xkcd

by **Taikand** » Mon Mar 19, 2012 4:54 pm UTC

I have heard about some experiments in quantum physics where particles would pop in and out of existence at random. This has led me to think that if it is true then our universe is nondeterministic therefore our current sciences are all wrong because a set of conditions can lead to multiple outcomes if the experiment is repeated many time. The problem is if quantum particles are nondeterministic then why do macroscopic object look deterministic? Is it that with a sufficiently large statistical population the object becomes relatively stable therefore creating the illusion of determinism? And finally a bit off-topic, is the hidden variable hypothesis taken seriously or it's somewhere out there?

by **LaserGuy** » Mon Mar 19, 2012 6:02 pm UTC

Taikand wrote:I have heard about some experiments in quantum physics where particles would pop in and out of existence at random. This has led me to think that if it is true then our universe is nondeterministic therefore our current sciences are all wrong because a set of conditions can lead to multiple outcomes if the experiment is repeated many time. The problem is if quantum particles are nondeterministic then why do macroscopic object look deterministic? Is it that with a sufficiently large statistical population the object becomes relatively stable therefore creating the illusion of determinism? And finally a bit off-topic, is the hidden variable hypothesis taken seriously or it's somewhere out there?

It's pretty much the statistical argument. Quantum events have certain probabilities of happening. But if you do a large number of trials over a large number of particles, you will find that the distribution, regardless of what it originally looks like, will converge on the most probable value with increasingly small error (Central Limit Theorem, essentially). On an individual particle level, the effect is random; however, on the bulk scale, the behaviour is extremely deterministic. This phenomenon is actually pretty common. For example, if you're looking at the flow of people through a shopping mall, you'll find that the behaviour of any given person cannot be predicted accurately; however, if you look at the collective behaviour of large numbers of people, you can get a pretty good idea of how an "average" person would behave, and design your mall accordingly.

There are very, very few situations in which a single quantum event will lead to two dramatically different macroscopic outcomes, so, for the most part, this isn't a problem.

Hidden variable theory has been pretty solidly demolished by Bell's Theorem. Or at least, most people are more willing to accept Bell's Theorem than they are willing to accept non-local hidden variables.

by **mfb** » Mon Mar 19, 2012 6:10 pm UTC

Quantum mechanics is a deterministic theory. In fact, you can call it the "most deterministic theory", as it has a method to transform every non-deterministic theory in a deterministic one*.

Ok, that might be a bit confusing, but consider the standard example of a photon hitting a half-transparent mirror: The wave-function of the photon is split up into two parts. One part is reflected, and one passes through the mirror. The two parts at the same time are necessary to understand interference effects which can be observed.
The most simple thing you can do is to put two detectors in the beam lines: If the photon hits detector A, it was reflected at the mirror. If it hits detector B, it was not. We always see the photon in one detector, never at both. But what happened to the other part of the wave function?

That is the point where interpretations of QM get interesting:
- The Kopenhagen interpretation says something like "you observed the particle at A, the wave function going to B is removed from the world at the moment of your measurement" (by magic?). Here, it is nondeterministic which detector detects the photon, which is a non-deterministic feature of the world itself.
- The Many-World interpretation says "there is one part of the world where detector A sees the photon (and humans can discuss why it went to A) and one part of the world where detector B sees the photon (and humans can discuss why it went to B)." This is purely deterministic, and follows the (deterministic) equations of quantum mechanics everywhere. Here, our location in this structure of many parts of the world (often called multiple different worls) can be considered as non-deterministic, while the universe itself is deterministic.
- In the de Broglie–Bohm theory, the wave functions determine how the particles move, but they are not the particles itself. At the mirror, the photon will take one of the possible ways in a deterministic way.
- some other interpretations do some other stuff

>> then why do macroscopic object look deterministic
The deterministic look or something really close to it has a probability which is much larger than any large deviation. But keep in mind that "macroscopic" is not the important point - quantum effects have been demonstrated with objects of ~50µm size. The important point is the interaction with other objects. Macroscopic objects just happen to have much larger interactions than elementary particles.

*Edit: What I forgot to add:
Just split the world in multiple parts, one for each possible "outcome" of anything which might appear random. This directly leads to many worlds and can make every theory deterministic.

by **eSOANEM** » Mon Mar 19, 2012 6:32 pm UTC

Determinism is a tricky concept.

In quantum mechanics, the specifics of the motion do not evolve deterministically this is true. That said, it's wavefunction (and therefore the distribution of possible future states) does.

In this sense, a quantum universe is "quasi-deterministic" (not sure if there's a proper term for this, but this is what I'll use for now).

So, if we have a single particle sitting in a box, we put it in, leave it for a bit, open the box and see where it is and what it's doing, we cannot, unlike classical mechanics, say with certainty where it will be, what direction it will be moving in and with what speed. Instead we can calculate the probability of it being in any given position, moving in any given direction at any given speed.

The reason macroscopic objects appear to have precisely deterministic motion is that they contain lots of particles.

When you start taking into account all the possible motions of each individual particle, they start to settle around a mean. This is similar to how, if I take n dice, roll them, add them together and divide the result by the maximum I could get (6n) then plot the probability of getting an individual result for a given n and compare the graphs for different ns, we'll see that the peak becomes taller and narrower.

So, if we put a ball made of a large number of particles (for ease of argument let's say they're identical) into a box. When we close the box, the particles' wavefunctions all spread out over the box. When we consider the wavefunction of the ball however, the quantum corrections start getting smaller and smaller and the position, direction of motion and speed of the ball all settle around one value.

...

For a slightly different argument, you'll probably have heard the uncertainty principle stated as "you can't know both your position and speed at the same time" which is all well and good but misses a lot of information in the uncertainty principle in particular its specificity as to the relationship between the two uncertainties.

The proper expression for the uncertainty in the momentum of a particle localised in an space of given width is:

\sigma_p \cdot \Delta x \ge \pi \hbar

now hbar is of the order of 10^-34Js which is pretty small. What this means is, if we have a 1kg ball and a box with a side length of 1m, we get that the standard deviation in the velocity of the ball is given by:

\sigma_v \ge \pi \hbar \approx 10^{-33.5} ms^{-1}

That's so small there isn't an SI prefix for it and, if the mean was 0 (say we put the particle in the box and made sure it was stationary then closed it), less than 3% of all such particles would cross the box in less than 5*10^25 years which is over a quadrillion times the age of the universe.

...

In short, even if it weren't for the fact that macroscopic objects are made out of many particles, the macroscopic scale is simply far too large for quantum effects to have any even remotely noticeable effect.

...

As for hidden variable theories, because of Bell's theorem, there doesn't exist a local hidden variable theory of quantum mechanics which can reproduce the predictions of non-hidden variable quantum mechanics (which is well tested).

Specifically, Bell's theorem says you have to choose between locality (the property of a theory whereby the behaviour of a particle is determined only by those other particles in its local vicinity) or counterfactual definiteness (CFD) (the property of a theory whereby it is meaningful to make calculations using the results of measurements not taken) in a similar way to how, in SR you must choose two from FTL, causality or locality.

The usual approach is to ditch counterfactual definiteness because locality is nice and without it, we run into problems with SR (see above) whilst CFD seems somewhat arbitrary. It is however perfectly possible to construct non-local interpretations of quantum mechanics with CFD which do produce correct results, one such example is the causal interpretation.

by **Taikand** » Tue Mar 20, 2012 1:01 pm UTC

If we put a particle in a box and it starts moving does it not get kinetic energy, therefore creating it out of literally nothing?
If that is true then we also need a mechanism by which energy is lost to the nether or we get a universe that is gradually gaining energy.If those happen than our current understanding of thermodynamics is false.

by **LaserGuy** » Tue Mar 20, 2012 2:24 pm UTC

Taikand wrote:If we put a particle in a box and it starts moving does it not get kinetic energy, therefore creating it out of literally nothing?
If that is true then we also need a mechanism by which energy is lost to the nether or we get a universe that is gradually gaining energy.If those happen than our current understanding of thermodynamics is false.

Why do you think the particle would have zero kinetic energy to start with? Just because the particle is confined does not mean it is not moving within the area that it is confined. The uncertainty principle predicts that it is impossible to have a particle that is perfectly stationary

by **capefeather** » Tue Mar 20, 2012 5:34 pm UTC

It is, in fact, a scientific theory (quantum field theory) that predicted virtual particles (what you described in your post) in the first place. What you refer to as "current sciences" is, in fact, not "current" at all, but rather the everyday physics that you may have learned in middle and early high school. Quantum physics (among other things, but this is the main subject of this thread) compelled us (well, almost, anyway) to abandon the idea that there is a perfect order in the universe (at least, as we would normally view it) where every event is caused entirely by a collection of events in the past. That was well over 100 years ago. Nonetheless, as the other posts have already touched on, we still *can* predict things, just not the exact properties of a single particle.

by **Danny Uncanny7** » Tue Mar 20, 2012 5:35 pm UTC

Multiworld theory isn't really a theory at all: To say that we will randomly be in a universe which is one of a set of many universes where every possibility has occurred, is EXACTLY the same thing as saying that the result is some random function. You're either randomly placed in one of many universes which are differentiated only by the outcome of some event, or the outcome of the event is randomly chosen... what is the difference?

Consider this: the universe is defined as everything that exists. Other universes therefore don't exist. Multiworld theory therefore predicts the existence of non-existent entities. I also have a theory, it predicts an invisible man who watches everything we do and judges us throughout all of space and time, but he doesn't interact with the universe in any measurable way. Prove me wrong.

What is the alternative to a deterministic universe? A random universe? Either way, there is no room in the universe for free will.

by **eSOANEM** » Tue Mar 20, 2012 6:39 pm UTC

Danny Uncanny7 wrote:Multiworld theory isn't really a theory at all: To say that we will randomly be in a universe which is one of a set of many universes where every possibility has occurred, is EXACTLY the same thing as saying that the result is some random function. You're either randomly placed in one of many universes which are differentiated only by the outcome of some event, or the outcome of the event is randomly chosen... what is the difference?

The many-world interpretation (MWI) isn't a theory and, I don't think anyone's said otherwise here. It's an interpretation of quantum mechanics (and one which avoids the pesky idea of when wavefunction collapse occurs), the entire point is that it gives the same answers as Copenhagen-like interpretations, just with a different philosophical interpretation.

Danny Uncanny7 wrote:Consider this: the universe is defined as everything that exists.

Colloquially, yes; scientifically, no. In a scientific context, universe has no generally accepted definition and any used will be largely contextual (in fact, it often excludes almost all of the world we live in when it's used as shorthand for "the observable universe"). Most stuff I've seen about MWI have been careful to try and avoid this confusion by referring to "worlds" or "histories" instead.

by **mfb** » Tue Mar 20, 2012 7:09 pm UTC

Danny Uncanny7 wrote:Multiworld theory isn't really a theory at all: To say that we will randomly be in a universe which is one of a set of many universes where every possibility has occurred, is EXACTLY the same thing as saying that the result is some random function. You're either randomly placed in one of many universes which are differentiated only by the outcome of some event, or the outcome of the event is randomly chosen... what is the difference?

It is a different interpretation, which gives the same observables (and the calculations are the same in all interpretations), but for a different reason.
In some interpretations, the universe is fundamentally random, in others, it is deterministic and "randomness" is just an illusion.

>> Consider this: the universe is defined as everything that exists. Other universes therefore don't exist. Multiworld theory therefore predicts the existence of non-existent entities.
Sorry, you just play around with words here. You can call the MWI "one-world-interpretation" and consider all elements of its world-view as part of a single universe/world (which is one thing I personally prefer btw.), and your argument is gone.

>> Either way, there is no room in the universe for free will.
Very true.

by **Danny Uncanny7** » Tue Mar 20, 2012 7:33 pm UTC

mfb wrote:
Danny Uncanny7 wrote:Sorry, you just play around with words here. You can call the MWI "one-world-interpretation" and consider all elements of its world-view as part of a single universe/world (which is one thing I personally prefer btw.), and your argument is gone.

But now your definition of the word universe has no common use, or logical basis. Your definition of the universe includes everything existent, and non-existent. At least my definition is tied to the reality we inhabit and generally accepted by most people I've spoken with.

As far as I am concerned, if two entities have no interactions, directly or indirectly, then they do not inhabit the same universe. All of the mass, information, and energy in our universe has some interaction with all other mass, information, and energy. Since we need at least one thing inside the universe to define the other things that interact with it, it makes sense to start with myself. Since I inhabit the universe, the universe is everything that interacts with me on any level or in any way.

As a sort of philosophical aside, I think what the really interesting thing to think about is what determines the universe. The anthropic principle suggests that we have observation bias towards seeing the universe that allows us to exist. But consider that same principle applied to an individual. You can only exist in the exact specific universe that gives rise to your individual existence. Would that mean that your identity defines the universe that you inhabit? Or further, that the entire universe, and your identity spontaneously exist together as two definitions of the same thing.

by **eSOANEM** » Tue Mar 20, 2012 8:00 pm UTC

Danny Uncanny7 wrote:But now your definition of the word universe has no common use, or logical basis. Your definition of the universe includes everything existent, and non-existent. At least my definition is tied to the reality we inhabit and generally accepted by most people I've spoken with.

As far as I am concerned, if two entities have no interactions, directly or indirectly, then they do not inhabit the same universe. All of the mass, information, and energy in our universe has some interaction with all other mass, information, and energy. Since we need at least one thing inside the universe to define the other things that interact with it, it makes sense to start with myself. Since I inhabit the universe, the universe is everything that interacts with me on any level or in any way.

Now you're using two different and possibly contradictory definitions (1. the universe is everything that exists, 2. the universe is everything which interacts with a given reference particle) in an attempt to prove your point. 704 springs to mind.

If we try to force your two definitions to live happily together along with observation, we end up with "universe" being used to mean "contained within my past lightcone". This runs into all sorts of difficulties:

1. What happens at the edge? What would happen to a galaxy near the edge which moves towards it. Without introducing extra axioms, it moves outside of your lightcone and ceases to exist violating conservation of energy and momentum which is bad news for the laws of physics because it would mean they're not actually translation invariant in spacetime.

2. Your universe is getting bigger and gaining more stuff. As time progresses, your lightcone gets bigger and so does your universe. Without introducing new axioms, that new space should, by all rights be, approximately, empty. Except we're pretty sure it isn't. If it were, assuming the laws of physics are constant throughout time (and if they're not we've got bigger problems), the edge of the observable universe (in fact all of it other than me) should be empty and it isn't.

The simplest way to resolve both of these is to let things exist on either side of the lightcone (outside of your universe) so that objects can move out of it without violating conservation laws and stuff can still appear as our lightcone gets bigger. This leads to the usual cosmological meaning of the term "universe" which is roughly the observable universe except extended beyond its boundary in all directions, usually an infinite amount.

With this definition of a universe (which differs from the colloquial one you describe), two particles which couldn't have ever interacted can still be in the same universe, they just exist outside of each others' light cones.

This definition of universe also fits quite nicely with the use of the term "world" or "history" in MWI (although there might be issues with locality if applied too literally) without introducing any contradictions.

tl;dr you're using a colloquial definition contradictory to observation in a scientific discussion, your conclusion is wrong because of this.

by **Taikand** » Tue Mar 20, 2012 8:20 pm UTC

LaserGuy wrote:
Taikand wrote:If we put a particle in a box and it starts moving does it not get kinetic energy, therefore creating it out of literally nothing?
If that is true then we also need a mechanism by which energy is lost to the nether or we get a universe that is gradually gaining energy.If those happen than our current understanding of thermodynamics is false.

Why do you think the particle would have zero kinetic energy to start with? Just because the particle is confined does not mean it is not moving within the area that it is confined. The uncertainty principle predicts that it is impossible to have a particle that is perfectly stationary

But, if we repeat the same experiment 1000 times with the same exact beginning conditions will all of them have the same result? (practically, at quantum level I believe there can be all sorts of interferences that can screw up my 1 thousand perfect experiments but I'm just talking about the mathematical model.)
If conditon-set A can only lead to result B then that's what I call determinism, whether or not we can predict it.

by **eSOANEM** » Tue Mar 20, 2012 8:29 pm UTC

Taikand wrote:
LaserGuy wrote:
Taikand wrote:If we put a particle in a box and it starts moving does it not get kinetic energy, therefore creating it out of literally nothing?
If that is true then we also need a mechanism by which energy is lost to the nether or we get a universe that is gradually gaining energy.If those happen than our current understanding of thermodynamics is false.

Why do you think the particle would have zero kinetic energy to start with? Just because the particle is confined does not mean it is not moving within the area that it is confined. The uncertainty principle predicts that it is impossible to have a particle that is perfectly stationary

But, if we repeat the same experiment 1000 times with the same exact beginning conditions will all of them have the same result? (practically, at quantum level I believe there can be all sorts of interferences that can screw up my 1 thousand perfect experiments but I'm just talking about the mathematical model.)
If conditon-set A can only lead to result B then that's what I call determinism, whether or not we can predict it.

The wavefunction evolves deterministically through the Schroedinger equation (or its equivalents for spinning, relativistic and/or interacting particles) and that will be the same every time you perform the experiment. The exact measurement will vary randomly however (beyond simple experimental error) because the wavefunction does not give a single state but determines the probability of each possible state.

by **LaserGuy** » Tue Mar 20, 2012 8:45 pm UTC

Taikand wrote:
LaserGuy wrote:
Taikand wrote:If we put a particle in a box and it starts moving does it not get kinetic energy, therefore creating it out of literally nothing?
If that is true then we also need a mechanism by which energy is lost to the nether or we get a universe that is gradually gaining energy.If those happen than our current understanding of thermodynamics is false.

Why do you think the particle would have zero kinetic energy to start with? Just because the particle is confined does not mean it is not moving within the area that it is confined. The uncertainty principle predicts that it is impossible to have a particle that is perfectly stationary

But, if we repeat the same experiment 1000 times with the same exact beginning conditions will all of them have the same result? (practically, at quantum level I believe there can be all sorts of interferences that can screw up my 1 thousand perfect experiments but I'm just talking about the mathematical model.)
If conditon-set A can only lead to result B then that's what I call determinism, whether or not we can predict it.

For a quantum system, not necessarily. If you send a photon through a beam splitter and into one of two detectors, there is no way to predict which detector will click. If you do 1000 iterations, you should end up with approximately 500 clicks in each detector, but there's no guarantee that you'll get exactly 500 clicks in each detector, any more than if you flip a coin 1000 times, you'll get exactly 500 heads and 500 tails. Probability doesn't work like that. But as you do more trials, your relative deviation from the mean will decrease.

I'll mention too that we can't even necessarily get identical initial conditions even in macroscopic conditions, a lot of the time. Some systems are just too chaotic, and even very tiny deviations from the starting point will produce radically different endpoints.

by **eSOANEM** » Tue Mar 20, 2012 9:02 pm UTC

LaserGuy wrote:For a quantum system, not necessarily. If you send a photon through a beam splitter and into one of two detectors, there is no way to predict which detector will click. If you do 1000 iterations, you should end up with approximately 500 clicks in each detector, but there's no guarantee that you'll get exactly 500 clicks in each detector, any more than if you flip a coin 1000 times, you'll get exactly 500 heads and 500 tails. Probability doesn't work like that. But as you do more trials, your relative deviation from the mean will decrease.

It's also worth noting that, from the wave function, we can predict not only the mean, but the variance of the results, in fact, the wavefunction tells us what the exact probability distribution will be. Obviously, the observed distribution will not match this exactly, if nothing else because it has discrete trials, but if the experiment were performed an infinite number of times, the distribution predicted by the wavefunction would be observed.

by **Danny Uncanny7** » Tue Mar 20, 2012 10:21 pm UTC

eSOANEM wrote:
Danny Uncanny7 wrote:But now your definition of the word universe has no common use, or logical basis. Your definition of the universe includes everything existent, and non-existent. At least my definition is tied to the reality we inhabit and generally accepted by most people I've spoken with.

As far as I am concerned, if two entities have no interactions, directly or indirectly, then they do not inhabit the same universe. All of the mass, information, and energy in our universe has some interaction with all other mass, information, and energy. Since we need at least one thing inside the universe to define the other things that interact with it, it makes sense to start with myself. Since I inhabit the universe, the universe is everything that interacts with me on any level or in any way.

Now you're using two different and possibly contradictory definitions (1. the universe is everything that exists, 2. the universe is everything which interacts with a given reference particle) in an attempt to prove your point. 704 springs to mind.

If we try to force your two definitions to live happily together along with observation, we end up with "universe" being used to mean "contained within my past lightcone". This runs into all sorts of difficulties:

1. What happens at the edge? What would happen to a galaxy near the edge which moves towards it. Without introducing extra axioms, it moves outside of your lightcone and ceases to exist violating conservation of energy and momentum which is bad news for the laws of physics because it would mean they're not actually translation invariant in spacetime.

2. Your universe is getting bigger and gaining more stuff. As time progresses, your lightcone gets bigger and so does your universe. Without introducing new axioms, that new space should, by all rights be, approximately, empty. Except we're pretty sure it isn't. If it were, assuming the laws of physics are constant throughout time (and if they're not we've got bigger problems), the edge of the observable universe (in fact all of it other than me) should be empty and it isn't.

The simplest way to resolve both of these is to let things exist on either side of the lightcone (outside of your universe) so that objects can move out of it without violating conservation laws and stuff can still appear as our lightcone gets bigger. This leads to the usual cosmological meaning of the term "universe" which is roughly the observable universe except extended beyond its boundary in all directions, usually an infinite amount.

With this definition of a universe (which differs from the colloquial one you describe), two particles which couldn't have ever interacted can still be in the same universe, they just exist outside of each others' light cones.

This definition of universe also fits quite nicely with the use of the term "world" or "history" in MWI (although there might be issues with locality if applied too literally) without introducing any contradictions.

tl;dr you're using a colloquial definition contradictory to observation in a scientific discussion, your conclusion is wrong because of this.

To use your in concept of a light cone, For a galaxy to move beyond the universe it would need to travel faster than light. This would probably violate a lot of laws beyond conservation of momentum. For something to enter the universe it would have to have existed before the big bang but not been affexted by the big bang. This probably also violates some principles of physics. But my original idea was based on definitions across all time and space. Not for specific time reference points. So anything that interacts at all in past or future counts as part of the universe.

by **eSOANEM** » Tue Mar 20, 2012 10:54 pm UTC

Danny Uncanny7 wrote:To use your in concept of a light cone, For a galaxy to move beyond the universe it would need to travel faster than light. This would probably violate a lot of laws beyond conservation of momentum. For something to enter the universe it would have to have existed before the big bang but not been affexted by the big bang. This probably also violates some principles of physics. But my original idea was based on definitions across all time and space. Not for specific time reference points. So anything that interacts at all in past or future counts as part of the universe.

It's not my notion of a lightcone. It's one of the most fundamental ideas from special relativity. It determines what things are causally linked to an object (which is equivalent to the "interact/can interact/could have interacted with" idea of a universe you proposed).

You're quite right actually, things can't escape your lightcone without travelling faster than c (superluminal inflation might mess with this a bit though) so that criticism doesn't really work (except for superluminal inflation which would provide a brief period of time where it was a valid concern).

...

For something to enter the universe would indeed be dodgy. For something to enter the lightcone is perfectly ok.

This is easy to show diagrammatically.

I don't have an easily useable scanner and I don't have time to take a decent photo of the diagram myself right now so I'll describe how to draw the relevant Minkowski diagram to you.

First draw a large set of axes, the vertical (y) axis is time and the horizontal (x) axis is distance "r".

Obviously, I'm the centre of the universe so I call myself r=0 and me now is r=0, t=0. This means that my world line is the time axis.

If we now draw two lines through r=0 t=0 (me now) at 45 degrees to the axes. This is my lightcone. It shows where a ray of light emitted by me now can be at any point in time. The area above me now between the two lines and the time axis is my future lightcone and everything below me now between the two lines and the time axis is my past lightcone. Everything else (between the lines and the distance axis) is outside the lightcone.

If we now mark a galaxy some distance away (it doesn't matter how far) but still at t=0 and again draw a vertical line through it (this is saying that it is stationary with respect to us).

This vertical line starts (at t=0) outside my lightcone.

If we now draw lines parallel to the lightcone we've already drawn such that it crosses the galaxy's worldline. This line can be extended to where it crosses the time axis. If we mark this point in time as "future me", we can draw future me's lightcone.

We constructed the lightcone specifically so that the lightcone includes the galaxy which was previously outside the lightcone and you can see this because the galaxy's worldline crosses into future me's lightcone from outside me now's.

This diagram is one of the simplest two-body minkowski diagrams which can be drawn and is fully consistent with relativity. You are saying that this diagram is not allowed (because things cannot enter the "universe" (for your definition of the term)) which introduces extra assumptions which Occam's razor won't like.

...

That's not quite how the big bang works either because the big bang was everywhere not at a single point.

...

If your definition of a universe is "anything that interacts at all in past or future counts as part of the universe" then the entire multiverse (for want of a better term) of MWI would qualify as a universe because in MWI the histories branch off each other. Because any two forks of a branch will share interactions, and so count as one universe as a whole.

I don't know of any good definition of a universe consistent with cosmological observations which does not allow for MWI.

by **Danny Uncanny7** » Tue Mar 20, 2012 11:22 pm UTC

What you've just described is an event occurring at that galaxy entering the light cone. The past galaxy of course already interacted with us. The galaxy exists and existed previously, from the reference frame of r=0 t=0, the event you have described as occurring at t=0 and r=galaxy does not yet exist. From a time dependent reference frame, relative to a particle at a specific point at a specific time, the universe IS the past light cone. It contains all of the objects and energy and information carried forward from the big bang. Events which occur in the future are part of the universe from that time reference. Events which occurred in the objective past but beyond the speed of light are also not part of that universe, but they may be predictable from the information of the universe.

by **Xanthir** » Wed Mar 21, 2012 12:52 am UTC

eSOANEM wrote:You're quite right actually, things can't escape your lightcone without travelling faster than c (superluminal inflation might mess with this a bit though) so that criticism doesn't really work (except for superluminal inflation which would provide a brief period of time where it was a valid concern).

Actually, inflation allows things to advance "superluminally" away from you right now. The lightspeed limit doesn't apply to expansion, because things aren't actually "moving"; the space between you is expanding instead.

DannyUncanny, it's also possible for "new" parts of the universe to enter our lightcone even now. During hyperinflation at the beginning of the universe, the separation between us and some portion of the universe may have been growing superluminally, but then slowed to subluminal afterwards. This would allow our lightcone to "catch up" with those portions over time.

by **starslayer** » Wed Mar 21, 2012 2:28 am UTC

Do note that inflation has a very specific cosmological definition. It refers to the proposed period very early in the universe (like, 10^-36 s early) where the universe suddenly started expanding exponentially. This period ended sometime around 10^-18 s, IIRC. The expansion of the universe today is not inflation, just expansion. And yes, we can see things that are moving away from faster than light. The reason is precisely because the universe is expanding, or rather, because the expansion was decelerating at some point in the past. As the photons emitted by the superluminally receding object move towards us, the Hubble radius* also grows. If the photons are able to get within a Hubble radius of us, they will eventually reach us, so we can see the object.

*The Hubble radius is the distance from us at which objects recede from us at c due to the expansion of the universe, and in comoving coordinates is equal to c/H₀, where H₀ is the present-day Hubble "constant" (it isn't really constant - it changes with time depending on the composition of the universe). This should also explain why deceleration is a necessary condition for us to see superluminally receding objects. As the expansion slows, the Hubble constant decreases, and the (comoving) Hubble radius increases. If the universe's expansion then begins to accelerate, the Hubble constant grows, and the comoving Hubble radius decreases. If the Hubble constant is truly constant, the Hubble radius never changes and is far as we are ever able to see.

by **eSOANEM** » Wed Mar 21, 2012 7:51 am UTC

Danny Uncanny7 wrote:What you've just described is an event occurring at that galaxy entering the light cone. The past galaxy of course already interacted with us.

This is only necessarily the case given an infinite amount of time before "me now". For any finite-ly old universe (such as our own), there are subluminal paths which enter the past lightcone. I can't do it yet, but when I get back home from school I'll sketch an example.

Danny Uncanny7 wrote: the event you have described as occurring at t=0 and r=galaxy does not yet exist.

It hasn't yet occurred in me now's reference frame yes because the two are spacelike separated. However, the horizontal "t=0" line serves a function similar to the big bang and so there is no "past galaxy" to worry about.

Danny Uncanny7 wrote:From a time dependent reference frame, relative to a particle at a specific point at a specific time, the universe IS the past light cone. It contains all of the objects and energy and information carried forward from the big bang.

This doesn't follow. As I said, I'll sketch the diagram when I get back from school for you. Because the big bang is, by definition, the earliest a worldline can go, it makes sense to label it as the "absolute" t=0. In this case, at the big bang, no point is in any other's lightcone.

This is what I mean about your definitions being contrary to observations because the lightcone of "you" initially contained your reference particle but now, clearly contains far more. If you postulate a big bang and that everything that exists is contained within your past lightcone, you are the only thing which can exist without introducing additional assumptions about what happens as the lightcone gets bigger.

Xanthir wrote:
eSOANEM wrote:You're quite right actually, things can't escape your lightcone without travelling faster than c (superluminal inflation might mess with this a bit though) so that criticism doesn't really work (except for superluminal inflation which would provide a brief period of time where it was a valid concern).

Actually, inflation allows things to advance "superluminally" away from you right now. The lightspeed limit doesn't apply to expansion, because things aren't actually "moving"; the space between you is expanding instead.

True, it still doesn't allow things to leave the lightcone though (at least if I'm visualising the diagrams right) because it will carry the lightcone with it.

by **The Geoff** » Wed Mar 21, 2012 2:29 pm UTC

Danny Uncanny7 wrote:Multiworld theory isn't really a theory at all: To say that we will randomly be in a universe which is one of a set of many universes where every possibility has occurred, is EXACTLY the same thing as saying that the result is some random function. You're either randomly placed in one of many universes which are differentiated only by the outcome of some event, or the outcome of the event is randomly chosen... what is the difference?

Consider this: the universe is defined as everything that exists. Other universes therefore don't exist. Multiworld theory therefore predicts the existence of non-existent entities. I also have a theory, it predicts an invisible man who watches everything we do and judges us throughout all of space and time, but he doesn't interact with the universe in any measurable way. Prove me wrong.

What is the alternative to a deterministic universe? A random universe? Either way, there is no room in the universe for free will.

Assuming the MWI is correct, there are a lot of different universes in my future, including one where I finish this post with a "P" and one where I don't. If there is free will then that's where it lies, I am able to make a choice of whether I type that P or not, in essence I can move freely between a limited set of closely related universes.

Whether I do so out of "free will" or simply as a result of a cascade of quantum->biochemical reactions, well, that's the big question, and currently just as un-testable as the MWI.

Q

by **starslayer** » Wed Mar 21, 2012 3:36 pm UTC

eSOANEM wrote:True, it still doesn't allow things to leave the lightcone though (at least if I'm visualising the diagrams right) because it will carry the lightcone with it.

You may want to read my post again. Cosmic expansion can carry objects out of our lightcone as long as the expansion of the universe is accelerating.

by **eSOANEM** » Wed Mar 21, 2012 6:39 pm UTC

starslayer wrote:
eSOANEM wrote:True, it still doesn't allow things to leave the lightcone though (at least if I'm visualising the diagrams right) because it will carry the lightcone with it.
You may want to read my post again. Cosmic expansion can carry objects out of our lightcone as long as the expansion of the universe is accelerating.

I should have been clearer. By "things leaving our lightcone" I meant that a worldline being at least part contained within our past lightcone at some earlier point in our history no longer having any part within our past lightcone.

I know that this definition isn't really a very useful one, but it was the one which seemed most appropriate given the definition of a universe I was working with.

by **eSOANEM** » Thu Mar 22, 2012 7:02 pm UTC

Here's the diagram I promised.

This shows that it is possible for an object whose worldline was entirely outside an observer's past lightcone at one point in time can have some (or all) of its worldline contained within the observer's past lightcone (it can enter the observer's lightcone) given a big bang (that time does not extend infinitely into the past).

by **JWalker** » Fri Mar 23, 2012 1:11 am UTC

mfb wrote:Quantum mechanics is a deterministic theory. In fact, you can call it the "most deterministic theory", as it has a method to transform every non-deterministic theory in a deterministic one*.

*Edit: What I forgot to add:
Just split the world in multiple parts, one for each possible "outcome" of anything which might appear random. This directly leads to many worlds and can make every theory deterministic.

Can people please stop saying this? It is highly misleading since in QM observables evolve non-deterministically*, and observables are what you really should be talking about.

*Don't confuse the deterministic evolution of the operator corresponding to the observable with deterministic evolution of the observable itself. The fact that the statistical distribution of an observable evolves deterministically does not mean the observable does. Consider what the results of an experiment designed to track the time evolution of the position of a quantum particle would look like, for example.

by **Danny Uncanny7** » Fri Mar 23, 2012 2:28 am UTC

eSOANEM wrote:Here's the diagram I promised.

This shows that it is possible for an object whose worldline was entirely outside an observer's past lightcone at one point in time can have some (or all) of its worldline contained within the observer's past lightcone (it can enter the observer's lightcone) given a big bang (that time does not extend infinitely into the past).

And like I said before, that is only possible if the galaxy started existence outside of the big bang. Notice how it was already far away from us at the start of the universe. That means that at the time of the big bang, this galaxy wasn't interacting with anything. In objective terms it came into existence at the same time as the universe, but was already sitting very far away from the big bang. This probably violates our understanding of the universe, and it's equivalent to something spontaneously appearing.

by **Dopefish** » Fri Mar 23, 2012 2:46 am UTC

I think you're getting confused about the nature of the big bang. From an earlier post:

eSOANEM wrote:That's not quite how the big bang works either because the big bang was everywhere not at a single point.

It really did start 'everywhere', so it doesn't make sense for something to be far away (in a spatial sense) from the big bang. At the time of the big bang, some stuff was 'here' and some stuff was 'there', and at t=0 nothing at all was interacting with anything else* since it simply didn't have time to yet. It's not the case that there was a whole bunch of stuff gathered at one point already interacting at t=0 that makes up our universe, and then that all expanded at c like a balloon, stuff really was everywhere in some sense.

*=I'm not especially comfortable with this comment since relativity is weird and super early universe stuff is even weirder. It seems to me like it ouaght to take some t>0 for force carriers and the like to actually reach other stuff in order to interact though.

edit: I should note relativity and early universe stuff is very much not my thing, so knowledgable folks should correct me if I've said anything especially wrong. QM is more my thing, on which note I'd probably lean towards QM being non-deterministic (not in a way that gives rise to free will though), even if you allow for a universal wavefunction. Sure, such a wavefunction evolves in a deterministic way, but that wavefunction just governs probablistic (as in, non-deterministic) outcomes. (There could be further semantics surrounding that and more detail on MWI, but that tends to lead to a debate on the validity of MWI which has been done plenty of times already elsewhere.)

by **Argency** » Fri Mar 23, 2012 6:22 am UTC

To reply directly to the OP...
"Logical determinism or Determinateness is the notion that all propositions, whether about the past, present, or future, are either true or false. Note that one can support Causal Determinism without necessarily supporting Logical Determinism and vice versa (depending on one's views on the nature of time, but also randomness)."

So it's totally possible to support one variety of determinism whilst acknowledging that quantum events may be partially or wholly acausal. All you have to argue is that whilst the event in question may not have been contingent on earlier events, it WAS inevitable because it wasn't contingent at all. In fact, I think that this line of reasoning is correct and that a truly non-deterministic universe is logically impossible, although I agree that the causal brand of determinism seems to break down at the quantum level.

Danny Uncanny7 wrote:What is the alternative to a deterministic universe? A random universe? Either way, there is no room in the universe for free will.

Spoiler:

by **eSOANEM** » Fri Mar 23, 2012 7:44 am UTC

Danny Uncanny7 wrote:
eSOANEM wrote:Here's the diagram I promised.

This shows that it is possible for an object whose worldline was entirely outside an observer's past lightcone at one point in time can have some (or all) of its worldline contained within the observer's past lightcone (it can enter the observer's lightcone) given a big bang (that time does not extend infinitely into the past).

And like I said before, that is only possible if the galaxy started existence outside of the big bang. Notice how it was already far away from us at the start of the universe. That means that at the time of the big bang, this galaxy wasn't interacting with anything. In objective terms it came into existence at the same time as the universe, but was already sitting very far away from the big bang. This probably violates our understanding of the universe, and it's equivalent to something spontaneously appearing.

If the galaxy is "outside of the universe" at the beginning there, so is everything other than the particle whose reference frame we're in. By that and your definition that nothing exists outside the universe, there should be a single particle in the universe. That whose frame we're in.

This is clearly contrary to observation so your assumptions ("the universe is everything that exists", "the universe is everything which is/was interacting with stuff" and "these two assumptions describe reality") must be contradictory. This means that at least one of them is wrong. Assuming we want to keep it describing reality, you must either admit that things outside the universe exist or that the universe includes things which cannot yet have interacted with us.

Dopefish wrote:I think you're getting confused about the nature of the big bang. From an earlier post:

eSOANEM wrote:That's not quite how the big bang works either because the big bang was everywhere not at a single point.

It really did start 'everywhere', so it doesn't make sense for something to be far away (in a spatial sense) from the big bang. At the time of the big bang, some stuff was 'here' and some stuff was 'there', and at t=0 nothing at all was interacting with anything else* since it simply didn't have time to yet. It's not the case that there was a whole bunch of stuff gathered at one point already interacting at t=0 that makes up our universe, and then that all expanded at c like a balloon, stuff really was everywhere in some sense.

*=I'm not especially comfortable with this comment since relativity is weird and super early universe stuff is even weirder. It seems to me like it ouaght to take some t>0 for force carriers and the like to actually reach other stuff in order to interact though.

This is the fundamental issue. At the moment of the big bang (if such a moment actually exists), no particle could have interacted with any other due to the finiteness of c. All this really assumes is that there is an earliest co-ordinate time, the finiteness of c and some finite separation between particles. The first is a necessary condition for a conventional big bang, the second comes straight from observation and the third comes from the fact that it's thought that various quantum effects will prevent a true singularity from existing.

by **SU3SU2U1** » Fri Mar 23, 2012 3:25 pm UTC

mfb wrote:It (many worlds) is a different interpretation, which gives the same observables (and the calculations are the same in all interpretations), but for a different reason.

Many worlds does not give the same observables, AND calculations are not the same in all interpretations. Have you ever worked with the Bohm or consistent histories interpretation? Bohm mechanics looks very different than copenhagen quantum, consistent histories most important operator is a consistency operator on a class of histories, which is something you'll never see in copenhagen calculations. Interpretations change the axioms, which necessarily entails changing the calculations.

Now, you will never see a calculation done with many worlds, but thats only because no one knows how to do a calculation with many worlds- its an 'interpretation' with no way to get predictions out! See my thread on many worlds.

by **Danny Uncanny7** » Fri Mar 23, 2012 5:26 pm UTC

eSOANEM wrote:If the galaxy is "outside of the universe" at the beginning there, so is everything other than the particle whose reference frame we're in. By that and your definition that nothing exists outside the universe, there should be a single particle in the universe. That whose frame we're in.

This is clearly contrary to observation so your assumptions ("the universe is everything that exists", "the universe is everything which is/was interacting with stuff" and "these two assumptions describe reality") must be contradictory. This means that at least one of them is wrong. Assuming we want to keep it describing reality, you must either admit that things outside the universe exist or that the universe includes things which cannot yet have interacted with us.

...

This is the fundamental issue. At the moment of the big bang (if such a moment actually exists), no particle could have interacted with any other due to the finiteness of c. All this really assumes is that there is an earliest co-ordinate time, the finiteness of c and some finite separation between particles. The first is a necessary condition for a conventional big bang, the second comes straight from observation and the third comes from the fact that it's thought that various quantum effects will prevent a true singularity from existing.

Most cosmologists accept that the big bang started with a singularity, which is exactly what you are saying can't happen: infinite density, 0 space, all of mass occupying the same point with no distance between anything.

And as for things spontaneously appearing in the universe. There is no logical rule that says that things can't suddenly pop out of nowhere and enter the universe. It's just never happened, so we don't expect it to ever happen. If a galaxy ever did appear at the edge of the universe where no galaxy was before, we would probably have to rebuild most of our understanding of the universe. But as of yet, nothing has ever left the light cone for any reference particle in the known universe, and nothing has entered the light cone except for the future. I fail to see the contradiction that you see. If something was outside the light cone and entered it, it would be as though that object spontaneously sprang into existence. This has yet to happen.

by **starslayer** » Fri Mar 23, 2012 6:40 pm UTC

You misunderstand what a singularity is and how the term is used in cosmology. Yes, the Big Bang is a singularity, but unless the universe is closed, it is not a spatial singularity, but instead one of density. All the word "singularity" means in physics, astronomy, and cosmology is that some quantity is going to infinity. This does not necessarily imply that any other quantity is doing so, or is going to zero at the same time. It is entirely possible for the universe to have always had infinite spatial extent, have finite density today, and have had infinite density at time zero - though we don't think this is really what happens; GR says it does, but we know/suspect that GR breaks down when the energy scales become absurdly large.

by **gmalivuk** » Fri Mar 23, 2012 7:36 pm UTC

Danny Uncanny7 wrote:And as for things spontaneously appearing in the universe. There is no logical rule that says that things can't suddenly pop out of nowhere and enter the universe.

There is, if the laws of physics don't change over time.

And if the early inflation of the universe happened fast enough, then there are absolutely things that didn't interact with us at that time, but which could eventually enter our light cone in the future, if the relative motion and expansion rate happen to be right for that.

Also, what about things leaving our light cone? Accelerating expansion implies that this will happen eventually.

by **Danny Uncanny7** » Fri Mar 23, 2012 8:54 pm UTC

gmalivuk wrote:And if the early inflation of the universe happened fast enough, then there are absolutely things that didn't interact with us at that time, but which could eventually enter our light cone in the future, if the relative motion and expansion rate happen to be right for that.

Also, what about things leaving our light cone? Accelerating expansion implies that this will happen eventually.

Then they are no longer part of the same universe as us. If there is no way to get any information about them or have an interaction with them, then that means it doesn't exist. If the light from other galaxies ceased to reach us, then we would have no basis for conjecture about their existence other than their past interactions with us. Those galaxies would have vanished from our universe at that time, and they would inhabit a completely separate universe with a shared past. From the viewpoint of all of time, they are still part of the same universe, but to take any single reference time after we started separating beyond the speed of light, they are in separate universes.

by **Technical Ben** » Fri Mar 23, 2012 9:31 pm UTC

I see a problem with defining "universe" as "things able to effect us or be detected by us". For example, the matter falling inside a black hole, is that now in a separate universe? What about it's information? If I theoretically throw a ball FTL out side of my/the universes light cone, I'd define it as "far away (in space and/or time)" not "in another universe".

I guess that's why new ideas tend to need new words (hence "multiverse" is used, not a retcon of "universe"). Although, "existence" tends to apply to just "all things ever/to exist". "Universe" to the space/time and stars and stuff.

by **eSOANEM** » Fri Mar 23, 2012 11:26 pm UTC

Danny Uncanny7 wrote:
eSOANEM wrote:If the galaxy is "outside of the universe" at the beginning there, so is everything other than the particle whose reference frame we're in. By that and your definition that nothing exists outside the universe, there should be a single particle in the universe. That whose frame we're in.

This is clearly contrary to observation so your assumptions ("the universe is everything that exists", "the universe is everything which is/was interacting with stuff" and "these two assumptions describe reality") must be contradictory. This means that at least one of them is wrong. Assuming we want to keep it describing reality, you must either admit that things outside the universe exist or that the universe includes things which cannot yet have interacted with us.

...

This is the fundamental issue. At the moment of the big bang (if such a moment actually exists), no particle could have interacted with any other due to the finiteness of c. All this really assumes is that there is an earliest co-ordinate time, the finiteness of c and some finite separation between particles. The first is a necessary condition for a conventional big bang, the second comes straight from observation and the third comes from the fact that it's thought that various quantum effects will prevent a true singularity from existing.

Most cosmologists accept that the big bang started with a singularity, which is exactly what you are saying can't happen: infinite density, 0 space, all of mass occupying the same point with no distance between anything.

The big bang singularity is universally agreed not to be of 0 size amongst serious scientists. There are those who will say it has infinite density (but the quantum gravity theoreticians will tell you such a thing isn't physically valid). Really, all we can say about the big bang with any degree of certainty is that its density was bloody huge.

Danny Uncanny7 wrote:
gmalivuk wrote:And if the early inflation of the universe happened fast enough, then there are absolutely things that didn't interact with us at that time, but which could eventually enter our light cone in the future, if the relative motion and expansion rate happen to be right for that.

Also, what about things leaving our light cone? Accelerating expansion implies that this will happen eventually.

Then they are no longer part of the same universe as us. If there is no way to get any information about them or have an interaction with them, then that means it doesn't exist. If the light from other galaxies ceased to reach us, then we would have no basis for conjecture about their existence other than their past interactions with us. Those galaxies would have vanished from our universe at that time, and they would inhabit a completely separate universe with a shared past. From the viewpoint of all of time, they are still part of the same universe, but to take any single reference time after we started separating beyond the speed of light, they are in separate universes.

This is false. Look at the diagram I drew.

That galaxy didn't have any way it could have interacted with me but, later on did. Clearly it is possible to enter a past lightcone.

Furthermore, without requiring approximately-luminal expansion for the entire history of the universe (which seems unlikely seeing as it's currently substantially less than that) and perfect singularities, such a phenomenon is necessary in order to have anything in the observable universe.

by **starslayer** » Fri Mar 23, 2012 11:46 pm UTC

eSOANEM wrote:Furthermore, without requiring approximately-luminal expansion for the entire history of the universe (which seems unlikely seeing as it's currently substantially less than that) and perfect singularities, such a phenomenon is necessary in order to have anything in the observable universe.

What do you mean by this? If you mean the present day Hubble constant is much less than c, well, for one it doesn't have the right units (it has units of inverse time), and two, you can always rescale it so that it is c per some distance unit.

by **eSOANEM** » Sat Mar 24, 2012 8:56 am UTC

starslayer wrote:
eSOANEM wrote:Furthermore, without requiring approximately-luminal expansion for the entire history of the universe (which seems unlikely seeing as it's currently substantially less than that) and perfect singularities, such a phenomenon is necessary in order to have anything in the observable universe.
What do you mean by this? If you mean the present day Hubble constant is much less than c, well, for one it doesn't have the right units (it has units of inverse time), and two, you can always rescale it so that it is c per some distance unit.

By "approximately luminal expansion" I mean expansion such that matter "keeps up with" the lightcone as the lightcone expands. For this to be the case, the hubble radius (c/H₀) approximately the same as the radius of the lightcone.

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