What happens to a particle after it stops being observed?

[Endercreeper01]

If a particle is observed for a certain period of time, and then it stops being observed, will it go back to it's original wave-function?

Also, what happens when a particle is observed multiple times?

[Ankit Gupta]

I think we cannot say any thing about it ,it would be like Schrödinger's cat (if you about it) which say if we put a cat into a box and then close it then at any time we cannot tell whether it is dead or alive until we open the box and peep into it .

[Implicate Order]

It's probably best to view it this way.

 

The original particle is described quantum mechanically as a mathematical wavefunction. We do not know the properties of this wave until after measurement. The way for a classical observer to view this wavefunction is by how this wavefunction can be described in terms of a superposition of states (eigenstates). The eigenstates of the wavefunction represent the ways that that wavefunction can only be classically described once measurement occurs. The classical expressions of this superposition of states is defined in terms of probabilities. The schrodinger wave function fully describes the probabilities of where and when the properties of a classical particle will take shape under measurement.

 

The original wavefunction is interrogated by a measurement to determine how this superposition will classically collapse on classical interaction. What is happening here however is that in this interaction event we are superimposing a new wavefunction associated with the measuring device on top of the original wavefunction to create a new wavefunction that can then be described classically when referring to the orthogonal components of this new merged wavefunction. Now there are different interpretations on whether or not a collapse is real or whether it is just a way we classically view things. The bottom line is that a merged wavefunction (whether it collapses or not) fully describes the collapsed state (it's classical properties).

 

Understanding this allows you to perhaps realise that the measuring instrument is actually applying a wavefunction comprising defined classical eigenstates at the wavefunction under investigation. The classical measuring device is therefore looking for how this wavefunction is described classically (eg. where it is, what is its momentum and other classical complementary attributes). These properties are often conjugate pairs that can only be measured simultaneously for classical objects. In QM we know that we can only measure one or the other of a conjugate pair and not both at the same time (eg. position and momentum). An electron in this instance is a quantum object. For this entire description let's assume I want to find an electron's position on collapse. I could use the same interpretation used in this post to find an electron's momentum but remember that I cannot find both at the same time through a single measurement.

 

So the measuring device is throwing a wavefunction with defined classical eigenstates at the wavefunction under investigation so that the merged resolution will provide classical answers to the questions thrown at it. The interrogation looks at orthogonal relationships between the eigenstates of the measuring device and the wavefunction under investigation.

 

As soon as the measurement is over (the interaction event), the new wavefunction and its superposition of eigenstates (which describes the prior collapsed state) then exists and on any future measurement will then merge with another observers wavefunction and so on and so forth. This new wavefunction once again is fully described mathematically as a Schrodinger wavefunction.

 

With this knowledge in hand you can then recover prior uncollapsed state descriptions playing around with a knowledge of what eigenstates you need to apply in your measurement to recover a prior state description of a particle.

 

EDIT: Another way to think of it is as follows.

 

We have a measuring instrument which is trying to find out the properties of a 'classically described thing' at a particular spacetime position which is interrogating an unknown wavefunction prior to measurement. That mathematical wave might be anything but as I have being using a gun that on my understanding fires electrons into this experiment, then I am looking for electrons. The measuring instrument then says, ok I want to describe this thing in terms of a defined classical particle we know as an electron.

 

I am therefore going to interrogate that thing with a 'contrived' wave that interrogates that wavefunction with an orthogonal wave description of a classical electron to see if a classical electron description exists at this location in spacetime. I therefore use as my measuring device an 'electron' detector as I want to find electrons. By using a device that finds electrons we know that the interrogation wave will be designed to look for electrons. I also understand that in finding that classical description I am going to have to take into account the probability of finding that classical description at this point in spacetime. The more I undertake this exact experiment then I am reliably informed that probabilities will reflect when I conclude that an electron is found there.

 

What in effect you are doing is superimposing a classicaly contrived wavefunction at an unknown wavefunction to see how the combined effects collapse classically and then recording the result.

Edited February 13, 2014 by Implicate Order

[Bill Angel]

"Also, what happens when a particle is observed multiple times?"

Consider the Heisenberg Uncertainty Principle:

If multiple measurements of a particle's momentum could reduce the uncertainty in that quantity to a very small amount, then knowledge of that particle's position would become more uncertain.

[ACG52]

 

 

What happens to a particle after it stops being observed?

It steps out back and has a drink and lights up a smoke.

[PeterJ]

This is odd. I'm receiving notifications of new posts in this thread, but when I come here I can now only see the first four posts and nothing else. I used to see the whole thread. Maybe my browser is misbehaving.

.

[Strange]

This is odd. I'm receiving notifications of new posts in this thread, but when I come here I can now only see the first four posts and nothing else. I used to see the whole thread. Maybe my browser is misbehaving.

.

 

Your hijack about consciousness was moved to Trash.

[PeterJ]

My hijack? I never hijacked anything. It was other people who started banging on about consciousness. I just wanted to keep the discussion away from the realms of fantasy.

 

This forum is fascinating. It is the only place I've ever been where it is impossible to have a sensible conversation. One mention of a trigger-word and all hell breaks loose. It's like an evangelist rally.

 

Anyway, removing my comments seems to have had the effect of banning me from the discussion, since I can't see it anymore. I assume this is intentional. Sorry that I cannot take part to reply to the endless barrage of daft comments directed at the imaginary person that is being attacked here.

[swansont]

!

Moderator Note

It was not PeterJ's hijack (it was MirceaKitsune's), but the whole kit and kaboodle was OT and was moved.

 

http://www.scienceforums.net/topic/85174-hijack-from-what-happens-to-a-particle-after-it-stops-being-observed/

[PeterJ]

In that case pardon my paranoia. It was a good idea to cut it all out.

[jaydnul]

If multiple measurements of a particle's momentum could reduce the uncertainty in that quantity to a very small amount, then knowledge of that particle's position would become more uncertain.

This is not necessarily true. The particle's position and momentum could both be known to an arbitrary accuracy given the quality of the measuring apparatus. The HUP is about what can be predicted if the experiment was repeated, not about what can be measured.

[swansont]

This is not necessarily true. The particle's position and momentum could both be known to an arbitrary accuracy given the quality of the measuring apparatus. The HUP is about what can be predicted if the experiment was repeated, not about what can be measured.

 

No, the HUP is a fundamental limit of simultaneous measurement, assuming perfect apparatus.

[jaydnul]

A particles position and momentum can be known to exact precision. Sure, once you confine it to a small space, the momentum for future measurements will be uncertain in accordance with the HUP, but the values for instantaneous position and momentum can be known exactly.

Edited September 3, 2014 by jaydnul

[swansont]

A particles position and momentum can be known to exact precision. Sure, once you confine it to a small space, the momentum for future measurements will be uncertain in accordance with the HUP, but the values for instantaneous position and momentum can be known exactly.

 

No, not really. First of all, one must take care not to confuse the HUP with the observer effect; those are distinct. Conjugate variable such as momentum and position have an inherent uncertainty in them as their wave functions are Fourier transforms of each other.

 

If the argument is that one can get an arbitrarily precise value from the measurement and claim that the variable is known exactly, one needs to explain how one can determine the error with a single measurement. Multiple measurements won't yield the exact same answer, so which one is the right one?

[jaydnul]

If we setup a single slit experiment, the slit width would be our uncertainty in x. If the particle hits the detector we know it went through the slit. We can then calculate the momentum with the position on the detector and the time it took to get there. What I'm saying is that those two uncertainties have nothing to do with HUP. HUP is about what would happen if we repeated the experiment and tried to predict the two values beforehand.

[Strange]

First of all, one must take care not to confuse the HUP with the observer effect; those are distinct.

 

There was a recent experiment which used weak measurements to minimize the observer effect to almost zero. They showed that the measurements were still limited by uncertainty. (I will have a look, but I doubt I can find it again...)

 

Edit: this might have been it: http://spectrum.ieee.org/tech-talk/at-work/test-and-measurement/uncertainty-over-the-uncertainty-principle (the conclusions are somewhat subtler than I remembered).

Edited September 3, 2014 by Strange

[imatfaal]

 

There was a recent experiment which used weak measurements to minimize the observer effect to almost zero. They showed that the measurements were still limited by uncertainty. (I will have a look, but I doubt I can find it again...)

 

Edit: this might have been it: http://spectrum.ieee.org/tech-talk/at-work/test-and-measurement/uncertainty-over-the-uncertainty-principle (the conclusions are somewhat subtler than I remembered).

 

It is remarkable that every time I see an experiment on weak measurement reported in the press the hype would lead one to believe that the results challenge the HUP etc. - but that when I read the actual paper (and I am no expert) that the actual scientist never even come close to claiming that. I can sympathise - the memory was probably of one of those damned press releases and upon revisiting the paper itself the subtlety of the claims is rediscovered.

[tar]

Throughout the main body of his original 1927 paper, written in German, Heisenberg used the word, "Ungenauigkeit" ("indeterminacy"),^[1] to describe the basic theoretical principle. Only in the endnote did he switch to the word, "Unsicherheit" ("uncertainty"). When the English-language version of Heisenberg's textbook, The Physical Principles of the Quantum Theory, was published in 1930, however, the translation "uncertainty" was used, and it became the more commonly used term in the English language thereafter.^[56

 

^{The above is taken from the Wiki article on Uncertainty Principle. Important, because being unable to determine something exactly, has slightly different conotations than being uncertain about something. The uninitiated may take uncertainty as some sort of failure or weakness, or "limitation", where I do not believe that is the purpose of the principle. The purpose of the principle, I think, is to point out, that when looking at something smaller than the wavelength of light you are looking at it with, you reach a point at which your resolution can get no finer. The method you are using to "take the picture" becomes part of the picture and you have the choice of either having your thumb in the picture, or having a shakey/blurry picture, without your thumb.}

 

^{The thread question here, is what happens to a particle after its been measured. I would guess its somewhat like asking what happens to a blueberry after you taste it. You have to break the skin to get to the juice, so the particle is not likely to be undisturbed, since you have taken something from, or added something to what the particle or its partner was doing before the interaction that resulted in a measurement, occurred.}

 

^{HUP for me suggests more of an engineering tradeoff, type of consideration. "What do you want to know, to a higher precision, the position of the thing, or the momentum? If we establish the one any finer we are going to have to get a little coarser on the other, we can't determine the both, to the limits of our technology, at the same time." This, we are fairly "certain" is the case when measuring the position and momentum of tiny things.}

 

^{Regards, TAR}

[imatfaal]

Throughout the main body of his original 1927 paper, written in German, Heisenberg used the word, "Ungenauigkeit" ("indeterminacy"),^[1] to describe the basic theoretical principle. Only in the endnote did he switch to the word, "Unsicherheit" ("uncertainty"). When the English-language version of Heisenberg's textbook, The Physical Principles of the Quantum Theory, was published in 1930, however, the translation "uncertainty" was used, and it became the more commonly used term in the English language thereafter.^[56

 

^{The above is taken from the Wiki article on Uncertainty Principle. Important, because being unable to determine something exactly, has slightly different conotations than being uncertain about something. The uninitiated may take uncertainty as some sort of failure or weakness, or "limitation", where I do not believe that is the purpose of the principle. The purpose of the principle, I think, is to point out, that when looking at something smaller than the wavelength of light you are looking at it with, you reach a point at which your resolution can get no finer. The method you are using to "take the picture" becomes part of the picture and you have the choice of either having your thumb in the picture, or having a shakey/blurry picture, without your thumb.}

 

^{The thread question here, is what happens to a particle after its been measured. I would guess its somewhat like asking what happens to a blueberry after you taste it. You have to break the skin to get to the juice, so the particle is not likely to be undisturbed, since you have taken something from, or added something to what the particle or its partner was doing before the interaction that resulted in a measurement, occurred.}

 

^{HUP for me suggests more of an engineering tradeoff, type of consideration. "What do you want to know, to a higher precision, the position of the thing, or the momentum? If we establish the one any finer we are going to have to get a little coarser on the other, we can't determine the both, to the limits of our technology, at the same time." This, we are fairly "certain" is the case when measuring the position and momentum of tiny things.}

 

^{Regards, TAR}

 

But your idea of an engineering trade-off - which sounds like an experimental constraint - is not he whole story. It is not that we cannot measure these accurately at the same time - it is that quantum mechanics is based on an idea (or rather two ideas whch both show) that shows that these qualities do not exists with a certain accuracy at the same time.

 

Your post follows an idea called Heisenburgs microscope - which is a common way to teach HUP; unfortunately it is simple and does not encompass the whole idea.

[tar]

Imatfaal,

 

I was not thinking so much an experimental constraint as a tradeoff between whether you wanted to look at the thing from a probablistic quantum mechanics predictiion type statistical view, or whether you wanted to look at the thing from a location realist existing point of view.

 

You say the thing does not exist similutaneously in both an exact position and with an exact momentum, and that is what someone with a deeper and complete undertanding of the math/principle would grasp.

 

Except, to have a position one moment, and another another moment, would require a particle to "get" from the one place to the other in a certain amount of time. That is, that regardless of the precision of our measurements, and regardless of the effects of our manner of measurement on the particle, the particle really did have an exact position at every planck tick of the clock, and its up to our interpretation and definitions as to whether it "got" from the one end of the planck length to the other, in a smooth way with intermediate positions, or physically jumped instantaneously to the other end of the planck.

 

Seems at this point there is more of a philosophical/interpretation limit than a physical experimentational limitation.

 

Regards, TAR

[elfmotat]

Okay TAR, I'll work out the math for you since you seem to be having trouble understanding that it's not just a matter of measurement, the momentum for a particle with known location is undefined, and vice versa.

 

Say we measure an electron's momentum, and we have determined it to be exactly p₀. That means the particle's wave function satisfies the following equation:

[math]-i \frac{\partial \psi }{\partial x}=p_0 \psi[/math]

 

(It must satisfy that equation because its momentum must be an eigenvalue of the momentum operator when its momentum is a single value.) The solution to this equation is:

 

[math]\psi (x)=e^{ip_0 x}[/math]

 

Its probability distribution is therefore:

 

[math]P(x)= \psi^* \psi =e^{ip_0 x} e^{-ip_0 x}=1[/math]

 

This distribution is not integrable over space. I.e. when you try to integrate it to see where the particle is likely to be you get nonsensical answers. (For a probability distribution to be valid, the integral of P(x) from -∞ to ∞ must equal one. If you try integrating the above, you get infinity.) Its position is undefined. You also can show that the opposite is true, i.e. if we have a single precise value for the position then the momentum is undefined.

Edited September 14, 2014 by elfmotat

[tar]

elfmotat,

 

Well if that is what has been decided upon as true, then we will have to go with that.

 

Regards, TAR

[elfmotat]

elfmotat,

 

Well if that is what has been decided upon as true, then we will have to go with that.

 

Regards, TAR

 

It's not what anyone decided, it's what experiment tells us.

[tar]

elfmotat,

 

I apologize for posting in the physics section. I don't have the credentials to say anything authoritative. And I don't have the knowledge to "to get" what it is that experimentation has so clearly shown us is true.

 

You laid out the math for me, and suggested there was no such thing as an exact position for a moving thing to be in, because you can't take an integral of an exponential function. That sounds like a decision based on math rules, like you can not divide by zero because the answer is undefined. That does not sound to me, like experimentation told us that a moving thing can not have a position, or that something with a position can not move.

 

But, I will stop there. This is a science board and there is much science that has already been agreed upon, in terms of definitions and what "works", and how the universe operates and such, and its not important if something does not make sense to me. Not here, where solid "proven" knowledge is shared. I should stay in speculations and philosophy and religion, were I can do less harm.

 

Regards, TAR

[elfmotat]

 

 

That sounds like a decision based on math rules, like you can not divide by zero because the answer is undefined. That does not sound to me, like experimentation told us that a moving thing can not have a position, or that something with a position can not move.

 

What I meant was, we have a mathematical model that agrees with experiment. QM isn't some untested hypothesis, and the math didn't come out of the sky. The math was tailor made to fit and predict experimental data, and it works.

Edited September 16, 2014 by elfmotat