# Can changing the past ever be a coherent concept?

First, let me emphasize that I'm talking about changing THE past. Accounts with multiple timelines, say where travelling back in time causes a branching timeline, don't have this problem.

Here is the problem stripped down to its bare essentials: Suppose you have a pool table with two balls: a cue ball C and a nine ball N. You also have a time machine just big enough to fit C. You set up the time machine at time t1 so that if a ball appears in it, then the ball will roll out, hit N and knock N into a corner pocket, P, thus changing the past. Nothing happens. At time t2, you put the cue ball C into the time machine, fiddle the knobs to send it back to t1, and press the power button. C disappears. Did C go back in time and change the past? Well, no, because I've already stipulated that nothing happened at t1.

Well, let's change the story. Let's say that at t1, a ball appears in the time machine, rolls out, and knocks N into the corner pocket. Then at t2, you send C back to t1. Have you changed the past? No, because the past has not changed. It was always the case that a ball appeared and knocked N into the pocket, so once again, the past has not changed.

Where do we get the idea that the past can change? In time travel stories, it usually involves some time traveler who remembers an alternative past, and we assume for dramatic purposes that the individual is not hallucinating. So let's incorporate a form of memory into our experiment.

At time t1, nothing happens. At time t2, we write on C a message: "At time t1, no ball came out of the time machine". Then we put C in the time machine and send it back to t1 as before. What happened at t1? Nothing. Again, no change.

But let's say that at t1 C comes out of the time machine and hits the nine ball and sends it into the pocket. We pick C up and there, in our own handwriting is the message, "At time t1, no ball came out of the time machine". Ah hah! Proof that the past has changed, right? Not so fast. At what point in time did the past change? When you say something changed, you mean that at one time, say t_a, it was in one state, and at another time, say t_b, it was in another state. Presumably, t_b here is t1 since at t1 the past had already changed. When was t_a? There is no time at which t_a could have been.

You have to assume a second timeline. There are two ways I can think of to do this: first, there are two parallel timelines and t_a is t1 in the second timeline. What happened is not that the past changed, but that sending C "back in time" actually sent it to an earlier point in a different timeline. You have not changed the past; you have only influenced another timeline. This model is at least coherent, meaning that I can grasp what it means.

Alternatively, the second timeline can be a sort of meta-timeline in which our normal time is an object that can change. I think this is the sort of vague notion most people have in mind when they think of changing the past. In this model, the past is not something fixed; it is something that can change from the perspective of this meta-timeline. But this notion is bizarre. When C comes back with the writing on it, the time when the writing is no more. But then the cause of C having the writing on it is no more. So why does C still have the writing on it? The writing is uncaused. This meta timeline has to hold not only the timeline of changing timelines, but also has to be a repository of ghost causes from past states of the changing timeline.

I don't see how anyone can take this seriously once they follow out the implications. I think it's a consequence of the geometricization of time. It is useful in physics to view time geometrically, and once you are taught to do that, things like time travel seem to make sense because you are unconsciously treating time as a dimension of space where things can change, but time really isn't like that; it's only a way of visualizing time.

• this is a good question, when I was still in uni, the orthodoxy was that it was not coherent. Would be interesting to see papers + references for answers Commented Oct 2, 2022 at 22:15
• There is a popular website Temporal Anomalies in Time Travel Movies where the author surveys various theories of what is shown in movies. To accommodate what most of them present coherently, he came up with what he calls "replacement theory". Roughly, there is a single growing block universe timeline, but it is terminated and replaced once a time machine is activated and someone arrives in the past. The timeline is then rewritten from that point, but may again be terminated if the changes lead to causality violations. Commented Oct 2, 2022 at 23:09
• It seems there are stories about time travel as old as the Arthurian legend, so our science/technology oriented culture is probably not the key factor here. I wonder if it does not mostly have to do with language. "I went back in time and killed my grandpa" is a perfectly grammatically correct sentence, making this story a valid narrative that our brain can entertain. Examples abound: Athena came out of Jupiter's head, people changed into statues, ufo going faster than light, people resurecting from the dead, travelling to parallel universes... Commented Oct 2, 2022 at 23:17
• @armand, you make a good point about time travel stories. Maybe I can retreat to a position, not that the very idea of time travel is inspired by modern physics, but that the notion of changing the present by using time travel to change the past is inspired by modern physics (BTW, by "modern physics" I mean Galileo, not Einstein). Commented Oct 3, 2022 at 2:21
• Given that we cannot even agree what is happening in the present, then yes. Likewise the past isn't a single known objective reality cast in stone. It is subject to interpretation. And once a new fact comes to light that was previously unknown, the entire past can be thrown into doubt. Commented Oct 3, 2022 at 20:39

According to Einstein's General Theory of Relativity, time is variable and can bend. For a stationary astronaut (V=0) when 32 years passes, for his twin moving at 95% of the light speed (V=0.95 C) 10 years will pass, That's the equation: t = t0/(1-v^2/c^2)^(1/2), which means if you speed up, you are likely to stay younger. So practically if you can move at 0.99999 C, as you stay at your age, everything else will get older very fast.

That doesn't mean that you can go back. There is no coming back. What happened, happened, even if you stand still, or you fly in close to light speed, or you go in or around a black hole, all happened has happened, and will not happen again.

That is because we have a speed limit in our universe, which is the light speed C, to speed that up you need infinite amount of energy, how clever you are or how good time machine you can build, doesn't matter, you'll never have infinite energy, even for the smallest particle.

So light has no timeline, no time, light stays always at the same time, everything else have timelines with varying speeds with respect to a reference frame, the time slowing down is called time dilation, and time dilation is always greater than zero. At least, that is what the formula says.

So if the time t1 for an object has simply passed, if it's current time t=t1+10^−43 s time, there is no coherent physics, no infinite energy to send it back to t1. Time can speed up , time can slow down, it can branch, practically stop, but there is no going back.

• It's not the velocity in the twin paradox, it's the relative acceleration Commented Oct 16, 2022 at 19:32

Your question assumes that if you send the cue ball back in time to t1, the pool table and nine ball are still there waiting to meet it, whereas in fact the table and nine ball are no longer at t1 but at t2, so there is nothing at t1 for the cue ball to interact with.

In most branches of mainstream physics, reality is successfully modelled by assuming that matter is moving through a four dimensional spacetime. By moving through, I mean that individual particles trace out worldlines along which their time coordinate (in whatever frame you choose to measure it) is increasing. The particle exists as a point moving along the worldlines, so when a particle reaches t2 it is no longer at t1.

Given that, almost all of the talk about time travel and grandfather paradoxes is simply misguided. If you could find a way to travel back fifty years, you would not find your grandfather there, as the particles that once comprised your grandfather are in a different region of spacetime- along with the rest of the Universe- where you left them in 2022.

• "Your question assumes that if you send the cue ball back in time to t1, the pool table and nine ball are still there waiting to meet it" I very carefully described the thought experiment to make no such assumption. Can you explain where you see this assumption appearing? Commented Dec 15, 2022 at 8:18
• Your question explicitly states that you are sending a cue ball back from t2 to t1, and when it gets to t1 there is a pool table there. In other words, you are assuming that the objects that were present at t1 will 'still' be there if the cue-ball goes back to t1. Commented Dec 15, 2022 at 8:32
• No, my question does not explicitly state that I'm sending a cue ball back. I simply describe various scenarios of what might be observed. I didn't say that the cue ball goes back in time because the point of the question is that I don't know what it means to say that. Commented Dec 15, 2022 at 8:38
• But your equation actually contains the words 'Then at T2 you send C back to T1'. Commented Dec 15, 2022 at 13:00
• OK, I did say that. I thought it was clear from my previous wording, "fiddle the knobs to send it back to t1" that I was talking about the intentions of the experimenter and not what was actually happening, especially since my point was that the intentions of the experimenter don't make sense. Commented Dec 15, 2022 at 18:26