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the model versus the "reality".


geordief

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I thought I had organized my (basic) appreciation of GR in that the curvature of spacetime refers to the curvature of the GR model(I still don't understand the nuts and bolts of that but it seems to be bound up with tensors , I think)

 

As for the reality and whether it is actually curved , I thought the idea was that we don't actually know . (the model includes a curvature and successfully predicts the dynamics of space time within its area of applicability)

 

But my understanding is being shaken by the language employed by Prof. Brian Cox who is a popular science presenter on the BBC and as far as I can make out is actually a well respected scientist in this area.

 

He seemed to insist on the notion that space (sometimes he referred to it as spacetime) is actually curved by mass,etc.

 

Does this matter.?Is it in large part semantics? Is Prof Brian Cox trying to shock and awe the audience? Is he actually right?

 

If the model is curved does it follow that the reality is also curved?

 

If the universe is actually a hologram is the question academic ? (reality is a model ?)

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This is a purely philosophical question.

 

Does the mathematics of GR describe what is really happening to space-time?

If that's what you want to think, yes.

 

Is the mathematics of GR just a useful tool that seems to correspond to some underlying reality, which may be different?

If that's what you want to think, yes.

 

Is the mathematics of GR purely a model that works and there is no underlying reality?

If that's what you want to think, yes.

 

This is a matter of personal preference. There is no way of telling them apart.

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Thanks . That is a question that has bugged me for a long time . I will take your explanation on board.

 

(it would help if I had more of a handle on the actual maths ,of course -a shame that it has been too hard for me to crack so far :( )

Edited by geordief
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Is spacetime a real thing, or is it a conceptual construct? I go with the latter. You can't grab a bit of spacetime and hand it to me.

 

So saying spacetime is curves is another way of saying the natural geometry that describes what's going on is curved.

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Can someone please tell me how to copy and paste part of a previous post using the process that includes the two-toned gray headings? Thanks.

Swansont: You state: Is spacetime a real thing, or is it a conceptual construct? I go with the latter. You can't grab a bit of spacetime and hand it to me.

So saying spacetime is curves is another way of saying the natural geometry that describes what's going on is curved.

 

Does it not depend upon what ones expectations are when one asks if it is a "thing." Of course, we cannot grab it like we can a wrench and hand it to someone. And no, I am not davigating off into the dubious realm of arguing that abstract things such as space, time, beauty and honesty are "things" pertinent to the study of physics. Arguably, spacetime is all that exists anyway, or rather, that "things," (as defined as objects having mass) are really just symptomatic of warps, of whatever kind, in spacetime anyway.

 

But yes, if one looks at 3D representations of the geometry of spacetime (e.g., the trampoline with spheres rolling around on it), one then sees what we commonly refer to as curves. But we don't actually "see" the supposedly curved or curving of space that apparently causes light to bend or curve as it passes the sun. No doubt, physicists often grab the most useful verbal (as opposed to mathematical) term to describe the effects that they are describing with the mathematics.

 

Indeed, given that spacetime may ultimately be found to be just an abstract concept that works, and there may be other reasons that better explain the effects found in relativity, e.g., time dilation. For example, the time dilation effects reported by clocks (e.g., atomic ones) can arguably be explained in terms of the slowing down of the mass of things within the clock, and not slowing down of time. Then there is the argument that spacetime is "immaterial" so how can it affect nonmaterial things or even photons via gravity, an alleged product of the curving of spacetime?

 

As to possible alternative or variant explanations, I refer you to

  • "Gravitation", by Misner, Thorne and Wheeler, e.g., p. 1005
  • "Space,Time, and Spacetime by L. Sklar e.g., comments about the inconclusiveness of Einstein's non-Euclidean view of the universe
  • "The Living Universe" by James Carter

 

 

 

Edited by disarray
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Can someone please tell me how to copy and paste part of a previous post using the process that includes the two-toned gray headings? Thanks.

Swansont: You state: Is spacetime a real thing, or is it a conceptual construct? I go with the latter. You can't grab a bit of spacetime and hand it to me.

So saying spacetime is curves is another way of saying the natural geometry that describes what's going on is curved.

 

Does it not depend upon what ones expectations are when one asks if it is a "thing." Of course, we cannot grab it like we can a wrench and hand it to someone. And no, I am not davigating off into the dubious realm of arguing that abstract things such as space, time, beauty and honesty are "things" pertinent to the study of physics. Arguably, spacetime is all that exists anyway, or rather, that "things," (as defined as objects having mass) are really just symptomatic of warps, of whatever kind, in spacetime anyway.

 

Yes, it depends on what you mean by real, which is why I gave my example. One could mean real vs illusion, or fake, but that really doesn't fit the dialog because it doesn't come down to whether a choice of geometry is being used to trick somebody. So my view is that it's physical vs conceptual.

 

Spacetime isn't all that exists. You are not made of spacetime.

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Swansont:

Your example being that you can't grab a handful of it, therefore it can't be real? Um, I can't grab a handful of gravity....would you say that gravity is not real? I suppose that I could say that one cannot grab air, but that only serves to illustrate that your example can't be taken all that literally. I am not suggesting that space-time is all that exists, but rather, perhaps that space-time somehow has a hand in creating matter...perhaps some perturbation, as they say, in the Higgs-Boson field, which is, I gather, getting pretty close to saying what spacetime "really" is.

 

I don't agree that the opposite of "real" is just fakery and illusions. Indeed, quantum physicists will be the first ones to tell you that mathematical models are all they have...that is, they are all "illusory," or that indeed, we don't know what reality is "real-ly" like, or what reality really is, so we have no way of saying that something is or is not "real" when talking about such things as the reality of spacetime.

 

For the moment, we don't know whether time is a fundamental property of the universe or not, or that, like 'temperature' which used to be thought of as a fundamental "thing," we now think of as just an increase in the rate of movement of molecules.

 

In this regard, I think that the 'real' issue is that of the relation between space and time. A representative article states that:

 

"While 4D spacetime is usually considered to consist of three dimensions of space and one dimension of time, the researchers’ view suggests that it’s more correct to imagine spacetime as four dimensions of space. In other words, as they say, the Universe is “timeless.”

http://www.dailygalaxy.com/my_weblog/2012/04/weekend-feature-space-is-4d-theory-claims-that-time-is-not-the-4th-dimension.html

Edited by disarray
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Can someone please tell me how to copy and paste part of a previous post using the process that includes the two-toned gray headings? Thanks.

Highlight selection in the post > Right-click it > Click Copy > Click the speech bubble icon to the left of of the Twitter icon > Paste selection. There will be no name header though it will just say 'Quote'. Like this:

 

Can someone please tell me how to copy and paste part of a previous post using the process that includes the two-toned gray headings? Thanks.

To have the name attributed like the first one I clicked Quote in the post then deleted the bit's I didn't want.

Edited by StringJunky
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All my life I have been an avid outdoorsman - I hike, I kayak, I camp, and all of it in really remote areas. When I set off on a hike I always take detailed topographic maps of the area with me ( not a fan of GPS, except in emergencies ); the map shows me the structure of the landscape, and by the density of altitude lines I can judge just exactly how steep an ascent or descent is going to be. It is obvious that the map is not identical with the terrain itself - I hike in the real world, not on a map. Nonetheless, there is a clear and very definitive relationship between the map and the territory it represents - the map isn't the territory, but it accurately reflects all its relevant features, such as the shape and geometry of rivers, lakes, hills and mountains, and the steepness of inclines. These features are quite real.

 

The same is true for GR. It is a mathematical model that allows us to describe the relationship between events in spacetime, by considering these events to be points on a 4-dimensional manifold. The presence of curvature just means that events are related differently to one another, as compared to regions which are not curved. This is an abstract description ( =map ), yet once again there is a definitive relationship between the map and the territory it depicts, because when I go and take clocks and rulers to physically measure those relationships, then I am going to find exactly what my map tells me I would find, just like when I go hiking.

 

So is curvature real or not ? Curved spacetime ( = the map ) is not identical to the territory it describes ( = the real universe ), but it captures and accurately describes all relevant features of the real world, just like any really good map would. In that sense, curvature is quite real, because when I go and measure with clocks and rulers ( e.g. Pound-Rebka ), I find relationships between events that correspond exactly to what my map tells me.

 

The precise relationship between map and territory, and what constitutes "reality" in that context and what does not, is largely a philosophical matter. Physics does not do philosophy, it concern itself only with making increasingly accurate models / maps of the universe around us. As such, GR is pretty much as "real" as it gets.

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All my life I have been an avid outdoorsman - I hike, I kayak, I camp, and all of it in really remote areas. When I set off on a hike I always take detailed topographic maps of the area with me ( not a fan of GPS, except in emergencies ); the map shows me the structure of the landscape, and by the density of altitude lines I can judge just exactly how steep an ascent or descent is going to be. It is obvious that the map is not identical with the terrain itself - I hike in the real world, not on a map. Nonetheless, there is a clear and very definitive relationship between the map and the territory it represents - the map isn't the territory, but it accurately reflects all its relevant features, such as the shape and geometry of rivers, lakes, hills and mountains, and the steepness of inclines. These features are quite real.

 

The same is true for GR. It is a mathematical model that allows us to describe the relationship between events in spacetime, by considering these events to be points on a 4-dimensional manifold. The presence of curvature just means that events are related differently to one another, as compared to regions which are not curved. This is an abstract description ( =map ), yet once again there is a definitive relationship between the map and the territory it depicts, because when I go and take clocks and rulers to physically measure those relationships, then I am going to find exactly what my map tells me I would find, just like when I go hiking.

 

So is curvature real or not ? Curved spacetime ( = the map ) is not identical to the territory it describes ( = the real universe ), but it captures and accurately describes all relevant features of the real world, just like any really good map would. In that sense, curvature is quite real, because when I go and measure with clocks and rulers ( e.g. Pound-Rebka ), I find relationships between events that correspond exactly to what my map tells me.

 

The precise relationship between map and territory, and what constitutes "reality" in that context and what does not, is largely a philosophical matter. Physics does not do philosophy, it concern itself only with making increasingly accurate models / maps of the universe around us. As such, GR is pretty much as "real" as it gets.

Very nice and lucid description, thanks Markus. +1

Edited by StringJunky
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My own perspective is that it is impossible to disentangle theory from reality in a satisfactory way. What we see as 'reality' comes from experiments and observations. We take our machines and produce arrays of numbers - but to make sense of any of that we need a theory. Thus, one cannot really separate the two. It is also quite possible that a data set can fit two different theoreies well; two scientists can look at the same data and see very different things.

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So is curvature real or not ? Curved spacetime ( = the map ) is not identical to the territory it describes ( = the real universe ), but it captures and accurately describes all relevant features of the real world, just like any really good map would.

 

 

Excellent post, Markus.

 

However, there is a difference. In the case of landscape and maps, we can look at both and compare them. But in the case of GR, we only have the map. We know nothing else about "reality" (we don't even know if it exists!)

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My own perspective is that it is impossible to disentangle theory from reality in a satisfactory way. What we see as 'reality' comes from experiments and observations. We take our machines and produce arrays of numbers - but to make sense of any of that we need a theory. Thus, one cannot really separate the two. It is also quite possible that a data set can fit two different theoreies well; two scientists can look at the same data and see very different things.

 

Yes, the data can be a sort of Rorschach test, and indeed, I think that we can apply more criteria to a model than just saying that, in a pragmatic sense. it works.

 

And again, sometimes we can "see" the difference between the model and the modelled (the sign and the signified). We can see that a topographical map, especially a very realistic one, visually matches up with the terrain that it describes. Indeed, in that case we start with what is modeled, the terrain, and then make the map. Not so with quantum reality, where what is modeled (philosophically referred to as the noumena) is inaccessible, so that we can't start with the modeled and make the phenomena (e.g. we can't see atoms and then make our models from that).

 

Physical maps provide a special case that I don't think that one can automatically apply to all models that might be said to be scientific to one extent or another. Indeed, when it comes to economic, political, sociological, and political models, there seems to be an even greater range of interpretations that might be made of a person, a group of people, the interactions between a group of people, etc. Indeed, we can find interpretations that are in many respects diametrically opposed to each other, particularly when the models are meant to be prescriptive as well as descriptive, as, for example, the economic models of capitalism and socialism (and indeed we can have various mixtures or hybrids of these two models).

 

An example of such opposition in the field of psychology (which some say can be classified as a science and some say it can't) could be said to be found in the contrast between, say, existential psychology and Skinnerian behavioral psychology (e.g., in that the former emphasizes free will and the latter denies it). I think that this is a good example in that a patient could be seeing both types of psychologists and getting diametrically opposed advice and treatment.

 

Just as their are criteria for determining the 'validity' of a given cause-effect relationship, so too should there be criteria for at least attempting to determine the 'validity' of any given model. Such criteria might include popular belief, predictive value, reliability, ease of manipulating what is modeled, heuristic value, utilitarian value, theoretical consistency, etc.

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In the case of landscape and maps, we can look at both and compare them. But in the case of GR, we only have the map. We know nothing else about "reality" (we don't even know if it exists!)

 

 

While I understand what you are trying to say, I nonetheless disagree with you. "Reality" in the context of physics is what we can measure with our instruments; in the specific case of GR, reality is what clocks and rulers measure. We can very easily compare our map ( = curved spacetime ) against real, physical measurements taken of space ( rulers ) and time ( clocks ). That is why I mentioned the Pound-Rebka experiment, since it is a nice case-in-hand to demonstrate this.

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Excellent post, Markus.

 

However, there is a difference. In the case of landscape and maps, we can look at both and compare them. But in the case of GR, we only have the map. We know nothing else about "reality" (we don't even know if it exists!)

I know what you you mean but Markus's example illustrates what's happening between transferring the numbers into a pictorial representation, which is happening the same when you represent the spacetime plot values as a picture.in terms of curvature distribution. It's just that we can actually see the physical terrain of land to understand his comparison with spacetime curvature.. Ordnance Survey maps are not photographs of the terrain but abstract representations of it; just like spacetime maps.

 

Edit: removed misplaced word.

Edited by StringJunky
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MODEL needs to represent REALITY exactly to qualify for being a 100 % Model

 

If this 100% Model is used to observe that Reality by 100% sane, logical & unbiased Observers, then this Group of Observers will accept this Model as TRUE

 

However TRUTH about Reality will be only perceived / understood RELATIVELY by ALL as it needs 100% understanding of the Definitions of the Model, 100% ability to apply it on the Reality and 100% ability to interpret, mathematically analyze and assimilate the Observed Results !

Edited by Commander
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While I understand what you are trying to say, I nonetheless disagree with you. "Reality" in the context of physics is what we can measure with our instruments; in the specific case of GR, reality is what clocks and rulers measure. We can very easily compare our map ( = curved spacetime ) against real, physical measurements taken of space ( rulers ) and time ( clocks ). That is why I mentioned the Pound-Rebka experiment, since it is a nice case-in-hand to demonstrate this.

 

 

That is actually exactly what I was [trying] to say!

I know what you you mean but the Markus's example illustrates what's happening between transferring the numbers into a pictorial representation, which is happening the same when you represent the spacetime plot values as a picture.in terms of curvature distribution. It's just that we can actually see the physical terrain of land to understand his comparison with spacetime curvature.. Ordnance Survey maps are not photographs of the terrain but abstract representations of it; just like spacetime maps.

 

OK, in Markus's analogy, the numbers are the reality that is mapped by GR.

 

But the numbers aren't "reality", they are just what we are able measure with our instruments. (But that is probably getting further into the philosophy than we need to!)

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But the numbers aren't "reality", they are just what we are able measure with our instruments. (But that is probably getting further into the philosophy than we need to!)

This is it, as you you know, the parameter numbers or measurements are as close to 'touching' reality as we are going to get.

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I am not sure that one should avoid philosphy when discussing the relationship between models and modeled (aka "reality")

 

So we can have sets of numbers that we can use to create a topographical map with wavy concentric-like lines (as well as numbers next to them) that have some vague visual correlation with a pictorial map, which in turn has some vague visual correlation with the images that our brain recreates from the light waves that come to it from the retina, that presumably has an even better visual correlation with the world as it supposedly really is. Seems like we're putting a heck of a lot of emphasis on the visualization factor in all of this. (Indeed, we are getting into Truth theories dealing with correlation an representation).

 

Note that we are using "visual" correlation (e.g., much like we might compare a hand drawn picture of a horse on a transparent sheet of plastic by placing it over the picture of a horse, or over the horse itself). But again, visual correlation is just one way to value the verisimilitude of the model.

 

I would make the point that if one could see things from a hypothetical God's eye view, as to how they "really" are, one would see something like the old-fashioned tv screens after broadcasting stopped...just a hodge podge of static, not mountains and rivers, which are the images that our brain puts together (best guess and analogy I could come up with).

 

Science of course is fundamentally meant to do things and thus has traditionally not spent too much time talking about why, but rather about "how." However, since science seems to have reached something of an impasse when it comes to such things as finding common ground between Relativity and Quantum theories, I think that there is nothing wrong with a little armchair philosophizing about such things as the Copenhagen theory...

 

Indeed, a bit of philosophical clarification might be of use not only to scientists in that they are less likely to go down cul de sacs of reasoning (or to be mislead by their own use of everyday language), but also to avoid the sort of haphazard popularization of things such as quantum theory in the hands of the general public, e.g., the idea that quantum theory proves that free will exists, or that quantum theory proves that your dreams can come true because you just need to visualize something and it will come true, because our minds can turn light into particles or waves depending upon what we expect to see, etc.

 

In a simplistic nutshell, there is something of a difference between the science of making a mechanical clock, and the science behind the issue of Schrodinger's cat. For one thing, the accessibility of direct sensory information is a crucial factor.

Edited by disarray
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...'validity' of any given model.

The only validity we use - and should only use - is that it must match nature well, taking into account domain of validity, experimental errors and so on.

 

Such criteria might include popular belief, predictive value, reliability, ease of manipulating what is modeled, heuristic value, utilitarian value, theoretical consistency, etc.

Some of these are already used to some extent. But forget popular beleif.

 

A theory must have some predictive power, or really it is not a physical theory. The ease of use and huristic value come into play when using a theory, but do not define a fully meaningful way of deciding if one theory is 'better' than another. Effective theoreis are built with utilitarian value in mind, but are not fundamental. Theoretical consistency I think is important, but this is not at all clear in general.

 

I am not sure that one should avoid philosphy when discussing the relationship between models and modeled (aka "reality")

You are right, and this whole mess is metaphysics :) I try to avoid deep metaphysical wells!

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This is it, as you you know, the parameter numbers or measurements are as close to 'touching' reality as we are going to get.

 

 

Exactly.

 

I am not sure that one should avoid philosphy when discussing the relationship between models and modeled (aka "reality")

 

 

You can't avoid it. It is a philosophical question.

 

 

 

Indeed, a bit of philosophical clarification might be of use not only to scientists in that they are less likely to go down cul de sacs of reasoning (or to be mislead by their own use of everyday language), but also to avoid the sort of haphazard popularization of things such as quantum theory in the hands of the general public, e.g., the idea that quantum theory proves that free will exists, or that quantum theory proves that your dreams can come true because you just need to visualize something and it will come true, because our minds can turn light into particles or waves depending upon what we expect to see, etc.

 

Do you have any evidence that scientists are misled by such things?

 

 

 

In a simplistic nutshell, there is something of a difference between the science of making a mechanical clock, and the science behind the issue of Schrodinger's cat. For one thing, the accessibility of direct sensory information is a crucial factor.

 

Not really. Measurements are measurements. Whether made by something we are familiar with (rulers and clocks) or more sensitive instruments that seem to reveal obscure counter-intuitive results.

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But the numbers aren't "reality", they are just what we are able measure with our instruments. (But that is probably getting further into the philosophy than we need to!)

 

 

I think that, within the context of physics ( as opposed to other domains of enquiry ), the numerical outcome of measurements taken is precisely what constitutes objective reality, and that premise is what the scientific method is based on. One can philosophise about some type of "hidden" reality somewhere "behind" the outcome of measurements taken, but that is at best metaphysics, at worst full-blown philosophy. This may be a tenable point of view if one constricts himself to the classical domain only, but it demonstrably fails if you look at the bigger picture and consider the quantum domain also. Here, if one simultaneously assumes both Einstein locality and counterfactual definiteness ( i.e. the notion that there is an objective reality independent from any measurements performed ), there is an upper bound as to how strongly measurement outcomes can possibly be correlated - that's precisely the Bell inequalities. It is experimental fact that in the real world those inequalities are violated, which means we need to give up either Einstein locality or counterfactual definiteness ( = realism ) in order to correctly model the universe. It is difficult to imagine how giving up Einstein locality can be meaningfully reconciled with the observed causal structure of spacetime - especially given the fact that Lorentz invariance, and hence CPT invariance, appear to be fundamental symmetries -, so my argument stands that we are pretty much forced to let go of the idea that there is some type of reality separate from what we can measure, unless some future model ( quantum gravity ? ) completely overturns our understanding of spacetime and causality, which of course I can't rule out.

 

None of this is really relevant for GR as such, but it does become relevant when one looks beyond GR at the bigger picture.

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I think that, within the context of physics ( as opposed to other domains of enquiry ), the numerical outcome of measurements taken is precisely what constitutes objective reality, and that premise is what the scientific method is based on. One can philosophise about some type of "hidden" reality somewhere "behind" the outcome of measurements taken, but that is at best metaphysics, at worst full-blown philosophy. This may be a tenable point of view if one constricts himself to the classical domain only, but it demonstrably fails if you look at the bigger picture and consider the quantum domain also. Here, if one simultaneously assumes both Einstein locality and counterfactual definiteness ( i.e. the notion that there is an objective reality independent from any measurements performed ), there is an upper bound as to how strongly measurement outcomes can possibly be correlated - that's precisely the Bell inequalities. It is experimental fact that in the real world those inequalities are violated, which means we need to give up either Einstein locality or counterfactual definiteness ( = realism ) in order to correctly model the universe. It is difficult to imagine how giving up Einstein locality can be meaningfully reconciled with the observed causal structure of spacetime - especially given the fact that Lorentz invariance, and hence CPT invariance, appear to be fundamental symmetries -, so my argument stands that we are pretty much forced to let go of the idea that there is some type of reality separate from what we can measure, unless some future model ( quantum gravity ? ) completely overturns our understanding of spacetime and causality, which of course I can't rule out.

 

None of this is really relevant for GR as such, but it does become relevant when one looks beyond GR at the bigger picture.

For myself, I liken modelling reality to trying to describe an object in a black bag with holes in for your hands as the only means of extracting information about it. From that you build a model which is necessarily incomplete.

Edited by StringJunky
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Swansont:

 

Your example being that you can't grab a handful of it, therefore it can't be real? Um, I can't grab a handful of gravity....would you say that gravity is not real? I suppose that I could say that one cannot grab air, but that only serves to illustrate that your example can't be taken all that literally. I am not suggesting that space-time is all that exists, but rather, perhaps that space-time somehow has a hand in creating matter...perhaps some perturbation, as they say, in the Higgs-Boson field, which is, I gather, getting pretty close to saying what spacetime "really" is.

It seemed to me that we talking about objects rather than phenomena. Gravity isn't a substance. The effect of curved spacetime is real, but that's the second definition I mentioned. It's not an illusion.

 

Don't take "grab" so literally. You can't hand me a container of air?

 

I don't agree that the opposite of "real" is just fakery and illusions. Indeed, quantum physicists will be the first ones to tell you that mathematical models are all they have...that is, they are all "illusory," or that indeed, we don't know what reality is "real-ly" like, or what reality really is, so we have no way of saying that something is or is not "real" when talking about such things as the reality of spacetime.

I'm a quantum physicist, and I'm not claiming that QM is an illusion. I can't speak for others, but I'm confident that they would tell you no, QM actually works that way. Outcomes are probabilistic, rather than being a smokescreen for some classical physics working behind the scenes.

 

For the moment, we don't know whether time is a fundamental property of the universe or not, or that, like 'temperature' which used to be thought of as a fundamental "thing," we now think of as just an increase in the rate of movement of molecules.

 

In this regard, I think that the 'real' issue is that of the relation between space and time. A representative article states that:

 

"While 4D spacetime is usually considered to consist of three dimensions of space and one dimension of time, the researchers’ view suggests that it’s more correct to imagine spacetime as four dimensions of space. In other words, as they say, the Universe is “timeless.”

http://www.dailygalaxy.com/my_weblog/2012/04/weekend-feature-space-is-4d-theory-claims-that-time-is-not-the-4th-dimension.html

 

It's not representative if it's touted as a new finding. Too much to go into here, but that article leaves a lot to be desired. (The mentions of absolute time, for one. That's debunking a notion that relativity dismantled more than a century ago. Hardly a "stop the presses!" moment)

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