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I have been thinking about this question for quiet a long time but, couldn't make up an answer myself. Usually when someone asks about why a system is the way it is we answer it by saying that it is the most stable lowest energy state(to know about why a system should be at its lowest energy state for its stability click here). But, what about the uncertainty principle? What benefit does the universe/nature get by following this principle?

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why are systems most stable at the lowest energy state? –  gregsan Nov 21 '13 at 15:28
    
@gregsan I thought about this question that you asked while I was typing this one and I have just posted another question on it before you commented. –  Rajath Krishna R Nov 21 '13 at 15:29
    
here, this should interest you lesswrong.com/lw/99c/… –  gregsan Nov 21 '13 at 15:34
    
I think that you're carrying the minumum energy explanation too far... –  jinawee Nov 21 '13 at 15:36
    
@gregsan I had seen the whole video interview of R.P Feynman sir. –  Rajath Krishna R Nov 21 '13 at 15:40
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5 Answers 5

The uncertainty principle is a mathematical consequence of wave behaviour. It is true for sound waves, electrical signals, radio waves, etc. Anywhere you might want to work with Fourier transforms.

Let's say you want to send a pulse via a radio wave. Furthermore, lets say you make the amplitude of the pulse a Gaussian function with time:

$f(t) \sim e^{-\alpha t^2}$

This pulse has width $\frac{1}{\sqrt{\alpha}}$.

Then in frequency space, the Fourier transform of this function is another Gaussian:

$F(\omega) \sim e^{-\frac{\omega^2}{\alpha}}$

This pulse has width $\sqrt{\alpha}$.

Generally, the more you localize the signal in time, the wider it gets in frequency, and vice versa. A signal having an exact frequency $\omega$ is completley delocalized in time: $\sin\omega \,t$. If we were talking about a particle instead of a radio wave, we would say that the energy of the particle is definite, and therefore its wave function will unchanged for an infinite amount of time.

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No, it is untrue. What is uncertain with radio waves if one does not consider quantum behavior? -1 –  Anixx Nov 21 '13 at 21:48
    
The uncertainty principle is the statement that you can't squeeze a signal in frequency domain without spreading it out in the time domain. Holds for radio waves too. –  lionelbrits Nov 21 '13 at 22:16
    
what? please write an equation so we could see what you are talking about. –  Anixx Nov 21 '13 at 22:27
    
I've edited my response. You can read more about it here I –  lionelbrits Nov 22 '13 at 0:08
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It most certainly does introduce uncertainty about the location of the wave. The wave packet can't be localized in real space and in wave-vector space simultaneously. You are giving a quantum interpretation to what is a generic property of waves. –  lionelbrits Nov 22 '13 at 1:03
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The answer depends on the interpretation of quantum mechanics you like the most. As they are mathematically equivalent, the question is metaphysical rather than scientific.

Some of the ways to explain:

  • There is no uncertainty in the system. The uncertainty is in the observer. By making the measurement the observer introduces the uncertainty because he cannot for sure know his own state due to self-reference. (Bohm interpretation)

  • There is no uncertainty in the system, because the measured value actually does not exist. What is real is the wave function, which is always certain (MWI, von Neumann etc)

  • The uncertainty is introduced by vacuum fluctuations. Virtual particles of vacuum bombard all real particles so they conduct chaotic motion within certain limits. Vacuum thus can be seen as a medium having lowest possible, but non-zero energy.

  • The measured values are densely packed: two or more variables can be stored in 1 bit of information in nature (each carrying less than a bit). As our brain (and most instruments we use) cannot manipulate with amounts of information less than 1 bit, we can measure in one experiment only 1 value for which we use the whole bit while the other part becomes lost.

There are multiple other explanations as well.

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If by "metaphysical" you mean "choice of axioms that allow the formulation of mathematical models which describe observations". –  anna v Nov 22 '13 at 7:52
    
@anna v mathematical models do not differ. –  Anixx Nov 22 '13 at 15:07
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Physics isn't entitled in answering the question "why" but rather "how". The question "why" is always diverted to philosophy, and some liars use it to make religions.

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Why is it that physics explains the why question until it gets to the most fundamental level and the last one is put to answer by philosophers? Are you trying to say that scientists have not yet arrived at an answer to it? –  Rajath Krishna R Nov 21 '13 at 16:11
    
Exactly, if we knew, scientist would be doing more usefull things, like fixing the pipes of my kitchen - Quote to Walter Lewin. –  Angel Joaniquet Tukiainen Nov 21 '13 at 16:14
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This reply probably would be more suitable as comment, but i'm unable to comment yet, so: First of all we can't really describe universe as a system that even close to entropy which actually would be a lowest energy and most stable state for universe. So, following from that: universe is unstable, and as it's unstable there is no really a problem for Universe to follow uncertainty.

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Usually when someone asks about why a system is the way it is we answer it by saying that it is the most stable lowest energy state.

That's a lousy explanation. A system doesn't have to be in the lowest energy state (in that case the Universe would be very boring). In fact, some systems don't even have a definite energy.

To visualize what I've said, you can think of an object which is in a minimum energy state, hence it will be in equilibrium. This is not the case in QM, where an object will experience strange effects like going through walls and bouncing back when it's going to fall off a cliff.

But, what about the uncertainty principle? What benefit does the universe/nature get by following this principle?

I think no benefit. You can derive the HUP from the postulates of QM. Physics is more complicated than the lowest energy principle.

The HUP is an experimental fact which can be deduced from the non-commutativity of QM observables. See How does non-commutativity lead to uncertainty? and Heisenberg Uncertainty Principle scientific proof.

TIP: Why questions in Physics are usually useless.

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How did you came to the conclusion that the universe would have no benefit? –  Rajath Krishna R Nov 21 '13 at 18:58
    
@RajathKrishnaR Because it doesn't even make sense, as I've stated in the answer. It's like asking Would the Universe be happier if Newton's law were valid? And by your reasoning, every physical law obey make the universe have some benefit. –  jinawee Nov 25 '13 at 16:49
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