Quantum events near a black hole

[gnnmartin]

TL;DR

Is the expectation of a quantum event a density in space/time?

I apologise for my very limited understanding of quantum physics: my background is in General Relativity. A wave function is said to represent the probability of a particle being at some point in space/time, and I take that to mean that the probability of a quantum event is a density on space/time. That implies (does it not?) that the rate of quantum events (other things being equal) is a density in local time. In particular, the rate of quantum events close to a black hole should be very low when expressed as a rate in (say) Schwarzschild coordinate time. The literature that I read seems to contradict that. Where am I going wrong?

 

[Demystifier]

In quantum physics, you cannot talk of probability of the event without specifying something about the measurement of the event. In particular, you have to specify the frame with respect to which the measuring apparatus is at rest. So if you talk about events near the black hole, you have to say whether the measuring apparatus is static (with respect to black hole) or in free fall. For definiteness, let as assume that the apparatus is static and positioned close to the horizon. Furthermore, let us suppose that every time the apparatus detects a particle, it also sends signal to an observer far from the horizon. Under those conditions, the time between signals as seen by the far observer will be much larger than the time between detections at the apparatus, in agreement with your expectations.

The literature that I read seems to contradict that.

Can you specify what literature?

 

[PeroK]

A wave function is said to represent the probability of a particle being at some point in space/time,

Actually it represents a complex probability amplitude. And the modulus squared of the wave function represents the probability of measurement detecting the particle at that point in spacetime. The particle does not have a definite position unless you measure its position.

and I take that to mean that the probability of a quantum event is a density on space/time.

You would need to specify a context for that statement. As it's stands I'm not sure what it might mean.

 

[gnnmartin]

Thanks, that it is as I thought, but I feared I was wrong.

Can you specify what literature?

My question was not prompted by a particular paper, more by an uneasy feeling from papers I have glanced at. I want to be able use my assumption in a paper that I hope to write, so wanted to be sure it was not obviously incorrect.

 

[gnnmartin]

... the modulus squared of the wave function represents the probability of measurement detecting the particle at that point in spacetime. ...

Indeed, that is (I think) what I was trying to say, except I was trying to be a bit more precise about the verb 'detecting', because of course quantum events occur whether or not they are detected, just as Schrödinger's cat is definitely dead (or has definitely survived) whether or not anybody looks.

 

[PeroK]

Indeed, that is (I think) what I was trying to say, except I was trying to be a bit more precise about the verb 'detecting', because of course quantum events occur whether or not they are detected

That's being less precise, in the sense that you cannot say or know that something has happened unless you detect it. That's a cornerstone of orthodox QM.

just as Schrödinger's cat is definitely dead (or has definitely survived) whether or not anybody looks.

A cat is a complex macroscopic object that interacts continually with its environment. It's not an isolated QM system.

The point of Schrödinger's thought experiment was to highlight that cats do not behave according to basic QM. And the question is then why not?

 

[Lord Jestocost]

Carl Friedrich von Weizsäcker on Schrödingers so-called cat paradox in his book “The Structure of Physics” (the book is a newly arranged and revised English version of "Aufbau der Physik" by Carl Friedrich von Weizsäcker)):

“In an article from 1935 (see Jammer 1974, pp. 215—218) he [Schrödinger] treats with irony the Copenhagen point of view by means a thought experiment. Let a living cat be locked up in a box and with it a deadly poison which can be released by a single radioactive atom inside the box. After one half-life of the atom the probability is $1/2$ for the cat being still alive, and $1/2$ for being dead. Schrödinger describes the $\psi$-function of the system at this time with the words: ‘The half-alive and the half-dead cat are smeared out over the entire box.’

The answer is trivial: the $\psi$-function is the list of all possible predictions. A probability $1/2$ for the two alternative possibilities (here: "living or dead") means that the two incompatible situations must now be considered equally possible at the instant of time meant by the prediction. There is no trace of a paradox.

Schrödinger's reason to consider the situation as paradoxical lay in his hope to interpret the $\psi$-function as an ‘objective’ wave field.....”

 

[gnnmartin]

That's being less precise, in the sense that you cannot say or know that something has happened unless you detect it. That's a cornerstone of orthodox QM.

Thanks. Yes, you cannot say some specific outcome has occurred, but I wish to be able to assert (roughly speaking) the probable order of the number of quantum events that will occur in a coordinate unit of space/time in the material of a star shortly before an event horizon forms.

If you drop a glass jar down a coal mine, you do not know that it has broken, but you can be fairly certain, and the breaking will involve a large number of quantum events. In fact (if my understanding is correct) a glass jar standing safely on the table remains intact by virtue of a large number of quantum events, none of which are directly detected.

I do recognise that the idea of a coordinate unit is only meaningful if the context is specified, which is why I referred to Schwarzschild space. Also the notion of an event horizon has various definitions. I hope my question can be understood and answered without being more precise, since that will take a lot more words.

 

[PeroK]

Your missing the point by continually drawing an analogy between the classical behaviour of objects like glass bottles and the behaviour of elementary particles. QM is not analogous to classical mechanics. It is something entirely different.

The probabilities involved in QM are fundamentally different from the probability that a glass bottle will smash if you drop it from a certain height.

 

[gnnmartin]

Your missing the point by continually drawing an analogy between the classical behaviour of objects like glass bottles and the behaviour of elementary particles. QM is not analogous to classical mechanics. It is something entirely different.

The probabilities involved in QM are fundamentally different from the probability that a glass bottle will smash if you drop it from a certain height.

OK, thanks. I'll just have to hope I am not missing the point when I write my paper.

 

[PeroK]

OK, thanks. I'll just have to hope I am not missing the point when I write my paper.

You could always learn QM first!

 

[gnnmartin]

You could always learn QM first!

I ought perhaps to retire from this thread, so forgive me continuing.

If an electron in a cathode ray tube hits the screen, and causes a flash which is seen by the operator, is that a quantum event?

If yes, then if the operator was not watching, did a quantum event occur none the less?

If your answer is yes, and yes, then don't you see the scope for estimating the frequency of unobserved quantum events?

If your answer is not yes & yes, then I do indeed need to learn more about QM, but I shall be interested to know your answer so that I can think about it.

 

[DaveC426913]

A cat is a complex macroscopic object that interacts continually with its environment. It's not an isolated QM system.

The point of Schrödinger's thought experiment was to highlight that cats do not behave according to basic QM. And the question is then why not?

This raises the question: scientists are always increasing the size/mass/complexity of objects that can be superposed/entangled - (what size molecule are we up to now?); surely it is only a matter of time, determination and a bit of malfeasance before we reach cat-size?

 

[PeterDonis]

If an electron in a cathode ray tube hits the screen, and causes a flash which is seen by the operator, is that a quantum event?

I don't know. What's your definition of "a quantum event"? A reference would help.

 

[Lord Jestocost]

If yes, then if the operator was not watching, did a quantum event occur none the less?

An "unobserved event" sounds like a contradiciton in terms in quantum physics!

 

[gnnmartin]

Yours (PeterDonis's) is an interesting reply, which does indeed go to the heart of my problem. I had assumed that QM experts would be happy with the term 'quantum event', and so look to you (in this case) to tell me what it means if you think I am using it incorrectly.

The closest I can get to defining a quantum event is 'action at a distance'. Action at a distance is inherent in measurement, since measurement deals in finite quantities and local action deals in infinitesimals, so the association with 'action at a distance' and observables is inevitable. However, I did not think that anyone actually thinks the human observer is more than a metaphor when talking about observables.

I did not expect to get into this detail, but if you are interested, I wrote an amateur paper http://vixra.org/abs/1805.0166 "On the dichotomy of causality and measurement".

 

[gnnmartin]

...
The closest I can get to defining a quantum event is 'action at a distance'. ...

Perhaps more accurately, I assumed a quantum event was a reasonable way of referring to a discontinuity in the 'action at a distance' upon a point. I could have perhaps talked about the collapse of the wave function, but I thought that would be more presumptuous.

 

[PeterDonis]

The closest I can get to defining a quantum event is 'action at a distance'. Action at a distance is inherent in measurement

I have no idea what you are talking about here. Where are you getting this from?

 

[PeterDonis]

I wrote an amateur paper http://vixra.org/abs/1805.0166 "On the dichotomy of causality and measurement".

PF is not for discussing personal research.

 

[PeterDonis]

had assumed that QM experts would be happy with the term 'quantum event'

Have you ever seen that term used in an actual reference about QM (a textbook or peer-reviewed paper)? If not, why would you assume that QM experts would be happy with the term?

 

[PeterDonis]

the rate of quantum events close to a black hole should be very low when expressed as a rate in (say) Schwarzschild coordinate time. The literature that I read seems to contradict that.

My question was not prompted by a particular paper, more by an uneasy feeling from papers I have glanced at.

This is all way too vague. You need to be much more specific about a particular scenario that can be properly analyzed.

 

[Nugatory]

but if you are interested, I wrote an amateur paper http://vixra.org/abs/1805.0166 "On the dichotomy of causality and measurement".

From the forum rules on acceptable sources:

References that appear only on viXra (http://www.vixra.org) are never allowed.

 

[Nugatory]

I could have perhaps talked about the collapse of the wave function, but I thought that would be more presumptuous.

Not presumptuous but misdirected. Collapse is part of some interpretations of quantum mechanics, but not the mathematical formalism itself. We’ll only think in terms of collapse when doing so helps us reason about the problem at hand - and collapse is pretty much incompatible with relativity so is only used when non-relativistic physics is an adequate approximation. Here we are considering the especially strong relativistic effects in the vicinity of a black hole, and introducing collapse into the discussion will only add confusion.

 

[gnnmartin]

I have no idea what you are talking about here. Where are you getting this from?

From Misner Thorne & Wheeler 'Gravitation', quoting Newton:

https://en.wikipedia.org/wiki/Action_at_a_distance#Einstein gives a good summary of the notion of action at a distance. Einstein's theory led people initially to assume that all action was local. Bell's paper was perhaps the turning point after which people realized that action at a distance was irrefutable.

However, I expect, indeed am sure, that you knew this, so I will stop trying to explain myself. Thanks for the replies.

 

[gnnmartin]

Not presumptuous but misdirected. ...

Thanks. And sorry for the Vixra reference. I was being pressed to explain what i meant, and I had explained it there.

 

[PeterDonis]

Bell's paper was perhaps the turning point after which people realized that action at a distance was irrefutable.

Bell's paper shows no such thing.

At this point I think this thread has run its course. You appear to have some fundamental misunderstandings about QM, and you have not been able to give any specific scenario that can serve as a basis for discussion.

Thread closed.