Reality, No Matter How You Slice It

Abstract

In order to reject the notion that information is always about something, the “It from Bit” idea relies on the nonexistence of a realistic framework that might underly quantum theory. This essay develops the case that there is a plausible underlying reality: one actual spacetime-based history, although with behavior that appears strange when analyzed dynamically (one time-slice at a time). By using a simple model with no dynamical laws, it becomes evident that this behavior is actually quite natural when analyzed “all-at-once” (as in classical statistical mechanics). The “It from Bit” argument against a spacetime-based reality must then somehow defend the importance of dynamical laws, even as it denies a reality on which such fundamental laws could operate.

Appendices

Appendix I: The Universe is Not a Computer

Isaac Newton taught us some powerful and useful mathematics, dubbed it the “System of the World”, and ever since we’ve assumed that the universe actually runs according to Newton’s overall scheme. Even though the details have changed, we still basically hold that the universe is a computational mechanism that takes some initial state as an input and generates future states as an output.

Such a view is so pervasive that only recently has anyone bothered to give it a name: Lee Smolin now calls this style of mathematics the “Newtonian Schema” [14]. Despite the classical-sounding title, this viewpoint is thought to encompass all of modern physics, including quantum theory. This assumption that we live in a Newtonian Schema Universe (NSU) is so strong that many physicists can’t even articulate what other type of universe might be conceptually possible.

When examined critically, the NSU assumption is exactly the sort of anthropocentric argument that physicists usually shy away from. It is essentially the assumption that the way we solve physics problems must be the way the universe actually operates. In the Newtonian Schema, we first map our knowledge of the physical world onto some mathematical state, then use dynamical laws to transform that state into a new state, and finally map the resulting (computed) state back onto the physical world. This is useful mathematics, because it allows us to predict what we don’t know (the future), from what we do know (the past). But it is possible we have erred by assuming the universe must operate as some corporeal image of our calculations.

The alternative to the NSU is well-developed and well-known: Lagrangian-based action principles. These are perhaps thought of as more a mathematical trick than as an alternative to dynamical equations, but the fact remains that all of classical physics can be recovered from action-extremization, and Lagrangian Quantum Field Theory is strongly based on these principles as well. This indicates an alternate way to do physics, without dynamical equations—deserving of the title “the Lagrangian Schema”.

Like the Newtonian Schema, the Lagrangian Schema is a mathematical technique for solving physics problems. One sets up a (reversible) two-way map between physical events and mathematical parameters, partially constrains those parameters on some spacetime boundary at both the beginning and the end, and then uses a global rule to find the values of the unconstrained parameters and/or a transition amplitude. This analysis does not proceed via dynamical equations, but rather is enforced on entire regions of spacetime “all at once”.

While it’s a common claim that these two schemas are equivalent, different parameters are being constrained in the two approaches. Even if the Lagrangian Schema yields equivalent dynamics to the Newtonian Schema, the fact that one uses different inputs and outputs for the two schemas (i.e., the final boundary condition is an input to the Lagrangian Schema) implies they are not exactly equivalent. And conflating these two schemas simply because they often lead to the same result is missing the point: These are still two different ways to solve problems. When new problems come around, different schemas suggest different approaches. Tackling every new problem in an NSU (or assuming that there is always a Newtonian Schema equivalent to every possible theory) will therefore miss promising alternatives.

Given the difficulties in finding a realistic interpretation of quantum phenomena, it’s perhaps worth considering another approach: looking to the Lagrangian Schema not as equivalent mathematics, but as a different framework that can be altered to generate physical theories not available to Newtonian Schema approaches [6].

Appendix II: Previous Work

In quantum foundations, analyzing four-dimensional histories “all at once” is uncommon but certainly not unheard of; several different research programs have pursued this approach. Still, in seemingly every one of these programs, the history-analysis is accompanied with a substantial modification to (A) ordinary spacetime, or (B) ordinary probability and logic. Looking at previous research, one might conclude that it is not the all-at-once analysis that resolves problems in quantum foundations, but instead one of these other dramatic modifications. But such a conclusion is incorrect; a history-based framework can naturally resolve all of the key problems without requiring any changes to (A) or (B).

Any approach that incorporates the standard quantum state is already a dramatic modification to spacetime (A), because multiparticle wavefunctions do not reside in ordinary spacetime. (They instead reside in a higher-dimensional configuration space.) This includes approaches that (arguably) have some all-at-once element (including GRW-style flash ontologies [15–17], Cramer’s Transactional Interpretation [18] and the Aharonov-Vaidman two-state approach [19]). Even if these approaches somehow argued that they did not use the standard quantum state, they are still using functions on configuration space, not spacetime—and therefore fall in category (A).

Several history-based approaches in the literature do not take anything like the standard quantum state to be a “real” part of the theory. Griffiths’ “Consistent Histories” framework [20] is one example, although it is not a full explanation, as there are many cases where no consistent history can be found. Also, there is never one fine-grained history that can be said to occur. Gell-Mann and Hartle have recently [21] attempted to resolve these problems, but in the process they modify probabilistic logic (B), enabling the use of negative probabilities.

Several history-based approaches have been championed by Sorkin and colleagues. A research program motivated and based upon the path integral [22] is of particular relevance, although it is almost always presented in the context of a non-classical logic (B). (Not all such work falls in this category; one notable exception is a recent preprint by Kent [23]). This path-integral analysis is rather separate from Sorkin’s causal set program [24], which seeks to discretize spacetime in a Lorentz-covariant manner. While this is also history-based, it clearly modifies spacetime (A).

Another approach by Stuckey and Silberstein (the Relational Blockworld [25]) is strongly aligned against dynamical laws, and the all-at-once aspect is central to that program. But again, this history-based framework comes with a severe modification of spacetime (A), in that the Relational Blockworld replaces spacetime with a discrete substructure. It is therefore unclear to what extent this program resolves interpretational questions via the non-existence of ordinary spacetime rather than simply relying on the features of all-at-once analysis.

Finally, an interesting approach that maps the standard quantum formalism onto a more time-neutral framework is recent work by Leifer and Spekkens [26]. Notably, it explicitly allows updating one’s description of the past upon learning about future events. Because the quantum conditional states defined in this work are clearly analogous to states of knowledge rather than states of reality, the fact that they exist in a large configuration space is not problematic (and indeed there is a strong connection to work built on spacetime-based entities [13]). Still, the logical rules required to extract probabilities from these states differ somewhat from classical probability theory (B).

Any of the above research programs may turn out to be on the right track; after all, there is no guarantee that the entities that make up our universe do exist in spacetime. But the fact that most of these approaches modify spacetime (or logic) has thoroughly obscured a crucial point: A history-based analysis, with no dynamical laws, need not modify spacetime or logic to resolve quantum mysteries, even taking the quantum no-go theorems into account. For further discussion of this point, see [9].

Appendix III: Model Details

The model in Fig. 16.2 (reproduced below) has the following rules. Each circle can be in the state heads (H) or tails (T), and each line connects two circles. Each line has one of three internal colors; red (R), green (G), or blue (B), but these colors are unobservable. The model’s only “law” is that red lines must connect opposite-state circles ($H\!-\!T$ or $T\!-\!H$), while blue and green lines must connect similar-state circles ($H\!-\!H$ or $T\!-\!T$).

When analyzing the state-space, the key is to remember that connecting links between same-state circles have two possible internal colors (G or B), while links between opposite-state circles only have one possible color (R). Combined with the equal a priori probability of each complete microstate (both links and circles), this means that for an isolated two-circle system, the circles are twice as likely to be the same as they are to be different.

In Fig. 16.2a, given that the bottom circle is H, there are four different microstates compatible with an H on the left and an H on the right. This is because there are two links, and they can each be either blue or green. (Specifically, listing the states of the three circles and the two links, the four possible “HH” microstates are HBHBH, HBHGH, HGHBH, and HGHGH.) According to the fundamental postulate of statistical mechanics, an HH will be four times as likely as a TT, for which only red links are possible (TRHRT). The full table for Fig. 16.2a is:

Figure 16.2b is more complex, in that there is now a fourth circle at the top. The fact that there are four links also means that there are 16 different microstates corresponding to all H’s (4 green or blue links, $2^4=16$), but only one microstate corresponding to the case with T’s on the right and left and another H on the top (4 red links). The 2b table is:

However, since we are not interested in the status of the top circle in this model, the relevant numbers are the total number of ways in which one might have (say) an H on the left and right. To get the total number of such states, one simply sums the first two rows of the previous table. In other words, there are 20 different states that have HH in the dotted box of Fig. 16.2b; 16 with H on top and 4 with T on top. The more useful 2b table is therefore:

Notice there are 25 ways in which the right and left circles match, versus 16 ways in which they do not match. This contrasts with a 5:4 ratio for Fig. 16.2a.