Markus Hanke

For the purpose of attempting reduction. I may not have formulated this very clearly, I just meant that knowledge of the parts here does not equal knowledge of the whole system; there’s extra information there. Measurement of any part of the system breaks entanglement. Yes, it’s what I meant.

To me entanglement is a correlation between measurement outcomes, due to non-separability of the system. Note that non-separability does not equal non-locality. Also note that it is meaningless to talk of ‘correlation’ in a quantum system unless there’s an observer there who measures both parts, and compares results (remember counterfactual definiteness) - thus entanglement is a relationship between parts as much as a relationship of a system with its environment. Lastly, an entangled system seems to me a good example of where reductionism arguably becomes problematic, because knowledge of the system does not imply knowledge of the parts. You need to know the correlation plus at least one measurement outcome on one part.

The metric which describes large-scale spacetime of the universe does not resemble a ‘gravity well’.

Yes, indeed. That’s an example of tidal gravity. As a general rule of thumb, “local” means a region in the order of ~1/g, so near Earth’s surface for example it would be a box no larger than ~10cm. But of course it depends on your required level of accuracy. I think the recent spread of FET has more to do with the algorithms on social media platforms such as YouTube, than with understandings of gravity.

It is not constant, it is invariant. That’s a really important difference! The other thing is that this invariance is a local statement. If you send EM radiation through a larger region of curved spacetime, and you naively calculate the speed using your own clocks and rulers, you will come out with a smaller value - this is called Shapiro delay, and is one of the classic tests of GR. Nonetheless, the speed remains at exactly c at each point of the trajectory taken. That’s because what changes is the relationship between events in spacetime - not Maxwell’s equations.

Yes indeed. There wouldn’t be any purely local way to tell, but you can construct some scheme that relies on outside references, or on longer-lasting measurements (to detect tidal forces).

Entanglement does not involve any exchange of information, or any kind of action - it’s simply a statistical correlation between measurement outcomes. So there’s no conflict with the principles of relativity.

I don’t know if there is any objective definition of the term. Personally I would use it only in cases where there are demonstrable neurological differences (as the term itself implies), such as is the case for for autism, or Down Syndrom; the profiles here are often spiky, meaning they have large variations between traits. A single outlier on an otherwise typical profile doesn’t qualify, in my opinion.

Yes, though in the real world the limitation on locality is most often given by the spatial extension of the frame, since gravity due to sources such as planets is tidal in nature; so if the frame becomes too large, then tidal effects become detectable, which destroys the equivalence.

The salient point though is that there is no local experiment you can perform which distinguishes these cases. The equivalence principle is always a purely local statement. Measuring force and distance over long periods of time gives you a region of spacetime that is too large to be considered ‘local’, so of course there is no equivalence. But if you put an astronaut into a windowless box and ask him to tell whether the downward force is due to gravity or due to acceleration, without any outside references, then there isn’t anything he can do to tell the difference.

It’s quite alright to ponder these issues. That’s how understanding is made. But here’s another thing - in the GR field equations, Lambda is not directly identified with any kind of energy. Regardless of which side of the equation you choose to put it, what happens is that, in vacuum, it stops the Einstein tensor from being zero. The physical meaning of this tensor is that, once a future time direction is chosen, it gives the average of scalar curvature in the spatial directions. This means that, taken at face value, Lambda is best understood as a background curvature that is always present, even in the absence of all gravitational sources. It’s purely a geometric entity that modifies the global geometry of the manifold. Identifying this background curvature with Dark Energy is one possible hypothesis - but there’s no principle that requires us to posit this. There are other options.

I second that +1

You would be moving pretty fast relative to your starting point, but not faster than c. Remember the laws of Special Relativity!

Yes. Also, remember previous discussions we had about degrees of freedom. Scalar curvature (I presume you mean the Ricci scalar) only measures one particular aspect of curvature; it can’t account for all necessary degrees of freedom.

So does it require agency? Does it presuppose an independent agent who ‘has’ free will, or is it more akin to a self-regulating complex system with multiple feedback loops? Could you explain further? If (in my specific example) the action is initiated before the motivation and decision making process becomes conscious, then how was the decision ‘free’? Are you familiar with Carlo Rovelli’s ‘relational QM’? It resolves the issue rather elegantly.

True, it is, at least in some sense. But even if you disregard inflation completely, you can only extend the Lambda-CDM model as far back as ~10^(-32)s or so - and you’d struggle to explain the large-structure of the universe without inflation. But under no circumstances can you extend it to the Planck epoch, that’s outside its domain of applicability, since GR is a purely classical model.

It’s far more complex than that, because determinism does not imply predictability; and determinism+predictability don’t imply computability. That notwithstanding, it has been known for some time that consciously intentional actions (eg moving your arm) are preceded by motor neuron activity in the brain by ~10ms. That means the brain physically initiates motor action before you ever become aware of any decision-making to act. Where does that leave free will? I personally think free will is a silly concept, as you need to make a ‘causal gap’ argument to postulate it. It also requires independent agency, which is also an extremely dubious concept, to say the least.

The Lambda-CDM model is a model based on classical General Relativity, so it only describes the evolution of spacetime after the inflationary epoch. You cannot extend it further back than that.

What do you mean exactly by ‘radius of curvature of spacetime’? Again, I don’t know what you mean by this, since the tidal curvature of spacetime certainly does not follow a linear relationship like this. For a radial infall such as the one I spoke about the relevant quantity is the (t,r,t,r) component of the Riemann tensor - which is an inverse cube law.

That’s not the case though, not even in the most symmetric spacetimes. Consider a freely falling particle in Schwarzschild spacetime - a faraway observer will see the particle recede, and then slowing down and getting dimmer and redder as it approaches the horizon. Another observer falling in parallel to the particle (at not too great a distance) will not see this effect, for him the particle appears the same the entire time, and will actually get closer to him as they fall. So visual appearance in curved spacetime does depend on the observer, because different events are linked by different sets of null geodesics.

A point in 3-space can be considered as the limit of the volume of a sphere with r-> 0. You can formally set up the volume as an integral function, and then take the limit.

I remember having gone through Young/Freedman many years ago, an older edition. From what I remember, you will only really need (1)-(5), as well as (8) and (9) of the topics in your maths text. I would recommend going through the whole thing though!

What do you mean by “observe”? You mean visually?

Actually, distances generally become longer as compared to a far-away reference ruler, though it depends on the type of spacetime you are in. And this is precisely the physical meaning of mathematical curvature - that relationships between events (ie measurements of space and time) now depend on where and when you make them, relative to a reference point. Emphasis here being on the word ‘relationships’ - these aren’t effects that locally happen to clocks and rulers; it is how two or more such measurements are related in spacetime, which is why you can only detect them by comparing measurements. Locally all clocks tick at 1 second per second, and all rulers measure 1 meter per meter.

Good point. Example: Hyperion Cantos tetralogy by Dan Simmons. Very much recommended to anyone who hasn’t read it yet. Another one is Solaris by Stanislaw Lem. And for the brave ones, there’s always Roadside Picnic by the Strugatski brothers.