> The answer most physical laws are of a particular form, so this this one > must be also really isn't very satisfactory, though.
But the thing is that if the _specific_ model they put up - based on general relativity - dont have any third order derivatives, then they have a consistent model which works and is uncontradicted, which is pretty satisfactory in some sense.
Of course, one should always be critical and test the assumptions one makes (in this case that general relativity describes cosmology well).
I guess my point was that they did not just ignore the third term, but simply found the values of the terms they had in their theory. Which is slightly less unsatisfactory than just assuming something to be zero just because one cant measure it.
But yes, I would also like to know whether anyone actually did measure those third (and fourth, and...) order derivatives.
> My question is what, if any then, are the areas where we need similar > paradigm shifts to answer current outstanding questions? It seems to me, > at least, that maybe there aren't any, and today's scientists are left working > harder and harder simply to add a few significant digits to existing theories. > What are your thoughts?
Whether it classifies as paradigm shift or not, I can not say, but we have a bunch of extremely important problems to solve (most or all of which somehow revolve around the concept of mass... quite interesting). Off the top of my head:
1) We havent yet arrived at any fundamental explanation of gravity.
2) Particles in the current Standard Model of Particle Physics can't have mass, as mass terms violate some fundamental symmetries. The so-called Higgs mechanism might provide a way around this, but introduces more problems itself.
3) Dark matter. Is it some kind of so far unknown particle lying around out there?
4) The CP violation (i.e. the asymmetry between matter and anti-matter) within the Standard Model is not large enough to explain how equal amounts of matter and anti-matter in the early universe could have evolved into the matter dominated universe we have today.
5) Why do the different particles have the masses that they have? Why is the muon 200 times heavier than the electron? What determines that number?
If I had to gamble, I would gamble that any revolutions will be connected to the understanding of mass.
> Supposing a collapse-type end of the universe, is there any possibility that > this could result in another big-bang type event, which would really make this > not an "end" of the universe, but something more akin to a "reboot" of the universe?
We probably need a working model of quantum gravity before we can even hope to have an answer for that (intriguing) question. Otherwise we are just extrapolating our theories into a realm where we know they dont work.
Maybe when the Large Hadron Collider starts up at CERN in five years, we can get a little step closer to the answer.
> The thing I don't understand is why we can conclude that from measuring > the second derivative of the size of the Universe (acceleration). If > the third derivative were negative, it wouldn't matter (to the fate of the > Universe) that the first two were positive. The Universe would still end in > a big crunch, right? How closely have scientists measured the function that > governs the size of the Universe? And what do they know about it?
It is a valid point. The Cosmological Standard Model IIRC allows the first and second derivatives to be non-zero, but not the third. In general, almost all differential equations in physics are second or first order.
Maybe thats the reason they dare leave out the third derivative?
disclaimer: IANAC (cosmologist) - IAAPP (particle physicist) though. It has been a couple of years since my cosmology class though...
jeeezz... you could have warned me about the sound on that site. For a moment i thought my harddrive was dying on me or something (with those scratchy noises).
Then i remembered i had opened that link in the background. Phew...:-)
> This guy seems to have found a way around the use of the infinitely small > quantities calculus deals with. So his approach might be valuable in giving > a different approach to the mathematics behind physics, and therefore > yielding a new perspective on physics. The article doesn't say that > he's getting different results, only the means of getting there is different.
but there is only a problem if time is discretized while space is not. That seems highly unlikely (especially in view of relativity which tells us that what is time from one perspective is space from perspective).
If space is also discretized then Achilles cant take the required infinite amount of small steps.
But yes, if they both are discretized then Newtons infinitesimal approach to the equation of motion etc. is wrong. But guess what - that is actually the case and has to be taken into account when doing path integrals in Quantum Field(*). This is a relatively old thing (20-50 years) - nothing new there (but a field with a lot of unanswered problems).
(*): very hardcore stuff - but also very fundamental! For discussions about these fundamental things ordinary quantum mechanics does definitely not suffice. Its like discussing curvature of space using only Newtonian mechanics.
If Heisenbergs uncertainty principle does not come from a simple Cauchy inequality then what does inequality show us? Remember that Heisenbergs uncertainty principle has nothing to do with uncertaincties in the measurements, but can be simply understood in terms of the wave nature of particles.
Also remember that quantum mechanics has been confirmed down to 15 decimals or so in atomic spectra (when including corrections from quantum field theory, but anyway). If something this fundamental was wrong, then it would surely have influenced on the results.
The tortoise vs. Achilles paradox has not really plagued modern physics in that it is not a paradox (anymore - it might have been to the Greeks). The supposed paradox lies in the misconception that an sum with infinite terms will always yield an infinite number. This is obviously not true - As Achilles needs to traverse ever smaller distances he also does that in ever smaller amounts of time. And the times add nicely up to a finite time - the time when he overtakes the tortoise.
The article claims that this is still a paradox. I think based on the idea in this quote:
> With some thought it should become clear that no matter how small the time > interval, or how slowly an object moves during that interval, it is still > in motion and it's position is constantly changing, so it can't have > a determined relative position at any time, whether during a interval, > however small, or at an instant. Indeed, if it did, it couldn't be in motion."
Say WHAT?!?
Please tell me why you can't have a well determined position as a function of time and be in motion as well?
He goes on to claim that uncertainties in the values of times is somehow a profound proof that no instant in time exists. Hey, you could say the same thing about the distance the poor fella has to transverse - thus spoiling the whole 'ever smaller distances' thing.
> Du yuoo eccept zee fullooeeng egreement, in vheech yuoo let svedeeshcheff.cum >lueds toons und toons ooff cuukeees streeet frum oooor brund noo oofee durectly tu > yuoor veb soorffer fur nu epperent coose-a et ell?
lol:-)
but to be pedantic that looks like dutch and not like swedish at all to me (for some reasons americans always portray swedish as dutch?)
anyway, maybe it is simply because i speak a language similar to swedish (danish*).
> A number of colleagues have contacted me since the web posting > (on a rather obscure British web site of "e-print physics archives", > http://uk.arXiv.org.) The British publication, "New Scientist," > ran an article...
uh, excuse me, but arxiv.org is most certainly not a rather obscure web-site. In particle physics (and other fields), it has become the defacto standard place to search for articles (along with SPIRES at SLAC).
Maybe he is referring to the fact that articles posted there are not necessarily peer-reviewed (but many peer-reviewed articles have a copy there as well). If you want to tell another physicist where to find an article online, the easiest way is to provide its arxiv.org key (e.g. hep-ph/somenumber).
apart from that, Louis Friedman is right though - Gold appears to be a bit of a nutcase.
>I'm a physicist myself, so this is not a "raving of a random science fiction fan."
well ok, i apologize for that rude outburst.:-)
> As a physicist, you are surely aware that physics is about models, not about > reality itself. Why do you assume aliens model reality in the same way as we do?
I dont assume anything about how they MODEL reality, but, as i argued, it is unlikely* that their physical forms/bodies could have developed in an environment where the difference between classical and non-classical physics could be perceived before the onset of high-intelligence.
at least, saying that it is unlikely to have happened in that way is a far-fetched statement.
However way they do model reality, i am sure it is with some model which in the appropriate limits will effectively reproduce classic physics.
For instance, I think it quite likely that a lot of life will take form on the surface of planets where classic physics govern (or seems to do) most of everyday life.
Physics is not just about models, it is about models of reality as it is perceived/measured.
> I mean, we humans already know (from quantum mechanics) that the concepts of space and time > are of limited value as models of reality, although we cannot escape the way our brains > are hardwired. Extraterrestrials will probably think in completely different categories, which > are as much beyond our imagination as space and time are to them.
I think it is a fairly model independent assumption to say that any intelligent lifeform must be rather complex and therefore orders of magnitudes larger than the typical quantum mechanical regime of atoms and molecules.
To be able to have a level of consciousness it is also a fairly safe assumption that the physical proportions of a being ('s "brain") must be small enough that the speed of light doesnt seriously restrict the exchange of information between the various parts of the brain.
Therefore any (or at the very least, most) intelligent life should exist in a regime where the classic concepts of space and time are an EXCELLENT approximation to reality.
Why you think it is UNLIKELY that they would think in concepts of space and time* is beyond me.
*:there is btw. nothing wrong with the concepts of space and time. For instance time is NOT just a "fourth dimension" as some folks believe. And QM doesnt discard space and time.
from-a-physicist-who-is-tired-of-the-ravings-of- ra ndom-science-fiction-fans
I dont think the VAT need to be reimbursed inside the EU any longer. The reason for this whole charade is instead that cars have a special (high) tax in Denmark (which is a good thing imnsho, because it encourages puplic transportation).
But what this thing does show is that the car industry is able to sell their cars at a much lower price and still make a profit. Too large profit margins is usually a sign of something rotten in the industry (they charge what they want, not what they need to).
>A Matrix is any multidimensional array which contains data.
Well not in my world where anything with more than two indices is a tensor.
But it is quite possible that people in different fields use different conventions - it is after all just a matter of terminology.
For me a matrix is a useful object because i can invert it, take its determinant, find its eigenvalues, etc. I can't really do that if the entries does not (at least) belong to a group.
If a matrix is nothing more than a table (or a multi-dimensional table) why not just call it that instead?
Slashdot Mirror
It seems that we have a Christian source of information related to walking on water?
:-)
At least it is their own IP
> sorry, I'm not an english native speaker, so I don't know the word for swedish "sandpapper"
I think its just sandpaper.
disclaimer:also-not-native-english-speaker
> will be glad when SCO is no more. I really, really dislike sharing my
:-)
> initials with such a sleazy company
maybe you can sue SCO for infringing on your intellectual property
> The answer most physical laws are of a particular form, so this this one
...) order derivatives.
> must be also really isn't very satisfactory, though.
But the thing is that if the _specific_ model they put up - based on general relativity - dont have any third order derivatives, then they have a consistent model which works and is uncontradicted, which is pretty satisfactory in some sense.
Of course, one should always be critical and test the assumptions one makes (in this case that general relativity describes cosmology well).
I guess my point was that they did not just ignore the third term, but simply found the values of the terms they had in their theory. Which is slightly less unsatisfactory than just assuming something to be zero just because one cant measure it.
But yes, I would also like to know whether anyone actually did measure those third (and fourth, and
> My question is what, if any then, are the areas where we need similar
> paradigm shifts to answer current outstanding questions? It seems to me,
> at least, that maybe there aren't any, and today's scientists are left working
> harder and harder simply to add a few significant digits to existing theories.
> What are your thoughts?
Whether it classifies as paradigm shift or not, I can not say, but we have a bunch of extremely important problems to solve (most or all of which somehow revolve around the concept of mass... quite interesting). Off the top of my head:
1) We havent yet arrived at any fundamental explanation of gravity.
2) Particles in the current Standard Model of Particle Physics can't have mass, as mass terms violate some fundamental symmetries. The so-called Higgs mechanism might provide a way around this, but introduces more problems itself.
3) Dark matter. Is it some kind of so far unknown particle lying around out there?
4) The CP violation (i.e. the asymmetry between matter and anti-matter) within the Standard Model is not large enough to explain how equal amounts of matter and anti-matter in the early universe could have evolved into the matter dominated universe we have today.
5) Why do the different particles have the masses that they have? Why is the muon 200 times heavier than the electron? What determines that number?
If I had to gamble, I would gamble that any revolutions will be connected to the understanding of mass.
> Supposing a collapse-type end of the universe, is there any possibility that
> this could result in another big-bang type event, which would really make this
> not an "end" of the universe, but something more akin to a "reboot" of the universe?
We probably need a working model of quantum gravity before we can even hope to have an answer for that (intriguing) question. Otherwise we are just extrapolating our theories into a realm where we know they dont work.
Maybe when the Large Hadron Collider starts up at CERN in five years, we can get a little step closer to the answer.
> The thing I don't understand is why we can conclude that from measuring
> the second derivative of the size of the Universe (acceleration). If
> the third derivative were negative, it wouldn't matter (to the fate of the
> Universe) that the first two were positive. The Universe would still end in
> a big crunch, right? How closely have scientists measured the function that
> governs the size of the Universe? And what do they know about it?
It is a valid point. The Cosmological Standard Model IIRC allows the first and second derivatives to be non-zero, but not the third. In general, almost all differential equations in physics are second or first order.
Maybe thats the reason they dare leave out the third derivative?
disclaimer: IANAC (cosmologist) - IAAPP (particle physicist) though. It has been a couple of years since my cosmology class though...
> Or, if you want, try .
:-)
jeeezz... you could have warned me about the sound on that site. For a moment i thought my harddrive was dying on me or something (with those scratchy noises).
Then i remembered i had opened that link in the background. Phew...
> This guy seems to have found a way around the use of the infinitely small
> quantities calculus deals with. So his approach might be valuable in giving
> a different approach to the mathematics behind physics, and therefore
> yielding a new perspective on physics. The article doesn't say that
> he's getting different results, only the means of getting there is different.
but there is only a problem if time is discretized while space is not. That seems highly unlikely (especially in view of relativity which tells us that what is time from one perspective is space from perspective).
If space is also discretized then Achilles cant take the required infinite amount of small steps.
But yes, if they both are discretized then Newtons infinitesimal approach to the equation of motion etc. is wrong. But guess what - that is actually the case and has to be taken into account when doing path integrals in Quantum Field(*). This is a relatively old thing (20-50 years) - nothing new there (but a field with a lot of unanswered problems).
(*): very hardcore stuff - but also very fundamental! For discussions about these fundamental things ordinary quantum mechanics does definitely not suffice. Its like discussing curvature of space using only Newtonian mechanics.
Could not have said it better myself...
If Heisenbergs uncertainty principle does not come from a simple Cauchy inequality then what does inequality show us? Remember that Heisenbergs uncertainty principle has nothing to do with uncertaincties in the measurements, but can be simply understood in terms of the wave nature of particles.
Also remember that quantum mechanics has been confirmed down to 15 decimals or so in atomic spectra (when including corrections from quantum field theory, but anyway). If something this fundamental was wrong, then it would surely have influenced on the results.
OK, I RTFA but i didn't RTFP (paper).
The tortoise vs. Achilles paradox has not really plagued modern physics in that it is not a paradox (anymore - it might have been to the Greeks). The supposed paradox lies in the misconception that an sum with infinite terms will always yield an infinite number. This is obviously not true - As Achilles needs to traverse ever smaller distances he also does that in ever smaller amounts of time.
And the times add nicely up to a finite time - the time when he overtakes the tortoise.
The article claims that this is still a paradox. I think based on the idea in this quote:
> With some thought it should become clear that no matter how small the time
> interval, or how slowly an object moves during that interval, it is still
> in motion and it's position is constantly changing, so it can't have
> a determined relative position at any time, whether during a interval,
> however small, or at an instant. Indeed, if it did, it couldn't be in motion."
Say WHAT?!?
Please tell me why you can't have a well determined position as a function of time and be in motion as well?
He goes on to claim that uncertainties in the values of times is somehow a profound proof that no instant in time exists. Hey, you could say the same thing about the distance the poor fella has to transverse - thus spoiling the whole 'ever smaller distances' thing.
Please enlighten me.
For a pedagogical treatment of the fundamental particles and forces considered in physics I can highly recommend:
http://particleadventure.org
Full of nice illustrations, and even has little multiple choice questions along the way to keep the reader on track.
You won't be able to do calculations in field theory afterwards, but it is a great start - especially as a motivator.
Hey, don't kick a man when he's down, OK? :-)
I actually tried that once - I put 127.0.0.1 slashdot.org in my hosts file, and it worked fine ... for about two hours!!
Then i found myself circumventing the hostfile by writing blah.slashdot.org...
I guess the little guy with the pitchfork on my shoulder is more powerful that the little winged guy...
hmmm... maybe it was just a combination of the many double wovels and my internal narration (or something...)
> Du yuoo eccept zee fullooeeng egreement, in vheech yuoo let svedeeshcheff.cum
:-)
>lueds toons und toons ooff cuukeees streeet frum oooor brund noo oofee durectly tu
> yuoor veb soorffer fur nu epperent coose-a et ell?
lol
but to be pedantic that looks like dutch and not like swedish at all to me (for some reasons americans always portray swedish as dutch?)
anyway, maybe it is simply because i speak a language similar to swedish (danish*).
* no, not something you eat!
Seems like there will be an awful lot of nice stewardesses on tapes in the boss's drawer, no?
6. ????
7. Prof...
nah, this IS getting old...
> A number of colleagues have contacted me since the web posting
> (on a rather obscure British web site of "e-print physics archives",
> http://uk.arXiv.org.) The British publication, "New Scientist,"
> ran an article...
uh, excuse me, but arxiv.org is most certainly not a rather obscure web-site. In particle physics (and other fields), it has become the defacto standard place to search for articles (along with SPIRES at SLAC).
Maybe he is referring to the fact that articles posted there are not necessarily peer-reviewed (but many peer-reviewed articles have a copy there as well). If you want to tell another physicist where to find an article online, the easiest way is to provide its arxiv.org key (e.g. hep-ph/somenumber).
apart from that, Louis Friedman is right though - Gold appears to be a bit of a nutcase.
> Um... C is C(\+)*.
:-)
yeah, he obviously meant C(\+)+
>I'm a physicist myself, so this is not a "raving of a random science fiction fan."
:-)
well ok, i apologize for that rude outburst.
> As a physicist, you are surely aware that physics is about models, not about
> reality itself. Why do you assume aliens model reality in the same way as we do?
I dont assume anything about how they MODEL reality, but, as i argued, it is unlikely* that their physical forms/bodies could have developed in an environment where the difference between classical and non-classical physics could be perceived before the onset of high-intelligence.
at least, saying that it is unlikely to have happened in that way is a far-fetched statement.
However way they do model reality, i am sure it is with some model which in the appropriate limits will effectively reproduce classic physics.
For instance, I think it quite likely that a lot of life will take form on the surface of planets where classic physics govern (or seems to do) most of everyday life.
Physics is not just about models, it is about models of reality as it is perceived/measured.
*: i.e., not impossible, merely unlikely.
> I mean, we humans already know (from quantum mechanics) that the concepts of space and time
- ra ndom-science-fiction-fans
> are of limited value as models of reality, although we cannot escape the way our brains
> are hardwired. Extraterrestrials will probably think in completely different categories, which
> are as much beyond our imagination as space and time are to them.
I think it is a fairly model independent assumption to say that any intelligent lifeform must be rather complex and therefore orders of magnitudes larger than the typical quantum mechanical regime of atoms and molecules.
To be able to have a level of consciousness it is also a fairly safe assumption that the physical proportions of a being ('s "brain") must be small enough that the speed of light doesnt seriously restrict the exchange of information between the various parts of the brain.
Therefore any (or at the very least, most) intelligent life should exist in a regime where the classic concepts of space and time are an EXCELLENT approximation to reality.
Why you think it is UNLIKELY that they would think in concepts of space and time* is beyond me.
*:there is btw. nothing wrong with the concepts of space and time. For instance time is NOT just a "fourth dimension" as some folks believe. And QM doesnt discard space and time.
from-a-physicist-who-is-tired-of-the-ravings-of
I dont think the VAT need to be reimbursed inside the EU any longer. The reason for this whole charade is instead that cars have a special (high) tax in Denmark (which is a good thing imnsho, because it encourages puplic transportation).
But what this thing does show is that the car industry is able to sell their cars at a much lower price and still make a profit. Too large profit margins is usually a sign of something rotten in the industry (they charge what they want, not what they need to).
They put the poor frog in 16 TESLA?!?
IIRC the typical internal magnetic fields of atoms are of the same order.
Wonder if the little frog doesnt get cancer or something later on...
>A Matrix is any multidimensional array which contains data.
Well not in my world where anything with more than two indices is a tensor.
But it is quite possible that people in different fields use different conventions - it is after all just a matter of terminology.
For me a matrix is a useful object because i can invert it, take its determinant, find its eigenvalues, etc. I can't really do that if the entries does not (at least) belong to a group.
If a matrix is nothing more than a table (or a multi-dimensional table) why not just call it that instead?