So I came across this site on my internet travels (actually, through a naturalism group on facebook) and it provides a really good introduction to a number of difficult topics within the realms of physics and cosmology. In this piece, physicist Andrew Thomas elucidates on the topic of the reality of the universe, the nature of time and its implications in revealing that the universe seems to be a dimensional block. This also has huge ramifications for the notion of free will, or lack thereof (in this case, the stock compatibilist approach of the author, denying libertarian free will ideals).
Give it a read. It’s good stuff and very palatable:
Time and the Block Universe
This page considers the nature of time itself. Using a purely logical argument – involving no physics or mathematics whatsoever – we shall see that time must behave in a way which is completely at odds with our usual mental conception of the passage of time. As Einstein himself said, the flow of time is only a “stubbornly persistent illusion”.
This page might very well shake the way you view the nature of time.
“There is nothing outside the universe”
On the previous page, Reality Is Relative, we were introduced to Lee Smolin’s simple maxim: “There is nothing outside the universe” which he described as the “first principle of cosmology”. This means there can be no absolute coordinate system for space or time outside the universe by which object positions and times can be defined. Instead, the position of every object in the universe must be defined solely in terms of the position of other objects in the universe.
This is an incredibly profound and important result – it is the principle underyling Einstein’s theory of relativity – and, as we will see, it has staggering implications for our conception of how time operates in our universe.
Two Theories of Time
There are two dominant – and incompatible – theories of time: the tensed theory, and thetenseless theory. The tensed theory of time most resembles the popularly-held view of time. The tensed theory requires there to be a present moment (the “now”), and a distinction between an event in the past, present, and future (an event in the past was real, an event in the present is real, and an event in the future will be real). Notice that the “now” moves. This apparent movement of the “now” is an essential feature of the tensed theory of time.
However, there is a philosophical (and logical) problem to this idea of a moving “now”. Put simply, it raises the question which has puzzled philosophers: “How fast does time flow?”. If the “now” moves then it must move with respect to some time reference. So is it moving with respect to itself? Surely not. To say “Time moves at the rate of one second per second” is meaningless. Rather, the rate of time flow would have to be measured with respect to some secondary, external time reference. However, in our earlier discussion on this page it was stressed that there was no clock outside the universe, so there could not be any such external time reference. It is simply logically impossible for there to be a moving “now”. Time does not “flow”!
So what is the alternative? The alternative is to consider a universe in which all of time is laid-out (just as the space dimension is laid-out), and there is no moving “now”. All times are equally real: as there is no special “now”, there is no distinction between past and future. This forms the tenseless theory of time.
Most physicists would favour the tenseless theory as the most accurate representation of time. It is also called a block universe because all of spacetime can be viewed as being laid-out as an unchanging four-dimensional block:
For a clear explanation of the block universe, see this excellent Scientific American articleby Paul Davies.
But we all feel a “flow” of time in which an unknown and unfixed future becomes our present moment before being relegated to the past. How can we reconcile this feeling with the block universe in which all of time is laid-out, and there is no moving “now”? It emerges that the feeling we have of the passing of time is nothing more than an illusion of human perception due to the asymmetry of the time axis: we can remember the past, but we cannot remember the future. This then gives the illusion of a flow of time with the unknown future becoming the fixed past. For more details on this, see the Arrow of Time page.
Eternal Life
It might come as a surprise that this orthodox “block universe” view of time in fact leads us to conclude that we possess a form of eternal life! This is a consequence of the principle that in the block time model all periods of time are equally real. If a loved one dies, you might take some comfort from the knowledge that this period of time in which your loved one is dead has, in fact, no greater reality than the time when your loved one was alive. According to physics, it is just as valid to consider your loved one as alive as it is to consider them dead!
Einstein took comfort from this knowledge when his lifelong friend Michele Besso died. He wrote a letter consoling Besso’s family: “Now he has departed from this strange world a little ahead of me. That means nothing. People like us, who believe in physics, know that the distinction between past, present, and future is only a stubbornly persistent illusion.”
Of course, the flip-side is that you’re already dead!
The Astounding Implications of the Block Universe
I do not believe the implications of the orthodox block universe model are widely realised – even among physicists! I regularly read phrases in published papers (even from highly-reputable authors) which make no sense at all from the point of view of the block universe. As Lee Smolin says in his book Three Roads to Quantum Gravity: “There are unfortunately not a few good professional physicists who still think about the world as if space and time had an absolute meaning”. The conclusions presented here relating to the block universe model follow directly from Einstein’s theory of general relativity and so should be considered to be orthodox physics.
According to the block universe model, every moment in time is equally real, so the whole of space and time must be laid-out in one unchanging spacetime block:
It is true that there is a time dimension defined within the universe. And for an observerwithin the universe, objects appear to change with respect to this time axis. However, this apparent flow of time is just an illusion of human perception due to the asymmetry of the time dimension. As there is no clock outside the universe, there is no “external” time axis, and the external view of the entire universe structure can therefore never change with respect to that non-existent external time axis. This lack of temporal change in the entire universe structure has the following implications:
- The “Big Bang” does not represent the “start” of the universe. Remember, all times are equally real in the block universe – there is nothing special about time at the “Big Bang”. As all times are equally real, the final state of the universe is just as real as the initial state. So the so-called “initial” Big Bang tells us nothing more about the existence of the universe than the “final” state does. While it is true that to an observerwithin the universe the Big Bang might appear like the start of the universe this is revealed to be an illusion of human perception caused by the psychological arrow of time (for more details on this, see the Arrow of Time page).The structure of the universe at the Big Bang does seem unusual because of its peculiar spatial geometry. But that does not make it the “start” of the universe. All we can say about the entire universe structure at the Big Bang is a comment about that unusual spatial geometry: “Along one of its dimensional axes (the backward time dimension), we find the spatial dimension decreasing in size until it reaches a point”(this is essentially describing the “cone” structure in the diagram above).
- The universe did not “emerge from nothing”. It is meaningless to talk of the “start” of the universe, or the “emergence of the universe from nothing”, or any other term which implies change of the entire block universe structure over time. The entire spacetime block is laid out as one unchanging structure. Here’s a quote from Stephen Hawking’s book “A Brief History of Time”: “If the universe is really completely self-contained, having no boundary or edge, it would have neither beginning nor end: it would simply be.”This means that any theory which attempts to explain the existence of the universe solely in terms of events which happened at the Big Bang would appear to be plain wrong. This includes any theory which suggests the reason for the existence of the universe is because the universe “emerged from nothing” (so-called ex nihilosolutions). This includes the theories of Tryon and Vilenkin (considered at the top of this page) which suggest that the reason the universe exists is because it quantum tunnelled into existence from nothing.Ex nihilo explanations for the existence of the universe are a red herring.
- The universe is not expanding. Again, there is no temporal change in the entire universe structure, so it is meaningless to talk of a universe which is expanding with time. After all, expansion means an increase in size with respect to some time reference. With no external time reference axes, there is no absolute directional reference axis for time for you to say “the universe is expanding” rather than “the universe is contracting” – one is obviously just the reverse of the other, and with no external time reference axis how could you possibly prefer one statement over the other? (Also see Julian Barbour’s article The Non-Expanding Universe).It seems to my mind (and to John Cruickshank who made this suggestion in a comment posted on the Arrow of Time page) that we are relying far to heavily on the psychological arrow of time to determine our time directionality, and hence decide whether the universe is expanding or contracting. We “perceive” the universe to be expanding because our brains determine our feeling of directional time flow in the forward time direction. But that psychological arrow of time is always going to align itself from a low entropy universe state to a high entropy universe state. That is no basis to say “the universe is expanding” – that just says something about the distribution of entropy in the entire universe structure. It is more accurate to say the universe is neither expanding or contracting. It just has a structure. It just is.
- The Grandfather Paradox is solved. If you’ve seen the movie Back to the Future(or virtually any episode of Star Trek) then you are aware of the so-called grandfather paradox. The paradox poses the question: “What happens if you were to travel back in time to kill your own grandfather?” If you do kill your own grandfather, then you are never born. But if you are never born, then you cannot go back in time to kill your own grandfather. So it’s a real puzzle: your grandfather appears to be in an oscillatory state of being dead, then alive, then dead, then alive again, etc.But the block universe model provides a solution to the grandfather paradox. And, as the block universe model has been derived by a solid, logical approach, we can say that this is a definitive solution. According to the block universe model, all of space and time is laid-out in an unchanging spacetime block. There can be no place for an oscillatory grandfather: the grandfather must be defined as being in an unchanging state of either dead or alive. It can never be possible to change that state. The only possible time loops would be consistent time loops.
The Wheeler-DeWitt Equation
A great puzzle in physics has been how to reconcile Einstein’s theory of general relativity with quantum mechanics. General relativity remains our main theory for describing gravity, and is extremely accurate for with large objects (stars and planets, etc.). Quantum mechanics, on the other hand, is our main theory for dealing with microscopic objects, and the other three fundamental forces which act at the atomic scale. General relativity describes space as being a smooth surface, but quantum mechanics reveals a discontinuous microscopic world with constant fluctuations and activity. So, each of these theories is accurate in its own right but they describe the nature of space and matter so differently that it has proven highly problematic to combine the theories into a single unified theory.
As part of the effort to reconcile quantum mechanics and gravity, many physicists are seeking to find a quantum theory of gravity. As part of this quest, we are going to introduce the Hamiltonian. The Hamiltonian is an incredibly useful property of a system, which represents the total energy of a system – the sum of the kinetic and potential energy. To be precise, the Hamiltonian is the sum of the kinetic and potential energy of a closed system expressed in terms of momentum, position, and time (see here).
But if we want to consider the Hamiltonian (total energy) of the universe we come up against a problem. As we have just seen, there are no axes of reference outside the universe. Hence, it is impossible to define a position for our “universe object” (so we cannot say it has a potential energy) and it is impossible to define a speed (so we cannot say it has kinetic energy). As Misner, Thorne, and Wheeler say on page 457 of their book “Gravitation”: “There is no such thing as the energy (or angular momentum, or charge) of a closed universe, according to general relativity, and this for a simple reason. To weigh something one needs a platform on which to stand to do the weighing” (see here). So in this case, the Hamiltonian (the total energy) of the universe is zero:
This is called the Hamiltonian constraint (it is actually true that the Hamiltonian is zero for any system which has general covariance – for a derivation of this, see here).
You may find it hard to accept this idea that the total energy of the universe is zero. This is only possible if we consider gravity to provide “negative energy”. This is described well in this article by Filippenko and Pasachoff: “You can easily see that gravity is associated with negative energy: If you drop a ball from rest (defined to be a state of zero energy), it gains energy of motion (kinetic energy) as it falls. But this gain is exactly balanced by a larger negative gravitational energy as it comes closer to Earth’s center, so the sum of the two energies remains zero.”
Stephen Hawking also explains this principle clearly in this extract from his book “A Brief History of Time”: “The total energy of the universe is exactly zero. The matter in the universe is made out of positive energy. However, the matter is all attracting itself by gravity. Two pieces of matter that are close to each other have less energy than the same two pieces a long way apart, because you have to expend energy to separate them against the gravitational force that is pulling them together. Thus in a sense, the gravitational field has negative energy. In the case of a universe that is approximately uniform in space, one can show that this negative gravitational energy exactly cancels the positive energy represented by the matter. So the total energy of the universe is zero.”Also see this New Scientist article by Lawrence Krauss.
In order to convert the Hamiltonian to its quantum mechanical form, we have to consider the Hamiltonian as representing the total energy. We can then use the quantum mechanical formula for energy which we derived previously on the Quantum Casino page:
As this is an energy operator, we need something for it to operate on. So we have had to again introduce this strange concept of a wavefunction,
, extending through space. So another new concept must now be introduced: the wavefunction of the universe. The principle of the “wavefunction of the universe” imagines the entire universe as a single object, a quantum object. Michio Kaku explains it well: “When the universe was born, it was smaller than an electron, which is a quantum object that can exist simultaneously in many states. So the universe must also be a quantum object and exist in many states.” (see here). So we can apply our Hamiltonian operator to our “wavefunction of the universe”:
This is the Wheeler-DeWitt equation – a sort of Schrödinger equation for the gravitational field. It is the most famous equation in quantum gravity.
(A variation on this canonical quantization of gravity eventually leads to the recent, cutting-edge theory of loop quantum gravity – see this Physics World article by Carlo Rovelli, or Lee Smolin’s Scientific American article Atoms of Space and Time).
Time and the Wheeler-DeWitt Equation
There’s something remarkable about the Wheeler-DeWitt equation, and it can be seen if we expand the Hamiltonian operator:
Or, expressed in words, the rate of change of the state of the universe with respect to time is zero. The universe isn’t changing with time! But we look around us and we see things changing all the time: people are walking, birds are flying. So is the equation wrong? Well, no. What the equation is once again telling us is that there is no external time reference by which we can measure the progress of time within the universe: there is no clock outside the universe! As Andrei Linde explains: “The notion of evolution is not applicable to the universe as a whole since there is no external observer with respect to the universe, and there is no external clock that does not belong to the universe” (see page 25 of Andre Linde’s paper Inflation, Quantum Cosmology and the Anthropic Principle).
Therefore, the Wheeler-DeWitt equation agrees with our earlier analysis of the nature of time because it suggests a block universe model in which all of time is laid-out (just as the space dimension is laid-out), and all times are equally real: there is no special “now”, no distinction between past and future. In fact, “past” and “present” do not exist – the movement of time is considered to be just an illusion of human perception.
Free Will in a Block Universe
Some people have suggested that the block universe model is incompatible with any notion of free will. This, they would say, is because the future appears to be set-in-stone in the block universe model, so we are never at liberty to change it by our choices. I would disagree with this reasoning as I believe it shows a fundamental misunderstanding of what the block universe implies. We will see that the block universe is completely compatible with the notion of free will.
The misunderstanding arises because the notion of free will is so poorly defined. We all think we know what “free will” is, we have a feeling, but it is very hard to write down what the phrase actually means and implies. In the absence of a satisfactory definition, I am going to define “free will” in what I believe is the best and most accurate description:
Free will is defined as the ability to make decisions.
(This appears to be the same definition of free will used by the Compatibilism school of philosophy which states that you have free will if you feel free to make a conscious decision without, for example, someone forcing you to make a particular decision by pointing a gun at your head. Hence, the Compatibilists believe you can have free will even in a deterministic universe. But I am taking the Compatibilist view further by saying that not only can you have free will in a deterministic universe, but you can also have free will in a deterministic blockuniverse).
So what do I mean by “making a decision”? It means the ability to consider a range of many possible courses of action, and to select only one course of action from that range of possibilities. To all intents and purposes, I think that is a reasonable definition of free will.
This definition of free will is completely compatible with the block universe model. The key thing is that only one course of action results when we make a decision. There is only one outcome. There is only ever one stream of events. For example, the sequence of events when we come to a fork in the road might be:
EVENT 1) You walk along the road and come to a fork in the road.
EVENT 2) You decide to turn to the left.
EVENT 3) You continue your journey along the left road.
This is just a sequence of three events, and that’s all the block universe is: a sequence of successive events. So these three events can easily be incorporated into the block universe model.
In the block universe model, events are unchanging and “frozen-in-time”. But that does not mean that those events do not represent the expression of free will. For example, when we look back into the past we consider those past events to be “frozen”, and nothing could change those events. However, we might also remember some of those past events as representing moments when we made decisions, i.e., expressed our free will. So the notion of free will is in no way incompatible with the block universe “frozen-in-time” representation of unalterable events.
In his book The Fabric of Reality David Deutsch suggests that some sort of “branching” multiverse universe is required to account for free will and the human decision process (see the New Scientist article Taming the Multiverse). In Deutsch’s model, when the human comes to a fork in the road, the universe (and the person) splits into two different universes so the person is capable of travelling down both roads. Deutsch appears to think that this is the only way that the human can have free will. But Deutsch is ignoring the fact that a decision can only ever have one outcome, so only one road is travelled after the decision is made (i.e., after the human expresses his free will). This is therefore completely compatible with a single block universe: no branching “multiverses” are necessary.
