Sunday, October 11, 2009

This and That

70 comments:

Phil Warnell said...

Hi Bee,

In looking at PI’s posting for post docs it does appear to be more like they are writing their own CV, rather then it being a request for them. I have no problem with that, as it being in a effort to attain the best and the brightest available, yet I hope they understand as in any marketing effort, that one can’t substitute the streak with it's sizzle :-)

Best,

Phil

Bee said...

Steak? To me it looks mostly odd. Show me the th. phys. postdoc who'll chose his workplace because the facilities won an award.

Losang Tharchin said...

How about suggesting bloggers stop giving unsolicited advice. That's a great reason to unsubscribe.

Bee said...

Good bye!

Phil Warnell said...

Hi Bee,

Steak? To me it looks mostly odd.

Yes perhaps for you I should have said, they can’t substitute the crunch for the celery :-) I would agree that a post doc would not so much be attracted to an institute solely resultant of it winning an award, yet I would say they might be persuaded by who represent to be the faculty, associates and fellow post docs. Going back some years, the Neil Bohr Institute would have represented what I’m referring to, with it being largely instrumental in the creation and development of Quantum Mechanics.

Best,

Phil

Bee said...

Sure.

Phil Warnell said...

HI Bee,

Then again Albert Einstein made ground breaking discovery while being entirely outside the ivory tower, with working in a Patent office. Perhaps the modern equivalent for a job that would afford some time to consider other matters would be working on Wall St. Then again, let’s forget that one, for we already know what the repercussions of this choice can be :-)

Best,

Phil

Bee said...

Hi Phil,

Jah. Albert Einstein and his patent office. There's many things to be said about this. Maybe the most important ones:

1) That was a century ago. Times change.

2) What could Einstein have achieved if he had been at PI instead?

3) There's no recipe for success in science. Thus the best I think you can offer a researcher is what works best for them, which might be individually very different. The question is of course how well they know themselves.


Best,

B.

Phil Warnell said...

Hi Bee,

Of course in general I agree with the gist of what you are saying, especially the part with someone having to know themselves coming before any other consideration. As to pointing out that being a century ago I would remind you of those like Garret Lisi and Antony Valentini although they may never make similar contribution I would suggest no one again may be able for a lot of reasons. In regards to Einstein and Perimeter if taken in the light of the pressure it brings to bear, related to competition and that of publishing, I would say he might have accomplished little if anything at all.

Best,

Phil

Bee said...

Oh-oh. Poor Perimeter. And that whilst they are looking so hard for the "new Einstein." I think you're judging PI too negatively though. They leave their researchers a lot of freedom. If you don't want to play with the other kids all day, you don't have to.

The point I was trying to make with 2) is that nobody knows and nobody will ever know. It is a poor argument to draw conclusions from a singular event like Albert Einstein in his patent office, when there's no way to find out how much the circumstances of his work had to do with his achievements. Best,

B.

Phil Warnell said...
This comment has been removed by the author.
Phil Warnell said...
This comment has been removed by the author.
Phil Warnell said...

Hi Bee,

Not that I’m attempting to draw any direct comparison, yet from my study of Einstein, both the person and the scientist, I have found his greatest worth and ability in being not simply a man of science, yet rather a person of ideas, opinion, conviction and strong social conscious. Since my first stumbling across this blog some two years ago I have found you to be a person with similar qualities.

Best,

Phil

As a post script, even though it may be uncertain if those like Einstein could have flourished under a system such as Pi’s, however I have some reason to believe he may have maintained a blog relative to waht I've stated earlier :-)

Also, I’ve come to realize I’m not the most humorous when attempting to be funny, yet rather resultant of my habit of not reviewing what I’ve written :-)

LT said...

Being opinionated is easy. Skillful is difficult. Thinking is the hardest.

The problem with physics these days is there are no deep thinkers and plenty of people who know how to turn knobs. Just take a look at who are considered the best now and compare them to those of the first half of the 20th century. To take just one example, Einstein's study of Mach had a deep influence on his development of relativity. The thinker has been replaced by the equation.

Phil Warnell said...

Hi LT,

I agree with what you say, as Einstein himself would have. What I meant to have understood is that being a great thinker extends beyond considering just the discipline itself, which Einstein indicated by saying the following on the subject:

“Somebody who only reads newspapers and at best books of contemporary authors looks to me like an extremely near-sighted person who scorns eyeglasses. He is completely dependent on the prejudices and fashions of his times, since he never gets to see or hear anything else. And what a person thinks on his own without being stimulated by the thoughts and experiences of other people is even in the best case rather paltry and monotonous. There are only a few enlightened people with a lucid mind and style and with good taste within a century. What has been preserved of their work belongs among the most precious possessions of mankind. We owe it to a few writers of antiquity (Plato, Aristotle, etc.) that the people in the Middle Ages could slowly extricate themselves from the superstitions and ignorance that had darkened life for more than half a millennium. Nothing is more needed to overcome the modernist's snobbishness.”

Best,

Phil

LT said...

Phil,

Great quote. Its nice to see there are others out there who think this way. I also find Lee Smolin's comment on this issue insightful. The part in "Trouble with Physics" on seers and craftspeople helped give me the words to express what I saw going on.

The case is proven by physicists' comments in the public arena. Lisa Randall, on Charlie Rose, said the 11 dimentions came out of the science. What science? These people have lost touch with thinking. Physics has no ontology and a lot is lost on not understanding this. It leads to riduculous talk of "theories of everything". The errors in these statements are endless.

Phil Warnell said...

Hi LT,

If you look closely there are many who share this opinion, including a growing body of scientists, beyond the few you mention, which unless I’m mistaken would include the author (s) of this blog. Also, I wouldn’t be so critical of those like Lisa Randal, for I have found her to be more sympathetic to what you express then what you might imagine. However, the central point of it all refers back to what Bee has called “the marketplace of ideas” which extends to not only those of the present yet those also of the past from which the foundations were laid.

Oh by the way, I don’t only consider what Einstein said as representing as being a challenge to his peers yet rather one to be extended to all of humanity.

Best,

Phil

Giotis said...

"...like Lisa Randal, for I have found her to be more sympathetic to what you express then what you might imagine."

And she is a very attractive woman too:-)

Per said...

I guess they warming him up for the noble price.. Since giving Obama the price for something he hasn't done, I'm sure they can give Higgs the price for something not found. At least he has some fancy equations to back up his claims.

Best, a Swede in Germany.

Phil Warnell said...

Hi Per,

Your cynicism for me betrays why you don’t understand either Obama’s selection or why Higgs hasn’t received his prize of yet. That being with the former it’s weighted on their assessment of potential and the latter on demonstrated result. That is true peace representing being a goal which none so far awarded has actually achieved, while the Higgs particle if identified with the LHC will have been realized. That is one is subjective by nature, while the other isn’t.

Best,

Phil

Bee said...

Hi LT,

Aren't you being a little opinionated as far as your judgement on "physics these days" is concerned? I agree with you though that there are too many people who just know how to turn knobs. Is what I refer to as pursuing secondary criteria instead of primary goals. It however isn't as extremely bad as you make it sound. Best,

B.

Bee said...

Hi again LT,

Regarding your later comment about what is "proven by physicists' comments in the public arena." It is sad but true that what physicists say publicly might not reflect their actual scientific opinion. There is a lot of politics involved there. This isn't specific to string theory. Scientists who talk in public know pretty damned well their funding depends on how relevant they make their own research seem. I suggest you have a look at my post on the "Marketplace of Ideas". Is what I refer to as "public pressure," one of the 4 pressures that redirect research interests.

To give you some numbers from the previously mentioned survey that might illustrate the problem:

- 57.3% of physicists (active researchers in North America) agreed or strongly agreed that "It is relevant that my research area is considered important by the public"

- 20.2% disagreed or strongly disagreed that "Drawbacks of an approach are openly pointed out in publications and presentations"

- 25.4% agreed or strongly agreed that "One does not publicly criticize the research area one works in"

Best,

B.

Bee said...

Phil: What opinion do I allegedly share? That extra dimensions "came out of science?" I'm not even sure what that's supposed to mean given that Sean Carroll once declared on his blog that mathematics is not a science. So to avoid the linguistic problems, there is no experimental evidence for the existence of additional spacelike dimensions, and I doubt Lisa Randall would have said so. Best,

B.

John Joseph M. Carrasco said...

Hi Bee! I'm certainly curious to hear more about the `fine print' associated with either postdoc position.

Warm regards,
JJ

Giotis said...

Extra dimensions is not a mathematical construction, they come out of physical considerations. If you try to quantizize a bosonic string in the light cone gauge, you see that in order to preserve Lorentz symmetry you need 26 dimensions. Also if you want to preserve Weyl symmetry for the quantizized string again you see that you need 26 dimensions. On the other hand by preserving Weyl symmetry you get the Einstein filed equations in vacuum for the space-time background. Remarkably enough this background is built by the gravitons in the spectrum of a quantizized string. Why we like gravitons? Because this is how QFT works etc...

What I mean to say is that Extra dimensions didn't fall from the sky i.e. Let's imagine how the world would be if we had extra dimensions. A series of "evidence" lead to them. These evidence are physical considerations and some of them are based on experimental facts e.g. Lorentz invariance. In that sense I would say that indeed extra dimensions came out of science. Otherwise you must draw the conclusion that all the people involved in string theory or Quantum Gravity in general are not scientists but philosophers.

Bee said...

JJ: Are you applying this year? Send me an email, you find it on my homepage. Best,

B.

Bee said...

Hi Giotis,

I didn't say extra dimensions are a merely mathematical construction, I was just bringing up the question whether LT considers math a science to avoid talking past him (or her). I was just clarifying that there is no experimental evidence, and that the motivations for considering extra dimensions rest on (mathematical) consistency, as you say. However, theoretical physics is as a matter of fact heavily mathematical, so it is of little surprise that the boundaries are blurry in some areas.

This however shouldn't be confused with actual evidence. For example, as I asked earlier, what reason do we have to believe the quantization scheme is appropriate to use in its present form at energies far off where we have experimental tests? Answer: no reason except lack of imagination for an alternative. Which is a reason, but I leave it to you whether it's a good reason.

My motivation for considering extra dimensions stems more from the fact that we know no good reason why spacetime should be 3+1 dimensional, thus considering additional dimensions and asking how one could test their existence is an interesting question. It still isn't clear to me what either Phil or LT meant to say there, but I hope this clarifies my opinion.

Best,

B.

Phil Warnell said...

Hi Bee,

“What I meant to have understood is that being a great thinker extends beyond considering just the discipline itself”

What I thought you would agree with is noted above. I never meant it to be connected with LT’s complaint in regards to the debate about extra dimensions of which I’ve never been certain what your take on is. My own being its one possibility among many, with another being perhaps some phenomena we see are resultant of physical entities of lesser, not extra dimension. That’s to say who knows which it is, being in the context of what experimental evidence is there to support any theories thus proposed beyond the standard model.

Best,

Phil

Bee said...

Hi Phil,

I see. Sorry for the misunderstanding. I would agree, though the problem is that "great thinkers" much like "great artists" frequently are not appreciated in their own times. I suppose that's the price you pay for being ahead. Best,

B.

Phil Warnell said...

Hi Bee,

I should say it was my fault rather then yours, since I should have been more careful as to make the distinction. I find it difficult to understand for anyone that had read Lisa Randal’s book to consider her connected with the narrow view of a knob twister as LT was implying. It comes across plainly for me, as evident in both what she writes and her style of expression that her influences and considerations extend much further than that.

Best,

Phil

Giotis said...

"...what reason do we have to believe the quantization scheme is appropriate to use in its present form at energies far off where we have experimental tests?"

Bee that question doesn't help me much. The reverse is more useful:

What reason do we have to believe the quantization scheme is *not* appropriate to use in its present form at energies far off where we have experimental tests?

Bee said...

That using it hasn't lead us anywhere in more than two decades. Instead, it has lead us to something called the landscape problem. Imho, at that stage of uselessness you better carefully go through all the assumptions and see whether all of them are solidly grounded. And those that aren't should be reconsidered. Best,

B.

Giotis said...

Bee I don't think that the quantization scheme of string theory is your problem but the fact that you don't believe that nature is Quantum mechanical at fundamental level.

Bee said...

You are right, it's not my problem...

joel rice said...

... we know no good reason why spacetime should be 3+1, thus ..." another possible 'thus' is that there actually is a good reason, and we just have not thought of it yet. Not all of us have taken to 'eating lotus with the Platonists'.

Phil Warnell said...

Hi Joel,

“Not all of us have taken to 'eating lotus with the Platonists'.”

I think your difficulty may stem from you having the philosophies confused, as the the lotus is connected with the Buddhists , and not the Platonists. Also, they don’t eat them, rather emulate them metaphorically. Although, I would admit that the Lotus could have been appreciated by Plato for its beauty, which in turn would suggest it be resultant of some underlying truth, yet I don’t think he either would have found them to be appetizing :-)

Best,

Phil

Tkk said...

This thread has turned into a lot of talk what others have or have not done. Philosophical discussions about Einstein is irreverent in the reality of 21th century physics.

Sean's CV blog has posted a most interesting, provocative paper by Cornell cosmologist Rachel Bean and Bee has uttered a few words on it.

Bean analyzed vast amount of cosmological data for the express purpose of finding a fundamental flaw in GR. She appears to have found a flaw based on curvature incompatibility! I am sure lots of peers will poke holes into into it as they review.

The Bean approach shows one needs novel phenomenological approaches to find QG in additional to theoretical ones. My guts tell me the breakthrough insight would come from cosmology earlier than from LHC. Meaning I put breakthrough coming from pure theoretical approaches way down.

I for one would appreciate to hear what Bee the "Pheno Girl" have to say about Bean's phenomenological development.

I am beginning to appreciate why PI wants to put greater emphasis on cosmology.

Bee said...

Hi Tkk,

I haven't yet read the paper, so can't say anything about it. Best,

B.

Bee said...

Hi Joel,

Yes of course there might be a good reason that we haven't thought of for why we live in 3+1 dimensions. There might also be a good reason why we don't live in 3+1 dimensions (string theorists would argue we have already thought of that one). What I was saying that as long as we don't know, why don't we just look. Best,

B.

Arrow said...

Bee: "My motivation for considering extra dimensions stems more from the fact that we know no good reason why spacetime should be 3+1 dimensional"

Huh? We have plenty of very good reasons:

1. Our everyday experience, if world had more dimensions life would of course evolve to take advantage of them and we would therefore be able to experience them.

2. The fact that all successful theories are 4 dimensional and there is not a single known case where considering extra dimensions has lead to a better insight or theory.

3. Occham's razor

4. Someone might invoke compactification in opposition to 1 but there is zero evidence that compactified extra dimensions are anything other then a wishful thinking. Existence of such a compactified dimension would amount to the most brutal and fundamental violation of symmetry one can think of. It would also pose philosophical problems since it would invalidate one of the biggest successes of relativity - realization that dimensions are not separate entities but rather form a single whole spacetime whose three spatial and one temporal dimensions can "mix" together (I even suspect the distinction between time and space may very well turn out to result solely from asymmetry of mass-energy content and not in any fundamental difference between them). Such "mixing" would be impossible with one or more compactified dimensions since they are fundamentally different.

These are the strongest reasons one can ever get against an idea. Extra dimensions are nothing but a cheap way to protect ones pet theory from reality.

Bee said...

Arrow: We're talking past each other. Show me a proof according to which 3+1 dimensions (that's not the same as 4 dimensions) are necessary to obtain the standard model of particle physics. You might also want to ask what you mean with "successful" in 2), though I agree that adding extra dimensions to a quantum field theory doesn't exactly improve the situation. Taken together, the reasons you come up with are reasons why more dimensions haven't been considered earlier, but that wasn't what I was asking for.
The question I was raising is the following. Our present view of reality is that we live in a manifold with fields on it. Why does that manifold have 4 dimensions and Lorentzian signature? Tell me a mechanism how that happens or a reasons why everything else would be inconsistent. And in absence of such, consider that maybe it does actually have more dimensions. (In some scenarios these can be infinitely large.)
Best,

B.

Georg said...

as the the lotus is connected with the Buddhists

Hello Phil,
right, but lotos eaters (or "lotophagi")
are a population in Odyssey.
See here:
http://en.wikipedia.org/wiki/Lotophagi
Best
Georg

Phil Warnell said...

Hi Georg,

” The lotus fruits and flowers were the primary food of the island and were narcotic and addictive, causing the people to sleep in peaceful apathy.”
-Wikipedia

Interesting and yet I must admit I’m more familiar with Plato then Homer. None the less it is reminiscent of a complaint J.S. Bell had in regard to the way quantum theory is regarded by many theorists when he said:

"The Bohr-Heisenberg tranquilizing philosophy forms a gentle pillow from which the true believer cannot easily be roused."
-J.S. Bell- Speakable and Unspeakable in Quantum Mechanics

Best,

Phil

Georg said...

Hello Phil,
J.S. Bell maybe thought of Homer when he wrote that.
Naming such behaviour "lotus eaters"-like
was a bit too offensive in his thoughts presumably.
Best Georg

Arun said...

Dear Bee,

There is an infinite regress of whys, e.g., even if you could answer why 3+1 dimensions, why does it appear that we live on a manifold with fields?

Any particular "why" is scientifically interesting, if and only if the question can be addressed by the scientific method.

It would seem theoretically, via string theory, the question of the number of dimensions can be addressed. However, string theory opens more questions than it answers - why 4 dimensions instead of 26, 10 or 11? Experimentally so far there seems to be little support for any but the empirically determined 3+1 dimensions. I think it is still somewhat dubious that an explanation of the number of dimensions is within our scientific grasp.

Best,
-Arun

Arun said...

Oswaldo Zapata attempts to take on the myth of the lone creator:

http://spinningthesuperweb.blogspot.com/2009/10/superstring-world-i-of-iv.html

Anonymous said...

Hello bee,

strangely here I agree that main motivations for considering extra dimensions rest on mathematical consistency. And that being related to having no good reason why we live in 3+1 world. you say something about quantization should be done? I think also , yes. but in what way do you mean that (about quantization)?

A.

Bee said...

Hi A,

I don't know. What I am saying is that one should consider that the quantization scheme we know does a good deal in describing Nature at relatively low energies, might not be the right thing to do at high energies. In particular, it seems to me that the need of string theory to have additional dimensions (and the problems that come with their compactification) are in the end a consequence of the quantization, thus might potentially change (hopefully solving some problems) when one rethinks the quantization. I've been asking people about that for some years now, but to me it's more on a general-interest/I'm-just-saying basis, since I'm not a string theorist and this is actually quite far off my own work. What I learned though is that Thomas Thiemann tried a different quantization scheme for strings, I believe this is the relevant paper, and comes to the conclusion that it works in any number of dimension. I don't understand much of the calculation in the paper, so don't ask for details. It serves as an example though to what I said, that the issue with the # of dimensions is sensitive on the quantization scheme.

(Besides this, there is a little bit of confusion in this thread in that my believe in quantum mechanics not being fundamental that Giotis brought up earlier doesn't necessarily have something to do with the quantization scheme being potentially inappropriate.)

Best,

B.

Anonymous said...

hmm.

in a way I agree...

but let me explain how I mean it-

issue is deeper, and the need for quantization procedure modification is just a corollary of that.

and in fact - the issue is with DIMENSIONS itselfs.

so- quantization procedure should be modified as a consequence of conceptualizing dimensions.

A.

Giotis said...

Helling and Pollicastro strongly disputed that (hep-th/0409182 & hep-th/0610193). As a result I think Thiemann gave up the whole idea. That's why I think he never published the anticipated sequence for the LQG string in curved target space. But I'm not at all sure that this is the reason, it's just my impression.

Arrow said...

Bee: "The question I was raising is the following. Our present view of reality is that we live in a manifold with fields on it. Why does that manifold have 4 dimensions and Lorentzian signature?"

Science can only discover how Nature operates not why it operates a particular way. Even if I could explain how the number 4 follows from such and such more fundamental principle you could still ask why this principle holds and so on.

The fact that we cannot explain why there are 4 and not 4000 dimensions does not mean however that we should question this value, we get it from experiment and so it should be trusted.

Yes, people can invent elaborate conspiracy theories aimed at explaining how we only see 4 dimensions when in fact there are 4000 but as all conspiracy theories they should not be taken seriously unless there are extraordinary evidence to back them up.

The only valid reason to doubt 4 dimensions would arise if someone were to develop a much more successful physical theory assuming a different number of dimensions. Such a theory would have to be irreducible to 4D or at least vastly more complex when expressed in it. If this theory were to pass rigorous experimental verification it would give us a valid reason to question the actual number of dimensions but even then it would be far from clear what to believe. No one could guarantee that there won't be a successor to that theory successfully explaining even more while returning to four dimensions.

Giotis said...

", we get it from experiment and so it should be trusted."

Arrow, in the brane world scenarios only gravity can probe the extra dimensions and gravity has been tested accurately only down to a fraction of a mm. So we could well have large extra dimensions of that order. If experiment indeed had excluded extra dimensions then no one would talk about them. If on the other hand you have good theoretical reasons to believe in extra dimensions (like solving the hierarchy problem for example) and the experiment does not forbid it then of course you are allowed to hypothesize and construct entire theories based on them. But I'm explaining the obvious I guess.

Thomas Larsson said...

"If experiment indeed had excluded extra dimensions then no one would talk about them"

Show me the theorist who would abandon a good theory just because of something as trivial as the experimental verdict.

Ptolemy's epicycle theory survived for 1,500 years. Now that's something to be inspired by.

Bee said...

Arrow:

The fact that we cannot explain why there are 4 and not 4000 dimensions does not mean however that we should question this value, we get it from experiment and so it should be trusted.

People are calculating how the existence of extra dimensions would affect our experiments and analyze the data to see if it contains indications for the existence of additional spatial dimensions. As Giotis said above, the data that we currently have is not sufficient to outrule more than 4 dimensions, otherwise nobody would be talking about it. (One might argue that data will never actually outrule the existence of extra dimensions, which is true. If the parameters are constrained enough however it will become very implausible. Similar like mod of GR/SR are never actually outruled, they are just so constrained that sensible people don't consider them anymore.)

The only valid reason to doubt 4 dimensions would arise if someone were to develop a much more successful physical theory assuming a different number of dimensions.

If experimental data was explained better by a model with extra dimensions, that would be a "more successful physical theory." And that despite the fact that it might neither be fundamental nor particularly compelling.

You seem to have a too narrowminded idea of how progress in science works. It's either lead by experiment (new data, theorists explain), or it's lead by theory (new theory, experimentalists look).

The other point you're picking around is the very common attitude that science should stick to the "how" and not bother about the "why." It always makes me yawn if people come up with that. It is of course correct that when we write down a model it's the how that we're concerned with. But the why is frequently a motivation. I would agree that there will always be more "why's" that we can't answer, but that doesn't mean why questions are generally out of range. Why is the sky blue? Well, if you like you can ask all the way down to why does the Standard Model of particle physics have a U(1) gauge group. But most of the time it's fine to explain Rayleigh scattering. If you read what I wrote, you will see that I clarified my question "Why 3+1 dimensions" to "Tell me a mechanism how that happens"

Best,

B.

Bee said...

Hi A,

Not sure what you mean there. Yes, maybe the issue with dimensions has something to do with the quantization, but who knows. I personally am more sympathetic to the idea that geometric quantities of whatever sort don't make much sense at subplanckian scales. Though there's often ways to define something akin dimensionality of a manifold by other means. Best,

B.

Bee said...

Dear Arun,

Yes, maybe it's not a question we will be able to find a satisfactory answer to at all. Note however that I was explicitly asking for a mechanism, eg a mechanism such that if you start with an arbitrary # of spatial dimensions, the dynamics is such that we always ends up having 3 large and the others small. I would consider that a satisfactory explanation. At least for now :-) There's other things you can think about, eg some sort of optimization principle, etc.

Lisa Randall in one of her papers, that we discussed here, made an attempt at such a mechanism. I didn't find it too convincing, but it goes into the direction I was thinking about. Best,

B.

Bee said...

Hi Giotis,

Thanks for pointing out, I didn't know that. In any case, this was just an example of roughly what I was talking about. As I said I didn't look into the details of that particular paper anyway. Best,

B.

Arrow said...

Giotis: "Arrow, in the brane world scenarios only gravity can probe the extra dimensions and gravity has been tested accurately only down to a fraction of a mm."

Yes, but this rests on the assumption that only gravity can probe extra dimensions which I find very suspect and unappealing, it not only breaks the unity of spacetime by introducing special dimensions it also ascribes arbitrary properties to forces and hardly offers anything in return. I also don't see it as a solution of hierarchy problem, rather the problem is simply being replaced with a much more elaborate and unsupported construction.

Bee: "People are calculating how the existence of extra dimensions would affect our experiments and analyze the data to see if it contains indications for the existence of additional spatial dimensions."
I'm not against people checking such possibilities, I am only opposed to claims that there are no good reasons to believe spacetime has four dimensions (it may not be what you meant but this is how I read it), as I've said we have all the reasons we could want - thousands of experiments, plenty of successful theories, our everyday experience, the fact that evolution would have took advantage of them, and Ockham's razor. Actually it's probably one of the best supported facts in the whole of physics.

As you said extra dimensions won't ever be ruled out but that hardly means we should take them seriously. To me the situation is analogous to other supernatural phenomena - if there is not a shred of evidence to support their existence they should be considered nothing but fantasy.

Bee said...

Arrow: There are never good reasons for believe, otherwise you'd know and not believe. A speculation without evidence is exactly that: a speculation without evidence. What differentiates believe and fantasies from scientific theories is testability and self-consistence. Models with extra dimensions offer both (the latter with constraints as previously mentioned, but then which of our theories is completely self-consistent?). Best,

B.

Christine said...

What intrigues me about spatial dimensions is not their number per se, but the very fact that the universe admits certain independent (countable) degrees of freedom. I wonder whether a universe could be conceived without independent directions. When we answer that first, we might be able to address dimensionality. Time is another mystery of its own.

I am 100% with Bee. We are motivated with the "whys", the "hows" are some kind of analysis, construction of laws, a hopeful path to the "whys". These procedures (scientific method) often (partially) answer the original "why", at a certain level. With time, we have proven to be able to turn a part of what we regarded as metaphysics into physics. The ultimate level at which this can lead to, if there is one at all, in terms of real understanding, is a philosophical question.

Best,
Christine

Anonymous said...

hi B.,

correction - I agree that number of dimensions mathematically should follow from something more fundamental, like algebra, but I'm not sure I would call it quantization. It's a tricky argument. An example (half-metaphor):

our perception screen is 2-dimensional, but as kids we learn from, you might say, mathematical experimental correlations that world "is" 3-dimensional.

Now, what happens is that in fact we project 3D space, we make it in our minds or wherever. We construct it from data, and it becomes automatic perception reflex.

My point before was that, in fact, to comprehend that algebra, or quantization, we nevertheless need precisely some geometric image in mind.

But I would contend that the issue of (let's call it) quantization becomes relevant only at high energies, or where gravity is present.

A.

Phil Warnell said...
This comment has been removed by the author.
Phil Warnell said...

Hi Christine,

“With time, we have proven to be able to turn a part of what we regarded as metaphysics into physics. The ultimate level at which this can lead to, if there is one at all, in terms of real understanding, is a philosophical question.”

I find your comment to be both an astute observation and contemplation, which in essence is what both good science and philosophy are. That’s to say that this thing we call dimension is in itself bandied about by physicists sometimes as not to be imagined for what it is.

The pat answer of course is that a dimension is a degree or level of freedom. So as most consider it we have up and down, back and forth, along with to and fro and this gives us physical space as we understand it, which lends us the ability to move. Then of course we have what we call time, which gives space for and with it an ability to change. These then are the limit to what many people can have to be considered as dimensions.

However, science with the aid of mathematics has come up with another level of or degrees of freedom, which is called configuration space and is considered by most as not real, yet rather simply a creation of mind, for it relates to potential and not actuality as normally considered. I would argue this has shown to be real, along with the others, as it demonstrates as being truly another degree of freedom and with it lends an a ability just the same. The way I have always thought of this, is it gives one the space in which to imagine what can , will or might be possible, which I would say gives us both the space and with it the ability to think.

I would ask then, are these place(s) where we can think any less real then the others mentioned before? So as you first alluded, perhaps this problem with extra dimension has less to do with what can actually exist, yet rather with our ability to imagine as to have known what they may be. This to me suggests that when considered properly there is no actual distinction to be made between science and philosophy.

Best,

Phil

joel rice said...

If the issue is how matter and geometry are related, there is a question: is it a mere coincidence that the number of generations is the same as the number of spatial dimensions ? Or perhaps they are related in some structural manner ?

Christine said...

Hi Phil,

(...) science with the aid of mathematics has come up with another level of or degrees of freedom, which is called configuration space and is considered by most as not real, yet rather simply a creation of mind (...)

Well, it is a question of experience (classically speaking for now) that if you consider at a given instant of time a system formed by particles (constituents) such that you can specify their position (e.g., by generalized coordinates), no determination for the subsequent system's state (at a subsequent instant) can be achieved. For that one needs to specify also the time derivatives of the coordinates (i.e., the velocities) in order to predict exactly the state of the system after an infinitesimal time interval.

Once you specify the coordinates and velocities of the particles at a given instant, you have the accelerations completely determined, so you have the equation of motion. This is quite clear with the Lagrangian formulation and the principle of least action. (The beauty of this principle is why it works at all).

(Note that it is all that is needed. Nature does not need the specification of the particle accelerations or other variables, whatever derivative orders, in order to compute the subsequent state.)

So the "phase space" for a system of N particles is a 6N dimensional space (3 position coordinates + 3 velocity components, for the N particles); the so-called "configuration space" usually represents the whole system as a point in the space, and so it is a 6 dimensional space. In any case, such "operational spaces" do always carry the notion of dimensionality as we usually attribute to "real space". There is nothing much mysterious by using whatever operational construction that serves to represent the state or to serve as a calculational tool.

The most interesting thing, I guess, is the fact that Nature is just like that: specify the coordinates and their derivatives and you compute the subsequent state by, e.g., the principle of least action. Why it is exactly like this is something interesting per se.

Best,
Christine

Arun said...

Dear Bee,

I post this link here to add to a global perspective of science and society.

-Arun

PS: if you find the reference to hypocrisy puzzling, google, or read this

Arun said...

I don't quite get the physical/philosophical point about configuration space. When two particle histories have the same values of position and time coordinates, then in spacetime they are in contact, while in the 6 N dimensional configuration space of N particles, this is not instantly obvious. In fact, in phase space, canonical transformations can turn generalized coordinates and momenta into each other, and the fact of contact can be made as unobvious as you like.

Christine said...

I don't quite get the physical/philosophical point about configuration space.

Neither do I.

Phil Warnell said...

Hi Christine,

.....for the N particles); the so-called "configuration space" usually represents the whole system as a point in the space, and so it is a 6 dimensional space.

All what you have said is of course quite true, yet in configuration space these 6 dimensions represents the space of one particle as it relates to itself, whose dimensionally increases as more particle are considered. The key point is the considered part, as this process binds each to all and with it their potential(s). You could say that this is state of mind that Einstein proclaimed he wished to know, yet here is revealed as a state of space (degrees of freedom).

That is as Arun has expressed, this is not immediately obvious, which is also quite true and for good reason, for one has to know all which are to be considered and as such binds the destiny and presence of one to the destiny and presence of all. That’s to say as Feynman realized, Lagrange was not simply a consideration of path, yet also a consideration of the potentials of all paths.

The point being, as normally and previously considered, there exists no space in time for these paths, yet never the less their potentials are required to exist, which in turn has use resign them to existing in configuration space. So here we find a space which has its presence to be shown in what we call our ordinary space(s), yet exists in a place that has never being positively identified; that is, at least for now, only in our minds.

Best,

Phil

Christine said...

Sorry for my previous post, I have inverted the definitions previously. So let me first correct myself:

Configuration space: 6N dimensional space in which the whole system is represented by one point in that space.

Phase space: 6 dimensional space in which the whole system is represented by N points in that space.

So the whole system is represented by one particle in configuration space. You don't add more particles in that space, but just follow the path (one path) of the system as it internally changes its state. If you increase the number of particles to that system, it is still represented by one point in 6N-D configuration space.

The question of potential, if I understand you correctly-- well, as I said, you just need the positions and velocities (or momenta) in order to predict the subsequent state. Sure, if the particles did not interact, they would pass each other as ghosts and follow their inertia. But if you use the least action principle and find that the accelerations are not null, this implies that the particles do have some kind of interaction and therefore the accelerations are given by the gradient of a potential function (for conservative systems). It happens that the form of the potential function do depend on the positions of all the other particles of the system. But this is just the fact that you have some (long range) interaction in which the particles are the source.

So, I still don't quite get the special meaning for the fact that the system is analyzed under an operational mathematical space...

best,
Christine