Pasts in superposition
In this site the state of a particle has an existence, a reality-experience of its own. For an observer a particle always is in a superposition of all its possible states, all states that lead to the same observation by the observer.
If a state contains remnants of its past, those remnants will tell a logically coherent story about what happened in earlier times. If we have no knowledge available of those happenings in earlier times nor about the remnants, then the (unknown) remnants will appear to us, wil be experienced by us, as a superposition of all possible sets of remnants that could have lead to the present state. This superposition will remain until some measurement (or just decoherence effects) will force us to enter one of those worlds.
The past of a particle necessarily always is the superposition of all possible pasts that could have preceded it, all possible pasts that could have led to its present state.
Let's shift to an example of the philosophy so far. First we give a line-out of an experiment we want to perform.
Erasing the photon's travelling information
Suppose we have an electron at space-time-point A that emits a photon. The photon is heading for another electron at location B.
At space-time-point B (represented by the electron there) an act is performed on the photon that erases its travelling information without destroying the photon. The past of photon B is the superposition of all possible pasts that could have preceded it, all possible pasts that could have led to its present state. By erasing knowledge of the photon's state suddenly quite a number of possible pasts join the superposition.
Most of those possibilities do not contain the photon's birth at A. The photon then must have been born somewhere else. When we measure the photon then, we most likely enter one of those newly added possibilities.
In the new world we are in now, the conservation laws of impulse and energy demand there still is emitted a photon at event A, but it went another path. Most likely it went through B at precise the same moment as before, but without reacting with the electron there.
Where our photon has been born now we can figure out by elongating its travelling path backwards. It might be born on a distant star in another galaxy far away and many years ago, provided there is open sky at point B. In doing so we changed the photon's past from containing the photon's birth at event A into the photon being born quite somewhere else.
The conservation laws of impulse and energy demand the photon coming from this new origin already existed in that first world from which we started, where the photon was moving from A to B.
Mind all this assumes a photon can be acted on (erasing travelling information at B) without destroying it (it passes B).
Changing the links between local environments
I wonder if I am right about the proposed restrictions that the conservation laws impose on new worlds. We assume in all superposed worlds the same laws of physics to hold. Otherwise an outside observer could not interpret the interference pattern it experiences according to one set of physics laws. The laws don't change when shifting from one world to another. The conservation laws hold in any of the superposed worlds.
But do the conservation laws apply to the shift itself? Could a measurement make us enter a complete different universe, with new and different outside observers, as long as the new universe obeys the old laws? It is not the universe that changes then, neither it is us. It is the link of our local environment to the outside, to the rest of the universe, that changes to a different link.
The superposed worlds differ. That is, they can differ, in net number of photons, in net baryon number and net lepton number, as long as the measureable quantities of the wavefunction will yield the same values when observed. The case of correlated particles (See Experiment 1 the EPR experiment at page 1 of EXPERIMENTS ON THE COLLAPSE OF THE WAVEFUNCTION) shows the differences might be distant to each other. But this is all meaningless. We are our local environment, local in space and time. The speed of light is the upper limit of an influence. We can gather observations from far away and long ago, but we know them only when data about it (read: particles) had actually reached us. Then we enter one of those possible worlds.
This is what I think Descartes meant by his expression
I think so I am. Nothing is for sure. The world may end just outside your visible horizon. The remembrance to the past might be fake memory. The future has always been uncertain. There is only one thing for sure:
I think so I am. Your here-and-now experience. Your local environment.
There is no influence to a local environment other than through the direct neighboring environments. You can't pass over environments. You can take a different route but that route too has to consist of a continuous row of events. You can't break up a particles worldline in disconnected points or line pieces.
The speed of light is established as the absolute upper limit of every kind of displacement in Experiment 2 The inverse square force law at page 2 of EXPERIMENTS ON THE COLLAPSE OF THE WAVEFUNCTION, amongst a number of other things about the adapted interpretation of quantum mechanics that I present in this site. Experiment 2 is considerably longer than Experiment 1.
This is in agreement with special relativity. In sr a frame of reference can be decomposed in a collection of linked neighboring local environments. The lorentz-transformations between two frames can be rewritten as a changing of the links only, see the storyline SR about Special Relativity, especially page 7. When you are changing speed, links are disconnected with neighbors in spacetime and are reconnected with other neighbors in the same spacetime. In fact that's all there is to special relativity.
It is in agreement with GR too. As is argued in TONE, Chapter 1, especially in 1.3 General Relativity, space is not curved. Absorption from the Higgs field curves space, and the subsequent actions of gravity curve space back to zero curvature. The vacuum consists of vacuum marbles. So anyway one can regard every single marble as a local environment. The curvature of space, including its curvature back to zero, can be reinterpretated as the links between vacuum marbles changing into other links with eventually other vacuum marbles.
Isn't it all about the question whether the local shift to another world is an event? Well, the only other worlds we have in qm (quantum mechanics) are the superposed worlds, the worlds in a superposition. E.g. the superposed states of an electron, which might feel as
inner worlds. Or the superposition of outer environments around the space time points that you are, call it your Local Spacetime, that indeed feels as
outer worlds. And the only thing we can do in qm is entering one of those worlds (by measuring), or not. So there is no point in a shift from one superposed world to another world in the superposition. Before such a measurement you are surrounded by a superposition of local environments, all environments that would sustain the existence of your Local Spacetime as you know it. After the measurement the situation is still a
you surrounded by a superposition of environments, but the ensemble of worlds in the superposition might have changed. Some worlds are out now, other worlds are new, maybe never seen before.
Each of the local environments is regarded as a whole, a coherent, existable whole of vacuum particles and eventually real particles and antiparticles therein. Mind, we better regard the entire 4-dim spacetime, not only the 3 dimensions of your local environment. So each of the local environments are the entire of space and all its past and all its future. And those space might differ from each other, their space as well as their fitting past and future. As long as the entire of each world can exist an does sustain your existence.
The outside observers experience the interference of all possible you's, as long as they don't observe you. But in fact there are more you's than an outside observer can experience. You - just one of them - experience the interference pattern of all possible outside observers, as long as you don't observe them. The same you's fitting with different outside observers.
When you enter an outside observer, do the other outside observers disappear then? This is the same question as in a superposition of states, entering one of them and then to ask whether the other possibilities disappear. The answer must be no. For every you entering an outside observer there is another you that didn't measure the outside yet. Or that entered a different outside observer.
Is it possible not to observe the outside observer? The outside observer consists of the rest of the universe - all of the universe including all past and all future, all except for your own local environment. The fabric of their spacetime bears some properties of the universe: its observable 3-dimensionality, its direction of time and its parity, that is what follow from the world of view TONE delivers. So in the way your local environment bears these properties then all your possible outside observers are bound to them too.
So at this stage the answer seems to be
Yes, the past can be changed, as long as the remnants of the past are outside your Local Spacetime and are not measured yet. The measurement of the electron and in doing so reducing its wavefunction, might shift all of its outside (in space and time) to a universe in which the electron had a very different ensemble of pasts, an ensemble that differs from the ensemble in your Local Spacetime as it was estimated so far.