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Jarwulf

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Does the wavefunction of a being have to have a possibility where the being changes their mind about something or can all possibilities of the wavefunction simply be ones where the being's mind stays the same?

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- Thread starter Jarwulf
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Jarwulf

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Does the wavefunction of a being have to have a possibility where the being changes their mind about something or can all possibilities of the wavefunction simply be ones where the being's mind stays the same?

- #2

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Does the wavefunction of a being have to have a possibility where the being changes their mind about something or can all possibilities of the wavefunction simply be ones where the being's mind stays the same?

When we solve for the equation of motion using Newtonian mechanics, what we first do is account for all the forces acting on the system, i.e. we do F=ma. So say you have an object falling to the ground, you then have

[tex]F_g = ma[/tex]

where [itex]F_g[/itex] is the force due to gravity. But if you want to include more realistic situation, you put in other facts, such as frictional force due to air friction [itex]F_f[/itex], and maybe the object itself has its own propulsion [itex]F_p[/itex]. Then you write

[tex]F_g + F_f + F_p = ma[/tex]

and then you solve (if you can) for the equation of motion.

The same thing occurs for the wavefunction. You first start with the Hamiltonian/Schrodinger equation. You need to know all of the potential landscape that the system has. This may or may not be trivial. In one of the simplest case, say for an infinite square well potential (which every student in intro QM classes should know), you write down the kinetic term and then the potential representing that square well. That's the whole system! So the wavefunction that you solve

But here's where it can get complicated, especially when you start adding complexity to the system.

1. You don't know what the exact Hamiltonian is, and so you have to make either an estimate or an approximation. This is true when you are dealing with a gazillion particles, as in condensed matter physics. It is impossible to write an exact Hamiltonian for a many-body system. So in such a case, you make some clever approximation for the potential, such as using the mean-field approximation. You say that, even though a particle in the system sees all the potential from other particles, we can simply make the approximation that, on average, it sees a constant "mean field" from all of the particles.

So your Hamiltonian will consist of the kinetic term, and a mean-field approximation of the potential term. Therefore, your wavefunction can only be as good as what you have done in the beginning. It cannot predict or describe something beyond that. In many situations, the mean-field approximation is perfectly valid and can account for a large number of phenomena. But in other situations, this approximation breaks down. It is not because the wavefunction is inadequate, it is rather our starting point and our knowledge of the system is inadequate.

So your Hamiltonian will consist of the kinetic term, and a mean-field approximation of the potential term. Therefore, your wavefunction can only be as good as what you have done in the beginning. It cannot predict or describe something beyond that. In many situations, the mean-field approximation is perfectly valid and can account for a large number of phenomena. But in other situations, this approximation breaks down. It is not because the wavefunction is inadequate, it is rather our starting point and our knowledge of the system is inadequate.

2. You know the exact Hamiltonian, but you cannot get a full, exact wavefunction. In many instances, you can write the exact wavefunction, but solving the differential equation is often a major problem. One also encounters this in classical newtonian mechanics (try to find exact, closed solution for the 3-body or more problem). This is where you either do numerical solutions, or in other cases, you make an approximate solution as a simplification, or even only consider special cases that gives you nice, analytical solutions. So obviously, it is not inconceivable that the solution could miss something when such simplifications are applied.

So in principle, the wavefunction should be able to describe ALL of the observables as described in the Hamiltonian. It depends on how well you can construct a Hamiltonian that accurately and fully describe the system you are looking at, and how well you can arrive as the wavefunction solution.

Zz.

- #3

qsa

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Does the wavefunction of a being have to have a possibility where the being changes their mind about something or can all possibilities of the wavefunction simply be ones where the being's mind stays the same?

QM does imply that one thing could in principle be in two different places at the same time, even macroscopic objects. so there are theories that try to explain away such possibility, like GRW

http://en.wikipedia.org/wiki/Ghirardi–Rimini–Weber_theory

from

Phys. Rev. D 34, 470–491 (1986)

Unified dynamics for microscopic and macroscopic systems

An explicit model allowing a unified description of microscopic and macroscopic systems is exhibited. First, a modified quantum dynamics for the

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- #4

The_Duck

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Do wavefunctions have to have every conceivable possibility? Say for instance you have a chair. Does the wavefunction of the chair necessarily have a possibility where the chair breaks apart spontaneously? Or a set of worlds where the chair breaks apart if MWI is true? Or can the wavefunction simply consist of possibilities where the chair does not splinter apart?

Yes, I think for for all reasonable physical systems every possible configuration will have a nonzero probability associated with it. For instance if you have a hydrogen atom the electron has a probability to be found literally anywhere in relation to the proton. However the probability is only non-negligible inside a very small volume of size about 10^-10 meters, and decays exponentially outside this volume. You can appreciate that while the probability of finding the electron on the other side of the room from the proton is nonzero, it is vanishingly small.

Similarly for a more complicated system like a chair the wave function should assign a nonzero probability to all possible configurations of the particles that make up the chair. However it is vanishingly unlikely that you will actually observe the particles of the chair adopt some configuration that is radically different from their current one, i.e. your chair is not going to spontaneously fall apart (absent some outside force like a sledgehammer).

- #5

Jarwulf

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Yes, I think for for all reasonable physical systems every possible configuration will have a nonzero probability associated with it. For instance if you have a hydrogen atom the electron has a probability to be found literally anywhere in relation to the proton. However the probability is only non-negligible inside a very small volume of size about 10^-10 meters, and decays exponentially outside this volume. You can appreciate that while the probability of finding the electron on the other side of the room from the proton is nonzero, it is vanishingly small.

Similarly for a more complicated system like a chair the wave function should assign a nonzero probability to all possible configurations of the particles that make up the chair. However it is vanishingly unlikely that you will actually observe the particles of the chair adopt some configuration that is radically different from their current one, i.e. your chair is not going to spontaneously fall apart (absent some outside force like a sledgehammer).

So basically there is a chance or if MWI is true there are an infinite number of universes where an army of 100 story tall pie eating sumo robots spontaneously materializes in NYC?

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StevieTNZ

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So basically there is a chance or if MWI is true there are an infinite number of universes where an army of 100 story tall pie eating sumo robots spontaneously materializes in NYC?

If the wavefunction of the 100 story tall pie eating sumo robots allows the state of NYC, then yes.

Interesting that in Quantum Philosophy by Roland Omnes, says:

If we consider from this perspective an ordinary object, an empty bottle, say, the quantum principles will only take into account the particles forming the botttle, and will therefore treat on an equal footing a multitude of different objects. This is due to the fact that the atoms that make up the bottle could, without changing their interactions, adopt thousands of shapes to form a thousand different objects: two smaller bottles, six wine glasses, or a chunk of melted glass. One could also seperate the atoms according to their kind and end up with a pile of sand and another pile of salt. A rearrangement of the protons and electrons to transmute the atomic nuclei without modifying the nature of their interactions could also produce a rose in a gold cup. All these variants belong to the realm of the possible, of the multitude of forms that the wave functions of a given system of paricles may take.

- #7

Jarwulf

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Yes, I think for for all reasonable physical systems every possible configuration will have a nonzero probability associated with it. For instance if you have a hydrogen atom the electron has a probability to be found literally anywhere in relation to the proton. However the probability is only non-negligible inside a very small volume of size about 10^-10 meters, and decays exponentially outside this volume. You can appreciate that while the probability of finding the electron on the other side of the room from the proton is nonzero, it is vanishingly small.

Similarly for a more complicated system like a chair the wave function should assign a nonzero probability to all possible configurations of the particles that make up the chair. However it is vanishingly unlikely that you will actually observe the particles of the chair adopt some configuration that is radically different from their current one, i.e. your chair is not going to spontaneously fall apart (absent some outside force like a sledgehammer).

I'm sort of confused what you're saying implies that the wavefunction has an infinite number of possibilities to collapse/decohere/do something else into but from reading the internet I get

Q11 How many worlds are there?

--------------------------

The thermodynamic Planck-Boltzmann relationship, S = k*log(W), counts

the branches of the wavefunction at each splitting, at the lowest,

maximally refined level of Gell-Mann's many-histories tree. (See "What

is many-histories?") The bottom or maximally divided level consists of

microstates which can be counted by the formula W = exp (S/k), where S

= entropy, k = Boltzmann's constant (approx 10^-23 Joules/Kelvin) and

W = number of worlds or macrostates. The number of coarser grained

worlds is lower, but still increasing with entropy by the same ratio,

ie the number of worlds a single world splits into at the site of an

irreversible event, entropy dS, is exp(dS/k). Because k is very small

a great many worlds split off at each macroscopic event.

Which seems to me to imply that there are a finite number of possibilities for the wavefunction to collapse/decohere/do something else into. Since MW claims that each possibility leads to another world.

- #8

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Q11 How many worlds are there?***

--------------------------

The thermodynamic Planck-Boltzmann relationship, S = k*log(W), counts

the branches of the wavefunction at each splitting, at the lowest,

maximally refined level of Gell-Mann's many-histories tree. (See "What

is many-histories?") The bottom or maximally divided level consists of

microstates which can be counted by the formula W = exp (S/k), where S

= entropy, k = Boltzmann's constant (approx 10^-23 Joules/Kelvin) and

W = number of worlds or macrostates. The number of coarser grained

worlds is lower, but still increasing with entropy by the same ratio,

ie the number of worlds a single world splits into at the site of an

irreversible event, entropy dS, is exp(dS/k). Because k is very small

a great many worlds split off at each macroscopic event.

Moderator Edit: *** From "The Everette FAQ" by M.C. Price.

- #9

QuantumClue

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Does the wavefunction of a being have to have a possibility where the being changes their mind about something or can all possibilities of the wavefunction simply be ones where the being's mind stays the same?

Yes. the wave function takes into account every conceivable possibility. Parts of that wave function will project items into deep space. It's not that it is there physically... only there as a possibility, which is to add, very small indeed.

- #10

StevieTNZ

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Does a quantum system (macroscopic in this case) have an infinite or finite amount of physical possiblities that can actualise upon measurement?

- #11

QuantumClue

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Does a quantum system (macroscopic in this case) have an infinite or finite amount of physical possiblities that can actualise upon measurement?

Yes, but the wavelength of matter is exceedingly small on large enough scales. Even your homework jotter will be statistically sitting as a possibility on the surface of venus as an extreme example. The only reason why it is not sitting there, is again, highly unlikely.

- #12

StevieTNZ

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Sorry I wasn't clear enough earlier

- #13

Jarwulf

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infiniteorfinitepossibilites.

Sorry I wasn't clear enough earlier

Same question. Everyone here seems to be leaning toward infinite but the FAQ author seems to think it is finite.

- #14

StevieTNZ

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I wonder if there will be an answer anytime soon?

- #15

QuantumClue

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I wonder if there will be an answer anytime soon?

Most agree it to be infinite. It's probabilities are spread infinitely throughout spacetime.

- #16

Jarwulf

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Most agree it to be infinite. It's probabilities are spread infinitely throughout spacetime.

Okay so the FAQ is wrong

- #17

QuantumClue

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Okay so the FAQ is wrong

Fields where designed in the sense they ''needed to touch'' vast areas. Most of the fields we deal with in quantum mechanics are infinite by nature.

The wave function is also a field, and can also be infinite by nature. It is a field of infinite possibilities, or a field representive of the probabilities of events. It must be infinite in many cases. A particles possible location is not situated to a small area, but has a range which scopes from [tex]-\infty[/tex] to [tex]\infty[/tex]. That means the wave function appreciates even the most unlikely of scenarios.

- #18

A. Neumaier

Science Advisor

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Okay so the FAQ is wrong

The quality of the Everett FAQ is very poor. See the section ''On the Many-Worlds-Interpretation'' of Chapter A4 of my theoretical physics FAQ at http://www.mat.univie.ac.at/~neum/physfaq/physics-faq.html#manyworlds

In particular, the entropy argument used in the answer to Q11 is funny since it implies a fractional number of worlds unless the ensemble of worlds is microcanonical. But then each world is equally probable, and we must be puzzled why we are in a world where the unlikely happens rarely...

The usual entropy formula from statistical mechanics employed only counts the number of energetically accessible energy eigenstates (not the number of all possible states at a given energy, which is infinite), and is applicable only to a bounded volume of matter in equilibrium.

But the many worlds interpretation must consider the whole universe as the physical system, and the latter is neither in equilibrium nor (most likely) bounded.

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StevieTNZ

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- #20

QuantumClue

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Well that is difficult to say. The wave length of matter at our levels of macroscopic objects are so small, that we don't even see a wave function which is physically projected through space, however an ethereal wave function exists for all objects, even your own body. Physical projections of possibilities have been observed though but they are very small objects which are not free from quantum effects.

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Jarwulf

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- #22

StevieTNZ

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however an ethereal wave function exists for all objects, even your own body. Physical projections of possibilities have been observed though but they are very small objects which are not free from quantum effects.

An ethereal wave function? Meaning?

Again my favourite paragraph from Quantum Philosophy by Roland Omnes:

If we consider from this perspective an ordinary object, an empty bottle, say, the quantum principles will only take into account the particles forming the botttle, and will therefore treat on an equal footing a multitude of different objects. This is due to the fact that the atoms that make up the bottle could, without changing their interactions, adopt thousands of shapes to form a thousand different objects: two smaller bottles, six wine glasses, or a chunk of melted glass. One could also seperate the atoms according to their kind and end up with a pile of sand and another pile of salt. A rearrangement of the protons and electrons to transmute the atomic nuclei without modifying the nature of their interactions could also produce a rose in a gold cup. All these variants belong to the realm of the possible, of the multitude of forms that the wave functions of a given system of paricles may take.

Always wondered what was meant by 'forms that the wave functions of a given system of particles may take' until I realised that a wave function can have one solution to it, i.e. two smaller bottles, and another can have the solution, i.e. in this case six wine glasses, which can add together to form another wave function of a superposition of two smaller bottles + six wine glasses.

- #23

QuantumClue

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An ethereal wave function? Meaning?

Again my favourite paragraph from Quantum Philosophy by Roland Omnes:

Always wondered what was meant by 'forms that the wave functions of a given system of particles may take' until I realised that a wave function can have one solution to it, i.e. two smaller bottles, and another can have the solution, i.e. in this case six wine glasses, which can add together to form another wave function of a superposition of two smaller bottles + six wine glasses.

I need to be careful now because I realize the word I choose could be misconstruded as to mean something else. It was just me trying to be over-elegant.

When we talk about probabilities, we tend to wonder what we mean. Probabilities are things which happen inside our heads. Probabilities are the world of mind-stuff. This is not to mean that somehow the world is created mentally, but in many ways this part of quantum mechanics mirrors this fascinating fact rather well. The brain is physical, thoughts seem a lot less physical, almost ethereal. Thoughts or probabilities inside our heads don't objectively exist in the outside world. Physical probabilities may exist in the objective world.

This is why when the wave function was formulated, many scientists in the beginning thought that wave function was merely a statistical way for the scientists mind to make sense of an otherwise, evading reality of possibilities.

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- #24

QuantumClue

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I'm not entirely sure how the subject of teleportation has arisen, as that would require to some theoreticians, the use of entangled particles.

However, with that said, there are many philosophical arguements rooted from the mathematics of such theories which cast doubt on whether teleportation is possible. Is a newly created, (new matter) but otherwise completely identical twin of an object be actually teleported? If you teleport information about a system and reconfigure those atoms into a complete duplicate, who is to say that it is the same object in question? All you have done is read from a recipe book and replicated your mothers apple pie. And the consciousness is not fully understood either... Personally I do not believe you can entangle particles over large distances and teleport something as complex as a human being. My consciousness inhabits the atoms in my body. Not the entangled states of particles over large distances.

Maybe you would like to make a post on the subject to see what others think.

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- #25

homology

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- #26

StevieTNZ

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I need to be careful now because I realize the word I choose could be misconstruded as to mean something else. It was just me trying to be over-elegant.

When we talk about probabilities, we tend to wonder what we mean. Probabilities are things which happen inside our heads. Probabilities are the world of mind-stuff. This is not to mean that somehow the world is created mentally, but in many ways this part of quantum mechanics mirrors this fascinating fact rather well. The brain is physical, thoughts seem a lot less physical, almost ethereal. Thoughts or probabilities inside our heads don't objectively exist in the outside world. Physical probabilities may exist in the objective world.

This is why when the wave function was formulated, many scientists in the beginning thought that wave function was merely a statistical way for the scientists mind to make sense of an otherwise, evading reality of possibilities.

I tend to think of quantum possibilites as potentialities. To quote Giancarlo Ghirardi

So in the double-slit experiment, the particle went from the source and made a 'quantum jump' to the screen (i.e. it didn't really go through either or both slits to get to the screen)?the assertion "the photon is in a superposition |O> + |E>" is logically different from all the following statements: "it propagates itself along path O or along path E" or "it follows both O and E" or "it follows other paths".

I guess what I was asking was whether there were an infinite number of physical states found in a solution to the Schrodinger equation, such as one of those physical states being

two smaller bottles, another physical state being six wine glasses, another state a chunk of melted glass.

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Jarwulf

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I'm not entirely sure how the subject of teleportation has arisen, as that would require to some theoreticians, the use of entangled particles.

However, with that said, there are many philosophical arguements rooted from the mathematics of such theories which cast doubt on whether teleportation is possible. Is a newly created, (new matter) but otherwise completely identical twin of an object be actually teleported? If you teleport information about a system and reconfigure those atoms into a complete duplicate, who is to say that it is the same object in question? All you have done is read from a recipe book and replicated your mothers apple pie. And the consciousness is not fully understood either... Personally I do not believe you can entangle particles over large distances and teleport something as complex as a human being. My consciousness inhabits the atoms in my body. Not the entangled states of particles over large distances.

Maybe you would like to make a post on the subject to see what others think.

If the wavefunction really does contain all possibilities than theoretically it should allow say for instance a quanta or maybe even Los Angeles to teleport to the other side of the visible universe or an infinite distance instantaneously right? Assuming an unbounded universe where quantum mechanics applies to all the relevant places.

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- #28

_PJ_

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We are dealing with probabilities, and ALL POSSIBLE probabilities ought to be considerred. Any statistician knows that such a chart would be infinite, there would be a peak around the most-probable, but as the line droips off either side to the unlikely, the probability will tend towards - but never reach - zero. This can only be infinite series.

In determining individual proability possibilities, we need to consider factors that themselves may be infinite: time, location etc.

Personally, I don't like infinity, and there is a belief (for me a hope), that what may seem like an infinite range, is actually finite. Consider ther Planck Length and a finite/bounded universe as a limiting facttor on time/distance, or more practical restrictions such as causality that might limit future options.

- #29

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There is a deeper question which should be answered first.... is "space" a real object or is it a conceptual construct we use to describe real objects. Then the question of its discreteness or boundedness is a question of which conceptual tool we best use to describe how objects behave.

I think there is a conceptual error which got reinforced by the elegance of the geometric formulation of General Relativity (and also the success of QFT). We have begun to reify space. This is, I think, an error. If we treat space and space-time as parametric manifolds e.g. constructs to express overlapping degrees of freedom for physical systems, then "quantum space-time" becomes meaningless as such. Its just as bad as trying to "quantize" the complex numbers or "quantize" a group. We "quantize" physical systems in that we recognize their observables as quantized. In the relativistic setting spatial position ceases to be a physical observable.

I know this seems like a tangent here but it affects the question of infinities which crop up in e.g. attempts to quantize gravity and in questions of possibilities vs actualities.

- #30

StevieTNZ

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- #31

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Not if the probably if it happening has a time period on the scale of the age of the universe! Then such a consideration of that happening is

Zz.

- #32

Jarwulf

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Personally, I don't like infinity, and there is a belief (for me a hope), that what may seem like an infinite range, is actually finite. Consider ther Planck Length and a finite/bounded universe as a limiting facttor on time/distance, or more practical restrictions such as causality that might limit future options.

I dunno I think a buffet would be a lot cooler with an infinite variety of food.

- #33

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Ultimately such a statement itself is uncertain, and a matter of the probability that the theory, which you are using to predict what CAN and CAN'T happen, is correct. At some point a probability becomes so small as to be less than the probability that all the experiments confirming the theory being used were accidentally way off the mark.

When you say "Clearly it COULD", how do you know? To what probability are you correct in your assertion?

Finally we may be ignorant of the impossibility of some event and thus we speak of it as something which "COULD" happen in the sense that we are unable to eliminate to exactly zero the probability of it happening. The statement is not one of actual possibility but a statement of our lack of infinite knowledge. It is important to identify if this is the case in what you are saying.

--------------

The above is all general concerns and context for the question at hand. The actual analysis assuming QM is correct, is this. When we speak of the wave-function for a quantum and the small probability of it "jumping to LA", we are really speaking of the small probability that it "was in LA all the time." so to speak...excepting the issue of what it means to say where it is or was at all in the absence of measurement.

It is more instructive to get down to cases. First in the non-relativistic case, you observe a quantum in NYC, at time t1. You write down a wave-function (a delta function) for its position given this knowledge. If you immediately observe its position again you will find it in NYC with probability 100% and LA with exactly 0%. You then evolve the wave-function for an interval of time so that at time t2 there is a finite small probability it will be observed in LA.

You haven't a clue as to its momentum and thus its velocity (which can be arbitrarily high in the non-relativistic setting) and so you cannot say that it couldn't be traveling so fast as to reach LA by the time t2 that you then observe it there. No teleportation involve here, simply the quantum having a very very small probability of moving very fast.

Now take the relativistic case. you observe a quantum in NYC, at time t1. You write down a wave-function (a delta function) for its position given this knowledge. You haven't a clue as to its momentum and thus its velocity (which must be less than c in the relativistic setting). If you then evolve the wave-function it will not exceed the speed of light in its propagation of probability. It is impossible to observe it in LA until it has had time to propagate there at some velocity < c. However once enough time has passed you have the same situation as before.

However some may misinterpret the point of maximum probability of a wave-function for an actual position of the corresponding quantum. In that case there is a finite probability that a later observation will find the actual quantum a distance greater than ct away from this peak. It is a surprise, not a sudden jump.

QM does not say we will see sudden jumps as implied by the term "teleportation" but rather explains that when we only look at discrete times we can only see a discrete series of positions i.e. jumps (but not sudden ones). In between looking we predict what might be seen (and how likely) with wave-functions.

Note: My analysis is based somewhat on my choice of interpretation (Orthodox CI) and others may describe the nature of the reality of the situation differently based on their interpretation. However I would point out that in the end all the other interpretations agree with the above in so far as

A final note. The phrase "quantum teleportation" has a distinct meaning not to be confused with the above described phenomena. It has to do with copying a quantum system completely (and necessarily destructively) by using an auxiliary system. Just as we shouldn't confuse "quantum cloning" with actual copying genetic material, we shouldn't confuse "quantum teleportation" with actual instantaneous jumping from point A to point B. These are romantic choices of terminology for more mundane actual phenomena.

- #34

mr.smart

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if it remains "solid" then this would explain why the chair does not posses the probability of falling apart spontaneously. presumably the wave function collapsed when the wood was first cut and now ,as a hard piece of wood, it responds to the physical reality classically.

if however, once an observed particle becomes again un-observed, it become a wave function again, then the chair does posses the probability to fall apart, but only if you stop looking at it.

is there an excepted answer to this one... could Schroedinger's cat come back to life if we closed the box?

- #35

StevieTNZ

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When you say "Clearly it COULD", how do you know? To what probability are you correct in your assertion?

Finally we may be ignorant of the impossibility of some event and thus we speak of it as something which "COULD" happen in the sense that we are unable to eliminate to exactly zero the probability of it happening. The statement is not one of actual possibility but a statement of our lack of infinite knowledge. It is important to identify if this is the case in what you are saying.

Nope, I'm referring to a probability for a physical state to actualise (extracted from the wave function), and someone saying it has a really really low probability of occuring that its practically not going to occur, I would think is wrong. For example, say I have 2% probability for sitting on this chair, and 98% for turning the TV off and walking out of the house. Even though it looks more probable that the turning off of the TV is going to occur, there is the possibility for me to go sit on the chair.

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