time-energy uncertainty

I was doing some reading on the time-energy uncertainty principle, which seems more obscure than posiition-momentum. The books refer almost entirely to the electron orbital energy levels in the atom. That is, the emitted wavelength dispersion, as the electron drops to a lower energy, is inversely related to the time emitted, in a probabilistic manner; the narrower the spectrum, the wider (more unpredictable) the time dispersion

But does the formula hold for every energy measurement? For example, circuit voltage - as on a capacitor - is a measure of energy. Does this uncertainty principle apply there? Does it place a limit on our time (frequency) resolution in every circumstance?

It's not clear to me what it means, in these classical situations.

-- Rich

Reply to
RichD
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If there is a particle accelerator out in your gaarden shed you probably won't enjoy the machine to the fullest unless you learn when and how to apply the principle.

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principle

It might be a good specification to ask about if your jeweller wants to sell you a quantum clock.

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Sue...

Reply to
Sue...

If you measure the voltage across the capacitor your voltmeter will draw a small current and change the voltage. This change will depend on the time you maintain the voltmeter connection and the capacity of the capacitor.

Yes. Suppose the voltmeter has a range switch and draws between 0.1 microamps to 1 microamp for a reading of 0-1 microvolts (0.000001V) or

0-100 kV (100,000 V). The resistor used is switched from zero to 1000 gigaohm, changing the resolution.

For any measurement made the act of measuring affects the outcome. The resolution isn't crucial for macroscopic measurements, but becomes increasingly important the smaller the measurement. If you use an electron microscope on something as large as a biological cell then you have sufficient resolution to make biological observations and reach biological conclusions, but the same electron microscope cannot be used to look at a molecule without bombarding the molecule with electrons and changing what you wanted to see. Heisenberg quantified that.

Reply to
Androcles

Time is t. Energy is h(nu). Frequency, nu, is 1/t.

/_\T/_\f = 1

Is that so difficult?

Look up the accuracy of the 21 cm hyperfine hydrogen transition line and its half-life, triplet to singlet hydrogen atom.

Given classical vacuum, you would know its energy content exactly - zero. Heisenberg uncertainty populates every allowed elecetromagnetic mode with a half-photon of uncertainty. This is directly measurable as the Casimir effect in an etalon excluding wavelength windows. It also fuels the Lamb shift, the electron anomalous g-factor, Rabi vacuum oscillation, etc.

Corresponence Principle for classical situations.

--
Uncle Al 
http://www.mazepath.com/uncleal/ 
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Reply to
Uncle Al

You can do the same with position and momentum, if you do the measurements out of context. I think that's what he was referring to. So the joke is on you.

Reply to
Igor

Hi Rich, I find the energy - time uncertainty relation perhaps easier. After all energy is proportional to the frequency. And if I have a longer time to count the frequency of something I can 'know' it with a smaller uncertainty.

My favorite energy uncertainy in electronics example is the quantum contact. Imagine a contact between to metals where the volume of the contact is so small that only one elctron can fit in it at a time. (I'm ignoring the electron spin). Now if I apply a voltage (V) across the contact I can get electrons to move from one side to the other with a current (I). What is the resistance? (V/I) Well the enegy uncertainty is eV, and the time uncertainty is e/I (I =3D charge/time)

Putting this together with the Heisenbreg relation gives. eV*e/I =3D h or with R=3DV/I=3D h/e^2 which is the quantum unit of resistance. Pretty cool if you ask me!

George H.

Reply to
George Herold

Of course it holds in classical cases. That is because the "uncertainty principle" arises out the nature of mathematics. The fact that these mathematical laws ALSO seem to apply to reality in certain cases is the interesting thing.

In classical cases one can see the "uncertainty principle" come right of various transforms; the Fourier transform in particular. Take a pulse of some type. Then calculate the frequency spectrum of that pulse. And lo as the pulse is made narrower the frequency spectrum becomes wider and vice versa! Hence there is an "uncertainty principle" between "time" the pulse width and "energy" the spectrum of frequencies due to that pulse. And moreover the same ideas apply where ever the mathematics is found. For example one can also find an "uncertainty principle" between the width of an aperture antenna and the angular distribution of energy. The interesting thing about Quantum uncertainty is that when one reduces the scale of dimensions to a certain size, the mathematics starts to crop up everywhere limiting the values that can be assumed by various parameters. At larger scales the principle is there but values are not limited. Quantizing values (like say the voltages allowed on a capacitor) is not quite the same thing as the uncertainty principle which in that case would have to do with how LONG a time one would have to measure the voltage to be assured of a certain accuracy.

Reply to
Benj

Mass is an infinitely dense C squared point of energy.

Mitch Raemsch

Reply to
BURT

blah blah You're rambling, old man.

Vacuum fluctuations etc. are not questioned, those are the textbook 'quantum' phenomena.

I'm interested in observing the voltage across a cap. How does time-energy uncertainty apply there? Let's say we digitize it - is there then some 'resolution vs. sample rate' uncertainty formula, which follows from the former?

fuzzy answer =3D no information

-- Rich

Reply to
RichD

Ordinarily, the noise on a capacitor will be thermal noise. That is easily calculated.

if you are at absolute zero, then their quantum nature takes over. Connect an inductor across the capacitor. You now have a quantum oscillator. Compared to typical quantum oscillators, such as atoms or molecules, the energy hf is going to be very low and require extremely low temperatures in order not to get thermally excited.

If you manage to achieve all these conditions, you can then be in a position to measure the energy of the oscillator by measuring its frequency. This assumes you have a clue as to which excited state the oscillator is. The frequency spread of such a measurement is limited by how long you observe. Turning on your measuring equipment introduces sidebands that increases frequency, and consequent energy error. This spread is inherent in the Fourier process in which you get an inverse relationship between the spread of a time signal and the frequency spread of the transformed signal.

Bill

--
An old man would be better off never having been born.
Reply to
Salmon Egg

It applies everywhere. An interesting application is this:

You can reconstruct a decaying particle's (such as a W boson or a neutron) rest mass by measuring the momenta and identification of all the daughter particles, and then combining them in the usual fashion: m^2 =3D (sum:E)^2 - (sum:p)^2. What you will find, even in a detector with exquisite momentum resolution, that the reconstructed mass distribution has a natural width. That natural width turns out to be related to the half-life of the decaying particle, in exactly the way you'd expect from the uncertainty principle.

For more plebian examples, a transmission signal chopped to a finite length sample will have a frequency (e.g. energy) spectrum whose minimum width is determined by the uncertainty principle.

PD

Reply to
PD

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common PD with your plebaian pompous patronizing talking you are not more than the [plebeian )!!

because Rich was right with his remark: quote :

Does it place a limit on our time (frequency)

end of quote

of course it is places an LIMIT A --- BOTTOM LIMIT!! to the energy amount thAt we can detect or measure RELIABLY !!!! THAT IS EXACTLY THE ESSENCE OF dt dE ~h !!! if dt becomes close to zero THE UNCERTAINTY OF E BECOMES INFINIT !!!

IOW THERE IS A BOTTOM LIMIT OF THE ENERGY AMOUNT THAT WE CAN AT ALL HANDLE !!

and that is an old mistake of PD (is spite of his lofty talking about deep understanding pose of the H U P against the 'Plebeian' understandings to claim that

'there is no smallest photon energy !!!

2 his mistake not to recognize that energy emission is TIME DEPENDENT !!!

ATB Y.Porat

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a transmission signal chopped to a finite

Reply to
Y.Porat

Only for a photon.

I don't follow this, can you elaborate?

According to QM, energy is an operator, which generates a random variable. Its standard deviation is the uncertainty. I don't see how you get eV.

Time is not an operator, 'time uncertainty' is not defined as a standard deviation. It derives from an esoteric formula, which I will not reproduce. Please define your notion of this quantity.

That is pretty cool, if true. I didn't know there's such a thing as ' quantum unit of resistance'.

-- Rich

Reply to
RichD

I'm assuming all the voltage drop is across the very small contact, with no resistance in the metal that is next to the contact. Then the uncertainty in the energy of the electron as it crosses the contact is the voltage drop V time the charge e. Where V is the voltage drop acorss the contact. It's not too hard to see this 'in real life' by the way. Google quantum contacts and gold wire.

Well t is the time it takes to cross the contact. I'm assuming all the resistance is in the quantum contact.

Oh yeah and if you get some thin gold wire and battery, make yourself a voltage source and opamp current to voltage converter, and have a digital scope then you can see it for yourself.

George H.

Reply to
George Herold

What about time uncertainty? What about those random events happening in a window of time? How will we measure how long it took at the subatomic level?

Mitch Raemsch

Reply to
BURT

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