Light absorption and linewidth (split from A rational explanation for the dual slit experiment)

[bangstrom]

1 hour ago, studiot said:

Absorbtion (and emission) is not instantaneous. Both processes take time.
That is why spectral lines are slightly 'blurred' or 'spread'.

I suspect the blurred lines are a result of the uncertainity of which atom will absorb the light rather than a matter of timing. From the reference frame of light, emission and absorption are simultaneous events.

 

[swansont]

7 minutes ago, bangstrom said:

I suspect the blurred lines are a result of the uncertainity of which atom will absorb the light rather than a matter of timing. From the reference frame of light, emission and absorption are simultaneous events.

 

We're not in the frame of the light.

The source of this is the energy-time uncertainty relation. ∆E∆t > hbar/2

The natural linewidth of any transition is related to its lifetime. And since E = hbar * w, you can see that this is just a relationship between frequency and time, which are Fourier transforms of each other. It's an inherent uncertainty from that.

 

[bangstrom]

57 minutes ago, swansont said:

We're not in the frame of the light.

The source of this is the energy-time uncertainty relation. ∆E∆t > hbar/2

The natural linewidth of any transition is related to its lifetime. And since E = hbar * w, you can see that this is just a relationship between frequency and time, which are Fourier transforms of each other. It's an inherent uncertainty from that.

 

Light is in the frame of light and that is where the transition takes place. Our perception from afar is not a determining factor. Light may land within the probability predicted by energy, distance, and time. That is based on previous observations of similar events in the past but the same interpretation may not apply to the reference frame of light which lacks a time interval even though the end results are the same.

And interpreting light as a particle in this case, isn’t that applying a classical model to a quantum event? And what is a “particle” in the quantum view?

“When an energy exchange occurs between, say, two molecules one wonders what is traveling between them. If we don’t know, we say it is a “photon” Giving it a name doesn’t add any knowledge, but it allows us to feel better and we can pretend we know what travels.” Milo Wolff

“What we observe as material bodies and forces are nothing but shapes and variations in the structure of space. Particles are just Schaumkommen.” (appearances)- Erwin Schroedinger 1937

 

[swansont]

25 minutes ago, bangstrom said:

Light is in the frame of light and that is where the transition takes place. Our perception from afar is not a determining factor. Light may land within the probability predicted by energy, distance, and time. That is based on previous observations of similar events in the past but the same interpretation may not apply to the reference frame of light which lacks a time interval even though the end results are the same.

"Reference frame of light" make no sense from a physics perspective; this is an issue of relativity and light does not have an inertial frame.

We observe that when you send a photons at atoms they can be absorbed, and the atoms emits light some time later. This observation takes place in the lab frame, not the photons. The physics used to describe this is also based in the lab frame. We don't have physics that can be used in a photon's frame, because there is no transform that gets us there and back; the equations diverge. 

 

25 minutes ago, bangstrom said:

And interpreting light as a particle in this case, isn’t that applying a classical model to a quantum event? And what is a “particle” in the quantum view?

No, we're talking about a photon being absorbed. Light has both wave and particle behaviors. Photons are most definitely quantum particles.

 

25 minutes ago, bangstrom said:

“When an energy exchange occurs between, say, two molecules one wonders what is traveling between them. If we don’t know, we say it is a “photon” Giving it a name doesn’t add any knowledge, but it allows us to feel better and we can pretend we know what travels.” Milo Wolff

“What we observe as material bodies and forces are nothing but shapes and variations in the structure of space. Particles are just Schaumkommen.” (appearances)- Erwin Schroedinger 1937

Argument by quotation is pretty meaningless. Similar to the Wolff quote above, it doesn't add to any knowledge.

[exchemist]

2 hours ago, swansont said:

We're not in the frame of the light.

The source of this is the energy-time uncertainty relation. ∆E∆t > hbar/2

The natural linewidth of any transition is related to its lifetime. And since E = hbar * w, you can see that this is just a relationship between frequency and time, which are Fourier transforms of each other. It's an inherent uncertainty from that.

 

Just to clarify, my understanding has always been that it is the lifetimes of the participating states that determine the uncertainty in energy of the transition, rather than the time it takes for the transition between states to occur. So, as I understand it, states with a short lifetime have large uncertainties in energy, whereas long-lived states have small uncertainties in energy.

Is that what you mean, or are you saying it is the duration of the transition process itself that is the issue?

1 hour ago, bangstrom said:

Light is in the frame of light and that is where the transition takes place. Our perception from afar is not a determining factor. Light may land within the probability predicted by energy, distance, and time. That is based on previous observations of similar events in the past but the same interpretation may not apply to the reference frame of light which lacks a time interval even though the end results are the same.

And interpreting light as a particle in this case, isn’t that applying a classical model to a quantum event? And what is a “particle” in the quantum view?

“When an energy exchange occurs between, say, two molecules one wonders what is traveling between them. If we don’t know, we say it is a “photon” Giving it a name doesn’t add any knowledge, but it allows us to feel better and we can pretend we know what travels.” Milo Wolff

“What we observe as material bodies and forces are nothing but shapes and variations in the structure of space. Particles are just Schaumkommen.” (appearances)- Erwin Schroedinger 1937

 

Untrue. The transition takes place within the atom or molecule that is absorbing or emitting.  

Uncertainty broadening is nothing to do with uncertainty as to which atom or molecule in an ensemble is going to absorb or emit. In principle it applies even to single, isolated atoms or molecules - though it would be fairly hard to measure in such a case, admittedly.

You may possibly be confusing this with pressure broadening, which is another line-broadening phenomenon, due to collisions between atoms or molecules shortening the lifetimes and/or perturbing the energies of their states.   

 

Edited November 8, 2021 by exchemist

[studiot]

2 hours ago, bangstrom said:

I suspect the blurred lines are a result of the uncertainity of which atom will absorb the light rather than a matter of timing. From the reference frame of light, emission and absorption are simultaneous events.

 

Spectroscopists have been successfully observing and predicting spectral line broadening for more than seventy years using swansont's (Heisenberg's) uncertainty principle.

Formulae and explanations for predicting line broadening are available in any half ways decent spectroscopy textbook

eg p19ff of Spectroscopy by D H Whiffen.

It is worth notibng that uncertainty broadening is not the only broadening mechanism and Whiffen discusses all the differnt ons and methods of combining their effects, when present, to predict a total broadening.

I have indicated the relevant paragraph.

[swansont]

1 hour ago, exchemist said:

Just to clarify, my understanding has always been that it is the lifetimes of the participating states that determine the uncertainty in energy of the transition, rather than the time it takes for the transition between states to occur. So, as I understand it, states with a short lifetime have large uncertainties in energy, whereas long-lived states have small uncertainties in energy.

Is that what you mean, or are you saying it is the duration of the transition process itself that is the issue?

Lifetime, as I said, but that also means you can't tell exactly when the transition took place.

 

 

[exchemist]

2 hours ago, studiot said:

Spectroscopists have been successfully observing and predicting spectral line broadening for more than seventy years using swansont's (Heisenberg's) uncertainty principle.

Formulae and explanations for predicting line broadening are available in any half ways decent spectroscopy textbook

eg p19ff of Spectroscopy by D H Whiffen.

It is worth notibng that uncertainty broadening is not the only broadening mechanism and Whiffen discusses all the differnt ons and methods of combining their effects, when present, to predict a total broadening.

I have indicated the relevant paragraph.

This passage is curious as it seems to say "yes, repeat no".

I can't at the moment see how if the uncertainty in energy results from the brevity, as it were, of the excited state, he can then also say it depends "in a sense" on the time the transition itself takes.  Unless what he has in mind that the lifetime of the excited state is so short that the duration of the transition process is comparable with it. But that is not going to be the case in general. 

Does he say anything else that sheds light on this odd "in a sense" comment?

[studiot]

19 minutes ago, exchemist said:

This passage is curious as it seems to say "yes, repeat no".

I can't at the moment see how if the uncertainty in energy results from the brevity, as it were, of the excited state, he can then also say it depends "in a sense" on the time the transition itself takes.  Unless what he has in mind that the lifetime of the excited state is so short that the duration of the transition process is comparable with it. But that is not going to be the case in general. 

Does he say anything else that sheds light on this odd "in a sense" comment?

We have a teams meeting/lecture for the next couple of hours, but I will elaborate as soon as I can.

Meanwhile there is a good sample calculation the hyperphysics website on a simple uncertainty calculation experiment.

I tried tofind it to include in the last post but couldn't.

I will try harder there as well.

[studiot]

Here are some calculations.

https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Book%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/07%3A_Quantum_Mechanics/7.03%3A_The_Heisenberg_Uncertainty_Principle

[exchemist]

12 hours ago, studiot said:

Here are some calculations.

https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Book%3A_University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/07%3A_Quantum_Mechanics/7.03%3A_The_Heisenberg_Uncertainty_Principle

The link accords with my understanding and makes no reference to the time taken for the transition to take place. So I'm afraid it sheds no light on this odd remark of Whiffen's about the duration of the transition.

[studiot]

2 hours ago, exchemist said:

The link accords with my understanding and makes no reference to the time taken for the transition to take place. So I'm afraid it sheds no light on this odd remark of Whiffen's about the duration of the transition.

I rather think it did in the examples at the end. question 7.3.1 specifically calculates line width.

Saying  both emission and absorbtion are processes with a beginning and an end and that they have a 'lifetime' are essentially the same thing.

Take emission. Claiming this be instantaneous cannot be true by itself.

At what point in the 'lifetime' does this instant occur ?  The beginning ? , The end ? What happens during the rest of the time duration of the 'lifetime' ?

Here is the conversation I was remembering from Physicshelpforums.com, where there was a similar question asked.

Quote

Write down the time-energy form of the Heisenberg Uncertainty Principle. In an experiment, a gas of atoms in an excited state emits light at a spectral line of 550 nm as the atoms decay back to the ground state. The intensity I of the emitted light is observed to decrease with time t, with I(t) = I0 exp (−t/τ ) where τ = 2 × 10−6
sec. Calculate the natural line width in terms of wavelength, ∆λ, of this spectral line:

My attempt:
I know how to do almost all this problem but im having an issue finding ∆t to plug into the uncertainty principle. Is it simply 2 × 10−6?

 

 

 

Yup.

-Dan

 

 

 

 

To Reinforce Dan's short post yes you can identify the time constant tau with the delta t uncertainty in time.

As usual Hyperphysics has the easiest presentation to digest along with a delat E, Delta tau calculator to check your working.

Particle lifetimes from the uncertainty principle

 

[bangstrom]

4 minutes ago, studiot said:

Take emission. Claiming this be instantaneous cannot be true by itself.

At what point in the 'lifetime' does this instant occur ?  The beginning ? , The end ? What happens during the rest of the time duration of the 'lifetime' ?

Here is the conversation I was remembering from Physicshelpforums.com, where there was a similar question asked.

 

It is my understanding that an atom gains energy when an electron jumps from a lower energy orbit to a higher orbit and one should not think of an electron in orbit about the nucleus as having a position in space as if it were a tiny planet in orbit about a star. Electrons are best thought of as probability waves rather than having a location.

I have never looked into the thinking behind the theory, but the speculation is that an electron “quantum leaps” from one orbital to the next without passing through the space between. It simply vanishes from one orbit and appears in another without a transition through either space or time so no time interval can be assigned to how long it takes an atom to gain energy.

[studiot]

31 minutes ago, bangstrom said:

It is my understanding that an atom gains energy when an electron jumps from a lower energy orbit to a higher orbit and one should not think of an electron in orbit about the nucleus as having a position in space as if it were a tiny planet in orbit about a star. Electrons are best thought of as probability waves rather than having a location.

I have never looked into the thinking behind the theory, but the speculation is that an electron “quantum leaps” from one orbital to the next without passing through the space between. It simply vanishes from one orbit and appears in another without a transition through either space or time so no time interval can be assigned to how long it takes an atom to gain energy.

I said absolutely nothing about electrons or orbits or quantum leaps through soace or time or wormholes or any such stuff.

But I did ask a fundamental question about the sequence of events.

Re phrasing for absorbtion,

Are you telling me you that the electron can 'jump' before absorbtion takes place ?

Surely the fundamental question is

Which must happen first, absorption, or the electron transition ?

or as swansont puts it

19 hours ago, swansont said:

Lifetime, as I said, but that also means you can't tell exactly when the transition took place.

 

The 'lifetime' is a convenient model to work (mathematically) with this concept, as is the resultant 'natural linewidth'.

 

You should also note in the hyperphysics link they point out that the broadening due to lifetime is orders of magnitude less than other broadening mechanisms

Quote

For optical spectroscopy it is a minor factor because the natural linewidth is typically 10^-7 eV, about a tenth as much as the Doppler broadening. Another source of linewidth is the recoil of the source, but that is negligible in the optical range.

 

Edited November 9, 2021 by studiot

[swansont]

42 minutes ago, studiot said:

 The 'lifetime' is a convenient model to work (mathematically) with this concept, as is the resultant 'natural linewidth'.

 

You should also note in the hyperphysics link they point out that the broadening due to lifetime is orders of magnitude less than other broadening mechanisms

 

Natural linewidth is not considered broadening, in my experience, as it is inherent to the transition. It's the starting point, and the other mechanisms give you broadening. Which is why efforts are made to reduce the other effects, such as doing Doppler-free spectroscopy to reduce/eliminate that source of broadening.

[studiot]

24 minutes ago, swansont said:

Natural linewidth is not considered broadening, in my experience, as it is inherent to the transition. It's the starting point, and the other mechanisms give you broadening. Which is why efforts are made to reduce the other effects, such as doing Doppler-free spectroscopy to reduce/eliminate that source of broadening.

However you chose to classify it, the fact that we need a 'natural linewidth' , is an indication that the process is not instantaneous.

And whether or not is is instantaneous is the subject of my comment.

Since it is not instantaneous, it makes sense to discuss the duration of the transition, just as it makes s ense to take other effewcts and mechanisms into account.

[swansont]

2 hours ago, bangstrom said:

It is my understanding that an atom gains energy when an electron jumps from a lower energy orbit to a higher orbit and one should not think of an electron in orbit about the nucleus as having a position in space as if it were a tiny planet in orbit about a star. Electrons are best thought of as probability waves rather than having a location.

Which has nothing to do with the topic of discussion

2 hours ago, bangstrom said:

I have never looked into the thinking behind the theory, but the speculation is that an electron “quantum leaps” from one orbital to the next without passing through the space between. It simply vanishes from one orbit and appears in another without a transition through either space or time so no time interval can be assigned to how long it takes an atom to gain energy.

 The "leaps" being discussed are ones of energy and not location, so this isn't really applicable. 

 

[studiot]

3 hours ago, bangstrom said:

I have never looked into the thinking behind the theory, but the speculation is that an electron “quantum leaps” from one orbital to the next without passing through the space between. It simply vanishes from one orbit and appears in another without a transition through either space or time so no time interval can be assigned to how long it takes an atom to gain energy.

It is really worth considering what is inherent in the best model we have and the phenomenon itself.

Are there any truly instantaneous natural processes ?

Or is it just that our best model offers this ?

Or is is like the concept of a point particle where we can say the size of the particle is insgnificant compared to the size of the system under consideration.

So does instantaneous really mean: of insignificant duration compared with the timescale of the process under consideration ?

 

Here is a classical example to think about for comparison.

In open channel hydraulic flow there is a phenomenon where the level of the water surface changes (rises) abruptly.
This is called a hydraulic jump.
The jump occurs where there is a sudden levelling off of the bed slope so the water coming down the slope is moving faster than the water in the level part.
The very best hydraulic models (equations) that we have predict this is an instaneous rise, over zero distance,  but in reality the 'vertical' part of the water surface always slopes slightly forward.
So there is a process which forms of a step in the water surface with a definite start and end point in time and space over very short intervals.
The step is due to the fact that the incoming faster water has more kinetic energy than the outgoing slower water.
So the surface must rise to transfer the energy to pressure energy.

[exchemist]

4 hours ago, studiot said:

I rather think it did in the examples at the end. question 7.3.1 specifically calculates line width.

Saying  both emission and absorbtion are processes with a beginning and an end and that they have a 'lifetime' are essentially the same thing.

Take emission. Claiming this be instantaneous cannot be true by itself.

At what point in the 'lifetime' does this instant occur ?  The beginning ? , The end ? What happens during the rest of the time duration of the 'lifetime' ?

Here is the conversation I was remembering from Physicshelpforums.com, where there was a similar question asked.

 

No. 7.3.1 calculates line width from the lifetime of the excited state, not from the duration of the transition process. 

And the other example you quote is again based on working out the lifetime of the excited state, from the decay curve as the population of them decays away. This is quite distinct from the duration of the transition process, i.e. the time it takes for an electron to emit a photon and change from the excited state to the ground state.

The latter is not referred to  in either example. 

 

 

 

4 hours ago, bangstrom said:

It is my understanding that an atom gains energy when an electron jumps from a lower energy orbit to a higher orbit and one should not think of an electron in orbit about the nucleus as having a position in space as if it were a tiny planet in orbit about a star. Electrons are best thought of as probability waves rather than having a location.

I have never looked into the thinking behind the theory, but the speculation is that an electron “quantum leaps” from one orbital to the next without passing through the space between. It simply vanishes from one orbit and appears in another without a transition through either space or time so no time interval can be assigned to how long it takes an atom to gain energy.

No, this notion of "leaps" became obsolete in about 1930.

The process is not mysterious. It has a duration: loosely speaking, the electric vector of the photon perturbs the wave function of the electron by changing the potential it experiences, causing it to gain energy and angular momentum, absorbing the photon as it does so. This is modelled by the time-dependent version of the wave equation, though admittedly it was 45 years ago I did this stuff at university, so I may not have all the details right any more. There is a bit about it in this short description of transition dipole moments: https://en.wikipedia.org/wiki/Transition_dipole_moment

And they are not "orbits" but "orbitals", the difference in nomenclature being intended to recognise that electrons do not follow fixed Newtonian orbits, but are described by "clouds" of what is more or less the square root of probability density. 

 

 

[bangstrom]

17 hours ago, studiot said:

So does instantaneous really mean: of insignificant duration compared with the timescale of the process under consideration ?

I consider "instantaneous" to be either without duration or having a duration too short to observe by any means. Quantum entanglement would be an example.

[studiot]

3 hours ago, bangstrom said:

I consider "instantaneous" to be either without duration or having a duration too short to observe by any means. Quantum entanglement would be an example.

Thank you for your reply.

A pity you only bothered to comment on a small part of my last post so I don't know what you made of the rest of it.

 

As regards the reply, "too short to observe by any means" is not quite the same as my proposal for the Earth as a point particle.
It is necessary so show that the process is too short to observe, just as we have to show (and do) that the actual size of the Earth makes an insignificant difference to our calculations.

Now entanglement is a process, which begins with two or more particles that are not entangled.
At this time they cannot act as though they were entangled.
At some time later they can definitely act as entangled particles.

You need to show that the time difference between these two situations, states whatever you care to call it, is insignificant to whatever calculations  you are making.

Then you can say the magic words

"May be regarded as Instantaneous. for my purposes."

Just as with the Earth, it does not mean that the Earth actually has zero size or that the time interval is actually instantaneous.

This definition is common in Engineering, for example with "Instantaneous water heaters".

 

Edited November 10, 2021 by studiot

[bangstrom]

13 hours ago, studiot said:

A pity you only bothered to comment on a small part of my last post so I don't know what you made of the rest of it.

You asked if there are any instantaneous natural processes and I mentioned entanglement.

As for your drawing with a stream, I didn’t see anything instantaneous. You can watch a leaf in a stream flow up and over a hydraulic jump and that’s not instant. There is also a static energy to pressure gradient but a gradient isn’t instant either.

What else is there to say?

13 hours ago, studiot said:

Now entanglement is a process, which begins with two or more particles that are not entangled.

At this time they cannot act as though they were entangled.
At some time later they can definitely act as entangled particles.

You need to show that the time difference between these two situations, states whatever you care to call it, is insignificant to whatever calculations  you are making.

I don't see how anyone could possibly observe the time it takes two particles to become entangled.

The "instant" I had in mind involves performing a measurement on one entangled particle and then timing how long it takes for the other paired particle to be influenced. The Chinese were perhaps the most recent to measure this with photons and they measured the time to be something like four orders faster than light. That could qualify as instant or too fast to measure.
 

 

 

 

[exchemist]

9 hours ago, bangstrom said:

You asked if there are any instantaneous natural processes and I mentioned entanglement.

As for your drawing with a stream, I didn’t see anything instantaneous. You can watch a leaf in a stream flow up and over a hydraulic jump and that’s not instant. There is also a static energy to pressure gradient but a gradient isn’t instant either.

What else is there to say?

I don't see how anyone could possibly observe the time it takes two particles to become entangled.

The "instant" I had in mind involves performing a measurement on one entangled particle and then timing how long it takes for the other paired particle to be influenced. The Chinese were perhaps the most recent to measure this with photons and they measured the time to be something like four orders faster than light. That could qualify as instant or too fast to measure.
 

 

 

 

Entanglement isn't a process, it's a state. 

[SergUpstart]

3 hours ago, exchemist said:

Entanglement isn't a process, it's a state. 

And the collapse of the wave function is just a process. And instantaneous.

[swansont]

5 hours ago, exchemist said:

Entanglement isn't a process, it's a state. 

It’s both. A floor wax and a dessert topping.

You have a process of entangling particles or creating particles that are entangled, and you have the state of entanglement 

15 hours ago, bangstrom said:

I don't see how anyone could possibly observe the time it takes two particles to become entangled.

Regardless of whether this can be demonstrated, “I don’t see” is not an argument that carries much weight. It’s argument from personal incredulity