General Relativity Quantum Mechanics and the new String Theory

[Bassnut (Fred)]

Originally Posted by Robh

To discover mathematics, one need only conceptualize and make mental and logical connections. Nature itself is irrelevant to this invention process.

Regards, Rob.

Man is a product of nature, so how can nature itself be "irrelevent" to human "conceptualizing and making mental and logical connections".

Or is there some aspect of human thought that was installed by something other than nature?.

[Nesti (Mark)]

Originally Posted by sjastro

On the subject of maths and behind the scenes action.....

The Standard Model may not be complete but one of it's components, Quantum Electrodynamics, is one of the most profound theories ever devised. The maths is very abstract but given that QE is able to produce theoretical values that are accurate to within 10 parts in a billion of the experimental (actual) values brings up the age old question. Is mathermatics discovered or invented?

Scientists like Paul Davies and the man who should won the Nobel Prize for Physics, Freeman Dyson (http://en.wikipedia.org/wiki/Freeman_Dyson) point to idea that if maths is a part of nature which is discovered, then nature possesses an intelligence which may indicate the existence of a Supreme Being.

Regards

Steven

Hi Steven,

I agree with you about the Standard Model and QED. What I was alluding to was the possibility of an Einstein/Bohm type Hidden Mechanism for determining one particular outcome over another. To have an array of possible outcomes and assigned probabilities, without a decision making mechanism which determines one outcome over another, is to me, an incomplete theory, because when I look outside the window, I don't see randomness, I see structure and order, and this is again no different to chaos being reclassified as deterministic chaos...it is only chaotic because we are not in possession of the full facts. I feel this is the case with much of QM.

I feel that Bells Inequality is an accidental 'sweeping under the carpet' of the true nature of reality.

M

[Nesti (Mark)]

Originally Posted by bojan

This is metaphysics, not physics.. with all due respect to aforementioned gentlemen, in short, it is not science.

That's a true enough statement however, this thread pertains to string theory, and since string theory is hailed as a possible TOE, then I personally feel Steven's statement holds true, simply because a true TOE, MUST encompass ALL phenomena of nature, not just the ones we conveniently pick and choose. I stipluate this exact point very clearly in my book; we must address ALL phenomena if we are to observe and quantify all of nature.

I feel the definitions and demarcations of what constitutes science and what constitutes philosophy is a manifestation of yet another typically flawed facet of the human mind.

[Nesti (Mark)]

Originally Posted by Bassnut

Man is a product of nature, so how can nature itself be "irrelevent" to human "conceptualizing and making mental and logical connections".

Or is there some aspect of human thought that was installed by something other than nature?.

I don't believe that human thought contains an element of destiny, but I feel the early universe held provision for conscious awareness. I believe conscious awareness gives rise to consciousness, and in turn consciousness gives rise to rational thought. For me this is like an element's condensation from plasma to gas to liquid to solid.

[Robh (Rob)]

Originally Posted by Bassnut

Man is a product of nature, so how can nature itself be "irrelevent" to human "conceptualizing and making mental and logical connections".

Or is there some aspect of human thought that was installed by something other than nature?.

The truths of pure mathematics exist independently of any conscious being or any particular Universe that supports that being. As a hypothetical situation- two conscious beings in separate Universes could theoretically communicate the logic of mathematics even though the physics of their particular Universes might be quite different. The mathematics is discoverable as a logical system but is not dependent on the physical Universe itself i.e. the home Universe (nature) is irrelevant to the mathematics.

Regards, Rob

[bojan]

Originally Posted by Nesti

I don't believe that human thought contains an element of destiny....
I believe conscious awareness gives rise to consciousness, and in turn ...

You believe... or you do not believe.
Again, this is not science.

Originally Posted by Robh

The truths of pure mathematics exist independently of any conscious being or any particular Universe that supports that being. As a hypothetical situation- two conscious beings in separate Universes could theoretically communicate the logic of mathematics even though the physics of their particular Universes might be quite different. The mathematics is discoverable as a logical system but is not dependent on the physical Universe itself i.e. the home Universe (nature) is irrelevant to the mathematics.

Regards, Rob

I believe (!!!) that mathematics does not exist as an entity (if I understood you correctly) it is a concept, that can be invented or developed even by artificial intelligence.
The fact that AI will be one day developed by help of mathematicians (among others) is not per se the reason those beings would be capable of math... only the processing capacity of their brains will determine this.

[Nesti (Mark)]

Originally Posted by sjastro

The maths is very abstract but given that QE is able to produce theoretical values that are accurate to within 10 parts in a billion of the experimental (actual) values brings up the age old question. Is mathermatics discovered or invented?

Regards

Steven

Hang-on Steven, doesn't QED outcomes rely upon the renormalization process? If so, there are a handful of numbers which need to be fed into the equations by hand in order to make the post-dictions (in contrast to a prediction) work; numbers which are derived AFTER the experiment has already produced an outcome, correct???

If it does include recookingthebooksation then my blurb below may be relevant, if not, please disregarded the rest of this post.

That mathematical process entirely bypasses the point I'm trying to show...the reason why we have different outcomes from identical [experimental] setups, is because we are missing a vital piece of the puzzle; what determines one outcome over the next. By taking values from the final boundary condition - that is, AFTER the experiment has ocured - and then plugging the numbers in, bypasses the region where a possible hidden variable could occur. That's not good science, that's science heresy!

Aharanov writes:
"Two identical particles with identical environments can subsequently exhibit different properties under identical measurements. These subsequent identical measurements provide fundamentally new information about the system which could not in principle be obtained from the initial conditions. Time-Symmetry in Quantum Mechanics suggests that two 'identical’ particles are not really identical, but there is no way to find their differences based only on information coming from the past, one must also know the future. We also show how the second generalization involving ‘destiny’ is consistent with free will...

...The concept of free will is mainly that the past may define the future, yet after this future effect takes place – i.e. after it becomes past – then it cannot be changed: we are free from the past, but, in this picture, we are not necessarily free from the future. Therefore, not knowing the future is a crucial requirement for the existence of free will. In other words, the destiny vector cannot be used to inform us in the present of the result of our future free choices."

Buy using inputs from the final boundary condition (final states of the event), we are effectively cutting future influence out of the loop and essentially factoring-in a numerical correction/s to realign the mismatch between the history vector and the destiny vector, therefore missing the process which displays the differences between two identical experiments, what I feel creates one reality instead of another reality which was also possible, in effect 'cooking the books'!

Therefore attaining a "10 parts in a billion of the experimental (actual) values" is not that spectacular at all. What that process is showing is that the equation/s are correct, it's not showing any power in predicting anything, or even showing that we have a handle on the quantum world...it's actually fooling ourselves.

"But no matter how clever the word, it is what I call a dippy process! Having to resort to such hocus pocus has prevented us from proving that the theory of quantum electrodynamics is mathematically self consistent. ... I suspect that renormalization is not mathematically legitimate."
- Richard Feynman -

[Nesti (Mark)]

Originally Posted by bojan

You believe... or you do not believe.
Again, this is not science.

This isn't science, it's a forum where people offer their opinions and beliefs...we're not in a lab ya-know!

I am merely stating what I believe, just as you are stating your belief/trust in science.

[Nesti (Mark)]

Originally Posted by bojan

I believe (!!!)

You just told me off for that!

Hang-on, just checked your profile...you work in the 'Black Art' of RF...and you're hitting people with the stick of science...tut-tut-tut, oh dear me!

[bojan]

Well.. I am also capable of self-criticisms you know

[Nesti (Mark)]

Originally Posted by bojan

Well.. I am also capable of self-criticisms you know

I work in data messaging, so that includes simulcasting data over a network of TX's...there's more intuition in setting that up than science.

I'm sorry, but I can't take comments from the 'Dark Side' seriously...

back at you!

[bojan]

Black art? RF?
Well, I like the idea people believe this is black art, this way of thinking keeps me still employed :-)

[Nesti (Mark)]

Originally Posted by bojan

Black art? RF?
Well, I like the idea people believe this is black art, this way of thinking keeps me still employed :-)

Agreed!

[orestis]

Hi everyone,
Very interesting discussions.Hi sebastion i too am 14 yrs old and love these topics on physics and maths.Thanks for starting thread.
The elegant universe series is very good.
Why do people always say parellel universes what about if there were unique universes which are completely diferent but have charachteristics which are the same.

Heres a very good topic-Albert Einstein said that nothing in the known universe can excell the speed of light but Theoretically WARP DRIVE can go faster than the speed of light. warp drive is a simple concept which uses gravity amplifiers to expand and contract space time at the rear and at the front of the spacecraft respectively. What do you think about warp drive.

If you like philosophy and science go to www.symphonyofscience.com
and watch the music videos .There great.

orestis
Warp drive is awesome.

[sjastro]

Originally Posted by Nesti

Hang-on Steven, doesn't QED outcomes rely upon the renormalization process? If so, there are a handful of numbers which need to be fed into the equations by hand in order to make the post-dictions (in contrast to a prediction) work; numbers which are derived AFTER the experiment has already produced an outcome, correct???

Mark,

QED does rely on the renormalization process when dealing with the S-matrix, but renormalization has a physical interpretation involving non quantum mechanical effects.
Renormalization involves removing these effects. It is not a fudging of the maths. Renormalization involves eliminating infinite theoretical values.
QED is renormalized prior to experimental verification.

Here is the theoretical vs experimental value of the fine structure constant under different conditions.

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

Interesting comment by Richard Feynman. Quite a contrast given that he referred to QED as "the jewel of physics".

Regards

Steven

[sjastro]

Originally Posted by Nesti

Hi Steven,

I agree with you about the Standard Model and QED. What I was alluding to was the possibility of an Einstein/Bohm type Hidden Mechanism for determining one particular outcome over another. To have an array of possible outcomes and assigned probabilities, without a decision making mechanism which determines one outcome over another, is to me, an incomplete theory, because when I look outside the window, I don't see randomness, I see structure and order, and this is again no different to chaos being reclassified as deterministic chaos...it is only chaotic because we are not in possession of the full facts. I feel this is the case with much of QM.

I feel that Bells Inequality is an accidental 'sweeping under the carpet' of the true nature of reality.

M

Mark,

Experimental physics shows through photon polarization testing that Bell's inequality is violated hence Hidden Variable theory doesn't apply.

Regards

Steven

[sjastro]

Getting back to the subject on whether mathematics is discovered or invented, I don't believe that classifying maths as "real maths" or "pure maths" validates the point one way or the other.

The issue is whether mathematical properties themselves are invariant.
Lets assume the Everett interpretation of QM is correct then multiple Universes exist. While prime numbers may appear to be an ad hoc invention with no physical significance, a property of prime numbers is that they form an infinite set as proven by the ancient Greeks. The question is are they an infinite set in all other Universes? If the answer is yes and the concept is applied to maths in general then one can argue that the maths is discovered. A Universe where prime numbers do not exist may simply reflect it hasn't been discovered yet

Steven

[bojan]

Originally Posted by sjastro

While prime numbers may appear to be an ad hoc invention with no physical significance, a property of prime numbers is that they form an infinite set as proven by the ancient Greeks. The question is are they an infinite set in all other Universes? If the answer is yes and the concept is applied to maths in general then one can argue that the maths is discovered. A Universe where prime numbers do not exist may simply reflect it hasn't been discovered yet

Steven

Wether other universes exist or not is one issue (to be proven or disproven in due time).
However, prime numbers exists as a mathematical, logical etc entity, with their properties, but not as physical entity (yes we can count individual physical pieces, but that is all)
And I bet it will be shown one day that they exist (in full, with all properties mentioned above) in any other universe, (even if other universes do not exist.. I know this sounds contradictory, but I am trying to make a point, perhaps too desperately... because I feel that you guys and some others are jumping into conclusions using logic which is not used properly despite it seems OK at the first glance)
Simply because (in this, and many other cases) this is mathematical concept. And it can exist as such even in the mind of a machine. Perhaps even in Matrix

[Robh (Rob)]

Originally Posted by sjastro

The issue is whether mathematical properties themselves are invariant.
Lets assume the Everett interpretation of QM is correct then multiple Universes exist. While prime numbers may appear to be an ad hoc invention with no physical significance, a property of prime numbers is that they form an infinite set as proven by the ancient Greeks. The question is are they an infinite set in all other Universes? If the answer is yes and the concept is applied to maths in general then one can argue that the maths is discovered. A Universe where prime numbers do not exist may simply reflect it hasn't been discovered yet

Steven

Perhaps, it is not clear exactly what my argument (opinion) is and maybe we agree at some level.
I believe that mathematical axioms, conjectures and theorems exist as a conceptual logical structure independent of the physical make-up of our Universe. Yes, you need a Universe and a conscious being to develop the logical structure but it exists as an independent body of ideas.
Initially, the concept of number probably originates from the need to count objects. Once defined, number can exist by itself e.g. 1<2 and 2<3 then 1<3 does not depend on any physical object but simply on the definition of "<". Mathematics can be applied to the Universe but is not discoverable in the sense that one discovers a physical law or theory (e.g. General Relativity), which through observations and measurement, we deem to govern some aspect of the Universe.
However, as I mentioned earlier I also think that the language of mathematics is communicable across the Universe (or, hypothetically, over to another Universe) to another intelligent being as it does not depend on the physical properties of that Universe. In this sense, the logic of mathematics is invariant of the Universe's material structure.
But I do not agree that there is an embedded wallpaper or backdrop of mathematical knowledge waiting to be discovered, like gold in a field. Mathematics is a conceptual body of logical theorems that are driven by human interest. The results attained will vary according to the path followed and they are not simply waiting there to be discovered. A particular path followed does not necessarily have to be relevant or have the need to be discovered in another Universe, even though the concepts may be communicable. Take, for example, the whole body of theory around complex numbers. This was developed as an interesting concept based on a definition of i (i^2=-1) and later on found applications, but was it a discovery or simply an invention? Another being in another Universe could live without it; it wasn't lying around waiting to be found.
Consider this. Someone invents the idea of a perfect number- a number that is the sum of all its factors other than itself. Example: 6 has the factors 1,2,3 and 6=1+2+3; 28 has the factors 1,2,4,7,14 and 28=1+2+4+7+14. This is a defined and constructed concept; it wasn't waiting around to be found. Any subsequent logical derivations or proofs exist from the initial definition. The human mind is capable of thinking of and defining whole new directions- from perfect numbers we can navigate to amicable numbers.
So, although number may be a consequence of the Universe at large, most mathematical discoveries (conjectures and theorems) will depend on a particular path followed starting from defined statements and axioms . These are not embedded in the Universe waiting to be "discovered" but are driven by human interest. Hypothetically, a comparison of the mathematics of two cultures from different Universes may find some overlap of mathematical theorems but I would tend to think they would differ significantly. However, the basic logical starting points from number would allow each culture to navigate the others mathematical directions and results.
At some level the logic is transferable but the content is not universal.

Regards, Rob.

[sjastro]

Originally Posted by Robh

Perhaps, it is not clear exactly what my argument (opinion) is and maybe we agree at some level.
I believe that mathematical axioms, conjectures and theorems exist as a conceptual logical structure independent of the physical make-up of our Universe. Yes, you need a Universe and a conscious being to develop the logical structure but it exists as an independent body of ideas.
Initially, the concept of number probably originates from the need to count objects. Once defined, number can exist by itself e.g. 1<2 and 2<3 then 1<3 does not depend on any physical object but simply on the definition of "<". Mathematics can be applied to the Universe but is not discoverable in the sense that one discovers a physical law or theory (e.g. General Relativity), which through observations and measurement, we deem to govern some aspect of the Universe.
However, as I mentioned earlier I also think that the language of mathematics is communicable across the Universe (or, hypothetically, over to another Universe) to another intelligent being as it does not depend on the physical properties of that Universe. In this sense, the logic of mathematics is invariant of the Universe's material structure.
But I do not agree that there is an embedded wallpaper or backdrop of mathematical knowledge waiting to be discovered, like gold in a field. Mathematics is a conceptual body of logical theorems that are driven by human interest. The results attained will vary according to the path followed and they are not simply waiting there to be discovered. A particular path followed does not necessarily have to be relevant or have the need to be discovered in another Universe, even though the concepts may be communicable. Take, for example, the whole body of theory around complex numbers. This was developed as an interesting concept based on a definition of i (i^2=-1) and later on found applications, but was it a discovery or simply an invention? Another being in another Universe could live without it; it wasn't lying around waiting to be found.
Consider this. Someone invents the idea of a perfect number- a number that is the sum of all its factors other than itself. Example: 6 has the factors 1,2,3 and 6=1+2+3; 28 has the factors 1,2,4,7,14 and 28=1+2+4+7+14. This is a defined and constructed concept; it wasn't waiting around to be found. Any subsequent logical derivations or proofs exist from the initial definition. The human mind is capable of thinking of and defining whole new directions- from perfect numbers we can navigate to amicable numbers.
So, although number may be a consequence of the Universe at large, most mathematical discoveries (conjectures and theorems) will depend on a particular path followed starting from defined statements and axioms . These are not embedded in the Universe waiting to be "discovered" but are driven by human interest. Hypothetically, a comparison of the mathematics of two cultures from different Universes may find some overlap of mathematical theorems but I would tend to think they would differ significantly. However, the basic logical starting points from number would allow each culture to navigate the others mathematical directions and results.
At some level the logic is transferable but the content is not universal.

Regards, Rob.

Rob,

Consider geometrical theorems/conjectures. The catalyst for geometrical concepts is through measurement. In a subtle way a geometrical theorem is analogous to a scientific theory except that individual measuresurements themselves do not prove the theorem.

As an example consider the Pythagorean theorem for right angle triangles c^2=a^2+b^2.
Did Pythagoras invent this geometric property for right angle triangles? Clearly no.
Mathematicians before Pythagoras knew of the relationship on the basis of measurement but where not able to prove it for all "a" and "b". Before Pythagoras the geometrical property was based on conjecture.

The geometrical property has always been around, measurement has simply confirmed it's existence.

The element of invention is through proof. There are at least 8 ways to prove the Pythagorean theorem. Each method is a product of logical processes at work but the ultimate objective of each proof is to confirm the existence of the mathematical property.

This example can be extended to mathematics in general.

In essence the theorems are "already there", how we proceed to prove them is where invention comes into the picture.

Regards

Steven