And then you say "putting ideas under the noses of the people who most hate them. That's what science fiction exists for." You sure about that? I suspect most readers who expressed a preference would say that they are generally rather keen on ideas. In fact, the literary-fiction crowd often use 'the idea is the protagonist' as a stick with which to beat SF. The problem is that the notion of travel comes from movement through space. When we're standing still, and on no conveyance, we are not traveling relative to the world around us (of course, the planet is traveling through space). But in the case of time, when we stand still, we are indeed moving forward at the pace of life in time. So, in that context, time travel must mean more than that standing still movement - it must mean traveling faster than that to the future, or at any speed at all to the past, which does not happen at all in natural life time. One view of time is that is does not actually "pass", as we experience it, and that there is nothing uniquely real about the present. There is a 21st century and there is a 16th Century, there are elephants and there are trilobites. The past or future are not less real because we do not coexist with them, any more than distant universes, separated from us by the speed of light, are less real because we cannot perceive them. As Einstein put it: "People like us, who believe in physics, know that the distinction between past, present, and future is only a stubbornly persistent illusion".
The events, say, in a person's life, can be viewed, not as a cradle to grave chronology, but as continuous whole that can be narrated in any order. Forwards, backwards, or hopping around like a knight on a chessboard. This view of time is explored in Vonnegut's "Slaughterhouse Five", and a 'backwards' version in Dick's "Counter-Clock World". This kind of time-travel is, I'd argue, consistent with physics; time cannot 'move' because it doesn't occupy a physical location from which it can move.
The idea of time travel was first set out by H. G. Wells (Fredric Brown makes a clever use of him in this book) but since then, like the internal combustion engine, very little of the idea has changed. We still generally think in terms of a machine or cabinet that propels the passenger backwards or forwards in time. Think for one moment however of the written word used by Mr. Wells and Mr. Brown to convey this idea. Well’s book was written in 1895 following thoughts happening inside his head. Without the written word, those thoughts would have remained trapped in 1895 unless some form of aural tradition of storytelling had taken it forward. Hence thoughts inside Mr. Wells' head have travelled from 1895 to 2017 and beyond as did the character Keith Winton (aka Karl Winston, his doppelgänger).
But Brown is not interested in time travel. As someone who is here and not there (possibly), I have noticed that there are two, possibly more universes, or realities in Portugal today. I cannot comment about other countries because, as I said, I am here, not there, yet it seems that, for many years now, the clear majority of people have been viewing the world through a screen. They awake and turn on the screen, then travel to work looking at the world through a screen, spend eight hours or so staring at another screen, sometime obeying the instructions that are displayed again and again and again, like Pavlov's dogs they salivate at each ping. Then they return home, looking at the world through a screen and doze off with a plastic tray on their knees staring wide eyed at another screen again. In this reality, there are a host of people who do not exist. Some of them are reported to have died years ago. I always understood that Adolf Hitler died in 1945, but there he is, still driving round Europe with his arm stretched out, shouting at people. And what is Henry VIII doing there? Apart from the dead people, there are many who believe that we should celebrate the fact that they do not exist. What is worse, they have award ceremonies to congratulate each other on their nonexistence. Recently I observed a new and disturbing phenomenon. These machine people from planet Screen now walk along the pavement with their eyes focused intently upon a tiny screen in their hands while jabbering away to an invisible man. I admit that my brain didn’t start to fall apart while reading “What Mad Universe”, but the massive torrent of ideas that Brown puts forward, and the startling consequences of those ideas are so interesting that I was reading it as the washing up piled up in the sink, and the house plants were dying around me. Too bad Brown was not more of a stylist. The prose is as wooden as a dead tree. But alas, the ideas are all there. Too bad Brown didn’t travel forward in time to 1957 to take full advantage of the fact that the many-worlds interpretation was not being really about the universe splitting per se, i.e., to avoid the problem of wave-function collapse that is invoked in measurement. The principle of superposition means that we can create states that are, for example, half spin up and half spin down. When we make a measurement of the spin, the wave-function collapses into only one of these states. However, these measurement processes are qualitatively different from unobserved processes, which allow the wave-function to evolve smoothly with time. This has led to a lot of discussions about the role of observers in quantum mechanics (Schrödinger's cat, etc.) The basic idea of many worlds is that there is nothing special about measurement. The wave-function only appears to collapse to the (necessarily quantum) observer, but all possible universes coexist in the same way that the states spin up and down can coexist for the electron.
There's more than one way to skin Schrodinger's cat. Dexter Palmer, 67 years later, wrote what Brown couldn’t.