This is an interesting, but obvious-in-retrospect, consequence of superposition. Amplitude is contributed by all paths, but it's contributed to a state (a way-that-the-universe-could-be). The history is irrelevant, unless it has an effect on the final state – which is always true in the macroscopic world, thanks to the second law of thermodynamics and historians and space probes and chaos theory, but not always true in the microscopic world, where things are simpler.
This means that multiple histories contribute to a final state-of-the-universe: If A→B→C and A→D→C are indistinguishable (because C is the same state as C) then they both contribute amplitude – in layperson's terms, both histories are happening in parallel, then combining when they get to the same state.
If you've got states X and Y, and you're doing something like XOR swap, then you can go (X, Y) → (X^Y, Y) → (X^Y, X) → (Y, X) or (X, Y) → (X, X^Y) → (Y, X^Y) → (Y, X). This isn't fundamentally different from the ABC / ADC case; it obviously follows that this would happen too, though I'd never though it of it before.
T-symmetry says that the laws of physics look the same even regardless of if you are traveling forwards or backwards in time.
Classically speaking, T-symmetry would suggest that A→B→C and A→D→C should be impossible, because the time-reversed universe starting at C can have only state.
On the other hand, if you assume T-symmetry, and that it is possible to create superposition, then there must be a case, C → |B> + |D>, where state C goes into a superposition of states B and D. This means that it is no longer a violation of T-symettry for us to have both B → C and D → C. At least from the perspective of someone living in the universe. Under a many worlds interpretation T-symmetry would require you to say that the starting state of both B → C and D → C were actually the superposition all along. However, for someone living in the universe, it would be impossible to tell the difference between the universe being in one of the two states, or a superposition of both.
This is another way of saying that T-symmetry implies that all possible histories must have occured.
It is worth mentioning, that T-symmetry is believed to be false. However, CPT-symmetry (charge, parity, time) is thought to hold and I think the overall argument above still makes sense under CPT symmetry.
> it is no longer a violation of T-symettry for us to have both B → C and D → C
But you don’t have A → B → C or A → D → C, you have A → E → C.
Where E is a state (that can written in different ways as a combination of other states)
Analogy: if a wall is purple → purple → purple, would you say that its color history was purple → red → purple and purple → blue → purple at the same time?
> This is another way of saying that T-symmetry implies that all possible histories must have occured.
Actually, it's the opposite. Consider:
• A→{B,C}
• B←(A,D}
• C←{A,E}
That doesn't mean that A, D and E are all possible histories; when you consider B and C separately, D and E appear to be possible histories, but considering both B and C, you find that D and E cancel out,¹ leaving only A. So you can't actually make a claim about how many histories there are.
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¹: This is horribly misleading. D and E aren't the same thing-I've-been-calling-a-state-but-that's-the-wrong-word-sorry, so their amplitude doesn't get summed, so they can't cancel each other out. My analogy wouldn't work as well if I'd used the same letter, though. (Consider also that I didn't use bra-ket notation. This is an analogy, not rigorous.)
> It is worth mentioning, that T-symmetry is believed to be false.
I think that T symmetry isn't just believed to be false, but has been ruled out experimentally. (Or maybe I'm confusing these with CP violations https://en.wikipedia.org/wiki/CP_violation, which are simply believed to be T violations?)
Maybe in the parent comment C is an state (like A) but neither B nor D are states but stand for something undefined to make some kind of analogy. It’s extremely misleading at best.
None of them are supposed to be states; I used the word wrong. I meant “particle X is here, particle Y is there”, not the actual quantum state (which would be a superposition). I'm not sure what the correct term for this is.
As a non physicist, this always seemed to be the most logical explanation of the double slit experiment. The particle by default carries out all possible variations weighted by their likelihood of happening, so you get the wavey pattern like a normal distribution. By measuring it at an earlier point, we restrict ourselves to the outcome of only one of its possible pasts.
Measuring something doesn't change its behavior, just the range of possibilities.
> engines normally need a hot and cold reservoir to work, with a quantum switch they could extract heat from reservoirs of equal temperature — a surprising use suggested a year ago by Oxford theorists.
This is something akin to maxwell's demon. All Quantum processes save for measurement are reversible, and as such many thermodynamics concepts don't apply or don't apply in all circumstances.
It's worth noting that the measurement thing is what binds us to entropy's cold embrace in the long run. There's no maxwell's demon type thing that could run indefinitely without eventually having to perform something non-reversable, unless there's some horrible hack we haven't thought of yet.
I've thought about similar things, it seems to me to be a sort of retroactive causality.
It seems to me that there will be mutually exclusive states of reality existing in different spatial contexts; it's only at the meeting of light cones that the contradiction is reconciled (the likelihood of superposition mutex events is zero).
I left out the reason that I think that this is important - it eliminates "spooky action at a distance".
There's a fundamental equivalency there in terms of the consequences of the events - you can never outrun the light-cone of the remote event to reach any illegal states.
I love reading more computer sciency takes on physics because they always give the distinct impression of God patching together a universe that juuuust barely works. Just something about the phrasing of it is delightful.
Sure, in a creepy time erasing histories that were hitherto possible kinda way - but not in an event notification hopping gallactic distances without any form of medium kinda way.
This means that multiple histories contribute to a final state-of-the-universe: If A→B→C and A→D→C are indistinguishable (because C is the same state as C) then they both contribute amplitude – in layperson's terms, both histories are happening in parallel, then combining when they get to the same state.
If you've got states X and Y, and you're doing something like XOR swap, then you can go (X, Y) → (X^Y, Y) → (X^Y, X) → (Y, X) or (X, Y) → (X, X^Y) → (Y, X^Y) → (Y, X). This isn't fundamentally different from the ABC / ADC case; it obviously follows that this would happen too, though I'd never though it of it before.
Very thought-provoking article.