Quantum Jumps: Do they really exist?

[Demystifier]

Processes in QFT are described perfectly locally.

That's true only if you do NOT include quantum jumps (somehow related to measurements). But when you introduce a jump into QFT, then it is no longer a local process.

 

[fzero]

The equations are correct, but what do you mean by "mostly"?

"Mostly" refers to the interactions that we are leaving out, i.e. anything that is not obtained at first order in the specific interaction term. Sorry for the confusing wording.

This claim is a total mystery. What does it mean that decay (jump) happens in mathematical terms? I guess it means that some quantity has a discontinuous dependence on time, but WHAT quantity? Is it c_1(t) and c_2(t)? Or something else?

The only discontinuity involved is the one where we actually make the measurement and find the state 2 instead of state 1. This is not a mathematical discontinuity, as the amplitudes are perfectly fine as described.

Interaction of WHAT with WHAT? If you say of "photon" with "electron", then what are "photon" and "electron" in mathematical terms? Is electron the state c_1(t)|1>+ c_2(t)|2>? Or something else?

I was clear that the interaction is between the photon and the electron, as can be seen from the operator I wrote down. In order to account for the fact that we could be dealing with atoms, I don't specify what else is contained in the states |1,2\rangle, since it doesn't change the mechanics at this order.

If you say that the electron is the state c_1(t)|1>+ c_2(t)|2>, then your correct expression above for c_1(t) and c_2(t) is obtained by assuming that interaction occurs for ALL times between t_1 and t_2, so it cannot be compatible with your claim that "interaction occurs instantaneously at the fixed time t_\gamma".

Again, when we measure the state 2 at some time we can only conclude that the decay occurred some time in the past. From the mechanics of QFT this occurs from a local operator, at a specific time (the interaction only occurs once in first order perturbation theory.). Since we don't actually measure the specific time that it occurred, we must compute the probability to find the system in the state 2 by summing over all possible times that the decay could have occurred.

There is no basis to conclude that the interaction is occurring at ALL times. Each possible event is a contribution to the sum, the event is not occurring continuously.

 

[Jano L.]

Sorry guys if it is inappropriate, but I can't help myself but to show my emotions about this here.

What bothers me with this jumping view is that I have no clue how to apply it to rest of physics.

Understanding of dispersion, absorption, nuclear resonance, thermal radiation, interaction of one piece of matter with another piece of matter, ... many pieces of beautiful physics, not only macroscopic but also in molecular physics, is based on picture of continuous phenomena described by differential equations.

I suppose in particle physics, one relies heavily on shooting detectors and does not need to accept existence of continuous phenomena, if he adheres to strict description of measurement and calculating probabilities of the outcomes. In his view, in calculations he uses continuous concepts, but the actual phenomena aer random and discontinuous.

But if it is possible that droplets of rain drumming on the roof are in fact falling down continuously, isn't it also possible that the discontinuous clicks of detectors are just an artifact of their inability to resolve these fast phenomena in time?

If it is possible that change of conformation of some photosensitive molecule is 0.1 ps (really fast!), isn't it possible that change of state of hydrogen atom takes some non-zero time too? Even more, when it radiates harmonic waves with fs periods?

Isn't it possible that seemingly discontinuous change of the appropriate wave function is just a simple enlightenment of our knowledge when we look at the real state of things?

The basic equations are continuous and there are no jumps in them, whether it is CM, CED, GR, QM or QFT. Only statistics has benefited from partial use of discontinuous variables. But statistics is not dynamics; it is determined by dynamics, as Einstein pointed out.

Damn, why should we erect some superficial assumptions about jumps on these beautiful equations? Should'nt we look upon the apparent discontinuous phenomena as if they were only some particular solutions of these equations with short characteristic time scale?

As if they were only temporal, imperfect simplification of a natural continuous phenomenon?

 

[Demystifier]

But if it is possible that droplets of rain drumming on the roof are in fact falling down continuously, isn't it also possible that the discontinuous clicks of detectors are just an artifact of their inability to resolve these fast phenomena in time?

If it is possible that change of conformation of some photosensitive molecule is 0.1 ps (really fast!), isn't it possible that change of state of hydrogen atom takes some non-zero time too? Even more, when it radiates harmonic waves with fs periods?

Isn't it possible that seemingly discontinuous change of the appropriate wave function is just a simple enlightenment of our knowledge when we look at the real state of things?

It's not only possible, decoherence is a strong evidence that this actually IS so.
Therefore, since you obviously like to think in continuous terms, you should definitely learn more about decoherence which will further reinforce your continuous view of nature.

 

[Demystifier]

I was clear that the interaction is between the photon and the electron, as can be seen from the operator I wrote down.

You mean
[e \bar{\psi} \gamma^\mu A_\mu \psi](x,t) ?
Fine, but then:

1. In the interaction picture, the only thing this interaction influences is the evolution of the state in the Hilbert space. But you said previously that you DON'T talk about states in the Hilbert space.

2. In practical applications of QFT this interaction is used to calculate the S-matrix, but NOT to describe the process of measurement.

Again, when we measure the state 2 at some time we can only conclude that the decay occurred some time in the past.

Such a conclusion is based on classical view of nature, but is not the only logically possible conclusion. Another logical possibility is that the superposition c_1(t)|1> + c_2(t)|2> collapsed into |1> or |2> not in the past, but in the very moment of measurement. Actually, this latter possibility is the standard view of quantum theory.

From the mechanics of QFT this occurs from a local operator, at a specific time (the interaction only occurs once in first order perturbation theory.)

You again fail to distinguish interaction used to calculate the S-matrix (which you really use in your calculations) from the interaction involved in the measurement process (which particle physicists usually don't take into account, but can be described by the fast-but-continuous process of decoherence, as I repeat over and over again).

There is no basis to conclude that the interaction is occurring at ALL times. Each possible event is a contribution to the sum, the event is not occurring continuously.

Again, one should specify which of the two interactions one is talking about.

The bottom line is:
Contrary to your (and not only your) classical intuition, there is no sharp decay before the system interacts with environment which may serve as a detector of decay. In a universe with one unstable particle in the vacuum and no detector, the sharp decay would never happen, except at t-> infinity due to the e^{-Gamma t} term in the slow continuous evolution of the state.

 

[Jano L.]

Demystifier, thanks for support and suggestions, I'll look into it.

Still, it is interesting that so many old famous calculations were partially successful with jumps without any comment on how they happen.

For example, take Einstein's quantum theory of radiation. He used jumps of atoms to derive the form of Planck's formula. Dirac published paper where he says he can even calculate probabilities of these jumps from Schroedinger's equation.

But in thermal radiation, nobody is measuring anything on the atoms, and the spectrum of radiation does not even have line character, so there is no question of the act of observer on the wave function.

Is there any reason known in decoherence theory, why the environment should force the atoms into certain preferred discrete states, like those assumed by Einstein? It seems to me that superpositions are equally good states when everything is chaotic.

 

[kith]

It's not only possible, decoherence is a strong evidence that this actually IS so.
Therefore, since you obviously like to think in continuous terms, you should definitely learn more about decoherence which will further reinforce your continuous view of nature.

But still you have the instantaneous transition from a mixed state to a pure one. In Bohmian mechanics, this is of course not a problem. But how would you resolve this in the Copenhagen interpretation?

 

[Demystifier]

But still you have the instantaneous transition from a mixed state to a pure one. In Bohmian mechanics, this is of course not a problem. But how would you resolve this in the Copenhagen interpretation?

Yes, that's a good point. One who still insists on Copenhagen interpretation may say that collapse happens at the level of quantum state of the brain, or something like that. I'm certainly not one of those who find such a hypothesis appealing, but frankly it is difficult to refute such a hypothesis experimentally.

 

[Demystifier]

Still, it is interesting that so many old famous calculations were partially successful with jumps without any comment on how they happen.

Decoherence explains that too, because it calculates the decoherence time explicitly, which turns out to be a very very short time (e.g. 10^(-22) seconds or so, depending on details of the case considered). Clearly, such a short decoherence time can be approximated by an instantaneous "jump".

Is there any reason known in decoherence theory, why the environment should force the atoms into certain preferred discrete states, like those assumed by Einstein?

Yes, that's precisely what decoherence explains. More precisely, decoherence predicts that quantum system will end up in an eigenstate of the total Hamiltonian of measured system coupled to its environment.

 

[granpa]

http://www.nbi.ku.dk/english/news/news11/new_record_for_measurement_of_atomic_lifetime_

Researchers at the Niels Bohr Institute have measured the lifetime of an extremely stable energy level of magnesium atoms with great precision. Magnesium atoms are used in research with ultra-precise atomic clocks. The new measurements show a lifetime of 2050 seconds, which corresponds to approximately ½ hour.

 

[Jano L.]

Granpa,
in fact, what was measured in that work was exponential decrease of fluorescence after irradiation. Characteristic time of decay does not falsify that atoms radiate continuously, it just requires that the coherence of the oscillations of the source (atom) decays in this time to cca 1/e of the initial value.

Jumps are not implied at all by such measurements.

Demystifier,
I think in spectroscopy the decoherence will have to work a bit slower. Decay rate of 10^{-22} s for an atom would imply linewidth 10^22 Hz, which is absurdly large.

For the hydrogen line 1s-2p, characteristic time of decay of radiative oscillations is 10^-9 s, which implies the atom has to be described by superposed wave function at least for that long.

 

[granpa]

it is clearly a transition from one electron energy level to another.

it would hardly be any use to atomic clock makers if it werent.

it is clearly a quantum jump yet it occurs gradually over a finite time
just like I said before in post #4
https://www.physicsforums.com/showthread.php?p=3824452#post3824452

the atoms jumps from one quantum state to another but it does so gradually.
there is a finite time during which it is in a superposition of both states.

 

[Jano L.]

Granpa, I agree that gradual jumps are much more compatible with the phenomena of wave optics and now these seem to me to be the most compatible with what I know of wave optics.

If the lifetime is 2050 s, what time does it take to make the corresponding jump?

In your opinion, what part of the experiment you refer to is the most clear evidence for these jumps? What makes you believe in them ?

I would be more cautious before saying " clearly jumps ". Many explanations are always possible and we cannot prove that one of them is right, but only disprove (falsify) some of them.

For example, Slater in 20s was developing theory with jumps, where atoms radiate not during the jumps, but when they are in stationary states, and the jumps are just instants when the radiation changes its character. This theory too explained well emission/absorption line spectra and scattering of light:

J. C. Slater, A Quantum Theory of Optical Phenomena, Phys. Rev. 25,4 (1925)

Nowadays this theory is totally neglected in courses. Maybe it was just abandoned with the onset of wave mechanics. Perhaps it was even falsified, but I do not know of any such paper.

 

[euquila]

But statistics is not dynamics; it is determined by dynamics, as Einstein pointed out.

I agree with you. Like in the Ensemble interpretation, the wave function is an abstract idea rather than having any physical meaning besides telling you what an ensemble of particles (governed by this wave f-n) will do.

I think we need to move beyond the Copenhagen interpretation!

One example that I like to think about (and I believe it can relate to the "jumps" that you are talking about) is the photon being emitted by an atom.

Between the time the photon is emitted and detected, QM says that it must be smeared out on a 2D spherical front whose radius grows at the speed of light.

When the photon is detected, the photon (which happens to be smeared out all over this 2D sphere) undergoes some kind of dynamic that removes its link to spacetime at all other points on the 2D surface. That seems pretty non-local to me -- or at least our notion of spacetime is lacking in framework.

Am I making sense? I'm in my head a lot and do not know if my thoughts are relevant.

 

[Demystifier]

Demystifier,
I think in spectroscopy the decoherence will have to work a bit slower. Decay rate of 10^{-22} s for an atom would imply linewidth 10^22 Hz, which is absurdly large.

For the hydrogen line 1s-2p, characteristic time of decay of radiative oscillations is 10^-9 s, which implies the atom has to be described by superposed wave function at least for that long.

You are mixing up two different things.

A typical life-time of some radioactive nucleus can be very large. (For example, it is 4.5 billion years for the alpha decay of U-238.) Yet, to measure whether a given nucleus at a certain time has decayed or not takes a fraction of a second. The decoherence time refers to the latter, not the former.

Even without decoherence, the standard "Copenhagen" interpretation of QM contains the rules such as:
1. When decay happens, the wave function collapses from a superposition c_1(t)|1> + c_2(t)|2> into the state |2>.
2. The collapse of wave function happens when the MEASUREMENT is performed.

Decoherence only provides a better (though still not complete) physical explanation of these rules.

So what will happen with U-238 mentioned above? If it is alone in vacuum not interacting with anything else, it will be in the superposition for a very very long time, even more than 4.5 billion years. But if you at any given time t (say t=2 years, or t=2 billion years, or t=20 billion years after the creation of the nucleus) decide to measure whether it has decayed or not, then you will produce interaction of the nucleus with the measuring apparatus, and then, during a very short decoherence time, the state will collapse into the either decayed or undecayed state. For larger t larger are chances that this state will be the decayed one.

 

[Jano L.]

I thought you are suggesting that decoherence theory could address " process of continuous transition from superposition to eigenfunction " in natural phenomena. But if it only addresses what happens when we force the system into eigenfunction by perturbing measurement (like with projections of magnetic moments of silver atoms), then it cannot predict that atoms change their behaviour in 10^-9 s naturally. Gas just radiates its lines, no matter what observer of apparatus does. There is no perturbing measurement of energy involved.

 

[Demystifier]

Gas just radiates its lines, no matter what observer of apparatus does.

Even if it does, it is impossible to confirm it experimentally. So what evidence can you present to support that claim?

 

[Jano L.]

Even if it does, it is impossible to confirm it experimentally.

Theories cannot be " confirmed experimentally ". They can be only falsified.

The assumption that nature works by itself with no need to be observed/measured by humans, is an original scientific strategy, working well since 16th century. I do not know of any evidence falsifying it.

Do you think that atoms and light exist, or that only wave function exists?

 

[Demystifier]

Do you think that atoms and light exist, or that only wave function exists?

Well, different interpretations of QM (none of which is falsified) suggest different answers.
My preferred interpretation is the Bohmian one, which to a large extent depends on decoherence. So in this interpretation, the picture is this:

Particles (atoms, photons, ...) exist, and their wave function exists as well as a separate entity. Both evolve continuously, without any jumps. However, interaction with the environment containing many degrees of freedom (e.g., a macroscopic measuring apparatus, or simply the gas of surrounding molecules) causes decoherence of the wave function, which, in turn, causes a very fast irreversible change that for practical purposes can very well be described as a "jump" or "collapse" of the wave function.

In other words, without environment there are atoms and photons but not their jumps.

 

[Jano L.]

Demystifier, you are right, we all are really mixing up two things mutually confusing each other here.

There are two _entirely_ different kinds of processes interfering in our discussion:

1) The first process is the natural change of state of the atoms, which I denote \tau.

a) In case of radiating hydrogen atoms, there is the process of coherent vibration of the atom. It is around \tau = 1 nanosecond. This should be partially accounted by the radiative damping of the oscillations (spontaneous emission), and also by the perturbing effect of the _environment_ (thermal radiation, collisions of atoms...).

b) In case of the radioactive atom, the mean time of substantial change of the atom U-238 is much longer - \tau = billions of years. There is strong evidence that this process is not due to perturbation by the environment (it seems it is quite independent of temperature and chemical state of the atoms). Also, there is no reason to think that it is influenced by the presence of the detector. Individual atoms of U-238 should always decay with the same mean rate, whether (passively) measured/observed or not.


2) The second process is the change of our knowledge on the state of _one_ particular radioactive atom (decayed or not decayed) when trapped inside of a detector.

This second process also takes some time t', mainly due to the time our brain takes to process the readout from the apparatus, say, 1 millisecond or so.

But the length of this second process (of measuring and "realizing" whether the atom has decayed or survived in its initial state), seems irrelevant for the actual physical process going on with the atom.

It is not very important to explain or calculate this time (1ms) from the theory, because it is purely due to properties of the observer (finite response of detector, and of our brain).



It may seem that 2) is instantaneous, especially when one uses the Copenhagen approach based on the instantaneous collapse of the wave function when the measurement is done. But from the above it is clear that even this process of knowledge change takes some time t' and is not about what the system naturally does, but about what the apparatus and the brain of the observer does.



I hope it is clear now that these are two different processes. I think that we should really concentrate the discussion on the process 1). So, my initial question (finally:-) is: are there any jumps in processes of the type 1) ? What are experimental results suggesting them ?


Fzero, Bill, I believe in some of your comments you in fact referred to the process 2) and the Copenhagen collapse of the wave function. Do you agree? What would you say about the process 1) ?

Demystifier, do you agree on the interpretation of the role of environment in 1)?

 

[fzero]

There is no reason to distinguish between cases 1 and 2, since the fundamental physics is the same. I already explained that the description of a first-order process, like spontaneous emission from a single atom, via QED leads to the conclusion that the process occurs instantaneously.

Whatever QM interpretation that one wants to apply to the actual measurement problem is not really something that I'm interested in. The way that I would think of the process is as before. If at time t_1 we measure an H-atom in the state 2p and at time t_2 we find it in the 1s state, we know that the decay happened at some time in between and it was instantaneous. The theory does not allow for any other description of the first-order process.

Now if you want to take into account higher-order processes, which would also include the microscopic description of the effects of the environment, things get a little bit more complicated, both technically and otherwise. For example, there will be processes where the 2p state absorbs a photon from the environment to move to an even higher excited state, say 3s. This is another process that occurs instantaneously, but the 3s state might exist for a finite amount of time before it emits another photon.

So higher-order processes can include new states that live for an indeterminate amount of time, but since there are no intermediate states between 2p and 1s, the first-order process must be a jump.

Now, the comments you make about the interpretation of half-life seem confusing. For example, "Individual atoms of U-238 should always decay with the same mean rate, whether (passively) measured/observed or not." Individual atoms or nuclei do not "decay with the mean rate," rather, the mean rate is directly related to the probability to measure that the state has decayed, as I used in https://www.physicsforums.com/showpost.php?p=3828463&postcount=27. Perhaps the linear combination of states is what you were referring to? That linear combination is what we choose to explain our ignorance of the actual state of the system between measurements. Experimentally, the mean rate is not obvious from a single measurement, but must be determined from studying a large sample. Theoretically, we can compute the mean rate by computing quantum amplitudes.

 

[Jano L.]

There is no reason to distinguish between cases 1 and 2, since the fundamental physics is the same.

The times of both processes are very different.

The first process: the atom is slowly decaying, it can take billions of years, but will decay eventually. Individual atoms have different times of decay and we cannot predict it now.

The second process begins when the atom has decayed into some other particles and these enter the detector and trigger the detection process in it. This is very fast, <milliseconds or so.

It is most natural to think that these are two different processes. If the Copenhagen explanation of the formalism does not distinguish them, I think so much worse for the tenability of that explanation.

The way that I would think of the process is as before. If at time t1 we measure an H-atom in the state 2p and at time t2 we find it in the 1s state, we know that the decay happened at some time in between and it was instantaneous.

I do not think one can measure which electronic state the atom is in. The 1s, 2p symbols only refer to terms of optical spectra, or eigenfunctions of Schroedinger's equation, but not to results of measurement of the state. Such measurement could be done by measuring X-rays scattered by the electron in the atom, but this would necessarily perturb the atom so much that its state would be far away from what it is in natural conditions (it would ionize).

I may be mistaken; do you have some reference to a paper which deals with direct measurement of electronic states?

What we can do is to resolve light radiated/scattered by the atoms. If one measure this, many features of the spectra (splitting in el./mag. field, sharpness of lines) is well explained by Schroedinger's wave mechanics, with no need to introduce instantaneous Copenhagen jumps.
There are transitions, but there is solid evidence that they are gradual - coherence time of 1s-2p line is 1 ns, interference and dispersion phenomena, ...

But let us suppose the electron really have jumped instantaneously from 2p to 1s state and radiated photon of frequency f = \frac{E_{2p} - E_{1s}}{h}.

Now what the frequency of the photon means if the process was instantaneous ?!

The frequency of radiation can only be defined within 1 ns coherence time if the wave has at least this extent. So the radiation has to be produced at least for 1 ns.

How can you explain the coherence of the radiated wave and preserve instantaneity of the transition? This was and is a serious problem for theory with instantaneous jumps.

 

[Demystifier]

But the length of this second process (of measuring and "realizing" whether the atom has decayed or survived in its initial state), seems irrelevant for the actual physical process going on with the atom.

This is very very deeply wrong. The best counterexample is the quantum Zeno effect, due to which a frequent observation of decay may significantly slow down the decay process, or even completely stop. I think THIS is the crucial thing to concentrate on. See e.g. the literature on decoherence I have already mentioned in one of the previous posts.

The measurement deeply influences quantum processes and properties, which is the fact known also as quantum contextuality, with dramatic consequences e.g. in spin measurements and Bell-inequality violations. E.g., measurement of spin in x-direction drastically influences spin in z-direction.

Even if you never heard about things such as quantum Zeno, contextuality, spin measurements in different directions and Bell-inequality violations (which you should inform yourself about if you didn't already), you must have heard about wave-particle duality. The quantum system behaves very differently when you measure its wave properties from the behavior when you measure its particle properties. For example, if you measure the particle position there is no interference, and vice versa.

In short, the behavior of quantum systems depends very much on the measurement you perform, which is probably the main conceptual difference between quantum and classical mechanics and the source of most (if not all) quantum weirdness.

 

[Demystifier]

Also, there is no reason to think that it is influenced by the presence of the detector. Individual atoms of U-238 should always decay with the same mean rate, whether (passively) measured/observed or not.

Quantum Zeno effect is not only a reason, but a proof that detector may influence decay a lot.

2) The second process is the change of our knowledge on the state of _one_ particular radioactive atom (decayed or not decayed) when trapped inside of a detector.

This second process also takes some time t', mainly due to the time our brain takes to process the readout from the apparatus, say, 1 millisecond or so.

Before this brain-process there is a much more important process caused by the measuring apparatus (or more precisely, the first thing that interacts strongly with the observed object) that determines how the observed object will behave.

 

[Jano L.]

This is very very deeply wrong. The best counterexample is the quantum Zeno effect, due to which a frequent observation of decay may significantly slow down the decay process, or even completely stop. I think THIS is the crucial thing to concentrate on. See e.g. the literature on decoherence I have already mentioned in one of the previous posts.

Letting atoms traverse a strong inhomogeneous magentic field surely changes their magnetic moments. It is natural that the magnet influences spins significantly.

In experimental examples of "quantum Zeno effect" Wikipedia mentions, strong perturbation of atoms by external radiation was used. No surprise the atoms changed their natural behaviour.

In case the measurement perturbs atoms significantly, I agree that the process of measurement has strong influence on the behaviour of atoms.

However, the situation with radioactive atom I was thinking about is very different. The atom sits inside the cavity, whose walls are able to detect fission products. The detector clicks when the products arrive at the wall.

There is no reason to believe that passive wall has any influence on the atom whatsoever. As far as I know, no passive observation/measurement has been reported in which the decay rate was altered. Temperature, chemical status of the atoms does not matter, the decay rate is always the same. Why should the detector, which is far away, make any difference? There is no evidence for any such effect.

Of course, if we irradiate the atom with gamma radiation, this can perturb the nucleus significantly. But this is not necessary. The detector can just wait for products to arrive.

In short, the behavior of quantum systems depends very much on the measurement you perform, which is probably the main conceptual difference between quantum and classical mechanics and the source of most (if not all) quantum weirdness.

I would say the behaviour of atoms depends on the way the measurement disturbs them. This is conceptually no different from classical mechanics.

But we can choose to not disturb the atom at all and just look how the natural process works.

There is no need to repeat the projection postulate of quantum theory whenever something is observed. Nature is far more rich than that, and physics can be too, we just have to think out of the box.

 

[lugita15]

In short, the behavior of quantum systems depends very much on the measurement you perform, which is probably the main conceptual difference between quantum and classical mechanics and the source of most (if not all) quantum weirdness.

But as a Bohmian, don't you view the contextuality of QM as nothing special or weird, just a consequence of the fact that measurement, like any other interaction, can have an effect on a system? Isn't that equally true of classical mechanics?

 

[Demystifier]

But as a Bohmian, don't you view the contextuality of QM as nothing special or weird, just a consequence of the fact that measurement, like any other interaction, can have an effect on a system? Isn't that equally true of classical mechanics?

Of course, it is natural to adopt that interpretation in which weird things do not longer look weird. But I wanted to present the known facts about QM which do not depend on interpretation. Part of the reason why people are not interested in foundations and interpretations of QM is because they are not aware how QM looks weird without better understanding of foundations and interpretations. That's why I want to increase the awareness of that weirdness.

 

[Demystifier]

In case the measurement perturbs atoms significantly, I agree that the process of measurement has strong influence on the behaviour of atoms.

That is true. But the right question is: Can we perform a measurement of atom WITHOUT strongly influencing it? The answer is that we cannot, except in a special case when the system is already in an eigenstate of the observable we want to measure.

As far as I know, no passive observation/measurement has been reported in which the decay rate was altered.

Of course it hasn't, but that is because passive measurements of microscopic isolated systems DO NOT EXIST (except in the the special case I mentioned in the sentence above).

Temperature, chemical status of the atoms does not matter, the decay rate is always the same.

It is APPROXIMATELY the same, and there is a good reason why is that so. This is because the probability of decay as a function of time is well approximated by the EXPONENTIAL law
p(t)=exp(- gamma t)
Namely, the exponential function has a special property
p(t/N)^N = p(t)
not shared by any other function. Let me explain what that means physically. If without measurement the probability of survival is given by some free-evolution function p(t), then one is interested to calculate what is the survival probability when the free evolution is disturbed N times at equal time intervals during the time t. Whenever you do the measurement to see whether the atom has decayed or not, the quantum state collapses into the either initial state or fully decayed state. Therefore, the probability of survival after N measurements during time t is p(t/N)^N. In general this is not p(t), except for the exponential law. For times much smaller than 1/gamma the exponential law is actually not a good approximation for free evolution, which is why quantum Zeno effect is effective only for such early times of decay.