Spacetime, physical or not really?

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I try to get the gist of the Special and General theories of relativity for more than two years now. And I still don't understand if the geometrical explanation really explains or just describes what is physically going on when talking about all the relativistic effects (like gravitation, time dilation and space contraction).

This is what I mean by the difference between "explains" and "describe":

Are the theories of relativity physical theories, in a sense that the mechanism of the relativistic effects can be explained by energy transfer or interaction (in whatever form), like I believe any physical theory should and does?

A related question is if spacetime itself is a form of energy and for example gravitational attraction can be exlained as an energy interaction between objects and curved spacetime or the curved spacetime is just an abstraction that let us model the outcome of some other physical (in the defined sense) processes but is not the physical process itself that is responsible for the relativistics effects?
 

atyy

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Special relativity is not really about time dilation or length contraction. It is about a symmetry in the laws of physics. Newtonian physics had a symmetry called Galilean symmetry. Special relativity replaces the Galilean symmetry of Newtonian physics with Lorentz symmetry.

General relativity is a theory of gravity. The gravitational field interacts with matter, and matter interacts with the gravitational field. Matter carries localizable energy, but the gravitational field does not. It is possible in some cases to say that the grvitational field carries non-local energy.
 
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Special relativity is not really about time dilation or length contraction. It is about a symmetry in the laws of physics. Newtonian physics had a symmetry called Galilean symmetry. Special relativity replaces the Galilean symmetry of Newtonian physics with Lorentz symmetry.
Well, take for example the twin paradox. One of the twins comes back to Earth and is evidently younger than the other twin that stayed on the Earth. Can you tell me what physical law (that involves exchange or transformation of energy) and by what mechanism caused the difference in age of the twins? Something physical happened there and a physical explanation is needed to explain how. I'm afraid that the answer that laws of physics follow the Lorentz symmetry doesn't quite explain how the change in age happened. It only states that the result in the age is to be expected.
It's a subtle but important difference that makes a distinction between a theory that explains by describing a mechanism of how known objects transform from one form to another and a theory that describes consequences of some other processes that it really doesn't take into account (or care about).

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To me the difference between the theory of Special or General relativity and another theory (that I hoped to learn instead) is like a difference between a theory that predicts that when you make a fire you will feel warm and a theory that says that when you make a fire the chemically interacting gasses that make it radiate also infrared electromagnetic radiation that will interact with atoms and molecules in your body in such a way that it will make them jiggle more and this is what you will perceive as warmth.
Unfortunately I see that the both of the relativity theories are more of the first kind than the second. Or am I wrong? (I'd rather be wrong :)

General relativity is a theory of gravity. The gravitational field interacts with matter, and matter interacts with the gravitational field.
You use a well defined term of "field" from particle physics and yet the General relativity is all about inertial movement in geodesics in curved spacetime. There is no relation to a field in its terminology in the particle theory sense because a field is a means (form of) of energy that mediates energy transfer or interaction. Do you consider spacetime to be a field in this sense?
Matter carries localizable energy, but the gravitational field does not. It is possible in some cases to say that the grvitational field carries non-local energy.
Can you elaborate on this? What do you mean by that "the gravitational field" carries non-local energy?
 
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Are the theories of relativity physical theories, in a sense that the mechanism of the relativistic effects can be explained by energy transfer or interaction (in whatever form), like I believe any physical theory should and does?
I think that according to this unusual definition of "physical theory" SR does not qualify. I would see that as a clear failing of the definition, not the theory.
 

atyy

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Your question about the "physical mechanism" of ageing in the twin paradox is interesting. It's too hard for me to answer off the top of my head.

You use a well defined term of "field" from particle physics and yet the General relativity is all about inertial movement in geodesics in curved spacetime. There is no relation to a field in its terminology in the particle theory sense because a field is a means (form of) of energy that mediates energy transfer or interaction. Do you consider spacetime to be a field in this sense?
I'm using field in the sense of classical field theory, with spacetime being a field. General relativity is not formulated fundamentally as geodesics in curved spacetime. Rather there are a bunch of fields like the electromagnetic field and spacetime, and equations describing their motion. The equations that describe the motion of the electromagnetic field are Maxwell's equations, and the analogous equation for spacetime is the Einstein Field Equation. This is not a field in the particle physics sense, where gravity is a spin-2 field on flat spacetime.

Can you elaborate on this? What do you mean by that "the gravitational field" carries non-local energy?
Yau gives a short introduction here.
 
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One of the twins comes back to Earth and is evidently younger than the other twin that stayed on the Earth. Can you tell me what physical law (that involves exchange or transformation of energy) and by what mechanism caused the difference in age of the twins?
The traveling twin has to fire rockets at some point in his trajectory in order to come back to Earth; the Earth twin can stay in free fall the whole time. (We are assuming that the Earth twin is really floating in space near the Earth, perhaps in a far orbit, so the question of the Earth's own gravity doesn't enter into it and the "Earth" twin can be in free fall the whole time.) Does the firing of rockets by the traveling twin qualify as "exchange or transformation of energy"?
 
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You use a well defined term of "field" from particle physics and yet the General relativity is all about inertial movement in geodesics in curved spacetime. There is no relation to a field in its terminology in the particle theory sense because a field is a means (form of) of energy that mediates energy transfer or interaction. Do you consider spacetime to be a field in this sense?
I'm using field in the sense of classical field theory, with spacetime being a field. General relativity is not formulated fundamentally as geodesics in curved spacetime. Rather there are a bunch of fields like the electromagnetic field and spacetime, and equations describing their motion. The equations that describe the motion of the electromagnetic field are Maxwell's equations, and the analogous equation for spacetime is the Einstein Field Equation. This is not a field in the particle physics sense, where gravity is a spin-2 field on flat spacetime.
To emphasize atyy's point, tensors are sometimes called tensor fields to emphasize the point that they are defined over some extended region of spacetime. In GR, the spacetime is represented by the manifold and "gravity" is a tensor field (the metric) on the manifold. You can also have matter fields represented by the stress-energy tensor. The Einstein field equations give the relationship between the matter fields and the gravity fields.

They are all classical fields, not quantum fields.
 
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The traveling twin has to fire rockets at some point in his trajectory in order to come back to Earth; the Earth twin can stay in free fall the whole time. (We are assuming that the Earth twin is really floating in space near the Earth, perhaps in a far orbit, so the question of the Earth's own gravity doesn't enter into it and the "Earth" twin can be in free fall the whole time.) Does the firing of rockets by the traveling twin qualify as "exchange or transformation of energy"?
Sure it does. Nothing else really happens or?
So the theory of Special relativity will say that (I'm quoting PAllen #9 from t=558360) "the path with greater deviation from an inertial path will accumulate less time".
Great, case closed. But does this answer really satisfy you? "Make a fire, you will feel warmth." A really practical theory it is. You can build a civilization based on this prediction of the theory.
You can make a satellite GPS navigation possible when you combine the Special and General theory of relativity. A remarkable practical achievement.
But does the theory explain how the fire will make you feel warmth? Does it explain how the increased movement of the rocket in space provided by the energy from the rocket engines will lead to real slower movement of every particle that is moving with it? Of course all that only relative to the "stationary twin". Or it will just say that it will happen? You tell me.
 

pervect

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Well, take for example the twin paradox. One of the twins comes back to Earth and is evidently younger than the other twin that stayed on the Earth. Can you tell me what physical law (that involves exchange or transformation of energy) and by what mechanism caused the difference in age of the twins?
Answering your question directly may not help you, because you're asking the wrong questions, probably based on false assumptions about what relativity is about. But here goes anyway. The law that makes one twin age less does not involve any exchange or transformation of energy. It's more of a mathematical law, than a physical law.

In Euclidean geometry, we have the triangle inequality. If you have a triangle with sides AB, AC, and BC, you can say that the length of AB, |AB| is greater than the sums of the lengths of the sides AC+BC, i.e |AB| <= |AC|+|BC|, where I use the || notation to indicate that one is measuring length.

The space-time geometry of special relativity is not Euclidean, but Miinkowskian. This sort of geometry has curves in both space and time, the former curves are called "spacelike" curves, and the later "timelike" curves. The length of a space-like curve on a diagram represents a physical length that you'd measure with a ruler. The length of a time-like curve on a space-time diagram represents a physical time , also known as a proper time, that you'd measure with a clock.

It's a feature of the geometry that the triangle law holds unmodified for spacelike curves , i.e. for spacelie curves |AB| <= |AC|+|CB|, while the triangle inequality is reversed for timelike curves, i.e. for timelike curves |AB| >= |AC|+|CB|. Going into the details of how the geometry works would take a very long post to do well (and you'd do better to study a textbook than to try to learn it from posts), so this is just a very brief sketch of what's actually needed to answer your question.

The point is that the triangle inequality, and the triangle inequality alone, is sufficient to say that if you have two twins that separate and reunite, the twin that travels in a straight line , going directly from A to B, will age more than the twin that makes a stop at some point C which is not on the line AB. (If point C is on AB, then the equality part of the inequality is used, and the two twins age the same).

You'll need more than this one property (the triangle inequality) of special relativity to get anywhere. I'd suggest "Space-time physics' by Taylor & Wheeler. You can find the first few chapters of an earlier edition on the web. Length contraction and time dilation are NOT the whole story of special relativity. The piece that usually goes missing is the relativity of simultaneity. I'm not sure why the piece goes missing, but it happens a lot. I guess people don't understand what "relativity of simultaneity" means, so they ignore the concept. "Just a string of words". Unfortunately, it's an important concept, and you get into all kinds of confusion if you ignore it.
 
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[..] To me the difference between the theory of Special or General relativity and another theory (that I hoped to learn instead) is like a difference between a theory that predicts that when you make a fire you will feel warm and a theory that says that when you make a fire the chemically interacting gasses that make it radiate also infrared electromagnetic radiation that will interact with atoms and molecules in your body in such a way that it will make them jiggle more and this is what you will perceive as warmth.
Unfortunately I see that the both of the relativity theories are more of the first kind than the second. Or am I wrong? (I'd rather be wrong :) [..]
Quite right - Newton would have called those theories, as well as quantum mechanics, "mathematical" theories of physics. And his theory was in part also just mathematical: he gave equations but no physical explanation for gravitation.

However, even a mathematical theory can hint at what may be "hidden" underneath it. In the case of GR, roughly two physical interpretations have been forwarded (that is to say that I don't know of a third one): either a physical "space" (or "ether") which determines the local speed of physical processes ("time"), or a physical "spacetime" (or "block universe") that governs everything. The first relates to a Lorentzian interpretation, and the second relates to a Minkowskian interpretation (although he was already dead when GR saw the light) - or as you say, a geometrical explanation. Depending on who you ask or which papers you read, Einstein favoured at certain times one or the other (or maybe both?); and that was possible because GR is a principle theory, and not based on a hidden physical model.

Addendum, I had missed:
I'm afraid that the answer that laws of physics follow the Lorentz symmetry doesn't quite explain how the change in age happened. It only states that the result in the age is to be expected.
It's a subtle but important difference that makes a distinction between a theory that explains by describing a mechanism of how known objects transform from one form to another and a theory that describes consequences of some other processes that it really doesn't take into account (or care about).
Pervect already provided the geometrical explanation. The Lorentzian explanation (if he really understood this) was given by Langevin in the sections of p.47 and 50-53 of http://en.wikisource.org/wiki/The_Evolution_of_Space_and_Time
 
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Can you tell me what physical law (that involves exchange or transformation of energy) and by what mechanism caused the difference in age of the twins?
I have a rectangular desk, the path from one corner to the opposite corner is longer if it goes straight along the edges than if it goes diagonally across. Can you tell me what physical law that involves exchange or transformation of energy causes the difference in path length?
 
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The law that makes one twin age less does not involve any exchange or transformation of energy. It's more of a mathematical law, than a physical law.
Ok, this is what I needed to know. My problem with this is more conceptual than physical, I guess. And I'm bumping to this problem from various sides again and again (as maybe DaleSpam will remember).

The problem is that I cannot see how a mathematical law operating within a seemingly man-made framework (spacetime) can have an influence on physical reality. If it really has an influence and can interact with it, that must mean that it or a part of it must be physically real too. If this is true and spacetime through its geometry really influences matter and energy then it means that the spacetime is real in the sense too. But when I ask this question I usually get the answer that atty mentioned here and DaleSpam confirmed. That the spacetime "is not a field in the particle physics sense". Then I am back again scratching my head trying to understand how can something non-physical have a physical influence.
You'll need more than this one property (the triangle inequality) of special relativity to get anywhere. I'd suggest "Space-time physics' by Taylor & Wheeler. You can find the first few chapters of an earlier edition on the web. Length contraction and time dilation are NOT the whole story of special relativity. The piece that usually goes missing is the relativity of simultaneity. I'm not sure why the piece goes missing, but it happens a lot. I guess people don't understand what "relativity of simultaneity" means, so they ignore the concept. "Just a string of words". Unfortunately, it's an important concept, and you get into all kinds of confusion if you ignore it.
Maybe you are right and deeply understanding the concept of "relativity of simultaneity" will help me to understand how the experimentally observed and theoretically predicted geometry of spacetime is a necessary and the only one way of how to maintain principle of causality in the Universe (I guess you wanted to hint to this). From this imperative I can imagine that the spacetime geometry and its effect on matter/energy will come out as necessary and logical. Thank you for your explanation and recommendation.
 
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ZirkMan, if you are interested in Special Relativity what pervect is a perfect way to formally introduce yourself to SR with little - no math.

I found the right-angle triangle explains alot and is a great way to introduce spacetime diagrams (which are a great way to introduce "relativity of simultaneity").

The classic "light-clock" of two mirrors with a photon bouncing back and forth is a great visual of the right-angle triangle "in action".

With all that being said, I found that actually playing with the simple math of the Pathagorean Theory and playing with spacetime diagrams the concepts of SR are fairly easily "discovered".

As far as the question does SR explain or simply desrcibe relativistic effects, I'd say the two postulates of SR "explains" the "mechanism" that determines relativistic effects.

Of course this is not the same as explaining the mechanics of the postulate itself. But you have to stop asking why at some point and just accept something as being fundamental.
 
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I have a rectangular desk, the path from one corner to the opposite corner is longer if it goes straight along the edges than if it goes diagonally across. Can you tell me what physical law that involves exchange or transformation of energy causes the difference in path length?
This is a very good question and analogy. I will need to think about this.
 
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The problem is that I cannot see how a mathematical law operating within a seemingly man-made framework (spacetime) can have an influence on physical reality. If it really has an influence and can interact with it, that must mean that it or a part of it must be physically real too. If this is true and spacetime through its geometry really influences matter and energy then it means that the spacetime is real in the sense too. But when I ask this question I usually get the answer that atty mentioned here and DaleSpam confirmed. That the spacetime "is not a field in the particle physics sense". Then I am back again scratching my head trying to understand how can something non-physical have a physical influence.
Do you somehow think that geometry is not physical?

Consider a table. You can make all sorts of material statements about it, it has a certain mass, a given temperature, etc. You can also make all sorts of geometric statements, it has a certain length, surface area, etc.

Do you believe that the material statements are "physical" while the geometric statements are non-"physical"? If so, I would suggest that your definition of "physical" needs some adjustment.

PS sorry about excessive furniture analogies :smile:
 
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Do you somehow think that geometry is not physical?

Consider a table. You can make all sorts of material statements about it, it has a certain mass, a given temperature, etc. You can also make all sorts of geometric statements, it has a certain length, surface area, etc.

Do you believe that the material statements are "physical" while the geometric statements are non-"physical"? If so, I would suggest that your definition of "physical" needs some adjustment.

PS sorry about excessive furniture analogies :smile:
Geometry of a physical object like any piece of furniture is of course physical.

But geometry of an invisible object that is not made by anything physical (virtual particles aside, we are talking about space as a dimension now) and one of its dimensions is temporal (which is even a higher order of abstraction) is another thing.
Since spacetime is not physical (like a table or an electromagnetic field is) I do not believe its geometry is physical either.
 

atyy

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ZirkMan, why can I drink coffee on an aeroplane without spilling it, just as if I were stationary on the ground? What is the physical mechanism that makes going very fast just the same as not moving?
 
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Geometry of a physical object like any piece of furniture is of course physical.
A table also has other geometrical features, such as duration (lifetime), etc. Those features of the table are just as physical as the other geometric features of the table. Do you agree with that?

But geometry of an invisible object that is not made by anything physical (virtual particles aside, we are talking about space as a dimension now) and one of its dimensions is temporal (which is even a higher order of abstraction) is another thing.
Since spacetime is not physical (like a table or an electromagnetic field is) I do not believe its geometry is physical either.
At this point I am just talking about the geometry of classical macroscopic material objects, not spacetime, fields, or quantum weirdness.
 

A.T.

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The problem is that I cannot see how a mathematical law operating within a seemingly man-made framework (spacetime) can have an influence on physical reality.
Humans develop mathematical models of the observable reality. The mathematical models don't influence reality. This applies to all of physics. not just GR.
 
Special relativity is not really about time dilation or length contraction. It is about a symmetry in the laws of physics. Newtonian physics had a symmetry called Galilean symmetry. Special relativity replaces the Galilean symmetry of Newtonian physics with Lorentz symmetry.

General relativity is a theory of gravity. The gravitational field interacts with matter, and matter interacts with the gravitational field. Matter carries localizable energy, but the gravitational field does not. It is possible in some cases to say that the grvitational field carries non-local energy.
First is right, second is only half right. GR is an extension of the principal of relativity to all frame, not just inertial. This is accomplished by replacing all equations with tensor equations. It was via thought experiment that once can conclude gravity = warped space-time if you assume the equivalence of inertial mass and gravitational mass. So, GR firstly extends SR into all coordinate systems (frames of reference), and secondly describes gravity via a correlation between accelerated reference frames and frames under gravity's pull.
 
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Matter carries localizable energy, but the gravitational field does not.
I agree with the second part but not with the first.

Could you explain what you mean by the first part with the understanding that where there is matter there is also a gravitational field.
 

atyy

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I agree with the second part but not with the first.

Could you explain what you mean by the first part with the understanding that where there is matter there is also a gravitational field.
Yes, there is that ambiguity that the stress energy of matter always requires the metric to be defined. But what I meant can be clarified by the "vacuum" of GR, where there is curvature but no matter. In those places the stress-energy tensor is zero, even though the curvature isn't.
 
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ZirkMan, why can I drink coffee on an aeroplane without spilling it, just as if I were stationary on the ground? What is the physical mechanism that makes going very fast just the same as not moving?
It's called inertia. And it's the reason why physical laws appear to be the same in all inertial frames. Details of how this is possible I would like to know too.
 
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A table also has other geometrical features, such as duration (lifetime), etc. Those features of the table are just as physical as the other geometric features of the table. Do you agree with that?
At this point I am just talking about the geometry of classical macroscopic material objects, not spacetime, fields, or quantum weirdness.
Well you can construct "a geometry" out of any set of variables that change as a function of basically anything that you are able to define. Be it a table or a concept of a Pink fairy Unicorn from the Netherworld. But the fact that an object has an geometry doesn't mean that the geometry has an impact of how physical objects behave.
The geometry of a table might have an impact of how many tables you are able to get into a car or how it rolls down stairs. The geometry of the concept of a Pink fairy Unicorn will most probably have zero influence on anything physical.
So it's really important when talking about an object's geometry to also say which kind of object we are talking about. Otherwise we are not able to assess if its geometry is physical (has an physical impact and consequences) or not.

Now let's come back to spacetime. I will use another analogy. Because spacetime is neither a table nor a concept of a Pink fairy Unicorn. It's more like a shadow because its very existence depends on existence of physical objects. So in a sense it is connected to the physical reality of matter and energy and one cannot live without the other. But does the spacetime have a physical impact? Does a shadow have an impact of whether a person will come through a door or how it rolls down stairs? I will leave you to decide as this is the question I am asking.
 
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[..] Then I am back again scratching my head trying to understand how can something non-physical have a physical influence. [..]
Obviously something non-physical can not have a physical influence; that's a wrong path to go!

Meanwhile in this thread you got presented two explanations: physical 4D space (the "geometrical" explanation) and physical 3D space (the "ether" explanation). I had forgotten that there also exist what appear to be intermediate explanations, such as by Harvey R. Brown. And as you can see from the following link, one quickly enters philosophy with that kind of discussions:
http://ndpr.nd.edu/news/25025-physical-relativity-space-time-structure-from-a-dynamical-perspective/
 

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