Reconciling Spacetime & Quantum Uncertainty

[bahamagreen]

These two ideas seem to be categorically opposed. The concept of an event as a point in spacetime seems to not square with uncertainty and the concept of quantum intrinsic randomness seems to not square with unchanging spacetime... Assuming it is unnecessary to explain further why this is a fundamental problem (or let me know otherwise), is there thinking or are there any ideas that suggest possible directions toward reconciliation?

 

[Dale]

Assuming it is unnecessary to explain further why this is a fundamental problem (or let me know otherwise),

Modern QFT is formulated on spacetime just fine. There seems to be no fundamental problem on its own. It is just when you try to combine it with GR that you get problems, but that isn’t a fundamental problem with QFT itself.

 

[bahamagreen]

Maybe I should ask what are the relationships among QFT, spacetime, and GR... and intrinsic randomness.
Does QFT not have intrinsic randomness?
Are there any forms of spacetime that allow intrinsic randomness?
Does "no fundamental problem on its own" mean QFT is founded without spacetime, or just that QFT is founded on "non-GR" spacetime?

 

[martinbn]

Why do you think it is a problem? If it is a problem, how is the theory QM even possible? One needs space and time to formulate QM.

 

[bahamagreen]

I don't understand how all events being fixed in unchanging 4D spacetime does not logically imply no randomness.

I could say that spacetime is deterministic, hence non-random, or that everything in any event's future light cone is also in some other events' past light cones, but these seem weak; I'm still trying to uncover quite why I'm more directly equating spacetime with no randomness.

Maybe you can suggest some lines of thought I have not considered?

 

[Dale]

Does QFT not have intrinsic randomness?

I have no idea what “intrinsic randomness” means. It is a term I have never heard before. How exactly (in a rigorous manner) is it defined.

If you can define it rigorously then we can simply apply the definition to QFT and see if it has “intrinsic randomness” or not.

Does "no fundamental problem on its own" mean QFT is founded without spacetime, or just that QFT is founded on "non-GR" spacetime?

QFT is formulated on a fixed background spacetime. You can do QFT on a flat or a curved spacetime, but you cannot have the curvature of spacetime change dynamically as a result of the system.

 

[PeterDonis]

QFT is formulated on a fixed background spacetime. You can do QFT on a flat or a curved spacetime, but you cannot have the curvature of spacetime change dynamically as a result of the system.

Actually, it's a little more complicated than that. You can do QFT on a background spacetime where one of the contributions to the stress-energy tensor is the expectation value of the SET of the quantum fields. There is a self-consistency requirement where the fields whose expectation value SET you are computing have to be valid solutions on the background spacetime you get from solving the EFE with that SET, which makes this more complicated than just doing QFT on a pre-determined fixed background; but it can be done, and is a way of including the effects of the quantum fields in the dynamics of the spacetime geometry.

The issue with this approach is that the expectation value of the SET is not, in general, going to be the same as any of the actual eigenvalues of whatever quantum field operator corresponds to the SET. So the effective SET that you are using to compute the spacetime geometry will be different from the actual stress-energy that is observed.

 

[bahamagreen]

I have no idea what “intrinsic randomness” means. It is a term I have never heard before. How exactly (in a rigorous manner) is it defined.

If you can define it rigorously then we can simply apply the definition to QFT and see if it has “intrinsic randomness” or not.

QFT is formulated on a fixed background spacetime. You can do QFT on a flat or a curved spacetime, but you cannot have the curvature of spacetime change dynamically as a result of the system.

Intrinsic randomness is innate distinguished from experimental, similar to uncertainty when quantum uncertainty is described as intrinsic, not just an artifact of measurement.

I have asked about dynamically changing spacetime before and was informed the concept made no sense. I can't tell if you are confirming there is no such thing or that there is such a thing but it does not support QFT.

 

[PeterDonis]

I have asked about dynamically changing spacetime before and was informed the concept made no sense.

It doesn't make sense if you are thinking of spacetime as changing from one time to another; spacetime already includes all "changes with time" in its 4-dimensional geometry.

However, in GR, physicists often talk about "dynamics" of spacetime to refer to the fact that the spacetime geometry is not fixed a priori, it depends on the stress-energy present via the Einstein Field Equation. (By contrast, in special relativity, the spacetime geometry is assumed a priori to be Minkowski spacetime; there is no room for "dynamically" determining the geometry based on the distribution of stress-energy or anything else.)

 

[bahamagreen]

...and is a way of including the effects of the quantum fields in the dynamics of the spacetime geometry.

As mentioned above, I have before asked here about dynamic spacetime and been informed there can be no such thing. Paraphrasing from memory, it is because spacetime is not embedded within a higher structure. If it is possible, if offers many explanatory ideas.

 

[bahamagreen]

It doesn't make sense if you are thinking of spacetime as changing from one time to another; spacetime already includes all "changes with time" in its 4-dimensional geometry.

However, in GR, physicists often talk about "dynamics" of spacetime to refer to the fact that the spacetime geometry is not fixed a priori, it depends on the stress-energy present via the Einstein Field Equation. (By contrast, in special relativity, the spacetime geometry is assumed a priori to be Minkowski spacetime; there is no room for "dynamically" determining the geometry based on the distribution of stress-energy or anything else.)

OK, sounds like "dynamic" applies to changes in selection possibilities of theories, not changes in the spacetime once selected.

Back to randomness; if spacetime already includes all "changes with time", is that not fully determined and without randomness?

How would a 4D object which were fully determined show randomness emerging in 3D slices?

Is there a requirement that randomness arise only from embedded structures?

 

[Ibix]

As mentioned above, I have before asked here about dynamic spacetime and been informed there can be no such thing. Paraphrasing from memory, it is because spacetime is not embedded within a higher structure. If it is possible, if offers many explanatory ideas.

Think of Schrödinger's cat. We can describe the spacetime we expect from a box containing a dead cat in a heap on the bottom of the box. We can describe the spacetime we expect from a box containing a cat stalking around inside it. What we don't know how to do is describe the spacetime around a box containing a superposition of a live and a dead cat. Talking about a superposition of spacetimes doesn't really make sense. I don't think it's the randomness that's the problem - it's the superposition of gravitational field states implied by the superposition of source states.

Note that the dead cat spacetime is static (modulo pedantry about rotting and past history of a live cat) while the live cat spacetime contains (ridiculously weak) gravitational waves and other such fun stuff. This is the point that Peter is making about the meaning of "dynamic" - spacetime can be dynamical in the sense that the 3-geometry changes along some timelike direction (so we see gravitational waves pass by us as the cat moves around). But the 4-geometry is completely determined by the initial conditions in either case (assuming "initial conditions" includes a complete working model of a grumpy feline).

 

[PeterDonis]

if spacetime already includes all "changes with time", is that not fully determined and without randomness?

Since GR is a classical, non-quantum theory, any particular solution in GR describes a single spacetime whose geometry, including all past, present, and future, is fully determined to be a single geometry, yes.

How would a 4D object which were fully determined show randomness emerging in 3D slices?

Is there a requirement that randomness arise only from embedded structures?

These are not answerable because you have not defined what you mean by "randomness".

 

[bahamagreen]

...you have not defined what you mean by "randomness".

You used "fully determined" so you know what that means; can we define randomness as the opposite?

How about randomness means "Not fully determined"?

 

[PeterDonis]

You used "fully determined" so you know what that means

I know what it means in the context of classical GR: it means that the theory has a well posed initial value problem. But unitary quantum mechanics (or quantum field theory) also has a well posed initial value problem; yet you are talking about QM/QFT having "intrinsic randomness". So clearly your "intrinsic randomness" can't mean the same as the negation of my "fully determined".

 

[bahamagreen]

I know what it means in the context of classical GR: it means that the theory has a well posed initial value problem. But unitary quantum mechanics (or quantum field theory) also has a well posed initial value problem; yet you are talking about QM/QFT having "intrinsic randomness". So clearly your "intrinsic randomness" can't mean the same as the negation of my "fully determined".

I labeled my thread as intermediate and I think we may be getting squishy on the distinction between the attributes of a theory itself vs the attributes of the objects of the theory. It looks to me like GR is deterministic and its objects are deterministic. However, the Schrödinger equation is deterministic but its objects are not... is that right?
I'm not familiar with QFT, but if an initial value problem is said to be well-posed if among other conditions a solution for it is unique, do the solutions represent "the theory" or "the theory's objects"? Uniqueness in the sense of "one determined answer" looks like it would prevent the "one of multiple potential answers" required for randomness.

 

[PeterDonis]

the distinction between the attributes of a theory itself vs the attributes of the objects of the theory

What are "the objects of the theory"? Different answers to that question will give you different answers to the questions you are struggling with.

For example: the Schrödinger equation is deterministic, but what is the Schrödinger equation an equation for? The wave function. So the time evolution of the wave function is deterministic, provided that evolution is governed by the Schrödinger equation. But whether or not this is true is interpretation dependent. On no collapse interpretations of QM, such as the MWI, the time evolution of the wave function is always governed by the Schrödinger equation, so it's always deterministic. But on a collapse interpretation, during a measurement, the time evolution of the wave function is not governed by the Schrödinger equation, so it would not always be deterministic. (Yes, this dichotomy about how to describe whether or not QM is deterministic is one way of describing the QM measurement problem.)

But the predictions we actually want to extract from QM are not about the value of the wave function; they are about the values of observables. And the time evolution of those values might not even be well-defined, so it might not even be possible to answer the question of whether it is deterministic or not, or whether, if it isn't deterministic, this fact can be usefully viewed as a simple negation of the "deterministic" property of a classical theory like GR.

 

[bahamagreen]

Alright, thanks; I think my original question may have been answered.

An oversimplification, but it looks like the quantum efforts have enjoyed about 100 years of change and development while relativity has been subject to some minor house cleaning, some removal of clumsy ideas and reinforcement of others, but for for the most part has changed little. The present result is that quantum theory trumps relativity theory when looking at the details of whether quantum needs to accommodate relativity or relativity needs to accommodate quantum - the asymmetry pointing to relativity having to accommodate the qualities of quantum; yet, the development of the accommodating connecting adjustment could originate from discovery on either side.

Let me know if that's so wrong it's not even wrong... :)

 

[PeterDonis]

The present result is that quantum theory trumps relativity theory when looking at the details of whether quantum needs to accommodate relativity or relativity needs to accommodate quantum

This is basically the prevailing opinion among physicists, but it is worth noting that there are some (including, for example, Freeman Dyson) who have proposed that there might not be any accommodation; we might be stuck with two fundamentally different theories without ever finding an underlying single "theory of everything" that includes both as appropriate approximations.

It's also worth noting that, while string theory basically looks like a quantum theory that can explain how GR arises as an approximation, other approaches to quantum gravity, in particular loop quantum gravity, don't look like that; they look more like something completely different that has both current QM and current GR as approximations.

 

[Dale]

Intrinsic randomness is innate distinguished from experimental, similar to uncertainty when quantum uncertainty is described as intrinsic, not just an artifact of measurement.

This isn’t a very clear definition. By “quantum uncertainty” are you referring to Heisenberg’s uncertainty principle? If so, then QFT also produces Heisenberg’s uncertainty principle. Which would make QFT have intrinsic randomness even with a determined spacetime.

 

[bahamagreen]

This isn’t a very clear definition. By “quantum uncertainty” are you referring to Heisenberg’s uncertainty principle? If so, then QFT also produces Heisenberg’s uncertainty principle. Which would make QFT have intrinsic randomness even with a determined spacetime.

Dale, you see much that is hidden.

For physicists theorizing about the HUP and intrinsic randomness, are these considered two independent things, two related things, and if the latter, is one thought to be the fundamental basis of the other?

"Which would make QFT have intrinsic randomness even with a determined spacetime."

This brings us back to my initial question. Is this considered an issue, problem, or paradox? If not, can you help explain what line of thinking allows determined spacetime to accommodate, support, or even require uncertainty/randomness?

 

[romsofia]

It isn't paradoxical.

I'll give you a scenario: You have two guys, one who lives in Jamaica, and one who lives in Sweden. You ask each of them to tell you about the condition of the sky in front of them. The guy in Jamaica says the sky is blue today, and the guy in Sweden says it's gray. Is there any paradox to this situation? It's apparent that they both see different things.

If you ask GR to "talk" about the universe, it will tell you about the dynamics of spacetime. If you ask QFT to "talk" about the universe, it will talk about transition amplitudes, and probabilities of certain outcomes. Now, just like above, is there any paradox? It's apparent that they both see different things. We use theories where they are valid. In other words... If you're going on vacation in Jamaica, talk to the guy in Jamaica.

(However, there are a bunch of papers on this, and it's even it's own field: Quantum general relativity. You can start with this paper and move on: https://arxiv.org/pdf/gr-qc/0610140.pdf).

 

[Dale]

For physicists theorizing about the HUP and intrinsic randomness, are these considered two independent things, two related things, and if the latter, is one thought to be the fundamental basis of the other?

I have never heard anyone discuss “intrinsic randomness” before this thread. From what I understand of your definition they are defined to be the same thing.

Is this considered an issue, problem, or paradox? If not, can you help explain what line of thinking allows determined spacetime to accommodate, support, or even require uncertainty/randomness?

No, it is not considered a paradox. In QFT the fields don’t modify the spacetime, so why should there be any conflict?