I’ve just read Marcus Chown’s outstanding book for people wanting their science served without equations, Quantum Theory Cannot Hurt You. As the title suggests, half the book covers QM and half the book covers relativity. Chown is a regular contributor to New Scientist, and this book reflects his journalistic ease at discussing esoteric topics in physics. He says, right at the beginning, that he brings his own interpretation to these topics but it’s an erudite and well informed one.
No where is Nature’s paradoxical nature more apparent than the constant speed of light, which was predicted by Maxwell’s equations, not empirical evidence. Of course this paradox was resolved by Einstein’s theories of relativity; both of them (the special theory and the general theory). Other paradoxes that seem built into the Universe are not so easily resolved, but I will come to them.
As Chown explicates, the constant speed of light has the same psychological effect as if it was infinite and the Lorentz transformation, which is the mathematical device used to describe relativistic effects, tends to infinity at its limit (the limit being the speed of light). If one could travel at the speed of light, a light beam would appear stationary and time would literally stand still. In fact, this is what Einstein imagined in one of his famous thought experiments that led him to his epiphanic theory.
The paradox is easily demonstrated if one imagines a spacecraft travelling at very high speed, which could be measured as a fraction of the speed of light. This craft transmits a laser both in front of it and behind it. Intuition tells us that someone ahead of the craft who is stationary relative to the craft (say on Earth) receives the signal at the speed of light plus the fraction that it is travelling relative to Earth. On the other hand, if the spacecraft was travelling away from Earth at the same relative speed, one would expect to measure the laser as being the speed of light minus the relative speed of the craft. However, contrary to intuition, the speed of light is exactly the same in both cases which is the same as measured by anyone on the spacecraft itself. The paradox is resolved by Einstein’s theory of special relativity that tells us that whilst the speed of light is constant for both observers (one on the spacecraft and one on Earth) their measurements of time and length will not be the same, which is entirely counter-intuitive. This is not only revealed in the mathematics but has been demonstrated by comparing clocks in real spacecraft compared to Earth. In fact, the Sat-Nav you use in your car or on your phone, takes relativistic effects into account to give you the accuracy you’ve become acquainted with.
However, there are other paradoxes associated with relativity that have not been resolved, including time itself. Chown touches on this and so did I, not so long ago, in a post titled, What is now? According to relativity, there is no objective now, and Chown goes so far as to say: ‘”now” is a fictitious concept’ (quotation marks in the original). He quotes Einstein: “For us physicists, the distinction between past, present and future is only an Illusion.” And Chown calls it ‘one of [Nature’s] great unsolved mysteries.’
Reading this, one may consider that Nature’s paradoxes are simply a consequence of the contradiction between our subjective perceptions and the reality that physics reveals. However, there are paradoxes within the physics itself. For example, we give an age to the Universe which does suggest that there is a universal “now”, and quantum entanglement (which Chown discusses separately) implies that simultaneity can occur over any distance in the Universe.
Quantum mechanics, of course, is so paradoxical that no one can agree on what it really means. Do we live in a multiverse, where every possibility predicted mathematically by QM exists, of which we experience only one? Or do things only exist when they are ‘observed’? Or is there a ‘hidden reality’ which the so-called real ‘classical’ world interacts with? I discussed this quite recently, so I will keep this discussion brief. If there is a multiverse (which many claim is the only ‘logical’ explanation) then they interfere with each other (as Chown points out) and some even cancel each other out completely, for every single quantum event. But another paradox, which goes to the heart of modern physics, is that quantum theory and Einstein’s general theory of relativity cannot be reconciled in their current forms. As Chown points out, String Theory is seen as the best bet but it requires 10 dimensions of which all but 3 cannot be detected with current technology.
Now I’m going to talk about something completely different, which everyone experiences, but which is also a paradox when analysed scientifically. I’m referring to free will, and like many of the topics I’ve touched on above, I discussed this recently as well. The latest issue of Philosophy Now (Issue 112, February / March 2016) has ‘Free Will’ as its theme. There is a very good editorial by Grant Bartley who discusses on one page all the various schools of thought on this issue. He makes the point, that I’ve made many times myself: ‘Why would consciousness evolve if it didn’t do anything?’ He also makes this statement: ‘So if there is free will, then there must be some way for a mind to direct the state of its brain.’ However, all the science tells us that the ‘mind’ is completely dependent on the ‘state of its brain’ so the reverse effect must be an illusion.
This interpretation would be consistent with the notion I mooted earlier that paradoxes are simply the consequence of our subjective experience contradicting the physical reality. However, as I pointed out in my above-referenced post, there are examples of the mind affecting states of the brain. In New Scientist (13 February 2016) Anil Ananthaswamy reviews Eliezer Sternberg’s Neurologic: The brain’s hidden rationale behind our irrational behaviour (which I haven’t read). According to Ananthaswamy, Sternberg discusses in depth the roles of the conscious and subconscious and concludes that the unconscious ‘can get things wrong’. He then asks the question: ‘Can the conscious right some of these wrongs? Can it influence the unconscious? Yes, says Sternberg.’ He gives the example of British athlete, Steve Backley ‘imagining the perfect [javelin] throw over and over again’ even though a sprained ankle stopped him from practicing, and he won Silver in the 1996 Atlanta Olympics.
My point is that paradoxes are a regular feature of the Universe at many levels, from quantum mechanics to time to consciousness. In fact, consciousness is arguably the least understood phenomenon in the entire Universe, yet, without it, the Universe’s existence would be truly meaningless. Consciousness is subjectivity incarnate yet we attempt to explain it with complete objectivity. Does that make it a paradox or an illusion?
Addendum: Since writing this post, I came across this video of John Searle discussing the paradox of free will. He introduces the subject by saying that no progress has been made on this topic in the last 100 years. Unlike my argument, he discusses the apparent contradiction between free will and cause and effect.