What Are the Implications of the Uncertainty Principle?

[bugatti79]

Hi folks,

I do read some of the interesting post on this forum particularly the discussions on the concept of uncertainty principle ie the more you know about the particle position the less you know about its momentum etc etc

I am a complete novice and am trying to get the big picture here in this field.

May I ask the question what is the big deal that we can't simultaneously have both information? So what?

Would the word be a different place if there wasnt such a problem?

Ie, what would be the physical implications if we were able to measure both simultaneously?

Pardon my ignorance! THanks

bugatti79

 

[revnaknuma]

I have a BS degree in physics but I am as ignorant as you about uncertainty principle.
How did Heisenberg find such a principle? He is an unbelievable genius.
my favorite is not Einstein but Heisenberg.

 

[bapowell]

I have a BS degree in physics but I am as ignorant as you about uncertainty principle.
How did Heisenberg find such a principle? He is an unbelievable genius.
my favorite is not Einstein but Heisenberg.

Not to discount the genius of Heisenberg, but the uncertainty principle is not so mysterious once you recognize that the position space wave function, $\psi(x)$, is related to the momentum space function, $\phi(p)$, by a Fourier transform:

$$\psi(x) = \frac{1}{\sqrt{2\pi}} \int \phi(p)e^{ipx}dp$$.

From here, it is evident that a localized particle (one for which the position is known precisely and thus represented by a delta function, $\delta(x)$) has a momentum space function $\phi(p) = const.$. In other words, if the position is known precisely, the momentum function is constant -- spread out evenly across the momentum (phase) space -- with maximum uncertainty.

And so there is a give-and-take at the level of the Fourier transform. Of course, Heisenberg's genius was in promoting this mathematical fact to a physical principle.

 

[bapowell]

Ie, what would be the physical implications if we were able to measure both simultaneously?

Quantum uncertainty is not only about measurement -- but one of reality. Suppose a particle is confined to a small region of space so that we are rather confident of its position. Heisenberg's principle states that, if we were then to try and measure its momentum, we'd obtain a large error on this value. However, this is not because our measuring device is flawed, but because the particle really does possesses such a large spread in momentum (its momentum-space wavefunction is not well-localized.) The effect is that the particle actually behaves as if it possesses this spread in momentum.

The most striking example of Heisenberg's principle at work in the universe that I can think of is in the stability of atoms. What do you think keeps the negatively charged electrons from spiraling into the positively charged nucleus? The above discussion is a big clue!

 

[bugatti79]

The most striking example of Heisenberg's principle at work in the universe that I can think of is in the stability of atoms. What do you think keeps the negatively charged electrons from spiraling into the positively charged nucleus? The above discussion is a big clue!

I was reading some other forum on this...it appears to do with the fact that two electrons cannot have the same energy at the same time but I don't see how this stops the electron collapsing into the nucleus?

 

[bapowell]

I was reading some other forum on this...it appears to do with the fact that two electrons cannot have the same energy at the same time but I don't see how this stops the electron collapsing into the nucleus?

I think you're referring to the Pauli Exclusion Principle, which is a different thing. It essentially states that two identical particles can occupy the same quantum state (possess the same quantum numbers). This is why, for example, the 2 electrons in the 1s orbital must have antiparallel spin, and why the multiple electrons in the n=2 level exist in different orbitals, 2s and 2p. This is not, however, why electrons exist in orbitals in the first place. The single electron of the hydrogen atom steers clear of the nucleus without any other electrons 'excluding' it from occupying this region.

 

[Drakkith]

I think you're referring to the Pauli Exclusion Principle, which is a different thing. It essentially states that two identical particles can occupy the same quantum state (possess the same quantum numbers).

He means that two identical particles CANNOT occupy the same quantum state.

In the macroscopic world there are only two "states". Position and time. 2 things cannot occupy the same spot at the same time. Once you get down to the quantum level there are actually more states than this. Two electrons can be in the same place at the same time as long as one of their quantum numbers (or states) is different than the other electrons. This is why you can have 2 electrons in the lowest orbital of an atom, but no more. There are only 1 state that can be different, so one of the electrons is in the opposite state than the other. After that there is no more room so to speak, and the next electron MUST go into a higher orbital, which is in effect, another quantum state.

 

[bapowell]

He means that two identical particles CANNOT occupy the same quantum state.

Whoops! Thanks for catching that...kinda important.

 

[Drakkith]

I was reading some other forum on this...it appears to do with the fact that two electrons cannot have the same energy at the same time but I don't see how this stops the electron collapsing into the nucleus?

Electrons actually have a small chance of being inside the nucleus. They don't get absorbed because they essentially can't be. The lowest state the electron can be in is in the first orbital. To absorb the electron would put the nucleus into a higher energy state, which is the opposite of what it wants. I'm sure its more complicated than that, but that's the basics as I understand it.

 

[bugatti79]

He means that two identical particles CANNOT occupy the same quantum state.

In the macroscopic world there are only two "states". Position and time. 2 things cannot occupy the same spot at the same time. Once you get down to the quantum level there are actually more states than this. Two electrons can be in the same place at the same time as long as one of their quantum numbers (or states) is different than the other electrons. This is why you can have 2 electrons in the lowest orbital of an atom, but no more. There are only 1 state that can be different, so one of the electrons is in the opposite state than the other. After that there is no more room so to speak, and the next electron MUST go into a higher orbital, which is in effect, another quantum state.

Thats interesting...So you mean there are multiple states at the quantum level ie because the electrons are waves and not particles, right?

How does a Quantum physicist think of particles?...I am trying to move away from the idea of little spheres orbiting around a bigger sphere...Would a cloud (wave) surrounding another cloud (nucleus) suffice?

 

[bapowell]

Thats interesting...So you mean there are multiple states at the quantum level ie because the electrons are waves and not particles, right?

How does a Quantum physicist think of particles?...I am trying to move away from the idea of little spheres orbiting around a bigger sphere...Would a cloud (wave) surrounding another cloud (nucleus) suffice?

Electrons are particles; they exhibit wavelike properties on account of their wavefunctions. But yes, it is a property of the wavefunctions of bound electrons that they should inhabit multiple distinct states.

The electron 'cloud' is the modern viewpoint. The wavefunction determines the probability amplitude of the electron and identifies regions of high relative likelihood of finding the electron. So even a single electron can, sort of, 'occupy' an extended region of space if there is a non-zero probability of it being there. The crazy thing is that the system actually behaves as if the electron really were 'sampling' this entire region.

 

[Calrid]

Actually I don't think its a big deal either or even surprising, so waves aren't pin point 1d quantities they are spread out through space. And like a rock thrown in a pool when we touch the surface of the waves they are disturbed and we cannot know the original pattern from the perspective of someone just arriving at the scene. What's so hard to comprehend about that?

With the right analogy I don't think its surprising or shocking its just kinda the way things are. I don't look in shocked awe when a duck lands on a rippling circle of water on a pond, I don't really see how anything at the nanoscopic scale and up is all that surprising either. Maybe I'm just not understanding it enough to be shocked by it.

It's interesting that we cannot pin point exact x at time t moments, but shocking not really.

There are some fricking odd things about QM but the uncertainty principle I think is a bit more mundane. I find even with an understanding of field theory (well up to a point) that the Casimir effect is pretty intriguing. The Copenhagen <or insert any other interpretation here> is a bit of a wild ride if not all that shocking. And anything with more than 4D aint shocking its just a bit esoteric.

 

[Drakkith]

I'm with you Caldrid. I've never had any problem with anything I've learned about quantum physics and such. Yet my roomate CANNOT believe half the things there for some reason. He says because it doesn't make sense, yet to me, it kind of does.

 

[bugatti79]

Electrons are particles; they exhibit wavelike properties on account of their wavefunctions. But yes, it is a property of the wavefunctions of bound electrons that they should inhabit multiple distinct states.

The electron 'cloud' is the modern viewpoint. The wavefunction determines the probability amplitude of the electron and identifies regions of high relative likelihood of finding the electron. So even a single electron can, sort of, 'occupy' an extended region of space if there is a non-zero probability of it being there. The crazy thing is that the system actually behaves as if the electron really were 'sampling' this entire region.

I like this explanation for the time being. You could say it like a cloud that surrounds the nucleus and doesn't orbit it..?

 

[bapowell]

I'm with you Caldrid. I've never had any problem with anything I've learned about quantum physics and such. Yet my roomate CANNOT believe half the things there for some reason. He says because it doesn't make sense, yet to me, it kind of does.

So you have no problem with the physical interpretation of QM? Or are you saying that the wave mechanics is physically sensible and you are comfortable with QM as a calculation tool. After all, you know what Feynman said... ;)

 

[Drakkith]

So you have no problem with the physical interpretation of QM? Or are you saying that the wave mechanics is physically sensible and you are comfortable with QM as a calculation tool. After all, you know what Feynman said... ;)

Im comfortable with whatever science says about QM lol. And I'm comfortable with the physical interpretations "not making sense" because I accept the fact that things at the atomic level DONT work like things do at our scale.

 

[madhatter106]

So you have no problem with the physical interpretation of QM? Or are you saying that the wave mechanics is physically sensible and you are comfortable with QM as a calculation tool. After all, you know what Feynman said... ;)

That's a good question, personally I didn't at first have any qualms with QM the use of it as a tool for practical use was enough to ignore the nagging unease of what it means. the more I have recently dug deeper into the research and thoughts of physicists on QM it went from a nagging unease to an unstable dizziness. If I really think about it it becomes very entangled -bad pun- Its akin to leaping into the unknown but worse, I imagine it similar for physics when QM left the determinism of classical.

 

[Calrid]

So you have no problem with the physical interpretation of QM? Or are you saying that the wave mechanics is physically sensible and you are comfortable with QM as a calculation tool. After all, you know what Feynman said... ;)

Well I have a problem with the interpretation sure, but then doesn't everyone?

It is interesting, and it certainly is at first sight quite intuitively unsettling. But once you get to grips with the maths and the theory it isn't really all that frightening.

The questions do not make me uncomfortable, only some of the wilder assertions like eternally unprovable dimensions, worlds or x.

I guess it is a matter of just how unsettling you find it to abandon the notion that the universe runs like clockwork.

What about reality has to conform to your standards though and why.

Just because you have evolved to make sense of the universe in a particular way, does not mean that you have evolved to make sense of the universe at the scales to which we can only really approximate with bounds. After all there has never been a time in our evolution where we needed to know what the universes rules were at a sub atomic scale to survive subject to the selection processes of the human species, only a curiosity to find them.

 

[Entropee]

That's a good question, personally I didn't at first have any qualms with QM the use of it as a tool for practical use was enough to ignore the nagging unease of what it means. the more I have recently dug deeper into the research and thoughts of physicists on QM it went from a nagging unease to an unstable dizziness. If I really think about it it becomes very entangled -bad pun- Its akin to leaping into the unknown but worse, I imagine it similar for physics when QM left the determinism of classical.

Lol nice pun, and while we're speaking of things that "don't make sense" we can add entanglement in this little discussion.

 

[aabottom]

Hi folks,

I do read some of the interesting post on this forum particularly the discussions on the concept of uncertainty principle ie the more you know about the particle position the less you know about its momentum etc etc

I am a complete novice and am trying to get the big picture here in this field.

May I ask the question what is the big deal that we can't simultaneously have both information? So what?

Would the word be a different place if there wasnt such a problem?

Ie, what would be the physical implications if we were able to measure both simultaneously?

Pardon my ignorance! THanks

bugatti79

As physicists, we can set up the Schrodinger wave equation to conform to the conditions of the hydrogen atom. Using this “model”, mathematical calculations of the atomic hydrogen spectral line agree quite well with the measured results. The results form part of the basis of accepting Quantum Mechanic and the Schrodinger wave equation as a useful model and a good tool to “predict” other possible outcomes.

The uncertainty principle is directly derivable from the Schrodinger wave equation. So to the extent that we accept the model, the uncertainty principle should not be surprising. Yet, it may be counter-intuitive to our everyday macroscopic experiences.

Even so, several measurements are also consistent with the uncertainty principle. The first example I can think of is diffraction of a particle beam (or a photon beam) through a small slit. The smaller the slit, the more precisely we know the transverse position of the particles. Yet, the smaller the slit, the wider is the angle of the beam spread, thus the less we know its transverse momentum when it passed through the slit.

Thus, the model is consistent with our measurement and that’s why we use the model. The more measurements we make that are consistent with the same model, the more we approve of our model.

To ask, “May I ask the question what is the big deal that we can’t simultaneously have both information? So what?”, serves little purpose in the Quantum world because that is not consistent with our measurements.

The big deal is that we can’t, and that’s just the way our world is. And, we have good models that are useful for observation, classification, prediction, and control.

Perhaps the main purposes of your questions are to, like Einstein, defy the results of your predecessors and discover something new.

Good luck in your quest.

 

[barzi]

I didn't have time to read all the replies, I hope someone did say that if the uncertainty principle wasn't holding this universe would collapse in a microsecond, simply because it is the consequences of this principle that prevent the electrons from falling into the nucleus!

 

[Drakkith]

I didn't have time to read all the replies, I hope someone did say that if the uncertainty principle wasn't holding this universe would collapse in a microsecond, simply because it is the consequences of this principle that prevent the electrons from falling into the nucleus!

You sure you don't mean the Pauli Exclusion Principle?

 

[bapowell]

You sure you don't mean the Pauli Exclusion Principle?

The electron in the hydrogen atom does not fall into the nucleus on account of the HUP, not the PEP.

 

[564102]

Excuse me if this is off-topic, but I have to ask... How does (or does it) the the uncertainty principle forbids the electron to "hit" the nucleus?

 

[yoda jedi]

Hi folks,

I do read some of the interesting post on this forum particularly the discussions on the concept of uncertainty principle ie the more you know about the particle position the less you know about its momentum etc etc

I am a complete novice and am trying to get the big picture here in this field.

May I ask the question what is the big deal that we can't simultaneously have both information? So what?

Would the word be a different place if there wasnt such a problem?

Ie, what would be the physical implications if we were able to measure both simultaneously?

Pardon my ignorance! THanks

bugatti79

the relevant issue is if the electron have the 2 values simultaneously, not that it can't be measured at the same time.

http://www.tau.ac.il/~yakir/yahp/yh30

..."A description of quantum systems at the time interval between two successive measurements is presented. Two wave functions, the first preselected by the initial measurement and the second post-selected by the final measurement describe quantum systems at a single time"...

and

http://arxiv.org/PS_cache/arxiv/pdf/1002/1002.3139v3.pdf

..."A quantum state is not discernible by means of a single replica, but can be reconstructed only by performing many measurements on identically prepared systems"...




----------
Some theoreticians postulate that the non locality of quantum mechanics is derived from the Uncertainity Principle:
http://qip2011.quantumlah.org/scientificprogramme/abstract/1004.2507.pdf

Ie, what would be the physical implications if we were able to measure both [STRIKE]simultaneously[/STRIKE]?
Pardon my ignorance! THanks

if the simultaneous uncertainty does not hold, there is not non-locality.


.

 

[bapowell]

Excuse me if this is off-topic, but I have to ask... How does (or does it) the the uncertainty principle forbids the electron to "hit" the nucleus?

It doesn't forbid the electron from hitting the nucleus. In fact, as Drakkith pointed out somewhere above, there is a small but finite probability that the electron will find itself in the nuclear because its wavefunction (in the H atom at least) overlaps with the nucleus slightly. It does sometimes occur in a process called electron capture. However, the bulk of the probability amplitude lies outside the nucleus. This is no accident, and has to do with the fact that we are looking at a central force problem -- while the central force seeks to confine the electron to an ever decreasing region about the nucleus, the variance in the electron's momentum becomes larger as a result of the HUP.

 

[Drakkith]

The electron in the hydrogen atom does not fall into the nucleus on account of the HUP, not the PEP.

Principles aside, I actually thought I had read that it doesn't "fall" into the nucleus because the atom is in a more stable and less energetic situation with electrons orbiting it than it is for the electron to combine with a proton and turn one of the protons into a neutron in the nucleus. (Hence why only immense pressure, like what you find in a neutron star, cause electrons to combine in mass with protons) What principle that might be, I don't know.

 

[barzi]

The PEP forbids that more than a certain number of fermions (this number depends on their spin) be in the same energy level thus its effect during the collapse of an atom as in a neutron star is to resist that electrons on the outer shells be pushed to the inner shells where other electrons sits but in hydrogen(one electron) or even hellium(two electrons) its the HUP that prevents the collapse.

 

[diliptiwari]

what is field theory? is this related to quantum mechanics?

 

[aabottom]

It doesn't forbid the electron from hitting the nucleus. In fact, as Drakkith pointed out somewhere above, there is a small but finite probability that the electron will find itself in the nuclear because its wavefunction (in the H atom at least) overlaps with the nucleus slightly. It does sometimes occur in a process called electron capture. However, the bulk of the probability amplitude lies outside the nucleus. This is no accident, and has to do with the fact that we are looking at a central force problem -- while the central force seeks to confine the electron to an ever decreasing region about the nucleus, the variance in the electron's momentum becomes larger as a result of the HUP.

Thank you bapowell. I think your statement is the clearest example of the HUP in this thread.