B Is a table levitating possible, even at a minuscule probability?

[syed]

TL;DR Summary

Title

I am not sure if this falls under classical physics or quantum physics or somewhere else (so feel free to put it in the right section), but is there any micro state of the universe one can think of which if evolved under the current laws of nature, inevitably results in outcomes such as a table levitating? That example is just a random one I decided to choose but I'm really asking about any event that would seem like a "miracle" to the ordinary person (i.e. any event that doesn't seem to have an obvious mechanism for it)

In other words, is this probability 0, extremely minuscule, or merely unknown? If it is extremely minuscule, how do physicists know that this is even true? Atleast in the case of ordinary events like a dice roll, we can come up with a local micro state and initial conditions preceding the dice roll that explains exactly why a dice rolls on 6 for example. How would one do this for something like a table levitating?

What about certain specific macro histories such as extraterrestrials evolving, visiting earth, and deciding to interfere with affairs on earth? Is the probability of this extremely minuscule, 0, or merely unknown?

I ask because atleast theoretically, one can imagine a great number of "macro histories" or "miraculous histories" that seem to exceed the number of even possible initial states. The longer this sequence of events is, the more it seems to combinatorially explode in total number. This would imply that the vast majority of macro states cannot be, even in principle, mapped to a particular initial state. So at first glance, it seems that the vast majority of these imaginable sequences of events would not just have a miniscule probability, but rather a probability of 0. But I'm not sure.

 

[DaveC426913]

How big is the table?
How high is levitating?
For how long?

It is arguably possible for a table to be bouncing around on an monatomic layer of air molecules for an arbitrarily short duration.

 

[Dale]

Or if you like the “nothing ever touches” thing then you can say that every table levitates all the time.

 

[JimWhoKnew]

TL;DR Summary: Title

That example is just a random one I decided to choose but I'm really asking about any event that would seem like a "miracle" to the ordinary person (i.e. any event that doesn't seem to have an obvious mechanism for it)

In other words, is this probability 0, extremely minuscule, or merely unknown? If it is extremely minuscule, how do physicists know that this is even true?

The assumptions of Statistical Physics say that the probability is extremely minuscule. How do we know it is true? We don't. But the theory is very successful with things that we can measure, so we stick with it.
In some simple cases it might be possible to estimate upper and lower bounds for the probability. Instead of a levitating table, consider the simpler "miracle" of a perfect gas returning momentarily to the right half of the container

 

[PeroK]

The assumptions of Statistical Physics say that the probability is extremely minuscule. How do we know it is true? We don't. But the theory is very successful with things that we can measure, so we stick with it.
In some simple cases it might be possible to estimate upper and lower bounds for the probability. Instead of a levitating table, consider the simpler "miracle" of a perfect gas returning momentarily to the right half of the container

Or, a fair coin coming up heads 200 times in a row. Or, a pack of cards being randomly shuffled into a given configration. Even these things would never happen in the lifetime of the universe (assuming, say, you tossed the coin or shuffled the deck one million times per second).

Something reqiring Avogadro's number of successful successive trials (rather than 200 or 52) is a different level of miracle altogether!

 

[Physics Detective]

Is a table levitating possible, even at a minuscule probability?

No. Some of the examples above are associated with genuine probability. Like tossing a coin. It's possible to get two heads in a row. It's also possible to get ten heads in a row, but the probability is reduced. The OP also refers to macro states et cetera. But it's important to understand that probabilistic quantum mechanics does not trump gravity. Setting aside "cheats" such as tables made from helium-filled balloons, or tables in the vomit comet, tables don't levitate. Tables fall down. And when they clatter to the floor and stop bouncing, that's where they stay.

 

[FactChecker]

Would you say it is "possible" even if the probability of it happening in the past life of the universe is minuscule?

 

[Dale]

There is a certain level of probability which is so close to 0 that if you did observe it then you would think that your theory was wrong because the observed probability was significantly greater than the theory. Not sure what that number is.

 

[phinds]

But it's important to understand that probabilistic quantum mechanics does not trump gravity. ... tables don't levitate.

You state something as categorically true that, I think, is not true. I believe that the probability is so close to zero as to "make no never-mind" as my uncle Billy Bob would say, but it is not zero, just vanishingly small. See post #8.

 

[syed]

Or, a fair coin coming up heads 200 times in a row. Or, a pack of cards being randomly shuffled into a given configration. Even these things would never happen in the lifetime of the universe (assuming, say, you tossed the coin or shuffled the deck one million times per second).

Something reqiring Avogadro's number of successful successive trials (rather than 200 or 52) is a different level of miracle altogether!

But that's exactly where I'm having trouble understanding this. Do we not have more evidence of a fair coin coming up heads as a possibility (even a million times in a row) than a table levitating in the air? It seems as if classical mechanics would deterministically allow for the former to happen but not the latter (as opposed to maybe statistical mechanics?)

 

[syed]

Is a table levitating possible, even at a minuscule probability?

No. Some of the examples above are associated with genuine probability. Like tossing a coin. It's possible to get two heads in a row. It's also possible to get ten heads in a row, but the probability is reduced. The OP also refers to macro states et cetera. But it's important to understand that probabilistic quantum mechanics does not trump gravity. Setting aside "cheats" such as tables made from helium-filled balloons, or tables in the vomit comet, tables don't levitate. Tables fall down. And when they clatter to the floor and stop bouncing, that's where they stay.

This is ultimately the basis of my question since something like a coin coming up heads many many times seems to have "more" evidence than a table potentially levitating but I'm not sure about this.

 

[Physics Detective]

You state something as categorically true that, I think, is not true. I believe that the probability is so close to zero as to "make no never-mind" as my uncle Billy Bob would say, but it is not zero, just vanishingly small. See post #8.

We will have to agree to differ on that.

 

[syed]

You state something as categorically true that, I think, is not true. I believe that the probability is so close to zero as to "make no never-mind" as my uncle Billy Bob would say, but it is not zero, just vanishingly small. See post #8.

Sure, but how do we know that all micro states are possible even at a minuscule probability rather than literally 0? I understand that predictions involving these theories work but it is not as if it would make a difference if we attached zero probability to micro states that would pertain to "extreme" looking macro states (such as all the atoms of all the molecules of a marble statue just happening to move in the same direction at the same moment)

 

[PeterDonis]

It seems as if classical mechanics would deterministically allow for the former to happen but not the latter

Classical mechanics doesn't say a table levitating is impossible, just extremely, extremely, extremely improbable. A classical model would look something like: all of the atoms in the floor that are in contact with the bottom of the table legs just happen to move upward at the same time, as part of the natural random vibrations of atoms in any object at finite temperature. That movement exerts a force on the bottom of the table legs that's sufficient to make the table levitate a very small amount for a very short time. There's nothing in the laws of classical physics that rules that out in principle.

 

[Physics Detective]

This is ultimately the basis of my question since something like a coin coming up heads many many times seems to have "more" evidence than a table potentially levitating but I'm not sure about this.

I think you can be sure of the distinction between genuinely possible things, and speculative things for which we have no evidence whatsoever. General relativity is one of the best-tested theories we've got. See The Confrontation between General Relativity and Experiment by Clifford M Will. There's absolutely nothing in the theory, or experiment, or experience, that says there's any possibility that gravity somehow turns itself off.

 

[Nugatory]

But that's exactly where I'm having trouble understanding this. Do we not have more evidence of a fair coin coming up heads as a possibility (even 5000 times in a row) than a table levitating in the air? It seems as if classical mechanics would give the former a nonzero probability but not the latter (as opposed to maybe statistical mechanics?)

The way to get a levitating table is through classical physics: just by random chance a substantial fraction of the air molecules under the table just happen to moving upwards. Depending on various back of the envelope assumptions you might calculate that such an event has a probability of occurring in any given second of $P=10^{-10^{20}}$.

Now can we construct an experiment that will distinguish between:
- this will not happen
- the probability of this happening is P

 

[PeroK]

But that's exactly where I'm having trouble understanding this. Do we not have more evidence of a fair coin coming up heads as a possibility (even a million times in a row) than a table levitating in the air? It seems as if classical mechanics would deterministically allow for the former to happen but not the latter (as opposed to maybe statistical mechanics?)

If you do a computer simulation of coin tossing, you might get 30 heads in a row (that's 1 in a billion), but probably not 50 heads in a row, even if you ran the program for the rest of your life.

 

[syed]

Classical mechanics doesn't say a table levitating is impossible, just extremely, extremely, extremely improbable. A classical model would look something like: all of the atoms in the floor that are in contact with the bottom of the table legs just happen to move upward at the same time, as part of the natural random vibrations of atoms in any object at finite temperature. That movement exerts a force on the bottom of the table legs that's sufficient to make the table levitate a very small amount for a very short time. There's nothing in the laws of classical physics that rules that out in principle.

Isn't this really describing an extreme thermal-fluctuation scenario from statistical mechanics, not the deterministic framework of classical mechanics? I thought under classical mechanics, a spontaneous levitation from “random atomic motion” is not allowed. As far as I'm aware, if you specify every particle’s initial position and velocity exactly in classical mechanics, their future motion is fixed. So, in what sense is there intrinsic randomness in classical mechanics?

 

[PeterDonis]

Isn't this really describing an extreme thermal-fluctuation scenario from statistical mechanics, not the deterministic framework of classical mechanics?

They're the same thing. "Statistical mechanics", at least if we're talking about classical physics, is derived from "the deterministic framework of classical mechanics"; it just averages over the individual particle motions. It doesn't introduce any non-deterministic physics; it just tells you what you can and can't predict if you don't know the individual particle motions.

 

[syed]

I think you can be sure of the distinction between genuinely possible things, and speculative things for which we have no evidence whatsoever. General relativity is one of the best-tested theories we've got. See The Confrontation between General Relativity and Experiment by Clifford M Will. There's absolutely nothing in the theory, or experiment, or experience, that says there's any possibility that gravity somehow turns itself off.

Okay, so ultimately what you're saying is that the actual probability of a table levitating is literally and exactly 0, correct? If so, I seem to be getting mixed responses on here, which is just adding to my confusion I tend to agree though that at least at first glance, there seems to be a distinction between even the unlikeliest of a dice roll and a table levitating

 

[PeterDonis]

I thought under classical mechanics, a spontaneous levitation from “random atomic motion” is not allowed.

I don't know where you're getting this from. Classical mechanics says that the motion is deterrmined by the initial conditions and the laws of physics. The scenario I described is one where the initial conditions just happen to be the right ones to produce a very brief levitation of the table. Classical mechanics in no way rules that out in principle. It only says that the reason we don't observe such things in practice is that those initial conditions are extremely, extremely, extremely unlikely to occur.

 

[PeterDonis]

There's absolutely nothing in the theory, or experiment, or experience, that says there's any possibility that gravity somehow turns itself off.

You don't need gravity to turn itself off for an extremely, extremely, extremely improbable set of conditions to make the table levitate, as described in the scenario I gave in post #14. So you are not giving an argument for such a thing being impossible.

 

[PeterDonis]

so ultimately what you're saying is that the actual probability of a table levitating is literally and exactly 0, correct?

If that's what he's trying to claim, he's wrong. See my post #22 just now.

 

[syed]

I don't know where you're getting this from. Classical mechanics says that the motion is deterrmined by the initial conditions and the laws of physics. The scenario I described is one where the initial conditions just happen to be the right ones to produce a very brief levitation of the table. Classical mechanics in no way rules that out in principle.

I just wanted to confirm that the "randomness" in the theory is merely a tool and not actually intrinsic, and it seems as if you agree on that point.

My question then is: how do we know that certain micro states are ruled in (i.e. actually have a non zero probability) rather than merely not ruled out in principle?

To use a dice analogy, even the most improbable dice roll sequence can likely be given a set of initial conditions that deterministically lead to that dice roll sequence. On the other hand, if a table levitating would correspond to a certain state of atoms, and this levitation will presumably be occurring over a period of time, how do we know that this process actually has a non zero probability?

 

[PeroK]

Sooner or later a hurricane will blow through your house or a freak gust of wind will raise your table into the air.

 

[syed]

To expand on my question further, once you add time in to the equation especially, the amount of possible "trajectories" over time seem to combinatorially explode. Thus, the amount of possible trajectories over time seem to vastly exceed the amount of possible initial states at an instant of time. But in classical mechanics, there are certain rules constraining all possible future states. In other words, some imagined trajectories could not correspond to any particular initial state. So does this not imply that most possible imagined trajectories have a physical probability of 0 of being realized?

 

[PeterDonis]

how do we know that certain micro states are ruled in (i.e. actually have a non zero probability) rather than merely not ruled out in principle?

We don't, because we don't know the exact state of the universe, and the knowledge we do have is not sufficient to rule out any microstate; the best we can to is to say that, for example, the microstate that would lead to the table levitating for a very short time in my scenario has an extremely, extremely, extremely low probability. But that's still not the same as saying it has zero probability.

 

[PeterDonis]

once you add time in to the equation, the amount of possible "trajectories" over time seem to combinatorially explode. Thus, the amount of possible trajectories over time seem to vastly exceed the amount of possible initial states at an instant of time.

I don't know what you're basing this on. In any deterministic theory, the number of trajectories and the number of initial states are the same. There is a one-to-one correspondence between them. Indeed, the phase space formulation of classical mechanics makes essential use of this fact.

 

[PeterDonis]

in classical mechanics, there are certain rules constraining all possible future states. In other words, some imagined trajectories could not correspond to any particular initial state.

I don't know where you're getting this from either. See my post #28 just now; the fact I stated there contradicts what you're claiming in the quote above.

 

[syed]

I don't know where you're getting this from either. See my post #28 just now; the fact I stated there contradicts what you're claiming in the quote above.

I think you're misreading.

I don't know what you're basing this on. In any deterministic theory, the number of trajectories and the number of initial states are the same. There is a one-to-one correspondence between them. Indeed, the phase space formulation of classical mechanics makes essential use of this fact.

Yes, the number of possible trajectories given the number of initial states are the same. But I'm talking about imagined trajectories. So for example, suppose that at any instant of time, you can describe the current state of particles in 200,000 different ways. This would mean there are 200,000 initial states and 200,000 physically possible trajectories.

But you can now imagine, say over three instants of time, (200,000)^3 trajectories. As you add more time, the amount of imagined trajectories combinatorially explodes, even if we can't (from what I know) rule out a particular state occurring at an instant of time. Wouldn't most of these imagined trajectories have a literal probability of 0 being realized?

 

[syed]

Just to rephrase to make sure there's no confusion, I'm not counting physical trajectories; I'm counting all the sequences of states you can “freely imagine” if you treat each instant as an independent choice.
For three discrete time-steps and 200 000 possible instantaneous states, you’re constructing (200k) ^ 3 possible sequences. But almost all of those sequences violate the dynamical laws: the state at time t1 has to be the time-evolution of the state at t0, not an arbitrary pick. The same goes for t2.

If you impose the actual equations of motion, the only surviving sequences are exactly those one-to-one trajectories that start from valid initial conditions, so the set collapses back to size 200,000

 

[PeterDonis]

I think you're misreading.

I think you're confused. See below.

I'm talking about imagined trajectories.

What does that even mean? Physics doesn't work by "imagining" things.

suppose that at any instant of time, you can describe the current state of particles in 200,000 different ways.

You can't. There's just one state. You might not know what it is, but there's just one.

What you might be groping towards (but I'm not sure--see further comments at the end of this post) is an epistemic concept of probability--the standard ignorance intepretation, where we assign probabilities to different possible states because we don't know what the actual state is. We have incomplete information, and we use that information to formulate some kind of statistical description of what we know, in order to make predictions as best we can.

In such a statistical description, if the underlying dynamics is chaotic, i.e., has sensitive dependence on initial conditions, then it is true that our ability to predict gets worse and worse as we try to predict further out in time, because of something like an exponential combinatorial explosion of possibilities. However:

Wouldn't most of these imagined trajectories have a literal probability of 0 being realized?

Not in the statistical description I just described, with chaotic underlying dynamics. The possible trajectories are not "imagined"; they're possible as far as we know, because the initial conditions could be the right ones to produce them. So all of them have nonzero probability.

I'm not counting physical trajectories

Then you're not doing physics. and your posts are off topic here, and you need to stop posting along these lines.

I'm counting all the sequences of states you can “freely imagine” if you treat each instant as an independent choice.

This is not physics. We're talking about physics here, where obviously the state at each instant is not independent of the previous states; the dynamical laws relate them.

I'm going to close this thread for moderation at this point, because it seems like your OP question was based on something that has nothing to do with physics. If you think there is still an actual physics question here that hasn't been answered, PM me and we can discuss it.

 

[Dale]

I think this is a poor question. It is not well defined. What counts as levitating? How far off the ground? How long? Are we allowed to use a jet pack? Ropes? EM fields?

This ranges all the way from any day every day to not in a trillion lifetimes of the universe.

So without some serious clarification we are better off counting hairs in our navel. Particularly since I get the impression that you don’t actually care about tables levitating but have some other question that you prefer to dance around.

Just consider that question carefully and then ask it directly.