Do you believe in gravity?

[Mr.Dysfunctional]

This is fabulous that so many of our posters have a good grasp (( and above )) of einstiens and Heisnbergs theories memorized so well..

I do have a quick question thou... to our more senior academics here...

I always wondered about the harmony between velocity and movement of time. Since if you traveled at the speed of light, you would divert all time motion into spatial movement... Wouldn't the reverse be true also ? could you theoritcally reduce your movement in relation to the universe to where all your movement would be in time versus spatial? Wouldn't you literally have time move at the speed of light?

Another question would have to do with gravity itself...
if constant accelration and gravity are indisdinguishable without outside viewpoints. Wouldn't constant acceleration beyond the speed of light create a black-hole? Obviously only in theory.

What does everyone think about it?

Please excuse my sentence structure.

 

[Dr.Who]

If I may bring this back to the main point of the thread let me remind us that the question/statement is the question of whether or not gravity is just a theory or if it established beyond doubt.

It has become clear that if our two resident experts can spend so much time intelligently disagreeing then the theory of gravity must not be so well established as to put our understanding of it beyond doubt.

 

[numinus]

Nums, you seem to be in a bad mood today. My post was largely an overview that non-physicists can also understand as in Dr. Who's request.

Me? In a bad mood? Not at all.

If you meant the post for dr who, you should have directed it at him -- and save me the trouble of trying to figure out how your post responds to my questions.

My last 3 paragraphs focussed on the difficulty (oops, I mean major stumbling block) of relating general relativity to the smallest dimensions - the froth, the infinities in the equations.

If there are 'difficulties' in relating gr to wave/particle properties, then you can't really be certain, if indeed, it travels at a finite speed, can you? At least not in the order (v/c)^2?

Round and round and round....

Your eyes must have glazed over when you read the following in my interminably long post,
"The currently held view is that general relativity is our best model, but a deeper theory has to be found to solve some of the problems."
That, of course, is my view.

Which is why i mentioned its speed of propagation in the first place.

The fundamental concept of Physics is to build mathematical models and test mathematical predictions derived from those models against reality via experiments. One can say "I believe that model is correct". That is the only way I can make sense of the phrase "believe in gravity".

Otherwise proofs of "I believe in gravity" would have to entail an experiment suggested by one unnamed person here throwing another unnamed person (rather than a lag bolt) out a window.

Oh yes, I don't think any Physicist comprehends the full extent of the nature of gravity, especially at the smallest volumes of space. Who is a pretend agnostic here? Bring him on.

LOL.

You make it seem that the problem only exists in quantum scales. This is not the case at all. The problem exists in cosmological scales as well. Even einstein realized this when he formulated his field equation.

The obvious question (even boneheads would surely ask) that arises from the notion that gravity is the curvature associated with a particular space-time geometry is -- WHY HASN'T ALL THE MASS AND ENERGY PULLED THE UNIVERSE ON ITSELF.

And before you go into another pointless and overly long post in response to the question -- the currently held view to explain this is the COSMOLOGICAL CONSTANT -- LAMBDA.

Now, you must admit, lambda is a curious something that arises from nothing. Not only does it violate lorentz invariance (able to propagate faster than the speed of light via hyper-inflation) it also violates the conservation principle (you need an increasing amount of it to accelerate the expansion of the universe -- as is seen by the hubble separation). Never mind that no one has held lambda to scientific scrutiny, if it is at all possible.

And it is the currently held view by default. Otherwise, gr doesn't make any sense.

In the words of our pathetic pretend-agnostic -- VOODOO MAGIC.

I can see the big picture! I just saw the Battle Star Galactica series. That was a really big picture. Well at least it was long.

Yes. I saw the movie as a kid -- and parts of the series.

They have ftl everywhere and all they can think of as strategic weapons are 6 nukes? I'm sure the writer didn't feel the need to be more creative since he meant to entertain the likes of topgun and mare.

It is the fabric of space-time that expanded faster than the speed of light, not the gravitons. Locally they travel at the speed of light. That also explains why I didn't bat an eyelash.

Nonsense.

Gravitons contract space, lambda expands it. And space cannot expand beyond the speed of light for the same reasons that gravitons can't travel faster than light. After all, expansion and contraction of space-time is the same thing -- only in opposite directions.

LOL. There's nothing like toilet humor. But I guess it would have been more off-topic than my limerick.

Perhaps it would make more sense than your attempts of explanation here.

 

[numinus]

If I may bring this back to the main point of the thread let me remind us that the question/statement is the question of whether or not gravity is just a theory or if it established beyond doubt.

It has become clear that if our two resident experts can spend so much time intelligently disagreeing then the theory of gravity must not be so well established as to put our understanding of it beyond doubt.

That is what I have been saying all along.

The existence of the first cause comes from the same logic as the existence of gravitation.

The operation of causation is as immutably true as the effects of gravitation.

That we cannot comprehend the full nature of the first cause (other than what logically follows from the cosmological argument) does not impugne its existence, any more than the questions I asked about gravity impugne the existence of gravitation.

That the scientific method only arrive at scientific truths -- not metaphysical ones.

 

[Lagboltz]

I always wondered about the harmony between velocity and movement of time. Since if you traveled at the speed of light, you would divert all time motion into spatial movement... Wouldn't the reverse be true also ? could you theoritcally reduce your movement in relation to the universe to where all your movement would be in time versus spatial? Wouldn't you literally have time move at the speed of light?

I think I understand your question. If I don't I will be answering the wrong question.

Suppose you had an extremely powerful telescope with a extraordinary zoom lens so that you could follow somebody going by you at a velocity almost the speed of light. As you watch him you see that he is acting very very slowly. The faster he goes by, the slower he seems to be acting, so to you, his time would seem to come close to a stand still. But to him, everything would be fine but he would see you acting very slowly.

In relativity you must talk in terms of events, which are points in space and time. The interval between events in the above example mostly becomes space-like (that's what it's called). This means that most events that the two people see most likely lack a cause and effect relation because time is needed for that.

If you have little or no motion compared to your friend, then your interactions are most likely "time-like". Cause and effect work because event intervals between you and your friend are predominantly in time.

if constant accelration and gravity are indisdinguishable without outside viewpoints. Wouldn't constant acceleration beyond the speed of light create a black-hole? Obviously only in theory.

It is hard to interpret your question, but I will try. I think you are referring to what happens at the surface of a black hole. The acceleration is so strong that you pass through an "event horizon" as they call it. Knowledge of the events happening to you are beyond the horizon of what a distant observer could see.

If your friend is accelerating constantly until he gets close to the speed of light, he will also approach an event horizon, which means that he could no longer see or contact you. He could not pass the event horizon, because he can't go faster than the speed of light, but he could get very close.

So in both cases, an event horizon comes into play, but you would not accurately call the second one a black hole even though there is some similarity in the effects.

 

[numinus]

I always wondered about the harmony between velocity and movement of time. Since if you traveled at the speed of light, you would divert all time motion into spatial movement... Wouldn't the reverse be true also ? could you theoritcally reduce your movement in relation to the universe to where all your movement would be in time versus spatial? Wouldn't you literally have time move at the speed of light?

I do not quite follow.

When you travel very near the speed of light, three things are observed by an observer in a fixed reference frame:

1. A time interval becomes infinitely long;
2. Spatial displacement contracts to zero.
3. Mass is reduced to zero.

For your part, you would observe exactly what you would observe as if you were in an inertial motion.

Another question would have to do with gravity itself...
if constant accelration and gravity are indisdinguishable without outside viewpoints. Wouldn't constant acceleration beyond the speed of light create a black-hole? Obviously only in theory.

The same thing can be observed as you approach the event horizon of a singularity or blackhole.

If you throw topgun or mare at the event horizon, you would observe them frozen in a ridiculous pose they are in when they enter it. Of course, they would experience all the excrutiating effect.

If you have a problem imagining that, you could simply read their posts. They feel that they are posting valid arguments and are making headway in debate but for the rest of us, they're going nowhere.

 

[Lagboltz]

If you meant the post for dr who, you should have directed it at him -- and save me the trouble of trying to figure out how your post responds to my questions.

Well, Mr. CrankyPants. I was talking in terms that everyone can understand. I deeply apologize for confusing you. When you politely requested that I get to the theme of the thread, I did exactly that. The theme is "Do you believe in gravity?"

The obvious question (even boneheads would surely ask) that arises from the notion that gravity is the curvature associated with a particular space-time geometry is -- WHY HASN'T ALL THE MASS AND ENERGY PULLED THE UNIVERSE ON ITSELF.

No need to shout Mr. Nums. The quantum froth problem is much much more theoretically difficult than the problem you are referring to. 10 or 11 dimensional spaces you know.

And before you go into another pointless and overly long post in response to the question -- the currently held view to explain this is the COSMOLOGICAL CONSTANT -- LAMBDA.

But if you are worried about high velocity of expansion, I will try to be real terse so you won't fall asleep and hit your head on your keyboard. Yes, what is also in vogue these days on the gee whiz science news is dark matter and dark energy, which complicates the big picture a bit, and seems to be a repulsive force. But not to worry, the lambda constant was worked by A. Einstein long ago, and now we have a use for it. .

Now, you must admit, lambda is a curious something that arises from nothing. Not only does it violate lorentz invariance (able to propagate faster than the speed of light via hyper-inflation) it also violates the conservation principle (you need an increasing amount of it to accelerate the expansion of the universe -- as is seen by the hubble separation). Never mind that no one has held lambda to scientific scrutiny, if it is at all possible.

And it is the currently held view by default. Otherwise, gr doesn't make any sense.

In the words of our pathetic pretend-agnostic -- VOODOO MAGIC.

Lambda is just a parameter built into the theory. Albert overreacted when he put it in, and was a bit hasty, but now it's useful. It doesn't complicate the mathematics of the theory any more than the theory was quite a few decades ago. It doesn't violate Lorentz invariance. The expansion of the cosmos beyond the speed of light? - not to worry. Local measurements of the speed of light will always be,... well, the speed of light, no faster and no slower.

Gravitons contract space, lambda expands it. And space cannot expand beyond the speed of light for the same reasons that gravitons can't travel faster than light. After all, expansion and contraction of space-time is the same thing -- only in opposite directions.

Gravitons don't do much of anything let alone contract space, until they figure out how they might work. The theory is still not much better than scribblings on napkins during a working lunch.

Space can expand beyond the speed of light. It gives an event horizon that you can see whenever you stand on your roof and strain your eyes to see radiation at a couple of degrees from absolute zero. Don't wear sunglasses. BTW gravity propagates at the speed of light, if that's a question people are worrying about.

 

[Lagboltz]

If I may bring this back to the main point of the thread let me remind us that the question/statement is the question of whether or not gravity is just a theory or if it established beyond doubt.

It has become clear that if our two resident experts can spend so much time intelligently disagreeing then the theory of gravity must not be so well established as to put our understanding of it beyond doubt.

Gravity is a theory. The job of a physicist is to devise a mathematical model that is consistent with observations. A good model will make mathematical predictions that can be tested by experiments. If new experiments show an inconsistency with a model, then a new model is needed. That goes on in all areas of physics. Physics can never establish anything beyond a doubt.

Examples of models and experiments are Newton's gravity. It looked good except for the orbit of Mercury around the sun. The model was replaced by Einstein's. Now Einstein's model has problems at the smallest scales of space, and is inconsistent with quantum mechanics. Scientists are trying to make a new model most likely with a particle model of gravity - gravitons. The model at the largest scales have some new twists with the discovery of dark matter, and an ultra-fast big bang, etc, but the model seems to hold for now, it is how dark matter affects the parameters in the model that are now under question.

 

[numinus]

Well, Mr. CrankyPants. I was talking in terms that everyone can understand. I deeply apologize for confusing you. When you politely requested that I get to the theme of the thread, I did exactly that. The theme is "Do you believe in gravity?"

No amount of name-calling on your part can hide the fact that you are not answering any of my questions.

No need to shout Mr. Nums. The quantum froth problem is much much more theoretically difficult than the problem you are referring to. 10 or 11 dimensional spaces you know.

So, you wish to discuss a theory involving n-dimensions when no experimental verification of it is even possible at this time?

10 or 11 dimensions, indeed!

But if you are worried about high velocity of expansion, I will try to be real terse so you won't fall asleep and hit your head on your keyboard. Yes, what is also in vogue these days on the gee whiz science news is dark matter and dark energy, which complicates the big picture a bit, and seems to be a repulsive force. But not to worry, the lambda constant was worked by A. Einstein long ago, and now we have a use for it.

.

Einstein inserted the cosmological constant to derive a steady state universe. Without it, space-time geometry would be spherical, and nothing would stop the universe from contracting on itself.

Lambda is just a parameter built into the theory. Albert overreacted when he put it in, and was a bit hasty, but now it's useful.

All terms of the field equation represent a particular parameter.

Do you even know what you are saying or are you just trying to be amusing for mare's benefit?

Here, you might want to refresh your memory:

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

The cosmological constant has the same effect as an intrinsic energy density of the vacuum, ρvac (and an associated pressure). In this context it is commonly defined with a proportionality factor of 8π: Λ = 8πρvac, where modern unit conventions of general relativity are followed (otherwise factors of G and c would also appear). It is common to quote values of energy density directly, though still using the name "cosmological constant".

Other than the gravity due to mass and energy, no other 'parameter' affects the geometry of space-time except lambda.

You might want to recall this too:

In lieu of the cosmological constant, cosmologists often quote the ratio between the energy density due to the cosmological constant and the critical density of the universe. This ratio is usually called ΩΛ. In a flat universe ΩΛ corresponds to the fraction of the energy density of the Universe which is associated with the cosmological constant.

Cosmologists even have a sense of humor, giving a paradoy of critical density that is originally associated with nuclear explosions. It is 'critical' because it is the value necessary to derive a flat space-time geometry of the universe, the one we are living in right now.

Any small deviation from this critical density would immediately result in either a spherical or psuedo-spherical (saddle-shaped) geometry which, in turn immediately results in either a big crunch or the universe 'escaping' itself.

To say 'today, it is useful' is an understatement of monumental proportions. The fact that the universe is expanding at an accelerating rate only means that the cosmological constant is doing so even against the tendency of gravity.

It doesn't complicate the mathematics of the theory any more than the theory was quite a few decades ago.

You have einstein to thank for that. His genius comes from the sublime beauty of its simplicity. It doesn't get much simpler than E=mc^2, does it?

It doesn't violate Lorentz invariance. The expansion of the cosmos beyond the speed of light? - not to worry. Local measurements of the speed of light will always be,... well, the speed of light, no faster and no slower.

Of course it does.

The speed of light does not just 'appear' to be so. It is so in ANY AND ALL reference frames. It is a UNIVERSAL SPEED LIMIT.

You keep mentioning 'local' as if there was some other reference frame in which something can go faster than the speed of light. I hate to break the news to you but, in relativity, there ain't.

The notion that space can somehow expand a couple of thousand times the speed of light, or inflationary cosmology, was contrived to give an explanation to the horizon problem. And this particular solution gives rise to more problems than it solves.

Gravitons don't do much of anything let alone contract space, until they figure out how they might work. The theory is still not much better than scribblings on napkins during a working lunch.

Space can expand beyond the speed of light. It gives an event horizon that you can see whenever you stand on your roof and strain your eyes to see radiation at a couple of degrees from absolute zero. Don't wear sunglasses. BTW gravity propagates at the speed of light, if that's a question people are worrying about.

Sigh.

The original problem is that there is something fundamentally wrong with gravity as an 'instantaneous action from a distance'. After all, there must be some sort of intermediary between a cause and its effect. A light source emits electro-magnetic waves 'bundled up' as photons to give the sensation of light. And because nothing can travel faster than c, so does these photons.

For gravity, it was 'theorized' that it propagates via gravitons. And gravity (hence gravitons, being the intermediary particle to it), by gr, serves to curve space-time.

Now, you say that the gravitons are unable to go faster than light but its effect, the expansion/contraction of space-time, can go faster than light.

To put it simply, the effect is vastly overtaking its cause. I may have a mere undergraduate degree but I think you need to explain this a little better than a vague and cursory mention of 'local measurements'

 

[numinus]

Gravity is a theory. The job of a physicist is to devise a mathematical model that is consistent with observations. A good model will make mathematical predictions that can be tested by experiments. If new experiments show an inconsistency with a model, then a new model is needed. That goes on in all areas of physics. Physics can never establish anything beyond a doubt.

Despite your arrogant criticisms of my posts, the underlined statement coincides with what I have been saying in the beginning -- that the thread starter who asked the question was ENTIRELY within reason to have asked it.

As for the other assertions, well, I can only chuckle at how painfully inadequate your comprehension of the 'big picture' truly is.

The validity of a theory rests on its ability to predict the experimental result of a particular phenomenon AND post-dict a perviously observed but inadequately explained phenomenon.

For instance, the strenght of relativity rests on its prediction of gravitational refraction of the light coming from stars as it passes very near the sun (observed during a solar eclipse) AND its post-diction of the previously observed but unexplainable rosetta orbit of mercury.

We do not simply conjure a mathematical model to fit demonstrable fact. I say this as criticism to string theory -- something you have brought up during this discussion (despite its irrelevance) a couple of times already.

For instance, I have known n-dimension mathematics was possible long before I knew about string. And since the math is already there, what is stopping the physicist from adding one or two more dimension to govern this or that previously unknown phenomenon? Remember, string came about from the 5-d, kaluza-klein model. And the development of this theory consists mainly of adding even more dimensions. And while everyone is busy doing 11-dimension math, hopelessly infatuated with its elegant complexity, we forget the principle of ockham's razor -- that science, after all, is about parsimony.

Which brings me to a question that has vexed me for the longest time -- what exactly is the relationship of mathematics and physics? Why are physical phenomena compelled to behave according to, say, natural logarithmic functions or binomial expansions? Is there some objective existence we are simply not aware of or are they so simply because they are so?

 

[Lagboltz]

No amount of name-calling on your part can hide the fact that you are not answering any of my questions

Mr. Cranky pants? Name calling? I've seen much worse in this forum. It's just a friendly moniker, but I think you are just kidding about that.

So, you wish to discuss a theory involving n-dimensions when no experimental verification of it is even possible at this time?
10 or 11 dimensions, indeed!

Physicists are looking for a coherent model that brings unity to the nature of the universe. It is a noble endeavor. If the large scale and small scale can be united, other things like the cosmological constant, inflation, etc may (or may not) follow. If the current large problems are solved by a new small scale model, then experimental verification will have been done.

Einstein inserted the cosmological constant to derive a steady state universe. Without it, space-time geometry would be spherical, and nothing would stop the universe from contracting on itself.

That was his intention, but the important thing he did was put a covariant tensor into his field equations that kept consistency. That term now has multiple purposes outside his original purpose. In simple terms, Einstein made his theory more flexible, and physicists are now using that flexibility in different ways.

All terms of the field equation represent a particular parameter.
Do you even know what you are saying or are you just trying to be amusing for mare's benefit?

Hey, Mr. Nasty Pants. Are you trying to put me down so you can woo Mare into thinking you are the most brilliant person in this thread? Just kidding, no need to answer.

Here, you might want to refresh your memory:
http://en.wikipedia.org/wiki/Cosmological_constant

You also may want to refresh your memory too. The reference you sited has the following passage:
"A major outstanding problem is that most quantum field theories predict a huge cosmological constant from the energy of the quantum vacuum."

Quantum vacuum - the froth at the bottom strikes again! This kind of shows that that string theory with the "10 or 11 dimensions indeed!" are kind of at the bottom of things, so to speak, and has a fundamental bearing on the cosmos. So don't you think you should look at the teeny picture at quantum scales too if you want to understand the big stuff?

You keep mentioning 'local' as if there was some other reference frame in which something can go faster than the speed of light. I hate to break the news to you but, in relativity, there ain't.

I was responding to your comment:
"Now, you must admit, lambda is a curious something that arises from nothing. Not only does it violate lorentz invariance (able to propagate faster than the speed of light via hyper-inflation)..... "

You were worried about something going faster than light. So now you agree that "local" is the operative word. Case closed.

The notion that space can somehow expand a couple of thousand times the speed of light, or inflationary cosmology, was contrived to give an explanation to the horizon problem. And this particular solution gives rise to more problems than it solves.

Not so. It was "contrived" to explain the apparent age of early galaxy formation, and other things. The fact that IR space telescopes stare at an event horizon 13.6 billion light years away came as a consequence.

Sigh.

Sigh. Sigh. (Note: "sigh" is a put down. I am up one sigh above his now.)

The original problem is that there is something fundamentally wrong with gravity as an 'instantaneous action from a distance'.

That's right. That Newton is sooo yesterday.

A light source emits electro-magnetic waves 'bundled up' as photons to give the sensation of light. A light source emits electro-magnetic waves 'bundled up' as photons to give the sensation of light. And because nothing can travel faster than c, so does these photons.

EM waves ain't got nuthin to do with bundled anythings. Quantum mechanics is not like that, but I'm further digressing from your digression, so I won't pursue it, unless anyone is interested in that off-topic.

For gravity, it was 'theorized' that it propagates via gravitons. And gravity (hence gravitons, being the intermediary particle to it), by gr, serves to curve space-time.

You are prejudging the potential theory. Gravitons may not necessarily curve space. Einstein's warped space was way outside the box of Newton's inverse square action at a distance. Likewise, graviton gravity (catchy little phrase isn't it) may not have anything to do with warped space. One requirement is the so-called "Correspondence Principle". A new theory must be able to include the old theory as an adequate approximation under loose enough conditions.

 

[Dr.Who]

Which brings me to a question that has vexed me for the longest time -- what exactly is the relationship of mathematics and physics? Why are physical phenomena compelled to behave according to, say, natural logarithmic functions or binomial expansions? Is there some objective existence we are simply not aware of or are they so simply because they are so?

Well the founders of the scientific method said that the Laws of Nature were the connection. This is still held by scientist today.

Of course the founders meant laws that were established by God and they used the word "law" specifically because they felt God's laws of the universe were like men's laws - created to rule.

It can't be proven and it is a faith based statement.

Today naturalist just say that they are laws because we have always observed them to be that way and we have never observed them to be any different. Which is of course inductive reasoning as soon as they say the laws are true and is also a faith based statement.

All of science must either be "agnostic" because it admits nothing can be proven or it must be faith based. Both positions are admirable. The second is practical. It is when people ascribe to the second position but then fall into dogmatism and forget that it is faith based that we have problems.

 

[Mr.Dysfunctional]

I do not quite follow.

When you travel very near the speed of light, three things are observed by an observer in a fixed reference frame:

1. A time interval becomes infinitely long;
2. Spatial displacement contracts to zero.
3. Mass is reduced to zero.

For your part, you would observe exactly what you would observe as if you were in an inertial motion.



The same thing can be observed as you approach the event horizon of a singularity or blackhole.

If you throw topgun or mare at the event horizon, you would observe them frozen in a ridiculous pose they are in when they enter it. Of course, they would experience all the excrutiating effect.

If you have a problem imagining that, you could simply read their posts. They feel that they are posting valid arguments and are making headway in debate but for the rest of us, they're going nowhere.

It seems i need to rephrase this... Aplogize about that.
Actually what I was getting at was the link between constant acceleration and gravity... Say.. your in a spaceship.. and all the windows are blacked out.. and you passed by a planet.. how would you be able to tell the differnce between gravity and/or your space ship simply accelerating on a course opposite the direction you feel the "tug" of gravity.. you wouldn't .. at least without someone on the outside telling you that you were. My question being is that if your space-ship were able to travel abovwe light-speed.. wouldn't you experince the same effects as if near the event horizen of a black-hole..

And about my first question.. I understand the slowing of time near light-speed or a signficant portion of it... however.. from the way i have been taught realtivity , everything is actually traveling at light-speed constantly because of the link between space and time. I.E. You start with a constant speed (( light-speed 187,000 miles a sec but of course you already know this )) and you divert some of that speed into forward progress of time. Meaning that even thou we are here on earth only moving at say 10,000 miles an hour (( i believe thats the earths rotational speed around its axis )) you are still traveling at light-speed ... its just the remainder of that speed has been diverted to forward motion in time. My question is .. what if you did the exact opposite of traveling at light-speed with forward motion across space .. and instead diverted all your speed into the forward progress of time. I.E. standing perfectly still with no forward motion in any of the three dimensions within relation to the universe.
Wouldn't you age at an increased rate? or would an outside viewer see you as if looking at a movie speed up ?!?! and if so.. couldn't you literally time-travel into the future because of it ?

 

[Lagboltz]

Despite your arrogant criticisms of my posts,

Well, we have both been arrogantly criticizing each others posts. I will stop if you do. Deal?

the underlined statement coincides with what I have been saying in the beginning -- that the thread starter who asked the question was ENTIRELY within reason to have asked it.

I never meant to imply otherwise.

As for the other assertions, well, I can only chuckle at how painfully inadequate your comprehension of the 'big picture' truly is.

Now, stop that.

11-dimension math, ... elegant complexity .. . ockham's razor

Yes, we gotta listen to Occam and his razor, but Einstein also amended "Everything should be made as simple as possible, but not simpler."

string theory -- something you have brought up during this discussion (despite its irrelevance)

I covered it's relevance in a previous post. I didn't see this post when I uploaded my last post. The number of dimensions in string theory are dictated by the properties of particles (barons, leptons, gluons, etc.) Ten dimensions is the lowest number that can accommodate string theory. Going to fewer dimensions is "simpler than possible" for what needs to be done there.

Which brings me to a question that has vexed me for the longest time -- what exactly is the relationship of mathematics and physics? Why are physical phenomena compelled to behave according to, say, natural logarithmic functions or binomial expansions? Is there some objective existence we are simply not aware of or are they so simply because they are so?

That is a great question. I vexes me and many scientists who care to think about it. What has happened, is an evolution of mathematical complexity. From algebra to 4-vectors and tensors, to group theory and other non-commutative algebras. (Note to others: That means an algebra where this can happen,
A times B is not equal to B times A.)

So far mathematical models (theories) have worked on many most fundamental aspects of describing nature. There are many unsolved problems at the large and small scale. Will math fail at some point? Will there be newer and more abstract mathematics that will satisfy future needs? If not, physicists will be out of business, but they won't know it and won't stop trying.

 

[Dr.Who]

So far mathematical models (theories) have worked on many most fundamental aspects of describing nature. There are many unsolved problems at the large and small scale. Will math fail at some point? Will there be newer and more abstract mathematics that will satisfy future needs? If not, physicists will be out of business, but they won't know it and won't stop trying.

Will math fail at some point?

Can you describe this sentence mathematically?

"This sentence is not true"