Quantum mechanics question (bordering on philosophy)

Factual Questions
1

As I understand QM, “things” can (and do) pop into existence randomly all the time. Empty space is filled with virtual particles that appear and disappear in minute fractions of a second.

There are also phenomena like Tunneling, whereby an electron (for example) can “borrow” enough energy from the void to surmount a theoretically impenetrable barrier, and appear on the other side spontaneously - I believe there are even devices (tunnel diodes?) that exploit this.

Further, it is my understanding that “the more you want to borrow, the less time you can borrow it for.” Thus, neutrino appearing out of nothing, living for a squillionth of a second, and disappearing -> reasonably probable. Fully-formed 747 appearing in Times Square, lasting for a year -> very improbable.

My question is about all these ‘improbable’ events. Surely there’s an infinite number of these possible events, even though we agree that each has an infinitessimal probability.

e.g.

basketball appearing on the desk next to me - probability = 1 squillionth
slightly smaller basketball appearing - probability = 2 squillionths
basketball appearing on the floor next to me = 1 squillionth[sup]*[/sup]
anvil appearing on my toe = 0.1 squillionth

etc. etc. ad inifinitum.

Why don’t all these minute probabilities add up, since there is an infinite number of them, to produce a constant series of improbable, “Improbability Drive”-like events? Why aren’t there macroscopic things popping into existence all around us like this?

The only idea I have is that this is some kind of quantum Zeno paradox: even though there’s an infinite number of possible, but very improbable events, the total still doesn’t add up to a whole hill of beans - not enough to make macroscopic events happen in any human timeframe, anyway. By observation (i.e., I don’t see any basketballs materializing around me), I’m guessing this must be so. I’m also reminded of things like the Cantor Dust, whereby you can “remove” material for an infinite amount of steps but still have something left at the “end”.

  • I’ll be submitting ‘squillionth’ to the SI committee as a new unit.
2

As I understand it (and it has been a good 20 years since I last did physics, so my memory may be a bit unreliable), the idea of “virtual particles” is based on the Uncertainty Princple applying to measurements of a vacuum, as well as to measurements of “real” particles.

If you measure the mass at a particular point and there isn’t a real particle there, the value you “should” get (neglecting quantum effects) is zero. However, the Uncertainty Principle states that the value you actually get won’t be zero, with range of values you can expect to get depending on the time taken to do the measurement; so there may appear to be a (virtual) particle in your instrument.

The average of lots of readings will still be zero, of course, otherwise the First Law of Thermodynamics would be violated. So there’s no chance of a macroscopic object (or even a single electron) popping into existence without popping back out of existence in a time given by Heisenberg’s equation. Even for electrons, this time is vanishingly small even on an atomic scale.

3

Because the likelyhood of such an event occuring at any particular point in space-time is outstandingly improbable at the background energy level of free vacuum. Over the continuum for infinte time one can speculate that any number of basketballs spontaneously appearing and disappearing, but the probability density is so low that for it to happen in any particular location is negligable throughout the lifespan of the universe.

Also, these “virtual particles” never exist for more than a tiny fraction of a second; they spontaneously emerge out of the vacuum, accompanied by a complementary anti-particle, and then recombine with the anti-particle, dumping the resultant energy back into the plenum without (generally) interacting with other particles. It is possible that virtual basketballs–and reciprical anti-basketballs–are emerging about you constantly, but it happens so quickly that they do not interact with other matter. One would think that you’d notice the massive energy fluctuations associated with matter condensing out of vacuum and back, but then remember how Mrs. Hardin complained about your not paying attention in fifth grade homeroom? (Oh wait, that was me…never mind.)

Anyway, not all physicists are even convinced that virtual pairs are created or that space bubbles with a froth of constantly emerging and evaporating particles. Paul Dirac first hypthesized virtual particles as a way of interpreting some aspects of quantum mechanics, and Feynman “formalized” this in his famous (or infamous) eponymous diagrams, but no one has ever directly witnessed pair creation, and while it is a useful theory to explain certain phenomena (like the Casimir Effect) it is, ultimately, just a model for vacuum plenum behavior.

Quantum tunnelling is an entirely different phenomenon from virtual particle creation; it doesn’t involve any particle creation per se, but rather a particle moving or transmitting its quantum state instantaneously from one place to another.

Stranger

4

It’s because you don’t really appreciate how tiny a squillionth really is. The probability of all the air molecules ending up in one corner of my office is really tiny – let’s say it’s a squillionth (And it’s not even a quantum effect – it’s statistical mechanics, but it’s an unlikely event, so take it from there). The probability that it’s in the diagonally opposite corner is also a squillionth (both corners are equally likely). so is the probability that it’s just a step away from the corner, and also a step away from there. If we add up all those probabilitities for all those points in the room, then surely the probability must be that I can observe all the air molecules in my room at some point, right?

Nope. Even adding up all those positions – billions of them, trillions if I divide up space into tiny enough chunks, the sum of all those probabilities is still unmeasurably tiny compared to one. The probability of quantum “miracles” is incredibly timy, almost beyond imagining. If it weren’t, we’d be seeing them all the time. There was an article about this in Scientific American back in the 1960s, talking about the unbelievably extremely tiny probability of observing events that seem to go “backwards” in time (the article was called “Time’s Arrow”, IIRC). Evwents on the microscopic scale are reversible, but on the macroscopic scale they don’t reverse. Atoms of perfume can diffuse out of a bottle into the air. But, even though the physical processes are allowed, they don’t diffuse back into the bottle. Quantum probabilities are similarly very tiny, Probably smaller.

5

I think I’m beginning to see the light at the end of the tunnel on this - I’ve been giving it a lot of thought.

I now see a couple of problems with the way I’ve been viewing this.

  1. I’m looking at it purely mathematically, like reality (space & time) can be divided up infinitely granularly -and-

  2. I’m letting myself believe that if you add up an infinite number of values, you must end up with ‘something significant’

(1) is refuted by the fact that modern thinking has it (correct me if I’m wrong) that both time and space are quantized, with the Planck length and time being the unit of each.

(2) Is a form of Zeno’s paradox - it’s counterintuitive but if the things you’re adding up are small enough, you never “get anywhere”, even if there’s an infinite number of them. (Classic example: 1 + 1/2 + 1/4 + 1/8 + … = 2)

6

Quantum phenomena are indeed probabilistic. (I think this thread answers many of your questions, Darren).

You’ve made something of an error in adding up your probabilities. Let’s take the number of quarks and leptons in a basketball, say. Firstly, for this number of particles to “appear” (ie. “borrow” their energy long enough to be detected) woud require a probability so minute that even observing the entire universe for all the time of the universe would still yield negligible odds. So, even without those partiularly improabable arrangements, such a number appearing in the first place is practically impossible.

So let’s put aside the virtual particles, and consider the quarks and lepton which are already about. What is the probability that a number of these could suddenly appear, far away from their recent positions, in a configuration that a human sensory apparatus would correlate with “basketball” or “anvil” or whatever? Again, for all intents and purposes, nil. For even a single atom to appear more than a few atom-widths away from its last position is actually straining at the lifetime-of-the-universe statistical leash.

Put simply, the infinities you are suggesting are always vastly, enormously outpaced by the infinities of the mundane alternatives, such that the probability of any such macroscopic quantum weirdness ever being observed is laughably remote.

7

universe (Big Bang) appearing right here - dunno the probability, but appears to have happened?

8

This isn’t exactly a direct reply to your question, but you also mentioned quantum tunneling.

You might find This experiment you can do at home of interest. Fascinating stuff.

9

The Big Bang did not “appear” - it was always here, and has only been expanding for 13.7 Bn years. Having these fine-tuned properties it seems highly improbable, but it may be that this is but one region of the universe and that the properties are indeed different in other regions (perhaps even having different (dimensionality).

10

I’m guessing he’s referring to the theory that postulate the universe originated as a massive quantum hiccup; the Big Bang theory only tells us what happened after the clock started, and says nothing about what happend at t <=0.

11

Well, there was no here here prior to the BB, but I have heard it posited — originally jokingly, then more seriously — that the entire universe is nothing but a vaccuum fluctuation. IANAPhD_Physics and I’m aware of Hawking’s positing of time and its rel to early expansion in BHOT such that it makes more sense to describe the forward motion of time as gradually accelerating from an infinitely-previous standing start along with space rather than positing a true temporally-finite-located singularity / true BB-event as classically imagined, but I’m not hip to what the current range of theories and/or consensus is w/regards to all that.

12

I see what you are getting at here but in your case I do not think it is fair to think of it as adding an infinitely decreasing probability as above. You are adding 1 squillionth + 1 squillionth + 1 squillionth…

Now, a squillionth may be so amazingly small as others suggested that even adding them up everywhere still amounts to “not much” but I think it is an improvement on the odds over Zeno’s paradox mentioned above.

Reading CalMeacham’s post above I understand that insanely small probabilities are just that…insanely small. Still, if I had a universe of rooms the size of the room CalMeacham is in and watch all of them wouldn’t I expect to see all the air end up in one corner of one room somewhere on something less than the timescale of the life of the Universe? I mean, as again per the OP, if the universe is infinite and I have an infinite number of rooms shouldn’t adding something as tiny as a squillionth probability appear somewhere? The chances of it happening in any particular room are vanishingly small but then isn’t a squillionth * infinity = infinity? If that is so air should be stacking up in corners of rooms all over the place on a infinite universe scale…just the chances of it being where “you” are in the timeframe you have to watch it are exceedingly unlikely.

As for quantum tunneling I think it happens all the time around us. Just put socks in your quantum tunneling machine at home (aka clothes dryer) and chances are fewer will come out than went in.

13

The flaw in your reasoning is that even if it were all true, the chances of you or any individual observer actually seeing a massively improbable event in an infinite universe are infinitely small. There is no privileged observer status that allows anyone to scan an infinite universe and pick out the weird happenings.

In our real universe, the speed of light is an absolute barrier. We live in a universe that is limited to an observable area. In such a tiny fraction of an infinite universe, the odds say that any event that occurs one in a squillionth times will not take place for a time interval squillions of time longer than our observable universe has been around.

And the odds of any individual observer seeing that event are still so low as to make seeing it essentially zero.

14

Unless, of course, the fact that you’re present in the first place implies that the event did indeed occur.

15

Nope. A squllionth is really tiny.

And the lifetime of the universe, according to several cosmological theories, is smaller than infinity. Infinitely smaller, you might say. The product of the lifetime of the universe with a squillionth is still unimaginably, remotely, small. That’s why I started out with the assertion that the Op didn’t appreciate how small a squillionth is. It’s so small that the probability of the wavefunction of a football manifesting itself on my desk outta the clear blue is indistinguishable from zero in the life of the universe.

16

I thought that was a result of parity breaking during the spin cycle…

17

When I started reading the thread, I was going to post both your (1) and (2) as a reply, so, in my opinion, you have nailed it.

18

The amount of energy that can spontaneously appear is inversely proportional to the time it can exist without breaking out of Heisenberg’s protection and severely violating Conservation of Mass-Energy. E times T must always be less than a small constant (I think I’m remembering it’s the Planck constant, but I’m probably wrong there).

So, while a tiny little electron-positron pair can show up for a fraction of a second before going away, a basketball could only appear for such a short amount of time that the Universe can’t understand such brevity. The shortest amount of time that makes sense in physics is the time it takes light to travel the smallest conceivable distance (known as the Planck time), and the time that your virtual basketball could exist is an even-shorter duration.

I just skimmed the thread, so forgive me if I missed someone posting this earlier.

19

CalMeacham already replied to this, but let me put some numbers on it. Let’s say a room is 10 feet by 10 feet by 10 feet. This is about 28300 liters. A mole of air at standard temperature and pressure takes up 22.4 liters, so there are about 1260 moles of air in the room. 1 mole of air contains 6 * 10[sup]23[/sup] molecules, so there are 7.6 * 10[sup]26[/sup] molecules in the room.

Let’s divide the room up into 2 foot cubes, and define “all the air in the corner” as “all molecules in the 2 foot cube in the corner”. There are 125 such 2 foot cubes, so assuming that the chance a molecule is in any one cube at any given time is 1/125, then in order to get all the molecules into that cube we need to raise 1/125 to the power of (7.6 * 10[sup]26[/sup]) If that didn’t just make you go “whoa” like Keanu, let’s continue.

This ends up being 1/N, where N is 125 raised to the power of 7.6 * 10[sup]26[/sup]. The log[sub]10/sub is 1.6 * 10[sup]27[/sup].

So, let’s say we have one such room, and every second we check to see if all the air is in the corner. In order for us to have roughly a 50% chance of seeing this happen, we’d have to wait N/2 seconds. There are approximately 3 * 10[sup]7[/sup] seconds in a year, so we’d have to wait N/6 *10[sup]7[/sup] years to see this happen. Let’s say we could use almost the entire observable universe filled with such rooms. Let’s say that the observable universe is a sphere with a radius of the Hubble distance, which is about 10^26 meters, or about 15 billion light years. This sphere has a volume of 3.6 * 10[sup]79[/sup] cubic meters, so there are 1.3 * 10[sup]78[/sup] such rooms in the observable universe.

We would still have to wait N/ (610[sup]7[/sup] * 1.3 * 10[sup]78[/sup]) years to observe all the air in the corner of a room. That’s N/7.610[sup]85[/sup] years. The log[sub]10[/sub] of this number is 1.6 * 10[sup]27[/sup] - 86 or so, which is so close to 1.6 * 10[sup]27[/sup] that nobody can tell the difference. And, when we raise 10 back up to that power, well, it’s still N. We haven’t even made a dent.

So even if we use the entire observable universe full of these rooms, the chance that even one of these rooms would exhibit this behavior is still as close to 0 that humans cannot comprehend the difference between it and 0.

20

I am mathematically challenged so bear with me when I say I do not follow this last bit.

If you have to wait 1.610[sup]27[/sup] years to see this happen in one room why is it when you have 1.310[sup]78[/sup] rooms in the entire universe this is not happening in roughly three rooms somewhere every second?

Mind you I completely understand the chances of my being in one of the rooms to observe this are vanishingly small but it still seems to me some quantum or probabilistic weirdness is likely occurring somewhere in the universe on a regular basis.