Additions:
====""""What is Spacetime?====
Deletions:
====""""What is spacetime?====
Additions:
<<**Answer 1.** There exists a [[http://plato.stanford.edu/entries/spacetime-theories/#5.2 substantive spacetime]], which is modelled (i.e. described) by the mathematical structure of a manifold.<<
Deletions:
<<**Answer 1.** There exists a [[http://plato.stanford.edu/entries/spacetime-theories/#5.2 substantive spacetime]], which is modelled (=described) by the mathematical structure of a manifold.<<
Additions:
Here the manifold simply replaces Newton’s conception of "" absolute space"" and "" absolute time"". This is what I call a metaphysical manifold, because there is no observation of a substantive spacetime, and nor can there be one. We //observe// the behaviour of matter, and //infer// the existence of space-time structure, but cannot actually observe it. Since substantive spacetime is scientifically unverifiable, at best it lies outside the realms of science. At worst (as I maintain), it is in conflict with observations in quantum theory.
The logical error lies in thinking that if we have a set of actual observations, B, and a theory, A with A=>B, then A must be true. In fact, there may be some other theory, C, which we may not know about, which also has C=>B, and such that C contradicts A. Modern physicists usually avoid the issue by denying that it is possible to describe nature:
Deletions:
In this conception, the manifold simply replaces Newton’s conception of "" absolute space"" and "" absolute time"". This is what I call a metaphysical manifold, because there is no observation of a substantive spacetime, and nor can there be one. We //observe// the behaviour of matter, and //infer// the existence of space-time structure, but cannot actually observe it. Since substantive spacetime is scientifically unverifiable, at best it lies outside the realms of science. At worst (as I maintain), it is in conflict with observations in quantum theory.
The logical error is in thinking that if we have a set of actual observations, B, and a theory A with A=>B, then A must be true. In fact, there may be some other theory, C, which we may not know about, which also has C=>B, and such that C contradicts A. Modern physicists usually avoid this issue by denying that it is possible to describe nature:
Additions:
Only measurements which are actually carried out have physical reality, and generate coordinates for physical events, whereas spacetime consists of all the ways in which this can conceivably be done. So, spacetime does not model reality — only the small subset of spacetime for which there are actual measurements corresponds to reality. Spacetime models our //conception// of reality, not reality itself. At the same time, spacetime does contain the real observational results required for comparison between theory and experiments.
Deletions:
Only measurements which are actually carried out have physical reality, and generate coordinates for physical events, whereas spacetime consists of all the ways in which this can conceivably be done. So, spacetime does not model reality ""&emdash;"" only the small subset of spacetime for which there are actual measurements corresponds to reality. Spacetime models our //conception// of reality, not reality itself. At the same time, spacetime does contain the real observational results required for comparison between theory and experiments.
Additions:
I always find it surprising when physicists advocate the idea that reality cannot be described, because it undermines the very purpose of physics. In fact, Einstein has already refuted the idea that science requires us to infer theory from agreement between prediction and experiment. [[FoundationsOfSpecialRelativity Special relativity]] is based on based on empirically verifiable //postulates//, the operational definitions of measurement. Einstein’s argument is the archetype according to which we should formulate modern scientific theory, starting with how we //define// the numerical quantities which we use in the scientific study of nature. Special relativity is imported, as local theory, into general relativity, and provides the basis for understanding what spacetime actually is:
Only measurements which are actually carried out have physical reality, and generate coordinates for physical events, whereas spacetime consists of all the ways in which this can conceivably be done. So, spacetime does not model reality ""&emdash;"" only the small subset of spacetime for which there are actual measurements corresponds to reality. Spacetime models our //conception// of reality, not reality itself. At the same time, spacetime does contain the real observational results required for comparison between theory and experiments.
Deletions:
I always find it surprising when physicists advance the idea that reality cannot be described, because it undermines the very purpose of physics. In fact, Einstein has already refuted the idea that science requires us to infer theory from agreement between prediction and experiment. [[FoundationsOfSpecialRelativity Special relativity]] is based on based on empirically verifiable //postulates//, the operational definitions of measurement. Einstein’s argument is the archetype according to which we should formulate modern scientific theory, starting with how we //define// the numerical quantities which we use in the scientific study of nature. Special relativity is imported, as local theory, into general relativity, and provides the basis for understanding what spacetime actually is:
Only measurements which are actually carried out have physical reality, and generate coordinates for physical events, whereas spacetime consists of all the ways in which this can conceivably be done. So, spacetime does not model reality &emdash; only the small subset of spacetime for which there are actual measurements corresponds to reality. Spacetime models our //conception// of reality, not reality itself. At the same time, spacetime does contain the real observational results required for comparison between theory and experiments.
Additions:
If we have some object, and we can show that that object has the properties of a manifold, then we can say that the object is a manifold. We do this, for example, when we say that the surface of a sphere is a manifold. However, to do that we must first have the object. We know how the manifold behaves in general relativity, but it is natural to pose the question, "What is spacetime?". I know of three possible answers:
I always find it surprising when physicists advance the idea that reality cannot be described, because it undermines the very purpose of physics. In fact, Einstein has already refuted the idea that science requires us to infer theory from agreement between prediction and experiment. [[FoundationsOfSpecialRelativity Special relativity]] is based on based on empirically verifiable //postulates//, the operational definitions of measurement. Einstein’s argument is the archetype according to which we should formulate modern scientific theory, starting with how we //define// the numerical quantities which we use in the scientific study of nature. Special relativity is imported, as local theory, into general relativity, and provides the basis for understanding what spacetime actually is:
Deletions:
If we have some object, and we can show that that object has the properties of a manifold, then we can say that the object is a manifold. We do this, for example, when we say that the surface of a sphere is a manifold. However, to do that we must first have the object. We know how the manifold behaves in general relativity, but it is natural to pose the question, "what is spacetime?". I know of three possible answers:
I always find it surprising when physicists advance the idea that reality cannot be described, because it undermines the very purpose of physics. In fact, Einstein has already refuted the idea that science requires us to infer theory from agreement between prediction and experiment. Special relativity is based on based on empirically verifiable //postulates//, the operational definitions of measurement. Einstein’s argument in special relativity is the archetype according to which we should formulate modern scientific theory, starting with how we //define// the numerical quantities which we use in the scientific study of nature. Special relativity is imported, as local theory, into general relativity, and provides the basis for understanding what spacetime actually is:
Additions:
<<""Definition: A manifold is a structure in which any point has a neighbourhood which can be described by a coordinate system or chart.""<<
Deletions:
<<""Definition: A manifold is a structure in which any point has a neighbourhood which can be described by a coordinate system or ""chart.""<<
Additions:
<<""Definition: A manifold is a structure in which any point has a neighbourhood which can be described by a coordinate system or ""chart.""<<
Typically a single coordinate system cannot be used to give a full description of a manifold. A collection of charts which describes the whole manifold is an ""atlas"".
<<**Answer 1.** There exists a [[http://plato.stanford.edu/entries/spacetime-theories/#5.2 substantive spacetime]], which is modelled (=described) by the mathematical structure of a manifold.<<
In this conception, the manifold simply replaces Newton’s conception of "" absolute space"" and "" absolute time"". This is what I call a metaphysical manifold, because there is no observation of a substantive spacetime, and nor can there be one. We //observe// the behaviour of matter, and //infer// the existence of space-time structure, but cannot actually observe it. Since substantive spacetime is scientifically unverifiable, at best it lies outside the realms of science. At worst (as I maintain), it is in conflict with observations in quantum theory.
Only measurements which are actually carried out have physical reality, and generate coordinates for physical events, whereas spacetime consists of all the ways in which this can conceivably be done. So, spacetime does not model reality &emdash; only the small subset of spacetime for which there are actual measurements corresponds to reality. Spacetime models our //conception// of reality, not reality itself. At the same time, spacetime does contain the real observational results required for comparison between theory and experiments.
Position 3 avoids both the unjustified metaphysical assumption of answer 1 and the feeble abdication of the purpose of science inherent in answer 2. Instead it correctly bases science on observation. The proper use of mathematics will enable predictions to be rigorously deduced, not inferred by induction. Modern science can thus escape the problem that a premise cannot be deduced from a conclusion.
Deletions:
<<""Definition: A manifold is a structure in which any point has a neighbourhood which can be described by a coordinate system.""<<
Typically a single coordinate system cannot be used to give a full description of a manifold.
<<**Answer 1.** There exists a "" substantive spacetime"", which is modelled (=described) by the mathematical structure of a manifold.<<
In this conception, the manifold simply replaces Newton’s conception of absolute space and absolute time. This is what I call a metaphysical manifold, because there is no observation of a substantive spacetime, and nor can there be one. We //observe// the behaviour of matter, and //infer// the existence of space-time structure, but cannot actually observe it. Since substantive spacetime is scientifically unverifiable, at best it lies outside the realms of science. At worst (as I maintain) it is in conflict with observations in quantum theory.
Only measurements which are actually carried out have physical reality, and generate coordinates for physical events, whereas spacetime consists of all the ways in which this can conceivably be done. So, spacetime does not model reality - only the small subset of spacetime for which there are actual measurements corresponds to reality. Spacetime models our //conception// of reality, not reality itself. At the same time, spacetime does contain the real observational results required for comparison between theory and experiments.
Position 3 avoids both the unjustified metaphysical assumption of answer 1 and the feeble abdication of the purpose of science inherent in answer 2. Instead it correctly bases science on observation. The proper use of mathematics will enable predictions to be rigorously deduced, not inferred by induction. Modern science can thus escape the proble that you cannot deduce a premise from a conclusion.
Additions:
We can describe spacetime as a manifold, a geometrical structure which can be mapped onto an ""atlas"", or collection of ""charts"". In common with many definitions of mathematical structures, this does not tell us what the manifold actually is. Instead it tells us what properties a manifold has, how a manifold behaves.
If we have some object, and we can show that that object has the properties of a manifold, then we can say that the object is a manifold. We do this, for example, when we say that the surface of a sphere is a manifold. However, to do that we must first have the object. We know how the manifold behaves in general relativity, but it is natural to pose the question, "what is spacetime?". I know of three possible answers:
<<**Answer 1.** There exists a "" substantive spacetime"", which is modelled (=described) by the mathematical structure of a manifold.<<
In this conception, the manifold simply replaces Newton’s conception of absolute space and absolute time. This is what I call a metaphysical manifold, because there is no observation of a substantive spacetime, and nor can there be one. We //observe// the behaviour of matter, and //infer// the existence of space-time structure, but cannot actually observe it. Since substantive spacetime is scientifically unverifiable, at best it lies outside the realms of science. At worst (as I maintain) it is in conflict with observations in quantum theory.
The logical error is in thinking that if we have a set of actual observations, B, and a theory A with A=>B, then A must be true. In fact, there may be some other theory, C, which we may not know about, which also has C=>B, and such that C contradicts A. Modern physicists usually avoid this issue by denying that it is possible to describe nature:
<<**Answer 2.** The mathematical structures of physics do not model anything. They are just algorithms whose validity rests only on correspondence between prediction and experiment.<<
This position can be regarded as the current orthodoxy. It is adopted by many theoretical physicists, especially quantum field theorists. There is no arguing with it. It is both as solid, and as absurd, as schoolboy [[http://en.wikipedia.org/wiki/Solipsism solipsism]]. It is clear to me that realism is a prerequisite for science as a meaningful activity, and that when I say "there is a tree in the park" I am describing reality. Our ability to describe a tree in the park refutes, at a very obvious level, the proposition that reality cannot be described.
I always find it surprising when physicists advance the idea that reality cannot be described, because it undermines the very purpose of physics. In fact, Einstein has already refuted the idea that science requires us to infer theory from agreement between prediction and experiment. Special relativity is based on based on empirically verifiable //postulates//, the operational definitions of measurement. Einstein’s argument in special relativity is the archetype according to which we should formulate modern scientific theory, starting with how we //define// the numerical quantities which we use in the scientific study of nature. Special relativity is imported, as local theory, into general relativity, and provides the basis for understanding what spacetime actually is:
<<**Answer 3.** I observe that I can, in principle, choose ""reference matter"" anywhere I wish, and that I can define ""Minkowski coordinates"" relative to that matter. I now define spacetime by //imagining// all the concievable ways in which coordinate systems can be set up in principle, dependent upon physical measurement.<<
Position 3 avoids both the unjustified metaphysical assumption of answer 1 and the feeble abdication of the purpose of science inherent in answer 2. Instead it correctly bases science on observation. The proper use of mathematics will enable predictions to be rigorously deduced, not inferred by induction. Modern science can thus escape the proble that you cannot deduce a premise from a conclusion.
Deletions:
We can describe spacetime as a manifold, a geometrical structure which can be mapped onto an ""atlas"", or collection of ""charts"". In common with many definitions of mathematical structures, this does not tell us what the manifold actually is. Instead it tells us how a manifold behaves.
If we have some object, and we can show that that object has the properties of a manifold, then we can say that the object is a manifold. We do this, for example, when we say that the surface of a sphere is a manifold. However, to do that we must first have the object. We know how the manifold behaves in general relativity, but it is natural to pose the question, "what is spacetime?". As far as I am aware, three answers are proposed:
**1. There exists a substantive spacetime, which is modelled (=described) by the mathematical structure of a manifold.**
In this conception, the manifold simply replaces Newton’s conception of absolute space and absolute time. This is what I call a metaphysical manifold, because there is no observation of a substantive spacetime, and nor can there be one. We observe the behaviour of matter, and infer the existence of space-time structure. Since substantive spacetime is scientifically unverifiable, at best it lies outside the realms of science. At worst (as I maintain) it is actually in conflict with observations in quantum theory.
The logical error is in thinking that if we have a set of actual observations, B, and a theory A with A=>B, then A must be true. There may be some other theory, C, which we may not know about, which also has C=>B, and such that C contradicts A. Modern physicists usually avoid this issue by denying that it is possible to describe nature:
**2. The mathematical structures of physics do not model anything. They are just algorithms whose validity rests only on correspondence between prediction and experiment.**
This position can be regarded as the current orthodoxy. It is adopted by many theoretical physicists, especially quantum field theorists. There is no arguing with it. It is both as solid, and as absurd, as schoolboy [[http://en.wikipedia.org/wiki/Solipsism solipsism]]. It is clear to me that realism is a prerequisite for science as a meaningful activity, and that when I say "there is a tree in the park" I am describing reality. Imv, this refutes, at a very obvious level, the proposition that reality cannot be described.
To me, the idea that reality cannot be described undermines the very purpose of theoretical research. In fact, Einstein has already refuted the idea that science requires us to infer theory from agreement between prediction and experiment. Special relativity is based on based on empirically verifiable //postulates//, the operational definitions of measurement. Einstein’s argument in special relativity is the archetype according to which we should formulate any modern scientific theory, starting with how we //define// the numerical quantities which we use in the scientific study of nature. Special relativity is imported, as local theory, into general relativity, and provides the basis for understanding what spacetime actually is:
**3. I observe that I can, in principle, choose ""reference matter"" anywhere I wish, and that I can define ""Minkowski coordinates"" relative to that matter. I now define spacetime by //imagining// all the concievable ways in which coordinate systems can be set up in principle, dependent upon physical measurement.**
Position 3 avoids both the unjustified metaphysical assumption of answer 1 and the feeble abdication of the purpose of science inherent in answer 2. Instead it correctly bases science on observation. The proper use of mathematics will enable predictions to be rigorously deduced, not inferred by induction.
Additions:
""What is Spacetime?""
<<""Definition: A manifold is a structure in which any point has a neighbourhood which can be described by a coordinate system.""<<
====""""What is spacetime?====
We can describe spacetime as a manifold, a geometrical structure which can be mapped onto an ""atlas"", or collection of ""charts"". In common with many definitions of mathematical structures, this does not tell us what the manifold actually is. Instead it tells us how a manifold behaves.
If we have some object, and we can show that that object has the properties of a manifold, then we can say that the object is a manifold. We do this, for example, when we say that the surface of a sphere is a manifold. However, to do that we must first have the object. We know how the manifold behaves in general relativity, but it is natural to pose the question, "what is spacetime?". As far as I am aware, three answers are proposed:
**1. There exists a substantive spacetime, which is modelled (=described) by the mathematical structure of a manifold.**
In this conception, the manifold simply replaces Newton’s conception of absolute space and absolute time. This is what I call a metaphysical manifold, because there is no observation of a substantive spacetime, and nor can there be one. We observe the behaviour of matter, and infer the existence of space-time structure. Since substantive spacetime is scientifically unverifiable, at best it lies outside the realms of science. At worst (as I maintain) it is actually in conflict with observations in quantum theory.
The logical error is in thinking that if we have a set of actual observations, B, and a theory A with A=>B, then A must be true. There may be some other theory, C, which we may not know about, which also has C=>B, and such that C contradicts A. Modern physicists usually avoid this issue by denying that it is possible to describe nature:
**2. The mathematical structures of physics do not model anything. They are just algorithms whose validity rests only on correspondence between prediction and experiment.**
This position can be regarded as the current orthodoxy. It is adopted by many theoretical physicists, especially quantum field theorists. There is no arguing with it. It is both as solid, and as absurd, as schoolboy [[http://en.wikipedia.org/wiki/Solipsism solipsism]]. It is clear to me that realism is a prerequisite for science as a meaningful activity, and that when I say "there is a tree in the park" I am describing reality. Imv, this refutes, at a very obvious level, the proposition that reality cannot be described.
To me, the idea that reality cannot be described undermines the very purpose of theoretical research. In fact, Einstein has already refuted the idea that science requires us to infer theory from agreement between prediction and experiment. Special relativity is based on based on empirically verifiable //postulates//, the operational definitions of measurement. Einstein’s argument in special relativity is the archetype according to which we should formulate any modern scientific theory, starting with how we //define// the numerical quantities which we use in the scientific study of nature. Special relativity is imported, as local theory, into general relativity, and provides the basis for understanding what spacetime actually is:
**3. I observe that I can, in principle, choose ""reference matter"" anywhere I wish, and that I can define ""Minkowski coordinates"" relative to that matter. I now define spacetime by //imagining// all the concievable ways in which coordinate systems can be set up in principle, dependent upon physical measurement.**
Only measurements which are actually carried out have physical reality, and generate coordinates for physical events, whereas spacetime consists of all the ways in which this can conceivably be done. So, spacetime does not model reality - only the small subset of spacetime for which there are actual measurements corresponds to reality. Spacetime models our //conception// of reality, not reality itself. At the same time, spacetime does contain the real observational results required for comparison between theory and experiments.
Position 3 avoids both the unjustified metaphysical assumption of answer 1 and the feeble abdication of the purpose of science inherent in answer 2. Instead it correctly bases science on observation. The proper use of mathematics will enable predictions to be rigorously deduced, not inferred by induction.
Deletions:
<<""Definition: A manifold is a structure in which any point has a neighbourhood which can be described by a cordinate system.""<<
Additions:
