5 hours ago, Moontanman said:

I know I am ignorant on this topic but I would be surprised to find out, that if no one knows how a charge creates an electrical field, that no one is looking into the problem.  

How would one test a hypothesis concerning this?

20 hours ago, Genady said:

Does the QFT provide a sufficient answer?

 

21 hours ago, Moontanman said:

how a charge creates an electrical field

It does not. Not in QED, the best current theory.

 

I didn't learn QED, but I found on Wikipedia:

Quote

QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of photons and represents the quantum counterpart of classical electromagnetism giving a complete account of matter and light interaction.^[2][3]

This is great. Exchange of photons is what I have in mind (although a bit differently).

The fact that the electromagnetic field was successfully "discarded", opens the possibility for the GR geometric model for gravity to be also replaced with some kind of quantum theory, as KJW suggested:

On 3/8/2024 at 9:53 PM, KJW said:

2, mass causes spacetime curvature through a mechanism associated with something like quantum physics, the fundamental forces of nature, or perhaps something entirely different.

 

3 minutes ago, DanMP said:

the electromagnetic field was successfully "discarded"

It was not. It is rather the other way around. Photons are quantum excitations of EM field. The QED and other QFT theories describe interactions of fields. (QFT = Quantum Field Theory.)

2 minutes ago, Genady said:

It was not. It is rather the other way around. Photons are quantum excitations of EM field. The QED and other QFT theories describe interactions of fields. (QFT = Quantum Field Theory.)

Indeed. Sorry.

Well, then the question about the field changes to: what are the fields and how they were created?

Just now, DanMP said:

Indeed. Sorry.

Well, then the question about the field changes to: what are the fields and how they were created?

What they are is described by specific QFT theories. Generally, field is an entity that pervades space and time and is defined by its properties such as spin.

"How they were created" goes back to the dawn of the universe.

Ok, thank you!

18 hours ago, swansont said:

How would one test a hypothesis concerning this?

Good question, I have no idea, I was not asserting that we need to be looking into it but knowing the curiosity of humans I would be surprised if no one has looked into it. 

Edited March 13, 20241 yr by Moontanman

2 hours ago, Moontanman said:

Good question, I have no idea, I was not asserting that we need to be looking into it but knowing the curiosity of humans I would be surprised if no one has looked into it. 

This is one of those “why are things the way they are” that physics can't address, because we can only observe how things behave. Bare charges and their electric field come as a set. 

13 hours ago, swansont said:

This is one of those “why are things the way they are” that physics can't address, because we can only observe how things behave. Bare charges and their electric field come as a set. 

Nicely put. I also do not know of masses that do not have a gravitational field, resp without 'curving' spacetime. And that is an important reason for me not to see a causal relationship between mass and curved spacetime. 

5 hours ago, Eise said:

Nicely put. I also do not know of masses that do not have a gravitational field, resp without 'curving' spacetime. And that is an important reason for me not to see a causal relationship between mass and curved spacetime. 

Can we bottle (or just create) spacetime curvature and thereby  create (or annihilate) mass?

That might  be a causal relationship. 

Edited March 14, 20241 yr by geordief

2 minutes ago, geordief said:

Can we bottle (or just create) spacetime curvature and thereby  create (or annihilate) mass?

That might  be a causal relationship. 

Spacetime curvature is associated with radiation. The latter does not have mass.

On 3/12/2024 at 11:10 PM, Eise said:

Hmm. I don't think naming it a cause, and even a mechanism, is a good way expressing the relationship between mass and spacetime curvature. In my opinion that would mean that physics would be able to describe the mechanism, and that implies new laws of nature. I think that we recognise mass because of its curvature (or inertia).

Nobody asks for how a charge 'causes' an electrical field. So why should one do it for a gravitational field, even if we now know that this field is a geometrical curvature of spacetime?

So if these are the only two possibilities, I opt for option 1.

Option 2 is saying that general relativity is not the most fundamental theory of physics. The dimension of mass is not only associated with gravitation, but is everywhere in physics. The current definition of a unit of mass is not even based on being a gravitational source, but rather specifies a numeric value of Planck's constant.

However, if mass is quantum mechanically producing spacetime curvature, then that spacetime curvature must also be consistent with general relativity.

There was a time that I believed in option 1 but in more recent times I have felt that spacetime curvature is too ethereal to provide us with anything other than gravitation. On the other hand, I find it difficult to accept that there may be some physics that isn't entirely based on the properties of spacetime.

 

The group of symmetry of electromagnetism is U(1) (complex numbers of length 1), and electrical charges are at the centre of it.

From the POV of symmetries, conservation laws, and irreducible representations of groups (particle multiplets) QFT of electromagnetism and its brethren --weak interaction, strong interaction-- is more user-friendly by orders of magnitude. Things kinda "fall into boxes."

GR is not like that. Not by a long shot.

The group of symmetry of GR is basically just any differentiable transformation of the coordinates. Once there, after one picks a set of coordinates that locally make a lot of sense (they solve the equations easy, yay!), they could go terribly wrong globally, so that one must introduce singular coordinate maps to fix the blunder.

Because the symmetry group of GR is this unholy mess, group theory doesn't help much, if at all. The equations are non-linear, so: Are there any solutions that might help clarify divergences, and so on, that we might have missed entirely? Who knows.

In my opinion, the very fact that the set of coordinates that, locally, happens to be the most reasonable one could (and sometimes does) totally obscure the meaning of the coordinates far away from the local choice, and thereby their predictive power out there, makes the status of any parameters that the theory suggests (mass in particular) much less helpful than charge is in EM.

Mass to GR is nowhere near anything like charge is to Yang-Mills theory (our paradigm of an honest-to-goodness QFT field theory).

 

14 hours ago, joigus said:

Mass to GR is nowhere near anything like charge is to Yang-Mills theory (our paradigm of an honest-to-goodness QFT field theory).

That’s because mass never appears in the GR field equations - what is generally called the source term here is the energy-momentum tensor. One must also remember what these equations actually say - they state a local equivalence between a certain combination of components of the Riemann tensor (the Einstein tensor) and the energy-momentum tensor. Nowhere does it claim a ‘causative relationship’, but instead it says that these two are the same thing (up to a constant of course); neither one comes first and ‘causes’ the other.

 

1 hour ago, Markus Hanke said:

Nowhere does it claim a ‘causative relationship’,

In spite of this, a 'causative relationship' exists operationally, i.e., we can, in principle, manipulate the source and this would affect geometry, but there is no way to manipulate geometry without manipulating the source. The 'symmetry' is broken.

 

4 hours ago, Markus Hanke said:

That’s because mass never appears in the GR field equations - what is generally called the source term here is the energy-momentum tensor. One must also remember what these equations actually say - they state a local equivalence between a certain combination of components of the Riemann tensor (the Einstein tensor) and the energy-momentum tensor. Nowhere does it claim a ‘causative relationship’, but instead it says that these two are the same thing (up to a constant of course); neither one comes first and ‘causes’ the other.

Indeed. I --and others, you among them-- have said it before elsewhere on the forums, actually. It's the energy-momentum that sources the gravitational field.

I also agree with the absence, of necessity, of any causal connection between the Einstein tensor and the energy-momentum tensor.

16 hours ago, Markus Hanke said:

That’s because mass never appears in the GR field equations - what is generally called the source term here is the energy-momentum tensor. One must also remember what these equations actually say - they state a local equivalence between a certain combination of components of the Riemann tensor (the Einstein tensor) and the energy-momentum tensor. Nowhere does it claim a ‘causative relationship’, but instead it says that these two are the same thing (up to a constant of course); neither one comes first and ‘causes’ the other.

One can't dismiss a causative relationship between two quantities simply because the mathematical relation between them is an equality. One really needs to examine the logical aspect of the relationship to establish whether there is a causative relationship and in which direction it occurs.

In the case of the Einstein equation, what one really has is a connection between the mathematical realm and the physical realm. Without the Einstein equation, all one has is Ricci Calculus. It is the Einstein equation that transforms this to General Relativity. The Einstein equation does two things: 1, it establishes that it is the mathematical Einstein tensor that corresponds to the physical energy-momentum tensor; and 2, it establishes a proportionality relationship between them, including the use of physical constants to ensure dimensional homogeneity.

 

 

18 hours ago, Genady said:

In spite of this, a 'causative relationship' exists operationally, i.e., we can, in principle, manipulate the source and this would affect geometry, but there is no way to manipulate geometry without manipulating the source. The 'symmetry' is broken.

 

2 hours ago, KJW said:

One can't dismiss a causative relationship between two quantities simply because the mathematical relation between them is an equality. One really needs to examine the logical aspect of the relationship to establish whether there is a causative relationship and in which direction it occurs.

While these comments are certainly true, I think the relationship isn’t as trivial as it might appear; after all, a vanishing Einstein tensor doesn’t necessarily imply a flat spacetime, so these equations form only a local constraint on geometry, but they don’t uniquely determine it. Any background geometry is as much considered to be a ‘source’ as is local energy-momentum, when it comes to working out the particular form of a metric at a certain event. Furthermore you have the non-linearities of the constraint itself, which, in some sense, might also be considered a ‘source’. But those contributions of course don’t explicitly appear.

Personally, I just think of spacetime as pure geometry - the only difference between vacuum and non-vacuum is how the Riemann tensor decomposes (Weyl and Ricci curvature), so I envision it purely geometrically all the way. In that way of thinking, no question of causation arises, you just have ever-shifting geometries.

But maybe that’s just weird old me

I don't know about you guys but to me this is one of the most interesting threads we've had in a while!

11 hours ago, Markus Hanke said:

Any background geometry is as much considered to be a ‘source’ as is local energy-momentum, when it comes to working out the particular form of a metric at a certain event.

Unclear to me what "any background geometry" would be here.  As @Genady pointed out, causation can be defined operationally, e.g.  I push two distant planets together and local curvature increases in "response" to greater local mass.  The stress-energy tensor includes mass, right?  Energy density is the whole thing in GR context - rest mass, pressure,  momentum etc?

I agree with @Moontanman on how interesting this thread is.  I wish I had spent more time in my youth on physics instead of counting cougar scat.

11 hours ago, TheVat said:

Unclear to me what "any background geometry" would be here. 

This would be contributions from distant sources, as opposed to local ones, as well as contributions from any non-zero cosmological constant. Basically anything that stops spacetime from being completely flat before you account for any local energy-momentum.

11 hours ago, TheVat said:

As @Genady pointed out, causation can be defined operationally, e.g.  I push two distant planets together and local curvature increases in "response" to greater local mass.

I agree, in this type of scenario you have clear causation in an operational sense. However, I was really thinking more of an isolated system where all parts remain in free fall at all times. Energy-momentum is locally conserved (the divergence of the tensor vanishes) - but then so is curvature (Einstein tensor). You cannot locally create nor destroy Einstein curvature, any more than you can create or destroy energy-momentum. You can only shift these around, and have them change form - so which ‘causes’ which?

11 hours ago, TheVat said:

The stress-energy tensor includes mass, right?

Not directly, but it contains energy density.