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Rational Gaze
04-04-2014, 08:00 PM
So, I was having a "debate" with a fellow regarding special relativity. My argument was that Bell's Inequality suggests that a Lorentzian interpretation of special relativity is correct.

The person I was debating argued that a Lorentzian interpretation of special relativity is false because it's mathematical formalism differs from special relativity in such a way that precludes general relativity. (I assume he is referring to the Minkowskian interpretation of special relativity here.)

The problem being, literally everything I have read on the subject has stated that all three interpretations of special relativity have the same mathematical formalism.They are simply different ways of physically representing the mathematics. Also, GR apparently predicts the 'aether' postulated by the Lorentzian interpretation of SR.

The fellow I am debating claims he has studied physics and mathematics for 5 years.

Any input?

Cheers.

Paprika
04-04-2014, 10:47 PM
I have a question: how does a Lorentzian perspective of SR extend into GR?

klaus54
04-05-2014, 08:38 AM
Bell's Theorem deals with quantum interactions. How does it apply to SR? Also, if the mathematics doesn't extend SR into GR, I don't see its physical relevance.

Interesting discussion topic!

K54

Rational Gaze
04-05-2014, 09:18 AM
The implication of Bell's Inequality is that the reality assumption and locality can't both be true at the same time. If locality is false, then this implies that the Lorentzian interpretation of special relativity is correct, because it allows for a privileged reference frame.

Rational Gaze
04-05-2014, 09:21 AM
I have a question: how does a Lorentzian perspective of SR extend into GR?
GR introduces the notion of cosmic, or absolute time. The Lorentzian interpretation of SR has a privileged reference frame allowing for absolute time.

Rational Gaze
04-05-2014, 09:22 AM
Anyway, this guy has since modified his argument. He is now saying that geometric gravitation cannot happen if we do not treat time as a dimension. However, the four-dimensionality of space-time is not an indispensable element of either SR or GR, so I don't see how this is so.

Paprika
04-05-2014, 09:30 AM
GR introduces the notion of cosmic, or absolute time. The Lorentzian interpretation of SR has a privileged reference frame allowing for absolute time.
I don't think it does. When used in cosmology to conceptualise of a beginning, yes, cosmic time is brought into the picture, but the notion of cosmic time isn't inherent in GR.

Paprika
04-05-2014, 09:31 AM
Anyway, this guy has since modified his argument. He is now saying that geometric gravitation cannot happen if we do not treat time as a dimension. However, the four-dimensionality of space-time is not an indispensable element of either SR or GR, so I don't see how this is so.
How is GR to be understood under 3+1 instead of Minkowskian 4-D spacetime?

Rational Gaze
04-05-2014, 09:57 AM
"The choice is not about the equations, it is about their interpretation. Einsteinís equations can be interpreted as indicating a curvature of space-time, unpicturable as it may be, or as describing a quantum field in three-dimensional space, similar to the other quantum force fields. To the physicist, it really doesnít make much difference. Physicists are more concerned with solving their equations than with interpreting them... So if you want, you can believe that gravitational effects are due to a curvature of space-time (even if you canít picture it). Or, like Weinberg, Wilczek (and me), you can view gravity as a force field that, like the other force fields in QFT, exists in three-dimensional space and evolves in time according to the field equations."
http://www.quantum-field-theory.net/app-b/

Paprika
04-05-2014, 10:10 AM
"The choice is not about the equations, it is about their interpretation. Einsteinís equations can be interpreted as indicating a curvature of space-time, unpicturable as it may be, or as describing a quantum field in three-dimensional space, similar to the other quantum force fields. To the physicist, it really doesnít make much difference. Physicists are more concerned with solving their equations than with interpreting them... So if you want, you can believe that gravitational effects are due to a curvature of space-time (even if you canít picture it). Or, like Weinberg, Wilczek (and me), you can view gravity as a force field that, like the other force fields in QFT, exists in three-dimensional space and evolves in time according to the field equations."
http://www.quantum-field-theory.net/app-b/
Most fascinating. My math just isn't sufficiently up to speed so I'll have to look it up later.

klaus54
04-05-2014, 10:23 AM
The closest thing to a cosmic reference frame is cosmic background radiation, but even that isn't isotropic. Right now you're talking about interpretations of SR. And the Lorentz equations that Einstein built upon with his postulates of constant c with no privileged frame explain time dilation. Of course GPS satellite use it all the time (as it were!). And so does GR with its much more difficult differential geometry and tensor analysis.

Also, a quick note that is probably not relevant -- there is a LOT of advanced completely consistent maths that don't have anything to do with reality. The truth of the maths is a necessary but not sufficient condition for it to apply to physics. E.g., Cauchy-Riemann manifolds have a robust mathematical presentation including tensor analysis but have absolutely no relation to reality.

K54

shunyadragon
04-05-2014, 12:34 PM
Lorentzian interpretation of Special Relativity (SR) is really no longer necessary in that up to a point their calculations are the same and SR has more explanatory value in understanding space/time and development of General Relativity.

Carrikature
04-16-2014, 09:14 AM
Also, a quick note that is probably not relevant -- there is a LOT of advanced completely consistent maths that don't have anything to do with reality. The truth of the maths is a necessary but not sufficient condition for it to apply to physics. E.g., Cauchy-Riemann manifolds have a robust mathematical presentation including tensor analysis but have absolutely no relation to reality.

I have to admit, the concept is not new but it has always baffled me. The layman version is that we can use math to figure out physics problems while claiming the math has nothing to do with reality, yes? I don't get how that's possible.

klaus54
04-20-2014, 08:39 PM
I have to admit, the concept is not new but it has always baffled me. The layman version is that we can use math to figure out physics problems while claiming the math has nothing to do with reality, yes? I don't get how that's possible.

Because mathematics is a LANGUAGE with which to express certain physical concepts. Maths by itself is abstract. A poem or a science fiction novel use language in a perfectly consistent manner but have no usefulness in a technical sense. There are no di-lithium crystals or warp drive.

Of course a poem or a fiction can express abstractions of reality. And maths is the ultimate abstract discipline.

Again, the proper logical statement is "Maths are necessary for a physics hypothesis to be correct, but not sufficient." If the maths don't work out, then the hypothesis ain't right.

K54

Carrikature
04-21-2014, 07:05 AM
*Edited*

Ignore this post. I'll re-post later when I can better express what it is I meant and what I was getting at.

klaus54
04-21-2014, 10:11 AM
*Edited*

Ignore this post. I'll re-post later when I can better express what it is I meant and what I was getting at.

Well, I thought the analogy of mathematics to human language was pretty transparent. Do you have a comment on this?

K54

Carrikature
04-21-2014, 11:59 AM
Well, I thought the analogy of mathematics to human language was pretty transparent. Do you have a comment on this?

K54

Mathematics as a comparison to human language is understandable enough, and it's definitely not new to me by any stretch. I think you have it wrong, though, and I'll try to explain why.



Because mathematics is a LANGUAGE with which to express certain physical concepts. Maths by itself is abstract. A poem or a science fiction novel use language in a perfectly consistent manner but have no usefulness in a technical sense. There are no di-lithium crystals or warp drive.

Of course a poem or a fiction can express abstractions of reality. And maths is the ultimate abstract discipline.

Again, the proper logical statement is "Maths are necessary for a physics hypothesis to be correct, but not sufficient." If the maths don't work out, then the hypothesis ain't right.

K54

I agree that mathematics can be considered a language. In the interest of establishing a base point, language uses a set of symbols to reference a set of concepts. A given language is a specific set of symbols and their references. Physical existence is a property of a concept. In fiction, it's understood by definition that the concepts expressed are not intended to possess physical existence even while they are presented as having just that. This is very different from how mathematics as a language functions.

There is nothing in mathematics that distinguishes between concepts with physical existence and those without. That by itself might be enough, but it doesn't end there. The basic concepts of mathematics (structure, quantity, space and change) are part and parcel of physical reality and our interaction with it. To claim that mathematics has nothing to do with reality as you did in Post #11 ignores this very fundamental truth.

Further, the proper logical statement you've presented here differs from that in Post #11. Obviously, the math is not sufficient for a physics hypothesis to be correct. However, what you said there was that it's insufficient "for it to apply to physics". Those are two very different statements. In truth, physics hypotheses as expressed in human language (as opposed to mathematical language) are interpretations. That's why the math is insufficient. All true hypotheses must agree with the math, but the math itself is independent of the interpretation.

I don't deny that there are cases where mathematics may seem divorced from reality. However, I think these are merely cases where the practical applications of pure mathematics have not yet been discovered. They certainly don't suffice as proof that math has nothing to do with reality.

In short, my statements in Post #13 shouldn't be taken as expressing confusion about how physics and math interact. Rather, it's an expression of puzzlement that anyone can seriously believe the two aren't interrelated. As I said then, this isn't an idea that's new to me. It just seems to misunderstand the basic concept of what math is and how it functions.

klaus54
04-21-2014, 01:07 PM
Mathematics as a comparison to human language is understandable enough, and it's definitely not new to me by any stretch. I think you have it wrong, though, and I'll try to explain why.




I agree that mathematics can be considered a language. In the interest of establishing a base point, language uses a set of symbols to reference a set of concepts. A given language is a specific set of symbols and their references. Physical existence is a property of a concept. In fiction, it's understood by definition that the concepts expressed are not intended to possess physical existence even while they are presented as having just that. This is very different from how mathematics as a language functions.

There is nothing in mathematics that distinguishes between concepts with physical existence and those without. That by itself might be enough, but it doesn't end there. The basic concepts of mathematics (structure, quantity, space and change) are part and parcel of physical reality and our interaction with it. To claim that mathematics has nothing to do with reality as you did in Post #11 ignores this very fundamental truth.

Further, the proper logical statement you've presented here differs from that in Post #11. Obviously, the math is not sufficient for a physics hypothesis to be correct. However, what you said there was that it's insufficient "for it to apply to physics". Those are two very different statements. In truth, physics hypotheses as expressed in human language (as opposed to mathematical language) are interpretations. That's why the math is insufficient. All true hypotheses must agree with the math, but the math itself is independent of the interpretation.

I don't deny that there are cases where mathematics may seem divorced from reality. However, I think these are merely cases where the practical applications of pure mathematics have not yet been discovered. They certainly don't suffice as proof that math has nothing to do with reality.

In short, my statements in Post #13 shouldn't be taken as expressing confusion about how physics and math interact. Rather, it's an expression of puzzlement that anyone can seriously believe the two aren't interrelated. As I said then, this isn't an idea that's new to me. It just seems to misunderstand the basic concept of what math is and how it functions.

I made it exceedingly clear that maths and physics are interrelated. If the maths are wrong, then the physics are wrong. Maths are necessary but not sufficient.

Q.E.D.

K54

Carrikature
04-21-2014, 01:24 PM
I made it exceedingly clear that maths and physics are interrelated. If the maths are wrong, then the physics are wrong. Maths are necessary but not sufficient.

Q.E.D.

K54

You did so while also stating repeatedly that the maths had nothing to do with reality. You don't get to claim both. Further, you made a direct comparison between math and fiction, a comparison that also fails.

klaus54
04-21-2014, 03:19 PM
You did so while also stating repeatedly that the maths had nothing to do with reality. You don't get to claim both. Further, you made a direct comparison between math and fiction, a comparison that also fails.

Human language is an abstraction (for the most part) that is distinguished from non-human animal "signaling". Human language has both rules of grammar and syntax and is internally consistent and is obviously applicable to reality. One can generate nonsense sentences that are completely grammatically correct. Being grammatically correct does not mean these sentences have meaning in real life.

Maths is an internally consistent abstract system, SOME of which applies to physical reality. When it DOES apply to physical reality it must be CONSISTENT. Often the maths are over-simplified but give an approximation to reality in certain cases -- e.g., Newtonian vs. Relativistic mechanics.

But AGAIN, if maths applied to an hypothesis in physics are wrong, then the hypothesis is wrong. The maths then becomes an important tool for determining whether an hypothesis needs to be tweaked or discarded. The maths can't PROVE an hypothesis, just as nothing in scientific method has absolute "proof".

To summarize: 1) Math is the appropriate language for framing relationships in physics. If you don't accept this, please show me a case where it is not. 2) If the hypothesis involves incorrect maths, then the hypothesis is wrong. Necessary but not sufficient.

One HUGE difference between maths and human language is that the latter can be rife with grammatical and semantic errors and still be understood, e.g, "I could care less." Whereas in maths the grammar and syntax are precise, one error and the whole framework falls apart.

In summary, math is an internally-consistent abstraction that at times is applicable to reality as a tool when the physical concept can be framed in mathematical terms. In that case, if the maths doesn't work out, then...

K54

Paprika
04-22-2014, 01:02 AM
I agree that mathematics can be considered a language.
I disagree. Mathematics isn't a language but it is expressed through languages, that is, various forms of mathematical notation. An example would be the difference between the Hindu-Arabic 1, 2, 3, 4, 5... and the Roman I, II, III, IV, V, ...; another would be the different notations used for calculus.

Carrikature
04-22-2014, 06:34 AM
Maths is an internally consistent abstract system, SOME of which applies to physical reality.

In summary, math is an internally-consistent abstraction that at times is applicable to reality as a tool when the physical concept can be framed in mathematical terms. In that case, if the maths doesn't work out, then...

You would have us believe that physics hypotheses outright fail if the math doesn't work (with which I agree) while simultaneously claiming that only some math applies to physical reality (which I dispute). To have the latter be the case would necessarily entail the possibility that physics hypotheses could be invalidated based on math that has nothing to do with physical reality. That doesn't make any sense, and simply repeating it doesn't make your case.

Carrikature
04-22-2014, 06:40 AM
I disagree. Mathematics isn't a language but it is expressed through languages, that is, various forms of mathematical notation. An example would be the difference between the Hindu-Arabic 1, 2, 3, 4, 5... and the Roman I, II, III, IV, V, ...; another would be the different notations used for calculus.

I'm not sure I understand why you think it doesn't qualify as a language. I pointed to the criteria for a language being symbols that reference concepts. The forms of mathematical notations would be those symbols, where Roman numerals vs calculus notations are just different 'words'. Mathematical notation even possesses recursivity, productivity and displacement. In that, it's just like human language (small wonder, that). Can you elaborate?

oxmixmudd
04-22-2014, 06:43 AM
I disagree. Mathematics isn't a language but it is expressed through languages, that is, various forms of mathematical notation. An example would be the difference between the Hindu-Arabic 1, 2, 3, 4, 5... and the Roman I, II, III, IV, V, ...; another would be the different notations used for calculus.

I think you are confusing the element of the universe the mathematics represents with the element itself. In the universe, there exists separate things. We can express enumeration, summation, subtraction, and so forth through the language of mathematics, or through the more cumbersome method I use here, a normal human langage. And yet what is behind the concepts and words is a real element of the universe itself. Mathematics is a concise and very accurate langage for expressing that reality. But it is a language, a communicative medium. What it represents is in fact 'real'.

What gets a bit odd however is that there are elements expressible in mathematics that have no known physical counterpart. Yet the ideas themselves are real, they flow out of the application of a set of rules and logical inferences. And they have existence outside our ability to express them. Or do they?

And If we except these concepts are mere representations of what is real, yet they have no physical counterpart, this challenges the notion that the 'material' is all there is.


Jim

Carrikature
04-22-2014, 06:58 AM
What gets a bit odd however is that there are elements expressible in mathematics that have no known physical counterpart. Yet the ideas themselves are real, they flow out of the application of a set of rules and logical inferences. And they have existence outside our ability to express them. Or do they?

And If we except these concepts are mere representations of what is real, yet they have no physical counterpart, this challenges the notion that the 'material' is all there is.


I completely agree! I'd quibble that they have no known physical counterpart (which I think is klaus' hangup), but I don't think the challenge is any less potent.

klaus54
04-22-2014, 10:24 AM
I disagree. Mathematics isn't a language but it is expressed through languages, that is, various forms of mathematical notation. An example would be the difference between the Hindu-Arabic 1, 2, 3, 4, 5... and the Roman I, II, III, IV, V, ...; another would be the different notations used for calculus.

It's a language in that it's abstract, uses symbols (some of which are standard but this is NOT necessary) and has a precise grammar depending on the axioms of a particular system. E.g., an algebraic "group" has a binary operation on a non-empty set, and that operation is associative, has an identity element, and inverses. It does matter what symbols you use as long as they follow these axioms.

In English: "I have a headache," In German: "Mir tut den Kopf weh." have the same meaning in different symbols (and grammar in this case. The German is word-for-word "To Me does the head woe.")

K54

klaus54
04-22-2014, 10:25 AM
I think you are confusing the element of the universe the mathematics represents with the element itself. In the universe, there exists separate things. We can express enumeration, summation, subtraction, and so forth through the language of mathematics, or through the more cumbersome method I use here, a normal human langage. And yet what is behind the concepts and words is a real element of the universe itself. Mathematics is a concise and very accurate langage for expressing that reality. But it is a language, a communicative medium. What it represents is in fact 'real'.

What gets a bit odd however is that there are elements expressible in mathematics that have no known physical counterpart. Yet the ideas themselves are real, they flow out of the application of a set of rules and logical inferences. And they have existence outside our ability to express them. Or do they?

And If we except these concepts are mere representations of what is real, yet they have no physical counterpart, this challenges the notion that the 'material' is all there is.


Jim

Bingo! That's EXACTLY what I said but in different words. ;-)

K54

Paprika
04-22-2014, 10:53 PM
I'm not sure I understand why you think it doesn't qualify as a language. I pointed to the criteria for a language being symbols that reference concepts. The forms of mathematical notations would be those symbols, where Roman numerals vs calculus notations are just different 'words'. Mathematical notation even possesses recursivity, productivity and displacement. In that, it's just like human language (small wonder, that). Can you elaborate?
Precisely. It's the mathematical notations that are the languages, and not mathematics itself.

Paprika
04-22-2014, 10:59 PM
I think you are confusing the element of the universe the mathematics represents with the element itself. In the universe, there exists separate things.

No. I am carefully distinguishing between the way mathematical concepts and knowledge are conveyed - that is, through the various languages/mathematical notations- and the concepts and knowledge.

Carrikature
04-23-2014, 06:27 AM
Precisely. It's the mathematical notations that are the languages, and not mathematics itself.

That makes sense. :smile: