DrRocket

Hello

 

What is the relation between the resistance and lost Thermal energy in a circuit ?

 

I mean >>

 

If we put a ((big)) resistance .. the Intensity of the current will lessen

 

 

If we are trying to lessen the lost energy (it is lost as heat) >>

 

what should we do ??

 

use a material that has low Resistivity ?

 

or high Resistivity ??

 

the first will make the intensity of the current increase >> and that it self affects the lost energy as heat

 

and

 

related to this

 

in "coldeg's X-ray tube" why do we use copper (attached to the target of the Wolfram) ??

 

Thanks

Energy dissipated in a resistor is [math]I^2R[/math]

The maximum energy transfer to a resistive load by a voltage source occurs when the load resistance is

equal to the internal resistance of the source.

Quantum mechanics is more often than not counter-intuitive. There is rarely a clean classical analogy that "makes sense". Just know that, as ajb stated, quantum mechanics has endured the experimental test of fire and passed with flying colors.

 

"There was a time when the newspapers said that only twelve men understood the theory of relativity. I do not believe that there ever was such a time. There might have been a time when only one man did, because he was the only guy who caught on, before he wrote his paper. But after people read the paper, a lot of people understood the theory of relativity in some way or other, certainly more than twelve. On the other hand, I can safely say that nobody understands quantum mechanics." – Richard P. Feynman in The Character of Physical Law

Yes, maybe there's another way to propose it: as an object approaches C, it takes increasing amounts of energy to accelerate it relatively less, right? So, for example, as an object orbiting a black hole approaches C, it doesn't accelerate to a higher orbit but continues at the same speed and altitude but with higher energy, right? So isn't that higher energy that it expresses at relativistic speeds similar to the propagation energy expressed by photons, which express mass only as momentum over spacetime? In other words, isn't energy through spacetime the same thing as gravitational mass? I.e. a photon or material object in motion expresses energy as mass to the extent that its speed approaches C? E.g. light expresses mass as energy moving at C, but material objects may express mass-gravitation AS WELL AS gravitation due to motion-energy according to their speed relative to C. This idea is making loads of sense to me, but maybe I need some clear explanation as to how its misguided.

You seem to think that you are going to re-discover and understand general relativity by introspection. That was only marginally successful for Einstein, who needed a lot of outside expert help. You are not Einstein. Read a book.

More old business, and then back to "Iggy's two questions."

Dr Rocket:

"In general relativity, space is NOT a 3-D volume and time is NOT duration between two chosen events."

 

Your first statement above is not an absolute truth just because it is now so well accepted in the relativity community.

 

Blindingly, utterly wrong.

What I said is absolutely true in general relativity, precisely as stated. If you have some other view, that view is most certainly not general relativity.

Yep, not even in the ballpark. Talking to yourself.

So we are looking in our telescopes, and after 50 days, we observe the spaceship making the U-turn.

 

.

.

.

 

Where am I wrong?

You are wrong all over the place,

Pay attention to what swansont, Sysiphus and Janus are telling you.

Correcting your mistakes is beginning to resemble "wack a mole". You really do need to read a book that will give you a complete and consistent treatment of relativity. Rindler's Essential Relativiity, Special, General and Cosmological might be appropriate. His Introduction to Special Relativity is also pretty good.

I like Naber's The Geometry of Minkowski Spacetime but you might find it a bit too heavy on mathematical abstraction.

Someone else might have better recommendations.

Hi all,

 

My question is:

Is there a good source that defines "tensor rank" for me? Yes, I have seen several already, but perhaps I am mostly interested in a definition that is more mathematical (rigid)...For example, how do we define the rank of a multilinear form?

If I have f: V x V x V...x V --------> k,

what should the rank of this map be?

Thank you

k

In physics a "tensor" is usually really a tensor field on some manifold.

A covariant tensor is a tensor field, a field of multilinear forms, on the tangent bundle. A contravariant tensor field acts on the cotangent bundle. A tensor of order, or type, (q,p) or (q+p) acts on T x T x ... x T x T* x T* x ... x T* with q copies of T and p copies of T*.

People who fool around with this stuff regularly do this without thinking. I have to stop and remember what the notation means. If you haven't become confused by this yet, you will be sometime.

Wouldn't "increasing curvature" imply strengthening of the gravity well being orbited?

Yes. The point is that you can't do that by adopting a reference frame in which an object is moving. The curvature will be the same as in the rest frame.

I was thinking in terms of increasing curvature relative to the thing moving, or in relation to a gravity well, straightening of the curvature of the gravity well due to counter-curvature caused by the satellite and its motion.

Motion won't help.

Counter-curvature ?

The mass stress-energy tensor incorporates information, about not only the mass density in space, but also the motions of that mass. Moving mass gravitates differently, than the same static.

This is not correct.

The stress energy tensor, like the curvature tensor to which it is equated by the Einstein field equations is invariant -- independent of the observer. Motion is not an invariant.

You cannot increase curvature by adopting a reference frame in motion with respect to your initial frame.

If what you are suggesting were true, light would see anything with non-zero rest mass as the source of a black hole. It would be really dark around here.

Mods: Is this acceptable, I am not asking people how they made the stuff, where they got it etc. I'm just wondering what the most dangerous thing you think you've seen / used

 

I saw these when we were clearing out an old cupboard in the chemistry lad last week:

 

I think the most dangerous chemical I have ever seen was something labelled [ce]Hg(ONC)_2[/ce] and it was in the back of one of the school chemistry cupboards... I did some reasearch and this stuff is explosive. My chemistry teacher said he never knew it was there - he said it has probably been there for years, the next day the bomb squad were called up to remove the stuff... I just wish I could have seen it explode!

 

Or... it may have been the really concentrated solution of Hydrogen Peroxide, I've heard that stuff is pretty powerful. My teacher managed to dispose of that one - I'm not shure how he made us leave the room incase of any problems. Apparently it was about 83% concentrated but I'm not shure about that.

 

Edit: then again, the Nitrogen Triiodide reaction was pretty powerful - I'm staying clear of that one too!

 

Anyone else have anything interesting to share? Please do not post how to make the stuff - danger is bad!

 

Cheers,

 

Ryan Jones

A nitroglycerine storeage tank .

 

How is it possible then that the spaceship has been observed making the return trip in only 25 days?

 

It is because you are using the term "observed" in terms of what would be recorded by a camera held by A and not in terms of what is actually occuring relative to the reference frame of A.

What you "see", optically in special relativity is not what one would measure. This is due to the finite speed of light and relativity of simultaneity.

If you consider a circular hoop, circular in the rest frame of the hoop, passing an observer at relativistic speed then length contraction in the direction of motion would present that hoop to the observer as an ellipse. That is correct. But when light transit times are included in the calculation, the observer, and his camera, would "see" a circle. Roger Penrose was the first to recognize this.

The "paradox" that you have noted is the result of failing to discriminate between "what you see" and "what you get". WYSIWYG does not hold in relativity.

Summary:

Iggy and Michael are talking past one another.

Iggy is correct, but one has to think in the abstract setting of Minkowski space to see why. Such thinking is necessary in special relativity.

Michael123456 is trying in good faith, but can't seem to grasp the difference between Minkowski space with the Minkowski metric as opposed to Euclidean space with the Euclidean metric.

Michael is out somewhere in left field. He should listen to Iggy.

Owl is not even in the ballpark. He is talking to himself.

Scenario 1

A mathematician and an engineer are in a cabin by a stream, which they can see through a curtained window. There is an empty bucket on the floor. The curtains are on fire.

The engineer takes the bucket to the stream, fills it with water, returns to the cabin and uses the water to put out the fire.

The mathematician does likewise.

Scenario 2

Identical to scenario 1, except that the bucket on the floor is full of water.

The engineer picks up the bucket of water and puts out the fire.

The mathematician picks up the bucket and pours the water on the floor, reducing the problem to that of scenario 1, which he has already solved.

You normally have to worry about if the matter content is "physical", so obeys what you would expect it to (have positive mass for instance) or impose some topological constraint like global hyperbolicity (or both).

If you assume global hyperbolicity the question of existence of CTCs is settled immediately -- they don't.

The third part was wrong. Here is the correct version:

 

[math] \int_{a}^{b} \frac{dx}{dt}\frac{d^2x}{dt^2}dt = \int_{a}^{b} \frac{d^2x}{dt^2} dx = \frac{1}{2}x'(b)^2 - \frac{1}{2}x'(a)^2 [/math]

Look at [math] \int_{a}^{b} \frac{dx}{dt}\frac{d^2x}{dt^2}dt[/math] and integrate by parts.

Or let [math]u=\frac {dx}{dt}[/math]

[math] \int_{a}^{b} \frac{dx}{dt}\frac{d^2x}{dt^2}dt = \int_{x'(a)}^{x'(b)} u \frac{du}{dt} dt[/math] [math] = \int_{x'(a)}^{x'(b)} u du = \frac{1}{2}x'(b)^2 - \frac{1}{2}x'(a)^2 [/math]

Thanks!

 

Sorry to be really slow here, but I'm not sure I get how you got to this step:

Shouldn't the sum in the right hand be s=1 to N now?

No, the "x" in front takes care of that, but adds an "N+1" term that is subtracted out in the last term.

I'm just trying to understand the steps. The 1+ came from n=0, right?

right

[math] \int_{a}^{b} \frac{dx}{dt}\frac{d^2x}{dt^2}dt = \int_{a}^{b} \frac{d^2x}{dt^2} dx = \frac{1}{2}\frac{dx}{dt} - \frac{1}{2}\frac{dx}{dt} [/math]

 

What I am having trouble is understanding is going from the second step to the third step. I don't understand how you can integrate with respect to dx and still integrate [math] \frac{d^2x}{dt^2} [/math]

Suppose [math] x(t)=t^2[/math]

[math] \frac {dx}{dt} = 2t [/math]

[math]\frac{d^2x}{dt^2} = 2 [/math]

[math] \int_{a}^{b} \frac{dx}{dt}\frac{d^2x}{dt^2}\ dt = \int_a^b 4t \ dt[/math] [math]= 2b^2-2a^2[/math] [math] \ne\frac{1}{2}\frac{dx}{dt} - \frac{1}{2}\frac{dx}{dt} [/math] [math]=0[/math]

You have mis-stated something.

Hey guys,

 

I'm practicing for a thermo test later this week. We have this question in the book:

 

Zipper Problem: A zipper has N links; each links has a state in which it is closed with energy 0 or open with energy [math]\varepsilon[/math]. We require, however, that the zipper can only unzip from the left end, and that the link number s can only open if all links to the left (1,2,...s-1) are already open.

(a) Show that the partition function can be summed in the form:

[math]Z=\frac{1-\exp{(\frac{-(N+1)\varepsilon}{\tau})}}{1-exp{(\frac{\varepsilon}{\tau})}}[/math]

 

Okay, so I approaced the problem by defining the possible energies as a sum of epsilon(n) where it goes from 0, 1, 2, 3 etc.

Hence, my partition equation:

 

[math]Z=\sum \exp{(\frac{-n\varepsilon}{\tau})} = \sum (\exp{(\frac{-\varepsilon}{\tau})} )^n[/math]

 

I have been trying to manipulate this further forever. I know it should look like something starting with 1 + exp(..) since with n=0, the exponent will be =1, but I couldn't see how to transform it.

 

Finally, I resorted to the answer sheet, and it says that the above is right, and therefore it's obviously [math]Z=\frac{1-\exp{(\frac{-(N+1)\varepsilon}{\tau})}}{1-exp{(\frac{\varepsilon}{\tau})}}[/math]

 

Obviously? What am I missing? How did they get from the ^n to that?

 

meh. Help!

 

~mooey

 

 

 

p.s

 

I see in another source that they rewrote the summation as:

 

[math]\sum_{s=0}^{N} x^s = \frac{1-x^{N+1}}{1-x}[/math] where [math]x=\exp{(\frac{-\varepsilon}{\tau})}[/math]

 

Great... that looks like an expansion of a power series, and I guess it makes sense if you have the instinct to translate it like the above. Assuming I got stuck with this for an hour, is there any other way to do this, or is this simple a "remember your power series expansion" problem... ?

[math]\sum_{s=0}^{N} x^s = 1 +x \sum_{s=0}^{N} x^s - x^{N+1}[/math]

[math] (1-x) \sum_{s=0}^{N} x^s = 1-x^{N+1}[/math]

[math]\sum_{s=0}^{N} x^s = \dfrac {1-x^{N+1}}{1-x}[/math]

Sorry to butt in on a very interesting discussion between guys who obviously know their stuff, but I have a slight worry.

 

First I am not a physicist and I am most emphatically not a philosopher, but I am familiar with Einstein's field equations.

 

So it seems there are solutions to these equations (I believe Goedel found one) that allow CTCs, which you guys are more-or-less dismissing as "non-physical".

 

My question: What is the basis for this dismissal as being non-physical? Is it experimental? Or is it that you just don't think the universe works that way? Is this is a good argument? Is there a better one? Or am I just making a fool of myself in an area where I am a complete baby?

 

Don't get me wrong: I am as sceptical about time travel as the next moron, but I am struggling to follow the argument here

The solutions of the Einstein field equations depend on the distribution of matter/energy in the universe. Exact solutions, and Godel's spacetime is an exact solution, are known for only a handful of assumed mass/energy distributions. Godel assumed a homogeneous distribution of swirling dust (particles that interact only through gravity. This solution does not exhibit Hubble expansion, unlike the "real" universe. http://en.wikipedia.org/wiki/G%C3%B6del_metric

Using the chronological protection conjecture to outlaw CTCs as unphysical is just the statement that the conjecture is true.

 

There is some evidence based on semi-classical gravity.

 

But I don't think one should employ the conjecture absolutely. This of course does not mean that I think CTCs are necessarily physical in the context of GR.

Absolutely.

A conjecture should never be taken as a fact.

I tend to think the conjecture is true, but that simply means that I think an attempt to prove the conjecture has a better chance of success than a project to build a time machine. If I were looking for a counter-example I would start by learning about Kerr black holes.

I don't think we are disagreeing on anything fundamental.

 

In the context of classical GR you have to decide if space -time with CTCs are "physical". To decide if a space-time is physical you have to add other constraints like various energy conditions or insist that the space-time be globally hyperbolic. So, in this sense classical GR by itself does allow CTCs. But adding other physical conditions may mean they are not realised in nature, like the weak energy condition you mention. So, in classical GR it is not at all obvious that time travel is not allowed.

 

In fact the situation for semi-classical gravity is very interesting. It is very difficult to build quantum theories that do not violate the weak energy condition. So, the weak energy condition is not likely to hold at the microscopic level.

 

As for Mallet, I have not really made my mind up about him. However, his is certainly out on a limb actually trying to build a time machine. I have not looked into his analysis of the proposed experiment. I suspect that some effect he has not taken care of will spoil the time machine. It could be very interesting to find out exactly why it won't work.

 

People I know who investigate time machines (my old MPhys supervisor was one) are not really trying to contact the past, rather they are trying to push GR to its limit in order to point at new physics. Maybe even hints at what quantum gravity should be.

There is no question that GR, without some sort of additional constraint like an energy condition, admits CTCs. Several solutions are known. A prohibition of physical CTCs, i.e. CTCs in the real universe, in the context of general relativity is the "Chronology Protection Conjecture". That conjecture remains a conjecture, but I think it fair to say that it would be a major surprise if it were shown to be false. We have been surprised before.

There are certainly legitimate physicists who have worked on or are currently working on the problem. Hawking and Thorne leap to mind. Mallet doesn't.

Mallet's approach has apparently been looked at in detail and errors identified -- see comments in the wiki article noted in an earlier post.

You might find this piece by Thorne interesting.

http://www.its.caltech.edu/~kip/scripts/ClosedTimelikeCurves-II121.pdf

One question that I have, and have no clue to the answer, is whether CTCs are allowed in Einstein-Cartan theory. I know no one who knows much about EC theory.

So, Hawking's conjecture is based on semi-classical gravity, that is quantum field theory on a curved background space-time. Here is seems that the expectation value of the energy-momentum diverges near CTCs. Thought, to my knowledge, there is no general proof of this.

 

Also, quantum effects of gravity could presumably make this much more complicated. One possibility is that the expectation value of the energy-momentum gets regulated near CTC's and then time machines could be realised! Or at least on the microscopic scale.

 

So, right now I would say that

1. classical general relativity probabily does not disallow CTCs
2. Semi-classical gravity suggests that CTCs are not allowed
3. Quantum gravity (whatever that is!) will have the final say on CTCs

I don't have access to the whole paper, but I read the abstract a bit differently.

1. GR plus the weak energy condition disallows CTCs

2. Quantum theory might allow some violation of the weak energy condition, but (the expected value of) the stress energy tensor would be very large (indicating large local curvature).

3. Quantum gravity (whatever that is!) will have the final say on CTCs.

Note: 1. GR by itself is known to admit spacetimes with CTCs.

2. Mallet is still a nut.

The Twins Paradox can also be explained using special relativity. It involves time dilation and the Dopper effect. And the turn-around of the traveling twin is the key. It isn't brief, but I find it the easiest explanation for my small brain to understand. I wrote up a version on my website: Link: http://www.marksmodernphysics.com/ Click on It's Relative, Archives, Twins Paradox

The explanation in terms of special relativity is quite simple"

-- Special relativity is explicitly a theory regarding physics as described in inertial reference frames

-- In the twin paradox only the reference frame of the non-traveling twin is inertial.

Ergo analysis in the reference frame of the non-traveling twin is the correct analysis.

Note: Thw traveling twin experiences measurable acceleration at take-off, and at return, and similarly at the distant star, and therefore his reference frame is not inertial. The problem is not symmetric.

 

Enter "Philosophy of Science, Relativity Section." If space is 3-D volume, basically that "emptiness" in which all things and forces exist and operate... with no "end in sight," or even conceptually possible... Remember, before it became "something" which contracts, expands, has shape... curves, etc.),...

and "time" is not "something" either... just duration between any two *chosen* instants, Then...

In general relativity, space is NOT a 3-D volume and time is NOT duration between two chosen events.

In fact, in general relativity, there is no such thing as space and no such thing as time. What there is is a 4-dimensional Lorentzian manifold, spacetime. The usual concepts of "time" and "space" the concepts that you clearly consider as absolute, are not absolute, but in fact are quantities that are applicable to the tangent space at a point, and not to the spacetime manifold itself.

The study of special relativity alone gives rise to confusion because a global decomposition, though not a unique such decomposition, into "space" and "time' is possible and is central to the presentation of special relativity in introductory textbooks.

The perspective of general relativity is needed to understand the real nature of spacetime.

This has nothing to do with any ridiculous philosophical pigeon-holing of thought (e.g. subjective realism), but rather with a theory the validity of which is based on real measurements -- and a great many such measurements.

The problem is quite clearly that, despite your protests to the contrary, you do not understand relativity. You don't begin to understand it. That is a condition that is relatively easily remedied.

What is not so easily remedied is that you don't understand that you don't understand.

 

PS This is the celebrated "continuum hypothesis". Anyone know if it has been proven?

Paul Cohen proved that the Continuum Hypothesis is independet of the Zermelo-Fraenkel axioms plus the Axiom of Choice.

It is fair to say that within classical general relativity it is not obvious that time travel is not allowed.

Nicely weasel worded.

http://prd.aps.org/abstract/PRD/v46/i2/p603_1