncertainty principle in anyway ?

No it's not.

I suggest using Google and Wikipedia to quickly gather information in these subjects -- this is simply more efficient than posting on a community board. This information is plentiful and high quality, on the web.

To understand quantum mechanics, one must understand the mathematics. I remember when my professor first walked into the room and said, "now you all may have read about quantum mechanics, you all probably think you have a grasp on the topic, but in all reality I am the only one in this room who knows about this subject, and you all know absolutely nothing." It sounded arrogant at the time, but he was absolutely correct.

It is to any person who is a trained physicist that any person can have a grasp on the subject without knowing the math, and taking the actual course.

So if you want to know my opinion, as a physicist, the internet is a horrible place for ANY physics information, because Joe Schmo's website on quantum mechanics does not do the subject any justice.

Well I'm uncertain about the "Uncertainty Principle"

but I know you can't be in two places at once, when your not anywhere at all.

So if you want to know my opinion, as a physicist, the internet is a horrible place for ANY physics information, because Joe Schmo's website on quantum mechanics does not do the subject any justice.

To conceptualize mathematical equations is paramount to the understanding of physics. Without that ability it is all number mumbo-jumbo. Physics equations should paint whole tapestries for the adherents of such thought.


[edit on 4/28/2006 by bodebliss]

Reply without math. One has not completely understood a subject until he/she can explain it in simple words without math.

Originally posted by siddharthsma
First of what exactly is it ?

The Quantum Uncertainty Principle says that we can not measure a particle's position and velocity at the same time.

Why does it exist

No one knows. If you ask

why do we think there is an uncertainty?

then the my opinion is that we do not have the tools to properly measure both quantities. Measuring a particle's position and velocity is like trying to catch an object which is tied to your hands by sticks: each time you move your hands, the object changes position and velocity.

Please note that there are no hidden variables, as Bell's inequalities prove to us.

what is the reasoning behind it ?

We have found the uncertainty principle by experimentation. There is no reasoning behind it, as it is not a human creation.

What are the implications of the principle ?

There are great implications from the principle. If we can predict all the particles' exact positions and velocities all the time, then the universe is deterministic. If, on the other hand, we can not predict the exact positions and velocities of particles, then the universe is random.

This question (if the universe is deterministic or not) is a great philosophical question that even goes down to religious subjects.

Personally I believe the universe is deterministic, because up until now no one has observed an effect that defies laws of physics. Of course that is no scientific proof, it is only Occam's razor.

I think modern physics have a foundamental flaw that prohibits us to see the true nature of the universe. Observations agree with the mathematical models, but I think we have fallen into the trap of finding a correct answer with the wrong/incomplete formulas.

Why is there a conflict between General Relativity and Quantum mechanics ?

Because the random nature of quantum mechanics does not agree with the deterministic nature of the theory of relativity.

I would really appreciate it if someone told me the answers to these questions, as they have been tormenting me for a while.

Of course someone will now say "those are not scientific answers, you are wrong there and there, yada yada yada". It's ok, ignore them. With the above in your mind, go read wikipedia for truly helpful analysis of quantum mechanics...then come back here and we will discuss any further questions you have.

Of course someone will now say "those are not scientific answers, you are wrong there and there, yada yada yada". It's ok, ignore them. With the above in your mind, go read wikipedia for truly helpful analysis of quantum mechanics...then come back here and we will discuss any further questions you have.

Explaining quantum mechanics without math is like explaining ants by saying they are brown, sometimes black, and oh yeah there are red ones, also. Fini.

Thanks masterp, that helped. I was getting confused with the Maths.

I hope the next post will not say something like :

If you don't understand the math, then why do you bother asking about Quantum mechanics. Quantum mechanics is all about Maths ! I suggest you take a course in Maths before you ask questions like these again.

Originally posted by siddharthsma
Thanks masterp, that helped. I was getting confused with the Maths.

I hope the next post will not say something like :

If you don't understand the math, then why do you bother asking about Quantum mechanics. Quantum mechanics is all about Maths ! I suggest you take a course in Maths before you ask questions like these again.

My moto is "words first, math later". If the target audience can not built a mental image from a few words, then math will only confuse them more.

Of course math is necessary, but I think that after one has undestood a concept without math, math comes easier.

Masterp, I totally agree with you

All I can say is that I've taken Quantum Mechanics, and anyone can think they have a grasp on something if they want to, but if you don't understand the math - and this goes for ANY physics, you don't understand the concept. Math does not compliment the concept - math IS the concept.

Originally posted by T_Jesus
All I can say is that I've taken Quantum Mechanics, and anyone can think they have a grasp on something if they want to, but if you don't understand the math - and this goes for ANY physics, you don't understand the concept. Math does not compliment the concept - math IS the concept.

Not really. The concept can be easily understood without math, just like any other concept. Math is the boring details. I actually understood relativity and QM from reading material that had minimum math. Math is necessary only if one wants to be involved with computations. Otherwise, it is largely reduntant.

Einstein proved that Browian motion proved the existence of molecules.
I still have not found a good text, none of my Physics books give details.
He published it in the Annals of Physics along with other ground breaking
ideas.

Many probability distributons are mentioned as well but I think the basis is
the Poisson that is the exponential in time.

Why that proves anything got passed me if mentioned in class.
If you see particles and any time period, the movemment requires the
came percentage of time. It seems related to a constant process such
as the time between telephone rings.

But I did not see anything mathmatical to help.


The Plank or Fermi probabilities give rise to uncertainty noted by Heinsenberg.
I recall Energy equals (h/2pi) nu, nu = Greek letter v that looks like a vee,
is the initial quanta.

Some how it further states that one cannot determine the location or position of
the object (electron?) and its momentum at the same instance in time.
There may be good equation that points this out, but I think its a probability
integral that proves the determination.