Does quantum physics imply the existence of randomness?

[raphalbatros]

So, I am not an expert in quantum physic, I just watched a lot of videos about it.

If I understand correctly, particles do not have a particular position as long as you don't observe them. With a certain equation, we can draw a cloud of probabilities which describes how likely the particle is to be at any location at any time. As I heard, this theory of quantum physics has proven itself to be extremely effective.

More than once, I had discussions with friends about whether or not our universe is purely deterministic or if it contains randomness. I am more on the deterministic side, and a argument that I often face is that quantum physics theory implies the existence of randomness.

On the surface, it seems to me like I can compare quantum physic's probabilistic nature to that of a coin toss. Probability theory is extremely effective to predict the distribution the multiple results of many throws will respect, even though these events have a deterministic nature.

Could it be that the same thing is happening with quantum physic?
Could it be that some deterministic processus is what generate the probabilistic distribution that lies within quantum physic?
Or is there some aspect of the theory I fail to understand?

 

[Orodruin]

Could it be that the same thing is happening with quantum physic?
Could it be that some deterministic processus is what generate the probabilistic distribution that lies within quantum physic?
How is there some aspect of the theory I fail to understand?

No, what you are talking about would be a hidden variable theory, where the "true" state is deterministic. I suggest you read up on Bell's theorem.

So, I am not an expert in quantum physic, I just watched a lot of videos about it.

Then you are certainly not qualified to start an A-level thread on the subject. Marking your post A-level indicates that you have an understanding of the subject at the level of a graduate student or higher. I will relabel your thread B.

 

[raphalbatros]

Orodruin
Thank you, I will look at that.

And sorry, my bad, I thought it was the level required to be able to answer to my question (I should have been more careful).

 

[Khashishi]

There are two parts to quantum mechanics. 1, There is Schrodinger's equation which describes how wavefunctions evolve over time when nobody is looking at it. And then 2, there's the collapse of the wavefunction, which happens whenever a measurement is made. The first part is very well understood and is purely deterministic. The second part appears to be random, but isn't as well understood so people aren't really sure. Many people do not believe a collapse actually occurs, but it is just an illusion caused by irreversible interactions with a complex environment.

At your level, it is probably safe to say that quantum mechanics is truly random. Whenever a measurement is made, the wavefunction is "projected" into one of the allowable measured states (eigenstates), picked randomly via the Born rule.

 

[raphalbatros]

Khashishi
If you think the first part is deterministic, how do you avercome Bell's theorem ?

 

[Khashishi]

You can't measure anything without the second part.

 

[Isaac0427]

The experimental evidence (specifically the two-slit experiment) and the equations based off of the experimental evidence do suggest randomness. As @Khashishi said, the schrodinger equation is well understood, but the wavefunction collapse is not, and the wavefunction collapse (and things associated with it, such as the observer effect implied by experimental evidence) implies randomness. In fact, many scientists, just like you do, have grappled with the concept of randomness in physics. Most notably, Einstein's remarks that "My god does not play with dice," basically implying that randomness is not how the universe works. In fact, look at this article to see all the different interpretations of quantum mechanics, more specifically randomness and wavefunction collapses (nobody really disagrees about things concerning the schrodinger equation as there really isn't much to disagree on).

 

[ebos]

I'm not a physicist either but am also very interested in all things, especially physics. I try to look at the quantum world and 'our' world as looking at flocks of ducks and individual ducks. Even though they are the same thing one is a constituent of the other and has different behaviours. I understand that it is a simplistic way of trying to understand it but we use balloons to try to understand the universe, don't we?

 

[bhobba]

As far as QM goes we have all sorts of takes on your query - but they are all interpretations so there is no way to tell them apart.

The most interesting one is likely Bohmian Mechanics. It's completely deterministic. Randomness enters into it due to lack of knowledge of initial condions.

There are others - do some further posts if you want to know more.

Thanks
Bill

 

[raphalbatros]

1, There is Schrodinger's equation which describes how wavefunctions evolve over time when nobody is looking at it.

The first part is very well understood and is purely deterministic.

I just don't understand how you can see that phenomenon as a deterministic one if it behaves as if it was completely random. The equation describes a wave of probabilities, and thus does not represent a deterministic feature. Do I miss something here?

In fact, look at this article to see all the different interpretations of quantum mechanics, more specifically randomness and wavefunction collapses (nobody really disagrees about things concerning the schrodinger equation as there really isn't much to disagree on).

Thank you I will look at that. And what do you think of my answer to Khashishi ?

ebos and bhobba
Thank you for your answers.

 

[Isaac0427]

I just don't understand how you can see that phenomenon as a deterministic one if it behaves as if it was completely random. The equation describes a wave of probabilities, and thus does not represent a deterministic feature. Do I miss something here?

I'm not 100% confident in this answer but I am about 80-90% confident. Yes, the position of the particle is subject to probability, but that is not what the Schrodinger equation talks about. From a theoretical standpoint, saying a particle is in the state $\psi$ is enough, and what that state is is completely deterministic. The Schrodinger equation has no probability associated with it; it deterministicly shows how the wavefunction evolves with time. Now, say you want to get more specific than to say the particle is in the state $\psi$. You would need to then measure the particle's exact position, which brings up wavefunction collapses and the observer effect. Basically, the particle's wavefunction $\psi$ can be viewed as not something that is used to predict the particle's state that is subject to a random probability, but the particle's state itself. Note that it is a very different definition of state as we use in classical mechanics, but that is classical mechanics, and this is quantum mechanics. The same rules don't apply.

I hope I was clear in that.

 

[raphalbatros]

Yes, the position of the particle is subject to probability, but that is not what the Schrodinger equation talks about.

The Schrodinger equation has no probability associated with it; it deterministicly shows how the wavefunction evolves with time.

Schrodinger equation is "describing the time-evolution of the system's wave function"
"The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements made on the system can be derived from it"
-Wiki
I think a logical conclusion would be to deduce the Schrodinger equation talks about how the particle is subject to probability. Where do you think is my line of reasonning wrong ?

 

[bhobba]

Where do you think is my line of reasonning wrong ?

The wave-function is the representation of this thing called the state. States of themselves have nothing to do with probabilities (technically its a positive operator of unit trace) - that's the job of the Born Rule:
https://en.wikipedia.org/wiki/Born_rule

Thanks
Bill

 

[atyy]

On the surface, it seems to me like I can compare quantum physic's probabilistic nature to that of a coin toss. Probability theory is extremely effective to predict the distribution the multiple results of many throws will respect, even though these events have a deterministic nature.

Could it be that the same thing is happening with quantum physic?
Could it be that some deterministic processus is what generate the probabilistic distribution that lies within quantum physic?
Or is there some aspect of the theory I fail to understand?

Take a look at Bell's theorem.

Roughly:

Yes, if locality is violated.

No, if locality is not violated.

Since in everyday life, locality is not violated, we can use the violation of a Bell inequality to guarantee randomness.

However, at a fundamental level, locality may be violated, the random results of quantum mechanics may arise from deterministic processes like a coin toss.

 

[Isaac0427]

Schrodinger equation is "describing the time-evolution of the system's wave function"
"The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements made on the system can be derived from it"
-Wiki
I think a logical conclusion would be to deduce the Schrodinger equation talks about how the particle is subject to probability. Where do you think is my line of reasonning wrong ?

Read the rest of my post you quoted. We can classically define a state as the exact position, momentum, etc. of a particle. We can also define a particle's quantum state which is just the particle's wavefunction. The wavefunction evolves with time deterministicly. The exact position, momentum etc. of the particle doesn't. The Schrodinger equation shows the time evolution of the wavefunction, not the time evolution of the particle's exact position as, for example, some of the kinematic equations show (classically, of course). The exact "classical" state (a slight abuse of terminology, but you get what I mean) is subject to randomness, but the wavefunction itself isn't.

 

[lavinia]

While am am new to this stuff it seems that purely mathematically the Schrodinger equation for a free particle is the same as the Heat equation except with a complex constant coefficient. One would expect that it describes a diffusion process similar to a continuous time Brownian motion. In Feynmann's Lectures on Physics Book 3, he describes how this actually works. The Shrodinger equation for a free particle describes a continuous stochastic process similar to a Markov process except that instead of conditional probabilities, there are conditional complex amplitudes. Much as in Brownian motion one would imagine continuous nowhere differentiable complex valued paths of states though I have not yet worked this out.

 

[MrRobotoToo]

The postulates themselves don't imply that randomness is intrinsic: such a conclusion will depend on which interpretation you buy into. For example, in Bohmian mechanics and the many-worlds interpretation the randomness is only apparent: the state of the system always evolves deterministically.

 

[raphalbatros]

Am I right in saying that the wavefunction is a wave of probabilities ?

 

[haushofer]

What does that mean? The wavefunction gives the amplitude. Only the absolute value squared gives you the probability.

 

[Delta2]

There is randomness but its not chaotic randomness. The schrodinger equation always hold. If for one short interval of time dt the particle's wavefunction followed the schrodinger equation, the next interval (dt,2dt) it followed the equation $\psi''+c\psi=0$ and the interval (2dt,3dt) followed the equation $\psi=0$ that would be sort of hardcore (chaotic) randomness.

 

[bhobba]

Am I right in saying that the wavefunction is a wave of probabilities ?

No.

Technicality its the representation of a state in terms of position eigenfunctions. If you know linear algebra I can explain the detail.

Probabilities do not come from the state - that requires another axiom called the Born rule:
https://en.wikipedia.org/wiki/Born_rule

Thanks
Bill

 

[entropy1]

Raphalbatros: If the collapse of the wavefunction is deterministic, then the value that is yielded after the collapse has to be able to be expressed in terms of other (independent) parameters, such as other, seemingly unrelated collapses, that is to say: all collapses (in the universe) have to be related and balance with each other. Perhaps this is measurable, but an experiment has never been done to my knowledge, so maybe the math excludes this possibility.

 

[write4u]

The word "randomness" sounds misleading to me. It gives the impression that there are multiple *choices* from which a "certainty" is derived. What if it is an either or choice. Would that still qualify as random?

 

[Isaac0427]

Am I right in saying that the wavefunction is a wave of probabilities ?

No, but it is a very logical conclusion. Again, the wavefunction of an electron is not a wave of probabilities for the electron, but the electron's state.

 

[Mark Harder]

I'm curious to hear what the experts here think about the following thought experiment. You have a radioactive atom that was created in a nuclear reactor some years ago. You place the atom under a powerful detector that will signal you when the atom disintegrates. You know the half-life of the atom. Can you, at any time, predict with definiteness (up to that permitted by the uncertainty relation between time and energy) when that atom will decay? I say no, thinking as follows. Statistical properties like the half-life can give you definite information in the infinite limit of sample size, i.e. in this case, an infinite number of atoms, or infinite waiting time. I'm not sure right now, but I think that estimate of the probability of the particle decaying in the time interval dt>0 is the best you could do. Of course, you would know that the particle will decay if you wait eternally. Not only that, but you cannot discern the atom's history from your observation. You would have absolutely no idea when that batch of radioisotope was created (Well, only that it was more recent than 1941).
If, on the other hand the atom's nucleus possessed some internal machinery that determined the atom's fate, then ascertaining the values of parameters that govern the machinery's behavior might tell you when the atom will decay, and it might be a possible to learn how long the machinery has been ticking away. But, thanks to Bell and his theorem, we know that such an internal mechanism in a quantum particle cannot exist because that would entail the existence of forbidden "hidden variables".

 

[Mark Harder]

While am am new to this stuff it seems that purely mathematically the Schrodinger equation for a free particle is the same as the Heat equation except with a complex constant coefficient. One would expect that it describes a diffusion process similar to a continuous time Brownian motion. In Feynmann's Lectures on Physics Book 3, he describes how this actually works. The Shrodinger equation for a free particle describes a continuous stochastic process similar to a Markov process except that instead of conditional probabilities, there are conditional complex amplitudes. Much as in Brownian motion one would imagine continuous nowhere differentiable complex valued paths of states though I have not yet worked this out.

Are the paths of molecules truly random, or deterministicly chaotic? I'm trying to think of examples of truly non-deterministic processes other than the quantum-mechanical.

 

[Mark Harder]

There is randomness but its not chaotic randomness. The schrodinger equation always hold. If for one short interval of time dt the particle's wavefunction followed the schrodinger equation, the next interval (dt,2dt) it followed the equation $\psi''+c\psi=0$ and the interval (2dt,3dt) followed the equation $\psi=0$ that would be sort of hardcore (chaotic) randomness.

You bring up what seems to me to be the deepest question in this topic. It seems that when physical processes are deterministically chaotic, probably theory is only a model of something that, though deterministic, is so complex that in practice is practically impossible to calculate. In such cases - like tossing a coin or casting dice, - choosing probability as a model for the process is a kind of "fudging". Here, probability describes non-stochastic systems for which we can have incomplete knowledge only. On the other hand, assigning probabilities to a quantum event is an appropriate description of a truly random process that exists in nature. The physical meaning of stochastic variables is not the same for all cases, in other words.

 

[write4u]

A perfect example of apparent randomness occurs often in weather forecasting. While each molecule in the local system behaves deterministically, there are just too many mathematical forces in play for us to make precise predictions, except in the most general terms such as the probable direction of the storm front.

 

[bhobba]

No, but it is a very logical conclusion. Again, the wavefunction of an electron is not a wave of probabilities for the electron, but the electron's state.

Technical point - it's not the state, but a representation of the state. Again its basic linear algebra.

Thanks
Bill

 

[Grinkle]

For me the conceptual difficulty lies in finding an intuitive mapping of the particle state as represented by the wave equation to one of many possible classical mechanical states that can be represented by position and momentum. Or else I am very confused and am already well past a more basic conceptual difficulty that I didn't notice and am off in never-never land.

My mental picture:
- mapping the wave-state to some specific classical state is the same thing as "collapse"
- this mapping is not at all understood
- there is no way to predict, for a single particle, which of an infinite number of possible specific mechanical states one single well-defined wave state will map to (or collapse to)

The closest I can come to an analogy is to think of a weird guitar string and if I put a finger on a fret, the nature of the guitar string is such that if I pick a fret to produce a certain tone, the volume of that tone will be random. If I time the placement of my finger on a fret such that I can say for sure what the volume will be, the tone will be random. That makes no sense / is a very broken analogy, but it at least shows how far my mind can go in trying to make QM more intuitive.

 

[Nugatory]

If, on the other hand the atom's nucleus possessed some internal machinery that determined the atom's fate, then ascertaining the values of parameters that govern the machinery's behavior might tell you when the atom will decay, and it might be a possible to learn how long the machinery has been ticking away. But, thanks to Bell and his theorem, we know that such an internal mechanism in a quantum particle cannot exist because that would entail the existence of forbidden "hidden variables".

Bell's inequality does not preclude all internal machinery of the type that you're describing. It does preclude any mechanism in which the theory governing the behavior of the hypothetical hidden variables is local (where "local" means that the response of a detector can be predicted using only the value of hidden variables in the past light cone of the detection event).

Thus, Bell's theorem leaves room for deterministic theories (as well as hidden variable theories that are not deterministic) as long as they are non-local.

 

[vanhees71]

In quantum theory a certain kind of states, socalled "pure states", are represented by a vector $|\psi \rangle$ in an infinite-dimensional vector space called Hilbert space. One realization of the Hilbert space is the space of square integrable functions. That refers to the socalled position representation,
$$\psi(\vec{x})=\langle \vec{x}|\psi \rangle.$$
The physical meaning is that
$$P(\vec{\psi})=|\psi(\vec{x})|^2$$
is the probability density for finding the particle, prepared in the state described by this particular square-integrable wave function, at position $\vec{x}$. Square integrable means that the integral over $P(\vec{x})$ exists, and you can normalize it properly,
$$\int_{\mathbb{R}^3} \mathrm{d}^3 \vec{x} P(\vec{x})=1,$$
i.e. the particle is present somewhere in space with certainty.

Now, of course you cannot only measure the position of the particle but also, e.g., its momentum. Then the quantum theoretical formalism tells you that the corresponding momentum-wave function is given as the Fourier transform of the position wave function,
$$\tilde{\psi}(\vec{p})=\left (\frac{1}{2 \pi \hbar} \right)^3 \int_{\mathbb{R}} \mathrm{d}^3 \vec{x} \psi(\vec{x}) \exp \left (-\frac{\mathrm{i} \vec{x} \cdot \vec{p}}{\hbar} \right ).$$
Then the probability distribution for the momentum of the particle is given by
$$\tilde{P}(\vec{p}) = |\tilde{\psi}(\vec{p})|^2.$$
From the math of the Fourier integral it follows that also this probability distribution is properly normalized too.

 

[Chris1983]

Picture a six-sided dice. There are only six possible values when the dice is rolled. If you want to roll a specific value, then if that number is a whole integer with a value in the range of one through 6 you might say the dice gives a random result. The universe is random. If your desired result is not within that range, and the range was determined by another factor, then you might say that the result is predetermined to not give you your desired value. The universe is deterministic.

Do you consider a dice to be random because, in theory, it could return any of a range of values on any given roll? Or is it deterministic because it can only give value from a range that was determined when the dice was first made a cube?

What if you don't need a specific value, just any value within the range available on a dice? Then any roll will always return your desired value. Or the same if your want any value that is not in the dice range.

Deterministic vs random could be seen as a question of how accurate your measurement needs to be; or, they are not mutually exclusive. The universe proceeds along a course determined by its earliest state, but it has an unknowable amount of variation, at random.

Perhaps "god doesn't play dice" just rolls off of the tongue better than "god doesn't make Rube-Goldberg machines."

 

[Mark Harder]

A perfect example of apparent randomness occurs often in weather forecasting. While each molecule in the local system behaves deterministically, there are just too many mathematical forces in play for us to make precise predictions, except in the most general terms such as the probable direction of the storm front.

Yes, the key word being 'apparent'. When considering chaotic systems that are deterministic, random behavior is a model of the true dynamics. Probability theory is applied as if the system is truly random. I still wonder if there if there is a component of molecular dynamics that is truly random. Is heat random? Given a dose of thermal energy, are molecular motions deterministic while thermal energy itself is randomly partitioned among them? In performing computer simulations of molecular motion for example, the software applies to each atom the mean energy specified by statistical dynamics, then let's the simulation run according to the appropriate deterministic differential equations of the atoms to yield their not-quite-predictable behavior. But, in nature, isn't the thermal energy apportioned apparently at random, in which case the initial conditions for those equations should have random components? Obviously, I'm a little confused and the discussion is a little off-topic, having little to do with QM..

 

[Zafa Pi]

The postulates themselves don't imply that randomness is intrinsic: such a conclusion will depend on which interpretation you buy into. For example, in Bohmian mechanics and the many-worlds interpretation the randomness is only apparent: the state of the system always evolves deterministically.

Not true. It depends on the postulates. Copenhagen with collapse has intrinsic randomness with regard to measurements.