Darby, a few more thoughts.
Energy can not be created or destroyed?
Yet it can be arranged. This arrangement is a kind of memory.
Now does this persist eternally into the future?
I think it has to.
The past is the foundation stone upon which the future is built.
If we have no persistent past, we are like Rutger Hauer in Blade Runner.
I believe there is a mirror 5th dimension in addition to our 4.
In this dimension is reflection, memory, ghosts, the past and even possible futures.
You're on the right track. Mass-Energy is a conserved quantity in a closed system. But then along comes general relativity and an ongoing debate over conservation of mass-energy in an open system (like the entire universe) marches on for almost a century.
Not intended to be rigorous:
Without going into the details, the Einstein stress-energy tensor in general relativity can be expressed in differential form. Doing that you can look at an infinitesimally small volume of space and it appears to be absolutely flat. No problem so far with conservation of mass-energy. But the tensor has a time component in it. Expand the volume of space in a gravitational field and it no longer appears flat. The time component is dependent on the local spacetime curvature. The curvature tensor depends on the time component. Spacetime varies dependent on the local curvature. This means that both the measuring rod (space) and clock (time), which are used to measure the mass-energy component of the system, vary.
The debate goes on as there are other mathematical approaches to the problem that appear to reduce the situation to a frame independent situation. But it hasn't been resolved. General relativity is a well tested theory and it includes as part of it's definition it's own downfall. Like all theories is it an approximation of "reality". The underlying issue in the on-going debate is that the theory is defined by the stress-energy tensor but the tensor itself is internally defined by other variavbles in general relativity. Such an important issue usually depends on definition by first principles (externally defined by some fundamental rule, law or theory).
Anyway...
The record of information, whether it is a book, tape, DVD, human brain, chemical, etc. is subject to degredation over time. If classical thermodynamics was strictly true it would be possible in principle to trace the path of every subatomic particle in the universe back in time and recreate every event in history back to the Big Bang. In that case all information is strictly conserved. Obviously, it is impossible to trace every particle or even a few particles back in time one second. Too many particles and time marches on while we look at just one of the particles.
However, classical thermodynamics is not strictly true. Quantum thermodynamics is a much better approximation of reality than the classical theory. In quantum physics particles do not have discrete positions, velocities, mass or energy before a measurement is made. In that case is becomes very difficult to state on the quantum scale that information is conserved.
The real question that we are asking is not so much that information is recorded and preserved in approximately an intact long lasting form because we know that it can be so preserved. What we are exploring is whether or not "the past" in its physical form is preserved such that we can use some device, a time machine, in order to travel from the present to the past and visit there "in real time", interact with it and possibly alter it - either intentionally or accidentally. That's the fundamental question that I was refering to. And it brings us back to the question of conservation of mass-energy.
As a
gedankenexperiment we propose a scenario:
The time travel experimenter invents a working time machine. The machine is in his/her lab and the plan is to travel back not to the Middle Ages but just 20 minutes. The plan includes building a spatial offset in the spacetime coordinates so that the gadget arrives in the lab next to the launch point not on it. The researcher climbs aboard, dials in the coordinates, flips the switch and appears in the lab 20 minutes earlier. In the lab we now have two working time machines and two identical researchers.
One hour prior to the experiment the researcher wrote, in pen - not typewritten - instructions for himself:
"If the experiment is successful give this note to your earlier self.
Self - if this experiment is successful I will not travel back to the future. Instead I will stay in the past with you. Twenty minutes later, when I'm back in my "present" we will not conduct the experiment."
When he was finished writing the note he signed it and had every other researcher in the lab sign it. They then all put an inked impression of their right thumbprint next to their signiture. This was to ensure that there was no question about forgery of the note.
On arrival he shares the note with himself. His twin also has a "copy" of the note. They compare and agree that it is the same note. Twenty minutes pass, they don't perform the experiment and two identical researchers, two identical time machines and two identical notes move forward in time. This is a paradox because we have three items that have created themselves because they did
not perform the experiment. There is one difference, which is yet another paradox. One of the twins remembers performing the experiment, the other does not share that memory. Yet when the appointed times comes the action is not performed by either. There's even a third confounding paradox. Why didn't the researcher who recalled performing the experiment also recall its outcome, his twin, the extra gadget, the note and their resolve not to perform the experiment
before flipping the switch? He both performed the experiment and followed the instructions not to perform the experiment and had no memory of any of it other than flipping the switch.
One argument could be Many Worlds. He landed in another universe. That doesn't really resolved the issue. The researcher and gadget are not individual subatomic particles. They are very massive classical objects. The probability wave for their outcome would be virtually straight up and down. There might be an infinite number of universes created but they would all be virtually the same - an extra researcher, note and gadget that seem to create themselves. By this method infinite mass-energy can be created.
The question of whether traveling to the past is possible or if the past persists is still open.
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