Lubos Motl writes that “dead and alive cats have different gravitational fields.” I wasn’t sure if this was a joke. Is it?
Update:
A little bit of research shows that the gravitational field differential between dead and alive cats originated with Lubos Motl in his 2005 post called John Baez and quantum gravity:
One can’t imagine that gravity is classical; my simpler argument for the same statement is that the fate of the Schrodinger cat is decided probabilistically (via the radioactive atom), and because a dead cat creates a different gravitational field than an alive cat (imagine a planetary-size cat if you have problems to imagine a cat’s gravitational field), the gravitational field can’t evolve “classically” either: everything must be probabilistic if something is probabilistic.
About a year later Philip Dorrell includeded the quip in his blog post intending “to write the shortest possible explanation of what is really going on with Schroedinger’s Cat.”
But maybe other types of information propagation are sufficient. No doubt there are significant electromagnetic effects – probably the cat has a slight electric charge on it’s fur. (Changes in static electric field would travel at close to the speed of light.) Maybe the difference in gravitational field between a live and a dead cat is enough to correlate your wave function and the cat’s wave function. (And we know that gravitational waves travel at the speed of light.)
In 2007 Q_Goest repeats a variation of the story in a physics forums post on QM and gravity:
But instead, let’s put the box on a set of weight scales that will tell where the center of gravity of the entire box is and thus the location of the cat. If the cat is walking around the box, we know it’s alive and thus gravity must prevent this cat from being in this state of dead/alive. If on the other hand, if the cat drops dead we might detect the cat falling to the floor by using these weight sensors which might registar a momentary decrease in weight as the cat’s legs buckle, then increase in weight as the cat hits the floor. Gravity alone is all that’s required to distinguish a live/dead cat.
But the question if Lubos Motl intended this as a joke is not resolved. Leucipo commenting on the original post wasn’t sure:
Lubos, you should refine a bit your SchrCat argument: charge, mass and energy and preserved under collapse, so gravity does not feel it.
(Or was it suppossed to be a joke?)
7 Comments
What I wrote was meant completely seriously and it is very important. But I meant the whole profile (or shape) of the gravitational field, not just some monopole (point mass) approximation at infinity.
Dead and alive cats have different profiles of the stress-energy tensor T_mn(x) as functions of space, and because the latter enters the right-hand side of Einstein’s equations, the left-hand side, the curvature, must have different profiles for these two states, too. Both sides have “hats”. In practice, cats’ gravitational fields are too weak to measure them – especially their dipoles – but they surely differ in principle. If explosives are inserted into a would-be supernova and launched by an observation of a dead cat, this effect can be magnified and made observable in practice.
This comment is primarily meant to disprove the naive viewpoint that “classical gravity” can be interacting with “quantum matter”. It can’t. Einstein’s equations must be operator equations. And because the stress-energy tensor (Hamiltonian density etc.) is an operator in any quantum theory, the metric and its curvature must be operators (as opposed to classical numbers), too, for Einstein’s equations to hold.
One can also show the inconsistency of all conceivable alternative pictures. For example, if someone thought that Einstein’s equations only become “classical Ricci tensor equals the expectation value of the stress-energy”, such an equation would violate the linearity of quantum mechanics because the expectation value of the stress-energy tensor depends nonlinearly on the state. However, the metric influences – through geodesics – the motion of matter, so if the metric depended on the state vector nonlinearly, the evolution for the wave function of matter itself would be nonlinear, too.
That would inevitably cripple either unitarity or locality: the “unrealized” portion of the wave function would still influence the outcomes of measurements. The whole world must be quantum and all observables must correspond to operators and only probabilities of different outcomes (eigenvalues) may be predicted. This is a completely universal fact.
Hi Lubos,
# What I wrote was meant completely seriously and
# it is very important.
Many thanks for your comment and explanation. This answers my question.
# But I meant the whole profile (or shape) of the gravitational field,
# not just some monopole (point mass) approximation at infinity.
# Dead and alive cats have different profiles of the stress-energy tensor
# T_mn(x) as functions of space, and because [space] enters the
# right-hand side of Einstein’s equations, the left-hand side, the curvature,
# must have different profiles for these two states, too.
So dead and live cats curve space differently? My understanding of the topic is Wikipedia level, so, if you could talk at that level, that would be great. If these are the components of the stress energy tensor
T00 = energy density
T10 T20 T30 = momentum density
T01 T02 T03 = energy flux
T11 T22 T33 = pressure
T12 T13 T21 T23 T31 T32 = shear stress
1. what are the sample values of these components for a cat?
2. which terms differentiate between live and dead cats?
3. Are these components properties of the cat?
# In practice, cats’ gravitational fields are too weak
# to measure them – especially their dipoles – but they
# surely differ in principle.
I can imagine a live galaxy and a dead galaxy in a box. Do they have gravitational fields strong enough to measure? But I seem to have a problem with what is meant by a dead cat. Can you clarify that a bit? What is understood by a dead cat in this context? Clinical, criminal, theological or medical death? If medical death is meant, it seems that classical (Newtonian) mechanics should be able to differentiate energies of dead and live cats, for instance, by heat radiation differential or lack of oscillations on the dead cat.
# If explosives are inserted into a would-be
# supernova and launched by an observation of a dead
# cat, this effect can be magnified and made observable in practice.
I don’t understand this example (what is meant by “launched by an observation of a dead cat?)
# This comment is primarily meant to disprove the naive viewpoint
# that “classical gravity” can be interacting with “quantum matter”.
#It can’t. Einstein’s equations must be operator equations.
# And because the stress-energy tensor (Hamiltonian density etc.)
# is an operator in any quantum theory, the metric and its curvature
# must be operators (as opposed to classical numbers), too,
# for Einstein’s equations to hold.
I assume you refer to “linear map” explained here But what is not clear to me is that “classical gravity” does not interact with quantum mechanics because quantum mechanics is operational and Einstein’s equations are not? And what is the relation to cats?
# The whole world must be quantum and all
# observables must correspond to operators
# and only probabilities of different outcomes
# (eigenvalues) may be predicted. This is a
# completely universal fact.
Maybe I am misunderstanding this but does this mean that a mixing of the quantum (radiation) and non-quantum (cats) is not legitimate as is done in Schro-cats parable?
Thanks again for your comment.
Lubos,
your comments about the operator nature of quantum gravity are well understood. However i do not understand why you choose to refer to cats.
“the “unrealized” portion of the wave function would still influence the outcomes of measurements”
With this comment, i sense an effort of making a connection with the paradox of Schroedinger’s cat. So are you trying to evoke this paradox for the case of quantum gravity?
And as far as the scientific part is concerned.
You wrote “everything must be probabilistic if something is probabilistic”. We all know that at the classical limit, physical theories are (classically) deterministic – do not involve probabilities – in contrast to the statistically deterministic nature of quantum theories. What does your comment refer to? Do you think that classical theories should be abandonned alltogether?
———————————————————
As far as Philip Dorrell’s interpretation of Schroedingers cat paradox, i have to say that is just a recreation of the (unorthodox) Copenhagen interpretation that was based on a misunderstanding of the nature of mathematical probabilities.
A cat is not a quantum object. Even if it was, its wave function would not be a superposition of states but an eigenstate of either dead or alive, in the same way that a single electron cannot pass through both holes in a double slit experiment.
Dear zeynel,
I think that the point you are overlooking is that space around us has more than 0 dimensions. Cats are not described just by their overall mass (or “overall pressure” which is a meaningless concept for mass points, anyway) but by the complete shape and the distribution of the mass density and momentum density in space, as functions of coordinates x,y,z. Dead and alive cats have different “shapes”.
All the “types” of death of a cat you enumerate are pretty much equivalent. When a cat dies chemically, she usually dies visually, too, stops breathing, and physicians say that she died clinically, too.
That distinction of “types of deaths” is completely irrelevant for the argument.
What matter is that if a cat dies – because of poison or the hammer, as in the normal Schrödinger cat setup – the head drops down, getting closer to the floor. A cat lying dead on the floor has e.g. a higher quadrupole moment than the alive cat, because it is flatter while the alive one is more spherical, so this can be measured not only in the vicinity of the box but even at infinity.
If your problem is something else than sorry, I simply don’t understand what you can possibly misunderstand about this obvious point that the fields around different objects are different. I also fail to understand what you can possibly misunderstand about a setup where a supernova is attached to a detector of dead cats, in order to amplify the effect, so I can’t say anything more specific about it.
I wrote it very carefully so that it had to be nearly 100% clear and nearly 100% correct and because of this simple reason, the only thing I could do would be to repeat myself. The only point why supernova was inserted on top of the cat was to show that the effect can be very real and observable even in practice – supernovae that have exploded have demonstrably different fields from supernovae that haven’t.
Spyros, yes, of course, I am talking about a cat because this is nothing else than the normal Schrödinger cat discussed in the context of interpretation of quantum mechanics. And my point is nothing else than to say the obvious point that nothing changes – and nothing can change – about the basic facts of quantum mechanics in the presence of gravity. Much like all other physical systems, gravitational fields are (and must be) generally found in complex linear superpositions of different states in the Hilbert space. Only when an observation is completed – when the states decohere from each other – one can say which of them was realized.
Schrödinger’s cat is a thought experiment and it is only described as a “paradox” by those who don’t understand how quantum mechanics works. It is not a paradox in any well-functioning interpretation of quantum mechanics. Each of them has a very clear and unambiguous description what is going on here and all observable aspects of these descriptions coincide for all the interpretations.
A question of yours: Yes, of course. Classical theories must be abandoned altogether whenever we want our description of natural phenomena to be consistent with at least one quantum effect. Classical theories are only approximations of the full, quantum theories, for the situations where all quantum phenomena are too weak to matter, and there doesn’t exist any consistent way to “mix” classical theories and quantum theories into one framework.
In other words, a cat, much like any physical system in this Universe, is a quantum object, of course. The only laws that describe it accurately are the laws of quantum mechanics. The only aspect in which cats differ from electrons is that their number of degrees of freedom is so high that decoherence proceeds almost immediately which allows us to use the classical intuition – and imagine that the probabilities predicted by the full (quantum) theory of the cat are classical probabilities. The fathers of quantum mechanics – and the Copenhagen interpretation – didn’t know the word “decoherence” but they knew the correct conclusion: the classical intuition is OK for cats. But they also knew the other part of the story: all the atoms and molecules in a cat follow the laws of quantum mechanics. They didn’t know why these two things were quite consistent but we know it today.
But the validity of the “classical intuition” for macroscopic objects (cats…) doesn’t change anything about the fact that only probabilities can be computed; and only a quantum mechanical theory is the correct theory that actually knows what is happening “inside” the cat.
Best
Luboš
Lubos,
i agree with you that classical mechanics is a limiting case of the underlying quantum theory. However, from your comments, one might misunderstand the qualitative differences that exist between those two realms. For instance in the classical world, the notion of non-commutativity does not exist.
From this point of view i disagree on the comment that classical theories must be abandoned. For instance, we all know that you cannot do quantum mechanics even with atoms with a few electrons. And there is no possible way to solve a classical problem with quantum mechanics.
This is just a clarification. I totally agree with your comments on quantum decoherence.
And a last comment. You wrote “only probabilities can be computed”. In classical mechanics we don’t compute probabilities. Newtonian theory is mechanically deterministic. “only a quantum mechanical theory is the correct theory that actually knows what is happening “inside” ” I totally agree with this, however, i think that the nature and validity of the physical laws depends on the level of observation.
Luboš Motl wrote:
# A cat lying dead on the floor has e.g. a
# higher quadrupole moment than the alive cat . . .
Your sole criterion for death is that cat is lying on the floor. My cat is lying on the floor like 90 per cent of the time but she is not dead, she is sleeping:) If that’s your only criterion for death your model may superimpose sleep-death, sleep-awake, sleep-alive, death-alive, death-awake and thus will add new dimensions to the Schrodinger’s cat parable that I think needs to be added to the Wikipedia page. So maybe we need to modify the parable to distinguish between sleeping and awake cats and not dead and alive cats. Instead of a poison the vial may contain a sleeping pill.
According to Wikipedia Schrodinger intended this parable as a caveat emptor not to mix theories applicable in different scales, not to mix metaphors, so to speak. I didn’t know this. So for me there is no paradox. The cat is not a quantum observable.
## The only aspect in which cats differ from electrons is that their number of degrees of freedom is so high . . .
There is another fundamental difference. Cat is conscious. Electron is not. Unless you are saying that counscioussnes is the result of the additional degrees of freedom, which makes sense to me. But knowing physics I won’t be surprised to learn if there is a conscious-electron-causes-collapse interpretation of Quantum Mechanics.
## a cat, much like any physical system in this Universe,
## is a quantum object, of course.
When you say a “quantum object” you must of course specify which legal interpretation of quantum mechanics that quantum object is gauged to. A quantum object in Copenhagen interpretation is fundamentally different than a quantum object of many worlds interpretation or a quantum object on a practical laboratory bench. I don’t think that all these academic interpretations exist simultaneously in nature? As its name suggests quantum mechanics is not scale independent.
## The only laws that describe it accurately are the laws of quantum mechanics.
You have chosen scale A as your unit scale and you are asserting that the scale A is the true scale and therefore it is more fundamental than scale B. This cannot be true if we take experiment as the sole authority.
In other words, if we are able to measure scale A only with Instrument A, and Scale B only with Instrument B then they measure different scales. And this is the case because different scales are defined by instruments of different precisions. Instrument A tells nothing about scale B and Instrument B tells nothing about scale A. For instance can we know if optical or x-ray rendition of a star is the “true” rendition? We cannot.
Instrument A –> measures only scale A
Instrument B –> measures only scale B
Which one is the true scale? Which one is the true representation? We cannot know. There is no true representation if you uphold experiment as the supreme authority.
In general, physicists take the legal physics as the supreme authority, not experiment, as I suspect you are doing here. Correct me if I am wrong. In the legal interpretation of nature physicists will choose a legal physics interpretation and call it the absolute true interpretation.
But in terms of scientific rationalism we can never prove if macroscopic cat rules the microscopic cat or microscopic cat rules the macroscopic cat. As I said, except by authority.
A football team can be treated as an organism of its own that lives 90 minutes and then dies. Is it the team members who rule the organism or is it the organism that decides a game? The laws that govern a game are not the laws of quantum mechanics but the rules set by FIFA, of course. And the rules of the game apply on the scale of the game in general. Do you think quantum mechanics are that general and works across scales? I don’t think so. The world is operational and not legal. Contracts can superimpose and coexist. There is no reason why microscopic and macroscopic not work together. Including the FIFA rules.
Thanks for dropping by and for your comments.
1. “According to Wikipedia Schrodinger intended this parable as a caveat emptor not to mix theories applicable in different scales”
You are absolutely wright Zeynel. This Gedankenexperiment was treated as a paradox by physicists who didn’t understand this fact.
2. “Unless you are saying that counscioussnes is the result of the additional degrees of freedom, which makes sense to me. But knowing physics I won’t be surprised to learn if there is a conscious-electron-causes-collapse interpretation of Quantum Mechanics. ”
Consciousness is a property of the highest level of organization of matter only (that is organisms). It cannot be explained by physics. Physics only studies the fundamental level of organization of matter. Then again some physicists of the Copenhagen school tried to attribute free will and consciousness to electrons. This is however counterscientific reductionism.
3. “A quantum object in Copenhagen interpretation is fundamentally different than a quantum object of many worlds interpretation or a quantum object on a practical laboratory bench”
A quantum object is an object that can be described by quantum mechanics. This is independent of the interpretation you choose. Of course i strongly disagree with Lubos that a cat is a quantum object.
4. I didn’t understand your last comment. There is no microscopic cat. A cat is not the sum of the cat’s atoms. This is what Laplace thought and of course it is wrong.
The question was addressed to Lubos though, and these comments reflect solely my personal beliefs.