When it comes to the very nature of quantum mechanics -- about the inherent uncertainty and indeterminism to reality -- it's one of the most difficult things to accept. Perhaps, you imagine, there's some underlying cause, some hidden reality beneath what's visible that actually is deterministic.
After all, a cat can't simultaneously be dead and alive until someone looks... can it? That's one of the problems that both Einstein and Schrödinger wrestled with during their lives, and an investigation of that story, their work on that front, and their friendship that ensued as both pursued that same end, is what led Paul Halpern to write his book: Einstein's dice and Schrödinger's Cat.
I admire and praise both of them for their sincere and successful efforts to search out the basics and guidelines for themselves and also for generations of scientists to find out and explain the realities of our incomprehensible universe. We all owe them a lot.
When are these physicists going to get it that reality has both an inside and an outside. The laws of physics on the outside are different than those on the inside. On the inside we can look across space, but we can not look across time. We are always confined to the present or real-time. The outside is all time other than the present. In other words, it is the remainder of that dimension known as Time, that dimension which is just one dimension of the 4 dimensional structure known as Space-Time. If an event is governed from the outside, circumstances extending across a certain measure of time, and space, are all taken into account to determine what the event will be. Thus, for instance, if the 2 slit experiment is run for say 5 minutes, and it produces the interference pattern, from the outside it is being governed and it is seen from the outside as being a single 5 minute event, a 4D event. However, if you repeat the experiment but place photon detectors anywhere within the experiment setup, each detection is an event in itself, thus you have inserted real-time events into the experiment, thus you have broken it down into real-time events, thus it can no longer be governed from the outside as a single 4D event.
In other strange experiments, an effect seems to occur before the cause. However, such events are being governed from the outside. It is a 4D event and thus both the effect and the cause are both being seen simultaneously when viewed from the outside. Thus from the outside, there is nothing strange about this at all.
But these days, even Einstein's theory of Special Relativity seems to be misunderstood by most folk, thus they can not see beyond the 2 postulates that it is based upon, thus they can not see the absolute cause of Special Relativity.
I'd always considered the cat thought experiment a bit rubbish, both as a gotcha to show the interpretation was wrong and the use of it to show it correct (the point that "they only proved it right for "an electron taking place of a cat, which isn't the point, duh!" being irrelevant: they aren't showing it happens to an actual cat but that there "really is" a duality of nature at the quantum level).
The problem is this:
What's the quantum equation for a cat that's alive and how (and when) does it change to a cat that's dead?
Quantum mechanically, there's no property of "dead". Or even alive for that matter. Even at the relatively macro scale of cells, there's a hell of a lot of dead cat in every very alive one, and a lot of alive cat in the most dead of moggies. Quantum mechanically, the point would only work to show the ideas of the time about QM wrong if there were such a quantum state as "dead cat". It's just not a way to describe a cat's wavefunction. Even when it's dead, Jim.
What that means for the thought experiment is that the actual real cat REALLY IS both alive and dead and is a superposition of both types of cat. Dead skin cells, dead material being digested, dead material ready to evacuate, nonliving particles being exhausted and inhaled. And once the radioactive particle hits the detector, the *detector* is in a definite state otherwise there's no emission of poison. And then the cat is "dying" which is a superposition of dead and alive, isn't it?
The only take-out I ever got from the query posed by Schroedinger is that you have to be very careful reifying things in Quantum Mechanics that are really macro shorthands for an unspecified situation that has no actual demarcation of event.
Partly because Erwin made the same damn mistake when he proposed the idea to show how others were doing it wrong.
Which is a little ironic.
@Wow #3: I think your complaint that we can't write down "the wavefunction of a dead cat" is a bit misdirected. It smacks of the same fallacious argument from ignorance that some of the posters here we both know and, er, "love" use to rail against gravity, quantum physics, astronomy, etc.
The wavefunction of _anything_ more complicated than a simple molecule is too complex for us to know how to write down explicitly. In the case of a cat (or a cell, or a virus), you're going to be treating roughly 10^24 terms in a product wavefunction, plus multivariate correlations which treat collective behaviour.
However, I can certainly identify any number of microstates which could reliably distinguish the wavefunctions of a living vs. a dead cat, even if I can't write down the whole thing. For example, the resting potentials (voltages) across neuron cell membranes; various ion chemcial potentials across cells of all kinds; densities of various intracellular enzymes and other proteins (which can be represented as number counts of creation operators, if you prefer that formalism); and so on.
You're right in your implication that the product wavefunction of the "individual atoms" or even "individual molecules" are pretty close to identical between living vs. dead, but the overall wavefunction must include additional terms which identify the interactions and correlations between those pieces.
One of the active areas of research in the foundations of QM (of which I am certain you're aware) is identifying the boundary (both its existence and its fuzzyness!) between quantum and classical behaviour. How large an object can show interference in a double-slit experiment? How large an object can be put into a quantum superposition? How many atoms of a gas do you need before irreversible (i.e., classical) thermodynamics kicks in?
The wavefunction of _anything_ more complicated than a simple molecule is too complex for us to know how to write down explicitly.
That's absolutely NOT what I'm talking about.
I'm talking about what is the difference between alive and dead quantum mechanically speaking.
The point being that "alive" or "dead" aren't terms that are defined AT ALL in quantum mechanics. There's no modifier to ANY quantum state that means "It's dead".
But it isn't a concept that even notionally applies to the quantum state of *anything*. It's a system level description of a fuzzy and ill defined region of biology.
Talking about "Is the cat both alive and dead" in nonsensical because you have to define what those terms mean to a wavefunction description.
Not solve it.
We can describe the quantum numbers of, for example, an electron.
We can *describe* the for a heavy atom, despite the fact we can't in fact WRITE the equations.
But what would you describe a "dead atom" as opposed to an "alive atom"?
However, I can certainly identify any number of microstates which could reliably distinguish the wavefunctions of a living vs. a dead cat,
No you can't.
Those microstates are evident on either side of your demarcation in both living and dead cats.
Many cells in the pork sausage you ate last week were still "alive" when you cooked it.
The *pig* may have been dead, but then again you died ten years ago since almost all your cells that comprised you then do no longer. Tooth enamel and much of the calcium deposits in your bones are pretty much the only cells you still have from then.
@ Michael & Wow
I find the cat scenario both wrong and right, meaning it can be used to explain qm and statistics, but is very wrong in implying what reality is and has been used by most prominent physicist to IMHO throw a very twisted picture of what QM math is.
1. You can setup an equation with simple states yes/no for participants (cat, decaying element, gun etc..) and setup the equation of state.. and since the equation is statistical in nature.. it will give a statistical answer.. since you don't know when the element will decay, the odds of mechanism going yes/no and thus cat being yes/no.. will be in most simple case 50-50... It gets much more complicated the more interactions and possibilities there are.. but the basics are those. And there is nothing bizzare with that. The bizzare part is that statistical mechanics work and not any other form of math. But the result is not bizzare.
2. The problem is that this is used to say that REALITY is dual and that REALITY is that cat is alive and dead at the same time and that we all live in supperposition of all states.. and then everet universe and qm mutliverse...bla bla.. (i have nothing against inflationary multiverse.. it's the QM one I don't believe in). to me that's twisting and maybe trying to put QM math where it was never intended to go. If for nothing else, then because the colapse of the wavefunction happens every instant. Reality of anything bigger than isolated particles is already colapsed because of those same QM rules, and we know that from that same QM math.
@Sinisa #7: I think you've hit the nail on the head here.
Schrodinger introduced his cat as an _analogy_, along the lines of "what would quantum mechanics look like if we magnified it to the real world?" This is rather similar to discussions of "what would things look like if c = 100 km/hr?"
However, I think your second point is misplaced, or at least is begging the question (in the proper, technical sense). Taken at face value, QM predicts exactly what you describe: as you add elements to a system, the wavefunction gets more and more complex, but those added elements will become part of the superposition.
What we seem to have discovered, or at least the consensus interpretation, is that the "weird superpositions" disappear (or are projected out) via uncontrollable and unmeasurable interactions with the environment. Yes, _if_ you could track and measure all the molecules of air around you, etc., etc., then you'd end up with a macroscopic superposition state. But you can't do that, and so the density matrix ends up in a block diagonal form because the off-diagonal correlations get averaged away.
We don't use the term "collapse" any more. The modern description is that the wavefunction can be written as a sum of basis vectors (like x, y, z coordinates), and decoherence projects out one of those bases.
Schrodinger introduced his cat as an _analogy_, along the lines of “what would quantum mechanics look like if we magnified it to the real world?”
No he didn't. He produced it to show that the idea that the quantum explanation of both states existing until observation was not a good one since it didn't apply to macro concepts like a cat.
It was to indicate that the current meme was incorrect.
Which is why it changed eventually to the idea of decoherence.
It wasn't an analogy, it was an illustration along the lines of "spherical cow": cows aren't spherical and cats are either alive or dead, not both.
SL your point #2 is true. It's one reason why "proving the cat really IS both alive and dead" wasn't being done when showing that quantum particles were both states at the same time is correct.
Even though "from a certain point of view" (/voice=Alec Guiness) it "really" is like that.
It's a definitional problem, much like "What happened before time began?" or "What's North of the North Pole?". The word being asked is poorly defined in the realm the question is being asked for.
And alive or dead isn't relevantly defined in quantum terms.
Michael, a layperson question, re.: "We don’t use the term “collapse” any more. The modern description is that the wave function can be written as a sum of basis vectors (like x, y, z coordinates), and decoherence projects out one of those bases."
What's the current language for "collapse of the wave function"? (Or is the language you used the current version and I just haven't seen it until now?)
When I think of wave function collapse, the mental image I have for that is:
First, there is a statistically-described area of spacetime that vaguely resembles a Gaussian distribution, that describes the area in which a wave exists and can be measured as a particle. In theory the metaphorical "tails of the normal distribution" of this area of spacetime spread out to encompass the known universe but for practical purposes the area is much less.
Next, a measurement is made that determines the specific location of the particle in spacetime. At that point the math that describes the possible "spread" of a wave, converts to or produces an outcome that describes the location of a particle, and we can say that we have located a particle in a specific place.
Firstly, is that mental model any good, or is it rubbish, or is it obsolete?
Second, if rubbish or obsolete, what's the replacement for it?, and what language is used to describe it?
Third, I've heard the phrase "state-vector collapse" used as the equivalent of "wave function collapse." Are those phrases even remotely equivalent? The only difference I can think of is that "state-vector collapse" implies that there is a signed quantity (a positive or negative value, presumably positive) that provides a complete description of the wave before it is measured and localized as a particle. Is that approximately right, or where's the mistake?
Other: I'm a little concerned or skeptical as the case may be, about some of the language Halpern uses to describe the relationship break between Einstein and Schroedinger: to my ears it sounds dramatized and emotionalized in the manner of much current writing. Was there any evidence of angry correspondence between them, or did they simply say, in effect, "we disagree and we're going our separate ways"? Understandably, anyone would have considerable sadness over the loss of a close friendship, but to my mind that's not the same thing as an angry blow-up.
Most importantly the history should be told with accuracy, whether it was more dramatic and emotional or less so. But, subject to the necessity of historic accuracy, what good comes of turning the sad ending of one aspect of two brilliant lives, into a kind of defining chapter for both?
Lastly, anyone care to speculate what might have happened had they stuck together? And, is there any current consensus in physics about the question of fundamental determinism vs. indeterminacy?
@ Michael & Wow
I really think that there is still an effort to make QM (not in terms of math) more complicated and strange, then it is. And it's done by physicists who should really be doing the opposite. Whenever anyone speaks to large audiances and qm is the topic, the words generally used will be: it's strange, it's un-intuitive, you can't really understand it (susskind's favourite), there IS really 2 of you (brian greene etc..), in that universe you REALLY did make that other choice... etc etc..
When you buy a lotto ticket.. MATHEMATICALLY, if expressed through STATISTICS.. you can say you are in a superpossition of winning or loosing, until numbers are drawn. But you don't see many statisticians or stock market people saying to their bosses "look at it this way.. the reality is that your company is in a suppersposition of states, and don't feel bad if you go bankrupt tomorrow, it's just a decoherence and in some way there might be a reality where you became a millioner." .. A joke, right.. Because they know what reality is. Yet this type of jargon is common please in QM, and I feel it's incorrect. IMO it's caused by physicists being thought for years to expect fixed solid numbers in certain areas, and when they were presented with percentages and some obscure math never before used in particle physics, they went a bit bonkers. Quantum world obeys laws of statistics and mathematically it's calculated a certain way using vectors etc.. So what? Live with it I say to it. Just because there is probability and randomness doesn't mean that reality is any different then it was. The reality in the case of the cat is that it is alive unless an element decays, regardless if you ever look in the box or not. And using semantics just to add "glitter" is wrong.
What I'm trying to say is that people should stop painting fantasy pictures of what QM would be on macroscopic scales, because IT ISN'T. That tool isn't built for macroscopic scales and it confuses the lay population even more. In best case scenario you get simple statistical odds.. in worst you get nonsense.
I agree with Michael, that there are question which need answering... I just feel it's due time to stop mistifying statistics when we all know why and how you don't see people going through walls even though naively speaking QM math says that in some percentage they should.
What’s the current language for “collapse of the wave function”?
The wave function, like any function, is similar to
Which has no result until a value of x is entered. For a wavefunction, selecting the "x" collapses the wavefunction into an actual value.
So the next time you hear "collapse the wavefunction", replace with "solved for x".
@Sinisa, G, Wow, et al. This is an awesome discussion, of a very hard problem. The problem is hard because quantum mechanics really is non-intuitive: it's mathematically tractable (moreso than general relativity!), and make very firm, experimentally testable predictions, but it is hard to guess those predictions based on human experience.
There is no 100% consensus on how to interpret the mathematics of QM (see the table https://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics#Comp…, for example). Decoherence is the most mainstream version, and is the modern replacement for "collapse." G asked about terminology, and I would say that's it: where you read "collapse", replace it with "decoherence."
The best demonstrations of this are the experiments involving macroscopic superposition states: things like extremely large organic molecules (tens of kilodaltons), micron-sized vibrating cantilevers, and the like. So long as these systems are isolated from the environment (vacuum, cryogenic temperatures, etc.) they can be prepared in, and will persist in, non-classical quantum states for fairly long periods of time. Without that isolation, they behave classically and intuitively.
To Sinisa, you need to be careful when comparing quantum statistics to classical probability. The wavefunction is complex valued, and it is the _square_ of the wavefunction (or the square of the state matrix) which tells you the probability distribution. In particular, calculating quantum statistics for correlated systems will produce results which are _NOT_ equivalent to the classical joint probability for the two separate systems. It's this inequivalence which is at the heart of Bell's theorem and related quantum statistics results.
The way I see it, Schrodinger's cat proves one thing in all of physics. It proves that we can never know the true laws that the universe obeys because certain things just wont happen at the same time. But if you look closely at Newton's 1st law of motion it implied that the more force you have so is the acceleration and this goes with regards to the amount of force, Einstein showed that there is basically a speed that can't be exceeded. Whereas Newtons law would imply constant acceleration. This is then seen with rain drops that continuously accelerate way beyond their terminal velocity. As far as i am concerned the only things that have some form of scientific explanation are those that already have a law explaining them and beyond that there is still a vacuum of what is not recognised by science
One issue I see of interest is that while we experience time as a sequence of events, with the point of the present seeming to move from past to future, which physics codifies as measures of duration, the underlaying reality is the creation and dissolution of these events in the context of what physically exists, the present, then the future becomes past. Tomorrow becomes yesterday, rather than moving along a vector from yesterday to tomorrow.
This way, instead of going from a determined past into a probabilistic future, it is the causal events of the present which determine the course of events that recede into the past. So that probability precedes actuality and causality yields determination, not a determined past setting the course of events. The present creates the past, not the other way around.
Duration is simply the state of the present, as these events form and dissolve.
This makes time an effect of action, not its basis and what we measure is frequency. Which makes time similar to temperature, since what we measure with temperature is cumulative amplitude.
Different clocks run at different speeds because they are separate actions. A faster clock uses energy quicker and so recedes into the past faster.
Like temperature, the overall effect of change is cumulative, but to measure time, we have to isolate a particular action, whether rotation of the planet, or oscillation of a chasm atom.
Suffice to say, this point is beyond the pale in physics conversations, so I don't get much feedback on it.
One issue I see of interest is that while we experience time as a sequence of events,
We don't. We experience an extended present, where we note the events and only approximately their timings. We THINK we feel the pinprick at the same time we see the pin go in, but the delay is around 1/5th of a second.
Secondly, your comment was off topic. Please don't pollute threads just because you want to get your latest woomancer rubbish out there in front of people, thinking you're being smart when you're actually being incredibly dumb.
This is not the case in any way, shape or form:
faster clock uses energy quicker and so recedes into the past faster.
For one, clocks do not use more energy, except mechanical ones, and only because the mechanism does so, not because measuring time does. Second, using energy doesn't push you into the past quicker.
It just doesn't. We've looked. We would have noticed.
Suffice to say, this point is beyond the pale in physics conversations, so I don’t get much feedback on it.
It goes beyond the point of nonsense, which is why you don't get much feedback on it. And this is feedback, yet you will pout and whine about it and say that I'm being mean and closed to the possible truth because I'm religious about science or some bullshit like that.
Which is another reason why you don't get much feedback: the only feedback you'll accept without hating it and the one giving it is adulatory acceptance.
blockquote, not being a dictionary word is misspelt whether you spell it correctly or not, therefore it is a pain in the arse using it to set quotes up.
Using quote would work better, it's a real word that can be misspelt, but I don't know if that works yet. It didn't used to.
"quote" doesn't work.
I agree it's just the present, though I would describe it as dynamic, not extended.
I'm trying to think of a clock that isn't composed of energy. Actually I'm trying to think of anything that isn't manifested by energy at some level. Doesn't E=mc2 make energy the medium of pretty much all form/structure/mass?
With the twins example, the one in the faster frame ages quicker. That likely means she would die quicker and thus recede into the past faster. In this world, animals with faster metabolism age faster.
I have thick skin for reasons beyond internet debates, so no worry.
A clock isn't time, John.
The thought-experiment of a clock ticking by reflecting photons isn't energy, though the constituents of them are, the clock is the periodicity of the events separated by the interval of time measured.
And it doesn't use up the photons.
With the twins example, the one in the faster frame ages quicker.
Either tautological or nonsense. If you mean the one in the faster frame is the one who ages quicker than the other, it's a tautological statement. If you mean the one in the faster moving frame, then it's nonsense. The one that accelerated, that had a force applied to move it to a different inertial frame, aged SLOWER. Not faster. The twin left alone didn't age faster.
Animals age faster because their metabolic process happens faster, not because time moves faster. Metabolites damage genetic material. Oxygen is toxic and corrosive, which is why it's used in metabolic processes, but that also means it damages the organism using it.
Time doesn't flow faster for them.
You're taking totally unconnected factoids, misunderstanding them, then tying them together in a web of unreasoned conjecture to produce an explanation that you accept because you thought of it, not because it makes sense.
Clocks don't go back in time faster, animals don't age quicker because time moves faster, E=mc2 doesn't mean that clocks are energy are time.
One problem may be that you need a thinner skin. Obstinacy is no better than histrionics.
Obviously a faster clock can progress much more rapidly. Witness the evolution rate of various societies. Yet it requires much more energy to do so and ultimately energy is a finite resource.
When we measure time, we measure frequency. Oscillations/rotations/whatever. That would seem an effect of energy.
Yes, there isn't much friction in a system composed of photons, so it wouldn't degenerate.
Thanks for the response, but have to work this morning, will return latter.
Obviously a faster clock can progress much more rapidly.
Tautological but irrelevant. A clock that is inaccurate would go faster or slower but that doesn't make TIME go faster or slower.
Witness the evolution rate of various societies.
Since clocks weren't invented for most of recorded history, the progress of society cannot be linked to the rate at which clocks mark off time. And if I wind my watch on, society doesn't progress faster than if the battery ran out and it's not working.
Yet it requires much more energy to do so
No it doesn't.
When we measure time, we measure frequency
No we don't we measure an interval. Time between sunrise and sunset. Time the candle burns between two marks. The time it takes the second hand to move on another tick. The time between peaks of a quartz crustal under an electric field. The time before an atom de-excites.
Oscillations/rotations/whatever. That would seem an effect of energy.
No, it doesn't.
Thanks for the response, but have to work this morning
And it's a sunday.
But if you DO return, your offtopic waffle should go here where it won't clog up this thread with redundant offtopic rubbish:
Or wait until a relevant thread turns up and post there.