How are quantum superpositions fundamentally different from ambiguous macrostates?

Factual Questions
1

The title pretty much sums up my basic question, but I can provide a couple examples of these macro-phenomena for clarity:

Example 1: You toss a coin and you see it land in a shadow. It might be heads, tails, on its edge, lost, etc.

Example 2: You see a small puddle on the floor. It may have been from an ice cube, a shoe, a leak, condensation, etc. (Generally speaking, and perhaps off-topic, this happens to be a state with an ambiguous cause, while the former example was a state with an ambiguous effect).

My current understanding is that quantum superpositions are categorically different in some way from these ambiguous macrostates (which is why Schrodinger needed to include the radioactive substance in there with the cat), but I’m curious as to what this difference actually is from a physics standpoint.

2

Here’s what I hope is a helpful example:

If you let light pass through a polarizer (like polaroid glasses), not all the light gets through - this is easy to understand as a macrostate composed of some light that is polarized the same way as the polaroid, and some not, and only the correctly polarized light getting through. Add another polaroid strip at right angles to the first, and no light gets through both - again, easy to understand - you eliminated all the light polarized (say) vertically with the first strip and all the light polarized horizontally with the other strip. But if you add a third strip, between the first two, oriented diagonally, you’d expect it to have no effect - no light should get through. But that’s not what happens - add the third strip, and light starts getting through. So understanding each photon as having a particular polarization doesn’t work - you have to think about it quantum-mechnically; at each polarizer, each photon has a probability of getting through, based on the orientation of its polarization relative to that of the polariod strip, no matter how many strips it goes through.

Hope that helps.

3

The way I’d put it is this. In the macro examples the probability is just a tool to help us predict what will happen in a complex system, it does not actually represent what is going on. If you wanted to (and you have unlimited computing power) you could model the way your coin moves through the air and predict what side would be facing upwards. However doing so is hard because of Chaos Theory so we prefer to just consider the odds of one side or the other facing up.

In quantum theory the probability is not there to hide an underlying more complex system it actually represents what is happening to the sub atomic particle in question. Andy L’s example is a very good demonstration of what this actually means.

4

A search of the boards should produce many similar past threads.

For some keywords and some additional info: Bell’s inequality.

5

Yeah, I came in here to mention Bell’s Theorem too. There’s a fundamental difference between “hidden variables” (what you call ambiguous macrostates) and the predictions of quantum mechanics.

6

Here’s another way to look at it.

Quantum effects don’t have analogies in the macro world. They are really, truly different from anything we understand from “common sense.”

Superpositions are not indeterminate. They are not in between. They are not fuzzy or almost or partly like this and partly like that.

They are both. Completely absolutely two opposite things at once. Pretend that a quantum thing like “spin” is something like a top. (It isn’t, but bear with me.) A top has an upside and a downside. In the macro world, a top either spins on its top or on its bottom. It may fall on its side or you may not be able to tell which side it’s spinning on. But while it’s spinning it’s always one side or the other.

Quantum spin isn’t like that. Until measured (or the waveform collapses or however it gets put in the various interpretations) a particle’s spin can be both up and down. Not part one, part the other. Not indeterminate. Not in between. Fully up and fully down.

This is nothing like anything in the macro world. The math can describe this with precision. Words can’t. Quantum states are fundamentally unlike anything we are familiar with. Most treatments of the subject fail to stress this. People keep wanting to use macro “common sense” and get frustrated. You have to start with this in mind before you go off to read something like that Wiki page on Bell’s Theorem, because that assumes you already know the difference.

7

To emphasize the difference, I’ll deal with the first of the OP’s examples:

Let’s say the three possible states of the coin, wherever it is, are heads, tails, and on edge. Using classical reasoning, when you find the coin, whatever state you find it in, you can conclude it was in that state before you found it. If you shine a flashlight into the darkness and George Washington’s profile comes reflecting back at you, you will decide that the coin was heads up from the moment it landed until the moment you ‘measured’ it with the flashlight.

If this were a quantum coin, from the moment of landing to the moment of measuring, the coin would literally not have a well defined state of up-ness or down-ness. It would then be your act of flashlight measurement that forced the coin into having one face or neither facing up. The reason other posters are linking to the Bell inequality is because that is the mathematical proof that there is a measurable difference depending on which type of behavior the coin exhibits: ambiguous but existing states, or undefined states. When the experiment was actually done in 1982, it was found that quantum systems have undefined states (until they are measured).

8

Thanks, Spatial. That cleared up a lot of things for me…

9

That was a great explanation Spatial (and thanks to Andy, griffin, Exapno as well). So my current understanding is that a “qucoin” would have different physical properties than a “shadow coin”; a physically undefined qucoin vs. an unknown but defined shadow coin…and experiments have been designed and successfully run to demonstrate this fundamental difference. Hopefully that’s accurate.

10

But also the shadow coin would be a QM object except for: 1. mass 2. interaction with air molecules and photons.

The shadow coin is being bombarded with air. Even in a vacuum it’s still bombarded with light. Even in darkness it’s still bombarded with thermal IR. Unlike with subatomic particles, it remains closely coupled with the surrounding environment. That’s the shadow coin, but if your qucoin was thus interacting, it’s uncertain state is destroyed in picoseconds and it has a genuine heads-tails state.

Contrarily, if we flip a macro coin in dark cold vacuum in a reflective shield chilled to nanokelvins, the coin is still too massive, so any uncertainty in it’s position/velocity is tiny. So …add a shrod-cat macro mechanism that couples it to a quantized process. “Shrodinger’s flipped-coin” only remains in superposed states if it’s cut off from the rest of the universe and behaves like a subatomic particle with long time between collisions. It’s not Shrodinger’s Glance that does the measurement. Simply opening the box is enough.

On the other hand, people are now finding that warm moist biology may have discovered ways to engineer quantum processes by somehow preserving them regardless of strong interaction. Bird retinas seeing b-fields as if they had SQUID superconductors.

11

Do you have a little more detail than that?

12

Another way to think about this that builds some intuition is considering self-interference in the classic double-slit experiment. Usually, this experiment is used to demonstrate wave/particle duality, but that won’t exactly concern us right now.

Think of light being shined (that sounds awkward!) on a plate, with two narrow open slits. On a screen behind that plate, you will observe an interference pattern of lighter and darker areas – thinking of light as a wave, this can be easily explained, like so.

However, if you position detectors at each slit, what you will find is something different – far from observing a continuous variation, each detector will register sharply defined ‘packets of energy’, i.e. light particles – photons (and sure enough, if you do this observation, the interference pattern will disappear, being replaced by just two narrow bands behind the slits, just as you’d get if you’d thrown baseballs instead of photons). Still, it seems in principle possible to account for the interference pattern with this model: a photon travelling through one path in some way interferes with a photon that has taken the other path. This would be the ‘classical’ expectation; photons may do weird things when they’re not being observed, but each of them takes a definite path – it’s just our ignorance, or some sort of loss or hiding of information, that makes us unable to describe them in such a definite way.

However, what you do then is that you attenuate the intensity of your light source up to such a level that you can be sure that only individual photons are being emitted, one at a time. The classical expectation would tell you that no interference pattern should build up – there’s only one photon present at any one time, so what should it interfere with?

Yet, experimental reality disagrees with this expectation: let the experiment run long enough, and an interference pattern will build up that’s indistinguishable from the original one! The conclusion then must be that there is no definite path that is taken by a photon; it doesn’t go either through slit A or through slit B, but, in a sense, through both at once – it doesn’t take one path, but a superposition of paths (or is, as it travels, in a superposition of the states ‘taking path A’ and ‘taking path B’), and this superposition is irreducible, unlike in the classical case where, before looking, the coin is in an uncertain state only descriptionally, but really has definitely landed either heads or tails.

Well, us seeing ordinary light is also dependent on a quantum process – an incident photon changing the structure of some opsin, inducing an electrochemical response. Is there anything substantially different in the way birds see magnetic fields?

13

That may not be entirely true. I posted awhile back on scientists observing a macro quantum effect.

14

It should also be noted that quantum superpostion is fundamentally different from an ambigious quantum state (microstate).

15

I thought it was clear, but I meant that nothing in anybody’s everyday experience is quantum. That scientists can make a maybe sorta macro state out of a few atoms in a lab doesn’t change that at all. What happens in a lab stays in a lab.

16

Granted that only happened in a lab but what do you define as a macro state? Didn’t that experiment show a quantum effect in a macro (albeit still tiny) object?

17

Whether a statiscal ensemble of microstates is a macrostate or not can be fairly subjective. Just as whether an object is macroscopic or not can be failry subjective.

To elbaorate a little on what I said further though quantum statistics deals with quantum mechanical systems where the exact quantum state is ambigious. Quantum statisctics does not describe the state of a quantum system who’s exact quantum state is unknown in terms of superpostion of quantum states (of course a superpsotion of quantum states is itself a quantum state), it describes them in terms of a density matrix. A desnity matrix describes states which can be reduced to an exact quantum state (pure states) and states which cannot (mixed states).

So therefore you can see straight away that quantum physics deals with ambiguity of the results of measurements due to a) the fundamentally stochastic (probablistic) nature of quantum mechanics b) ambiguity in the quantum state in completely different ways.

Whether there’s something else going on is where hidden variable theories and Bell’s inequality comes in.

18

The difference is crucial. It is the difference between everyday “common sense” observation and things that only happen out of sight to 99.9999% of the people on earth.

Yes, scientists can do spectacular things in labs. The highest temperature in the universe was, temporarily, in a lab on earth. The coldest temperature in the universe was, temporarily, in a lab on earth. That doesn’t make the notion of absolute zero where motion ceases comparable to a cold day outside.

There is nothing in any person’s sensory experience – including those scientists in the lab – that is the equivalent of quantum superposition. There are lots and lots of experiences that are simple indeterminacy or fuzziness or not knowing. When people ask questions about superpositions, they always, without fail, are using those everyday experiences as the model they make assumptions from, the model they have to consciously abandon. It simply doesn’t matter if a macro superimposed object can exist in the universe. You’ve never seen one. The OP has never seen one. Leaving our world is the place that the discussion must start. Pointing to a few atoms in a lab doesn’t help understanding if that understanding isn’t there to begin with.

When people talk about objects gaining mass or time and losing length close to the speed of light because of relativistic effects, there is a similar jump of understanding that has to be made. They have to viscerally understand that these are effects from from outside the object’s reference frame. You don’t feel them yourself inside the thought spaceship. Yet, there have been a million threads that start confused and stay confused because the people who get it forget that everybody else doesn’t.

I’m harping on this distinction because I’ve seen too many threads derailed by this point. You have to start by saying that you can’t use everyday experience and can’t use familiar responses as equivalents, only as the most metaphorical analogies. Physics people have gotten this. Questioners haven’t, as you can see by the way they phrase their questions. So start there, before you thrown in Bell. Is it talking down? No, it’s talking straight.

19

Well, I confess that the to my layman’s mind quantum weirdness does impinge on the macro world.

To wit the double-slit experiment.

You get interference lines as long as no one tries to observe which slit the photon went thought.

As soon as you try to figure out which slit the photon went through the interference pattern disappears (no matter how cleverly you design the experiment…a machine looking will do it).

I know that has been used for all sorts of new-agey hocus-pocus and I do not subscribe to that but here you have a quantum fuzziness effect completely undone if a macro entity tries to witness it. Seems odd. Moreso because presumably in the lab there are numerous atoms between the emitter, the double slits and the screen behind it. Why doesn’t the quantum probability collapse when the photon hits those objects in its travels? Why does it seem a consciousness causes the collapse and nothing else?

Again I want to be very, very clear on this. I am NOT pushing new age pseudo-science here. Just saying these things are confusing to me and I have not been able to sort them out in my head.

I am guessing Schrodinger had the same (albeit better informed) confusion I am experiencing.

20

On the other hand, you could argue that everything we experience is quantum phenomena. They’re just quantum phenomena in the high-action, high-angular-momentum limit.