Causation, Time Symmetry and Russell’s Directionality Argument

[pdf of this article]

In a recent publication for the project (links: published version; preprint) Matt Farr (Centre for Time, Sydney) and Alexander Reutlinger (Munich Center for Mathematical Philosophy) assess whether the time symmetry of physical theories excludes causation from the picture of the world given by fundamental physics.

Bertrand Russell (1913) argued that causation is “a relic of a bygone age,” famously comparing it to the British monarchy in that each survives “only because it is erroneously supposed to do no harm” (more of that here). Russell’s contention is that fundamental physics simply does not concern itself with anything suitably related to our everyday notion of cause. A primary reason for this concerns the role of time in physics.

The ‘folk’ concept of causation has a couple of key features that correlate with the folk understanding of time. Firstly, Directionality: the direction of causation aligns with the direction from past to future: if A causes B, then A must be earlier than B. It is central to our understanding of causation that what we do now can affect future events, but not past events. If I were able to make decisions now that influence events in my past, then there is a sense in which causality would be violated. (This is not to say that it is incoherent for there to be past-directed causes; there appears to be logical space for backwards-in-time causation in quantum mechanics.) Secondly, and perhaps more subtly, Asymmetry: we generally hold that causation is asymmetric – there is a basic distinction between cause and effect insofar as if A causes B, then it follows that B does not cause A. Among other things, this rules out causal loops, such as being one’s own father, which although not being an outright logical impossibility, is curiously counterintuitive. This matches with the standard intuition that time is open – it does not go back on itself. We can see that Asymmetry is more basic than Directionality insofar as causation can have a direction only if there is a distinction between causes and effects: if Asymmetry fails, then so does Directionality.

So, how does fundamental physics threaten Directionality and Asymmetry? Firstly, the equations of fundamental physics are (given some caveats[1]) invariant under reversal in time. This means that for any sequence of states of the universe that is described by fundamental physics, the reverse of that sequence in time is also described by fundamental physics. This means that, in principle, any physically possible process can run both forwards and in reverse, directly undermining Asymmetry, and hence also undermining Directionality.

Does this argument work? Farr and Reutlinger argue that there is a gap in the argument here. The problem comes from inferring from time reversal invariance that if state S1 can ‘cause’ state S2, then equally S2 can cause S1. This is what’s needed to rule out folk causation, but it is not directly entailed by time reversal invariance. The time reversal invariance of a theory tells us something about the relationship between possible states of systems that it describes, namely that if there is a possible evolution from S1 to S2, then a “time reversal” transformation maps these states to other possible states S1* and S2* such that S2* to S1* is another possible evolution. Within the space of possible states defined by the theory, states S1 and S1* will often be different states – for example, in Newtonian mechanics, time reversal changes the sign of velocity, so if a point particle is moving with velocity v, a time reversal transformation takes us to a state defined by a particle with velocity –v. The interesting philosophical question here is whether S1 and S1*, although being different mathematical states, correspond to the same physical state in the world. Assuming that fundamental physics is invariant under time reversal, it follows that no possible measurement could distinguish between pairs of time reversed states, providing reason to think that S1 and S1* do pick out the same physical state. However, it is consistent to hold that these really do correspond to distinct ways the world could be, and given this, we must reject the claim that time reversal invariance is incompatible with Asymmetry and Directionality, and hence folk causation is not ruled out. So, even assuming that the fundamental laws of nature are fully time reversal invariant, it does not follow that there can be no direction of causation.

Let us suppose that the fundamental laws of nature have a feature called One-Way Dependence – i.e. they describe only future-directed processes and not past-directed processes. The idea is that dynamical laws should be read as describing how states depend upon earlier states, and importantly not upon later states. It is natural to think of physical laws in this way; for example an evolution of a system being determined by the combination of the dynamical laws and the initial conditions. Clearly, this way of thinking about physics is consistent with Directionality. Moreover, this is the case regardless of whether the relevant physics meets the criteria for being time reversal invariant. However, do contemporary fundamental physical theories have this form?

It is not obvious that this is the sort of question that can be simply read-off from a physical theory. However, it does appear relevantly connected to the issue of determinism and indeterminism. Classical physics is (with some exceptions) deterministic and time reversible. It follows from this that classical physics tells us, given the complete present state of the universe, its entire history, both past and future. In this sense, classical physics is ‘nomologically’ (as a matter of law) two-way dependent. Quantum mechanics, conversely, is (on most popular versions) probabilistic – given a complete state of the world, the theory provides us only probabilities of future and past states. And moreover, we take these probabilities to have a time-asymmetric character: we have knowledge of certain past states, but no knowledge of future states, and we can control initial states of systems but not final states of systems. What these time asymmetries entail is that we can take the quantum probabilities to accurately predict future states, but not to accurately retrodict past states. Why? Because we can perform an experiment in which we set up a system in some initial state such that, no matter how many times we run the experiment, the initial state remains the same. In such cases, we can show that the backwards-in-time quantum probabilities fail to match the actual recorded frequencies. Does this mean that quantum mechanics is one-way dependent? Well, no. But the issue now turns to questions about the nature of probabilities, the time-asymmetry of control, and whether time-symmetric formulations of quantum mechanics ought to be preferred to standard formulations.

Matt Farr
Postdoctoral Research Fellow
Centre for Time
University of Sydney.


Aharonov, Y., Popescu, S., & Tollaksen, J. (2010). A time-symmetric formulation of quantum mechanics. Phys. Today63(11), 27–32.
Farr, M. & Reutlinger, A. (2013). A Relic of a Bygone Age? Causation, Time Symmetry and the Directionality Argument. Erkenntnis78(2), 215–235.
Norton, J. D. (2008). The dome: An unexpectedly simple failure of determinism.”Philosophy of Science 75(5) 786–798.
Price, H. (2014) Where would we be without counterfactuals? In Galavotti, M. C., Dieks, D., Gonzalez, W., Hartmann, S., Uebel, T., and Weber, W., (eds), New Directions in the Philosophy of Science, Springer.
Price, H. & Wharton, K. (2013). Dispelling the Quantum Spooks – a Clue that Einstein Missed? arXiv:1307.7744.
Russell, B. (1913). On the notion of cause. Proceedings of the Aristotelian Society 13, pp. 1–26.


[1]It is well known that time reversal invariance is violated in some weak interactions, involving the decays of K and B mesons. It is not clear that these particular cases are relevant to the wider issue of causation in physics: even if we thought that such processes distinguish causes and effects, this says nothing about the wider issue of causation in normal cases where time reversal invariance does hold, and as such, the relationship between time reversal invariance and causation is not clarified.

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6 Responses to Causation, Time Symmetry and Russell’s Directionality Argument

  1. Bryan says:

    If two bodies have different momenta, or different spin, then one normally says they’re in different physical states. But you seem to suggest in Par.5 that we are free to deny that claim. I don’t understand this.

    In classical mechanics, time reversing a state S1=(q,p) gives you S1*=(q,-p). In QM, time-reversing the state S1=z-spin-up gives you the state S1*=z-spin-down. Are Farr and Reutlinger suggesting that we can interpret S1 and S1* as representing “the physical same state” in either of these cases? I’m not sure what criterion of “sameness” this involves, but if that’s what asymmetric causation requires, it seems like a pretty drastic price to pay…

    • mwefarr says:

      Hey Bryan! Thanks for the comment – this is a pretty central issue of the paper.

      – “If two bodies have different momenta, or different spin, then one normally says they’re in different physical states. But you seem to suggest in Par.5 that we are free to deny that claim. I don’t understand this.”

      The issue is whether the two states (q, p) and (q, -p) correspond to two distinct physically possible ways the world could be. In the case of momenta, we can coherently speak of different states corresponding to the same physical state insofar as the velocity is frame-dependent. This is just coordinative – it’s not to say that active velocity boosts aren’t physically real. For time reversal: suppose we have a tennis ball in motion between our racquets. From our ordinary perspective, I hit it, so it’s traveling towards you with velocity v. But this situation is described by classical mechanics only if its time reversal is. So, while it’s conventional to hold that the ball has velocity v, we can coherently describe it as having velocity -v, but in that case everything else would also be described with from the opposite temporal perspective to the our original one. The latter case may be unconventional, but all we’ve done is relabelled the situation – nothing physical has changed. To be clear, that’s not to say that from the original perspective the velocities v and -v are equivalent.

      – “In classical mechanics, time reversing a state S1=(q,p) gives you S1*=(q,-p). In QM, time-reversing the state S1=z-spin-up gives you the state S1*=z-spin-down. Are Farr and Reutlinger suggesting that we can interpret S1 and S1* as representing “the physical same state” in either of these cases?”

      I can’t speak for both conjuncts, but yes – I accept this, but only in the passive sense mentioned above. A world with two particles, both in z-spin-up eigenstates is different from world with two particles with opposite z-spin, so “z-spin-up” and “z-spin-down” don’t represent the same physical state here. But assuming T-symmetry, it is a matter of coordination whether you take a single particle to be described by one spin state or its time reverse. Once you’ve done this, this fixes the time-directed description for the rest of the system. For a single particle, unless T-symmetry fails, it shouldn’t make a difference whether I represent it by some particular state or its time reverse. However, quantum mechanics is perhaps complicated in that different ontic interpretations differ with respect to the T-symmetry/asymmetry of the underlying ontology.

      – “I’m not sure what criterion of “sameness” this involves, but if that’s what asymmetric causation requires, it seems like a pretty drastic price to pay…”

      There are other options for the defender of time-asymmetric causation, such as appealing to different theories of causation, such as counterfactual theories, dispositional theories, causal networks etc. where some further factor can give back the relevant asymmetry – we have nothing to say about these in the present paper. The idea in our paper is roughly that time reversal invariance could ‘exclude’ causation if causal relations hold between state tokens, and that these relations invert under time reversal.

      • Bryan says:

        I’m still worried this leads to contradiction. Take your initial state to be two particles about to collide. The time reverse is two particles that are separating. How can these two situations represent the same thing? To make it dramatic: suppose the collision would cause a bomb to detonate that destroys the world. Then one state leads to the world’s destruction, while the other doesn’t. Isn’t it a logical contradiction to say they are the same?

      • mwefarr says:

        I don’t think so. One leads to the world’s destruction, the other leads from the world’s anti-destruction. These can be taken to be different descriptions of one world. If the bomb introduces some irreversible process then this either takes us away from T-symmetry anyway, or the irreversibility is higher-level/emergent and so not directly relevant. But I agree that the causal aspect of this is unsatisfactory – if we take the two processes (the original and the time reverse) to refer to the same world, then we either give up causal talk, or we say it’s underdetermined. Neither is attractive, which lends credence to other ways to ground causal relations.

      • Bryan says:

        In one description the proposition P=”earth has a finite lifetime” is true. In the other description, P is not true. If you’re claiming these are both correct descriptions of our world, then that sure sounds a lot like asserting P&¬P….

      • mwefarr says:

        As I see it, if it’s true for one description it’s true for both. In the time reversed case, the Earth has a finite past, assuming T-symmetry.

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