Physics Help Forum Heisenberg Uncertainty

 Quantum Physics Quantum Physics Help Forum

 Dec 4th 2016, 07:21 AM #1 Junior Member   Join Date: Apr 2016 Posts: 2 Heisenberg Uncertainty 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?
Dec 4th 2016, 09:01 AM   #2

Join Date: Apr 2008
Location: On the dance floor, baby!
Posts: 2,493
 Originally Posted by keanu 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
__________________
Do not meddle in the affairs of dragons for you are crunchy and taste good with ketchup.

See the forum rules here.

 Nov 29th 2017, 09:44 PM #3 Physics Team   Join Date: Apr 2009 Location: Boston's North Shore Posts: 1,573 Don't let the name fool you. It's not an actual Heisenberg uncertainty relation because dt is not an uncertainty in time. Dt therefore represents the amount of time it takes the expectation value of Q to change by one standard deviation. See: Time-Energy Uncertainty Relation
 Nov 30th 2017, 07:48 AM #4 Senior Member   Join Date: Apr 2015 Location: Somerset, England Posts: 995 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
 Nov 30th 2017, 09:00 AM #5 Physics Team   Join Date: Apr 2009 Location: Boston's North Shore Posts: 1,573 Knowing studiot as well as I do I'm certain that he's falsely claiming that the delta t is an "uncertainty in time" which is a meaningless concept in quantum mechanics. Take my word for it. Never accept what studiot says with anything but a grain of sand. I've already explained the meaning of delta t in that page I linked to. You can read the exact same thing in many good books on particle physics and quantum mechanics such as those by David Griffiths which is currently being used at MIT for their QM course. Unfortunately for this forum studiot doesn't know a great deal of physic and can never be taken at his word. Don't trust him. It's a matter of fact that he can never substantiate his claims but merely repeat them whereas I can both derive them and show the sources from multiple respected physics sources. Care to see a few on this subject keanu? If you go by what studiot claims you're in for some serous trouble in the future. studiot doesn't even understand what the term "uncertainty" means and as such why it cannot be applied to time. Aravanov and Bohm wrote extensively on ths subject and why studiot's view is totally wrong. Last edited by Pmb; Dec 16th 2017 at 07:00 PM.
Dec 1st 2017, 08:12 AM   #6
Senior Member

Join Date: Oct 2017
Location: Glasgow
Posts: 270
 Originally Posted by Pmb Knowing studiot as well as I don't I'm certain that he's falsely claiming that the delta t is an "uncertainty in time" which is a meaningless concept in quantum mechanics. Take my word for it. Never accept what studiot says with anything but a grain of sand. I've already explained the meaning of delta t in that page I linked to. You can read the exact same thing in many good books on particle physics and quantum mechanics such as those by David Griffiths which is currently being used at MIT for their QM course. Unfortunately for this forum studiot doesn't know a great deal of physic and can never be taken at his word. Don't trust him. It's a matter of fact that he can never substantiate his claims but merely repeat them whereas I can both derive them and show the sources from multiple respected physics sources. Care to see a few on this subject keanu? If you go by what studiot claims you're in for some serous trouble in the future. studiot doesn't even understand what the term "uncertainty" means and as such why it cannot be applied to time. Aravanov and Bohm wrote extensively on ths subject and why studiot's view is totally wrong.
C'mon. The theory you quoted on your web-page is correct, but it only applies to one possible derivation of the energy-time uncertainty relation based on a theory that treats time as a parameter. Other derivations consider time as an observable, measurable quantity and they can also derive an energy-time uncertainty relation where the Delta t term has a different meaning.

Consider, for example http://iopscience.iop.org/article/10...9/1/012002/pdf

Note that the paper states "... the ∆t is not the duration of the measurement but the accuracy of the time measurement."

The conclusion recommended by the authors in that paper is that whenever someone mentions the energy-time uncertainty relation, they carefully define their terms.

Dec 1st 2017, 12:10 PM   #7
Physics Team

Join Date: Apr 2009
Location: Boston's North Shore
Posts: 1,573
 Originally Posted by benit13 C'mon. The theory you quoted on your web-page is correct, but it only applies to one possible derivation of the energy-time uncertainty relation based on a theory that treats time as a parameter.
While I'm sure that there are different derivations of the time-energy uncertainty relation, the end results are all the same, i.e. they all are the same equation with the same meaning

studiot was speaking as if the phrase "uncertainty in time" actually has a real meaning in physics. It does not. Time is a parameter and as such not an observable in the quantum mechanical sense.

 Originally Posted by benit13 Other derivations consider time as an observable, ...
And they are all wrong.

 Originally Posted by benit13 Note that the paper states "... the ∆t is not the duration of the measurement but the accuracy of the time measurement."
That's wrong too. And I can provide a mountain of evidence to demonstrate/explain for those interested. There's no such thing as the accuracy of a time measurement in QM. In fact both the accuracy and precision of measurements plays almost no role in the uncertainty principle.

 Originally Posted by benit13 The conclusion recommended by the authors in that paper is that whenever someone mentions the energy-time uncertainty relation, they carefully define their terms.
As David Griffiths says in is particle physics text (Paraphrasing) talks about the time-energy uncertainty relation place your hand on your wallet"

It's not as I haven't studied this topic extensively in the last 25 years. I referred to the literature where its explained.

I can give exact references to the important papers and can make them available to anybody who wants to read them. There is no debate about this among the authorities in this area. Although many physicsts fail to understand it.

Dec 5th 2017, 04:12 AM   #8
Senior Member

Join Date: Oct 2017
Location: Glasgow
Posts: 270
 Originally Posted by Pmb And they are all wrong.
Well... okay. Do you plan to publish rebuttals to Briggs' papers? If not... perhaps you should!

Dec 7th 2017, 06:11 PM   #9
Physics Team

Join Date: Apr 2009
Location: Boston's North Shore
Posts: 1,573
 Originally Posted by benit13 Well... okay. Do you plan to publish rebuttals to Briggs' papers? If not... perhaps you should!
The main reason is that I'm disabled due to a chronic illness, namely chronic pain from degenerative disk disease which ruins my concentration. However there's a section under my physics website for misconceptions. Perhaps I'll add this to it someday. But lately I've had a terrible time concentrating due to the pain and writing an article requires good concentration. Even when I'm able to get some concentration back I have much more worthy goals to attend to.

Besides, what is there to gain from doing so? There have been many people who have published a ton of literature on this exact subject which is 100% consistent with what I said, what's observed in nature and how its currently described in the QM texts being used to teach QM at places like MIT. So why would I bother? You should realize that its not uncommon for articles to be published in journals which are quite incorrect. Its well explained in the physics literature why there is no such thing as a "time operator." The author simply doesn't know what he's talking a out. Shame on the peer reviewers for being so ignorant on the subject.

 There's an energy operator in quantum mechanics, usually called the Hamiltonian and written H. But the problem is, there's no "time operator" in quantum mechanics! This makes people argue a lot about the time-energy uncertainty relation - whether it exists, what it would mean if it did exist, and so on.
Here's a bit more on the subject: https://en.wikipedia.org/wiki/Uncertainty_principle

Scroll down to where it says In non-relativistic mechanics, time is privileged as an independent variable. Nevertheless, in 1945, L. I. Mandelshtam and I. E. Tamm derived a non-relativistic time–energy uncertainty relation, as follows
 For a quantum system in a non-stationary state ψ and an observable B represented by a self-adjoint operator B ^ {\displaystyle {\hat {B}}} {\hat {B}}, the following formula holds: σ E σ B | d ⟨ B ^ ⟩ d t | ≥ ℏ 2 . {\displaystyle \sigma _{E}~{\frac {\sigma _{B}}{\left|{\frac {\mathrm {d} \langle {\hat {B}}\rangle }{\mathrm {d} t}}\right|}}\geq {\frac {\hbar }{2}}.} {\displaystyle \sigma _{E}~{\frac {\sigma _{B}}{\left|{\frac {\mathrm {d} \langle {\hat {B}}\rangle }{\mathrm {d} t}}\right|}}\geq {\frac {\hbar }{2}}.}where σE is the standard deviation of the energy operator (Hamiltonian) in the state ψ, σB stands for the standard deviation of B. Although the second factor in the left-hand side has dimension of time, it is different from the time parameter that enters the Schrödinger equation. It is a lifetime of the state ψ with respect to the observable B: In other words, this is the time interval (Δt) after which the expectation value ⟨ B ^ ⟩ {\displaystyle \langle {\hat {B}}\rangle } \langle {\hat {B}}\rangle changes appreciably.
I assume that you didn't read the article I referenced at the bottom on my webpage on the subject. Perhaps you should. See [i]Time as an Observable[/], by William Unruh at http://arxiv.org/abs/quant-ph/9807058 The author is well known in physics. He's popular for the phenomena named after him, i.e. Unruh radiation.

The author, John Baez , is a well known authority in physics.
Instead of listening to me, why not simply read the literature itself and learn why I'm saying what I am? For example: go to https://arxiv.org and do a search on the subject. Read the portions of the books I described.

I should point out that, at least in classical mechanics, the numerical value of the Hamiltonian is not always equal to the energy.

Last edited by Pmb; Dec 7th 2017 at 10:35 PM.

Dec 8th 2017, 03:53 AM   #10
Senior Member

Join Date: Oct 2017
Location: Glasgow
Posts: 270
 Originally Posted by Pmb The main reason is that I'm disabled due to a chronic illness, namely chronic pain from degenerative disk disease which ruins my concentration.
I'm sorry to hear that.

 See also: uncertainty Here's a bit more on the subject: https://en.wikipedia.org/wiki/Uncertainty_principle Scroll down to where it says In non-relativistic mechanics, time is privileged as an independent variable. Nevertheless, in 1945, L. I. Mandelshtam and I. E. Tamm derived a non-relativistic time–energy uncertainty relation, as follows I assume that you didn't read the article I referenced at the bottom on my webpage on the subject. Perhaps you should. See [i]Time as an Observable[/], by William Unruh at http://arxiv.org/abs/quant-ph/9807058 The author is well known in physics. He's popular for the phenomena named after him, i.e. Unruh radiation.