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Quantum mechanics vs general relativity 
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#1
Aug308, 01:56 AM

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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 nonmacroscopic 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? 


#2
Aug308, 05:05 AM

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


#3
Aug308, 12:42 PM

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#4
Aug808, 08:31 AM

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Quantum mechanics vs general relativity
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 newsworthy 'running commentary' on its progress to discovery. 


#5
Aug808, 08:51 AM

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#6
Aug808, 09:02 AM

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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 


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Aug808, 09:08 AM

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#8
Aug808, 09:10 AM

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#9
Aug808, 10:31 AM

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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. 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 stressenergy tensor represents the distribution and interactions of matter, and we already know that those can't be described classically. 


#10
Aug808, 05:50 PM

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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



#11
Aug1308, 06:17 PM

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#12
Aug1308, 06:25 PM

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#13
Aug1308, 06:48 PM

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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. 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". 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. 


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Aug1308, 10:08 PM

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


#15
Aug1408, 09:04 PM

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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 spacetime 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. 


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Aug1508, 03:38 PM

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