# The nature of measurement

Does the measurement of the particle change it's physical state? Or does it only seem to do that?

Ex. if a particle was measured before the slits, would we see an interference pattern, or a particle pattern?

And if the wave function is physically collapsed does it say like that forever or does it ever revert back to it's "superposition" state.

• What we see on the observation screen are always particles (is always made from particles). – HolgerFiedler Apr 8 '15 at 7:35
• Yogi DMT: "Does the measurement of the particle change it's physical state?" -- No. To measure means to derive real or Boolean values from given observational data. (The only change of state involved in measurement is the state of the experimenter carrying out these calculations, or the state of anyone to whom the result values are communicated.) Of course, often there are several observational data concerning the same particle (e.g. "having been issued by a source" and "having reached the screen"). p.s. I'm planning and looking forward to expanding this comment into an answer. – user12262 Apr 8 '15 at 21:45
• @HolgerFiedler That would be indicative of a measurement altering the physical state of the system correct? – Yogi DMT Apr 9 '15 at 6:34
• @user12262 To gain information about a system you need to interact/affect it in some way. – Yogi DMT Apr 9 '15 at 6:35
• Perhaps you could read this answer. – HolgerFiedler Apr 9 '15 at 17:49

Quantum mechanical entities are described by solutions of the Schrodinger equation, the wave function, with specific boundary conditions. A measurement changes the boundary conditions and thus the subsequent wavefunction describing the particle measured will be a different one.

A measurement picks an instant from the probability distribution describing the entity, and this is called "collapse" to confuse people. It is one entry in a distribution

Lets take the simple example of the harmonic oscillator:

On the right is the square of the wave function, and one sees oscilations in the probability distribution in the displacement x.

Suppose we have one atom the electron's dependence described by a harmonic oscillator . If we measure the displacement, it means we probed the atom and we will get one value in the distribution. A second atom will give a second point etc, and we will develop histograms that will have the shapes on the right. Each atom-electron after the measurement will be described by different wavefunctions because the boundary conditions will have changed, for example "scattered out" , "on a different energy level, etc. It will be very hard to follow what happens collectively from then on to determine the new probability functions because the boundary conditions will depend on the scatter.

Measurements of elementary particles, quantum mechanical entities, usually manifest the particle side . In this electron double slit one at a time one sees the particle

Electron buildup over time

as it leaves a spot on the screen, and each spot with its relevant probability looks random. The accumulation of spots though shows that the probability of finding the screen has a wave nature. This is analogous to the example above. When the electron hits the screen the problem changes because the boundary conditions change due to the screen

Ex. if a particle was measured before the slits, would we see an interference pattern, or a particle pattern?

It will depend on the boundary conditions of the measurements before. If it is a screen it is self evident . If the experiment is set up that the boundary conditions after the first measure allow again a coherent wavefunction plot with the boundary conditions of "two slits electron" the experiment will be the same as in the picture. There have been experiments interfering with the incoming beam statistically and maybe you can understand them.

And if the wave function is physically collapsed does it say like that forever or does it ever revert back to it's "superposition" state.

It always hinges on boundary conditions of the experiment changing the wavefunction solutions relevant to the experiment.

• Very thorough and informative answer but i'm not sure it completely answers my question. I'm trying to figure out when we measure the system if it physically changes (ie. stays in particle form after measurement is taken) or if it only produces a result indicative of particle-like nature but the system remains the same wave-like entity at all times. If the system is indeed altered does it ever go back to it's wave-like form? Also how is the particle in wave like form to begin with if it's being fired out of the particle gun or whatever? – Yogi DMT Apr 9 '15 at 6:41
• One has to stop thinking of "quantum mechanical entities" either as particles or as waves. They are best represented by a probability function which is the probability to appear as a particle at an (x,y,z,t). In between measurements the psi changes because the measurement changes the boundary conditions which define the psi. The probability has a wave structure as shown above, in all its manifestations. It is particles that leave a signal in the detector and then in that detector a new probability fucntion will exist for the electron until it is completely absorbed in an atom. – anna v Apr 9 '15 at 9:30
• and then it has the atomic probability function. QM probabilities are the same as classical ones. Just that the curve for our probable lifetime ( for example) is not sinusoidal in time :).medicine.ox.ac.uk/bandolier/booth/Risk/dyingage.html – anna v Apr 9 '15 at 9:35
• My only concern is that taking a measurement at the slit causes a different pattern to be produced over multiple trials. That means that measurement has to be affecting the system in some way. However, knowing this doesn't tell us what exactly is happening because a wave originating from one of the slits can produce a particle pattern just as a particle-like entity would. – Yogi DMT May 6 '15 at 6:06
• That leaves us with two scenarios. Measuring a particle in some way "redefines" that wave, or probability wave as you say, with it's point of origin being from the location of measurement, as opposed to it's original source. The second scenario is that measuring the system physically alters it's state, "converting" it into a "particle" for some period of time. Both scenarios are equally plausible given the basic understanding of the experiment that i have. – Yogi DMT May 6 '15 at 6:07

The double slit experiment basically shows these results, which is quite extraordinary in my view.

If an electron is fired from a gun one at a time towards a double slit, we will see interference pattern (vertical bars), which kind of shows what water wave will show if it hits a shore for instance. Because of interference, some systematic areas on the board are much higher because waves are interfering and interfered areas have high probability of catching the electron.

Here is the tricky part.

• Looking at the electron when it flies towards the double slits, we will see that only one electron went through only one of the slits or bounced back -> no interference pattern
• Not looking at the flying electron but just observing the sheet behind the slits -> interference pattern
• Looking at the electron before it goes through the slits -> no interference (just like a ball going through a large slit (you will see one electron flying)
• Looking at the electron after it went through the slits -> there is no interference (just one electron flying)
• Putting a camera and turning off the camera -> interference pattern
• Looking at the camera - > no interference (just one electron flying)

Because the sheet behind the slits are trying to measure the electron, the sheet itself collapses the wave like nature of the electron, and nature says since it hit the sheet/detector, wave function collapsed and electron acted like an object. Looking at the electron while in flight, it exactly appears like one electron. When not looking at the electron while in flight, the electron is everywhere at the same time and interfered with itself (because it is at all possible locations at the same time in flight, kind of like a wave) at the same time and landed/wave function collapsed on the back detector.

I think therefore in my opinion not observing the electron, the electron is a wave. Once it collapses on the sheet/detector, it is over and collapsed. But if the electron went through the sheet/detector and detector catched the electron at (X, Y) coordinate and flew out the other end and we not measure that passed through electron, the wave function is again back. I think this WFC is a reaction to observation. When not observing, it will revert back in my opinion. WFC is not the end, it reacted to observation bounced back and reverted to its superposition of states and continue. The critical thing is observation is measurement. I look at a chair and see that this chair is this far from the table and this far from the wall, which is observation and it is measurement. But according to quantum mechanics, this chair is at all the place at the same time when I turn around and instantly collapses to one chair when I look (from this distances from table and wall), in my humble opinion.

According to Quantum mechanics a particle exists in a state $|{\Psi}\rangle$ which belongs to a hilbert space of states. When you make a measurement, you act on the state with an operator, say $A$. And by doing this you project the state $|{\Psi}\rangle$ onto the subspace spanned by the eigenvectors of $A$, so now your state is one of the eigenvectors of $A$ with a corresponding value of the measurement being the eigenvalue corresponding to that eigenvector. So your state has now changed to $|A\rangle$.

• So measurement does permanently alter the state of a system? – Yogi DMT May 6 '15 at 3:49

No a measurement doesn't have to change the state of the system, but it has to at least has the possibility to change the apparatus; otherwise you wouldn't call it measurement. The change to the environment(the apparatus , the scientist and everything that interact with it) is what cause you to lose interference pattern. This is usually called decoherence procedure and a large number of publications are available.

If you do not like to think about it inside the system/ environment scheme, you can also look at it this way: Wave function is the function of coordinates of all particles. In simple terms, to interfere all particles have to line up at the same time, and this includes all the particles on the apparatus. Say there are two possible states of the system, and you make a measurement and get definite information, then in the two schemes particles in your apparatus will very likely be in different places, and when you try to interfere the system there'll be no coherence . On the other limit, if the apparatus are the same in both schemes, then you likely don't know anything from the measurement. A real measurement is usually somewhere in between.

Does the measurement of the particle change it's physical state?

A measurement, as an evaluation of given observational data, does not have any direct physical effect other than being accompanied by a change of state by whoever carries out the evaluation; the state changing from not yet knowing the result value (or indeed whether one could be obtained at all), into knowing the value (or knowing that the given observational data is insufficient or unsuitable for a successful evaluation). As a comprehensive example consider

Consider as an example the measurement of the invariant mass of a (short-lived) particle which had been produced and which decayed within a particle detector: its decay products must have been identified by analyzing the detector data collected for the recorded event under consideration, their energies and momenta are (generally) determined separately, and finally the evaluation of the quantity to be measured.

Changes of state (such as "decay", or various "interactions") are instead generally involved in the generation and collection of observational data.

Ex. if a particle was measured before the slits, would we see an interference pattern, or a particle pattern?

Considering experiments in which particles are emitted by a source and being detected (and spatially resolved on) a screen, obviously it should be possible to conclude (as a measured result) that each such particle had been emitted initially at the source; regardless of which pattern would eventually be determined at the screen.

And if the wave function is physically collapsed [...]

A specific wave function serves as a statistical representation of (consistent, "coherent") observational data, usually involving numerous individual trials. Speaking of any individual trial as "a collapse" doesn't add to this understanding.

• "Considering experiments in which particles are emitted by a source and being detected (and spatially resolved on) a screen, obviously it should be possible to conclude (as a measured result) that each such particle had been emitted initially at the source; regardless of which pattern would eventually be determined at the screen." - Not sure how this answers the question... – Yogi DMT May 6 '15 at 3:50
• @Yogi DMT: "Not sure how this answers the question..." -- Let me express my answer to your first/main question concisely: No, measurement of a particle doesn't change its physical state. (Measurement means to draw a definite conclusion from given observational data; e.g. the particle having changed its state from coincidence with the source but not the screen into conicidence with the screen. Drawing conclusions from this doesn't induce further state changes of the particle). Regarding your second/minor question: Don't pretend to know number/arrangement of "slits" before measuring. – user12262 May 6 '15 at 5:08
• so measuring the particle before it hits the slits will result in an interference pattern being produced? @user12262 – Yogi DMT May 6 '15 at 5:16
• @Yogi DMT: "so measuring the particle before it hits the slits will result in an interf. pattern being produced?" -- This doesn't seem a sensible question. We can and should ask instead: How to measure the (most probable) number and shape of "slits" (vs. "potential walls") in the region between a given source and screen; wrt. specific particles having been exchanged in specific trials? Answer: from the "pattern" on the screen (if indeed there was any); in geometric relation to the source. So "measuring the particle before it hit the screen" means only to assert that it had left the source. – user12262 May 6 '15 at 19:44

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