Dear Dr. B: What do physicists mean when they say time doesn’t exist?

That was a question Brian Clegg didn’t ask but should have asked. What he asked instead in a recent blogpost was: “When physicists say many processes are independent of time, are they cheating?” He then answered his own question with yes. Let me explain first what’s wrong with Brian’s question, then I’ll tell you something about the existence of time.

What is time-reversal invariance?

The problem with Brian’s question is that no physicist I know would ever say that “many processes are independent of time.” Brian, I believe, didn’t mean time-independent processes but time-reversal invariant laws. The difference is important. The former is a process that doesn’t depend on time. The latter is a symmetry of the equations determining the process. Having a time reversal-invariant law means that the equations remain the same when the direction of time is reversed. This doesn’t mean the processes remain the same.

The mistake is twofold. Firstly, a time-independent process is a very special case. If you watch a video that shows a still image, it doesn’t matter if you watch it forward or backward. So, yes, time-independence implies time-reversal invariance. But secondly, if the underlying laws are time-reversal invariant, the processes themselves are reversible, but not necessarily invariant under this reversal. You can watch any movie backwards with the same technology that you can watch it forwards, yet the plot will look very different. The difference is the starting point, the “initial condition.”

The fundamental laws of nature, for all we know today, are time-reversal invariant*. This means you can rewind any movie and watch it backwards using the same laws. The reason that movies look very different backwards than forwards is a probabilistic one, captured in the second law of thermodynamics: entropy never decreases. In large open systems, it instead tends to increase. The initial state is thus almost always very different from the final state.

Probabilities enter not through the laws themselves, but through these initial conditions. It is easy enough to set up a bowl with flour, sugar, butter, and eggs (initial condition), and then mix it (the law) to a smooth dough. But it is for all practical purposes impossible to set up dough so that a reverse-spinning mixer would separate the eggs from the flour.

In principle the initial state for this unmixing exists. We know it exists because we can create its time-reversed version. But you would have to arrange the molecules in the dough so precisely that it’s impossible to do. Consequently, you never see dough unmixing, never see eggs unbreaking, and facelifts don’t make you younger.

It is worth noting that all of this is true only in very large systems, with a large number of constituents. This is always the case for daily life experience. But if a system is small enough, it is indeed possible for entropy to decrease every once in a while just by chance. So you can ‘unmix’ very small patches of dough.

What does any of this have to do with the existence of time? Not very much. Time arguably does exist. In a previous blogpost I explained that the property of being reality isn’t binary (true or false), but it is graded from “mostly true” to “most likely false.” Things don’t either exist or don’t exist, they exist at various levels of immediacy, depending on how detached they are from direct sensory exploration.

Space and time are something we experience every day. Einstein taught us space and time are combined in space-time, and its curvature is the origin of gravity. We move around in space-time. If space-time wasn’t there, we wouldn’t be there because there wouldn’t be any “there” to be at, and since space and time belong together time exists the same way as space does.

Claiming that time doesn’t exist is therefore misusing language. In General Relativity, time is a coordinate, one that is relevant to obtain predictions for observables. It isn’t uniquely defined, and it is not itself observable, but that doesn’t make it non-existent. If you’d ask me what it means for time to exist, I’d say it’s the Lorentzian signature of the metric, and that is something which we need for our theories to work. Time is, essentially, the label to order frames in the movie of our universe.

Why do some physicists say that time isn’t real?

When physicists say that time doesn’t exist they mean one of two things: 1) The passage of time is an illusion, or 2) Time isn’t fundamental.

As to 1). In our current description of the universe, the past isn’t fundamentally different from the future. It will look different in outcome, but it will be made of the same stuff and it work the same way. There is no dividing line that separates past and future, and that demarks the present moment.

Our experience of there being a “present” comes from the one-sidedness of memory-formation. We can only form memory about things from a time where entropy was smaller, so we can’t remember the future. The perception of time passing comes from the update of our memory in the direction of entropy increase.

In this view, every moment in time exists in some way, though from our personal experience at each moment most of them are remote from experience (the past) or inaccessible from experience (the future). The perception of existence itself is time-dependent and also individual. You might say that the future is so remote to your perception, and prediction so close to impossible, that it is on the level of non-existence. I wouldn’t argue with you about that, but if you learn some more General Relativity your perception might shift.

Now this point of view irks some people, by which I mean Lee Smolin. Lee doesn’t like it that the laws of nature we know today do not give a special relevance to a present moment. He argues that this signals there is something missing in our theories, and that time should be “real.” What he means by that is that the laws of nature themselves must give rise to something like a present moment, which is not presently the case.

As to 2). We know that General Relativity cannot be the fundamental theory of space and time because it breaks down when gravity becomes very strong. The underlying theory might not have a notion of time, instead space and/or time might be emergent – they might be built up of something more fundamental.

I have some sympathy for this idea because I find it plausible that Euclidean and Lorentzian signatures are two different phases of the same underlying structure. This necessarily implies that time isn’t fundamental, but that it comes about in some phase transition.

Some people say that in this case “time doesn’t exist” but I find this extremely misleading. Any such theory would have to reproduce General Relativity and give rise to the notion of time we presently use. Saying that something isn’t real because it’s emergent is a meaningless abuse of terminology. It’s like saying the forest doesn’t exist because it’s made of trees.

In summary, time is real in a well-defined way, has always been real, and will always be real. When physicists say that time isn’t real they normally use it as a short-hand to refer to specific properties of their favorite theories, for example that the laws are time-reversal invariant, or that space-time is emergent. The one exception is Lee Smolin who means something else. I’m not entirely sure what, but he has written a book or two about it.

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* Actually they’re not, they’re CPT invariant. But if you know the difference then I don’t have to explain you the difference.