Curved spacetime?

[JonG]

I believe that Einstein himself had serious reservations about the notion of Minkowski spacetime, dismissing it as "superfluous learnedness", before adopting it as a significant foundation stone in his General Theory of Relativity.

 

The idea that a massive body causes spacetime to become curved has always seemed odd, but that doesn't stop many people accepting it without question. In fact to question it might be seen as a form of blasphemy to some.

 

But how can a massive object cause something which is itself massless to become curved. In fact, one could see spacetime as simply a mathematical device without real existence at all. Does anyone else find something peculiar about this?

Edited December 13, 2013 by JonG

[ajb]

The idea that a massive body causes spacetime to become curved has always seemed odd, but that doesn't stop many people accepting it without question. In fact to question it might be seen as a form of blasphemy to some.

 

But how can a massive object cause something which is itself massless to become curved.

It is what the mathematical model of gravity known as general relatvity tells us happens. This model has been well tested to some large degree of accuracy and todate there is no evidence to suggest that general relativity is not a good model of gravity.

 

It is not blasphemy to questions this, it is what people do when testing general relativity.

 

In fact, one could see spacetime as simply a mathematical device without real existence at all. Does anyone else find something peculiar about this?

But then how does this differ from all other constructions found in theoretical physics?

[swansont]

In fact, one could see spacetime as simply a mathematical device without real existence at all. Does anyone else find something peculiar about this?

 

I agree with ajb. Why is this a problem with GR, but not all of the rest of the mathematical abstractions one finds in physics?

[JonG]

It is what the mathematical model of gravity known as general relatvity tells us happens.

 

 

 

I don't think it could be claimed that general relativity "tells us" that spacetime is curved. Rather, it is "assumed" that spacetime can be curved and the effects of gravitry are then explained on the basis of this assumption.

 

 

 

This model has been well tested to some large degree of accuracy and todate there is no evidence to suggest that general relativity is not a good model of gravity.

 

 

I don't see this as relevant. Newton's theory of gravitation was in accord with the evidence available to Netwon, but he was the first to acknowledge that he could offer no explanation of why his theory worked. The notion of a force acting at a distance was particularly problematic at the time. To question assumptions made in a theory does not imply that the predictions of the theory are incorrect.

 

 

My point is that to assert that some non-material entity (spacetime) can become curved by the action of massive objects is by no means obvious and I would have expected it to raise a few questions. One could probably explain any field of force by bending and modifying spacetime appropriately. In fact, the Kaluza-Klein theory did something like this in order to unify gravitational and electromagnetic fields.

[Delta1212]

"Accepting without question" doesn't seem like a particularly accurate description of how science actually works. It is, granted, something that a lot of people do with regard to scientific theories, but very few of those people are scientists (who spend a great deal of time poking, prodding and questioning even theories they think are accurate in order to further test them, refine their accuracy and discover their limits).

 

Regardless, "science" doesn't ask you to believe that space is actually curved. You do, however, have to accept that the mathematics of curved space predicts the movement of matter due to gravity more accurately than anything else we've got, which we can state because the mathematical predictions have been repeatedly checked against what actually happens and been found correct to a high degree of precision.

 

Whether you belief that the ability to accurately model gravity as curved space represents a physical truth or is merely an artifact of math that accurately describes the behavior of gravity but doesn't reveal deeper truths about its physical nature is entirely up to you. Just make sure you understand that most people who study it don't accept that space curves "because Einstein says so" (or whoever else). In general, they accept it because the math for curved space works really, really well for predicting the behavior of gravity in all of the many, many tests that have been done.

[swansont]

 

I don't think it could be claimed that general relativity "tells us" that spacetime is curved. Rather, it is "assumed" that spacetime can be curved and the effects of gravitry are then explained on the basis of this assumption.

 

 

 

 

I don't see this as relevant. Newton's theory of gravitation was in accord with the evidence available to Netwon, but he was the first to acknowledge that he could offer no explanation of why his theory worked. The notion of a force acting at a distance was particularly problematic at the time. To question assumptions made in a theory does not imply that the predictions of the theory are incorrect.

 

 

My point is that to assert that some non-material entity (spacetime) can become curved by the action of massive objects is by no means obvious and I would have expected it to raise a few questions. One could probably explain any field of force by bending and modifying spacetime appropriately. In fact, the Kaluza-Klein theory did something like this in order to unify gravitational and electromagnetic fields.

 

It's fairly clear that spacetime cannot be represented by a Cartesian geometry, i.e. one that is flat; Einstein discussed this in terms of the radius vs circumference of a circle in an accelerated reference frame as a bridge to developing GR. Remember that this theory is now ~100 years old. Some fundamental question would have been answered long ago, and there's no need to reinvent the wheel. The theory works and continues to pass every test

[Delta1212]

I'm also wondering what the difference between a material and non-material entity and what qualifies spacetime as being the latter? Ok, I realize that sounds like a silly question on the face of it, but...

 

What makes an entity material? That it's made of "stuff?" What is an electron made of? But ok, an electron has mass so maybe that means it's material.

 

Is a photon non-material, then? But you can interact with a photon, and since the argument is that you can affect spacetime because it is non-material (or at least, that it seems counter-intuitive that you should be able to affect a non-material entity) then I have to assume photons are material.

 

So if it's not mass, is it that material entities have a defined locations? But again, electrons only have a very broadly defined location, and really, everything can only sometimes be defined as having a specific location when the scale is small enough, and since I'm assuming things don't constantly switch between being material and non-material...

 

What makes spacetime special that you shouldn't be able to alter its geometry? This seems like one of those things in science that is "really weird" but still no less weird than a ton of other results that initially seem counter-intuitive until you've adjusted your perspective of how the universe works to be more in line with what experiment says happens instead of what your preconceptions say should happen. If reality was intuitive, science would be superfluous.

[JonG]

 

I agree with ajb. Why is this a problem with GR, but not all of the rest of the mathematical abstractions one finds in physics?

 

You haven't specified an example so I will take one at random - Feynman diagrams. I doubt that anyone believes that Feynman diagrams have any real existence. But conclusions arrived at with the aid of such diagrams are considered to be valid.

 

Spacetime however, is seen to be very different. For example, it is often pointed out that the expanding universe is not due to galaxies receding from each other - spacetime itself is expanding. This appears to endow spacetime with objective existence.

This seems like one of those things in science that is "really weird" but still no less weird than a ton of other results that initially seem counter-intuitive until you've adjusted your perspective of how the universe works to be more in line with what experiment says happens instead of what your preconceptions say should happen. If reality was intuitive, science would be superfluous.

 

I have often wondered about this. As I mentioned earlier, the notion of action at a distance was once seen as a major obstacle in the understanding of gravitational, electric and magnetic fields. How can two bodies which are separated by empty space exert a force on each other? These concerns gradually faded with time and, when I was a kid at school, the idea of action at a distance wasn't seen as problematic at all (not because we knew all about second quantization - we hadn't heard of it then). I don't think it was because anyone had acquired a deeper or more mature understanding, but simply because we had, as you put it, "adjusted our perspective" - although not necessarily for rational or defensible reasons.

[StringJunky]

JonG, on 13 Dec 2013 - 5:26 PM, said:JonG, on 13 Dec 2013 - 5:26 PM, said:JonG, on 13 Dec 2013 - 5:26 PM, said:

 

You haven't specified an example so I will take one at random - Feynman diagrams. I doubt that anyone believes that Feynman diagrams have any real existence. But conclusions arrived at with the aid of such diagrams are considered to be valid.

 

Spacetime however, is seen to be very different. For example, it is often pointed out that the expanding universe is not due to galaxies receding from each other - spacetime itself is expanding. This appears to endow spacetime with objective existence.

I might be wrong, but I see it as a mathematically-derived framework superimposed on space that describes and predicts the behaviour of objects in it.. Spacetime is the physics version of an ontological description (What something is) of space and is useful. Physicists are interested in behaviour and properties from which they build models that they use to understand and predict things i.e. they are not interested what something is made of. Once you start getting into the real fundamentals, classical ideas as to the 'substance' of things become meaningless...it all seems to be about fields.

 

http://en.wikipedia.org/wiki/Field_(physics)

Edited December 13, 2013 by StringJunky

[ajb]

I don't think it could be claimed that general relativity "tells us" that spacetime is curved. Rather, it is "assumed" that spacetime can be curved and the effects of gravitry are then explained on the basis of this assumption.

The notion of space-time is one of the "inputs" of the theory. General relativity then allows for space-time to have non-trivial geometry and more than this it gives us the interpretation of gravity as this curvature. This is all part of the mathematical construction of general relativity.

 

 

I don't see this as relevant.

The relevancy is that one has to accept that general relativity agrees with nature very well.

 

Newton's theory of gravitation was in accord with the evidence available to Netwon, but he was the first to acknowledge that he could offer no explanation of why his theory worked.

Can anybody really offer an explanation as to why any theory works?

 

I don't think so and all one can really do is describe mechanisms within that theory. Newton knew how to calculate within this theory and these calculations agree with nature to an acceptable level for a wide range of gravitational phenomena, but not all.

 

In fact in much the same way as electrostatics can describe lots of electromagnetic phenomena, but not everything.

 

 

The notion of a force acting at a distance was particularly problematic at the time. To question assumptions made in a theory does not imply that the predictions of the theory are incorrect.

Sure, I agree with this totally.

 

 

My point is that to assert that some non-material entity (spacetime) can become curved by the action of massive objects is by no means obvious and I would have expected it to raise a few questions.

It has raised lots of questions and still does today.

 

However as I have said, all evidence to date suggests that general relativity is a good theory and that we must take the notion of curved space-time seriously.

 

One could probably explain any field of force by bending and modifying spacetime appropriately. In fact, the Kaluza-Klein theory did something like this in order to unify gravitational and electromagnetic fields.

Almost, there are some problems with KK theory.

 

Anyway, you are right that classically at least fields can be explained geometrically and the notion of curvature plays a big role. I am not sure what your background is and how much more I can say without just confusing you.

You haven't specified an example so I will take one at random - Feynman diagrams. I doubt that anyone believes that Feynman diagrams have any real existence. But conclusions arrived at with the aid of such diagrams are considered to be valid.

 

You could have picked any concept, calculational method or approximation used in physics here.

 

We could easy talk about energy or momentum here, or phase space, or tools from perturbation theory and so on...

 

Spacetime however, is seen to be very different. For example, it is often pointed out that the expanding universe is not due to galaxies receding from each other - spacetime itself is expanding. This appears to endow spacetime with objective existence.

I think the difference here is very superficial.

 

Using an expanding space-time to model the Universe seems to agree very well with what we see.

 

Asking of space-time is real or not is something we cannot really answer. All we can really say is that using space-time in our models works really well.

[md65536]

I don't think it could be claimed that general relativity "tells us" that spacetime is curved. Rather, it is "assumed" that spacetime can be curved and the effects of gravitry are then explained on the basis of this assumption.

No, this is not the right way to look at it.

 

Spacetime isn't some thing that is created in imagination and then described. Nor is it something that is confined to the realm of math.

 

Spacetime, and what it means to be curved, has a specific definition. It is defined not based on what exists, but based on what is observed. The reason that it is not just a mathematical device is that it can be measured. Experimental measurements agree with the math. Somehow you're treating it both as an entity and as physically baseless, when really it's neither. Just because it is defined and measurable, doesn't mean it exists as a thing, only that it is a useful model.

Edited December 13, 2013 by md65536

[Delta1212]

I have often wondered about this. As I mentioned earlier, the notion of action at a distance was once seen as a major obstacle in the understanding of gravitational, electric and magnetic fields. How can two bodies which are separated by empty space exert a force on each other? These concerns gradually faded with time and, when I was a kid at school, the idea of action at a distance wasn't seen as problematic at all (not because we knew all about second quantization - we hadn't heard of it then). I don't think it was because anyone had acquired a deeper or more mature understanding, but simply because we had, as you put it, "adjusted our perspective" - although not necessarily for rational or defensible reasons.

Adjusting my perspective on something to more closely match the way it behaves seems both rational and defensible to me. That doesn't mean that my new perspective is "the real ultimate truth of the universe" but it certainly more closely matches the behavior of the universe than my old perspective.

 

It's not as if that original perspective has an innately better claim to being true simply by virtue of coming first, after all. Our initial conception of how reality works is essentially just a model of reality based on our experiences, but we develop it at an age where we're too young to realize we're doing that and often don't remember most of the experiences that led us to form and refine our ideas about how reality works.

 

Since we don't realize we're creating a mental model, we tend to accept the assumptions we've made as being true until they are indisputably challenged (and sometimes not even then). The only difference between changing our perspective based on scientific evidence and the development of our initial perspective is that we're aware of what we're doing and why we're changing it in the case of conforming to the evidence.

 

"Counter-intuitive" results are really just results that are unlikely to happen in daily life and so fail to be incorporated into our initial conception of reality. There's nothing that makes them inherently more problematic than the intuitive ideas except that we're more used to them.

[decraig]

Can anybody really offer an explanation as to why any theory works?

 

 

I think so, at least in one manner. The force between charged particles could be seen as action at a distance. But by positing electric fields we can now say charge acts to create fields, and fields act on charge.

 

Relativity theory explains Newton's gravitational action at a distance as the weak field vacuum solution where matter shapes spacetime and spacetime acts back on matter.

 

One theory can "explain" another theory. But its and endless task, as the superseding theory demands explaining as well. It's turtles all the way down.

 

So I don't think it's such a bad idea to wonder how to explain a theory.

Edited December 16, 2013 by decraig

[ajb]

So I don't think it's such a bad idea to wonder how to explain a theory.

This is different to asking why a theory works.

 

You example of Newtonian gravity as a limit of general relativity tells us that just that. It means that as along as we are careful the two theories are not really in competition, but rather complement each other. However, this does not really explain why either GR or Newtonian gravity works so well.

 

We could pay similar games with classical and quantum mechanics. We know how the two are generally tied to each other and we know the physical principals here. We just don't know why either works, they just do.

Edited December 16, 2013 by ajb

[decraig]

This is different to asking why a theory works.

 

You example of Newtonian gravity as a limit of general relativity tells us that just that. It means that as along as we are careful the two theories are not really in competition, but rather complement each other. However, this does not really explain why either GR or Newtonian gravity works so well.

 

We could pay similar games with classical and quantum mechanics. We know how the two are generally tied to each other and we know the physical principals here. We just don't know why either works, they just do.

 

???

 

Yes.... The examples I gave explaining why a theory works, rather than asking why. But I think I know what you mean.

 

Do sr and gr compliment each other? I don't know what that means, except we can expect to good accuracy that space is mostly flat for most experimental outcomes. My opinion is different: one is better than another at generalizing what nature is. We differ wildly in our points of view in this regard. I think using a former theory degrades what is subsequently developed using this theory, such as qed conducted on the background of special relativity.

 

As you might recall, Einstein developed a theory of gravity by taking Newtonian inertial-gravitational mass equivalence to the next step: "why are they equivalent?," giving rise to the EEP.

 

Per your second paragraph, I do play similar games with quantum, and classical mechanics (where I assume you mean relativistic theory is to be categorized as classical). Now, I don't recall making any headway asking why quantum mechanics works. The direct approach seems hopeless. I do ask why relativity theory should be formulated as it is. It's evolved, for the most part, on the adaption of vector bundles to tensor bundles. I reject this (mostly) and advance alternate formulation of my own. In so doing I've found an unexpected parallel in gr to wave-particle duality. My 'why' questions or demands for explanation are a little more abstract, such as: why are the formulations of gr so goofy?

 

I think we who wish for better theory always, always ask why. It doesn't matter what others say who will tell us we can't ask why questions of physics. Those who are not interested in this, don't ask why, but are interested in becoming proficient in accepted theory. These are two different species.

Edited December 17, 2013 by decraig

[ajb]

Do sr and gr compliment each other? I don't know what that means, except we can expect to good accuracy that space is mostly flat for most experimental outcomes.

In the sense that Minkwoski space-time is a vacuum solution to the field equations and that in small enough regions a curved space-time looks like Minkowski space-time.

 

My opinion is different: one is better than another at generalizing what nature is. We differ wildly in our points of view in this regard. I think using a former theory degrades what is subsequently developed using this theory, such as qed conducted on the background of special relativity.

I don't think we are in much disagreement on this. GR is "better" in the sense that it can describe a wider range of phenomena than SR. As I have stated SR can be seen to "sit inside" GR.

 

Using a former theory theory as you put it, maybe fine if the corrections due to the newer theory are small. For example, lot of gravitational physic is well modeled using Newtonian gravity, but for sure not everything.

 

Now, I don't recall making any headway asking why quantum mechanics works.

You won't really make any headway in explaining why any theory works, other than maybe understanding one theory as a limit or special case of another that also works well.

 

The direct approach seems hopeless.

If you assume quantum mechanics to be a good theory, then you can get an understanding as to why we expect classical theory to be good taking care with domains of validity and the accuracy required.

 

The other way round is less clear, though we have good prescriptions of what it means to "quantise".

 

I do ask why relativity theory should be formulated as it is. It's evolved, for the most part, on the adaption of vector bundles to tensor bundles.

This is not actually a special feature of Einstein's relativity.

 

We expect all (classical for sure) physics to be geometric in nature. In particular we have the gauge principal which says "nature does not care about the details of how we chose to describe physics". Meaning nothing should depend in a fundamental way on the local description in terms of coordinates.

 

This leads us to consider differential manifolds and similar objects as the basic arena of physics.

 

I reject this (mostly) and advance alternate formulation of my own.

What do you reject exactly?

 

In so doing I've found an unexpected parallel in gr to wave-particle duality. My 'why' questions or demands for explanation are a little more abstract, such as: why are the formulations of gr so goofy?

You are free to start a new thread on this... or better write a paper.

 

I think we who wish for better theory always, always ask why. It doesn't matter what others say who will tell us we can't ask why questions of physics. Those who are not interested in this, don't ask why, but are interested in becoming proficient in accepted theory. These are two different species.

You have to be very careful what you mean by "why". At best we can give interpretations of calculations and constructions within a given theory and then treat these as the "why". Any deeper meaning than this is in the realms of philosophy.

[JonG]

Just a few notes regarding various comments made:

 

1) To question whether spacetime is a real entity is not the same as questioning the validity or accuracy of General Relativity. It has nothing to do with that whatsoever. We know that a solution of Schrodinger's equation gives us a wavefunction, but no one seriously believes that wavefunctions are real entities in themselves. One can't directly observe a wavefunction, it doesn't have a property such as mass. But the fact that a wavefunction is considered to be an abstract concept rather than a real entity in no way invalidates quantum theory. Pointing out that General relativity is consistent with observation is irrelevant, just as pointing out that quantum theory is successful does not prove that wavefunctions are real entities..

 

2) So why should anyone be concerned about whether curved spacetime is a real entity? Because, unlike the quantum mechanical example I mentioned, nothing lies behind curved spacetime. In quantum theory, we know that the wavefunction describes properties of particles such as electrons which are considered to be real, but there is nothing analogous to these particles in the relativistic theory of gravitation - unless one wishes to include things like "gravitons" in some way.

 

To assert that some massive object can interact with an abstract concept which cannot be directly observed is, to me, on a par with a belief in ghosts. Curved spacetime enables a very good description of gravitation. But, surely it can't be the whole story.

 

Please note; THIS IS NOT QUESTIONING THAT THE RELATIVISTIC DESCRIPTION OF GRAVITY LEADS TO THE VIEW THAT SPACETIME IS CURVED. It is to do with whether curved spacetime is something which actually exists - other than in people's heads.

Edited December 17, 2013 by JonG

[ajb]

To assert that some massive object can interact with an abstract concept which cannot be directly observed is, to me, on a par with a belief in ghosts.

There are lots of things in physics like that.

 

Other examples similar to what you have said would include gauge fields. So in what sense is the electromagnetic field real?

 

It is to do with whether curved spacetime is something which actually exists - other than in people's heads.

You can substitute anything you like from physics into that question.

[JonG]

There are lots of things in physics like that.

 

Other examples similar to what you have said would include gauge fields. So in what sense is the electromagnetic field real?

 

 

You can substitute anything you like from physics into that question.

 

An interesting example. In everyday speech, many would refer to an electric field as if it were real. But that isn't actually how it is regarded in Physics. It would be seen as graphical way of describing the interaction between charged objects (which would be considered to be real) through the agency of virtual photons (how many people would see those as real is open to question). However, if we didn't have a more fundamental description of electromagnetic fields, we would indeed be left with the same puzzle as we have with gravity. We just don't have such an underlying theory of gravity.

Edited December 17, 2013 by JonG

[ajb]

We just don't have such an underlying and theory of gravity.

You mean the quantum theory of gravity?

 

Classically I would say that the foundations of both EM and GR are both well understood. One problem of course is the practical handling of GR which is inherently non-linear.

[JonG]

You mean the quantum theory of gravity?

 

 

 

That could sort the problem out - but that in itself doesn't suggest that a viable quantum theory of gravity could be assembled - I just don't know.

 

My moderate interest in this stems from the sort of comment I referred to earlier in which it is often claimed that an expanding universe entails the expansion of spacetime itself. This is not quite the same as saying that an expanding universe has to be described by an expanding curved coordinate system.It implies that spacetime is something which exists in itself and that could be described as expanding - in fact, the expansion of the surface of a balloon which is being blown up is often cited as an analogy - the two dimensional surface of the balloon being analogous to spacetime.

 

Take this as an example: "If we examine a piece of `empty' space we see it is not truly empty, it is filled with spacetime, "

 

from here: http://abyss.uoregon.edu/~js/ast123/lectures/lec17.html

 

and the following from Stanford : " however, the equations of general relativity are perfectly consistent with spacetimes that contain no matter at all. Flat (Minkowski) spacetime is a trivial example, but empty spacetime can also be curved, as demonstrated by Willem de Sitter in 1916."

 

from here: http://einstein.stanford.edu/SPACETIME/spacetime2.html

 

However, this quote is also given:

"General relativity as developed by Albert Einstein, says, and this is a direct quote from Einstein, that

'Space-time does not claim existence in its own right, but only as a structural quality of the [gravitational] field' ".

 

also from Stanford: http://einstein.stanford.edu/content/relativity/q909.html

Edited December 17, 2013 by JonG

[ajb]

My moderate interest in this stems from the sort of comment I referred to earlier in which it is often claimed that an expanding universe entails the expansion of spacetime itself. This is not quite the same as saying that an expanding universe has to be described by an expanding curved coordinate system.It implies that spacetime is something which exists in itself and that could be described as expanding - in fact, the expansion of the surface of a balloon which is being blown up is often cited as an analogy - the two dimensional surface of the balloon being analogous to spacetime.

I think this is a problem with the language of theoretical physics. I have commented on this before to theoretical physicists. Typically one is very sloppy with what is "real" in the sense that it can actually be measured and what are mathematical constructions. This permeates all of physics and I understand your trail of thought here.

[PeterJ]

I have nothing intelligent to add, but I would like to recommend Ulrich Mohrhoff's recent book, The World According to Quantum Mechanics: Why the Laws of Physics make Perfect Sense After All. It seems directly relevant. He has a blog here http://ujm.thisquantumworld.com/wp/ . A tag at the top marked 'Book' links to the relevant stuff.

 

And no, I am not the author. Just a fan.

Edited January 2, 2014 by PeterJ

[jduff]

To help you out. I recommend reading this PDF. http://iopscience.iop.org/1742-6596/189/1/012012/pdf/1742-6596_189_1_012012.pdf

 

Will help with the question asked!

Edited January 2, 2014 by jduff

[Alan McDougall]

I believe that Einstein himself had serious reservations about the notion of Minkowski spacetime, dismissing it as "superfluous learnedness", before adopting it as a significant foundation stone in his General Theory of Relativity.

 

The idea that a massive body causes spacetime to become curved has always seemed odd, but that doesn't stop many people accepting it without question. In fact to question it might be seen as a form of blasphemy to some.

 

But how can a massive object cause something which is itself massless to become curved. In fact, one could see spacetime as simply a mathematical device without real existence at all. Does anyone else find something peculiar about this?

 

Space-time is not nothing, it is a fabric, that has been proved to distort or curve around the mass of a huge object. Read it up Arthur Ellington proved this in the 1910's Of course there is much more to say about this topic.

 

http://en.wikipedia.org/wiki/Tests_of_general_relativity

 

.At its introduction in 1915, the general theory of relativity did not have a solid empirical foundation. It was known that it correctly accounted for the "anomalous" precession of the perihelion of Mercury and on philosophical grounds it was considered satisfying that it was able to unify Newton's law of universal gravitation with special relativity. That light appeared to bend in gravitational fields in line with the predictions of general relativity was found in 1919 but it was not until a program of precision tests was started in 1959 that the various predictions of general relativity were tested to any further degree of accuracy in the weak gravitational field limit, severely limiting possible deviations from the theory. Beginning in 1974,

Edited January 6, 2014 by Alan McDougall