Theories of Hidden Variables
- Noah Heywood
- Feb 24
- 4 min read
Updated: Feb 26
According to Einstein, Podolsky, and Rosen, Relativity is the be-all and end-all for Physics. But why can relativity break in the Copenhagen interpretation? Step into the world of Hidden Variables, which solves this problem, somewhat...
When Quantum Mechanics emerged, Albert Einstein naturally had many issues. Being influential for his intuition and infamous for his disdain for mathematics, he saw an issue with the nature of entanglement.
When a particle becomes entangled with another, variables that usually describe each individual particle's state become correlated with the other. As you consider both particles in this system at once, you will notice that one particle's state cannot be calculated without knowledge of the other particle's state.
What does that all mean?
The principle behind this is exactly the same as why you can't factorise certain variables in algebra.
If you consider the scenario of finding the volume of Richard Feynman's Bongos, you want to focus on the larger part, the 'hembra', H, and the smaller 'macho', M.
By letting each part be defined in their volume exclusively by the height of the drum, y(H), and y(M), and the width of the respective calfskins (H and M), you can construct the volume in an assortment of ways, depending on what you know about the dimensions at the time (let's say you forgot a ruler or haven't yet measured the width of one of the parts, happens to the best of us.)
For some unknown reason, the manufacturer finds this equation for the volume of the drum to be true.
V = ( H x y(M) ) + ( M x y(H) )
where each part sums to the overall volume of the bongos.
Since you cannot regroup terms in this equation to become only in terms of variables that only describe one side of the drum, Feynman would tell you that each part of the bongo is entangled with the other - thus, measuring the width of the 'hembra 'calfskin can tell us more information about the height of the 'macho', when considering what the volume of the bongos are.
Fundamentally, unlike the equation:
V = ( H x y(H) ) + ( M x y(M) )
We cannot know everything about the volume of just one of the bongos in the first case without knowing about both parts of the bongos.
So what was Einstein's issue?
This was more subtle - something you might have noticed from the above is that when two objects become entangled, if you measure all of the dimensions of one part of the bongo, and you know the volume of the set of bongos, you can make certain predictions about the dimensions of the other set, such as not setting the height of the 'hembra' too high that the overall volume itself exceeds the V that you already know.
This mechanism seems to imply that as soon as you measure the dimensions of one bongo, you instantly have some knowledge of the dimensions of the other, even if one part of the bongo is on the other end of the universe!
This violates Einstein's theory of relativity by allowing the transfer of information to occur faster than the speed of light, which remains the speed limit of all real things in the universe. The resulting measurement of the size of the 'macho' is therefore sending a signal back in time to inform the measurement of the 'hembra', on the other side of the universe.
Time travelling bongos aside, David Bohm thinks something else is at play here - something that predicts the state of each bongo before the dimensions of one bongo get measured - these are the hidden variables - terms in equations that predict what H, M, y(h) and y(M) are before they get measured, so that nothing needs to be sent back in time - the only trouble now is whether we can find such variables...
In philosophy, this theory would be considered limited in its applications for many reasons.
First of all, the theory has few practical applications - it is unlikely that the world will flock towards theories of hidden variables, as there aren't very many practical applications yet. In philosophy, we would say this theory has not produced a paradigm shift - an idea which was applied to physics by Thomas Kuhn.
Furthermore, this theory is difficult to falsify exactly because we cannot directly measure the variables; this would disappoint the philosopher Karl Popper, who says that the best theories of science can be proven wrong but are not.
Are theories of Hidden Variables helpful?
Yes - they can accurately describe the whole universe
Yes - so long as we can eventually measure them!
No - QM is complete, we just need to understand it
No - If we can't measure it, its not useful to physics
Our recommendations in the world of Hidden Variable Theory:
Check out Veritasium's amazing explainer, with more on probability-testing experiments with and without hidden variables
This video by 'Domain of Science' explains more about the nature of locality, including why only Bohm's non-local theory remains viable in modern quantum mechanics
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