Reality Is Relative
On this page we will consider the implications of relativity in the most general sense, the idea that everything in the universe can only be defined in terms other things in the universe. We will see that the implications of this apparently unremarkable statement are quite astounding. We will also reveal surprising links between the two great theories of relativity and quantum mechanics!
"There is nothing outside the universe"
In his excellent book Three Roads to Quantum Gravity, Lee Smolin introduces a simple maxim: there is nothing outside the universe. This statement is fairly self-evident and should not be controversial. If we define the "universe" to be the sum total of absolutely everything that exists, then there can clearly be nothing "outside" the universe. But this seemingly unremarkable maxim has astounding implications for our picture of nature - implications which are not generally realised.
If there is nothing outside the universe, then everything "inside" the universe can only be defined in terms of other objects "inside" the universe: every object in the universe is defined in terms of every other object in the universe.
"Isolated material particles are abstractions, their properties being definable and observable only through their interactions with other systems"
- Niels Bohr
There is simply no other way to define the properties of an object other than by how it relates to the rest of the universe. There is no absolute measurement scale outside the universe by which we can unequivocally say "The object is five metres long", or "The object is blue", or even "The object exists". In the absence of any external absolute scale, the only way we can define an object's properties is by, for example, measuring it with equipment already located inside the universe, i.e., the object's properties are defined by its relationships with other objects inside the universe. The object's properties simply cannot be defined in any other way.
It was Wilhelm Leibniz who first rejected Newton's ideas of absolute space and time. Leibniz believed that space arose due to the relationships between objects - space did not exist as an entity in its own right. If there is "nothing outside the universe" then Leibniz was surely correct. As we see in the diagram below, the men define their positions in terms of each other, and the notion of "space" arises purely as a result of these relationships:
If there could be such a thing as absolute space, with coordinate axes "outside the universe" then space would exist in its own right as a box, containing the men. Absolute space would exist even if there were no objects in it. This is perhaps our intuitive notion of space. The diagram below shows the same men, this time positioned in a box of absolute space. This time they give their positions individually, as coordinates in absolute space, with no reference to their friends:
However, space is not a box. This unfriendly picture is wrong. Objects cannot be considered as isolated entities. With "nothing outside the universe" this must surely be the wrong model of space.
This principle, of space emerging purely from the relationships between objects, is a guiding feature of the theory of loop quantum gravity where it is called background independence.
And the next step we can take in analyzing the relative universe is rather remarkable. In the absence of any absolutes in the universe, absolutely everything must be relative. This means not only the location property must be relative to other objects, but every property must be defined relative to every other object in the universe!
Multi-Valued Reality
We all have an intuitive picture of why an object is a particular type of object. For example, we might recognise an object as a duck. And we imagine that that duck has an innate, unvarying quality about it which makes it a duck (let's call it "duckness") so that object always has been a duck and that object always will be a duck. We imagine that if we could isolate that duck from the rest of the universe, it would still be a duck. It's duckness is in-built, is intrinsic to the object, and requires no support from any other object to be recognised as a duck.
But, of course, with a little bit of thought you realise that it is impossible to completely isolate an object from the rest of the universe, to remove it to a position "outside" the universe (remember: "There is nothing outside the universe", and see the Niels Bohr quote further up this page: "Isolated material particles are abstractions"). More to the point, we realise that the only way we recognise a duck object is by that object's interactions with the rest of the universe. For example, we recognise the sound of the duck quacking by intercepting the sound waves produced by the duck, or we recognise the shape of the duck by intercepting the light waves which reflect off the duck. We actually recognise the duck not by any innate "duckness", but instead we recognise it purely by its interactions with the rest of the universe.
"If it looks like a duck, swims like a duck, and quacks like a duck, then it's a duck." - James Whitcomb Riley
Bearing in mind what we have just said, we're going to conduct a thought experiment to illustrate the remarkable implications of this principle that an object is defined purely in relation to the other objects in the universe. We're going to be using a simplified, idealised model of the universe which is capable of behaving in a rather bizarre manner, but this is just to illustrate the general principle. It's worth it - the conclusion is going to be fairly mind-bending.
Let's just ask a few questions about one of the objects in the diagram below - the object indicated by the red question mark. Firstly, let's just ask how long it is by trying to measure its length:
Bear in mind that in order to obtain our measurement we are limited by the tools we have at our disposal. And, as the previous discussion has just indicated, this we can only use objects already present inside the universe. This means we can only use the rulers, gauges, etc. which exist inside the universe. There is no alternative way to obtain this reading. There is no absolute axis of length outside the universe which we could use to obtain an absolute, unequivocal reading.
Ok, so now let's say we use our ruler to measure the object, and, according to the ruler, the object is one metre long. Now, bear with me on this, let's presume something really strange happens. Let's imagine every object in existence in our peculiar universe - apart from our mystery object - bizarrely shrinks by 50% (the reason why this happens is unimportant for this discussion). We now find that our mystery object has become two metres long - according to our ruler.
But this is to be expected, you might argue. There is nothing surprising here. The mystery object has not really doubled in size, you might argue, it is merely our ruler which is giving an incorrect reading. Our mystery object was previously measured as being one metre long and, in the absence of any external influence acting on the object, it is always going to be one metre long. The property of being "one metre long" is an intrinsic, unvarying property of the object. At least, that is what you are arguing ...
Well, you'd be wrong. Remember that any object in the universe can only be defined in terms of every other object in the universe - there is no other way of defining it. There is no absolute axis of size outside the universe to which we can refer. If the universe tells us the object has doubled in size then, by definition, the object really has doubled in size!
So we are left with an apparently bizarre conclusion which goes against all intuition. No force has acted on the object, and yet it has doubled in size. It's as though some self-contained internal magic of the object has made it change its state, whereas nothing could be further from the truth. A property of the object which should have been innate and unvarying has been radically modified, purely because of this principle that objects can only be defined solely in terms of their relationships with other objects.
So this makes us doubt that objects have in-built, unvarying properties at all. Instead, these properties could any value from the range of possible values, and it is only through that property's interactions with the rest of the universe that those properties get "tied-down" and determined to a final value. It is as though the object is initially multi-valued, and it is the universe which selects the final value from the range of possible values.
But does all this madness ring a bell with you? It should do if you have read the previous pages on quantum mechanics, because this is pure quantum mechanical behaviour:
- On the Quantum Casino page we saw that - before observation - a particle's properties are multi-valued in just the same way as we have seen on this page. In a relative universe, the property values of a particle are not intrinsic to the object, but instead emerge as the particle interacts with the rest of the universe. Before observation, the particle's property value must be considered as being in a superposition of all possible states. Hence, we find peculiar behaviour such as particles appearing to be in two places at once. In the relative universe model we can see that this is due to the position property of the particle not yet being completely defined.
- Then on the
Quantum Entanglement page we saw that when two particles interact they form a single "entangled" state,
and you then have to consider the system as a whole rather than considering just a single particle. This is why in a relative universe you cannot
consider particles in isolation - objects are defined in terms of all other objects in the universe. There was also a discussion about Bell's
Inequality which revealed that objects do not have intrinsic property values - just as we have found on this page when we have considered the
implications of the relative universe.
This principle that objects' property values are determined when we measure them - measurement creates reality - has now been proven experimentally: "We now have to face the possibility that there is nothing inherently real about the properties of an object that we measure. In other words, measuring those properties is what brings them into existence. Rather than passively observing it, we in fact create reality" (see here). - Then on the
Quantum Decoherence page we saw how the environment (i.e., the rest of the universe) can reduce a superposition
state to a single value. In other words, in a relative universe it is the rest of the universe which decides the property values of a particle
after measurement.
We also saw how various interpretations of quantum mechanics have arisen, such as the "many-worlds" parallel universe interpretation and Bohm's pilot wave interpretation, in order to explain the counter-intuitive nature of multi-valued reality in quantum mechanics. None of these interpretations have appreciated the full implications of the relative universe, these interpretations being locked into a closed mind-set in which particles can be considered as being isolated from the universe, as entirely independent entities with inherent property values of their own. However, it is the idea described on this page - that all of reality is relative - which explains quantum behaviour as being an inevitable consequence of objects having to be defined in terms of all other objects in the universe.
So are there any more similar connections between relativity and quantum mechanics ...
Observer Dependence
Let's consider the simple principle of relative velocity, which underlies Einstein's theory of relativity. And let's start by asking a simple question: how fast is the spaceship travelling in the image below?
It's not such an easy question as you might imagine. As we have discussed earlier on this page, in the absence of any absolute measurement scale outside the universe we cannot assign any absolute speed to the ship - we have nothing to measure it against. We cannot assign a speed to the spaceship on which all observers in the universe will agree. In fact, the only way we can assign any numerical value to the speed of the ship is by giving up all hope on finding an absolute, observer-independent speed, and by considering its relative speed instead.
So, if we want to obtain a numerical value for the speed of the spaceship, we have to first define our observer (or, more precisely, our observer's frame of reference):
In the image above, we have defined a position for our observer and we can now obtain a value for the velocity of the spaceship (relative to our observer) which happens to be 600mph, travelling to the right.
Now let's make things a bit more interesting by imagining we have a second observer on a second spaceship travelling to the left at 400mph:
According to this second observer, the first rocket is in fact travelling to the right with a relative velocity of 1000mph (the sum of 600mph + 400mph). So we've got two different observers, and they're both getting two different measurements for velocity of the spaceship, showing just how observer-dependent this measurement is.
So now we see how observer-dependent relativity is, and we already know the importance of the act of observation in quantum mechanics, so why has not more been made of this apparent commonality between the two theories? Carlo Rovelli has commented on this link: "Quantum state and values that an observable takes are relational notions, in the same sense in which velocity is relational in classical mechanics (it is a relation between two systems, not a property of a single system). I find the consonance between this relationalism in quantum mechanics and the relationalism in general relativity quite striking. It is tempting to speculate that they are related." (see here).
Why has this not triggered more investigation into the possibility that this indicates a shared fundamental principle behind the two great theories of physics? In a relative universe, the observer is everything.
But having two different answers to our question "How fast is the spaceship travelling?" is not a very satisfactory answer. Can't we do any better? Can't we get an observer-independent, absolute value for the velocity of the spaceship - before any observer-dependent measurement is taken? Well, the standard answer is, no, in our universe only relative velocity has a meaning. But, you might say, that's totally unsatisfactory. Before any measurement is taken, the spaceship clearly has a velocity - we know it's moving. So why can't we determine its value before observation? Its velocity clearly has a reality before observation - why can't we assign a value to it?
Well, I suppose the best we could do is assign the spaceship with a potential velocity which has to take any possible value from zero up to the speed of light. For example, if the purple spaceship is travelling at a million miles an hour, we now find our final measurement of the grey spaceship's relative speed is 1,000,600mph. With an infinity of potential observers in the universe in the universe, we could say that the before-measurement, observer-independent velocity of the spaceship is any possible value.
So let's recap: Before measurement, we know the spaceship's velocity has a reality (we know the spaceship is moving), but we cannot assign a value to it. If we want to obtain a measurement then we have to specify an observer as the value is completely observer-dependent. But if we want to assign a velocity to the spaceship before observation we have to assign all possible velocity values to it. So where have we heard all this before? There are clear parallels with quantum mechanics!
Let's see how accurately this scenario follows quantum mechanics. In an example from quantum mechanics, let's say we want to measure the location of a particle. We can only obtain a value for the location of the particle by measuring it, and this means defining an observer (which takes the form of some sort of measuring apparatus). Before measurement, we cannot say it has any particular value for location - the only description we have of the particle before observation is a wavefunction, which is arguably just a mathematical tool. If we are going to be controversial and try to assign any form of reality to the location property of the particle before observation then we have to assign some form of reality to the wavefunction. But, on studying the multi-valued nature of the wavefunction, this means we can only come to the conclusion that before observation the value of the object's position must be a superposition of all possible values (hence, we observe strange phenomena such as particles apparently being in two places at once, and passing through two slits).
So clearly the two scenarios - relative velocity (which leads to relativity) and quantum mechanics - show astounding similarities! So much so that I'm fairly astonished that, as far as I can see, no one has pointed this out before. And it is all because relativity and quantum mechanics share a common root to their behaviour: a universe in which everything must be defined in terms of everything else, and in which all of reality is relative.