It's 1999 and John is still devastated because of his dad's death 30 years earlier. The father, Frank, was a firefighter. On the night before his fatal fire in 1969, he would turn his ham radio on. And the man on the other side was John calling from the year 1999 and from the same ham radio. It just happens that both men could listen to Brian Greene on TV who was just explaining that string theory had 10 or 11 dimensions and perhaps, the number of time dimensions could be higher, too. It is not explained in the movie how a mature Brian Greene got to 1969 when the actual Brian Greene was 6 years old. Maybe we should send an e-mail to Brian who could explain how he managed to do that.
This communication across time was possible due to the aurora borealis (northern lights) that surrounded their house both in 1969 and 1999, we're told. After an irritated beginning of the conversation, they convince each other that they're indeed the "father and son" calling from the same house across the 30-year time barrier.
Using valid "predictions" of baseball games, John ultimately convinces his father that he is the son calling from the future and tells him to choose a different escape route from the fire. Frank survives as a result and they create a new branch of the spacetime in which Frank didn't die in the fire. Instead, he would die of cancer 20 years later. Another detail: the son also convinces his dad to quite smoking 30 years earlier. However, Frank's wife i.e. John's mom is killed by a serial killer in the new branches, a consequence of the modifications they have caused. Finally, John (a cop) and his dad (firefighter) team up and neutralize the killer, a bad cop of a sort.
Finally, they manage to produce a satisfactory draft of the spacetime in which they are together in 1999 – including John's boy that wouldn't otherwise exist due to John's bitterness, either. A friend of John – a boy from 1969 named Gordo – was also given a great gift by the old John through the intertemporal ham radio. It was a secret word: Yahoo. In the optimized draft of the spacetime we see at the end, Gordo would probably buy stocks of Yahoo before they dropped.
The Yahoo stock went from $1 in 1996 to a high $108 in 1999 but it later returned up to $4 or so in 2001. Frequency was released in April 2000 ($60) so I guess that if its creators had known about the burst dot-com bubble, they would have been more careful about the timing in the portfolio recommendations. ;-)
Tons of science-fiction movies contain time machines of various kinds. They lead to paradoxes. People may usually "land" anywhere they want and modify anything they want. I would say that this "aurora borealis" wormhole through time is somewhat subtler although it is still inconsistent. Don't get me wrong: it is silly to identify deep and speculative wormholes that may be proposed in quantum gravity with mundane meteorological phenomena. But by localizing the bridge, one partially reduces its inconsistent implications. As the movie shows, such modifications still require several branches of the spacetime ("timelines" in the filmmakers' jargon) to exist.
First, why is the generic time machine with a single branch inconsistent?
It's inconsistent because of the closed time-like curves (CTCs). It's a closed i.e. "periodic" curve (its topology is a circle) that is time-like and non-singular everywhere (it therefore keeps the same future-past direction). What's wrong with CTCs? There are events along the curve whose probabilities may be calculated from the properties of the previous events. The events in 1999 follow from those in 1998 which follow from 1997, and so on. If the events in 1969 depended on those in 1999 in the same way (a loop), it would be pretty much impossible for the loop to close. The system of equations would be overdetermined.
More precisely, in classical physics, the deterministic laws just don't evolve the configuration in 1969 to configurations in 1970, 1971, ... and 1999 so that the 1999 configuration could be smoothly connected to 1969 again. Quantum mechanically, the evolution is not deterministic but similarly, the evolution at least at one point of the closed loop would have to include transformations that would be vastly unlikely according to the probabilistic laws of quantum physics.
So closed time-like curves – including their special examples such as Universes which respect the opposite arrows of time at different places – lead to a conflict with the dynamical laws of physics. At this moment, I must remind the dear reader of the incredible stupidity of the "deniers of irreversibility" such as Sean Carroll. I've done it many times but let me expose the incredibility of their stupidity in slightly newer way now.
Imagine that you have some basis of states \(\ket{\psi_i}\) at time \(t_0\) and some basis \(\ket{\psi_\alpha}\) at a later time \(t_1\). The evolution operator \(U\) (imagine the S-matrix) is composed of the matrix entries \(U_{\alpha i}\) which express the complex probability amplitude that the initial state \(\ket{\psi_i}\) at time \(t_0\) evolves to the final state \(\ket{\psi_\alpha}\) at a later time \(t_1\). The probability is computed as\[
P_{i\to\alpha} = |U_{\alpha i}|^2.
\] The probability with an arrowed subscript may sound a bit heuristic. Let's rewrite it a bit differently. The probability above is nothing else than\[
P(\alpha|i)\equiv P(\psi=\psi_\alpha\text{ at }t=t_1| \psi=\psi_i\text{ at }t=t_0).
\] It is the conditional probability that the state will be \(\alpha\) at the later time given i.e. if it were \(i\) at the earlier time; note that this statement is exact and kindly verify it. The irreversibility deniers who believe that the laws of physics may be used in both directions are pretty much explicitly saying that the same matrix elements \(U_{\alpha i}\) encode the probabilities for the opposite evolution as well. It means that they are saying that\[
|U_{\alpha i}|^2 = P(\alpha | i) = P(i|\alpha).
\] Because \(P(\alpha|i)\) is pretty much the most general form of a conditional probability, they are saying that\[
P(A|B) = P(B|A)
\] which, I hope you will agree, is breathtakingly stupid. Conditional probabilities just aren't symmetric at all. If the squared amplitudes \(|U_{\alpha i}|^2\) may be interpreted as \(P(\alpha|i)\), the forward evolution's probability, and the experiments show that they can, they just cannot determine the opposite conditional probabilities because the conditional probabilities \(P(A|B)\) aren't symmetric in \(A\) and \(B\). (More precisely, the pure-to-pure probability is indeed symmetric but the symmetry between \(A\) and \(B\) is broken as soon as these propositions start to represent ensembles of states i.e. "one pure state or another" etc.)
The most direct not stupid link between the two probabilities is Bayes' formula\[
P(A|B) = \frac{ P(B|A) P(A) }{ P(B) }.
\] The extra factor \(P(A)/P(B)\) is what guarantees that the processes with a decreasing entropy by \(\Delta S\) are \(\exp(\Delta S / k)\) times less likely than their increasing-entropy cousins. Retrodictions of the past don't have easily calculable probabilities. Instead, these probabilities must be determined by the Bayesian inference which always depends on some subjective priors and has other subtleties. The laws of physics only dictate well-defined probabilities in one direction, the forward-in-time direction! That's the logical arrow of time, a defining feature of time in any physical Universe. The future predictably (albeit probabilistically) follows from the past but not the other way around.
I was talking about the usual probabilities in quantum mechanics but it's important to know that everything I said would hold for the probabilities in statistical physics (even classical statistical physics), too. They also determine objective probabilities in the forward direction only. If you want to determine the past, you must "reverse engineer" the problem and due to reversibility, the laws of physics won't give you any clearcut canonical values of the probabilities.
The Frequency movie talks about the creation of several branches of the spacetime ("timelines"). I don't exactly understand how to physically interpret such a concept. I think it's inevitable that such a picture suffers from the same inconsistencies as the "many-worlds interpretation of QM taken too seriously". Even though a spacetime with branching points could possibly exist, I think that the branching points would be singular and therefore qualitatively different. The moment at which Frank's life is branching into several "timelines" – he is burned in one of them but survives in others – would have to look very different from other, generic moments of time. After all, we see the furniture in John's room as it is transforming in 1999. Proper physics of quantum gravity would probably require more dramatic events than changing clothes on the furniture – namely extreme firewall-like Planckian events.
To summarize: I do think that the laws of physics will always avoid closed time-like curves of all kinds. For this reason, they will also prohibit the 1969-1999 ham radio from the movie. However, in the discussions about time travel and similar things, people used to clump genuine time machines containing closed time-like curves with some other examples of an unusual spacetime topology. Some of those may be allowed by the laws of physics, despite their "superficial similarities" to the CTCs.
For example, the Einstein-Rosen bridge was legitimized by Maldacena and Susskind in 2013 (who presented evidence that such a bridge is as mundane as an ordinary entanglement – in fact, any entanglement is equivalent to such a bridge). This bridge contains a moment at which the horizons of the two connected black holes are directly touching – so they exist "at the same moment", too. Could you connect the interiors of black holes that existed at different times – in regions of the spacetime that look time-like-separated from the viewpoint of the surrounding spacetime? Could such a shared, intertemporal black hole interior resemble Peter Pan's Neverland (another movie playing with time we could watch a few days ago: trailer)? ;-) I remain mostly open-minded.
More detailed analyses of such questions don't reveal that "anything goes". There are things that remain forbidden. But "some things" that used to be assumed to be impossible sometimes become possible. Stereotypes sometimes melt and the newer picture of what is allowed and what is disallowed by the laws of physics is more structured than the previous overgeneralized, black-or-white beliefs.
For decades, it would be assumed in string theory that "really complicated" Penrose diagrams such as those on the picture above would be impossible. Cauchy horizons inside rotating or charged black holes are unstable, and so on. However, it's plausible that string theorists will return to these issues and they may find out that such dramatically nontrivial Penrose diagrams describe a legitimate way how to "perceive" some quantum information.
Yes, this blog post is just a less religious, more sci-fi-oriented cousin of Quantum gravity and afterlife.
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