B Does Spacetime Have Physical Existence?

[Uncle Thi]

Spacetime is the foundation of General Relativity, describing how mass and energy influence the curvature of space and the flow of time. However, an important question arises: Is spacetime a physical entity, or is it merely a mathematical framework?

Physics relies on measurable quantities and empirical evidence. Yet, when we discuss spacetime curvature, time dilation, and gravitational lensing, we often assume that space and time themselves are tangible, modifiable entities. But can these concepts be directly observed and measured, or are they just descriptions of how objects behave under certain conditions?

To explore this, I would like to raise three fundamental questions regarding space, time, and light in the context of spacetime theory.

1. Space: Does it have a physical structure to bend?

If spacetime is said to bend due to mass and energy, is space itself a physical entity that can actually bend?


2. Time: Can it stretch or contract if it has no physical existence?

If time is claimed to dilate, what exactly is the measurable unit of this dilation? Is there direct evidence beyond clock rate differences?


3. Light: Does it actually bend, or just change direction?

If light is bent by gravity, does that mean photons have mass? If not, how does gravity interact with them?

 

[PeroK]

Spacetime is the foundation of General Relativity, describing how mass and energy influence the curvature of space and the flow of time. However, an important question arises: Is spacetime a physical entity, or is it merely a mathematical framework?

This is more of a philosophical question than a question for physics.

Physics relies on measurable quantities and empirical evidence. Yet, when we discuss spacetime curvature, time dilation, and gravitational lensing, we often assume that space and time themselves are tangible, modifiable entities. But can these concepts be directly observed and measured, or are they just descriptions of how objects behave under certain conditions?

Space and time intervals can be measured. A second is defined in terms of transitions of a Caesium atomic clock; and a metre is defined as the distance light travels in vacuuum in some specified time.

To explore this, I would like to raise three fundamental questions regarding space, time, and light in the context of spacetime theory.

1. Space: Does it have a physical structure to bend?

If spacetime is said to bend due to mass and energy, is space itself a physical entity that can actually bend?

That question depends on how you define physical. If the definition of physical includes spacetime, then spacetime is physical; if not, then it isn't.

2. Time: Can it stretch or contract if it has no physical existence?

If time is claimed to dilate, what exactly is the measurable unit of this dilation? Is there direct evidence beyond clock rate differences?

Time dilation is a coordinate effect. Leaving that aside, the question is really philosophy rather than physics.

3. Light: Does it actually bend, or just change direction?

There is no such thing as an absolute direction - especially in curved spacetime. Light follows null geodesics in spacetime - which are the nearest things to straight lines in curved geometries. In fact, I would say that the concept of a straight line really only makes sense in Euclidean geometry. For example, is a line of longitude on the surface of the Earth a straight line?

If light is bent by gravity, does that mean photons have mass?

No.

If not, how does gravity interact with them?

Light follows null geodescics, which are the nearest things to straight lines. In any case, it's only in the Newtonian theory that gravity is an interaction between masses. Newtonian gravity is an approximation to a special case of General Relativity - not the other way round.

 

[Orodruin]

TLDR: It depends on what you put into the meaning of ”having physical existence”. Physics is about describing reality, not about philosophical debates of what is ”real”.

 

[Ibix]

I would say that spacetime is an object in the mathematical formulation of general relativity. Whether that means it's "real" or not is a matter of personal preference, not physics. Physicists will typically talk about it as real if they're using general relativity. If they're trying to replace general relativity they will usually talk about other entities and try to explain how spacetime emerges from their maths, just as you can derive Newton's force model of gravity from GR.

Generally the justification for believing in spacetime is post hoc: when we model geometry using a 4d manifold obeying Einstein's field equations, we make accurate predictions. When we finally figure out quantum gravity we'll probably replace it with something else. It may one day be replaced. Worrying about whether it's really real is kind of pointless unless you can go on to provide a consistent mathematical framework that matches all current observations of gravity to our available precision and makes different predictions for things we haven't measured yet. Then we can talk about whether those predictions are correct, and then (if they are) you can start worrying if the entities in that model are really real or not.

Is there direct evidence beyond clock rate differences?

Trying to treat "space" and "time" separately, as the OP's questions 1 and 2 do is never going to end well, but this is an interesting sub-question. What evidence of the behaviour of time could there be except the behaviour of clocks? Whatever time is, if you aren't using clocks you aren't measuring its behaviour (to paraphrase Einstein).

 

[Uncle Thi]

"That question depends on how you define physical. If the definition of physical includes spacetime, then spacetime is physical; if not, then it isn't.

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?

 

[Ibix]

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

By your definition, all three are non-physical abstractions in models of varying precision.

 

[PeroK]

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.

That just shifts the definition of "physical" to the definition of "objectively exist". One problem arises if you can describe the same physical phenomena using different physical models. One example is reflection and transmission of light using Maxwell's equations and the classical electromagnetic field. The EM field must, therefore, exist (by your definition). Note that, contrary to popular belief, there are no photons in classical EM. So, they do not exist.

But, if we use the Quantum Mechanical model of lights, then we have a probabilistic wave function, the uncertainty principle and the EM field is quantized (i.e. can be described in terms of photons).

What is real depends on what theory you are using. You might argue that currently QM is more fundamental than classical EM, so you might argue that photons really exist and EM waves do not. But, what happens if a theory of gravity changes this - what happens to the things that used to really exist.

---
Based on that definition, could you clearly define the following:

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

Space and time are well defined within the theory of GR. In the single concept of spacetime.

3. What is light?

As above, light is EM radiation. Or, a certain type of state of the quantized EM field.

 

[Dale]

an entity must objectively exist in the real world

Do you have an “objectivelyexistometer” that can measure whether or not something objectively exists?

this physical entity must have measurable quantities

Spacetime clearly satisfies the measurable quantities requirement. You can measure spacetime with clocks, rulers, protractors, speedometers, radars, and the like.

1. Space: Does it have a physical structure to bend?

Spacetime does curve. Space isn’t separate under either the model or experiments.

Spacetime curvature is tidal gravity. Consider two objects released side by side from a hovering platform in space. Initially they are at rest with respect to each other, so their worldlines are parallel. Their accelerometers read 0, so the worldlines are straight. Using radar or rulers, the distance between them changes. This combination of facts implies curved spacetime. In flat spacetime parallel straight worldlines are always equidistant. Since parallel straight worldlines do not remain equidistant in tidal gravity, tidal gravity is curved spacetime

2. Time: Can it stretch or contract if it has no physical existence?

In common scientific definitions time (specifically proper time) is what a clock measures. So time is by definition something that can be experimentally measured by physical devices.

So a claim that time “has no physical existence” must define “physical existence” in a way that doesn’t include things that can be experimentally measured by physical devices. Such a definition of “physical existence” is so weak that it is hard to see why anyone would care about it outside of philosophers.

I would point out your own requirement “this physical entity must have measurable quantities”. The usual scientific definition of time clearly satisfies that.

3. Light: Does it actually bend, or just change direction?

What is the difference between “actually bending” and “just changing direction”? What kind of experiment could detect the difference?

 

[Dale]

The thread has been reopened. Participants are reminded that the purpose of PF is to educate regarding mainstream science as described by the professional scientific literature. Personal opinions that are in conflict with that are not permitted.

 

[Uncle Thi]

Do you have an “objectivelyexistometer” that can measure whether or not something objectively exists?

Spacetime clearly satisfies the measurable quantities requirement. You can measure spacetime with clocks, rulers, protractors, speedometers, radars, and the like.

Spacetime does curve. Space isn’t separate under either the model or experiments.

Spacetime curvature is tidal gravity. Consider two objects released side by side from a hovering platform in space. Initially they are at rest with respect to each other, so their worldlines are parallel. Their accelerometers read 0, so the worldlines are straight. Using radar or rulers, the distance between them changes. This combination of facts implies curved spacetime. In flat spacetime parallel straight worldlines are always equidistant. Since parallel straight worldlines do not remain equidistant in tidal gravity, tidal gravity is curved spacetime

In common scientific definitions time (specifically proper time) is what a clock measures. So time is by definition something that can be experimentally measured by physical devices.

So a claim that time “has no physical existence” must define “physical existence” in a way that doesn’t include things that can be experimentally measured by physical devices. Such a definition of “physical existence” is so weak that it is hard to see why anyone would care about it outside of philosophers.

I would point out your own requirement “this physical entity must have measurable quantities”. The usual scientific definition of time clearly satisfies that.

What is the difference between “actually bending” and “just changing direction”? What kind of experiment could detect the difference?

Einstein's field equations are often used to describe gravity in General Relativity. I would like to understand better: What is the unit of gravitational force in these equations? Does it have the same unit as Newtonian force (kg·m/s²)?

 

[PeroK]

Einstein's field equations are often used to describe gravity in General Relativity. I would like to understand better: What is the unit of gravitational force in these equations? Does it have the same unit as Newtonian force (kg·m/s²)?

There is no force in the Field Equations. They essentially replace Newton's first law, which describes the motion of an object subject to no forces.

 

[Ibix]

What is the unit of gravitational force in these equations?

There is no gravitational force in these equations. General relativity models gravity as the geometry of spacetime. Things moving in a gravitational field follow straight line paths through 4d spacetime (called "geodesics"), which usually produce curved lines when you pick a slicing of spacetime that you want to call "space" and project the straight lines onto them.

 

[phinds]

If spacetime is said to bend due to mass and energy, is space itself a physical entity that can actually bend?

The concept of spacetime "bending" is due to a misapplication of Euclidean Geometry in a situation where it does not apply. Spacetime is NOT described by Euclidean Geometry but by pseudo-Riemann Geometry. "Geodesics" in that geometry are the equivalent of Euclidean "straight lines" but if you apply a Euclidean straight line onto a Geodesic then only in special cases would you get a match, whereas in most cases the Geodesic would look bent relative to the Euclidean line. SO ... to call the line "bent" you have to be applying Euclidean Geometry, which, again, is not what describes space-time.

If you still want to call a space-time geodesic "bent" then sure, knock yourself out ... it IS, after all "bent" in Euclidean Geometry. If, on the other hand, you want to talk actual physics, use the math that applies to the situation.

 

[Uncle Thi]

There is no force in the Field Equations. They essentially replace Newton's first law, which describes the motion of an object subject to no forces.

According to your explanation: "There is no force in the Field Equations."
Can I understand this as: there is no gravitational force, and therefore, no unit for gravitational force?
Thank you for your explaination.

 

[phinds]

Can I understand this as: there is no gravitational force, and therefore, no unit for gravitational force?

That is correct. Gravity is not a force in GR, it is a name given to a property of space-time geometry, namely that objects that do not have any force acting on them follow geodesics.

If you have a rocket with propellant coming out the back end, that is a force on the rocket and the rocket does not follow a geodesic. If the rocket is in free-fall with no force on it, then it is following a geodesic. The International Space Station, for example, is in orbit around the Earth, following a Geodesic.

 

[Ibix]

Can I understand this as: there is no gravitational force, and therefore, no unit for gravitational force?

There is no gravitational force in general relativity, so asking for its unit is like asking what units I use to measure the weight of the colour purple. It doesn't really make sense.

In theories of gravity that do have a force of gravity, you use the same units as any other force.

 

[jbriggs444]

Einstein's field equations are often used to describe gravity in General Relativity. I would like to understand better: What is the unit of gravitational force in these equations? Does it have the same unit as Newtonian force (kg·m/s²)?

The field equations tell you how an unaccelerated object will move -- along a geodesic. If you want to get an object to follow a different trajectory you will need to apply a force to do so. The required force is the familiar one from Newton's second law: $F = ma$.

For instance, a book sitting on a table is not following a geodesic trajectory. It is being accelerated upward and away from that free fall trajectory by the contact force from the table beneath. The required force to maintain its actual trajectory is given by the product of the mass of the book $m$ and the required proper acceleration $g$.

To be technically correct, the "force of gravity" is not the upward supporting force of table on book. It is the fictitious downward force that we imagine holds the book in place despite that upward force.

 

[Dale]

Can I understand this as: there is no gravitational force, and therefore, no unit for gravitational force?

There is no gravitational force in GR, but any force has units of newtons in SI.

There are fictitious forces. Those, like any force, have units of newtons. The Newtonian gravitational force is a fictitious force in General Relativity

Note that there are formulations of Newtonian gravity where Newtonian gravity is also a fictitious force and Newtonian spacetime is curved. So this formulation characterizes gravity, not relativity.

 

[PeroK]

I'm losing it!

Take the astronauts on the ISS. They are "weightless" despite the force of gravity acting on them. They feel nothing. Whereas, someone standing on Earth feels the real force pushing them upwards.

Even in elementary classical mechanics, we can model an external acceleration as the equivalent of a gravitational force. For example, a pendulum inside an accelerating vehicle. It behaves exactly as it would if gravity acted at an angle. The "effective" gravity being the vector sum of the Newtonian gravity and the fictitious force associated with the external acceleration.

 

[PeroK]

PS even before you get to GR, the seeds of gravity as a fictitious force are sown.

 

[Uncle Thi]

The field equations tell you how an unaccelerated object will move -- along a geodesic. If you want to get an object to follow a different trajectory you will need to apply a force to do so. The required force is the familiar one from Newton's second law: $F = ma$.

For instance, a book sitting on a table is not following a geodesic trajectory. It is being accelerated upward and away from that free fall trajectory by the contact force from the table beneath. The required force to maintain its actual trajectory is given by the product of the mass of the book $m$ and the required proper acceleration $g$.

To be technically correct, the "force of gravity" is not the upward supporting force of table on book. It is the fictitious downward force that we imagine holds the book in place despite that upward force.

In this case, how is it related to the unit of gravitational force that I mentioned?

*"For example, a book resting on a table does not follow a geodesic trajectory. It is being accelerated upward, away from the free-fall trajectory, by the contact force from the table below. The force required to maintain its actual trajectory is determined by the product of the book's mass and the required proper acceleration.

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."*

 

[Uncle Thi]

Take the astronauts on the ISS. They are "weightless" despite the force of gravity acting on them. They feel nothing. Whereas, someone standing on Earth feels the real force pushing them upwards.

Even in elementary classical mechanics, we can model an external acceleration as the equivalent of a gravitational force. For example, a pendulum inside an accelerating vehicle. It behaves exactly as it would if gravity acted at an angle. The "effective" gravity being the vector sum of the Newtonian gravity and the fictitious force associated with the external acceleration.

Are there any direct experimental measurements of spacetime curvature that do not rely on its effects on mass and energy?

 

[jbriggs444]

In this case, how is it related to the unit of gravitational force that I mentioned?

It comes from Newton's second law. $F=ma$ (or $F=dp/dt$ if you prefer).

As @Dale said, in SI this is kilogram meters per second squared.

 

[PeroK]

Are there any direct experimental measurements of spacetime curvature that do not rely on its effects on mass and energy?

The detection of gravitation waves at LIGO might be the best direct experiment.

 

[julian]

Have people explored Einstein's hole argument and its implications for spacetime ontology? It’s a fascinating way to rethink how we understand coordinates and reality. I've discussed it before, but I'm quite busy at the moment. If you're interested, I highly recommend checking out Chapter 2 of Rovelli's book, available for free here: https://www.cpt.univ-mrs.fr/~rovelli/book.pdf.

 

[Uncle Thi]

It comes from Newton's second law. $F=ma$ (or $F=dp/dt$ if you prefer).

As @Dale said, in SI this is kilogram meters per second squared.

My question: Why is the unit of force kg·m/s² instead of another unit?

 

[Dale]

Are there any direct experimental measurements of spacetime curvature that do not rely on its effects on mass and energy?

All measuring devices are made of mass and energy, so the answer is trivially “no”. That “no” answer is not particularly meaningful.

My question: Why is the unit of force kg·m/s² instead of another unit?

That is really a question that belongs in the classical physics forum. It has nothing to do with relativity. The brief answer is that is the units required for dimensional consistency in Newton’s 2nd law.

 

[PeroK]

My question: Why is the unit of force kg·m/s² instead of another unit?

How much physics do you actually know?

 

[jbriggs444]

My question: Why is the unit of force kg·m/s² instead of another unit?

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.

 

[PeterDonis]

You can do general relativity with slugs, furlongs and microfortnights.

My high school AP chemistry teacher wanted us to use tons, furlongs, and fortnights. I even worked out values for physical constants in the TFF system:

http://peterdonis.net/misc/tffunits.html