Physics Discussion Thread

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Re: Physics Thread.

Post by kasthuri »

SriKumar wrote: Not to belabour the point further but I did want to get clarified- by 'laws' of physics, what is meant?
As you said, the laws of physics are certain dogmas intelligently coded in the 'language' of math! They somehow cease to be dogmas after the coding...which may right after all - since we know the mechanism to code/decode...
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Re: Physics Thread.

Post by Amber G. »

SriKumar wrote:AmberG, your questions remind me of that book Physics for Entertainment by Yakov Perelman. I bought the first volume but did not buy the second one. If I can find it now, I'd pay 100 times the amount that I bought it for, back then..
The book is available here online:
http://www.archive.org/stream/physicsfo ... 7/mode/2up
:) (What is 100 times the amount you bought it for ? :) )
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Re: Physics Thread.

Post by Amber G. »

I think there was no solution (at least satisfactory solution) to this more than 2 year old post: (P2)
http://forums.bharat-rakshak.com/viewto ... aw#p587628

Here is slightly different version (weigh is now 300Kg swinging on rope of 3 meters :)
(I have had demo with 5Kg weigh though .. not with 300Kg).. being discussed in some other forums ..

A heavy 300 kg sandbag one meter tall is hung from a playground swing with a rope 3 meters long so that the bottom of the sandbag just clears the ground. A bottle is then placed on the ground a meter away from the sandbag as shown.

Image
Explain how to to knock the bottle over with the sandbag if you are given a paper drinking straw but are not allowed to touch anything (sandbag, rope, bottle, swing) with your body or with the straw.
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Re: Physics Thread.

Post by GuruPrabhu »

Amber G. wrote:RahulM, GP ... From news.harvard.edu (later update on the slow light story..)

Prof Hau' description in her words...
...Hau explains that light entering the atomic entanglement transfers its energy to the atoms. Light energy raises the atoms to higher energy levels in ways that depend on the frequency and intensity of the light. The laser illuminating the cloud at right angles to the incoming beam acts like a parking brake, stopping the beam inside the cloud when it is shut off. When it is turned on again, the brake is released, the atoms transfer their energy back to the light, and it leaves the end of the cloud at full speed and intensity.
If you think about the bolded part, you will appreciate why I called it a coherent phenomenon.
GuruPrabhu wrote:Actually, the particle picture of light does not have any way of explaining refractive index. Only the wave picture does. Refractive index is a bulk phenomenon, just like cerenkov radiation, transition radiation etc. Thus, they require coherent behavior from the medium -
So, how does "light transfer energy to the atoms"?

Bade Saar,

As I posted earlier, absorption and re-emission can not explain this. These are coherent phenomena that don't have particle physics explanations.
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Re: Physics Thread.

Post by GuruPrabhu »

Explain how to to knock the bottle over with the sandbag if you are given a paper drinking straw but are not allowed to touch anything (sandbag, rope, bottle, swing) with your body or with the straw.
You calculate the resonant frequency of the sandbag pendulum and blow puffs of air at exactly that time interval :D

It may take you a 100 year tapasyaa but you will get there.
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Re: Physics Thread.

Post by SaiK »

but are not allowed to touch anything (sandbag, rope, bottle, swing) with your body or with the straw.
okay, I will use something else like a stick. :P

..

cut both the support frame facing the bottle so that it falls exactly to a length enough to touch the bottle.
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Re: Physics Thread.

Post by Bade »

GuruPrabhu wrote: So, how does "light transfer energy to the atoms"?

Bade Saar,

As I posted earlier, absorption and re-emission can not explain this. These are coherent phenomena that don't have particle physics explanations.
LASERS are described as examples of coherent phenomena, but explained using the usual scheme of quantized energy levels and de-excitation, except that each such going down the levels is done 'coherently' as in stimulated emission after the initial pumping up done 'incoherently' . This was the UG/PG level explanation for the phenomenon in a nutshell.

In this case I see the additional cooling before the stimulated emission so to speak. Isn't holography where information can be carried forward using LASERs, so was wondering how this is radically different from that, except the latency of stored information.
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Re: Physics Thread.

Post by GuruPrabhu »

SriKumar wrote:
GuruPrabhu wrote:Well, the reasoning is quite simple really. Physics believes that the universe arose as described by big-bang cosmlogy. This event happened about 14 billion years ago, and the universe then evolved according to the laws of physics. No one will claim that *all* laws are known - the claim is that there were *some* set of laws that governed the evolution of the universe. No one also claims that they know *how* these laws came into being.
Not to belabour the point further but I did want to get clarified- by 'laws' of physics, what is meant? Does it 'merely' and exclusively refer to a set of observations of various systems in the universe, and a verbal and/or mathematical statement of those phenomena?
It is not exclusive - rather, it is all of the above. The "laws" are expressed in various ways:

1. There are principles, such as the Equivalence Principle, Principle of the Constancy of the Speed of Light, Gravitational Principle, ityadi. These don't need mathematics, but are easier stated using math. Mathematically, these would be considered axioms.

2. There are symmetries and Conservation Laws. I posted about these earlier. A special class of symmetries called Gauge Theories are the basis for all known forces except gravity. A gauge theory of gravity or "quantum gravity" has not yet been invented. These symmetries may be expressed without the use of math but very difficult to explain - e.g., how would one explain that "there exist 8 types of gluons because SU(3) of color has eight symmetry generators".

3. There are "equations of motions" derived from the principles and laws. This is where Math is very deeply involved, not only in formalism, but also in derivations, extensions and predictions.

Don't worry about "belaboring the point". It is a fascinating subject and there is no gyaani who has all the answers.

By the way, it is not possible to directly observe the 8 gluons, so all proof of their existence is indirect. This is a direct counter example to any statement that physics is based on observations alone.
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Re: Physics Thread.

Post by GuruPrabhu »

Bade wrote:LASERS are described as examples of coherent phenomena, but explained using the usual scheme of quantized energy levels and de-excitation, except that each such going down the levels is done 'coherently' as in stimulated emission after the initial pumping up done 'incoherently'.
Bade Saar,

Yes, that is a good example. And as you know, laser physics is explained by QM without any need for second quantization. Hence, light is treated as waves (just like everything else).

This was my point to you and Rahul earlier - there is no "particle" explanation for this.
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Re: Physics Thread.

Post by kasthuri »

GuruPrabhu wrote: 1. There are principles, such as the Equivalence Principle, Principle of the Constancy of the Speed of Light, Gravitational Principle, ityadi. These don't need mathematics, but are easier stated using math. Mathematically, these would be considered axioms.
Ji,
Is math a matter of convenience or necessity? Agreed that these principles don't need math and can be verbally formulated. What is the use of the axioms without any rules of derivation? In other words, what is the difference between these principles and my principle which states that "All human beings are made up of cells"?
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Re: Physics Thread.

Post by GuruPrabhu »

kasthuri wrote: Ji,
Is math a matter of convenience or necessity? Agreed that these principles don't need math and can be verbally formulated. What is the use of the axioms without any rules of derivation? In other words, what is the difference between these principles and my principle which states that "All human beings are made up of cells"?
Good questions. Are these rhetorical? I have typed all I can on this matter and explained the intricacies and you are asking 101 questions.

Why worry, be happy - you have a nice principle. :)

However, if you wish to address the dilemmas and frustrating interdependencies (between math and physics) that I have raised, I would be eager to read your views.
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Re: Physics Thread.

Post by Amber G. »

SriKumar wrote:. Your question about trucks and highway noise in the evening is something I experienced first hand. I used to hear trucks in the night from a highway that was almost 1.5 miles away from home, and I used to wonder how that could be.
Thanks. As Vina said, whales have learned to use that trick to communicate over hundreds (or thousands) of miles.. (BTW, I heard that lot of the pioneering work on whale communications in literature was first written by Ewing - the discover of sofar channel - apparently whales discovered it millions of years before) ... and US used the same principle (one of the most secretive work) to literally listen/monitor soviet atmospheric tests ( again from equipment hundreds of miles miles away).

Truly amazing
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Re: Physics Thread.

Post by Amber G. »

GuruPrabhu wrote:It may take you a 100 year tapasyaa but you will get there.
The original problem which I posted about 2 years ago, the pendulum weighed only 5kg.. how many years of tapasyaa one has to do for that?
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Re: Physics Thread.

Post by kasthuri »

I think you are getting annoyed by my questions thinking I am "belaboring the point"...what is there to my views...I am just on class 101. :-)
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Re: Physics Thread.

Post by GuruPrabhu »

Amber G. wrote:
GuruPrabhu wrote:It may take you a 100 year tapasyaa but you will get there.
The original problem which I posted about 2 years ago, the pendulum weighed only 5kg.. how many years of tapasyaa one has to do for that?
million years?
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Re: Physics Thread.

Post by GuruPrabhu »

kasthuri wrote:I think you are getting annoyed by my questions thinking I am "belaboring the point"...what is there to my views...I am just on class 101. :-)
Not annoyed at all.

I encouraged belaboring the point. However, what is the point?

Asking questions is fine, but not if it is a one-way street. Occasionally, try to provide some answers as well. (even if they are half-baked answers). This is not an "Ask Jeeves" website.
Last edited by GuruPrabhu on 03 Jul 2011 08:18, edited 1 time in total.
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Re: Physics Thread.

Post by negi »

It depends on who is blowing the straw. :wink:
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Re: Physics Thread.

Post by GuruPrabhu »

negi wrote:It depends on who is blowing the straw. :wink:
I nominate RaakitMard. He can have that bottle knocked off in a nanosecond. 8)
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Re: Physics Thread.

Post by Bade »

AmberG's super-JEE edition reminds of a qualifier prep question: How can you get up from a fallen position in a skating rink with no help of hands as one would normally. Assume a fallen flat shavasana position as the beginning point.

Someone thought spitting continuously would help. :)
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Re: Physics Thread.

Post by GuruPrabhu »

Bade wrote:AmberG's super-JEE edition reminds of a qualifier prep question: How can you get up from a fallen position in a skating rink with no help of hands as one would normally. Assume a fallen flat shavasana position as the beginning point.
Being able to SMS using one's toes would help.

This reminds me of the old joke about how to find the height of a building using a barometer.

A modern day answer that was not available then would be this: "Place the barometer at the bottom of the building and find its position with Google Earth GPS. Then place it on the top of the building, rinse and repeat"

:lol:
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Re: Physics Thread.

Post by Bade »

Very soon the Fizziks bradmin will come and start lathi charge in this safest corner. :-) Maybe the humor thread should have a physics special to educate us less humorous folks.
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Re: Physics Thread.

Post by GuruPrabhu »

Bade wrote:Very soon the Fizziks bradmin will come and start lathi charge in this safest corner. :-) Maybe the humor thread should have a physics special to educate us less humorous folks.
But, hey, one of the Bradmins was suggesting that refractive index can be explained by absorption and re-emission. As geek humor goes, that was pretty good. :D
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Re: Physics Thread.

Post by SaiK »

what is Geek for one, is Greek for the other. Still no fizzik gurus here answered my questions.
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Re: Physics Thread.

Post by GuruPrabhu »

SaiK wrote:what is Geek for one, is Greek for the other. Still no fizzik gurus here answered my questions.
Sir-ji,

With due respect I re-post your "questions" here:
SaiK wrote:Any gurus can get into general theory of relativity, that I always get into tussle keeping it in mind, in comparison with special theory that was more easier to comprehend.

So, how are the other observations in general theory actually "general" and not special?
and .. moving objects can't accelerate wrt each other.. this one beats the hell out me to understand?
and in aam-man terms, what is Einstein mushai is saying about the space-time curvature?
..ultimately I am gone bonkers on travelling at faster than the speed of light.
Let me try to simplify matters by enumerating said questions:

1. So, how are the other observations in general theory actually "general" and not special?

It is not about observations. It is "general" because it involves space-time itself, not just the "electrodynamics of moving objects", which would be "special".


2. and .. moving objects can't accelerate wrt each other.. this one beats the hell out me to understand?

As Dirac would have said, this seems like a statement.


3. and in aam-man terms, what is Einstein mushai is saying about the space-time curvature?

Einstein Musharraf is saying that mango-man should should view space-time curvature in comparison to Ash Rai curvature. Whenever Ash is "maroing light", all eyes turn to her onlee- this explains how light bends in the presence of serious "maal", err, Mass.
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Re: Physics Thread.

Post by Amber G. »

This reminds me of the old joke about how to find the height of a building using a barometer.
Though it got life of its own.. the first time I heard, I was told it was real (or almost real)..
Anyway .. this is the version I saw for the first time.... cut and paste below.. Told by Calandra..
Some time ago I received a call from a colleague who asked if I would be the referee on the grading of an examination question. He was about to give a student a zero for his answer to a physics question, while the student claimed he should receive a perfect score and would if the system were not set up against the student. The instructor and the student agreed to submit this to an impartial arbiter, and I was selected.

I went to my colleague's office and read the examination question, "Show how it is possible to determine the height of a tall building with the aid of a barometer."

The student had answered, "Take a barometer to the top of the building, attach a long rope to it, lower the barometer to the street and then bring it up, measuring the length of the rope. The length of the rope is the height of the building."

I pointed out that the student really had a strong case for full credit since he had answered the question completely and correctly. On the other hand, if full credit was given, it could well contribute to a high grade for the student in his physics course. A high grade is supposed to certify competence in physics, but the answer did not confirm this. I suggested that the student have another try at answering the question. I was not surprised that my colleague agreed, but I was surprised that the student did.

I gave the student six minutes to answer the question with the warning that the answer should show some knowledge of physics. At the end of five minutes, he had not written anything. I asked if he wished to give up, but he said no. He had many answers to this problem; he was just thinking of the best one. I excused myself for interrupting him and asked him to please go on. In the next minute he dashed off his answer which read, "Take the barometer to the top of the building and lean over the edge of the roof. Drop that barometer, timing its fall with a stopwatch. Then using the formula S = ½at², calculate the height of the building."

At this point I asked my colleague if he would give up. He conceded, and I gave the student almost full credit.

In leaving my colleague's office, I recalled that the student had said he had many other answers to the problem, so I asked him what they were. "Oh yes," said the student. "There are a great many ways of getting the height of a tall building with a barometer. For example, you could take the barometer out on a sunny day and measure the height of the barometer and the length of its shadow, and the length of the shadow of the building and by the use of a simple proportion, determine the height of the building."

"Fine," I asked. "And the others?"

"Yes," said the student." There is a very basic measurement method that you will like. In this method you take the barometer and begin to walk up the stairs. As you climb the stairs, you mark off the length of the barometer along the wall. You then count the number of marks, and this will give you the height of the building in barometer units. A very direct method."

"Of course, if you want a more sophisticated method, you can tie the barometer to the end of a string, swing it as a pendulum, and determine the value of 'g' at the street level and at the top of the building. From the difference of the two values of 'g' the height of the building can be calculated."

Finally, he concluded, there are many other ways of solving the problem. "Probably the best," he said, "is to take the barometer to the basement and knock on the superintendent's door. When the superintendent answers, you speak to him as follows, 'Mr. Superintendent, here I have a fine barometer. If you tell me the height of this building, I will give you this barometer.'"

At this point I asked the student if he really did know the conventional answer to this question. He admitted that he did, said that he was fed up with high school and college instructors trying to teach him how to think, using the "scientific method"…
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Re: Physics Thread.

Post by GuruPrabhu »

A modern day answer could also involve latest Backee Jinn Advances. We could get a nanha jinn-eologist to tie the barometer around his waist with a fake switch attached to it.

He could then make the following demands:

1. Gimme Cashmere
2. Deliver a Squadron of Eff-Solahs
3. Tell me height of building
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Re: Physics Thread.

Post by SriKumar »

kasthuri wrote:
SriKumar wrote: On a semi-related note, I was trying to see why are mathematical manipulations important i.e. what is their sancitity.... Why would it even be interesting?
Simply put, mathematical manipulations are interesting just because of our psychological urge in abstractions or generalizing things. Without question, there is a beauty in it. Derivative of sin(x) = cos(x) would have been a problem in high school books, but to represent dot product as an inner product and thus defining uncertainty in terms of certain non-commutative operators in function spaces is in fact an *interesting* pursuit.
Thanks for the response. I guess mathematical operations are interesting in and of themselves, and especially so when there is an elegant solution or an un-expected outcome. My point in bringing up differentiation was to question the basis for it- the differentiation that we end up doing, at a practical level, is really nothing more (as far as I know) than basic algebraic manipulation. We know the rules for differentiating trignometric, algebraic, exponential and any other functions. They have already been worked out. So it is matter of simply applying them to 'solve' a differential problem. My question was: if math is about reveling in manipulations (with no relevance to anything else), was there a good reason to study this form of an equation: (f(x+delta x)- f(x))/delta x and it properties; as opposed to other forms of equations: say; f(x + delta x) + f(x- delta x) -2 *f(x))/delta x^2. (I just ran this analytically for the simple case of f(x)= x^3 and it is the second differential). But this is what I am getting at: were there other forms such as, to give a crazy example, (f (x+ n*delta x) - f(x+ n*delta x))/n*delta x that were looked at, and discarded as trivial or not exciting. It does not matter that we looking for a 'differential'- the word is merely a label and nothing more.
As you said, the laws of physics are certain dogmas intelligently coded in the 'language' of math! They somehow cease to be dogmas after the coding...which may right after all - since we know the mechanism to code/decode...
I think I can agree with this. This is what brings me to the next step in the process- why are certain manipulations done and the basis for the rules of the manipulations. Could we, for example, adopt a completely different basis and make a self-consistent edifice of manipulations just by defining a different set of rules- rules which are at variance with the current set? I dont know the answer- may be the question isn't even valid.
Simply put, mathematical manipulations are interesting just because of our psychological urge in abstractions or generalizing things.
Sounds reasonable but I am not a mathematician. If true, one could potentially extrapolate this to suggest that those civilizations that gave primacy to abstract thinking (and philosophy) would have contributed the most to math- ancient India comes to mind (and perhaps Germany and ancient Greece). As a corollary, if certain civilizations contributed significantly to math, surely one could expect to find evidence of contributions to other forms of abstract thinking e.g philosophy. But this is OT.
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Re: Physics Thread.

Post by SriKumar »

Amber G. wrote:
SriKumar wrote:AmberG, your questions remind me of that book Physics for Entertainment by Yakov Perelman. I bought the first volume but did not buy the second one. If I can find it now, I'd pay 100 times the amount that I bought it for, back then..
The book is available here online:
http://www.archive.org/stream/physicsfo ... 7/mode/2up
:) (What is 100 times the amount you bought it for ? :) )
Arrey wah. Kyaa baat hai. Thanks a million Amber.G. I am bookmarking this.
As for the price, this might date me but I paid Rs 3.50 (or was it 4.50 ); and 100 times that comes to 350 Rs which is still a steal!
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Re: Physics Thread.

Post by kasthuri »

SriKumar wrote:My question was: if math is about reveling in manipulations (with no relevance to anything else), was there a good reason to study this form of an equation: (f(x+delta x)- f(x))/delta x and it properties; as opposed to other forms of equations: say; f(x + delta x) + f(x- delta x) -2 *f(x))/delta x^2. (I just ran this analytically for the simple case of f(x)= x^3 and it is the second differential). But this is what I am getting at: were there other forms such as, to give a crazy example, (f (x+ n*delta x) - f(x+ n*delta x))/n*delta x that were looked at, and discarded as trivial or not exciting. It does not matter that we looking for a 'differential'- the word is merely a label and nothing more.
SriKumar Ji,

Nothing gets discarded or trivialized in math. All relevant forms of expression around a concept will be scrutinized and a theory/theorem will be formed around the concept/definition if it is not already 'captured' by any existing theory. This way we can hope to bring counter examples into a regular body of thought. For example, all relevant *forms* of differential in different geometries (not necessarily linear) are explored in the area of differential geometry and the area differential topology further expands to explain the notion of differential (and other concepts) in the realm of manifolds. We have a perfect freedom to look into any form we like and call it as a 'differential' as the name 'differential' is just a label as you rightly pointed out. For instance, one is welcome to call '(f (x+ n*delta x) - f(x+ n*delta x))/n*delta x' as SriKumar differential and work his math/physics based on it. If the formulas based on SriKumar differential confines to the regular math, it is fine, otherwise it is fine too. One has to just keep in mind the distinction between the regular differential and SriKumar differential when explaining his math and if so nobody will dare to question the 'SriKumar' math [of course, things has to be consistent in SriKumar math]. I hope I answered your point. If not, please bear with my understanding.
This is what brings me to the next step in the process- why are certain manipulations done and the basis for the rules of the manipulations. Could we, for example, adopt a completely different basis and make a self-consistent edifice of manipulations just by defining a different set of rules- rules which are at variance with the current set? I dont know the answer- may be the question isn't even valid.
This is a beautiful point you have touched upon. This is *perfectly* valid and very relevant what we have been discussing about. Certain manipulations are done because they are consistent with the underlying rules of deduction and the basis of the rules of manipulations lie in both axioms and the rules of deduction. Yes, we are at liberty to adopt a completely different basis which is self-consistent and is variant with the current set. The whole world of mathematical logic is at our disposal for this task. The basis is already set up. We understand what it means by 'a theory being consistent' and all that stuff. I would suggest you to look into any introductory mathematical logic book. This is a beautiful subject that lies at the heart of several things that we do - math, physics, cs, philosophy and what not! And it exactly talks about what you are suggesting.
If true, one could potentially extrapolate this to suggest that those civilizations that gave primacy to abstract thinking (and philosophy) would have contributed the most to math- ancient India comes to mind (and perhaps Germany and ancient Greece). As a corollary, if certain civilizations contributed significantly to math, surely one could expect to find evidence of contributions to other forms of abstract thinking e.g philosophy. But this is OT.
I think this is not a reasonable extrapolation. The math that we now work is entirely based on Zermelo–Fraenkel set theory with the axiom of choice (also known as ZFC) which has deep connections with Aristotelian logic where as the abstract thinking/philosophy that we Indian's practice has its roots on Nyaya-Vaisheika stream of thoughts. There are large differences between the two. So the inter-connection between the present day math and abstract thinking/philosophy cannot be figured out. Or at least that is my HO!
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Re: Physics Thread.

Post by Bade »

We talked about "scales" before and now a new announcement of something even smaller than a Planck's scale at << 10^-35 m.

Integral challenges physics beyond Einstein
Some theories suggest that the quantum nature of space should manifest itself at the 'Planck scale': the minuscule 10-35 of a metre, where a millimetre is 10-3 m.

However, Integral's observations are about 10 000 times more accurate than any previous and show that any quantum graininess must be at a level of 10-48 m or smaller.

"This is a very important result in fundamental physics and will rule out some string theories and quantum loop gravity theories," says Dr Laurent.

Integral made a similar observation in 2006, when it detected polarised emission from the Crab Nebula, the remnant of a supernova explosion just 6500 light years from Earth in our own galaxy.

This new observation is much more stringent, however, because GRB 041219A was at a distance estimated to be at least 300 million light years.

In principle, the tiny twisting effect due to the quantum grains should have accumulated over the very large distance into a detectable signal. Because nothing was seen, the grains must be even smaller than previously suspected.

"Fundamental physics is a less obvious application for the gamma-ray observatory, Integral," notes Christoph Winkler, ESA's Integral Project Scientist. "Nevertheless, it has allowed us to take a big step forward in investigating the nature of space itself."

Now it's over to the theoreticians, who must re-examine their theories in the light of this new result.


vina
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Re: Physics Thread.

Post by vina »

Amber G. wrote:
A heavy 300 kg sandbag one meter tall is hung from a playground swing with a rope 3 meters long so that the bottom of the sandbag just clears the ground. A bottle is then placed on the ground a meter away from the sandbag as shown.

Image
Explain how to to knock the bottle over with the sandbag if you are given a paper drinking straw but are not allowed to touch anything (sandbag, rope, bottle, swing) with your body or with the straw.
Take the straw and blow between the bottle and the bag (I think you have to blow very close to the bag) and get it swinging. At each point of the max position the bag swings closer to the bottle, keep blowing with the straw in it's proximity , building amplitude, until the bag knocks the bottle over.

(I do hope it is more like a big hose than a teeny straw, getting a 300kg bag to swing takes some doing, though if you have a hose , like from a vacuum cleaner and can blow in it, makes life much easier)
Last edited by vina on 06 Jul 2011 11:45, edited 1 time in total.
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Re: Physics Thread.

Post by SaiK »

Guru Prabhu, thanks.. nice example. If I need to make Ash bend, all I need is a torch light. Just a small indulgence in OT.
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Re: Physics Thread.

Post by vina »

Amber G. wrote:The original problem which I posted about 2 years ago, the pendulum weighed only 5kg.. how many years of tapasyaa one has to do for that?
Once you get it swinging, the time to knock the bottle off is really not weight dependent.In fact (if I remember the Madrassa stuff correctly) , at resonant frequency, the amplitude builds exponentially and you should be able to knock the bottle over in a wink. So a tapasya of a couple of seconds. The big deal is to get it swinging initially, and there a 5kg weight will surely be far easier to get swinging than a 300 kg one. For that you have to do "kator tapasya" to get it moving.

Only thing to keep in mind is that the frequency varies with amplitude for the pendulum, so you can't have one "value" of resonant frequency to time it, you have to calculate it each time, or simply like I said, blow just as it reaches max amplitude (which is the same anyway, but you dont have to actually calculate anything).
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Re: Physics Thread.

Post by Amber G. »

vina wrote:
Amber G. wrote:The original problem which I posted about 2 years ago, the pendulum weighed only 5kg.. how many years of tapasyaa one has to do for that?
Once you get it swinging, the time to knock the bottle off is really not weight dependent.In fact (if I remember the Madrassa stuff correctly) , at resonant frequency, the amplitude builds exponentially and you should be able to knock the bottle over in a wink. So a tapasya of a couple of seconds.
Vinaji - What exactly do you mean? What Madarassa stuff and what exactly you mean by amplitude building 'exponentially' ? (to explain the difference between 100 years tapasyaa and wink/couple of seconds? It will be helpful if you can give the formula or stuff..:)..Some of us may have much less background in stuff which you know very well..Not asking you to derive or give all the details.. just main formula or a link where one can look it up.
The big deal is to get it swinging initially, and there a 5kg weight will surely be far easier to get swinging than a 300 kg one. For that you have to do "kator tapasya" to get it moving.
What is meant by swinging initially? (If the amplitude is less than 1mm, 1cm, 10cm?)
Only thing to keep in mind is that the frequency varies with amplitude for the pendulum, so you can't have one "value" of resonant frequency to time it....
Sure, as you said, you can time it with the pendulum, if you wish.. but isn't the frequency fairly constant ? .. I mean even at 15 degree swing the variation is less than half a percent (of the order of .02 second)

So practically speaking, is it kator tapasya in the beginning but then have to wait only for a few seconds...or continues tapasya of millions of years? ...
****
Changing the subject a little, and wondering out loud ..
(Also, to make it clear, it is not directed at any posters in this thread)

I see in other threads where some constantly claim to know more physics than giants like Bhabha, and others and call them incompetent and worse are quiet here (where bluffing can be easily exposed) .. This, I think, is note worthy.
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Re: Physics Thread.

Post by negi »

AmberG thanks for drawing the figure; from the specs given for the whole setup one can calculate the 'theta' (tan^-1(1/3) which comes to 0.322 radians i.e. <1 radian i.e. pendulum needs to only swing by 0.322 radians to hit the bottle so using small amplitude approximation for time period 'T' for pendulum T=(2*pi)* sqrt(l/g) (this haajmola from class IX physics )

where l is the length of the pendulum and g acceleration due to gravity . :mrgreen:

Assuming this experiment is being conducted in ideal conditions i.e. zero friction at point of suspension the amount of force required to displace this bag by 0.322 radians will be equal to the restoring force the bag will experience due to gravity when at that position (0.322 radians from the equilibrium position) , no ? :(

which comes to ~998 kg*m/s^2 :eek: ; looks like I messed up something doesn't look right , howver I will let my post stay for bebul to ROTFL.

--
AmberG what is force with which air is being blown from the straw ?
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Re: Physics Thread.

Post by vina »

Amber G. wrote:Vinaji - What exactly do you mean? What Madarassa stuff and what exactly you mean by amplitude building 'exponentially' ? (to explain the difference between 100 years tapasyaa and wink/couple of seconds? It will be helpful if you can give the formula or stuff..:)..Some of us may have much less background in stuff which you know very well..Not asking you to derive or give all the details.. just main formula or a link where one can look it up.
I was trying to remember /recollect stuff from vibrations and acoustics classes (other than some very basic stuff, the details of stuff like transfer functions etc are gone/erased/atrophied from memory).

The problem essentially is to get the ball swinging to hit the bottle. Now this is a forced oscillation problem and under perfect resonance (with zero damping) the amplitude is infinity. However, as the driving frequency builds up towards the resonant frequency, the amplitude starts increasing very rapidly. That is all that I can remember, nothing about the gory details about energy transfer functions all all the rest of it (electrical enggs do exactly similar things with transfer functions and their circuits for resonance etc).

A couple of links courtesy Google Chacha. Driven Oscillator..PPT, nice one and Mechanical Resonance pdf. I vaguely remember equations which showed build up of amplitude with time etc.
What is meant by swinging initially? (If the amplitude is less than 1mm, 1cm, 10cm?)
To get it moving from rest. Lets see how it happens (assuming perfectly still air), the initial motion is due to the Bernoulli effect/Venturi effect of the air flowing at close proximity to the side of the ball. That is where the weight of the ball makes a difference. To get a 300kg bag moving with such a tiny force vs a 5kg bag to overcome the initial inertia takes some doing. This takes "Maha Kator" tapasya , if you have a hose instead of a teeny straw, it will help because you can generate a larger force.

So once the bag gets "perturbed", the next step is to drive the oscillations with exactly timed forces (like in a clock with the escarpment and spring mechanism), so that the amplitude starts increasing and builds enough to knock the bottle over. This can happen in "a wink of an eye", ie a couple of oscillations to knock the bottle over.
Sure, as you said, you can time it with the pendulum, if you wish.. but isn't the frequency fairly constant ? .. I mean even at 15 degree swing the variation is less than half a percent (of the order of .02 second)
Remember, the simple harmonic motion (SHM) of the pendulum is due to a LINEAR APPROXIMATION, so that it it fits in the form of F = -kx , which is the generic form of the SHM equation that gives the answer in terms of a sin and cos function. That approximation is essentially for the pendulum type problems sin(theta) ~ theta ( the restoring force is -ksin(theta), which gets approximated to -k*theta) . That approximation holds for very small values of theta (upto 5 degs I think), beyond that, it goes to Pakistan very soon and it is no longer a simple harmonic motion approximation. This the same approximation for converting a oscillatory motion to a rotary motion like in a piston and crank with a connecting rod and the small angle approximation is the reason why you want to have a long connecting rod when compared to the piston stroke.

For a pendulum like system with a pretty low frequency, it probably wouldn't make such a big difference in terms of time period, but increase it to higher frequency system, then the linear approximations beyond the 5 deg or so will run into serious trouble I would think.
So practically speaking, is it kator tapasya in the beginning but then have to wait only for a few seconds...or continues tapasya of millions of years? ...
Yes. Kator Tapasya in the beginning and then a few seconds.
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Re: Physics Thread.

Post by vina »

Bade wrote:AmberG's super-JEE edition reminds of a qualifier prep question: How can you get up from a fallen position in a skating rink with no help of hands as one would normally. Assume a fallen flat shavasana position as the beginning point.

Someone thought spitting continuously would help. :)
Bring your hands from above your heads "shavasana position" to the sides of your thighs and at the same time, bend your knees so that your ankles come close to your butt, then if you clasp your knees and try rolling up as this happens (this will require some super skill so that you dont fall on your face), you can rotate up and as your torso comes up, straighten your knees and stand up.
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Re: Physics Thread.

Post by ramana »

AmberG, What is this Hessian operator? Where is it used and what are its advantages?
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Re: Physics Thread.

Post by anishns »

Maha Guru log!

Is this what is being discussed? If this is the case then a paki who has had a few spoonfuls of pindi chana will have no problem getting the air out from the other end with the right amount pressure. Preferably with a gas mask and not near any open flame :mrgreen:


BTW, is Bernoulli effect altered in hot air conditions?



Please check @1:05
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Re: Physics Thread.

Post by Amber G. »

negi wrote:AmberG thanks for drawing the figure; from the specs given for the whole setup one can calculate the 'theta' (tan^-1(1/3) which comes to 0.322 radians i.e. <1 radian i.e. pendulum needs to only swing by 0.322 radians to hit the bottle so using small amplitude approximation for time period 'T' for pendulum T=(2*pi)* sqrt(l/g) (this haajmola from class IX physics )
Not that it may matter much, but FWIW, the 'theta' (if one looks at the picture carefully and not ignore 1m length) is arcsin(1/4) or about 15 degrees.. at this amplitude, the variation on time period is about 1/2 a percent .. (practically speaking, that it, any one actually experimentally measures)
For more clarification see the original source of the problem:
http://www.phy.duke.edu/~hsg/physics-ch ... enges.html :)
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