Question about Quantum mechanics

[Roboramma]

Basically the question is, does the mathematics represent something that's actually happening, or is it simply a convenient way to arrive at the correct answer? Ptolemy's system could predict the movement of the planets relatively accurately, and in that way was useful, it but failed to accurately model what was actually happening in the real world. So, is the wave function more likely Ptolemy's system or that of Copernicus*?

Personally I suspect the latter.
*Or is it more like our modern understanding of the solar system?

 

[Perpetual Student]

Basically the question is, does the mathematics represent something that's actually happening, or is it simply a convenient way to arrive at the correct answer? Ptolemy's system could predict the movement of the planets relatively accurately, and in that way was useful, it but failed to accurately model what was actually happening in the real world. So, is the wave function more likely Ptolemy's system or that of Copernicus*?

Personally I suspect the latter.
*Or is it more like our modern understanding of the solar system?

As our ancestors moved from the Ptolemaic system to the Copernican, they benefited by using a better model. But it was still only a model, which was later improved by Kepler, which was even later improved by Newton and finally by Einstein. Nevertheless, GR is still only a model. There is no final definition of the nature of motion and gravity. The equations of GR are not "real" any more than Ptolemy's epicycles were real.
All we will ever have is models.

 

[randman]

All math is based on an idealized system of numbers that does not take all physical variables into account. Applying math to the physical world has very good results but it's always a proximation of probabilities within a range. It's just that on a lot of things the probability for something is quite high and the probability for something else is quite low.

 

[randman]

That's a good question. The current function itself is, of course, a mathematical description of what's going on, but it describes something going on. There really is charge in the circuit that really is moving, though. If someone says the current is real, I would presume they mean that there really is charge moving through the circuit rather than that some Platonic form of the current variable exists out there or whatever.

Saying the wave-function is real would similarly mean that the wave-function describes something actually going on. The electron really is spread out it a cloud around that proton, for instance. I don't think anyone means that the mathematical description itself is real, any more than they'd mean that the mathematical description of current is real rather than a representation.

This is one of the problems of proving something mathematically. Math is an approximation. Not all variables are included in the math but the math works because to describe a process with a high likelihood of repetition, it's not necessary to calculate all variables such as the exact position and time dilation sequence of all particles in a moving object, etc,.....

Most will not affect the outcome.

 

[Roboramma]

As our ancestors moved from the Ptolemaic system to the Copernican, they benefited by using a better model. But it was still only a model, which was later improved by Kepler, which was even later improved by Newton and finally by Einstein. Nevertheless, GR is still only a model. There is no final definition of the nature of motion and gravity. The equations of GR are not "real" any more than Ptolemy's epicycles were real.
All we will ever have is models.

That "all we will ever have is models" is fair enough. But the point I am trying to make is that the copernican system gives a relatively close approximation of the actual movement of the planets. The Ptolemaic system, on the other hand, does not: there is no movement of the planets can is approximated by epicycles. What it does give, though, is a way of calculating where those planets will be as seen from earth, but that calculation does not bare any resemblance to the actual physical system.

I chose to compare that with Copernicus' system because it isn't a perfect representation, but the difference between it and the Ptolemaic system is obviously that while it is imperfect, any accuracy it offers is because of it's closeness to the actual system, and any inaccuracies are because of the ways in which it differs from reality. Ptolemy's system is simply a finely tuned calculating tool.

As to GR being real, I suggest to you that the things represented by the mathematics of GR may not be exactly analogous to the real system, but they do have real analogues. Epicycles don't.

 

[sol invictus]

My (layman's) understanding of the wavefunction is that it describes the probability of something (e.g.: position) over time.

The most orthodox interpretation of the wavefunction is that it tells you the probability distribution on the results of measurements. The interpretation doesn't specify where the uncertainty comes from, i.e. why an identical measurement on an identical state can yield different results. According to it, the world is fundamentally random.

In the MWI, there is no uncertainty - the world is perfectly deterministic. All measurements yield all possible results. The "world" we perceive is a small part of an enormous branching tree of worlds, in many of which a version of us exists, but which differ in all possible ways.

How and why would the wavefunction be more "real" than that?

All we really know is that there is no sign of anything in the most precise tests of nature of anything that contradicts the MWI. Another fact about it is that some of the most strange seeming quantum experiments, like the delayed-choice-quantum-eraser, are simple and entirely unsurprising when viewed from the MW point of view. It is the simplest, most direct and minimal interpretation of the mathematics of quantum mechanics.

 

[randman]

Sol, going back the quantum eraser experiment and using someone else's words to say the same thing:

What is amazing about this experiment is that neither signal photons or the idle photons do anything much different as far as physical interaction with the lab equipment in either case of an interference pattern being formed or not. Going back to the regular double slit experiment it could be argued that the detector watching the photon going through the slit somehow physically interacted with it causing it to change from a wave to a particle. Here the decision of the whether a signal photon will interfere with itself is made based solely whether the information about which slit it went through is still available after the idle photon hits its detector.

For those people who believe in the Many Worlds interpretation the superposition never collapses and the universe, including the scientists doing the experiment is split four ways, one for each possible detector that the idle photon can arrive at.

http://www.unmuseum.org/quantum2.htm

Here's me beef with MWI. There is no reason for an interference pattern to always appear when passed through detectors where the information of which-way path is obscured. There's no difference here in terms of physical interaction. There is interaction without decoherence in one, and interaction with decoherence with another. Interaction should always produce decoherence in MWI, right?

So why is there decoherence only when the particles travel via a means of determining the which-way path?

 

[sol invictus]

Here's me beef with MWI. There is no reason for an interference pattern to always appear when passed through detectors where the information of which-way path is obscured.

Yes, there is. That's exactly what the MWI predicts, as I've tried to explain to you mathematically.

There's no difference here in terms of physical interaction. There is interaction without decoherence in one, and interaction with decoherence with another. Interaction should always produce decoherence in MWI, right?

So why is there decoherence only when the particles travel via a means of determining the which-way path?

There isn't - there is decoherence in all cases where a measurement (i.e. interaction with a macroscopic detector) is made.

 

[punshhh]

Yes, there is. That's exactly what the MWI predicts, as I've tried to explain to you mathematically.



There isn't - there is decoherence in all cases where a measurement (i.e. interaction with a macroscopic detector) is made.

From a laymans point of view does the MWI have a problem with the conservation of energy?

 

[sol invictus]

From a laymans point of view does the MWI have a problem with the conservation of energy?

No.

Mathematically many worlds is just the evolution of the Schrodinger equation as predicted by the laws of physics. If the laws of physics preserve energy (and they do), then so does MW.

Intuitively you can imagine an ensemble of nearly identical worlds that as time passes split off from each other.

Physically, each experimenter measures only one world - so the energy she measures can be conserved no matter how many other worlds split off.

 

[Perpetual Student]

I know, I know, I know, I know intuition does not work well with some of the concepts of modern physics, but the MWI seems so messy with a potentially infinite number of worlds popping into existence at every moment in time around this vast universe. Whew!

 

[edd]

I know, I know, I know, I know intuition does not work well with some of the concepts of modern physics, but the MWI seems so messy with a potentially infinite number of worlds popping into existence at every moment in time around this vast universe. Whew!

I and 10¹⁰³⁰⁰ others of me don't believe it either.

 

[sol invictus]

Our beliefs shouldn't be relevant. There is a reasonably well-defined notion of scientific model comparison, and the complexity of the predictions does not weigh against a theory. Instead, it's the complexity of the theory that matters, along with how well its predictions match experiment.

In this case, all the theories at hand agree on their predictions for the set of experiments that have been done (or will be for the forseeable future). But MW is the simplest theory - it requires nothing more or less than the Schrodinger equation. All other interpretations require the Schrodinger equation plus some other postulate or additional dynamics.

 

[steenkh]

I know, I know, I know, I know intuition does not work well with some of the concepts of modern physics, but the MWI seems so messy with a potentially infinite number of worlds popping into existence at every moment in time around this vast universe. Whew!

I think it is wrong to think that the worlds pop into existence. The idea is that they always exist but those that interest us here are those that split off from our world at every moment.

But it certainly is not helpful for my intuition to come to grips!

 

[Perpetual Student]

I know, I know, I know, I know intuition does not work well with some of the concepts of modern physics, but the MWI seems so messy with a potentially infinite number of worlds popping into existence at every moment in time around this vast universe. Whew!

Hey, if there's a version of the universe that allows me to understand the deepest mysteries of physics, I might be able to disprove all this MWI stuff.

 

[schrodingasdawg]

I don't think many worlds is the simplest interpretation, and would argue that Copenhagen is.

As far as the mathematical formalism goes, they both require something of a collapse postulate. Unless some major breakthrough I have no awareness of has been made, the Born probabilities have not been deduced from the postulates of quantum mechanics sans collapse, and thus need to be put into the theory as a postulate. Many worlds and Copenhagen have a different interpretation of what the probabilities mean---Copenhagen just says they're the probabilities of getting some outcomes, while many worlds states that they're proportions of numbers of worlds---but both need them.

Both interpretations assume the existence of subjects, or observers. Copenhagen has the observer as what makes physical observables determinate. Many worlds has the observer as something that can only experience certain kinds of states, and so finds itself in one of many split worlds (rather than in one of the superposition states that cannot be experienced).

What many worlds does that Copenhagen doesn't is assume the existence of an unobservable entity---is asserts that the wave-function is a physical entity. In Copenhagen, the wave-function is just a mathematical tool for evaluating probabilities, which we are forced to use because particles don't have a determinate location in space. The mathematical formalism is actually quite natural: we can represent integrable probability distributions by square-integrable complex functions which return the distribution when multiplied by their conjugate. The position operator, its infinitesimal translation generator, and the infinitesimal time translation generator (assuming it doesn't explicitly depend on time, anyway---I'm not sure about the general case, I always have trouble with time-dependent Hamiltonians) obey Hamilton's equations right off the bat, and if the distribution has all finite moments it obeys the central limit theorem. In the limit of very small standard deviations (compared to the mean values of the observables themselves) it's fair to say that the observables "are" the mean values, giving a correspondence with the classical position, momentum, and Hamiltonian.

All of the postulates of quantum mechanics make sense in this interpretation. Born probabilities involve taking the square of the wave-function because the wave-function is defined that way. "Collapse" isn't an actual, objective physical process (unlike in von Neumann's interpretation). In contrast, if the wave-function is a "real" physical entity, it isn't at all obvious that taking its square should produce a probability, nor that the 'mean value' of some observable O should take the form <\Psi|O|\Psi>. In addition to this, since many-worlds seems to suppose that the wave-function is fundamental, it's curious that there should be certain states of subjective experience which can be experienced (and thus constitute worlds) and which cannot be (and thus don't constitute individual worlds---the world had to split). In Copenhagen, experience is at least taken as given.

 

[W.D.Clinger]

Usual disclaimer: I am not a physicist.

I don't think many worlds is the simplest interpretation, and would argue that Copenhagen is.

As far as the mathematical formalism goes, they both require something of a collapse postulate. Unless some major breakthrough I have no awareness of has been made, the Born probabilities have not been deduced from the postulates of quantum mechanics sans collapse, and thus need to be put into the theory as a postulate. Many worlds and Copenhagen have a different interpretation of what the probabilities mean---Copenhagen just says they're the probabilities of getting some outcomes, while many worlds states that they're proportions of numbers of worlds---but both need them.

I suspect you're right about the many-worlds interpretation's need for a Born postulate, but I doubt whether the many-worlds interpretation needs a collapse postulate. Combining the Born postulate with conditional probabilities (conditioned on factors that identify the world(s) of interest) should be enough to calculate the probabilities that apply to the world(s) in which you think you find yourself. What the Copenhagen interpretation regards as renormalization after collapse should then fall out as a consequence of the usual rules for conditional probabilities.

 

[sol invictus]

I don't think many worlds is the simplest interpretation, and would argue that Copenhagen is.

As far as the mathematical formalism goes, they both require something of a collapse postulate. Unless some major breakthrough I have no awareness of has been made, the Born probabilities have not been deduced from the postulates of quantum mechanics sans collapse, and thus need to be put into the theory as a postulate.

Some MW advocates argue that the Born rule can be deduced from entirely from the behavior of the wavefunction. I don't fully agree with that, but I do agree that part of it can be deduced. In any case, at worst (for MW) both interpretations require it.

However MW does not require a collapse postulate. There is no such postulate in MW.

What many worlds does that Copenhagen doesn't is assume the existence of an unobservable entity---is asserts that the wave-function is a physical entity.

Except that the wavefunction is observable - it is reality, so it is all observables.

Copenhagen, at least in its most literal sense, requires some unknown dynamics that collapses the wavefunction upon a measurement and projects it onto one "world". That dynamics is necessarily non-linear, non-deterministic, non-relativistic, and inconsistent with everything we know about fundamental physics. It is left unspecified both in precisely what form it takes and in what constitutes a "measurement".

The MWI requires no additional postulates at all - it's simply Schrodinger evolution, plus some part of the Born rule to help interpret it.

 

[randman]

Some MW advocates argue that the Born rule can be deduced from entirely from the behavior of the wavefunction. I don't fully agree with that, but I do agree that part of it can be deduced. In any case, at worst (for MW) both interpretations require it.

However MW does not require a collapse postulate. There is no such postulate in MW.



Except that the wavefunction is observable - it is reality, so it is all observables.

Copenhagen, at least in its most literal sense, requires some unknown dynamics that collapses the wavefunction upon a measurement and projects it onto one "world". That dynamics is necessarily non-linear, non-deterministic, non-relativistic, and inconsistent with everything we know about fundamental physics. It is left unspecified both in precisely what form it takes and in what constitutes a "measurement".

The MWI requires no additional postulates at all - it's simply Schrodinger evolution, plus some part of the Born rule to help interpret it.

Maybe instead of postulating a gazillion alternate universes, the correct path to solving these issues is to rethink our concepts of space and time?

 

[Reality Check]

Maybe instead of postulating a gazillion alternate universes, the correct path to solving these issues is to rethink our concepts of space and time?

That will not work.
Space-time does not have anything to do with the MW interpretation of QM.