Einstein’s Aesthetic Palette
When I read about Albert Einstein and his ideas, I get the distinct impression that his physics emanated from a deep personal philosophy. What I mean is that his ideas appear to be greatly moulded by a set of ‘aesthetic guidelines’ which he envisioned the world and physical systems to adhere to. Of course, to COMPLETELY pigeonhole the approach of this genius, and reduce his method to a simplistic algorithm would be outrageously presumptuous and erroneous on my part, but it is safe to state that personal philosophy played some role, at the very least in determining the distinct palette of ideas Einstein introduced.
This historical context is necessary to grasp the origin of the EPR paradox. The EPR paradox is an astute critique of the general sort of weird thinking pervasive in quantum mechanics. Now Einstein’s ideas and beliefs are rooted in the concept of an objective reality; a reality that sits there and continues existing, regardless of an observer taking note of it or not.
Let’s take an example. The car keys which you casually fling onto the sofa will continue to STAY there, regardless of whether you anxiously recheck their location every two seconds or forget all about them, as you start watching your favourite sitcom. This excludes any horseplay consisting of someone moving the keys to a new location. It seems fairly obvious.
Einstein’s conventional belief in an objective reality is fed by intuition and common experience as well as by the spirit of classical physics. In classical physics, if a measurement of the position of a body yields an answer of say, 30 meters to the right of the congenial minotaur with a red hat, then that means that moments BEFORE our measurement, the body was indeed 30 meters to the right of the congenial minotaur with a red hat! (Though the semantics may vary, perhaps the body is in a state of relentless motion, and therefore, the moment you choose must be close enough to the moment of measurement for this interpretation to be intelligible).
It is all clearly laid out in a logical self-evident manner, except that quantum mechanics brazenly ignores any such notions.
Arthur Dent in a Quantum World
In constructing a portfolio for quantum mechanics, the phrase ‘probabilistic theory’ must be used repeatedly and in capitals. Classical physics, Newton’s physics, the physics you did in high school IS NOT probabilistic. It’s deterministic. If the clouds are at such a height, if the value with which earth’s gravity tugs at rainddrops is such, and the value of air resistance is this, then the speed of a single raindrop can be determined, as well as the force it imparts as it splatters on Arthur Dent’s face.
In the deterministic theory, everything is accounted for (from start to finish). If you have all the data and an adequate knowledge of physics, every future prediction is a matter of simple calculation: you take the initial conditions plug them into an equation and readily obtain answers.
Quantum Mechanics is another story. It was invented to understand the behaviour of microscopic particles (which we can’t see) and therefore operates in ways inaccessible to common intuition. Quantum Mechanics employs a mathematical construct called the wave function which charts information about a chosen ‘system’ (be it a system consisting of a single particle; a system consisting of many particles; a system consisting of many simpler systems).
If you were to try to examine the wavefunction in an attempt to deduce the position of a lone electron, then under no circumstance would the wavefunction ever respond with the words ’30 meters to the right of the congenial minotaur with a red hat’.
This is because the wavefunction only yields probabilities not definite answers. You’d only obtain a list of POSSIBLE locations where this electrons could be present. The wave function would probably say something like this: “there’s a 30% chance that the electron is to the right of the centaur, but there’s an even greater probability of 45% that it’s lying on the sofa, right where you left it (other places too might have lower but non zero probabilities).”
And that is what is meant by calling quantum mechanics ‘probabilistic’.
The Wave Function
The wave function takes the form of a curve (or distribution) which rises and dips at different points indicating how high or low the probability of finding the electron is at that point. But that’s simply accounting work we’re doing here. The wave function can give us clues, but finally we must find the exact location of the electron via grit, determination and the help of practical experiment. Bring along a microscope, a sensor or any other appropriate apparatus and go about electron hunting. Maybe you find this lone electron (surprisingly) on Arthur Dent’s towel.
Inform accounts to update records.
This information is conveyed to the wave function which is carrying all data related to this electron in a very specific way. The mathematical formalism asserts that whenever a measurement is made regarding a property of a system, the wavefunction related to that system is said to ‘collapse’. No longer is the wave function an agreeable curve which gracefully rises and dips at different points. Now it sharply peaks at one single value: the value you experimentally obtained. It hugs the zero level everywhere else. The wavefunction has ‘collapsed’ (aka peaked) at x = Arthur Dent’s towel; x being the position.
Getting back Einstein and his thoughts, he found the notion of a probabilistic science inelegant. Classical physics too uses probabilities in many places, where our moment to moment knowledge of a system’s various components may be inadequate for us to make deterministic forecasts (statistical mechanics for instance does so). But Einstein’s objection with Quantum Mechanics’ tailored used of probability goes deeper. Ask yourself, what exactly was the position of this electron just moments before you located it using your apparatus and made a measurement (the result of which we found to be ‘on the towel’).
If you think the electron had to be on the towel and continued being on it as the survellience of lab equipment caught up and finally captured its location, then you’re siding with Einstein. That’s great company to have but I’m going to escalate here. By siding with Einstein, you buy into the notion that, in those particular instants, the electron was on the towel regardless of whether you anxiously checked for it or conveniently forget about it as your favourite sitcom came on.
That is, you believe in objective reality. You believe that reality just sits there and continues existing regardless of whether there’s an observer there to take note of it or not. This is in spirit similar to the following sentence: “You believe that properties and statements of facts about the world (which ultimately constitute reality) make sense to talk about even when there’s no one doing the talking (or the measuring).”
Quantum Mechanics asserts there’s no sense in talking about position of an electron before a measurement is made. It asserts that there’s no sense in talking about properties of things in general before measurements (measuring those properties) are made. This unwillingness to do so is due to another quantum mechanical fixture- superposition. Superposition is a questionable state of existence. The electron is said exist everywhere and nowhere before a measurement is made pertaining to its position.
Roughly, what the mathematics tells us is that the position of an electron before measurement is a linear combination of all possible position state vectors available to it. What this mathematical truth translates into, when parsed through the engine of common language, is a couple of related statements.
First, you could say that pre-measurement the electron exists simultaneously on the towel, on the sofa, to the right and left of the centaur (who has lost his congeniality) and in a couple other places you could think of. You could also go and state that position itself isn’t a very well defined quantity before measurement. Therefore it is meaningless to talk about the electron’s position before measurement. Physicists go to great lengths to stress this point, and many such arguments involve the invocation of zen-koan like statements.
For example: if we are to evaluate the honesty of ‘XYZ’, and at the last minute I tell you that ‘XYZ’ is a placeholder term for the number 5, then would you be in the right frame of mind to answer my question intelligibly?
No. Because the question doesn’t make any sense. Similarly the electron’s state before measurement renders itself meaningless to ask a question regarding position.
Bohr & the Copenhagen Interpretation
Bohr was the originator of this style of thinking, known as the Copenhagen Interpretation of Quantum Mechanics. This was about the concept of ‘potentialities’ as being the only things that tangibly exist before measurement. The electron exhibits a plethora of unrealized potentialities- places it COULD be present, the viability of each location tied in with the probability it yields when you check with accounting. Remember our old friend the wavefunction and the probabilities it stores?
When you finally take the leap and measure a property of a system (in our case an electron’s position) then the wave function collapses, the long-going charade of superposition instantaneously vanishes as position suddenly becomes a well defined, meaningful quantity to talk about. The electron RANDOMLY chooses a position (a single point in space) to inhabit, and our reality for a moment aligns with common experience and intuition.
This quantum mechanical perspective changes the perceived nature of a physicist’s job from a passive, objective observer to a kind of participatory reveller who actively impinges on the very fabric of things she’s supposed to be quietly measuring. Einstein thought this was unacceptable.
Now quantum mechanics has one last quirk we must speak about. It limits the amount of credible information we can obtain on each outing of ‘electron hunting’. This is known as indeterminancy or complementarity and underpins a fuxture of QM which has received unusually great coverage in popular culture – Heisenberg’s Uncertainty Principle.
Heisenberg’s Uncertainty Principle
Heisenberg’s Uncertainty Principle states that there are pairs of properties of any system which are at constant loggerheads with each other. When we ‘interrogate’ the electron by means of an experiment to obtain valuable information about its position, we are simultaneously making ourselves more and more doubtful about its momentum.
If we were to try to rectify that and gather information about the electron’s momentum in a subsequent experiment, then we’d be invalidating the data we’ve gathered previously with respect to the electron’s position. This is because as we measure an electron’s position, its momentum is rendered a meaningless quantity to speak about. As we switch apparatus settings and start measuring the electron’s momentum, its position becomes a meaningless quantity to talk about. It is like using your digital camera to capture a very close and very distant object in a single frame. To know, simultaneously, both quantities: the electron’s accurate position and momentum is impossible. It is like trying to make sure that your camera keeps both the distant as well as the near object in equal focus.
Position and Momentum (and many such similar pairs of quantities) are declared to be ‘incompatible observables’. They limit the amount of knowledge you can gather about at a system at once, which is discouraging, but that’s just how it is and there’s no quarreling with it.
…No escaping the uncertainty…
So to summarize: Quantum Mechanics doesn’t give any definitive answers; it deals in probabilities.
It doesn’t subscribe to a notion of objective reality or what some philosophers of physics call ‘realism’. And finally it stops responding if you ask it too many questions: incompatible observables.
All these were considerations and ideas simply too ‘ugly’ for Einstein’s liking.
They gradually guided him towards devising the EPR Paradox.
Poundforabrown 