Quantum Mechanics

[Drotar]

Two questions:

Could someone explain to me WHY electrons would emit electromagnetic radiation if classical mechanics laws were applied on a sub-atomic level. I was reading up on this, and it was explained that if the classical laws of physics were at play on a sub-atomic level, the electron would slowly orbit into the nucleus of the atom. Why is that?

Could someone explain WHY there is a fundamental limit to the accuracy of quantum mechanics? In other words, why must we rely onprobabilities?

How does the uncertainty principle, coupled with Planck's constant equal virtual particles?


Thank you in advance to all who can answer those questions. TTYL Jesus loves you!

 

[Drotar]

Wait... no, something's not right.

I meant that I had THREE questions, instead of two.

That's an honest mistake.

 

[Jet Black]

Two questions:

Could someone explain to me WHY electrons would emit electromagnetic radiation if classical mechanics laws were applied on a sub-atomic level. I was reading up on this, and it was explained that if the classical laws of physics were at play on a sub-atomic level, the electron would slowly orbit into the nucleus of the atom. Why is that?

this is basically the principle that as an electron accelerates, it emits light. the electron is constantly accelerating towards the nucleus of the atom, and hence should be constantly emitting light and losing energy, and so should spiral into the nucleus in a fraction of a second. QM forbids this by only allowing vertain energy levels (complete integer multiples of the electron's wavelength)

Could someone explain WHY there is a fundamental limit to the accuracy of quantum mechanics? In other words, why must we rely on probabilities?

this is due to a couple of effects: the non-commutable nature of certain operators. certain operators (measurements on a system) do not commute, or to put it more simply, interfere with each other... for example, a position measurement in the x direction interferes with a momentum measurement in the x direction.
another issue is superposition. In quantum mechanics you can have a superposition of two different states, so a photon can be in a superposition of two different polarities. when you measure it, you will get one answer or another with a certain probability.

How does the uncertainty principle, coupled with Planck's constant equal virtual particles?

well virtual particles are a result of the non-commutability of the energy-time relation.

dEdt>=h/4pi

Thank you in advance to all who can answer those questions. TTYL Jesus loves you!

no worries. I hope someone can check up on that to make sure I am right.

 

[Drotar]

Man, I didn't understand any of that completely.

So, an electron emits light as it accelerates? By "accelerate" I'm assuming that you don't imply the proper definition (of a change in speed) but rather of the electron speeding up. So, are you saying that if you, say, heat up an object, for the purpose of causing the electrons to move faster, that it would emit light? Is that principle why things glow when you heat them to a certain point?

Are you saying that certain operators do or don't interfere with each other? I don't understand what you meant of the superposition and the polarities...

I'm going to copy/paste your answers and later on maybe I'll understand them.

But how can actual matter spontaneously appear as a result of uncertainty and probabilities?

 

[Jet Black]

So, an electron emits light as it accelerates? By "accelerate" I'm assuming that you don't imply the proper definition (of a change in speed) but rather of the electron speeding up. So, are you saying that if you, say, heat up an object, for the purpose of causing the electrons to move faster, that it would emit light? Is that principle why things glow when you heat them to a certain point?

or it can absorb photons too, sorry, basically momentum is conserved. I think I have made a mistake somewhere there, let me think about it for a minute....

heating things is different: you are adding energy to the particle(s) and this can be expressed in a number of degrees of freedom:

1) movement... it can increase it's velocity
2) vibrational... it cab vibrate
3) rotational... some molecules can rotate, like carbon dioxide
4) electronic... electrons may be excited to higher electron levels, where they may then decay by spontaneous emission when they drop some energy levels.

Are you saying that certain operators do or don't interfere with each other? I don't understand what you meant of the superposition and the polarities...

well we will just call operators measurements. say you want to measure the position (in the x axis) of a particle perfectly, you can do that, but then you cannot measure it's momentum (in the x axis)... other things you can do... so you can measure the x postion, and the y momentum to arbitrary accuracy.

about polarities. well say we have a photon polarised at 45 degrees to the vertical, then it will get through a horizontally polarising screen 50% of the time.

But how can actual matter spontaneously appear as a result of uncertainty and probabilities?

because it is allowed to

 

[Jet Black]

oh, by acceleration, I mean chance in momentum. momentum is a vector, speed isn't.

 

[Drotar]

Yep, no good.

The flaw, Jet Black, is not in your explaining it, but in my limited understanding. The fact that I can't understand what you're saying is really my fault. I didn't expect to be able to understand QM by reading a few websites off Yahoo! I've got to take a course in it. Thank you for responding. AGain, I've copy-pasted what you wrote so taht I may comprehend it at a later date. Right now, having just graduated high school taking basic math, I should just slow down a bit on trying to understand these upper-level sciences. TTYL Jesus loves you!

 

[Jet Black]

oh alot of these things are explainable, I am just not very good at explaining some things (can't see the wood for the trees an so on).. perhaps someone else will have better luck.

 

[Mainframes]

Two questions:

Could someone explain to me WHY electrons would emit electromagnetic radiation if classical mechanics laws were applied on a sub-atomic level. I was reading up on this, and it was explained that if the classical laws of physics were at play on a sub-atomic level, the electron would slowly orbit into the nucleus of the atom. Why is that?

I think JetBlack got it pretty good.

Could someone explain WHY there is a fundamental limit to the accuracy of quantum mechanics? In other words, why must we rely onprobabilities?

Basically the idea is that we can either measure the position OR velocity of an object on a Quantum scale but not both as the measurement itself change will change the other property ie measure velocity and you will alter the position and vice versa. Therefore it is impossible to state that a given particle is at a certain point going at a certain velocity. Instead we measure lots of velocities and lots of positions to get an idea of what the particle tends to do.

This is how we get such things as the shape of electron clouds around atoms and molecules. We can never get an exact position, just be able to predict where the electron is likely to be.

Maybe Jet can improve this for me....

 

[lucaspa]

Let's see if I can help Jetblack out a bit

Could someone explain to me WHY electrons would emit electromagnetic radiation if classical mechanics laws were applied on a sub-atomic level. I was reading up on this, and it was explained that if the classical laws of physics were at play on a sub-atomic level, the electron would slowly orbit into the nucleus of the atom. Why is that?

What's the charge on an electron? Negative, right? What's the charge on the protons in the nucleus? Positive, right? Opposite charges attract, right? So, if classical mechanic applied, the electron should spiral into the nucleus. Now, since electrons emit energy as they get closer to the nucleus (lower energy levels), then they would continuously emit energy (electromagnetic radiation) during the spiral.

Instead, as Jetblack said, there are specific levels at which the electron "orbits" the nucleus. Quanta. So, an electron jumps from one level to the next, going a discreet energy level and emitting (or absorbing if it is going out) a particular wavelength in the process.

Could someone explain WHY there is a fundamental limit to the accuracy of quantum mechanics? In other words, why must we rely onprobabilities?

Because individual events on the quantum level are uncaused. Shine a light on a mirror. 95% of the photons are reflected and 5% go thru. But if you look at the photons, they are identical. Thus, there is no reason for one to reflect and another to go thru. Yet that is what happens. You can't predict, looking at each photon in turn, whether it will reflect or go thru. That is, photon A reflects, photon B reflects, but photon C goes thru. Yet they are all identical. So why does one reflect and another go thru?

What gives the appearance of cause and effect on the macroscopic level is that the probabilities do hold. Each and every time you shine a light on a mirror, 95% of the photons reflect and 5% go thru.

How does the uncertainty principle, coupled with Planck's constant equal virtual particles?

It's not as simple as that. In fact, I've never seen it put in these terms before. Where did you get this?

The observation is that the vacuum has energy. This energy is "borrowed" such that E = mc^2 is used to convert the energy to a particle. However, the loan must be paid back very quickly, so the virtual particle only lasts 10^-22 seconds. That's 1/10 to the 22 power. Not very long at all.

Now, if you supply energy by, say, a particle accelerator, then you can convert the virtual particles to real ones.

 

[lucaspa]

Yep, no good.

The flaw, Jet Black, is not in your explaining it, but in my limited understanding. The fact that I can't understand what you're saying is really my fault. I didn't expect to be able to understand QM by reading a few websites off Yahoo! I've got to take a course in it. Thank you for responding. AGain, I've copy-pasted what you wrote so taht I may comprehend it at a later date. Right now, having just graduated high school taking basic math, I should just slow down a bit on trying to understand these upper-level sciences.

Drotar, one of the things you have to do with QM is discard "common sense". You can't trust it at the quantum level. QM is just plain weird! You have to accept that the data is what it is.

For instance, common sense tells us we can know the position and velocity of a car. Exactly. We know exactly where it is and how fast it is going.

But quantum particles have what are called "complementary properties". That is, two properties such that you can't know both exactly at the same time. The more precisely you measure one, the more indeterminant is the other. Indeterminancy

For an electron, one of the sets of complementary properties is position and momentum (related to velocity). The more precisely you measure the momentum, the less you know about where the electron is. If you know the momentum exactly (and this can be done), then you have no idea where the electron is. Conversely, if you know exactly where it is, you have no idea what the momentum is. So what you have is a set of probabilities as to the electron's position and momentum.

 

[Drotar]

Hey, that's kinda cool though. So, you're saying that if all we do is supply that energy by a partcile accelerator, we can create matter from nothing that will not warp back out of existence??

 

[Duane Morse]

Drotar, one of the things you have to do with QM is discard "common sense". You can't trust it at the quantum level. QM is just plain weird! You have to accept that the data is what it is.

For instance, common sense tells us we can know the position and velocity of a car. Exactly. We know exactly where it is and how fast it is going.

But quantum particles have what are called "complementary properties". That is, two properties such that you can't know both exactly at the same time. The more precisely you measure one, the more indeterminant is the other. Indeterminancy

For an electron, one of the sets of complementary properties is position and momentum (related to velocity). The more precisely you measure the momentum, the less you know about where the electron is. If you know the momentum exactly (and this can be done), then you have no idea where the electron is. Conversely, if you know exactly where it is, you have no idea what the momentum is. So what you have is a set of probabilities as to the electron's position and momentum.

It's funny. The same people that say "common sense" must be discarded where QM is concerned also say that "commom sense" must be used where God is concerned.

QM is accepted for being what it is even though common sense does not apply, yet when God says I AM THAT I AM it can not be accepted because it is not "common sense"?

It can not make "sense" that God just IS, but it does make "sense" that QM just IS?

Maybe God is just plain weirder than QM.

 

[Jet Black]

Hey, that's kinda cool though. So, you're saying that if all we do is supply that energy by a partcile accelerator, we can create matter from nothing that will not warp back out of existence??

well it's not from nothing as such, since you are "giving" it energy from a bunch of big superconducting magnets. energy-matter conversion.

 

[Jet Black]

It's funny. The same people that say "common sense" must be discarded where QM is concerned also say that "commom sense" must be used where God is concerned.

QM is accepted for being what it is even though common sense does not apply, yet when God says I AM THAT I AM it can not be accepted because it is not "common sense"?

It can not make "sense" that God just IS, but it does make "sense" that QM just IS?

Maybe God is just plain weirder than QM.

depends on your definition of sense. QM makes perfect sense mathematically. but the mathematical sense of QM does not translate into classical logic.

 

[Duane Morse]

depends on your definition of sense. QM makes perfect sense mathematically. but the mathematical sense of QM does not translate into classical logic.

I understand. But the same could also apply to God, couldn't it?

 

[Jet Black]

I understand. But the same could also apply to God, couldn't it?

QM is still confined by universal rules though.

 

[lucaspa]

It's funny. The same people that say "common sense" must be discarded where QM is concerned also say that "commom sense" must be used where God is concerned.

QM is accepted for being what it is even though common sense does not apply, yet when God says I AM THAT I AM it can not be accepted because it is not "common sense"?

Which people specifically? Have I ever argued against God saying "I am that I am"?

The difference is that the weirdness that is QM can be seen by anyone and everyone doing the same experiments. God is only seen by a few. The ones that don't see God accept what they see and either doubt the existence of God or say that God doesn't exist.

So, you see, it's not really so different.

It can not make "sense" that God just IS, but it does make "sense" that QM just IS?

You do realize there is a difference between the statements:

God exists and created.
God created by creationism.

Don't you?

 

[lucaspa]

Hey, that's kinda cool though. So, you're saying that if all we do is supply that energy by a partcile accelerator, we can create matter from nothing that will not warp back out of existence??

Not create, but promote virtual paticles to permanence. It's done in particle accelerators. I've read is described as colliding two refrigerators together and keeping the refigerators but also getting a toaster, breadmaker, and electric knife too.

 

[Plan 9]

Let's see if I can help Jetblack out a bit



What's the charge on an electron? Negative, right? What's the charge on the protons in the nucleus? Positive, right? Opposite charges attract, right? So, if classical mechanic applied, the electron should spiral into the nucleus. Now, since electrons emit energy as they get closer to the nucleus (lower energy levels), then they would continuously emit energy (electromagnetic radiation) during the spiral.

Instead, as Jetblack said, there are specific levels at which the electron "orbits" the nucleus. Quanta. So, an electron jumps from one level to the next, going a discreet energy level and emitting (or absorbing if it is going out) a particular wavelength in the process.



Because individual events on the quantum level are uncaused. Shine a light on a mirror. 95% of the photons are reflected and 5% go thru. But if you look at the photons, they are identical. Thus, there is no reason for one to reflect and another to go thru. Yet that is what happens. You can't predict, looking at each photon in turn, whether it will reflect or go thru. That is, photon A reflects, photon B reflects, but photon C goes thru. Yet they are all identical. So why does one reflect and another go thru?

What gives the appearance of cause and effect on the macroscopic level is that the probabilities do hold. Each and every time you shine a light on a mirror, 95% of the photons reflect and 5% go thru.



It's not as simple as that. In fact, I've never seen it put in these terms before. Where did you get this?

The observation is that the vacuum has energy. This energy is "borrowed" such that E = mc^2 is used to convert the energy to a particle. However, the loan must be paid back very quickly, so the virtual particle only lasts 10^-22 seconds. That's 1/10 to the 22 power. Not very long at all.

Now, if you supply energy by, say, a particle accelerator, then you can convert the virtual particles to real ones.

For a minute there, I thought I almost understood this.
What is a virtual particle?