"The Economics of Time Travel "

 From Seeds of Science, December 19:

Abstract
The lack of time travellers visiting us may be seen as evidence that time travel is not possible. In this article, I argue an alternative explanation is that we are not economically important enough to our descendants to justify the costs of time travel. Using a cost-benefit analysis, I elaborate on this argument. I suggest that the major cost of time travel is likely to be the energy cost, whilst the largest benefit of time travel is knowledge which the present possesses, but the future has lost. Focusing on this benefit, I argue it is extremely unlikely that we possess a piece of knowledge which is sufficiently important to a future civilisation (system critical), but also has been lost by said civilisation. This is to say, we may not have been visited by time travellers because we are not important enough.

Introduction
One experimental way to prove the feasibility of travel forwards and backwards in time (i.e., time travel) would be to stage a large, broadcasted event. The location for such an event should be temporally significant—say, Greenwich—and the advertising for the event should be substantial. By substantial, I mean significant enough to be remembered for all of human history (call this the chrono-permanency criterion). Assuming such a feat of marketing is accomplished, matters turn to the event itself. The event should be a welcoming party for our descendants. It should serve as a message that at the particular moment in history that the event takes place—perhaps New Year’s Eve, 2023?—our descendants are to send a chrononaut to make contact. If no one shows up, this suggests time travel is not possible. If someone shows up, time travel would be demonstrated.

The above experiment builds from a logical argument: that if time travel were possible, we would be awash with time travellers. As we are not, time travel is not possible. Yet, this argument assumes something quite significant: that we, or any civilisation prior to ours, are worth visiting.1 In this article, I propose an economic cost-benefit analysis of time travel. I argue the main economic benefit which our descendants may receive via time travel is knowledge which we currently possess, but they have lost. Furthermore, this knowledge must be sufficiently critical to our descendants to justify the costs of time travel, which are likely to be dominated by energy costs. I posit that even assuming the energy requirements for time travel are met by a human civilisation in the future, it is highly unlikely that that same civilisation will come to depend on a piece of knowledge which we currently possess, but they have lost and cannot rediscover by other means. In other words, I argue that even assuming time travel is possible, our epoch is unlikely to offer any economic benefit to a future, time travelling civilisation.

The Economics of Time Travel to Date
Various economic perspectives on time travel have been proposed. A notable flurry of commentary, albeit tongue-in-cheek, began in 2006 as Tyler Cowen (2006) began musing on the economics of relativity, drawing on Krugman’s (2010 [1978]) Theory of Interstellar Trade (also see Cowen, 2008a).2 Cowen (2008a, 2008b) and others (Gans, 2008; Morehouse, 2012; Whitman, 2008) would build on these ideas further to incorporate labour within ‘transtemporal markets.’ The basic argument of these perspectives is that future epochs would be incentivised to use time travel to exploit the cheaper labour of the past, select epoch-specific legal structures which were beneficial for business, and embrace arbitrage opportunities for resources across time-periods. Gans (2008) is an exception insofar as they are critical of these arguments, and suggest that the clear, overwhelming economic advantage for a time traveller comes from using knowledge of the future to play markets of the past. Indeed, in a recent paper, Swinton (2021) argues that the stock market proves time travel to be impossible, because markets are less rational than would be expected if a flurry of actors with enhanced foresight were actively trading.

What is surprising about this literature (besides its existence) are the dual assumptions that a) time travellers would broadly operate within the same or similar economic system to that of the present; and b) that the past offers efficiencies for this economic system which the present would not. These assumptions are not wholly unjustified. For instance, if time travel were invented tomorrow, any would-be time traveller would have globalised capitalism as their framework of economic reference, and with that in mind, might indeed travel to the past to purchase Apple shares....

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