- #1
michael879
- 698
- 7
first, Id just like to say that I am a 4th year physics major, so I've 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. Let's 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.
Let's 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 I am 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, I am 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 I am not sure how good of a description it is. I do prefer my interpretation over any of the other ones I've seen though, as it actually makes QM believable for me (I have trouble accepting that something can be truly random).
Second, I am 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?
Quantum
I prefer the many worlds interpretation for this, so Ill stick to that. Let's 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.
Let's 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 I am 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, I am 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 I am not sure how good of a description it is. I do prefer my interpretation over any of the other ones I've seen though, as it actually makes QM believable for me (I have trouble accepting that something can be truly random).
Second, I am 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?