# B Does quantum physics imply the existence of randomness?

1. Jun 2, 2016

### 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 physic 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 physic 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?

2. Jun 2, 2016

### Orodruin

Staff Emeritus
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.

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.

3. Jun 2, 2016

### 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).

4. Jun 2, 2016

### 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.

5. Jun 2, 2016

### raphalbatros

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

6. Jun 2, 2016

### Khashishi

You can't measure anything without the second part.

7. Jun 2, 2016

### 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).

8. Jun 2, 2016

### 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?

9. Jun 2, 2016

### 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

10. Jun 3, 2016

### raphalbatros

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?

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

ebos and bhobba

11. Jun 3, 2016

### Isaac0427

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.

12. Jun 4, 2016

### raphalbatros

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 ?

13. Jun 4, 2016

### bhobba

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

14. Jun 4, 2016

### atyy

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.

15. Jun 4, 2016

### Isaac0427

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.

16. Jun 4, 2016

### 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.

Last edited: Jun 4, 2016
17. Jun 4, 2016

### 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.

18. Jun 7, 2016

### raphalbatros

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

19. Jun 7, 2016

### haushofer

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

20. Jun 7, 2016

### 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.