Q: Do physicists really believe in true randomness?

Physicist: With very few exceptions, yes.  What we normally call “random” is not truly random, but only appears so.  The randomness is a reflection of our ignorance about the thing being observed, rather than something inherent to it.

For example: If you know everything about a craps table, and everything about the dice being thrown, and everything about the air around the table, then you will be able to predict the outcome.

Not actually random.

Not actually random.

If, on the other hand, you try to predict something like the moment that a radioactive atom will radioact, then you’ll find yourself at the corner of Poo Creek and No.  Einstein and many others believed that the randomness of things like radioactive decay, photons going through polarizers, and other bizarre quantum effects could be explained and predicted if only we knew the “hidden variables” involved.  Not surprisingly, this became known as “hidden variable theory”, and it turns out to be wrong.

If outcomes can be determined (by hidden variables or whatever), then any experiment will have a result.  More importantly, any experiment will have a result whether or not you choose to do that experiment, because the result is written into the hidden variables before the experiment is even done.  Like the dice, if you know all the variables in advance, then you don’t need to do the experiment (roll the dice, turn on the accelerator, etc.).  The idea that every experiment has an outcome, regardless of whether or not you choose to do that experiment is called “the reality assumption”, and it should make a lot of sense.  If you flip a coin, but don’t look at it, then it’ll land either heads or tails (this is an unobserved result) and it doesn’t make any difference if you look at it or not.  In this case the hidden variable is “heads” or “tails”, and it’s only hidden because you haven’t looked at it.

It took a while, but hidden variable theory was eventually disproved by John Bell, who showed that there are lots of experiments that cannot have unmeasured results.  Thus the results cannot be determined ahead of time, so there are no hidden variables, and the results are truly random.  That is, if it is physically and mathematically impossible to predict the results, then the results are truly, fundamentally random.


What follows is answer gravy: a description of one of the experiments that demonstrates Bell’s inequality and shows that the reality assumption is false.  If you’re already satisfied that true randomness exists, then there’s no reason to read on.  Here’s the experiment:

The set up: A photon is fired at a down-converter, which converts it into two entangled photons.  These photons then go through polarizers that are set at two different angles.  Finally, photo-detectors measure whether a photon passes through their polarizer or not.

The set up: A photon is fired at a down-converter, which converts it into two entangled photons. These photons then go through polarizers that are set at two different angles. Finally, photo-detectors measure whether a photon passes through their polarizer or not.

1) Generate a pair of entangled photons (you can do this with a down converter, which splits one photon into an entangled pair of photons).

2) Fire them at two polarizers.

3) Randomly change the angle of the polarizers after the photons are emitted.  This prevents information about one measurement to affect the other, since that would require that the information travels faster than light.

4) Measure both photons (do they go through the polarizers (1) or not (0)?) and record the results.

The amazing thing about entangled photons is that they always give the same result when you measure them at the same angle.  Entangled particles are in fact in a single state shared between the two particles.  So by making a measurement with the polarizers at different angles we can measure what one photon would do at two different angles.

It has been experimentally verified that if the polarizers are set at angles \theta and \phi, then the chance that the measurements are the same is: C(\theta, \phi) = \cos^2{(\theta-\phi)}.  This is only true for entangled photons.  If they are not entangled, then C = .5 = 50\%, since the results are random.  Now, notice that if C(a,b) = x and C(b,c) = y, then C(a,c) \ge x+y-1.  This is because:

\begin{array}{l}P(a=c)\\= P(a=b \cap b=c) + P(a \ne b \cap b \ne c)\\\ge P(a=b \cap b=c)\\= P(a=b) + P(b=c) - P(a=b \cup b=c)\\\ge P(a=b) + P(b=c) - 1\end{array}

We can do two experiments at 0°, 22.5°, 45°, 67.5°, and 90°.  The reality assumption says that the results of all of these experiments exist, but unfortunately we can only do two at a time.  So C(0°, 22.5°) = C(22.5°, 45°) = C(45°, 67.5°) = C(67.5°, 90°) = cos2(22.5°) = 0.85.  Now based only on this, and the reality assumption, we know that if we were to do all of these experiments (instead of only two) then:

C(0°, 22.5°) = 0.85

C(0°, 45°) ≥ C(0°, 22.5°) + C(22.5°, 45°) -1 = 0.70

C(0°, 67.5°) ≥ C(0°, 45°) + C(45°, 67.5°) -1 = 0.55

C(0°, 90°) ≥ C(0°, 67.5°) + C(67.5°, 90°) – 1 = 0.40

That is, if we could hypothetically do all of the experiments at the same time we would find that the measurement at 0° and the measurement at 90° are the same at least 40% of the time.  However, we find that C(0°, 90°) = cos2(90°) = 0 (they never give the same result).

Therefore, the result of an experiment only exists if the experiment is actually done.

Therefore, you can’t predict the result of the experiment before it’s done.

Therefore, true randomness exists.

As an aside, it turns out that the absolute randomness comes from the fact that every result of every interaction is expressed in parallel universes (you can’t predict two or more mutually exclusive, yet simultaneous results).  “Parallel universes” are not nearly as exciting as they sound.  Things are defined to be in different universes if they can’t coexist or interact.  For example: in the double slit experiment a single photon goes through two slits.  These two versions of the same photon exist in different universes from their own points of view (since they are mutually exclusive), but they are in the same universe from our perspective (since we can’t tell which slit they went through, and probably don’t care).  Don’t worry about it too much all at once.  You gotta pace your swearing.

As another aside, Bell’s Inequality only proves that the reality assumption and locality (nothing can travel faster then light) can’t both be true.  However, locality (and relativity) work perfectly, and there are almost no physicists who are willing to give it up.

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59 Responses to Q: Do physicists really believe in true randomness?

  1. Sean says:

    “Randomly change the angle of the polarizers after the photons are emitted.”

    This statement assumes randomness already exists in the brain of the tester and the seemingly unmeasurable variables in the rest of the universe. You can not prove nor disprove a statement without assuming your result proving randomness doesn’t exist with implying randomness already exists.

    It’s like describing the colour blue to a person that has never seen before. They may believe they understand the colour based on what the can visualise and they are not incorrect.

    I believe that there is randomness from the human perception of results, however as the human viewing the results is limited in their ability to measure the variables without impacting the variables. Thus there would be no true way to prove randomness in anything but concept. If you are unable to prove the concept to be adaptable to real world experiments then you would fundamentally be saying it’s possible if it exists already. So something is true if it’s already assumed to be true but false if it’s already assumed to be false.

    This was a very enjoyable read though, thank you for your time.

  2. Pingback: Thoughts on free will, predeterminism, and quantum mechanics. | Brandon James - Fictions

  3. Alan says:

    @Sean

    I totally missed the “Randomly change the angle” part…

    You’re right… definitely an assumption there. I’m a programmer and have tried and tried to create true randomness from binary logic and cannot do it, so I’m inclined to say that it doesn’t exist. Perhaps I’m wrong in my own assumption but I died a little bit after reading this article until I read your comment. Thanks : )

  4. David says:

    You have to get down to the quantum level. If you created bits based on quantum uncertainty then you would have what you are looking for.

  5. GregR says:

    Therefore, you can’t predict the result of the experiment before it’s done.
    Therefore, true randomness exists.

    Im troubled by this. If the results of flipping a perfect but weighted coin are random how do you explain that the result would fail a frequency when the results would be prejudiced by the added weight.

    I’m just confused about the idea of supposedly random numbers that contain a biased outcome.

  6. Chris says:

    “Therefore, you can’t predict the result of the experiment before it’s done.
    Therefore, true randomness exists.”

    Lack of predictability based on our current methods/intelligence/perspective can’t really give a definitive answer about randomness, we may not even be able to comprehend how everything works but that doesn’t conclude it therefore MUST be random.

    Have we technically proven that there are things that exist outside of cause/effect or been able to perform an identical experiment and get different results?
    (though I’m assuming we can never truly repeat any experiment unless we exist outside of time since the environment/conditions would be different, however minimal that difference may be)

  7. Sean Dolan says:

    I agree with Chris’ point. I think the biggest problem we face here is that the debate has included 2 questions. There is a big difference in being able to prove true randomness and perceived randomness. If you define randomness as something that can not be predicted by humans – then yes, randomness must exist. If you choose not to undertake study of circumstances then you will not know the result before the experiment has completed.

    The other argument is if true randomness exists outside the realms of probability and predictability. Can an experiment that always produces a colour of red or blue as a result, ever produce a new colour just for no reason or rationality. Again, if you classify it by human perception then yes, if you stand at a different angle or “change your perspective/environment” then maybe you will SEE a different result – well that must be random.

    The way I try and describe my thoughts on the matter to others is by taking a spec of dirt on the ground. If I knew every single force, decay, gravity, wind, water effect that has played a part on that spec of dirt – could I work out where it came from or which piece of rock it came from. I believe the answer is yes – but with a “but”. But it’s impossible for me to work all that out.. that doesn’t make me think it’s placement on the pavement next to me is random – just that I can’t perceive or even imagine the forces I would need to know to work out how it got there. I believe the rules of the universe are very specific and seem to return the same results time and time again.

  8. Greg Robert says:

    This discussion is a bit deep for me but …
    Predictability vs. randomness. I have one million dyed ping pong balls. They are all blue except for just one that is yellow.

    If I reach in and “randomly” choose a ball it will always be blue (the yellow one is discarded as experimental error or disregarded as an outlier).

    Please explain to me the nature of randomness and predictability in this scenario.

    For extraccredit please distinguish between random, uncaused, and free will.

  9. Bumble says:

    Nice that you tried to answer the question, but the answer is bogus.

    This experiment fails to prove that all effecting variables are measured.

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