Quantum mechanics, entanglement, gravity and time

I wrote a post on Louisa Gilder’s well researched book, The Age of Entanglement, 10 years ago, when I acquired it (copyright 2008). I started rereading it after someone on Quora, with more knowledge than me, challenged the veracity of Bell’s theorem, also known as Bell’s Inequality, which really changed our perception of quantum phenomena at its foundations. Gilder’s book is really all about Bell’s theorem and its consequences, whilst covering the history of quantum mechanics over most of the 20^th Century, from Bohr through to Feynman and beyond.

Gilder is not a physicist, from what I can tell, yet the book is very well researched with copious notes and references, and she garnered accolades from science publications as well as literary reviewers. Her exposition on Bell’s theorem is technically correct to the best of my knowledge, which she provides very early in the book. 

She goes to some length to explain that the resolution of Bell’s theorem is not the obvious intuitive answer that entangled particles are like a pair of shoes separated in space and time, so that if you find the right-handed shoe you automatically know that the other one must be left-handed. This is what my interlocutor on Quora was effectively claiming. No, according to Gilder, and everything else I’ve read on this subject, Bell’s theorem is akin to finding too many coincidences than one would expect to find by chance. The inequality means that if results are found on one side of the inequality then the intuitive scenario is correct, and if they are on the other side, then the QM world obeys rules not found in classical physics.

The result is called ‘non-local’, which is the opposite of ‘local’, a term with a specific meaning in QM. Local means that objects are only affected by ‘signals’ that travel at the speed of light. Non-local means that objects show a connectivity that is not dependent on lightspeed communication or linkage.

It was Schrodinger who coined the term ‘entanglement’, claiming that it was the defining characteristic of QM.

I would not call that ‘one’ but rather ‘the’ characteristic trait of quantum mechanics. The one that enforces its entire departure from classical lines of thought.

I’ve also recently read an e-book called An Intuitive Approach to Quantum Field Theory by Toni Semantana (only available in e-book, 2019), so it’s very recent. It’s very good in that Semantana obviously knows what he’s talking about, but, even though it has minimum mathematical formulae, it’s not easy to follow. Nevertheless, he covers esoteric topics like the Higgs field, gauge theories, Noether’s theorem (very erudite) and Feynman diagrams. It made me realise how little I know. It’s relevance to this topic is that he doesn’t discuss entanglement at all.

Back to Gilder, and it’s obvious that you can’t discuss entanglement and locality (or non-locality) without talking about time. If I can digress, someone else on Quora provided a link to an essay by J.C.N. Smith called Time – Illusion and Reality. Smith said you won’t find a definition of time that doesn’t include clocks or things that move. In fact, I’ve come across a few people who claim that, without motion, time has no reality. 

However, I have a definition that involves light. Basically, time is the separation between events as measured by light. This stems from the startling yet obvious fact, that if lightspeed was not finite (instantaneous) then everything would happen at once. And, because lightspeed is the same for all observers, it determines the time difference between events, even though the time measured may differ for different observers, as per Einstein’s special theory of relativity. (Spacetime between events for all observers is the same.)

When I was in primary school at the impressionable age of 10 or 11, I was introduced to relativity theory, without being told that is what it was. Nevertheless, it had such an impact on my still-developing brain that I’ve never forgotten it. I can’t remember the context, but the teacher (Mr Hinton) told us that if you travel fast enough clocks will slow down and so will your heart. I distinctly remember trying to mentally grasp the concept and I found that I could if time was a dimension and as you sped up the seconds, or whatever time was measured in, they became more frequent between each heartbeat, so, by comparison, your heart slowed down. One of the other students made the comment that ‘if a plane could fly fast enough it would come back to land before it took off’. I’m unsure if that was a product of his imagination or if he’d come across it somewhere else, which was the impression he gave at the time. Then, thinking aloud, I said, It’s impossible to go faster than time, as if time and speed were interdependent. And someone near me turned, in a light-bulb moment, and said, You’re right.

My attempt at conceptually grasping the concept was flawed but my comment was prescient. You can’t travel faster than time because you can’t travel faster than light. For a photon of light, time is zero. The link between time and light is an intrinsic feature of the Universe, and was a major revelation of Einstein’s theory of relativity.

J.C.N. Smith argues in his essay that we have the wrong definition of time by referring to local events like the rotation of the planet or its orbit about the sun, or, even more locally, the motions of a pendulum or an atomic clock. He argues that the definition of time should be the configuration of the entire universe, because at any point in time it has a unique configuration, and, even though we can’t observe it completely, it must exist. 

There is a serious problem with this because every observer of that configuration would see something completely different, even without relativistic effects. If you take the Magellanic Clouds, which you can see in the southern hemisphere with the naked eye on a cloudless, moonless night, you are looking 150,000 to 190,000 years into the past (there are 2 of them), which is roughly when homo sapiens emerged from Africa. So an observer on a world in the Magellanic Clouds, looking at the Milky Way galaxy, would see us 150,000 to 190,000 years in the past. In other words, no observer in the Universe could possibly see the same thing at the same time if they are far enough apart.

However, Smith is right in the sense that the age of the Universe infers that there is a universal ‘now’, which is the edge of the Big Bang (because it’s still in progress). The Cosmic Microwave Background Radiation is the earliest light we can see (from 380,000 years after the Big Bang) yet our observation of it is part of our ‘now’.

This has implications for entanglement if it’s non-local. If Freeman Dyson is correct that QM describes the future and classical physics describes the past, then the collapse or decoherence of the wave function represents ‘now’. So ‘now’ for an observer is when a photon hits your retina and you immediately see into the past, whether the photon is part of a reflection in a mirror or it comes from the Cosmic Background Radiation. It’s also the point when an entangled quantum particle (which could be a photon or something else) ‘fixes’ the outcome of its entangled partner wherever in the Universe it may be.

If entangled particles are in the future until one of them is observed then they infer a universal now. Or does it mean that it creates a link back in time across the Universe? 

John Wheeler believed that there was a possibility of a connection between an observer and the distant past across the Universe, but he wasn’t thinking of entanglement. He proposed a thought experiment involving the famous double-slit experiment, whereby one makes an observation after the particle (electron or photon) has passed through the slit but before it hits the target (where we observe the outcome). He predicted that this would change the pattern from a wave going through both slits to a particle going through one. He was later vindicated (after his death). Wheeler argued that this would imply that there is a ‘backwards-in-time’ signal or acausal connection to the source. He argued that this could equally apply to photons from a distant quasar, gravitationally lensed by an intervening galaxy.

Wheeler’s thought experiment makes sense if the wave function of the particle exists in the future until it is detected, meaning before it interacts with a classical physics object. Entanglement also becomes ‘known’ after one of the entangled particles interacts with a classical physics object. Signals into the so-called past are not so mysterious if everything is happening in the future of the ‘observer’. Even microwaves from the Cosmic Background Radiation exist in our future until we ‘detect’ them.

Einstein’s special theory of relativity tells us that simultaneity can’t be determined, which seems to contradict the non-locality of entanglement according to Bell’s theorem. According to Einstein, ‘now’ is subjective, dependent on the observer’s frame of reference. This implies that someone’s future could be another person’s past, but this has implications for causality. No matter where an observer is in the Universe, everywhere they look is in their past. Now, as I explained earlier, their past maybe different to your past but, because all observations are dependent on electromagnetic radiation, everything they ‘see’ has already happened.

The exception is the event horizon of a black hole. According to Viktor T Toth (a regular contributor to Quora), the event horizon is always in your future. This creates a paradox, because it is believed you could cross an event horizon without knowing it. On the other hand, an external observer would see you frozen in time. Kip Thorne argues there is no matter in a black hole, only warped spacetime. Most significantly, once you pass the event horizon, space effectively becomes uni-directional like time – you can’t go backwards the way you came.

As Toth has pointed out a number of times, Einstein’s theory of gravity (the general theory of relativity) is mathematically a geometrical theory. Toth also points out that We can do quantum field theory just fine on the curved spacetime background of general relativity. Another contributor, Terry Bollinger, explains why general relativity is not quantum:

GR is a purely geometric theory, which in turn means that the gravity force that it describes is also specified purely in terms of geometry. There are no particles in gravity itself, and in fact nothing even slightly quantum.

In effect, Bollinger argues that quantum phenomena ‘sit’ on top of general relativity. I contend that gravity ultimately determines the rate of time, and QM uses a ‘clock’ that exists outside of Hilbert space where QM ‘sits’ (according to Roger Penrose, as well as Anil Ananthaswamy, who writes for New Scientist). 

So what happens inside a black hole, which requires a theory of quantum gravity? As Freeman Dyson observed, no one can get inside a black hole to report or perform an experiment. But, if it’s always in one’s future, then maybe quantum gravity has no time. John Wheeler and Bryce de-Witt famously attempted to formulate Einstein’s theory of general relativity (gravity) in the same form as electromagnetism, and time (denoted as t) simply disappeared. And as Paul Davies pointed out in The Goldilocks Enigma, in quantum cosmology (as per the Wheeler de-Witt equation), time vanishes. But, if quantum cosmology is attempting to describe the future, then maybe one should expect time to disappear.

Another thought experiment: if you take an entangled particle to the other side of the visible universe (which would take something like the age of the Universe) and then they instantly ‘link’ or ‘connect’ non-locally, it still requires less than lightspeed to separate them. So you won’t achieve instantaneous transmission, even in principle, because you have to wait until its entangled ‘partner’ arrives at its destination. Or, as explained in the video below, the 'correlation' can only be checked in classical physics.

Addendum: This is the best explanation of QM entanglement and Bell's Theorem (for laypeople) that I've seen: