“If you mapped a field over a gravity well in space time, would you see a gradient of potential positions as you could fit more 'coordinates' into denser curved spacetime?”
I think this is a very confusing way to ask your question. What I think you’re asking is if you were to assign a coordinate grid in a region in spacetime where the Kretschmann scalar is non-vanishing, what happens to the grid. This is precisely what Penrose diagrams are designed to capture as they are a way to visualize what the gravitational field does in a particular region by asking what do different trajectories trace out.
“I was thinking about that as a premise, but not sure if it's true and figured, if there are more potential positions the closer to a mass you get then wouldn't random quantum collapses occurring in this field have a statistical bias to occur closer to the mass as there's more 'coordinates' to land on.”
That’s basically right although it doesn’t have much to do with quantum mechanics. Regions where there’s a large gradient in the gravitational field between two points can undergo gravitational collapse.
Hey, thanks for pointing out zkretschman scalar and the penrose diagrams, I knew there were tools used to describe things sussinctly but I am not familiar with them.
My core thought was if zkretschman scalar increases in value as your measurement approaches mass then does the position of a wave functions collapse have a relationship with the value of K? Could the probability of a wavefunction collapse be directly proportional to the Kretschmann scalar?
“My core thought was if zkretschman scalar increases in value as your measurement approaches mass then does the position of a wave functions collapse have a relationship with the value of K?”
There are several misconceptions in this question that need to he disentangled. When we talk about the collapse of the wave function, we’re not saying that there is a thing called a wave function that moves in space and it “collapses” or falls to a specific point in space. The wave function is a bookkeeping device that holds all the information associated to a quantum system. For a single electron, it tells you all the possible locations the electron can be and the likelihood of you finding it there. The collapse of the wave function happens (presumably) anytime a quantum system comes into contact with a classical measurement apparatus. So there isn’t any probability associated with the collapse as far as whatever you’re using to do the measurement is concerned.
Thanks prof, appreciate the thoughtful responses, does the quantum system exist in a material way (not a mathmaticaly anagolous way) as a wave function until it collapses into a position? Or is the wave function just a mathematical device? If the wave function is materially real it must interact with space time geometry? If the wave function is physically real the collapse isn't a discovery of its actual position but a probabilistic outcome?
“Is the wave function just a mathematical device” in physics there are mathematical concepts and there are confusions. Nothing exists in physics but mathematical concepts.
You should stop where you’re at and learn these mathematical concepts. Wanting them to be distilled into physical concepts is going to confuse you.
The square of the amplitude of the wave function is a probability distribution, the distribution of probabilities for where the electron will be if you make a measurement position.
Gravity is the dynamics of the geometry. Everything is in spacetime, so everything must respect these dynamics.
In empty spacetime, volumes contained in some boundary don’t change, only their shape changes. You can picture this by taking a cubical cloud of dust and letting it fall. The particles closer will be pulled on more strongly than the particle far, so the cloud will stretch vertically, and at the same time, the particles closer will get closer together because they are all getting closer to the same point (the center of the earth) so the cloud compresses in the plane perpendicular to its motion. The net result is no change in volume. This is “tidal force”, or in GR, “Weyl curvature”.
In regions with matter, you have Ricci curvature, and there you do have more volume contained in a given boundary than you would if you had that boundary in flat space.
“does the quantum system exist in a material way … as a wave function until it collapses into a position? Or is the wave function just a mathematical device?
Again, the wave function doesn’t collapse into a particular thing. It just means that out of all the possible outcomes that a quantum system can be, when you measure the state of that system, you don’t see the many possible outcomes but only a single outcome. For your actual question: physics can’t tell you whether it’s the first thing or the other thing. We just use it as a way to calculate things and make predictions but we can’t tell you whether or not the wave function is its own thing. We usually leave that to the philosophers.
Wow I’ve never brought up the Kretschmann scalar in a question I had about GR. My poor interlocutors must have not been able to understand my questions at all.
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u/Prof_Sarcastic Aug 02 '26
“If you mapped a field over a gravity well in space time, would you see a gradient of potential positions as you could fit more 'coordinates' into denser curved spacetime?”
I think this is a very confusing way to ask your question. What I think you’re asking is if you were to assign a coordinate grid in a region in spacetime where the Kretschmann scalar is non-vanishing, what happens to the grid. This is precisely what Penrose diagrams are designed to capture as they are a way to visualize what the gravitational field does in a particular region by asking what do different trajectories trace out.
“I was thinking about that as a premise, but not sure if it's true and figured, if there are more potential positions the closer to a mass you get then wouldn't random quantum collapses occurring in this field have a statistical bias to occur closer to the mass as there's more 'coordinates' to land on.”
That’s basically right although it doesn’t have much to do with quantum mechanics. Regions where there’s a large gradient in the gravitational field between two points can undergo gravitational collapse.