B Does Spacetime Have Physical Existence?

[Uncle Thi]

You can do $F=kma$ with slugs, furlongs and microfortnights if you choose. With the SI units, $k=1$ which makes life a bit easier.

This answer doesn't make me fully understand the meaning. You should be careful with your response, as it might get a warning, lead to the post being locked, or end the discussion. I'm just trying to learn, but it seems like not having formal education is an issue here?
Thank you.

 

[PeterDonis]

You should be careful with your response, as it might get a warning, lead to the post being locked, or end the discussion.

I'm not sure where you're getting that from, but nothing @jbriggs444 has posted comes anywhere near meriting any of those things.

it seems like not having formal education is an issue here?

I don't know where you're getting that from either. You have been getting good responses in this thread.

 

[PeterDonis]

Technically speaking, the "gravitational force" is not the upward supporting force of the table on the book. It is the fictitious downward force that we imagine to hold the book in place despite that upward force."*

In GR, no force needs to "hold the book in place despite that upward force". The upward force pushes the book off of the geodesic (free-falling) trajectory it would otherwise follow, so that the book now has nonzero proper acceleration due to the upward force on it. That is the relativistic version of Newton's Second Law: any nonzero proper acceleration has to be caused by a force.

In GR, if there were truly a downward force on the book equal and opposite to the upward force on it, it would not have a nonzero proper acceleration and it would follow a different trajectory--the same trajectory it would follow in free fall, since the net force on it would be zero.

Note that in the above analysis I have been implicitly using a local inertial frame. It is true that in a non-inertial frame, such as the rest frame of the table, a "fictitious" force is usually said to be acting downward on the book to "hold it in place". But this fictitious force cannot be felt and does not correspond to any proper acceleration. And in GR, that means it isn't a force at all; in GR, only things that cause nonzero proper acceleration are considered to be forces. This is a much simpler and more physically reasonable viewpoint than the viewpoint of Newtonian physics, where the "gravitational force" is considered to be a real force--and then a separate ad hoc explanation needs to be given for why this force is not felt; objects in free fall in a gravitational field are weightless, feeling no force at all.

 

[pervect]

In my view, the definition of 'physical' implies that an entity must objectively exist in the real world, and this physical entity must have measurable quantities.
---
Based on that definition, could you clearly define the following:

1. What is space?
2. What is time?
3. What is light?

I have no idea how you think you can tell if something "objectively exists", especially via experiment (which is what science is primarily about), so I won't address this part of your question. You're on your own, enjoy.

I think things might go better if we discuss Euclidean geometry for a moment, and once we have a common understanding or an agreement to disagree about that, we can revisit relativity. At least I'll attempt to -as I wrote this, things started to branch out a bit.

One can measure distance with a ruler. So, I'd assume you would share the belief that it's a physical quantity. "Entity" seems to be a bit on the wrong track to me, I don't usually think of distance as an "entity". But that may be just the way I use the words.

I would say that geometry, which I think of as the study of distance, is more of a mathematical structure. So, we have "physical" distance, and the theoretical structure of Euclidean geometry that organizes it. Note that we have some closely related alternatives to Euclidean geometry, for instance spherical and hyperbolic geometries. And, somewhat importantly for later on, we have Riemannian geometry.

Now, let's move on to relativity.

The organization principle of special (and general) relativity basically replaces "distance" with the "Lorentz interval".

So, the obvious the next question would be - is the Lorentz interval real? An argument for, is that it's the same for all observers. Distance, in special relativity, is NOT the same for all observers. Proper time, the sort of time one measures with a clock, falls into the category of a Lorentz interval, and proper distance, the sort of distance one measures with a ruler, also falls in the category of the Lorentz interval. So I would put proper distance, proper time, and the Lorentz interval all into the "physical" category.

As an aside, I view most tensor quantities as "existing". This may not help if you are not familiar with tensor quantites. The key point of tensor quantities is that while they may have components that depend on the observer, the structure as a whole has rules that allow these components to be transformed between observers. Sorry if you're not familiar with tensors, this may be moot. If you are familiar and have some thoughts about whether tensors are "real", you could consider sharing these thoughts in the intersts of communication and discussion.

Going back to the Lorentz interval - I imagine one could come up with an argument that The Lorentz interval is a mathematical construct of some sort, but that's not my view. While one could argue about that, my personal reaction is that it is the sort of argument that doesn't go anywhere I find interesting, it's mostly about semantics.

This discussion may not help if you're not familiar with the Lorentz interval. Sorry about that if that's the case. Taylor & Wheeler's "space-time physics" talks about them a lot, I have always found "The Prable of the Surveyor" to be particular helpful, for whatever that's worth. Realistically, though, if you're not already familiar with the term and its implications, it would probably be a huge digression to talk about it. If you're interested in relativity, it'd be worth your time, it's just wouldn't be appropriate for this thread.

We can regard the organizational principles of the Lorentzian geometry, the geometry of the Lorentz interval, in the same category that we put Euclidean geometry, the study of distances. Special relativity is then a particular case of the geometry of the Lorentz interval, one that applies to "flat" spacetimes. General relativity opens things up to different geometries. General relativity basically applies Riemannian geometry to the Lorentz interval. (Some purists call it pseudo-Riemannian geometry for technical reasons).

The fact that one can apply the structure of a geometry (Euclidean or Riemannian) to multiple physical concepts is one argument for why I think of them as being organizational structures rather than physical entities.

So to recap the points I think are most important. "Distance" and "Lorentz intervals" are IMO physically measurable quantities which exist independent of the observer. The organization of either into a geometry is more mathematical. The same math can be used to organize different things, the math assumes some basic axioms, if the axioms fit the physics, we apply the structure of the math to the physical objects to draw conclusions.

 

[Uncle Thi]

How much physics do you actually know?

My physics knowledge is just at a high school level and what I've gathered from the internet."

I thought science was about critical thinking and questioning to find the truth, not just memorizing knowledge without reasoning. Is physics about open-minded exploration, or is it just about repeating what has been taught?"

By the way, what I’m presenting here is actually mainstream science in Vietnam!

According to my high school knowledge: A theoretical model without any physical quantities cannot be considered a physical model. Is that correct?

 

[Uncle Thi]

In GR, no force needs to "hold the book in place despite that upward force". The upward force pushes the book off of the geodesic (free-falling) trajectory it would otherwise follow, so that the book now has nonzero proper acceleration due to the upward force on it. That is the relativistic version of Newton's Second Law: any nonzero proper acceleration has to be caused by a force.

In GR, if there were truly a downward force on the book equal and opposite to the upward force on it, it would not have a nonzero proper acceleration and it would follow a different trajectory--the same trajectory it would follow in free fall, since the net force on it would be zero.

Note that in the above analysis I have been implicitly using a local inertial frame. It is true that in a non-inertial frame, such as the rest frame of the table, a "fictitious" force is usually said to be acting downward on the book to "hold it in place". But this fictitious force cannot be felt and does not correspond to any proper acceleration. And in GR, that means it isn't a force at all; in GR, only things that cause nonzero proper acceleration are considered to be forces. This is a much simpler and more physically reasonable viewpoint than the viewpoint of Newtonian physics, where the "gravitational force" is considered to be a real force--and then a separate ad hoc explanation needs to be given for why this force is not felt; objects in free fall in a gravitational field are weightless, feeling no force at all.

Does your example actually fit the meaning of spacetime?

 

[jbriggs444]

My physics knowledge is just at a high school level and what I've gathered from the internet.

The information delivered here is more reliable than pretty much any high school and definitely better than 99% of the popular science videos on the internet.

By the way, what I’m presenting here is actually mainstream science in Vietnam!

If true, that is unfortunate for Vietnam.

According to my high school knowledge: A theoretical model without any physical quantities cannot be considered a physical model. Is that correct?

A theoretical model that makes predictions that can be experimentally tested can be considered a physical model. If those predictions turn out to be uniformly correct then it may be considered a reliable model.

That said, not many people run around worrying about the defining characteristics of a "physical model". It is more useful to shut up and do physics.

Does your example actually fit the meaning of spacetime?

As a rule, what @PeterDonis writes is highly reliable. The content in the passage you quote is not at all controversial and definitely fits with spacetime as described by general relativity.

 

[phinds]

I thought science was about critical thinking and questioning to find the truth, not just memorizing knowledge without reasoning.

That is correct. If you think that what is going on here at PF is anything other than this, then you are badly misunderstanding what IS going on.

I am puzzled. Presumably you have joined PF so as to get answers to science questions from people who know what they are talking about and if that is so, then you have come to the right place. What I don't understand is why you seem to believe that we are NOT giving you the right answers to your questions.

If you have "learned" your science from popular science presentations, then that would explain why you have a poor understanding of existing science.

 

[Dale]

I thought science was about critical thinking and questioning to find the truth, not just memorizing knowledge without reasoning.

Science is about the scientific method. Critical thinking is great, but only when one actually has the experimental evidence in mind while doing so.

I recommend that you start here: https://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html

Scientists don’t accept relativity because we find it appealing. We accept it because of the strength of the experimental evidence supporting it.

 

[PeterDonis]

I thought science was about critical thinking and questioning to find the truth, not just memorizing knowledge without reasoning. Is physics about open-minded exploration, or is it just about repeating what has been taught?"

I think you are under a serious misapprehension about why you were asked how much physics you actually know. The question was not asking how much formal physics education you have. It was asking how much physics you know--as in, how much physics have you actually exercised critical thinking and questioning about, instead of just memorizing knowledge without reasoning.

By the way, in your definition of science, you left out one critical component: experiments. Science is about critical thinking and questioning to find the truth by doing experiments to test our models.

(This, by the way, should help to point you to good answers to the questions I pose to you at the end of this post. You are expected to use critical thinking to answer them.)

By the way, what I’m presenting here is actually mainstream science in Vietnam!

Do you have a reference?

According to my high school knowledge: A theoretical model without any physical quantities cannot be considered a physical model.

What are "physical quantities"? If I hand you a theoretical model, how do you tell whether it has "physical quantities" in it or not?

 

[PeterDonis]

Does your example actually fit the meaning of spacetime?

Um, yes?

What do you think "the meaning of spacetime" is, if you're not sure whether my example fits it?

 

[Uncle Thi]

According to my high school knowledge: A theoretical model without any physical quantities cannot be considered a physical model. Is that correct?

You still haven't answered my question directly, have you?
Thank you.

 

[Orodruin]

You can do $F=kma$ with slugs, furlongs and microfortnights if you choose. With the SI units, $k=1$ which makes life a bit easier.

That doesn’t make $k\neq 1$ as long as you use the corresponding derived unit of force (slug furlongs per microfortnight squared).

It is always F = ma, but you can get a numerical factor for the measured value from unit conversion. This is no stranger than 1 cm = 0.01 m.

 

[Dale]

You still haven't answered my question directly, have you?

Your question is not relevant to the current discussion. Often, as here, when a post contains multiple questions people will naturally focus on the more important ones, leaving less useful ones unanswered.

However, in the interest of directness:

A theoretical model without any physical quantities cannot be considered a physical model. Is that correct?

That is correct.

It is irrelevant since we are not discussing a “theoretical model without any physical quantities”.

Let me also ask you a direct question: do you believe that the statement “the table top is flat and the legs are perpendicular to the table top” is a physical statement which could be experimentally observed and measured?

 

[PeterDonis]

You still haven't answered my question directly, have you?

You haven't answered the questions I posed to you in response at the bottom of post #40.

 

[Uncle Thi]

In the case of black holes we understand that spacetime takes on a remarkable physical existence, spacetime in such cases even acts as a physical object with mass and rotation for an external observer. It is true that in your daily life you have a normal and smooth relationship with spacetime, but you will think differently if you move at speeds close to the speed of light, or fall into a black hole.

According to your explanation, should I understand that spacetime is a physical entity with mass? If so, in Einstein’s field equations (EFE), can you point out the physical quantity that represents the mass of spacetime? I have been searching for it for a long time but have not found it.

Einstein’s field equations (EFE) are written as:
Gμν + Λ gμν = (8πG / c⁴) Tμν

-------
Thank you.

 

[phinds]

According to your explanation, should I understand that spacetime is a physical entity with mass?

His "explanation" is wrong and should be ignored.

can you point out the physical quantity that represents the mass of spacetime?

There is no such thing.

I have been searching for it for a long time but have not found it.

Not surprising since there is no such thing.

 

[phinds]

@Uncle Thi you REALLY need to read some actual physics texts and stop with these pop-sci questions.

 

[PeterDonis]

According to your explanation

Please note that the post you were responding to there is not a good description of how spacetime is treated in GR.

 

[PeterDonis]

should I understand that spacetime is a physical entity with mass?

Not the way you mean.

in Einstein’s field equations (EFE), can you point out the physical quantity that represents the mass of spacetime?

There isn't one.

What is true is that a black hole is a solution of the EFE which is vacuum (i.e., no matter present), but which looks to an external observer like an object with mass--for example, you can put things in orbit around it and calculate the mass using Kepler's Third Law. But that is not the same as saying there is a quantity in the EFE that represents "the mass of spacetime". There isn't.

 

[Uncle Thi]

His "explanation" is wrong and should be ignored.

There is no such thing.

Not surprising since there is no such thing.

Here is my question:

In Einstein's field equation:

$$G_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}$$

where is the energy-momentum tensor representing matter.
⟹ Spacetime is curved by matter (), but...

My question: If spacetime is not matter, how can this equation be valid when it requires both sides to be mathematically consistent in their physical nature?
---
Is the above question considered a popular science question?

 

[PeterDonis]

Spacetime is curved by matter

Or radiation, or anything else that is included in the stress-energy tensor. Yes, that's what the EFE describes: how spacetime is curved by stress-energy. The LHS is the Einstein tensor, which describes spacetime curvature. The RHS is the stress-energy tensor, which describes the matter and other stuff that causes the curvature.

If spacetime is not matter, how can this equation be valid when it requires both sides to be mathematically consistent in their physical nature?

What does "mathematically consistent in their physical nature" even mean?

Is the above question considered a popular science question?

No, it's considered a vague and ill-defined question.

 

[Orodruin]

My question: If spacetime is not matter, how can this equation be valid when it requires both sides to be mathematically consistent in their physical nature?

If electric field is not charge, how can Maxwell’s equations be valid if they require both sides to be mathematically consistent in their physical nature?

The above is the corresponding question for electromagnetism. I hope you are not suggesting electric fields are made of charge.

Is the above question considered a popular science question?

No. It just does not make sense. Both sides of an equation in physics need to be dimensionally consistent. That does not mean they represent the same thing.

 

[Uncle Thi]

Your question is not relevant to the current discussion. Often, as here, when a post contains multiple questions people will naturally focus on the more important ones, leaving less useful ones unanswered.

However, in the interest of directness:That is correct.

It is irrelevant since we are not discussing a “theoretical model without any physical quantities”.

Let me also ask you a direct question: do you believe that the statement “the table top is flat and the legs are perpendicular to the table top” is a physical statement which could be experimentally observed and measured?

Uncle Thi: A theoretical model without any physical quantities cannot be considered a physical model. Is that correct?

Dale: That is correct.

But it is irrelevant since we are not discussing a “theoretical model without any physical quantities.”
---

I think it is relevant: When you confirm that a theoretical model without any physical quantities cannot be considered a physical model.

Does this mean that spacetime is merely a mathematical model? Because I also cannot find any physical quantities in Einstein’s field equations.

Is that really the case? Am I mistaken?

 

[Ibix]

Because I also cannot find any physical quantities in Einstein’s field equations.

They constrain the metric, which is the quantity that defines distances and angles, to depend on the stress-energy tensor, which describes the matter and radiation content of a region. The angle between two lines or the length of a line is certainly relevant to physics, dictating things like whether two things will meet, or whether one needs to apply a force to stop them separating.

You seem to have categorised parts of the field equations in an arbitrary manner and are now finding that your arbitrary classification leads you into problems. The problem is your expectation that your arbitrary classification should have any consequence.

 

[martinbn]

The problem is that you think you are having a scientific discussion, but you are not. You are trying to have a discussion about the philisophy of science. The problem with that is that one needs to be familiar with the science itself first.

 

[Uncle Thi]

I have no idea how you think you can tell if something "objectively exists", especially via experiment (which is what science is primarily about), so I won't address this part of your question. You're on your own, enjoy.

I think things might go better if we discuss Euclidean geometry for a moment, and once we have a common understanding or an agreement to disagree about that, we can revisit relativity. At least I'll attempt to -as I wrote this, things started to branch out a bit.

One can measure distance with a ruler. So, I'd assume you would share the belief that it's a physical quantity. "Entity" seems to be a bit on the wrong track to me, I don't usually think of distance as an "entity". But that may be just the way I use the words.

I would say that geometry, which I think of as the study of distance, is more of a mathematical structure. So, we have "physical" distance, and the theoretical structure of Euclidean geometry that organizes it. Note that we have some closely related alternatives to Euclidean geometry, for instance spherical and hyperbolic geometries. And, somewhat importantly for later on, we have Riemannian geometry.

Now, let's move on to relativity.

The organization principle of special (and general) relativity basically replaces "distance" with the "Lorentz interval".

So, the obvious the next question would be - is the Lorentz interval real? An argument for, is that it's the same for all observers. Distance, in special relativity, is NOT the same for all observers. Proper time, the sort of time one measures with a clock, falls into the category of a Lorentz interval, and proper distance, the sort of distance one measures with a ruler, also falls in the category of the Lorentz interval. So I would put proper distance, proper time, and the Lorentz interval all into the "physical" category.

As an aside, I view most tensor quantities as "existing". This may not help if you are not familiar with tensor quantites. The key point of tensor quantities is that while they may have components that depend on the observer, the structure as a whole has rules that allow these components to be transformed between observers. Sorry if you're not familiar with tensors, this may be moot. If you are familiar and have some thoughts about whether tensors are "real", you could consider sharing these thoughts in the intersts of communication and discussion.

Going back to the Lorentz interval - I imagine one could come up with an argument that The Lorentz interval is a mathematical construct of some sort, but that's not my view. While one could argue about that, my personal reaction is that it is the sort of argument that doesn't go anywhere I find interesting, it's mostly about semantics.

This discussion may not help if you're not familiar with the Lorentz interval. Sorry about that if that's the case. Taylor & Wheeler's "space-time physics" talks about them a lot, I have always found "The Prable of the Surveyor" to be particular helpful, for whatever that's worth. Realistically, though, if you're not already familiar with the term and its implications, it would probably be a huge digression to talk about it. If you're interested in relativity, it'd be worth your time, it's just wouldn't be appropriate for this thread.

We can regard the organizational principles of the Lorentzian geometry, the geometry of the Lorentz interval, in the same category that we put Euclidean geometry, the study of distances. Special relativity is then a particular case of the geometry of the Lorentz interval, one that applies to "flat" spacetimes. General relativity opens things up to different geometries. General relativity basically applies Riemannian geometry to the Lorentz interval. (Some purists call it pseudo-Riemannian geometry for technical reasons).

The fact that one can apply the structure of a geometry (Euclidean or Riemannian) to multiple physical concepts is one argument for why I think of them as being organizational structures rather than physical entities.

So to recap the points I think are most important. "Distance" and "Lorentz intervals" are IMO physically measurable quantities which exist independent of the observer. The organization of either into a geometry is more mathematical. The same math can be used to organize different things, the math assumes some basic axioms, if the axioms fit the physics, we apply the structure of the math to the physical objects to draw conclusions.

Did Newton need to borrow mathematical formulas from others to explain the Law of Gravitation? No! I don't think so. Newton did not borrow mathematics from others to explain the Law of Gravitation in the way that Einstein borrowed Riemannian geometry to develop General Relativity.

1. Newton developed his own mathematics to describe gravity

When formulating the Law of Gravitation, Newton did not rely on any pre-existing geometric system.

He independently developed an entirely new mathematical framework: Calculus, along with the principles of differentiation and integration to describe motion.

Newton’s law required only basic arithmetic, Euclidean geometry, and algebra, all of which have a direct relationship with physical reality.


> Newton did not impose a mathematical model onto reality; he used mathematics to describe a real phenomenon in the physical world.


---

2. Newton introduced gravity as a physical entity that could be tested

Newton's Law of Gravitation is not just a theoretical mathematical model. It can be directly tested by measuring the force between two masses.

The formula applies to all massive objects, and this force can be measured experimentally.

He did not need curved space geometry or spacetime; he only required basic concepts of force and mass.


Newtonian gravity has a clear physical foundation and is measurable, unlike Einstein’s gravitational model, which is purely geometric and lacks a direct physical entity representing spacetime.


---

3. Einstein had to rely on pre-existing mathematics

Einstein did not develop Riemannian geometry; instead, he used it as the foundation for General Relativity.

In reality, Einstein did not derive an independent gravitational formula; he merely modified Riemann’s equations to fit his postulates.

There is no experimental tool to measure the curvature of spacetime directly; it is only interpreted indirectly through mathematical models.


General Relativity depends on an existing mathematical framework and cannot independently verify its own physical reality.


---

✔ Newton: Developed his own mathematics to describe a real phenomenon.
✔ Einstein: Used pre-existing mathematics to create a theoretical model without a physical entity.
✔ Newtonian gravity is measurable, whereas Einstein’s spacetime is not directly measurable.

Newton did not need to borrow mathematical formulas from others to explain gravity, but Einstein needed Riemannian geometry to construct spacetime.

 

[Dale]

I think it is relevant: When you confirm that a theoretical model without any physical quantities cannot be considered a physical model.

We are not discussing such a model. Every tensor in the EFE is a physical quantity.

Does this mean that spacetime is merely a mathematical model? Because I also cannot find any physical quantities in Einstein’s field equations.

Is that really the case? Am I mistaken?

You are very mistaken. All of the tensors in the EFE are physical quantities.

You did not answer my direct question. So I will do so myself, not asserting that it is your answer, just the correct answer.

do you believe that the statement “the table top is flat and the legs are perpendicular to the table top” is a physical statement which could be experimentally observed and measured?

Yes, it is a physical statement. Geometry is part of physics. There is a physically measurable geometrical difference between a flat table top and a bumpy one. There is a physically measurable geometrical difference between perpendicular legs and non-perpendicular. Geometry is part of physics.

Spacetime is the geometry of physics.

 

[PeterDonis]

Since the OP's question has been thoroughly answered, this thread is now closed. Thanks to all who participated.