Can someone explain Heisenberg's Uncertainty Principle to a non-physicist?

[Narmer]

I'm having a hard time understanding the wording of the example they give. If you put a cat in a box and put poison in there. You then close the box and release the poison. However, since the box is closed, you don't know if the cat is alive or dead. Therefore the cat must be alive and dead.

That last sentence is what gets me. It seems like a childish way of saying the cat is alive or dead. Or you can say that there is an X probability that the cat is alive (or 1-X that it is dead).

Why does the explanation have to sound so complicated when it isn't and how did an important branch of mathematical physics derive from this?

 

[MrMatt]

There is no cat.

 

[MJinZ]

Exactly. The fact that a cat can't be both alive and dead points to the incomplete theories of quantum mechanics.

Were you expecting it to be an actual model of reality? It was designed as a thought experiment to prove other theories (like Einstein's) wrong/incomplete.

 

[Nik]

I'm having a hard time understanding the wording of the example they give. If you put a cat in a box and put poison in there. You then close the box and release the poison. However, since the box is closed, you don't know if the cat is alive or dead. Therefore the cat must be alive and dead.

That last sentence is what gets me. It seems like a childish way of saying the cat is alive or dead. Or you can say that there is an X probability that the cat is alive (or 1-X that it is dead).

Why does the explanation have to sound so complicated when it isn't and how did an important branch of mathematical physics derive from this?

Maybe the cat's alive in one dimension and dead in another dimension? Maybe the cat ceased to exist at all in a 3rd dimension. Maybe the cat ceases to exist while the box is closed but then POOFs back into existence in a 4th dimension or something.

I think the biggest clue to this mystery is the fact that it's called the Uncertainty Principle.

The answer is just that: uncertain

 

[rcpratt]

It's a paradox, it simply doesn't make sense without the quantum mechanics metaphor.

Schrödinger's famous thought experiment poses the question, when does a quantum system stop existing as a superposition of states and become one or the other? (More technically, when does the actual quantum state stop being a linear combination of states, each of which resembles different classical states, and instead begins to have a unique classical description?) If the cat survives, it remembers only being alive. The purpose of the thought experiment is to illustrate this apparent paradox. Our intuition says that no observer can be in a mixture of states; yet the cat, it seems from the thought experiment, can be such a mixture. Is the cat required to be an observer, or does its existence in a single well-defined classical state require another external observer?

 

[IronWing]

Hmm, maybe we should throw the cat through a cheese slicer instead. While the cat is going through, it might appear that the cat is spitting out both sides of the blade. But if we block off one side of the blade then the wave function collapses and the cat only comes out one side.

 

[Crono]

It's a metaphor used to say that in quantum mechanics 2 states that are contradictory to each other can exist at the same time, while in normal (observed) reality it is either or.

It's a paradox, which is why it isn't a real experiment. It's like using the grandfather paradox to explain theories of time travel.

 

[yhelothar]

i confoos

 

[IronWing]

It's like using the grandfather paradox to explain theories of time travel.

Given cat genetics maybe this is what happened to the cat.

 

[PowerEngineer]

Where's silverpig when we need him...

The thought experiment about Schrodinger's Cat is not the same as Heisenberg's Uncertainty Principle.

Assuming you're read the Wikipedia description, the point is that quantum mechanics decrees that the actual state of a small particle isn't defined until it is measured (which is very, very different from not being known until it is measured). Without the Geiger counter reporting to us (outside the box) whether or not the atomic decay has occurred (releasing the poison), it is argued that the cat's state (i.e. dead or alive) is also undefined until we look in the box.

This business of needing an observer to force the determination of a quantum state is a puzzling one. Does this mean that without humans to observe the whole universe might be undefined? I think that's nonsense (but could be wrong). To my limited understanding, the state can remain undefined until some larger process demands the particle to choose. In this case, I'm thinking that the device rigged to release the poison is just such a process. This means the cat is either dead or alive before we look in the box and we just don't know which (which is a lot different than not determined until we look).

 

[WHAMPOM]

You only know if the cat is dead or alive when you open the box. That is all.

 

[disappoint]

It's not Schrodinger's uncertainty principle, it's Heisenberg's. Schrodinger came up with the cat thought experiment.

This is why I hate some analogies. Especially when what they are positing they are analogous to, aren't. The world of the very small (quantum) is very very different than the one you experience every day. And yet they are going on at the same time in the same space. But they really don't seem behave in the same way at all to us.

 

[Fenixgoon]

schroedinger's cat is used to describe the superposition of quantum states - ie, you can have multiple states exist simultaneously. once the observer disturbs that, you collapse the quantum state into the observation.

while the cat is in the box, you have no idea if it's dead or alive. quantum mechanically, it can be both dead *and* alive at the same time. the second you open the box, you reduce the quantum state (dead, alive, dead + alive) to a classical state (dead/alive).

as far as the uncertainty principle goes (heisenberg, btw), it basically means that you can never know the exact position and velocity (energy) of an object at the same time. if you know *exactly* where something is, you will have no clue about how fast it is moving, and vice versa.

this poses a problem for tiny objects like electrons, since their mass is so small. for big objects like a car, the uncertainty is nearly 0 (p*x ~ h). planck's constant is extremely small (10^-34) so only objects with very small momenta (electrons and such), will have appreciable uncertainties in their position.

the minimum uncertainty on a car's (2000 kg) position when it's moving 60mph (~25 m/s) is on the order of 10^-38 meters, or basically 0. so much for getting out of that speeding ticket

 

[Crono]

Given cat genetics maybe this is what happened to the cat.

Ahh yes, it's actually well known in theoretical physics circles as Crono's Cat Conjecture

 

[DrPizza]

Watch this video:
http://www.youtube.com/watch?v=DfPeprQ7oGc

When he starts talking about "exists in a superposition of states" and "collapses the wave function" - that's pretty much it. At the quantum level, the act of observing disturbs the observed. Until something is "observed" at the quantum level, it exists in a superposition of states.

One of my favorite 5 minutes of video on youtube.

edit: later on, Schroedinger regretted the cat thought experiment.

 

[disappoint]

Watch this video:
http://www.youtube.com/watch?v=DfPeprQ7oGc

When he starts talking about "exists in a superposition of states" and "collapses the wave function" - that's pretty much it. At the quantum level, the act of observing disturbs the observed. Until something is "observed" at the quantum level, it exists in a superposition of states.

One of my favorite 5 minutes of video on youtube.

edit: later on, Schroedinger regretted the cat thought experiment.

Teribad explanation though isn't it? They make it seem like the observer is observing with a human eye. Then they go on to tell you it's as if the electron knows it's being observed. Obviously this isn't the case. I think they do this just to 'sensationalize' the topic so it gets kids interested to learn further.

Unfortunately without further explanation they are led to incorrectly believe that the electron is embarassed that you saw it naked and started to behave like a particle instead of like a wave. As if the electron is a sentient being with a penchant for modesty who wants its privacy or something similarly ridiculous.

Teribad. Do not want half assed explanation. I are disappoint. Does not compute. Syntax error. General failure reading drive C. Abort, retry, ignore or ask General Failure to hand in his resignation?

I want an explanation of the device used to observe the electron and how it physically causes the wave function to collapse.



Even worse yet: http://www.youtube.com/watch?v=Jh8uZUzuRhk&feature=related
Downright misinformation trying to suggest that macroscopic objects are entangled to get you interested. If you can't hold someone's interest without lying to them then don't bother please. Teach real science or don't teach it at all. That is my stance, like it or not.

 

[Narmer]

It's not Schrodinger's uncertainty principle, it's Heisenberg's. Schrodinger came up with the cat thought experiment.

This is why I hate some analogies. Especially when what they are positing they are analogous to, aren't. The world of the very small (quantum) is very very different than the one you experience every day. And yet they are going on at the same time in the same space. But they really don't seem behave in the same way at all to us.

But isn't that part of the problem? At the atomic level, we cannot measure things so it isn't a certainty whether or not they are truly different. The problem is we simply do not know how to measure them without affecting the outcome.

The uncertainty is not a part of the atomic world, it is us, the observer.

 

[nerp]

Bad metaphor. Use a different one.

 

[novasatori]

the way i was taught heisenberg's uncertainty principle was like a pitcher throws a ball (electron), and the way you're measuring is a bat

when you hit the ball to measure its location its not on the path it was anymore

 

[Gigantopithecus]

Schroedinger's cat never made much sense to me, either. This, however, does: "it is impossible to determine simultaneously both the position and velocity of an electron or any other particle with any great degree of accuracy."

I understand this by thinking about a car. If I tell you only that a car is at an intersection, you know exactly where it is. But you don't know how fast it's going, which direction it's going, or if it's stopped. If I tell you only that a car is traveling east on a road at 30mph, you know what exactly its velocity is, but you do not know where it is any more specifically than somewhere along that road. Someone who's an expert on this topic might argue my metaphor is wrong, though...

Like Narmer said, the uncertainty is on the part of the observer, not reality.

Edit:

the way i was taught heisenberg's uncertainty principle was like a pitcher throws a ball (electron), and the way you're measuring is a bat

when you hit the ball to measure its location its not on the path it was anymore

I like that, better comparison than mine, haha.

 

[Kanalua]

For the observer, as long as the box is closed the cat is both dead and alive (because you can't observers can't observe the state of the cat while the box is closed).

Is someone watching too much Through the Wormhole?

 

[Cerpin Taxt]

OP, do you understand what a probability distribution is?

Position and velocity of an elementary particle are described as two interrelated probability distributions. The probability of a particle being in a certain position increases as the probability of it traveling at a certain velocity decreases, and vice versa. We can calculate these probabilities and their relationship to very high degrees of precision and accuracy, but the position and velocity of elementary particles remain probabilistic. This is the natural state of the particle

The probabilistic nature of the particles lead to some really strange effects, like Quantum Tunneling.

 

[Sea Moose]

Fuck you for hurting a cat.

I will find you and beat you.


/ethug

 

[Born2bwire]

The Heisenberg uncertainty principle gives a mathematical relationship between the variance of two observations over a statistical set. What we find is that for certain pairs of observables (measurable properties) we find that if we keep measuring identical systems again and again that we end up with a spread in the measured results.

The Heisenberg uncertainty principle makes no ascertations about the precision of a measurement. It is a consequence that describes the relationship between the statistical measurement of what are called incompatible observables. It does not mean that the measurements are inaccurate or incorrect. It just means that between certain observables, we will not get the same measurements over and over again over a statistical set.

Think of a machine that measures some quantum state. The machine projects the measurement in the form of marbles. Each measurement makes a sack of marbles that varies in color, number, and size. We will consider color and size to be compatible (or commutable) observables. That is, every marble that is 0.5 inches in diameter is always green and vice-versa. However, color (and by extension size) is incompatible (noncommutable) with number. That is, if we measure the state and have the machine make our sack of marbles, we might get 5 green marbles, or 3 green marbles, or 3 red marbles and so on.

So make 10,000 measurements on identical systems (say we make 10,000 jars, each jar starts out being the same and we then proceed to measure each jar) and we get 10,000 sacks of marbles of varying colors and numbers. If we were to separate out the sacks by groups of numbers, we would find that for sacks of 5 marbles we have 10% red, 50% green, and 40% blue. For sacks of 6 marbles we have 20% red, 30% green, and 50% blue. And so on. Thus, we measure the number of marbles EXACTLY, but because a sack of five marbles can be red, green or blue then we get a spread of colors in our set of measurement. This spread will be described by the wavefunction in terms of color for the given eigenvalue of N marbles. This is the same as when we get an eigenfunction of position for a given eigenvalue of E energy. If the system has energy E_0, then the eigenfunction describes the positional distribution of the measurements of the system in this state (assuming time-independence). So if we measure the position of a particle in a system of state E_0, there are many many positions that it could be in and thus we get a statistical spread of position measurements.

Likewise, if we arrange the sacks by color we may find that green came in sacks of 5 10% of the time, 6 40% of the time and so on. This is another eigenfunction that gives the distribution of number for an eigenvalue of color. In this manner, we see that the eigenfunctions that describe the system in terms of color are different than the eigenfunctions that describe the system in terms of number.

Heisenberg's uncertainty principle then gives us the relationship between the variance of color and number in all our measurements. If we go back to our sacks and map out the number and color of the marbles in the sacks, we will find that we have a mean color and number (if we can allow for a mean color, we could allow the color to gradually transist over the visual spectrum as opposed to being three discrete colors). However, there will be a spread in the measurements in numbers and colors. The minimum spread is related by the uncertainty principle.

The problems of measurement and precision do not come into the argument yet, this is purely a consequence of the mathematics of quantum mechanics.




As for the Schroedinger's cat, that is something different. It's often a much abused example. It is a description of how quantum systems can be in a superposition of states but will collapse into a single state when measured. There is a difference between saying that the system was always in state A out of a set of states and when we finally measured the system we found it in A and saying that the system was in a superposition of a set of states and when we measured the system we found it in A. The results between these two statements can differ and is the subject of a lot of research centering around such experiments and ideas like the EPR paradox and Bell's inequality. But the problem with the way that many people use Schroedinger's cat is that Schroedinger thought it up as a way to show the unintuitive behavior of quantum systems in comparison to our macroscopic world. He did not actually believe or wanted to imply that the cat is actually in a superposition. It was an example of how difficult it is to connect the quantum and macroscopic world and the absurdity that can arise. Those that hear about today and become confused by it only help demonstrate the efficacy of his example though it seems to be too effective.

It remains useful because it is a good thought experiment when applying an interpretation of quantum mechanics. It challenges one to use an interpretation to make sense of the problem without resorting to such absurdities as having the cat being in a superposition. I place such discussions on the backburner as something warranting only personal amusement. The various interpretations of quantum physics do not have many consequences. Obviously, all valid interpretations predict the same experimental behavior and as such when working a problem using the Copenhagen or Bohm interpretation becomes one of personal preference. It is mostly useful in finding easier ways work certain problems.

 

[Hayabusa Rider]

It just may be that you can design the experiment so that if you open the box and don't like the results you can change the past and get what you want, at least in principle. Don't quote me on that just yet.