Presented at: Measurement and Similarity, Proceedings of the 17-24 Feb. 1990 Zeinisjoch Conference (P.J. Plath, org.).

Text follows in two days:

Measuring the Future

Otto E. Rossler

Institute for Physical and Theoretical Chemistry, University of Tubingen , 72076 Tubingen, Germany

Abstract

0rdinarily, the past can be measured and the future be controlled (at best). In quantum mechanics, the past can be controlled as well (Wheeler). It is proposed here that a symmetric result applies to the future – that it can also be measured. This proposal is made in a model context. It is the same model (“endophysics”) in which an analogue to Wheeler’s delayed choice has been described previously. A Newtonian molecular-dynamics universe becomes nontrivial under “closed-loop” conditions, that is, when it contains an observer explicitly. The micro dynamics of the latter then irreducibly invades any measuring chain. The chain vacillates in its causal orientation in time. In the anti-causal phase, it becomes a controlling chain. This fact generates an instantaneous link to the past. It is shown that controlling chains suffer the same fate of causal vacillation as measuring chains. In the anti-causal phase, they become measuring chains. Controlling the future without measuring it is as impossible as measuring the past without changing it. “Delayed choice” (through a measuring decision) and “advance knowledge” (through a controlling decision) are dual implications of the model world considered. The possibility that a similar principle may apply to our own world is discussed.

(May 1st, 1991)

1. Introduction

A favorite item in the virtual realities of our time is the “glove.” It allows one not only to manipulate, but also to sense – an option which does not exist in the real world but can be simulated in a computer. The same technique (use of the glove) can also be applied to our own world, not only relative to remote-control objects (where the term Telecheir or remote hand is customary) but also relative to microscopic objects. An experiment of this type has reportedly been performed recently by Hollis [1]. Here, a scanning tunneling microscope was controlled, not by an automatic scanner as usual but by the movement of the fingers of a human controller in a glove-like device called a Flotor. The “bumpiness” of the molecules making up the surface of a gold crystal could reportedly be clearly felt.

The same type of experiment can in principle be performed also within a purely mechanical world [2]. Such a “Hamiltonian model world” is of theoretical interest when it comes to elucidating the measurement problem of physics. It is well known that in our own world, micro-physical measurements are beset with tantalizing anomalies. Both “nonlocal” [3] and “past-changing” [4] effects have been predicted and reported, [5] and [6], respectively. The Newtonian model approach leads to analogous implications.

Presently, the “molecular dynamics simulations” paradigm [7] is not yet advanced enough to include a whole model world. While a simple dissipative macroscopic structure – an autocatalytic chemical reaction – has already been simulated successfully [8], no temporally recurrent macroscopic dissipative structure (like a limit cycle oscillation or a chaotic attractor or an excitable system, that is, an observer) has so far been simulated from microscopic first principles [9].

Nevertheless there is tacit agreement that no fundamental problems will arise along the way. It is therefore possible to theoretically investigate the implications of such a model world as far as its “closed-loop aspects" are concerned.

The resulting subject matter of “Endophysics” was recently reviewed [10] and put into a historical perspective [11]. "Explicit observers” [12] can be studied both “from the outside” and with a view of how the rest of the model world appears to them, that is, “from the inside” [13,14]. It was found [2,10] that micro-objects necessarily appear perturbed in a diffusion-like manner to such observers.

In the following it will be shown that the existence of a “nonlocal link with the past” [2,10,12] is not the only implication: an analogous link does also exist with the future.

2. The Double-Edged Measuring Chain

To an internal observer in an explicit Hamiltonian model world, measuring chains are neccessarily “pseudo-reversible [2,10]. That is, their causal orientation in time is vacillating at a rapid pace. Every second "time slice" – when the center of mass of the observer inverts its direction of movement relative to an external object –, the measuring chain is turned into an anti-dissipative, anti-causal link with the object so that the latter is being perturbed rather than measured.

The explanation for this startling prediction lies in the fact that the direction of time cannot be determined from the inside of a Hamiltonian universe. This fact was known to Boltzmann already, cf. [15]. Its implications for a closed-loop universe valid for an internal observer, however, got apparently overlooked for a long time. In such a situation, the macroscopic direction of time remains well-defined, cf. [15]. The fact that the “objective” (externally valid) direction of time which underlies the macroscopic temporal time evolution is inaccessible makes no difference from the inside. However, this comforting state of affairs ceases to be valid on the micro level. Here, the problem returns “with a vengeance.”

Hamiltonian trajectories are mathematically defined only up to “bi-uniqueness” [12]: A “red” and a “green” trajectory do necessarily coexist, the former being valid in the one direction of time, the latter in the other. This is because the Newtonian formalism is momentum-free (contains no first-order derivatives of time). The introduction of such a Hamiltonian phase space therefore is necessarily non-unique. Moreover, the definition of momentum is not arbitrary (as common sense would have it) but rather is subjected to an intrinsic symmetry. It is this symmetry which has nontrivial consequences. It renders the two different physical situations – backwards and forwards motion, respectively – indistinguishable under certain conditions.

Only when the whole universe in question is being considered is there no change relative to the usual formalism. But as soon as a sub-system is singled out, so that an “interface” between the latter and the “rest of the world” is defined [16], the situation is different. Boscovich’s equivalence principle [11] implies that a subsystem can never distinguish between the two following cases: In the first, the subsystem’s own internal momenta point the one way relative to all external motions, in the second, all internal momenta of the subsystem are reversed while simultaneously also all external motions are reversed.

This observation appears innocuous at first sight. But suppose that only the motions inside the observer are inverted (or switched between two equivalence classes whose elements are pair-wise identical except for time reversal. Then the above equivalence implies that it is the external world that has undergone a reversal in its causal orientation, rather than the observer.

While exact momentum reversals are almost infinitely rare in physics [15], a switching between two equivalence classes of motion that are identical under time reversal is actually frequent. In such a case, the measurement chain vacillates between two causal orientations in time [2,10]. This fact renders the last-mentioned effect pseudo-reversible [2,10]. The secondary consequences then include an analog to Nelson diffusion [17] which in turn implies validity of the Schrödinger equation.

3. Pseudo-Reversibility of Controlling Chains

While the previous result, found valid in a model world, is not too far away from our own empirical reality governed by quantum mechanics, there is a second implication of the model world worth considering that is novel in kind: Not just measuring chains are vacillating in their causal orientation in time, but so are controlling chains.

Every second time slice, such a chain is turned from a disamplifying controlling chain into an amplifying measuring chain. The “impedance matching” of the former case between the controlling finger and the micro-object (so that a force of fitting magnitude is applied to the latter) is hereby replaced by a situation in which it is the object that applies a controlling force to the finger.

The consequence is , once more, the establishment of a pseudo-reversible connection. The amplification and the dis-amplification do cancel each other out completely except for a statistical rest. As in the previous case, the connection acquires the character of one that is being mediated by a pair of mechanical levers. Therefore the connection is action-preserving. The observer's unit action ετ (where ε is kT/2 with T the observer temperature and τ the average duration of a time slice) is being imposed on the object as before.

In spite of these similarities, there is also a crucial difference though. The previous pseudo-reversible connection had provided an instantaneous connection with the past across the intrinsic delay of a measurement chain (“delayed choice” in the sense of Wheeler [4]). In contrast, the present pseudo-reversible connection provides an instantaneous connection with the future arching across the intrinsic delay of the controlling chain.

4. Measuring the Future

One may object that the measuring chain is being turned into a controlling chain every second time slice, and that any controlling chain by definition applies to the future. This is correct. Nevertheless the “future” refers to the momentarily valid direction of time which can be time-inverted as we saw. Hereby still the very same point on the time axis is involved as in the non-inverted situation – a point in the past.

In the case of a controlling chain, the future is genuine. Again we have an alternation between a controlling event (relative to the future) and a measuring event (relative to the past). However, this time around the “past” refers to a future point on the time axis. Thus, the measuring part of the controlling link that is valid every second time slice refers to the future, this time around.

This state of affairs loses its mystery if an objective – an “exo” – point of view is adopted. The observer then again only suffers the illusion of a time inversion. There never “exists” a perturbation of the past, nor does there exist a measurement of the future: It is always the inability of the observer to distinguish between the causal and the anti-causal time slices which generates the illusion of a connection with either the past or the future.

5. Interference between Past and Future

The most interesting case is the combination of a measuring chain with a controlling chain – the case of the “Flotor.” Suppose the observer is linked to the micro-object in question by a two-way temporal link: What are the predictable consequences?

By definition, a controlling chain and a measuring chain can never be set up in complete parallelism simultaneously. This follows already from the fact that a delay is impossible to avoid along either leg. If there were no delays, however, the object would be connected, both by an amplifying link leading down to the finger and by a dis-amplifying link leading from the finger down to the object. Both channels, combined, would cancel each other out, leaving only a rigid, non-amplifying connection.

The reason why we can nevertheless use our own nervous system – and our finger – to simultaneously measure and control a macro-object lies in the fact that the two channels in question are not exactly parallel, neither in time nor in space. If the finger is replaced by a micro-device (the tip of a scanner), the contact with the object no longer involves different contact points in space. Only the time delays enable the two channels to still work independently.

In our present case of the Flotor, we have two sets of micro-alternating channels: Either channel is a two-way channel as we saw, alternating between causality and anti-causality. Since the alternation is very rapid, only a minimum disturbance (with the magnitude of an action) remains between observer and object. In the one leg (meant for measuring), this disturbance causes an uncertainty in the measurable features of the object. In the other leg (the controlling one), it is the object that leaves a disturbing impact on the observer through a strongly amplified signal arriving during every second time slice. The net disturbance is hereby the same as in the measuring leg.

How do the two channels interact when they are combined? In the one time-slice, the past is measured and the future is controlled; in the next, the past is controlled and the future is measured. In the former time slice, the finger feels the past state of the object and nudges it into a new future position. In the second time slice, the finger feels the future state of the object and unlocks it actively from a past position. It is the same Flotor which mediates both pairs of effect. Both time slices cannot be disentangled by the observer. Therefore, the prediction that an interference between the two must occur appears straightforward. What are its features?

First, brief interruptions of either the in-going sensing or the outgoing manipulating channel ought to make no difference. Second, rapid disjunctive interruptions (occurring in alternation) should also make no difference. Third, the duration of the delay (supposed to be equal in both legs) should make no difference. The finest-resolution results achievable (in the magnitude of one unit action (“ε times τ”) should therefore be invariant under an “elongation-of-the-chain” type mode of operation. The time delay of the transmission link between observer and object, that is, between Flotor and micro­ sensor-cum-manipulator, ought to make no difference: a very strange proposal indeed.

6. Discussion

A new implication of the model-universe approach to understanding the measurement problem has been offered. When it comes to observing micro­objects, the latter are subject to a diffusion-type perturbation, not only when being measured, but also when being controlled.

This fact is not entirely unfamiliar in our own world – in the context of quantum mechanics. Since quantum objects are believed to be subject to the Schrödinger equation not only at the moment of measurement, but also at intervening times, the prediction made above that they “cannot be controlled accurately” carries little surprise. On the other hand, we also have an even stronger second prediction now, which may or may not represent an element of physical reality, too:

“Preparing” an object for a measurement by irrevocably sending-off a decision for a controlling operation to be performed on it, should immediately throw the object into a quantum eigenstate – so as if it had already been measured. Unexpectedly, this “prediction” is not a new prediction at all but rather forms an implication of the quantum formalism. It reflects the impossibility to “undo” a state preparation once it has been sent-off firmly.

The combined third prediction of an “interference” between past and future being possible, may already have been observed in the quantum domain. Mandel [18] described an interference experiment in which two different photons are involved. It appears possible to interpret this experiment as an interference between an event lying in the past (emission of the first photon) and a second event lying in the future (the later emission of the second photon).

A related interpretation can also be given to interference experiments of the “quantum Zeno” type (cf. [19]) where an atom is simultaneously illuminated by a photon field of one frequency and subjected to photon measurements along a different frequency range. Here, the roles of the two fields may turn out to be interchangeable – provided the symmetry between the control and the measurement link, described above for a model world, carries over to our real world.

The most spectacular “prediction,” finally, would be that a quantum Telecheir (Flotor) should work as well when the latter is placed at a larger distance, being placed on distant Mars, for example. It is here that the present model starts to look outlandish because a violation of Einstein causality would potentially be implied. However, the effect would by definition be confined to single quantum states, not to any macroscopic observable. However, there remains the “weak” possibility that even if this modest new “nonlocal” effect could be confirmed empirically, then still Eberhard's theorem [20] protecting macroscopic causality could be extended to this case.

To conclude, a new look at the “model-world approach to Nature” has been attempted. The relationship between measurement and preparation might be even closer than previously thought, both in a Newtonian Endophysics and in the real world. The model world approach may thereby acquire the rank of a viable heuristic tool.

Acknowledgments

Paper motivated by discussions with Mohamed ElNaschie and Jonas Rossler. I thank Peter Plath for his encouragement.

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