Boltzmann's multiverse and fluctuations

[erotavlas]

Why is it stated that a fluctuation could occur and spontaneously gather all the molecules of air onto the corner of the room, or that a brain can spontaneously form in empty space if given enough time. Personally I don't agree with this because these events would contradict the laws of physics, wouldn't they?

 

[phinds]

Why is it stated that a fluctuation could occur and spontaneously gather all the molecules of air onto the corner of the room, or that a brain can spontaneously form in empty space if given enough time. Personally I don't agree with this because these events would contradict the laws of physics, wouldn't they?

No, they would not at all contradict the laws of physics (quantum mechanics), but they have such a tiny probability of occurring that you would have to wait a lot longer than the current age of the universe for them to happen, if even then. The fact that they CAN occur may or may not mean that they WILL occur (although I have seen statements that say anything that can happen will happen)

 

[erotavlas]

Take the confined box filled with a gas example. The probability that you witness all the particles confine themselves to one corner of the box is so small that as you say you would have to wait much longer than the current age of the universe to see it happen. But say you did wait that long, what would be happening in the box that would cause such an event? Wouldn't you need to have an external force to actually get the particles in that configuration? Because they would need to overcome each others repulsive forces on their own in order to get close together like that. Which if they could do already, we'd see rooms full of air collapsing more often, wouldn't we?

 

[MathematicalPhysicist]

No, they would not at all contradict the laws of physics (quantum mechanics), but they have such a tiny probability of occurring that you would have to wait a lot longer than the current age of the universe for them to happen, if even then. The fact that they CAN occur may or may not mean that they WILL occur (although I have seen statements that say anything that can happen will happen)

Well it's a mathematical statement that every event which has probability greater than zero will occur in an infinite universe, infinitely times.

 

[phinds]

But say you did wait that long, what would be happening in the box that would cause such an event?

it's the way quantum mechanics works. There is a tiny probability that a particle will change positions with no force applied because it is already "in" that "new" position statistically.

 

[marcus]

Take the confined box filled with a gas example. The probability that you witness all the particles confine themselves to one corner of the box is so small that as you say you would have to wait much longer than the current age of the universe to see it happen. But say you did wait that long, what would be happening in the box that would cause such an event? Wouldn't you need to have an external force to actually get the particles in that configuration? Because they would need to overcome each others repulsive forces on their own in order to get close together like that. Which if they could do already, we'd see rooms full of air collapsing more often, wouldn't we?

Erotavias, there is a classical way to look at this that is different from what posts #4 and #5 said and doesn't depend on quantum mechanics.

Think of starting with all the particles clustered in a corner. They are not at absolute zero so they are not absolutely still. The particles begin with some kinetic energy, some motion, but they happen to be all crowded in the corner. Take a movie of what happens as each particle continues to move and as they collide and bounce off each other, and as they bounce off the walls of the box, analogous to billiard balls.

Eventually they are approximately evenly spread throughout and all moving in what look like random directions as a result of many scattering collisions and bounces.

But all those collisions and bounces are REVERSIBLE. The laws of microscopic physics work in either direction: if you take the reversed output as input, then you get the reversed input as output. So you could take what looks like a random spread out state and RUN THE MOVIE BACKWARDS. The deterministic laws of individual bounce and collision say that
before too long you will see them crowded in the corner again.

 

[TumblingDice]

Why is it stated that a fluctuation could occur and spontaneously gather all the molecules of air onto the corner of the room, or that a brain can spontaneously form in empty space if given enough time.

It"s important to begin from a good foundation, so I hope you don't mind that I won't ask you to 'cite' where this is stated. Also, it would be presumptuous to suggest that the two scenarios you describe could occur from "a fluctuation", as in "just ONE flip of a coin".

What you may recall reading or hearing - one of the counter-intuitive aspects of quantum mechanics - is that at the microscopic, quantum level, particles can do things and go places that don't make sense or behave according to anything (and everything) you've experienced.

The significant point I want to convey is that QM does indeed include probabilities of events occurring at the QUANTUM level that would amaze you. BUT, the probability of the things that would be amazing can be very, very small at the microscopic/quantum level, and almost zilch if you want billions of improbabilities to happen, "just so".

Personally I don't agree with this because these events would contradict the laws of physics, wouldn't they?

This is a question you do need to clarify to make it proper. Which laws of physics? Classical or quantum or,...?

In any event, the odds of you being proven wrong are in the same league with a brain appearing in outer space. It doesn't mean neither can or cannot happen.

What if I told you it was impossible for you to win a lottery? On one hand you might agree, on the other hand you know it may be improbable, but not impossible.

So then, a brain appearing in space? Hmmm... Could you win every lottery, every day, for the rest of your life? That's kind of a similar thing. The significance is not to expect so many improbable things to occur that you could see miracles occur at the macroscopic level. Just keep an open mind when you jump into the pool if you'd like to enjoy understanding QM more.

 

[Chalnoth]

Why is it stated that a fluctuation could occur and spontaneously gather all the molecules of air onto the corner of the room, or that a brain can spontaneously form in empty space if given enough time. Personally I don't agree with this because these events would contradict the laws of physics, wouldn't they?

Empty space has a non-zero temperature. With a non-zero temperature, any and all particles are produced at some quantity. Because the temperature of space (currently 2.7K) is pretty low, this doesn't happen very often for particles with mass. And assemblages of particles that are of any significant degree of complexity are rarer still.

 

[phinds]

Erotavias, there is a classical way to look at this that is different from what posts #4 and #5 said and doesn't depend on quantum mechanics.

Marcus, I don't follow this at all. Well, I mean I DO follow what you said but I don't see the relevance to the OP's question and in fact, I think it is misleading. Unless I am mistaken, quantum mechanics does not at all require that the particles all start in one corner in order to end up in that corner eventually. Is that not correct?

 

[erotavlas]

It"s important to begin from a good foundation, so I hope you don't mind that I won't ask you to 'cite' where this is stated. Also, it would be presumptuous to suggest that the two scenarios you describe could occur from "a fluctuation", as in "just ONE flip of a coin".

What you may recall reading or hearing - one of the counter-intuitive aspects of quantum mechanics - is that at the microscopic, quantum level, particles can do things and go places that don't make sense or behave according to anything (and everything) you've experienced.

The significant point I want to convey is that QM does indeed include probabilities of events occurring at the QUANTUM level that would amaze you. BUT, the probability of the things that would be amazing can be very, very small at the microscopic/quantum level, and almost zilch if you want billions of improbabilities to happen, "just so".



This is a question you do need to clarify to make it proper. Which laws of physics? Classical or quantum or,...?

In any event, the odds of you being proven wrong are in the same league with a brain appearing in outer space. It doesn't mean neither can or cannot happen.

What if I told you it was impossible for you to win a lottery? On one hand you might agree, on the other hand you know it may be improbable, but not impossible.

So then, a brain appearing in space? Hmmm... Could you win every lottery, every day, for the rest of your life? That's kind of a similar thing. The significance is not to expect so many improbable things to occur that you could see miracles occur at the macroscopic level. Just keep an open mind when you jump into the pool if you'd like to enjoy understanding QM more.

I was watching a talk from TED by Sean Carroll Distant time and the hint of a multiverse
http://on.ted.com/carroll

"Carl Sagan once famously said that "in order to make an apple pie, you must first invent the universe." But he was not right. In Boltzmann's scenario, if you want to make an apple pie, you just wait for the random motion of atoms to make you an apple pie. That will happen much more frequently than the random motions of atoms making you an apple orchard and some sugar and an oven, and then making you an apple pie. So this scenario makes predictions. And the predictions are that the fluctuations that make us are minimal."

 

[erotavlas]

Erotavias, there is a classical way to look at this that is different from what posts #4 and #5 said and doesn't depend on quantum mechanics.

Think of starting with all the particles clustered in a corner. They are not at absolute zero so they are not absolutely still. The particles begin with some kinetic energy, some motion, but they happen to be all crowded in the corner. Take a movie of what happens as each particle continues to move and as they collide and bounce off each other, and as they bounce off the walls of the box, analogous to billiard balls.

Eventually they are approximately evenly spread throughout and all moving in what look like random directions as a result of many scattering collisions and bounces.

But all those collisions and bounces are REVERSIBLE. The laws of microscopic physics work in either direction: if you take the reversed output as input, then you get the reversed input as output. So you could take what looks like a random spread out state and RUN THE MOVIE BACKWARDS. The deterministic laws of individual bounce and collision say that
before too long you will see them crowded in the corner again.

They would be reversible if the universe was a machine like your movie player and you existed external to it and reversed the flow of time for it. However we exist inside the universe and we don't have that capability. The 'arrow of time' entropy or whatever you call it seems to be flowing only in one direction. From order to disorder. So I don't think you can take the movie example and directly apply it to our universe. The question is if the particles would collapse into a low entropy configuration by themselves inside a universe that is also flowing from low to high entropy.

 

[TumblingDice]

Ah-hah! I just spent some time reading wiki about the Fluctuation theorem and Loschmidt's paradox. Now have a better understanding of the OP topic as well as Marcus' reply. Appears to be all about contradictions with entropy and arrow of time.

Good topic, and better for me to listen and learn what more knowledgeable members have to say.

 

[Chronos]

The Boltzmann brain argument is just one among many that logically refutes the proposition of an infinitely old universe.

 

[MathematicalPhysicist]

The Boltzmann brain argument is just one among many that logically refutes the proposition of an infinitely old universe.

It doesn't do the job quite well.

I mean a brain/s were created eventually, the process might have taken time, but it doesn't mean that we don't live in a infinitely old universe.

I mean a finite old universe begs the question how did it have a beginning, I mean a beginning begs the question from what?

Which means there's no good argument to dispose with the infinite regression.

 

[Chalnoth]

The Boltzmann brain argument is just one among many that logically refutes the proposition of an infinitely old universe.

Not really. It's an argument about relative probability that states that in order for observers to exist, our universe must produce more new, low-entropy regions of space-time than you would predict from entropy arguments alone.