Schrödinger's cat

[Ethernos D Grace]

The state of a system in a quantum superposition is expressed mathematically something like this:

state = aA + bB

Here, A and B are what are called eigenstates of the system. (This example uses two eigenstates, but other systems might have many more eigenstates). When a measurement is made of the system, the eigenstates are the only possible observations that the measurement can output. The a and b are numbers that express, roughly speaking, the probability that any measurement on the system will result in outcomes A or B.

Applying this to the cat, the initial state might be something like:

cat = (50%)Alive + (50%)Dead

When somebody opens the box, that's the equivalent of making a measurement of the state of the system. The only possible (mutually exclusive) outcomes in this case are Alive or Dead, and in this example the chance of each outcome is the same.

A quantum measurement produces a random outcome that is weighted according to the probabilities in the initial state (in this case, the numbers a and b, both 50% in the cat example). But the measurement also does something else: it changes the state to whatever the outcome of the measurement was. For instance, if somebody opens the box and sees a live cat, then the state immediate becomes:

cat = (100%)Alive

We could, at this point, write

cat = (100%)Alive + (0%)Dead,

but since there's no chance at all now that the cat is dead, there's no need to write the part with the "Dead" state.

In a typical quantum system, after this particular measurement the quantum state of the cat could continue to evolve according to the usual laws of physics, so that at some later time we might get back to something like

cat = (70%)Alive + (30%)Dead,

hypothetically. However, in the example of Schrodinger's cat, the experiment is set up in such a way that the decay of a single radioactive quantum particle is linked to the fates of literally billions upon billions of particles that make up the macroscopic cat. When that initial measurement is made, there's a cascade effect that goes on. Those billions upon billions of particles lose that special quantum connectedness they had before, and whatever happens to them afterwards, we can be confident that a macroscopic "Alive" state will never spontaneously evolve back to some superposition of "Alive" and "Dead", at least while measurements (observations) are being continuously made on the system (the cat).

There are lots of arguments that go on about what "counts" as a measurement of a quantum system, and opinions on that vary. But it is clear that a superposition state always collapses to one of its eigenstates, and all observers always agree on which one it collapsed to.


It's not quite right that there's no wave function. I'd prefer to say that the wave function simply becomes equivalent to one of the eigenstates, rather than being, as it was before, a superposition of several eigenstates.

Thats when timeline and parallel world theories comes into play. Since there is no method to prove or unprove such theories it is difficult for scientist to determine the solution. Eg. Instead of cat we put a human in the box which is dead and alive at the same time. The alive one has an option of stopping the gas with a switch. If he does so observer will find him alive and at the same time if he is found dead people will start to say that there is a parallel verse where he is alive so it is hard to disprove.

 

[C C]

This cat is a bullshit hypothesis,
why not you ask Does the cat itself know it is alive or dead?

It could only "know" if in the state of being alive. Everett had the idea "that his many-worlds theory guaranteed him immortality: his consciousness, he argued, is bound at each branching to follow whatever path does not lead to death".

So in the context of such quantum immortality, the cat would "always" find itself alive from its own conscious perspective, though observers in another world could find it alternatively dead. No one would actually experience living forever as Everett seemed to believe. Only the maximum number of years possible for a body in terms of genetics and avoiding accidents and surviving illnesses.

Needless to say, the development and persistence of complex life also required an Earth that enjoyed an extraordinary sequence of "good luck" dodging total sterilization events and annihilation. But with countless worlds in both the observable and unobservable parts of the universe, at least one (or more) would still be probabilistically bound to appear as if it had an invisible hand watching over it.

 

[Ethernos D Grace]

Something like super position might make sense eg, if light is travelling a distance of 1mm in circle. We would observe the light or photon to exist in multiple places at once. But what we truly are observing is that photon is existing in same space but in different time. So when the superposition collapses. It is collapsing due to observer or detection. Collapse of parallel world or timeline or maybe it is the flow of time in quantum world which is most likely. Lol.

 

[phyti]

CptBork#73;

It's true that in Newtonian physics, one must disturb a particle's momentum in order to measure its position, and one must disturb its position in order to measure the momentum, but there's no classical limit on how small and insignificant these disturbances can be, thus there's no classical limit on how precisely one can simultaneously measure both values.

It's not possible to measure both values simultaneously.
Position requires one measurement. Momentum requires two measurements.
Light motion was instantaneous in Newton's era. Today it has a finite speed.
If you measure the position of a particle, it is historic info. You know where it was.
Therefore a complete knowledge of the state of the universe is impossible, preventing a deterministic theory of any kind.

Initial response unchanged.
The uncertainty is with the radioactive material.
The knowledge of the state of the cat requires an observation to form a conclusion.

 

[Write4U]

James R said: ↑
The state of a system in a quantum superposition is expressed mathematically something like this: state = aA + bB
Here, A and B are what are called eigenstates of the system. (This example uses two eigenstates, but other systems might have many more eigenstates). When a measurement is made of the system, the eigenstates are the only possible observations that the measurement can output. The a and b are numbers that express, roughly speaking, the probability that any measurement on the system will result in outcomes A or B.

Applying this to the cat, the initial state might be something like:

cat = (50%)Alive + (50%)Dead

Why do we need to assume equal possibilities?

Could the superposed state be cat = (64%) alive + (36% dead) ? We really don't know until we look. And should we not repeat the experiment many times to establish a mean?

When somebody opens the box, that's the equivalent of making a measurement of the state of the system. The only possible (mutually exclusive) outcomes in this case are Alive or Dead, and in this example the chance of each outcome is the same

Why must this be the same? Might it still be weighted to one side ever so slightly? For instance; the longer we wait, the greater the probability of a dead cat, no?

AFAIK a random probability does not necessarily (perhaps not possible) suggest a 50/50 probability.

Mario Livio demonstrated that what may appear as a 50/50 % probability is actually weighted in relation to Pi.

As we are speaking about probability, I hope this may relate. Note that in this calculation of Pi we are not talking about circles, but about pure probability (but not 50/50).

 

[DaveC426913]

It's not possible to measure both values simultaneously.

Correction: ...to an arbitrary degree of accuracy.

You can measure both position and momentum, you just can't expect they'll both be accurate downstream of the decimal point. If one is known to many decimals, the other will not be known very precisely.

But otherwise, as you said.

 

[phyti]

Measurements are made in terms of a predefined standard, with predefined limits of precision.
Physical constraints limit cutting a metal rod to 10 decimal precision, if atoms are spaced to 8 decimal precision.
By definition, speed is the ratio of (spatial interval)/(time interval), i.e. two distinct measurements.
That eliminates simultaneous.

 

[exchemist]

Measurements are made in terms of a predefined standard, with predefined limits of precision.
Physical constraints limit cutting a metal rod to 10 decimal precision, if atoms are spaced to 8 decimal precision.
By definition, speed is the ratio of (spatial interval)/(time interval), i.e. two distinct measurements.
That eliminates simultaneous.

That's nonsense. In the first place you measure speed directly, not by measuring a distance and a time separately. Look up how a speedometer works, for example.

In the second place, nothing in mechanics prevents two separate measurements from being made at the same instant.

The point about the uncertainty principle is not really to do with measurement anyway. It is that in QM position and momentum are not even defined exactly at the same instant of time. Simultaneous exact values for both simply do not even exist.

 

[Vociferous]

Why do we need to assume equal possibilities?

We don't. It's just presumed, for the sake of simplifying the thought experiment, in which the actual probability is irrelevant beyond not knowing the outcome over the given amount of time. And even once we open the box, we don't know the probability. For that, we'd need to kill many cats (or just observe enough atomic decay), to learn the probability.

 

[phyti]

1. That's nonsense. In the first place you measure speed directly, not by measuring a distance and a time separately. Look up how a speedometer works, for example.

2. In the second place, nothing in mechanics prevents two separate measurements from being made at the same instant.

3. The point about the uncertainty principle is not really to do with measurement anyway. It is that in QM position and momentum are not even defined exactly at the same instant of time. Simultaneous exact values for both simply do not even exist.

1. How do you measure the velocity of a particle in one measurement?
2. Two separate measurements made at different times.
3. Simultaneous knowledge of both was the subject. The underlined is what I said, maybe in a different context.

 

[exchemist]

1. How do you measure the velocity of a particle in one measurement?
2. Two separate measurements made at different times.
3. Simultaneous knowledge of both was the subject. The underlined is what I said, maybe in a different context.

As I said, read how a speedometer works.

You measure the torque exerted on a conductor, due to the eddy currents induced in it by a rotating magnet connected to the wheels of the vehicle. That's one measurement, of torque. Notice you don't actually need to measure either distance or time at all.

What you have underlined is not at all what you said, which is that you can't make 2 measurements simultaneously (which is in any case wrong).

 

[phyti]

exchemist;

The subject of my posts is determining the speed of a particle/object.
Motion is a change in position. Speed is the rate of change of position.
Thus one measurement of position cannot determine speed, since there is no change.
You have what the position was, but that by itself is not sufficient to determine speed, as noted above. These are fundamental definitions as are momentum, force, etc. There are no magical devices that can produce results without including these relationships.

There are different methods of determining speed, but the methods do not define speed.
For an aircraft, the difference in pressure of ambient air (static port) vs ram air (pitot tube) determines air speed.
The speedometer is a device that continuously measures the angular motion of a wheel, and transforms it to an indicator on a scale (because there is a relationship of the linear speed of the car, to the rotational rate of the wheel, if the tire is in contact with the road surface).
Rotation can be expressed as rpm, which is where the time component is a factor.
The perimeter of the tire is where the spatial component is a factor. You just aren't aware of those factors directly in the concept of 'speedometer'.
If a car is supported by its frame on a lift, with the engine on and in gear, the wheels will spin, and the speedometer will indicate x mph, yet the car is not moving.

 

[Write4U]

We don't. It's just presumed, for the sake of simplifying the thought experiment, in which the actual probability is irrelevant beyond not knowing the outcome over the given amount of time. And even once we open the box, we don't know the probability. For that, we'd need to kill many cats (or just observe enough atomic decay), to learn the probability.

Yep, that is the science of " Large number of rare events".

Large number of rare events

In statistics, large number of rare events (LNRE) modeling summarizes methods that allow improvements in frequency distribution estimation over the maximum likelihood estimation when "rare events are common".

It can be applied to problems in linguistics (see Zipf distribution), in various natural phenomena, in chemistry, in demography and in bibliography, amongst others.

https://en.wikipedia.org/wiki/Large_number_of_rare_events#

 

[QuarkHead]

Yep, that is the science of " Large number of rare events".

No it's not, it's called the "expectation value" of an operator acting on a quantum state.

 

[QuarkHead]

As I said, read how a speedometer works.

Trouble is, torque-based speedometers are of very little use in the quantum world.

 

[exchemist]

Trouble is, torque-based speedometers are of very little use in the quantum world.

True, but my point was that you don't need to measure distance and time separately, in order to measure velocity. A single measurement of an appropriate property suffices, doesn't it? .

But in any case this discussion is in danger of muddling up the uncertainty principle with the observer effect. All this about the practical difficulties in measurement relates to the observer effect, which is a different issue from that of the uncertainty principle.

 

[Write4U]

No it's not, it's called the "expectation value" of an operator acting on a quantum state.

Expectation value (quantum mechanics)

In quantum mechanics, the expectation value is the probabilistic expected value of the result (measurement) of an experiment. It can be thought of as an average of all the possible outcomes of a measurement as weighted by their likelihood, and as such it is not the most probable value of a measurement; indeed the expectation value may have zero probability of occurring (e.g. measurements which can only yield integer values may have a non-integer mean). It is a fundamental concept in all areas of quantum physics.

https://en.wikipedia.org/wiki/Expectation_value_(quantum_mechanics)

And I believe "Expectation value" rests on the statistics of "Large numbers of rare events" (LNRE)

Large number of rare events

In statistics, large number of rare events (LNRE) modeling summarizes methods that allow improvements in frequency distribution estimation over the maximum likelihood estimation when "rare events are common".[1]

It can be applied to problems in linguistics (see Zipf distribution), in various natural phenomena, in chemistry, in demography and in bibliography, amongst others.[2]

https://en.wikipedia.org/wiki/Large_number_of_rare_events

AFAIK, it calculates a "range" of expected values.

 

[QuarkHead]

And I believe "Expectation value" rests on the statistics of "Large numbers of rare events" (LNRE)

Believe what you you like. Some of us choose theory backed by evidence rather than belief

 

[Write4U]

Believe what you you like. Some of us choose theory backed by evidence rather than belief

My belief has nothing to do with the science of LNRE.
The NSA uses it in researching "authorship". Dr. Robert Hazen uses it in "mineralogy" and "origins of life".

The theory of "Large numbers of rare events" (LNRE) is well established science and usable in a variety of statistical models.

My belief (and implied question) is that it may be applicable in modeling "expectation values" in quantum physics.

 

[Write4U]

The alive one has an option of stopping the gas with a switch. If he does so observer will find him alive and at the same time if he is found dead people will start to say that there is a parallel verse where he is alive so it is hard to disprove

Might need a psychological profile to see if the test subject had any desire to commit suicide....