When the energy goes below one Planck unit, the sound wave is literally unable to cause the next molecule ahead to undergo a state change (it doesn’t move). At that point, the molecule ahead acts as an immovable barrier and the sound wave stops at that point.
The energy yielded by a photon is what the retina is detecting. If the photon had no energy, you would not have been able to see it.
That is correct, it isn’t zero. But one atom per cubic meter means that even if there is an interaction between two atoms, that interaction is even more unlikely to effect a third atom another meter over.
Like, really really unlikely.
What you have here is not a compression wave. What you have is particles moving and vibrating randomly.
What you’re going to have to face here is that your intuition about how far away things are are how small quantum effects work is not likely to be correct. Your intuition will do pretty good when thinking about things your brain evolved to think about–the behavior of rocks and trees and so on.
Again, think of an experiment I could do with you.
We take a tub full of water and I drop a drop of ink into the water. A minute later I let you see the tub. Can you tell where I dropped the ink? Yes, because you can see a part of the water that is darker than the other parts, so you have a record of where I dropped the ink.
Now we take a jaccuzzi full of water. We turn on the jets. Then I take another dropper of ink and I drop some ink at some coordinates in the hot tub. We let the jets churn for an hour. Then we let you investigate the hot tub. Where did the ink drop?
There is no way for you to answer that question, even if you really could measure the location of every molecule of ink in the tub. The ink molecules are so thoroughly mixed that there is no point in the hot tub that has a higher concentration than any other. Or rather, that there places with very slightly higher concentrations than others, but these concentrations are distributed at random, and the spot where the ink dropped is no more likely to have a higher concentration than any other spot.
So even when you can measure higher concentrations down to one-molecule differences you still can’t detect the location of the ink drop.
Or to put it another way, take a deck of cards in a particular order. I cut the cards and let you examine them. You are able to reconstruct a lot of the information about the original deck. Now I shuffle them once. You still might be able to reconstruct some information about the original order.
Now I shuffle them 10 times. There is no way to reconstruct the original order of the deck after 10 shuffles just by examining the current order of the cards, because you have no way to reconstruct the many random events that happened in each of the 10 shuffles. I can let you examine the deck with any instrument you choose, and you will never be able to tell, or make any sort of guess, what the original order was.
Good point. It becomes a philosophical question about the nature of reality and humanity’s relationship to it. A distinction should probably be made between signals that can theoretically be detected but cannot be detected at the current time due to limitations in technology and signals that cannot be detected at all under the laws of physics as they are currently known.
Signals in the second category could arguably be said to exist outside the universe, or at least outside the realm of Science’s ability to examine them. They would thus be non-scientific, and possibly religious in nature, since any sort of assertion as to their nature would be an unfalsifiable statement of belief.
You might be able to do it if the Heisenberg Uncertainty Principle could be worked around. Since it probably cannot, you are right.
This definitely does not happen at one Planck unit. For any sound wave ever observed, or even every one ever seriously hypothesized, the energy of the particles is vastly less than the Planck energy.
And as far as those signals persisting: There is in fact a distinction between the information being unrecoverable and the information actually being destroyed. It’s a fundamental tenet of quantum mechanics that the information can never be destroyed. Even if it’s swamped out by noise to the point that there’s no hope that it could ever conceivably be recovered, it’s still there.
Assuming one or another solution to the Black Hole Paradox anyway … 
Wow. So many replies that I will not read them all, and just spew my 2 cents.
If that last molecule that moves, does not move enough to move the molecule ahead of it. then the sound ends.
I believe that there is a cutoff on the energy that one thing can transfer, that will cross whatever gulf there is to actually affect another thing. At some point, there is no measurable or detectable effect. All the initial energy has dissipated. Being transformed to the intended measurement and other dissipation’s. Quanta. Half a Quanta is as good as no Quanta at some point. A thing may absorb all of an input energy, to various other actions, but not enough at that point to affect another thing.
That makes no sense. Nothing stops moving unless it’s stopped by something else, and if it’s stopped by something else, then it’s moving that something.
I suppose you could sort of apply that statement to a solid in hard vacuum. The atoms or molecules in the solid would move towards the edges of the solid and there they’d be unlikely to meet a gas molecule to transfer energy to, so the sound would “end” in that direction and be reflected instead. But I didn’t get the sense that this was what you meant.
This isn’t right. If we neglect quantum effects for a moment, then the precise knowledge of the position and movement of all of the molecules in the tub will allow us to ‘rewind’ the evolution exactly, up to the point where the ink first entered the water.
Of course, quantum mechanically, you can’t obtain that perfect knowledge. Nevertheless, the same general statement still holds true: quantum evolution is information-preserving (‘unitary’), so the precise knowledge of the quantum state at one point in time, plus the knowledge of its evolution, will allow you to calculate the system’s state at any other time. Only during a measurement does any randomness enter, and even then it depends on the interpretation somewhat.
But for every closed, isolated system, information is always conserved (and we can always move to a bigger system to incorporate any interaction with the outside).
This would violate the conservation of energy: you’d have a scenario where there is some energy at one point in time, and none anymore at another.
The quanta of the vibrational field of the atomic lattice—the phonons—can be treated, in many respects, just like ordinary particles. As such, they don’t just spontaneously vanish, and may propagate arbitrarily far.
If a signal falls in the woods…
HMHW, help me out here …
Two waves cancel each other out … how how is possible rewind from what is measurable what had been there?
A ball is at rest in a ditch (oh, call it an attractor basin) between a group of large hills … can you measure current data and determine which path it had taken to get there and its location at any particular t minus n?
How does the rewindable deterministic view of the universe fit with the idea that there is no emptiness but instead random quantum vacuum fluctuations (quantum foam)?
Two waves can cancel out at one particular location, or at one particular time. They can’t cancel out everywhere, everywhen.
Good article on how the sound waves from the eruption on Krakatoa were heard (felt) 3000 miles away and circled the earth 3 or 4 times.
I have to admit I’m not precisely sure what this example is meant to illustrate, but if you had two sources of em radiation and you wanted to reconstruct the contribution of each source it is fairly easily done by looking at the resultant wave and using the principle of superposition. A point I would make is that it would be impossible for two such waves to cancel over the whole of space, which can be gleaned just from the conservation of energy.
In a deterministic system with perfect knowledge then yes. The evidence of its path would exist in some form or other, even if you had to take into account the tiny movement of molecules of air miles away to reconstruct it. Of course such knowledge is a practical impossibility though.
The unitary evolution of a quantum field fully deterministic. However you still need a quantum measurement theory for the concept of vacuum and (at the moment at least) there isn’t a fully 100% satisfactory explanation of quantum measurement in terms of purely unitary evolution.
Chronos and Asympotically Fat have, I think, basically answered your questions, but just as a word of caution, the idea of ‘quantum fluctuations’ as it’s thrown around in the popular literature (you know, ‘particle-antiparticle pairs popping out of the vacuum, then annihilating again before the universe notices the borrowed mass-energy’) is really grossly misleading. The state of the vacuum is uniquely defined, and so is the expectation value of any energy measurement (it’s 0); however, the measurement of this value has a necessarily nonzero spread (variance), since each measurement takes a finite time.
The idea that there are ‘virtual particles’ popping in and out of existence comes ultimately from a way to visualize certain integrals necessary to calculate quantum mechanical quantities—the famous Feynman diagrams. These look very suggestively like the spacetime tracks of particles, and in fact, certain of their lines (those that go to infinity) can be interpreted in that way; but the internal lines—those corresponding to ‘virtual particles’ can’t. For one, a single of these pictures doesn’t have any physical interpretation—it corresponds to one term in a series of terms, where the full physical phenomenon corresponds to the series as a whole.
Secondly, virtual particles also occur at a level in this series in which there are no ‘loops’, but all the graphs are tree-like—but this level just describes the classical theory. Thus, there ought to be virtual particles in classical physics, as well.
Finally, in treatments of quantum field theories that don’t rely on these approximated integrals, such as lattice gauge theory, there are no virtual particles, period.
So, bottom line: the vacuum state is a state of zero particles of the QFT you’re concerned with, and if you don’t disturb it in any way, it will just continue to be that same vacuum state, making retro- as well as prediction trivial. Upon measurement, however, your results will show a certain spread; but also, note that to perform this measurement, you’ve already perturbed the state away from the vacuum, since it’s now the vacuum plus whatever apparatus you need to do the measurement.
Sorry in my previous post I meant to say:
“However you still need a quantum measurement theory for the concept of vacuum fluctuations”
Eh, you can say that virtual particles are only a calculational crutch and don’t really “exist”, but then, you can say the same thing about particles in general. And even if you accept that particles (of some sort) really exist (in some sense), you can also make the argument that the only particles that actually exist are the virtual ones, not the real ones (since the particles that “travel off to infinity” are ones that never interact with your detector).
I’m not sure if that isn’t itself overly reliant on perturbative methods, though—I’m no expert, but I think that you have a reasonably well-defined particle notion (or at least a way to calculate particle detection probabilities) in lattice gauge theory, while virtual particles are completely absent.
They’ve done an okay job but it does still come down to the Steven Wright joke about his map of the United States that you are standing on … or maybe getting Goedel Escher Bachish
If you had a computer that could contain all information about every particle in the universe, and a model that handled for each possible quantum randomness, it would be theoretically possible to rewind by information … except the theoretical possibility of such a computer existing would automatically create a theoretically larger universe that could contain a computer larger than itself …
I think the big difference is that ‘real’ particles are an empirical facts, so even if a description in terms of particles does not always leap out from QFT, it is a necessity to obtain such a description. However virtual particles are not an empirical fact and are purely an artifact of a particular way of doing calculations, so it is misleading to promote them to having the same ontological level as ‘real’ particles.