quantum mechanics vs general relativity

michael879

first, Id just like to say that Im a 4th year physics major, so Ive taken QM and GR and have a pretty good understanding of them. However, Id like to keep this question as well as any answers in "layman" terms, because that is where my understanding is lacking. While I understand the "math" part of the theories, my question is really more about what they actually say is going on. Ill give my layman interpretation of both theories and then ask my main question.

Quantum
I prefer the many worlds interpretation for this, so Ill stick to that. Lets say you have a particle whose position has just been measured. Its position space wave function will be a delta at the point it was measured, and its velocity will be completely unknown. There will be an infinite number of "universes" and in each one the particle will have a different velocity. In the "parent" universe this particle will appear to be in a superposition of velocities, while in any of the "child" universes, the particle will have a specific velocity and will travel in a straight line. As time evolves, each "version" of the particle will continue to travel in a straight line, while the position space wave function in the parent universe will appear to spread out.

Lets say a second measurement is made of the particle's velocity. The act of measuring entangles you with the particle. That is, your state is dependent on the measured state so that you now form a multi particle wave function with the particle. That will cause "you" to enter a random child universe, seemingly measuring a random velocity. I put you in quotes because what really happens is you split into an infinite number of "clones", each one measuring a different velocity. The randomness is just an illusion as each clone thinks they are the real you, when there is no "real" you.

I realized after writing this that it would have been a lot clearer if I had used spin states and non-macroscopic observers (i.e. a second particle). Hopefully you will understand what Im trying to say though.

General Relativity
This one is much shorter. Basically what GR says is that gravity is not a force in the typical sense (i.e. the quantum forces). It is just the curvature of spacetime due to mass being present at a distant location. This curvature causes the geodesics that normally appear to be straight lines to appear "distorted". Any object following these geodesics will appear to accelerate towards the massive object.

Question
First of all, Im wondering how accurate my interpretation of QM is. I have never actually seen the many worlds interpretation phrased like that (with "entanglement" causing the actual split), so Im not sure how good of a description it is. I do prefer my interpretation over any of the other ones Ive seen though, as it actually makes QM believable for me (I have trouble accepting that something can be truly random).

Second, Im trying to phrase the "problem" between the two theories in these terms. This is how I understand it: a particle in "its" universe would create a gravitational field. However, in a "parent" universe, there would appear to be an infinite superposition of these particles. So there are either two possibilities: A) each particle has an infinitesimal mass that when summed produce the measured mass in the parent universe. This would mean that the particle "wave" would act as a massive object of that shape and size. B) Each particle has its measured mass which when measured "collapses" the wave in the parent universe.

The problem with A is that it would be possible to experimentally measure the position space wave function of a particle without actually measuring it. This is a contradiction of quantum mechanics which says that the wave function of a particle can not be measured.

The problem with B is that it requires that gravity be a quantum force, which contradicts GR. This is because GR says that a massive object curves the space around it. In QM, this would mean that "observations" would be made on any object continuously, causing every object to appear to "classical" rather than "quantum" (since the gravitational force is effectively a measurement). Therefore for QM to be right in this case, gravity must be a force.

Is this an accurate description of the contradictions made between GR and QM?

Fra

I'm on my way out but I thought I'd throw in a quick comment on one thing.

I think the best way of understanding the quantum indeterminism, rather than think that something "is random" whatever that means, is that actions are based on the uncertainty at hand. This applies to human reasoning as (like I want to suggest) physical interactions.

Your actions are based upon considerations of all options. This is something different than picking an action at random. At some level the effective result can be that some things appear to behave as if many options really to exist at the same time.

In the same way action and belief (personal probabilities) are connected from the philosophical point of view in decision theory, it can be said to be so also in physics. Actions, information and probability are related.

That is my "interpretation".

/Fredrik

Crosson

Any quantum theory of gravity will be a quantum field theory, and so when you say:

Why does the interaction between the particle and the field would constitute an observation of the particle? Why is this not a problem for E&M ?

This is only a problem if the correspondence principle is violated, i.e. we only expect quantum gravity to look like GR in the macroscopic limit.

Maybe I don't understand you argument, but what you describe seems to be the same thing as measuring the distribution of a double-slit experiment. This allows us to measure the square of the position space wave function.

wawenspop

The Standard Model predicts a Higgs Boson which should have a velocity of c - the same as a photon. This particle will then account for the gravitational force.
Its very disappointing that its not been found yet (as of Aug 2008) and there seems
to be no news-worthy 'running commentary' on its progress to discovery.

Vanadium 50

No, it does not. The velocity will always be less than c.


No it does not.

malawi_glenn

Why will it have velocity of a photon?

Higgs field will give the explanation why particles have MASS, but that is only one ingredience of gravity.

And just a couple of days ago, this news were published: http://www.physicsforums.com/showthread.php?t=248479

wawenspop

Yes, I am getting confused with a graviton - I should not have commented because I am just getting up to speed with Higgs Bosons, but am very interested in the whole gravitation story as it unfolds.

malawi_glenn

Also, I don't think that one usally counts the graviton to the so called Standard Model

Fredrik

I don't think a physical interaction can produce a delta function wave function. A position measurement will just "squeeze" the wave function into a sharply peaked state.

It would contradict the formulation of QM that says that states are represented by vectors in a Hilbert space. (There are no delta functions in a Hilbert space). But maybe that's irrelevant, since there's something called the "rigged Hilbert space" formulation that I don't fully understand.

It will spread out in the "child" universes too. Also, note that the "children" are just subspaces of the "parent" Hllbert space. (I explained my interpretation of the MWI here, starting at #13, but you may be interested in the link I posted in #12 as well).

I think it's pretty accurate, and by that I mean that I don't think that what you're saying about the MWI is wrong. I wouldn't go so far as to say that I believe in the MWI. I would like to suggest that you consider the "no interpretation needed" interpretation: What if QM is actually the first example we have encountered of a theory that doesn't actually describe reality? What justification do we have for believing that wave functions correspond to something that actually exists in the real world? Maybe we should just think of QM as an algorithm that tells us how to calculate the probabilities of each possible result of every possible experiment. Do we really have a reason to expect something more than that from every scientific theory?

Definitely B.

I don't see why curvature would imply continuous observation.

There are many ways to see that there must be a conflict between gravity and QM. Maybe you should read about Penrose's argument about gravitational collapse of the wave function if you haven't already. (I think it would appeal to your taste). A simpler argument is just that the stress-energy tensor represents the distribution and interactions of matter, and we already know that those can't be described classically.

muppet

A point about your take on the MWI: the idea that in an act of measurement the observer becomes entangled with the system under observation is explicit in Everett's original presentation of the idea. You could in fact be even stronger in this statement; rather than
you can actually say that there is only one you, in a superposition of states.

michael879

Well I really meant that "einsteinian" (i.e. classical) curvature would imply a continuous observation. Since the curvature caused by some mass is non-zero to infinity, everything in the universe would be constantly "observing" it. Theoretically you could triangulate its exact position whenever you wanted (meaning that in a sense its position IS determined exactly at EVERY time).

I have read a bit about penrose's argument. From what I read it seems unnatural and pretty ugly, but I wouldnt be suprised if it just sounded that way cause the description I read was dumbed down (like how much of physics sounds insane after its been reduced to ambiguous analogies). From what Ive read the theory is basically just that gravity only causes a collapse after reaching some threshold (which is about the ugliest and most unnatural explanation I could imagine). Once this threshold is reached the object becomes "classical" and is no longer affected by quantum effects.

sorry, what is this an argument for? Im not seeing the connection..

michael879

Thats good, Im glad I didn't just post some crazy interpretation that doesnt hold up. Everything Ive read about it has been pretty vague and doesnt mention that aspect at all (I obviously havnt read everett's original work).

I was really referring to "your" consciousness. A lot of people Ive talked to make arguments such as: "but it IS random because I ended up in THIS universe". The answer to that would be to say that "you" split into two but can only be "conscious" of one. But yea your statement is definately a better way to put it.

michael879

Well I really dont know much QFT at all, but Ill try to explain my thinking here. There are some large differences between the E&M field and the gravitation "field". One big one is that gravity needs at least 4 dimensions to exist, while the E&M field can exist in 1. Another is that a particle in an E&M field can be expressed by a hamiltonian. From what I know I believe this is how E&M fields are expressed in QM. However, relativistic gravity is not an energy potential, so that method doesnt work.

Theres also the obvious answer, which is that we were able to easily make a quantum E&M theory but we havnt yet been able to encorporate gravity into QM. So I might be missing something above, but there is some key difference.



thats kind of my whole point. If GR is true, then gravity can't be a quantum force. If GR is false (because its postulate, the correspondence principle is violated), then gravity can be a quantum force. But the predictive strength of GR does not help in proving it false. As far as I know there are only a few freak mysteries that don't obey GR.
Then theres the fact that GR is one of the most beautiful physics theories that exists. Einstein started with a simple postulate of the correspondence principle and created GR from it. It would be kind of weird if somehow it was all just a coincidence and gravity was just a quantum force that is approximated by GR. I do agree with you though that there is no chance for GR to be anything but an approximation of some greater theory because its based on CM which we know is an approximation and it fails to explain certain observed phenomena. However I would be very suprised if spatial curvature played NO role in the gravitational "force".



No theres a key difference between the two, although I do see the striking similarities now. In measuring the double slit distribution, you arent measuring the wave function of a particle. You are measuring the "average" wave function of a group of particles, which all happen to have an identical wave function. Plus, theres still a random element so you can never be 100% sure that the distribution you are measuring is the true distribution of every particle.

If gravity were to emit from the wave function rather than from the particle, you would be able to make measurements that would allow you to determine the shape and size of the wave. Im not sure if this is a postulate, an emergent effect, or a proven "law", but I know that in QM it is not possible to make a measurement of the wave function (only of the "particle"). Similarly, its not possible to "clone" a wave function. In this scenario it would be though.

Fredrik

The paragraph I wrote started with "There are many ways to see that there must be a conflict between gravity and QM". That should have been a clue. (It explains one reason why the classical description of gravity must be replaced by a quantum theory).

I have to get some sleep. I'll probably write a longer answer tomorrow.

michael879

Ill wait for your longer answer but I think i get your point. Your basically just making the point that GR assumes particles have a definite position and velocity right? My answer is just that yea, GR is obviously not the full theory because it doesnt explain a lot of phenomena and is based on postulates that have been proven wrong.

HOWEVER, it seems like all the approaches to quantum gravity simply throw out the results of GR (at least from the little I know about them), ignoring its simplicity, beauty, and predictive power. What I mean by simplicity and beauty (because Im sure that could be misunderstood) is that the entire theory, like SR (whose refusal to reject led to QFT), is based off a single additional postulate to classical mechanics that is both incredibly simple and obvious in hindsight.

My question was really concerned with why minor modifications cant be made to both theories (while leaving both mainly intact) to unify them. Why cant gravity be a curvature of space-time rather than a quantum force?

Im also kind of tired right now and Im having trouble remembering exactly what my question was when I started this thread, so if the above doesnt make sense sorry.

Fredrik

Yes. I don't have a whole lot more to say about that. The reason my answer would have been longer if I had started writing it earlier is that I would have had time to comment on the other things you said.

I don't think they do, especially not loop quantum gravity, but I don't know much about these subjects either.

I don't have the best answer to that, but it seems to me that the only modification that could be considered "minor" enough to "leave both mainly intact" is to take a quantum version of the stress-energy tensor (because we know matter must be described by QM) and somehow use it to produce a classical stress-energy tensor. The obvious way to do that is to replace an operator with an expectation value, but you immediately run into problems. E.g., the expectation value of what quantum state? People have of course tried methods like this, and failed to overcome the difficulties. Someone who knows more about their attempts would probably be able to give you a much better answer. One of the appendices in Wald's book talks a little about this.

OK, I think I get what you're saying. I don't know what to say except that I don't see a reason to assume that curvature can be treated classically, except maybe Penrose's argument.