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About LinkBacksWhy are Planck length and Planck time the smallest unit of measurement for length and time respectively? I read that they are the smallest, but why are they not divisible? Why do no smaller units of measurement make physical sense?
April 3rd, 2010, 11:30 PM
Why are Planck length and Planck time the smallest unit of measurement for length and time respectively? I read that they are the smallest, but why are they not divisible? Why do no smaller units of measurement make physical sense?
April 3rd, 2010, 11:39 PM
They aren't.Originally Posted by biggofwi
Planck length/ 2 is still a length.
What is true is that the Planck unit of length is very small and there is no experimental data involving phenomena at that scale.
What about the whole "a unit smaller than a planck does not make physical sense"? Is that a misinformed statement on their part?
It is speculation.
ok thank you
i think you would use a Planck to measure a quark?
April 7th, 2010, 07:30 AM
I have also read that Planck length and time are the smallest units possible for distance and time.They aren't.
Planck length/ 2 is still a length.
What is true is that the Planck unit of length is very small and there is no experimental data involving phenomena at that scale.
If this is not so (and I am perfectly prepared to accept that) then why were these two units of measurement chosen as the smallest possible? Was it a purely arbitrary decision to pick them?
Also are there reasons for believing that space and time can be divided into smaller and smaller units with no limit, or end, to the process?
I think some string theorists believe that space itself is quantized.
The mind boggles.
April 7th, 2010, 11:20 AM
I have also read that Planck length and time are the smallest units possible for distance and time.They aren't.
Planck length/ 2 is still a length.
What is true is that the Planck unit of length is very small and there is no experimental data involving phenomena at that scale.
If this is not so (and I am perfectly prepared to accept that) then why were these two units of measurement chosen as the smallest possible? Was it a purely arbitrary decision to pick them?
Also are there reasons for believing that space and time can be divided into smaller and smaller units with no limit, or end, to the process?
They are not the smallest unit of anything. They were not chosen to be such either.
They are the result of some dimensinal analysis by Max Planck that resulted in some "natural" units of measurement based on known physical constants.
I had thought that the Planck constant was the potential solution to Zeno's paradoxes, those of the type where an infinite number of points/actions are being completed in a finite time.
I had thought that these logical paradoxes were a symptom of the fact that the universe has some sort of maximum resolution, to use computer generated images as a metaphor.
For example if a computer game attempted to render an object moving from A to B over an infinite number of points, the program would crash before it even got started.
It is a crude example, but illustrative of what im trying to illustrate for those not familiar with Zenos paradoxes.
You could say the computer clock (time) has an infinite number of cycles between specific points of time, resolving the computation problem of making an infinite number of calculations of position. But the infinities are still troublesome as being part of any physical theory. Surely there must be a minimal.
Clock cycle = Planck time (1 clock cycle per Planck time)
Resolution = Planck length (1 pixel per Planck length)
it makes a lot more sense to me than using infinities, otherwise we could have an infinite regress of scientific discovery of the quantum world.
I would be surprised to meet any scientist that could explain the whole of the quantum model after discoveries at 10,20,100,a million, a billion times the energy level of collisions of the LHC in such a scenario. Like Dr Rocket said, it is just speculation. Makes for interesting discussion though.
What are the mathematical methods used to resolve paradoxes such as these involving infinities? and what physical theory do they belong to, and where does the Planck constant fit in if it is just speculation? is it restricted only to string theory?
Is there a resolution within quantum mechanics?
thanks
Zeno's paradoxes aren't. They were resolved when it was shown that an infinite series can sum to a finite answer.
Right.
Zeno's paradoxes were never paradoxes. They simply represent falacious reasoning. Not even a good attempt.
Zeno apparently failed to take advantage of the simplest possible observations. If he were correct in his reasoning he could never have reached the supper table and would have quickly starved to death. Little kids catch tortoises all the time. And arrows definitely move.
Zeno was an idiot.
Or at least one of the earliest crackpots. You know the type, Always "proving" things as impossible, even after have already been demonstrated as being true.
Wow, what a bombshell. a cat also cant be dead and alive simultaneously, I guess that makes schrödinger a crackpot too. I cant beleive two clearly intelligent guys would say he meant it literally. it was his style of writing (bear in mind many hundreds of years ago!). He was exposing the fallacy of our perception of space. Hence why i mentioned the infinite cycles on the clock as well. which is partly how it is resolved using infinite sets in maths. Did you think Descartes thought his demon was real too? Rocket i guess you know arrows move from your time creating "ballistics for military use"?Little kids catch tortoises all the time. And arrows definitely move.
Mathematically they arent, as i said:Zeno's paradoxes aren't. They were resolved when it was shown that an infinite series can sum to a finite answer.
I know that 0.999... = 1, (for anyone debating that, im sure there is plenty in the maths section) which is essentially the same issue put as a number, but that doesnt detract from the problems of having infinities or infitisemal points of space in physics? Which is the point. Just as the Poincaré conjecture was solved, but that doesnt have any physical manifestation.resolving the computation problem of making an infinite number of calculations of position.
Without getting bogged down in the Zeno side of my post (which i still think illustrates the problem), i was actually trying to get at the underlying issue of infitisemal space, sigularities, the big bang, finding new particles/physics at ever smaller scales. But as usual some regular posters pick a weakness to derail valid points, rather than stick to the issue. You didnt even try to answer any of my questions. Im mostly intersted in the last three.
Thanks
Does this mean they were paradoxes before they were "resolved"?
I am quite prepared to accept that Zeno's paradoxes were examples of "fallacious reasoning" but the fact that, in reality, he would always "have reached the supper table" does not, in itself, say anything about whether some of his statements were paradoxes or not.
Whether they'd properly be considered paradoxes before would depend on your deefinition of paradox and your interpretation of Zeno's writings. Being hundreds of years since he and his peers died, it's hard to say exactly.
Currently, no one knows for sure whether or not the universe is continuous or discrete at the finest levels, but both QM and GR suggest that it's continuous.
Well i hope there are fundamental limits of scale, as it gives us an end goal, whether it is the Planck length or some other fundamental constant derived value.
If you take a box of finite size you can theoretically fit entire universes of new particles or physics in there providing that it is sufficiently tiny. It may be unobservable to us for whatever reason (maybe a limit on the energy we can use to observe), and not causally connected, but just as the unobservable universe (if it exists) is undetectable then we suffer from the same crisis at the macro scale. The apparent expansion or behaviour of the universe could be restricted to our observable universe (which may be tiny on comparison).
Having a potential infinity at both ends of the scale does not sit well with me. Yes you can say; "Well if you cant detect or prove its existence, then it may as well not exist". but anyone who says they havent thought about it is a liar.
Anyway it is a nice mind boggler, but I dont think the LHC is going to answer any questions of this regard, if they are even answerable.
If the question turns out to be unanswerable, then will will assume it's continuous, since that's the simpler case and the answer no longer really matters. I don't think it will be unanswerable though, but I'd be willing to bet that the universe really is continuous. Neither QM nor GR say anything about discretizing space nor time, so I doubt any new theory will either. (And no, I don't think any of the experiments at the LHC will have much to do with this question.)
There are no paradoxes in this thread.
Infinities are handled in mathematics, all branches, every day, with no hassles, and no contradictions.
Matmematics does not belong to physical theories at all. It is quite independent.
Planck's constant is a fundamental constant of physics. It occurs most naturally in the statement of the Heisenberg uncertainty principle. It is not at all restricted to string theory, and in fact there is really no such thing as string theory, just some promising hypotheses.
Is there a resolution of what within quantum mechanics ?
April 10th, 2010, 05:57 AM
In answer to the original question, Planck length and Planck time are theoretical, minimum discrete, spatial and temporal values based on Planck's constant. Being theoretical, I leave it up to you to decide on their veracity for yourself.
Planck's constant however is well proven and essential. The value of Planck's constant is 6.62606896 x 10^-34 Jules per second. It is the universal, minimum discrete value of energy. Planck's constant, Denoted "h", is used in the equation, E(energy)=h(Planck's constant) x v(wave frequency). This is the amount of energy associated with a single photon of a particular frequency(v).
The application of this equation solved "the ultra violet catastrophe". Classical physics predicted an infinite amount of ultraviolet radiation from black bodies.
Einstein used the equation in solving "the photoelectric effect". Which proved the existence of particulate photons and won him a Nobel prize.
Heisenberg's uncertainty principal uses Planck's reduced constant. The reduced constant is used when frequency is a function of radians as opposed to cycles. The reduced constant is (h-bar)=h/2 pi. The uncertainty principal is (delta position) x (delta momentum) >= 1/2 (h-bar).
It was (h) that gave rise to the term quantum mechanics. Quanta being Latin for "specific amount". So it is that quantum mechanics is almost a wholly discrete theory concerning energy. And in consideration of E=mc^2, I submit that all values for mass are also discrete in whole number multiples of (h). I also submit that Aristotle drool's and Democritus rule's.
Thats exactly what i was saying, just because infinite sets are handled in mathematics every day doesnt mean its OK to have them lurking about within physics. Does it?
Singularities, or any problem regarding infinities.resolution of what within quantum mechanics?
If space can indeed be regarded as having no lower limit to scale, can it ever be proven that there are not any more elementary particles beyond fermions and bosons?
The reason why i thought Plancks constant was relevant to this was it resolved the infinities present in the "ultraviolet catastrophe" paradox (or non-paradox, to be in line with the other posters! perhaps we should scrap the word now...) involving black body radiation, therefore proving its worth in eliminating infinities in physics, as well as being within the uncertainty principal, another underlying law. Although i am aware that its length/time derivatives are theoretical.
I am not trying to say the universe is like some multi-dimensional graph paper, just that after a certain threshold it is meaning less to talk of a length, as no physics operate at that scale, no particle can be pinpointed to an accuracy smaller than that, it cant be said to move between two points of that length apart. It only has a probablility of being in a certain area. so can you say that space is continuous?
April 12th, 2010, 05:33 PM
Wrong.
In string theories, the Planck length is roughly the length of a string in its lowest energy state. When strings gain energy they grow in length.
In order to experimentally detect features of a given length scale you need to use particles of a wavelenght smaller than that scale, which means of sufficiently high energy to have that small wavelength.
So, IF string theory is a valid physical theory, then experimental work at the Planck length will not be possible, because the smallest physical entities will be larger than that length.
That does not mean that in and of itself that distance makes no sense at smaller scales. It simply means that no new physics will be associated with such scales.
There is a big "IF" here. String theory currently has zero experimental support, and in fact has not been completely and rigorously defined. It is not even a single theory, but rather a class of potential theories.
April 12th, 2010, 10:37 PM
The following values were obtained from "physics.nist.gov". They are the 2006 CODATA values.
Planck mass; ([h-bar]x[c]/[G])^1/2;Planck's reduced constant, multiplied by the speed of light, divided by Newton's constant of universal gravitation. The whole mess being exponentiated by one half.
Planck mass=2.17644 x 10^-8 kg.
Planck length; [h-bar]/[mp]x[c]=([h-bar]x[G]/[c]^3)^1/2;Planck's reduced constant, divided by Planck mass, multiplied by the speed of light. All of which is also equal to;Planck's reduced constant, multiplied by Newton's constant of universal gravitation, divided by the 3rd degree of exponentiation of the speed of light. The whole mess being exponentiated by one half.
Planck length=1.616252 x 10^-35 m.
Planck time;[lp]/[c]=([h-bar]x[G]/[c]^5)^1/2;Planck length divided by the speed of light. All of which is also equal to;Planck's reduced constant, multiplied by Newton's constant of universal gravitation, divided by the 5th degree of exponentiation of the speed of light. The whole mess being exponentiated by one half.
Planck time=5.39124 x 10^-44 s.
None of these formula use any variables. They are all constants.
April 13th, 2010, 02:46 AM
Despite reading two or three books on the subject, I still cant get my head round the fact that this theory has gained so much momentum. 10 dimensions, 11 dimensions, tiny curled up dimenesions, braines, vibrations, closed, open, and then all the different variants (that are possibly one and the same). It all seems too elaborate for something that as far as i can tell, doesnt make any testable predictions.
Its like we know what the missing parts of our knowledge are, and are concocting some massively complex theory just to fit in the gap and connect the dots, throwing in whatever we can to make it work. If we cant test it, is this not the physics equivalent of making up a story to fit the facts? perhaps we could make up our own theory, and keep adding new mathematics to make it fit.
The five basic Planck units, length, mass, charge, time, and temperature were proposed by Max Planck in 1899. Before the turn of the last century.
The roots of string theory began in 1943 with a proposal of Werner Heisenbergs called S-matrix theory. While most of S-matrix theory had been discarded by the 1970's, other outgrowth's of it had become string theory in 1970.
Planck units predate string theory by 71 years.
As far as string theory itself, I think it is crap because it violates the principal of reductionism. Most physicists will say that a good unified field theory should fit on a t-shirt. String theory doesn't fit on a t-shirt.
This is the most ridiculous piece of illogic that I have seen in a long time.
April 13th, 2010, 01:33 PM
Yeah, at the moment they're making up the story. Once they've got that all hashed out, they can see how well that story matches up to reality. You can't really skip that first step though or you won't even have anything to test. String theory is a valid area of research, but not currently a valid physical theory.Despite reading two or three books on the subject, I still cant get my head round the fact that this theory has gained so much momentum. 10 dimensions, 11 dimensions, tiny curled up dimenesions, braines, vibrations, closed, open, and then all the different variants (that are possibly one and the same). It all seems too elaborate for something that as far as i can tell, doesnt make any testable predictions.
Its like we know what the missing parts of our knowledge are, and are concocting some massively complex theory just to fit in the gap and connect the dots, throwing in whatever we can to make it work. If we cant test it, is this not the physics equivalent of making up a story to fit the facts? perhaps we could make up our own theory, and keep adding new mathematics to make it fit.
A formula that fits on a t-shirt would be quite reductionist. Occam's razor and whatnot. So I was being assumptive, but not illogical.Physicist and bestselling author Michio Kaku has remarked that M-Theory may present us with a "Theory of Everything" which is so concise that its underlying formula would fit on a t-shirt.
A tensioned string will oscillate with a frequency that is inversely proportional to it's length. Short strings vibrate faster than long strings. According to the statement above, high energy's have low frequency, and low energy's have high frequency.In string theories, the Planck length is roughly the length of a string in its lowest energy state. When strings gain energy they grow in length.
Reductio ad absurdum.
Kaku may be a best selling author, but IMO he is not much of a physicist. He seems to be far more interested in selling books than in being truthful about scientific research.
There are some very smart string theorists out there. IMO Kaku is not one of them.
I have one book by Kaku, a relatively poor text on quantum field theory. It is unlikely that I will ever own 2. It is far and away the poorest book on that subject on my shelf -- purchased in a moment of weakness.
Fitting on a t-shrt is not much of a criteria. Within a constant general reltivity is contained in the expression G=T. Big deal. The guts of that statement lies much deeper and requires all of machinery of Riemannian geometry to appreciate. The depth of the theory lies in what it can predict, not in whether it fits on a t-shirt.
I've actually never read any books by Mr Kaku. I will take your word for it that he is like Reagan. Great actor, crappy president. Really, the t-shirt thing was a throw away line. Life is too short to not question, but probably long enough for a laugh or two.
Well, I guess we baked and fried up those Planck things pretty good. Here's to the next thread. 8)
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