People used to say that ‘nature abhors a vacuum’, which is more often than not used metaphorically. Arguably, contradiction avoidance is more fundamental in that you don’t even need a universe for it to be requisite. Many mathematical proofs are premised on the unstated axiom that you can’t have a contradiction - reductio ad absurdum.
However, the study of physics has revealed that nature seems to love paradoxes and the difference between a paradox and a contradiction is often subtle and sometimes inexplicable. So, following that criterion, I believe that reality exists in that sliver of possibility between paradox and contradiction.
Clifford A Pickover, who normally writes about mathematics and physics, wrote an entertaining and provocative book, The Paradox of God and the Science of Omniscience. One of the conclusions that I took from that book is that there are rules of logic that even God can’t break. And one of those rules is the rule of contradiction that something can’t ‘be’ and ‘not be’ at the same time. It turns the argument on its head that God created logic.
It’s obvious to anyone who reads this blog that I’m unceasingly fascinated by science and philosophy, and, in particular, where they meet and possibly crossover. So an unerring criterion for me is that you can’t have a contradiction. My recent exposition on the famous twin paradox demonstrates this. It can only be resolved if one accepts that only one twin experiences time dilation. If they both did, you would arrive at a contradiction, both mathematically and conceptually. Specifically, each twin would perceive the other one as younger, which is impossible.
The opposite to contradiction is consistency, and if you look at the mathematical analysis of the twin paradox, you’ll see it’s consistent throughout for both twins.
To give another example, physicists tell us that time does not flow (as Paul Davies points out in this presentation, 48.30min mark), yet we all experience time ‘flowing’. Davies and I agree that the sensation we have of time ‘flowing’ is a psychological experience; we disagree on how or why that happens.
Time is a dimension determined by the speed of light. Everything is separated, not only spatially, but also in time, because it takes a finite time for light to travel between events separated in space. This leads to the concept of spacetime, which is invariant for different observers, while space and time (independently) can be ‘measured’ to be different for different observers. Spacetime is effectively an extension of Pythagoras’s theorem into 4 dimensions, only it involves negatives.
Δs2 = c2Δt2 - Δx2 - Δy2 - Δz2
So Δs is the ‘interval’ that remains invariant, and cΔt is the time dimension converted into a spatial dimension, otherwise the equation wouldn’t work. But note that it’s c (the constant speed of light) that makes time a dimension, and it’s one of the dimensions of the Universe as a whole. Einstein’s equations work for the entire Universe, which is his greatest legacy.
I’ve been reading Brian Greene’s The Fabric of the Cosmos (2004), which I came across while browsing in a bookshop and bought it on impulse – I’m glad I did. It’s a 500 page book, covering all the relevant topics on cosmology, so it’s very ambitious, but also very readable.
Theories of gravity started with Newton, and he came up with a thought experiment that was still unresolved when Einstein revolutionised his theory. Greene discusses it in some detail. If you take a bucket of water and hang it from a rope, then turn the bucket many times so that the rope is twisted. When you release the rope the bucket spins and the water surface becomes concave in the bucket due to the centrifugal force. The point is, what is the reference frame that the bucket is spinning to? Is it the Universe as a whole? Newton would have argued that it was spinning relative to absolute space.
Now imagine that you could do this experiment in space; only, instead of a bucket of water, you have 2 rocks tied together. You could do it on the space station. As you spin them, you’d expect the rope or cord between them to tension. So again, what are they spinning in reference to? Greene gives a detailed historical account because it involves Mach’s principle. But in the end, when Einstein applied his theories of relativity, he came to the conclusion that they spin relative to spacetime. While we don’t have absolute space and absolute time, we have absolute spacetime, according to Einstein.
Why have I taken so much trouble to describe this? Because there is a frame of reference that is used to determine what direction and what speed our solar system travels in the context of the overall Universe. And it’s the Cosmic Microwave Background Radiation. Paul Davies described this in his book, About Time (1995). By measuring the difference in the Doppler effect (for CMBR) in different regions of the sky, we can deduce we are travelling in the direction of the Pisces constellation. Greene also points this out in his book.
All physicists that I’ve read, or listened to, argue that ‘now’ is totally dependent on the observer. They will tell you that if you move backwards and forwards here on Earth, then the time changes on some far off constellation will be in the order of hundreds of years because of the change in angle of the time slice across that part of the Universe. Greene himself explains this in a video, as well as in his book. But there is an ‘age’ for the Universe, so you have an implicit contradiction. Greene is the only person I’ve read who actually attempts to address this, though not very satisfactorily (for me).
But one doesn’t need to look at far off galaxies, one can look at Einstein’s original thought experiment involving 2 observers: one on a train and one on a platform. The reason physicists argue that there is no objective now is because simultaneity is different according to different observers, and Einstein uses a train as a thought experiment to demonstrate this.
If you have a light source in the centre of a moving carriage then a person in the carriage will observe that it gets to both ends at the same time. But a person on the platform will see that the back of the train will receive the light before the front of the train. However, the light source is moving relative to the observer on the platform, so they will see a Doppler shift in the light showing that it is moving relative to them. I contend that only the observer in the same frame of reference as the light source sees the true simultaneity. In other words, I argue that you can have 'true simultaneity' in the same way as you can have ‘true time’. Also, what many people don’t realise, that different observers not only see simultaneity happening at different times but different locations, as this video demonstrates.
I’m a subscriber to Quora, mainly because I get to read posts by lots of people in various fields, most of whom are more knowledgeable than me. In fact, I claim my only credential is that I read a lot of books by people much smarter than me. One of the regular contributors to Quora is Viktor T Toth, whom I’ve referenced before, and who calls himself a ‘part-time physicist’. Toth knows a lot about cosmology, QFT (quantum field theory) and black holes. He occasionally shows his considerable mathematical abilities in dealing with a question, but most of the time keeps them in reserve. What I like about Toth, is not just his considerable knowledge, but his no-nonsense approach. He doesn’t pretend or bluff; he has no problem admitting what he doesn’t know and is very respectful to his peers, while not tolerating fools.
Toth points out that while 2 observers can experience different durations in time (like the twins in the twin paradox) they agree on the time when they meet again. In other words, there is a time reference (like a space reference) that’s independent of the path they took to get there. As I pointed out in my post explaining relativity based on waves, it’s not only the time duration that 2 observers disagree on, but also the space duration. If someone was able to travel so fast that they could cross the galaxy in years instead of thousands of years, then they would also traverse a much shorter distance (according to them). In other words, not only does time shrink, but so does distance. We don’t tend to think that space can be just as rubbery as time.
And this brings me to a point that Toth and Greene seem to disagree on. Toth is adamant that space is not an entity but just the ‘distance’ between physical objects. Regarding the expanding universe, he says ‘space’ does not ‘stretch’ but it’s just that the ‘distance’ between ‘objects’ increases. Greene would probably disagree. Greene argues that wavelengths of light lengthen as space ‘stretches’.
What do I think? I tend to side with Greene. I think space is an entity because it has dimensions. John Barrow, in his book, The Constants of Nature, gives an excellent account of how a universe that didn’t exist in 3 dimensions would be virtually unworkable. In particular, the inverse square law for gravity, that keeps planets in stable orbits for hundreds of millions of years, would not work in any other dimensional universe.
But also, space can be curved by gravity, or more specifically, spacetime, as Toth readily acknowledges. I’ll return to Toth’s specific commentary on gravity and black holes later.
I’ve already mentioned that Greene discussed the age of the Universe. I recently did an online course provided by New Scientist on The Cosmos, and one of the lecturers was Chris Impey, Distinguished Professor, Department of Astronomy, University of Arizona. He made the point that the Universe has an ‘edge in time’, but not an edge in space. Greene expanded on this, by pointing out that everywhere in the Universe all clocks are ‘in synchronicity’, which contradicts the notion that there is no universal now. I’ll quote Greene directly on this, because it’s an important point. According to Greene (but not only Greene) whether an observer is moving away from a distant stellar object, or towards it, determines whether they would see into that object’s distant past or distant future. Mind you, because they are so far away, the object’s future is still in our past.
Each angled slice intersects the Universe in a range of different epochs and so the slices are far from uniform. This significantly complicates the description of cosmic history, which is why physicists and astronomers generally don’t contemplate such perspectives. Instead, they usually consider only the perspective of observers moving solely with the cosmic flow...
I don’t know the mathematics behind this, but I can think of an analogy that we all observe every day. You know when you walk along a street with the Sun low in the sky, so it seems to be moving with you. It will disappear behind a building then appear on the other side. And of course, another observer in another town will see the Sun in a completely different location with respect to their horizon. Does this mean that the Sun moved thousands of miles while you were walking along? No, of course not. It’s all to do with the angle of projection. In other words, the movement in the sky is an illusion, and we all know this because it happens all the time and it happens in sync with our own movements. I remember once travelling in a car with a passenger and we could see a plane low in the sky through the windscreen. My passenger commented that the plane was travelling really fast, and I pointed out that if we stopped, we’d find that the plane would suddenly slow down to a speed more commensurate with our expectations.
I think the phenomenon that Greene describes is a similar illusion, only we conjure it up mathematically. It makes sense to ignore it, as astronomers do (as he points out) because we don’t really expect it happens in actual fact.
Back in 2016, I wrote a post on a lecture by Allan Adams as part of MIT Open Courseware (8.04, Spring 2013) titled Lecture 6: Time Evolution and the Schrodinger Equation. This was a lecture for physics students, not for a lay audience. I found this very edifying, not least because it became obvious to me, from Adams’ exposition, that you could have a wave function with superposition as described by Schrodinger’s equation or you could have an observed particle (like an electron) but you couldn’t have both. Then I came across the famous quote by William Lawrence Bragg:
Everything that has already happened is particles, everything in the future is waves. The advancing sieve of time coagulates waves into particles at the moment ‘now’.
In that post on Adams’ lecture, I said how people (like Roger Penrose, among others) explained that ‘time’ in the famous time dependent Schrodinger equation exists outside the hypothetical Hilbert space where the wave function hypothetically exists. And it occurred to me that maybe that’s because the wave function exists in the future. And then I came across Freeman Dyson’s lecture and his unorthodox claim:
... the “role of the observer” in quantum mechanics is solely to make the distinction between past and future...
What really happens is that the quantum-mechanical description of an event ceases to be meaningful as the observer changes the point of reference from before the event to after it. We do not need a human observer to make quantum mechanics work. All we need is a point of reference, to separate past from future, to separate what has happened from what may happen, to separate facts from probabilities.
The inherent contradictions in attempting to incorporate classical physics into quantum mechanics (QM) disappear, if one is describing all the possible future paths of an event while the other describes what actually happened.
Viktor Toth, whom I’ve already mentioned, once made the interesting contention that the wave function is just a ‘mathematical construct’ (his words) and he’s not alone. He also argued that the ‘decoherence’ of the wave function is never observed, which infers that it’s already happened. Toth knows a great deal about QFC (and I don’t) but, if I understand him correctly, the field exists all the time and everywhere in spacetime.
Another contributor on Quora, whom I follow, is Mark John Fernee (PhD in physics, University of Queensland), who obviously knows a great deal more than me. He had this to say about ‘wave function collapse’ (or decoherence) which corroborates Toth.
The problem is that there is no means to detect the wavefunction, and consequently no way to detect a collapse. The collapse hypothesis is just an inference that can't be experimentally tested.
And, in a comment, he made this point:
In quantum mechanics, the measurement hypothesis, which includes the collapse of the wave function, is an irreversible process. As we perceive the world through measurements, time will naturally seem irreversible to us.
And I’ve made this exact same point, that we also get the ‘irreversibility’ or asymmetry between past and future, from QM physics becoming classical physics.
Dyson is also contentious when it comes to gravity and QM, arguing that we don’t need to combine them together and that, even if the graviton existed, it’s impossible to detect. Most physicists argue that we need a quantum gravity – that it’s the ‘missing link’ in a TOE (Theory of Everything).
It’s occurred to me that maybe the mathematics is telling us something when it appears obstructive to marrying general relativity with QM. Maybe they don’t go together, as Dyson intimated.
Again, I think Toth gives the best reasoning on this, as I elaborated on in another post.
We can do quantum field theory just fine on the curved spacetime background of general relativity.
Then he adds this caveat:
What we have so far been unable to do in a convincing manner is turn gravity itself into a quantum field theory.
Toth explains how and why they are ‘incompatible’, though he loathes that term, because he doesn’t think they’re incompatible at all.
Basically, Einstein’s field equations are geometrical, whereby one side of the equation gives the curvature of spacetime as a consequence of the energy, expressed on the other side of the equation. The energy, of course, can be expressed in QM, but the geometry can’t.
Someone else on Quora, Terry Bollinger (retired Chief Scientist), explains this better than me:
It all goes back to that earlier point that 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. Instead, you assume the existence of a smooth fabric called spacetime, and then start bending it. From that bending emerges the force we know as gravity.
Bollinger wrote a lengthy polemic on this, but I will leave you with his conclusion, because it is remarkably similar to Toth’s.
Even if you finally figure out a clever way to define a gravity-like quantum force that allows objects in spacetime to attract each other, what are those force particles traveling across?
He provides his own answer:
Underneath the quantum version, since like all of the other forces in the Standard Model this swarm-like quantum version of a gravity must ride on top of spacetime. (Emphasis in the original)
In other words, Bollinger claims you’ll have a redundancy: a quantum field gravity on top of a spacetime gravity. Spacetime provides the ‘background’ to QFT that Toth described, which doesn’t have to be quantum.
So what about quantum gravity that is apparently needed to explain black holes?
There is an inherent contradiction in relation to a black hole, and I’m not talking about the ‘information paradox’. There is a debate about whether information (meaning quantum information) gets lost in a black hole, which contradicts the conservation of quantum information. I’m not going to get into that as I don’t know enough about it.
There is a more fundamental issue: according to Toth (but not only Toth) the event horizon of a black hole is always in an observer’s future. Yet for someone at the event horizon, they could cross over it without even knowing they had done so, especially if it was a really big black hole and the tidal effects at the event horizon weren’t strong enough to spaghettify them. Of course, no one really knows this, because no one has ever been anywhere near a black hole event horizon.
The point is that, at the event horizon of a black hole, time stops according to an external observer, which is why, theoretically it’s always in their future. Toth makes this point many times. So, basically, for someone watching something fall into a black hole, it becomes frozen in time (at the event horizon). In fact, the Russian term for a black hole is ‘frozen star’.
What we can say is that light from any object gets red-shifted so much that it disappears even before it reaches the event horizon. But what about an observer at or near the event horizon looking back out at the Universe. Now, I don’t see any difference in this scenario to the twin paradox, only it’s in extremis. The observer at the event horizon, or just outside it, will see the whole universe pass by in their lifetime. Because, if they could come back and meet up with their twin, their twin would be a hologram frozen in time, thousands of years old. Now, Toth makes the point, that as far as an observer at or near the event horizon, the speed of light is still constant for them, so how can that be?
There is another horizon in the Universe, which is the theoretical and absolute practical limit that we can see. Because the Universe is expanding, there is a part of the Universe that is expanding faster than light, relative to us. Now, you will say, how is that possible? It’s possible because space can travel faster than light. Now Toth will confirm this, even though he claims space is not an entity. Note that some other observer in a completely different location, would see a different horizon, in the same way that sailors in different locations in the same ocean see different horizons.
So, a hypothetical observer, at the horizon of the Universe (with respect to us) would still see the speed of light as c relative to their spacetime. Likewise, an observer at the event horizon of a black hole also sees light as c relative to their spacetime.
Now most black holes, we assume, are spinning black holes and they drag an accretion disk around with them. They also drag space around with them. Is it possible then that the black hole drags space along with an observer across the event horizon into the black hole? I don’t know, but it would resolve the paradox. According to someone on Quora, Leonard Susskind argues that nothing ever crosses the event horizon, which is how he resolves the quantum information paradox.
This is a very lengthy post, even by my standards, but I need to say something quickly about entanglement. There appears to be a contradiction between relativity and entanglement, but not in practical terms. If there is a universal 'now', implicit in the Universe having an ‘edge in time’ (but not in space) and if QM describes the future, then entanglement is not a mystery, because it’s a correlation between events separated in space, but not in time.
Entanglement involves a ‘decoherence’ in the wave function that predicts the state of a decoherence in the particle it’s entangled with, because they share the same wave function. Schrodinger understood this better than anyone else, because he realised that entanglement was an intrinsic consequence of the wave function. He famously said that entanglement was the defining characteristic of quantum mechanics.
But there is no conflict with relativity because the entangled particles, whatever they are, can’t be separated at any greater rate than the speed of light. However, when the correlation occurs, it appears to happen instantaneously. But this is no different to a photon always being in the future of whatever it interacts with, even if it crosses the observable universe. However, for someone who detects such a photon, they instantaneously see something in the distant past as if there has been a backward-in-time connection to its source.
There is no reason to believe that anything I’ve said is true and correct. I’ve tried to follow a simple dictum that nature abhors a contradiction and apply it to what I know about the Universe, while acknowledging there are lots of people who know a great deal more than me, who probably disagree.
I see myself as an observer on the boundary line of the history of ideas. I try to make sense of the Universe by reading and listening to people much cleverer than me, including people I have philosophical differences with.
Addendum 1: I referenced Paul Davies 1995 book, About Time; Einstein's Unfinished Revolution. I mentioned that Earth is travelling relative to the CMBR towards Pisces (at 350 km/s), and according to Davies:
This is about 0.1 percent of the speed of light, and the time-dilation factor is only about one part in a million. Thus, to an excellent approximation, Earth's historical time coincides with cosmic time, so we can recount the history of the universe contemporaneously with the history of the Earth, in spite of the relativity of time. Similar hypothetical clocks could be located everywhere in the universe, in each case in a reference frame where the cosmic background heat radiation looks uniform... we can imagine the clocks out there, and legions of sentient beings dutifully inspecting them. This set of imaginary observers will agree on a common time scale and a common set of dates for major events in the universe, even though they are moving relative to each other as a result of the general expansion of the universe. They could cross-check dates and events by sending each other data by radio; everything would be consistent. So cosmic time as measured by this special set of observers constitutes a type of universal time... It is the existence of this pervasive time scale that enables cosmologists to put dates to events in cosmic history - indeed, to talk meaningfully at all about "the universe" as a single system. (my emphasis)
Addendum 2: This is a PBS video, which gives the conventional physics view on time. I don't know who the presenter is, but it would be fair to say he knows more about this topic than me. He effectively explains Einstein's 'block universe' and why 'now' is considered totally subjective. Remember Einstein's famous words in a letter to the mother of a friend who had died:
We physicists know that the past, present and future is only a stubbornly persistent illusion.
This was a consequence of simultaneity being different for different observers, as I discussed in the main text, and is described in the video. It's important to point out that this does not undermine causality, so it refers to events that are not causally related. The video presenter goes on to point out that different observers will see different pasts and different futures on worlds far far away, dependent on their motion on this world. This infers that all events are predetermined, which is what Einstein believed, and explains why so many physicists claim that the Universe is deterministic. But it contradicts the view, among cosmologists, that the Universe has an 'edge in time but not in space'.
It's certainly worth watching the video. Curiously, his logic leads him to the conclusion that we live in a quantum multiverse (the many worlds interpretation of QM). I agree with him that different observers in different parts of the Universe must have different views of 'Now'. That's just a logical consequence of the finite speed of light. Motion then distorts that further, as he demonstrates. My view is that what we perceive is not necessarily what actually 'is'. If one looks at the clock of a moving observer their time is dilated compared to ours, and likewise they see our clocks showing time dilation compared to them. But logic tells us that they both can't be right. The twin paradox is resolved only if one acknowledges that time dilation is an illusion for one observer but not the other. And that's because one of the twin travels relative to an absolute spacetime if not an absolute space or an absolute time.
Back to the video, my contention is that one observer can't see another observer's future, even though we can see another observer's 'present' in our 'past'; I don't find that contentious at all.
