4 hours ago, KJW said:

No, spacetime curvature is not merely an abstract theoretical notion. It is a measurable physical quantity. I've said on a number of occasions that the gravity with which we are familiar, including artificial gravity, is caused by time dilation. Time dilation is a measurable physical quantity, and by measuring how time dilation varies over the space surrounding the earth, one can prove that the spacetime surrounding the earth is curved. Thus, a correct theory of gravity must account for spacetime curvature.

Hmmm... Kip Thorne has a whole chapter in Black Holes and Time Warps wherein he states that we can't really know if spacetime is really curved. In his epigraph to chapter 11 "What is Reality", he writes:

in which spacetime is viewed as

curved on Sundays and flat on Mondays,

and horizons are made from

vacuum on Sundays and charge on Mondays,

but Sunday's experiments and Monday's experiments

agree in all details

(his new lines)

Other citation from that chapter:

Which viewpoint tells the "real truth" is irrelevant for experiments; it is a matter for philosophers to debate, not physicists.

His suggestion is that some calculations are easier in one paradigm, and others in the other.

As a philosopher I can only say that he is misusing Kuhn's concept of 'paradigm' slightly. A paradigm is not just another interpretation of empirically equivalent theories.

Oops, just saw that MigL already made that point.

Edited September 6Sep 6 by Eise

22 minutes ago, Eise said:

Hmmm... Kip Thorne has a whole chapter in Black Holes and Time Warps wherein he states that we can't really know if spacetime is really curved.

I don't know why he would say that. The curvature of the spacetime surrounding the earth is very small but ought to be measurable in principle or with high-precision instruments. It's not clear to me that there have been sufficient measurements to actually prove spacetime curvature, but the Pound-Rebka experiment plus some very reasonable assumptions do indicate spacetime curvature beyond doubt in my mind.

Edited September 6Sep 6 by KJW

56 minutes ago, KJW said:

The curvature of the spacetime surrounding the earth is very small but ought to be measurable in principle or with high-precision instruments.

And the 'curvature at the singularity of a Black Hole is infinite.
Which means that the equations which describe the singularity and the concept of curvature cannot be applied in that domain.
Mostly because it is a 'made up' concept, and while you can measure 'effects' because reality acts ( for the most part ) like it is curved, the 'concept is not applicable in some extreme situations.

6 hours ago, KJW said:

No, spacetime curvature is not merely an abstract theoretical notion. It is a measurable physical quantity.

Back when we looked at gravity as a force, was it considered merely an abstract theoretical notion, and not a measurable physical quantity? Or like spacetime curvature now, did we think gravity as a force "is not merely an abstract theoretical notion. It is a measurable physical quantity."?

Seems like many scientists opt for methodological naturalism, which is to take an "as if" approach to math descriptions of phenomena...the math works "as if" objects are following a curved spatial path in the areas where there are large masses. One can use the math but remain agnostic as to spacetime actually being curved. So one can call G a pseudoforce or a force, depending on how far you are willing to go with the curvature description. @zapatos and I start walking towards the North Pole and we will eventually meet as we travel a curved surface. Since we believe the Earth's curvature is real, the "force" that causes us to bump into each other at 90° N is understood as a pseudoforce.

If you don't like breaking Ockham's razor, you probably would prefer to take curvature as real rather than devise some complex scheme where space is actually flat but all these things keep manifesting redshifts, delays, lensing and deflections that weirdly imitate a curvature of spacetime.

Edited September 6Sep 6 by TheVat
Blsnfigurmgli

6 minutes ago, TheVat said:

Since we believe the Earth's curvature is real, the "force" that causes us to bump into each other at 90° N is understood as a pseudoforce.

One definition of force is rate of change of momentum, which is what happens when you bump into someone.

1 hour ago, MigL said:

And the 'curvature at the singularity of a Black Hole is infinite.
Which means that the equations which describe the singularity and the concept of curvature cannot be applied in that domain.
Mostly because it is a 'made up' concept, and while you can measure 'effects' because reality acts ( for the most part ) like it is curved, the 'concept is not applicable in some extreme situations.

That's irrelevant to the point I'm making, which is that spacetime curvature is a physically real quantity (or at least as physically real as anything else). Just because we don't understand what happens inside a black hole does not mean that spacetime curvature isn't physically real. However, I am making a distinction between the theory of general relativity and spacetime curvature. I'm not actually claiming that general relativity is correct. For one thing, I know that general relativity is a classical theory that doesn't describe the quantum domain. But spacetime curvature exists as a physical quantity quite independently of general relativity. The mere fact that spacetime curvature can be measured proves its existence as a physically real quantity. And my use of the word "proves" highlights the distinction I make between a theory and physical quantity.

1 hour ago, zapatos said:

Back when we looked at gravity as a force, was it considered merely an abstract theoretical notion, and not a measurable physical quantity? Or like spacetime curvature now, did we think gravity as a force "is not merely an abstract theoretical notion. It is a measurable physical quantity."?

Until we discovered general relativity, we did not know what caused gravity. We knew that two masses in close proximity tended to be attracted to each other, but we did not know why. The attraction is physically real as are the forces associated with gravity. General relativity didn't change that. But before general relativity it was implicitly assumed that spacetime is flat, and therefore we were missing the key to explaining the nature of gravity, and had to invoke a mysterious gravitational force. But we now know that spacetime curvature physically exists and that this provides a genuine explanation of gravity. But even if our knowledge of gravity does improve in the future, this is not going to remove spacetime curvature any more than the attraction between masses and the forces associated with gravity were removed by general relativity.

Edited September 6Sep 6 by KJW

2 minutes ago, studiot said:

One definition of force is rate of change of momentum, which is what happens when you bump into someone.

Irrelevant to my analogy which is that there's no invisible force pulling objects towards each other as they go towards the north pole. Forget the bumping part. It's just the geometry of a sphere.

49 minutes ago, KJW said:

The mere fact that spacetime curvature can be measured proves its existence as a physically real quantity. And my use of the word "proves" highlights the distinction I make between a theory and physical quantity.

You cannot put a measuring tape to space-time and measure the deviation from flat, but you can measure the effects of curved space-time on bodies, or phenomena, within it.
Similarly, I can measure the effects of a Phonon in a crystal lattice.
Should I take a Phonon as a 'real' particle ?
Or should I consider it a mathematical construct that aids calculation ?

We do not see, or measure, 'reality', only its effects.

Edited September 6Sep 6 by MigL

22 minutes ago, MigL said:

You cannot put a measuring tape to space-time and measure the deviation from flat

Why not?

22 minutes ago, MigL said:

We do not see, or measure, 'reality', only its effects.

Well, I did actually say in the beginning that the curvature of spacetime is as real as anything else. So, if you prefer to diminish the reality of everything else, then that doesn't conflict with what I said. I was merely making the distinction between an abstract theoretical notion and a physically measurable notion, with spacetime curvature being the latter rather than the former.

1 hour ago, TheVat said:

Irrelevant to my analogy which is that there's no invisible force pulling objects towards each other as they go towards the north pole. Forget the bumping part. It's just the geometry of a sphere.

Of course its not irrelevant.

A body cannot move itself without external interation.

(newton's first law)

So there must be

1 hour ago, TheVat said:

I start walking towards the North Pole and we will eventually meet as we travel a curved surface. Since we believe the Earth's curvature is real, the "force" that causes us to bump into each other at 90° N is understood as a pseudoforce

The walking involves some real force (probably friction).

The exzample is not a good one for gravity.

A bodies motion through the curved space is free fall.

42 minutes ago, MigL said:

You cannot put a measuring tape to space-time and measure the deviation from flat, b

Can't one measure a spacetime interval with two beams of light directed from an observer at two different events? (eg moon rise and moon set)

11 minutes ago, KJW said:

Why not?

You can measure how light bends around massive objects, Shapiro delay, gravitational lensing or interference fringes due to gravitational waves ( LIGO ).
You can measure how gravitational time dilation modifies clocks ( any type, even light frequency ).
You can measure the trajectory along geodesics of massive objects in free fall.
The bolded words are what is actually being measured.

The left hand side of the EFEs represent the geometry of space-time, and g , the metric tensor is the tangent space connector ( affine ).
This is not an actual measurement, but a mathematical construct to aid calculations.

I would say we have different definitions of 'real'.
( I hope you don't also believe space-time has a 'fabric' 🙂 )

1 hour ago, MigL said:

You can measure how light bends around massive objects, Shapiro delay, gravitational lensing or interference fringes due to gravitational waves ( LIGO ).
...
You can measure the trajectory along geodesics of massive objects in free fall.

I don't necessarily see these as proof of spacetime curvature, which is why I didn't mention them, but focused instead on spacetime geometry.

1 hour ago, MigL said:

You can measure how gravitational time dilation modifies clocks ( any type, even light frequency ).

I already mentioned the Pound-Rebka experiment. This actual experiment plus a number of very reasonable assumptions that could be the result of experiments yet to be performed would provide data that would prove the existence of spacetime curvature as a physical quantity. By the way, I don't need to determine all the independent components of the curvature tensor, one non-zero component will suffice.

You said I can't directly measure the geometry of spacetime, and I asked why not. You told me what has been measured but didn't answer why I can't measure the spacetime metric.

1 hour ago, MigL said:

The left hand side of the EFEs represent the geometry of space-time, and g , the metric tensor is the tangent space connector ( affine ).
This is not an actual measurement, but a mathematical construct to aid calculations.

The EFEs is a system of PDEs whose solution is the metric tensor field corresponding to the measured energy-momentum tensor field source term on the right-hand side of the equation. This is part of the theory and not what I'm talking about.

1 hour ago, MigL said:

I would say we have different definitions of 'real'.

If something can be physically measured, even if it involves some calculation based on a definition, it's real. Thus, because the Riemann curvature is mathematically defined in terms of the metric tensor, measuring the metric tensor makes the Riemann curvature physically real.

2 hours ago, studiot said:

Of course its not irrelevant.

A body cannot move itself without external interation.

(newton's first law)

So there must be

The walking involves some real force (probably friction).

The exzample is not a good one for gravity.

A bodies motion through the curved space is free fall.

My analogy was to the difference between a force and a pseudo force, with reference to geometry, not really about the details you speak of. It's an analogy I've heard pro physicists use. If it works better for you some other way, that's cool. If you reread my original comment, I hope this will be clearer in this context. If I'm speaking of G as a pseudo force, then of course there is still the electrostatic force from atoms of the earth on my atoms, resisting my normal free fall along a spacetime geodesic.

ETA: if you're more comfortable with, say, the coriolis effect, that can also be used as an example of an analogous pseudo force. As the missile launched towards the north pole seems to veer off-course this is not an invisible force but the effect of a rotating reference frame.

23 minutes ago, TheVat said:

My analogy was to the difference between a force and a pseudo force, with reference to geometry, not really about the details you speak of. It's an analogy I've heard pro physicists use. If it works better for you some other way, that's cool. If you reread my original comment, I hope this will be clearer in this context. If I'm speaking of G as a pseudo force, then of course there is still the electrostatic force from atoms of the earth on my atoms, resisting my normal free fall along a spacetime geodesic.

I fully understand virtual or imaginary forces as I prefer to call them (after D'Alembert who invented the method)

But my point is that your example was not a good one.

The walkers could just as easily stand still, involving no forces, pseudo or otherwise.

https://en.wikipedia.org/wiki/Free_fall

In classical mechanics, free fall is any motion of a body where gravity is the only force acting upon it

...

In the context of general relativity, where gravitation is reduced to a space-time curvature, a body in free fall has no force acting on it.

3 hours ago, studiot said:

But my point is that your example was not a good one.

The walkers could just as easily stand still, involving no forces, pseudo or otherwise.

I think somewhere along the way, you got the impression that the north pole analogy was meant to be an example of physical forces. The analogy was for the benefit of another member and was specifically about how geometry (in the analogy, of a sphere with designated poles) can create the illusion of a force. I'm sorry if that wasn't clear. All the stuff you're posting about free fall and so on I'm well aware of, as I had thought my posts had made clear. The polar trip analogy is only about imagining a mysterious force (i.e. an illusory force) which seems to be drawing two objects (starting at different longitudes) together and seeing how the illusion arises from converging lines of longitude. As an analogy, it is in no way, shape or form intended to provide some comprehensive bookkeeping on the actual forces acting upon northward moving objects.

Hope this clarifies it. The experience, on my end, has been something like showing someone young how seasons work by shining a lamp on a globe and someone else keeps objecting that the sun is really much farther from the earth and the globe should really be much smaller. All true statements, but not really germane to the simple concept that is being demonstrated.

Edited September 7Sep 7 by TheVat

17 hours ago, KJW said:

I don't know why he would say that.

Well, he wouldn't write a whole chapter about it, if it were not true, would he? As said before, some calculations are easier using the 'flat space'. E.g. he mentions calculations about gravitational waves produced by neutron stars orbiting each other.

The flat spacetime paradigm's laws of physics can be derived from the curved spacetime paradigm's laws, and conversely. This means that the two sets of laws are different mathematical representations of the same physical phenomena

<...>

Theoretical physicists, as they mature, gradually build up insight into which paradigm will be best for which situation, and they learn to flip their minds back and forth from one paradigm to the other, as needed.

So is spacetime really curved? The question has no empirical relevance.

A bit like wave/particle duality; is light a wave or a particle ?
Well, it depends on the experiment used to detect it ( ie, measure it ).

Could be both; could be neither.
Because we're not actually measuring it; we measure how it acts on other things.

8 hours ago, Eise said:

Well, he wouldn't write a whole chapter about it, if it were not true, would he? As said before, some calculations are easier using the 'flat space'. E.g. he mentions calculations about gravitational waves produced by neutron stars orbiting each other.

So is spacetime really curved? The question has no empirical relevance.

Was I wrong (or is it irrelevant) to see flat spacetime as a kind of curved spacetime?

"Flat spacetime" just being an idealized limit of spacetime which is always curved to one degree or another?

9 hours ago, Eise said:

Well, he wouldn't write a whole chapter about it, if it were not true, would he?

That's an argument from authority.

9 hours ago, Eise said:

As said before, some calculations are easier using the 'flat space'. E.g. he mentions calculations about gravitational waves produced by neutron stars orbiting each other.

Physicists do have a tendency to approximate physics for the sake of ease of calculation. I'm not a physicist. I'm not interested in approximations. I would rather see an exact expression, even if it is of an idealised universe. When you use an approximation, you may miss out on some salient point. For example, you mentioned gravitational waves. It is commonly believed that gravitational waves carry energy-momentum. No, they don't! (But that's another discussion for later.) The point is that the treatment of gravitational waves as an approximation is flawed.

9 hours ago, Eise said:

The flat spacetime paradigm's laws of physics can be derived from the curved spacetime paradigm's laws, and conversely. This means that the two sets of laws are different mathematical representations of the same physical phenomena

<...>

Theoretical physicists, as they mature, gradually build up insight into which paradigm will be best for which situation, and they learn to flip their minds back and forth from one paradigm to the other, as needed.

This doesn't say anything. Is he talking about the tetrad formalism? In that formalism, the metric is everywhere Minkowskian, but that doesn't make the spacetime flat because one now has an object of anholonomy to deal with and where the spacetime curvature resides.

9 hours ago, Eise said:

So is spacetime really curved? The question has no empirical relevance.

And yet, when I drop a pen, it falls to the ground.

21 minutes ago, KJW said:

That's an argument from authority.

Yes, it is. So what? I see Kip Thorne as an authority. Don't you agree? (Standard text book on Gravity, one of of scientific minds behind LIGO.)

22 minutes ago, KJW said:

I'm not a physicist.

That is obvious for me now.

24 minutes ago, KJW said:

Is he talking about the tetrad formalism?

No. Search further. (Or ask ChatGPT...)

24 minutes ago, KJW said:

And yet, when I drop a pen, it falls to the ground.

Yep. That is an empirical fact.

Stop being angry. Read Thorne, I would say.

3 hours ago, MigL said:

A bit like wave/particle duality; is light a wave or a particle ?

I would say Matrix mechanics and Wave Mechanics would be a better example.

1 hour ago, Eise said:

Yes, it is. So what? I see Kip Thorne as an authority. Don't you agree? (Standard text book on Gravity, one of of scientific minds behind LIGO.)

Perhaps. But I will look at the mathematics before I look at who wrote it. And yes, I've read stuff by Kip Thorne.

1 hour ago, Eise said:

1 hour ago, KJW said:

I'm not a physicist.

That is obvious for me now.

But don't take that to mean that I don't know what I'm talking about. What I'm saying is that I have a different mindset. Are you a physicist?

1 hour ago, Eise said:

No. Search further. (Or ask ChatGPT...)

What am I supposed to search for? I feel the need to point out that I've already read a lot about general relativity. And not pop-science books, actual textbooks, including textbooks on Ricci calculus. And I even perform mathematical derivations of my own.

1 hour ago, Eise said:

1 hour ago, KJW said:

And yet, when I drop a pen, it falls to the ground.

Yep. That is an empirical fact.

And why do things fall to the ground? It's because we are in an accelerated frame of reference. But people all over the globe can say the same thing. Everyone is accelerating away from the surface of the earth. And that implies that the spacetime around the earth is curved because there is no global frame of reference in which everyone's acceleration is zero.

1 hour ago, Eise said:

Stop being angry.

What makes you think I'm angry?

16 minutes ago, KJW said:

And that implies that the spacetime around the earth is curved because there is no global frame of reference in which everyone's acceleration is zero.

Why doesn't it Imply a universal force of attraction between objects with mass? (Still trying to understand the arguments.)

4 minutes ago, zapatos said:

24 minutes ago, KJW said:

And that implies that the spacetime around the earth is curved because there is no global frame of reference in which everyone's acceleration is zero.

Why doesn't it Imply a universal force of attraction between objects with mass? (Still trying to understand the arguments.)

The notion of gravity as a force contradicts itself: If you shine a beam of light upward, the gravitational force on the beam causes its frequency to decrease (the decrease in frequency is itself an empirical fact). This decrease in frequency is directly proportional to the frequency of the beam. This implies that the gravitational redshift is a time dilation. The time dilation¹ implies that the spacetime is curved. The curvature of spacetime contradicts that the gravitation is a force. It should be noted that when being accelerated upward in the absence of gravitation, there are the same forces experienced as there are in gravity, and the same time dilation¹, but no mass causing the attraction.

¹ Time dilation itself does not imply spacetime curvature. On earth, it does imply spacetime curvature, but in the accelerated spaceship it does not.

Edited September 7Sep 7 by KJW