# This is the thread that will answer your questions related to the field of Physics



## aleazk

The "TC Physics Department" (?!:lol:, recent group photo of the department's staff http://2.bp.blogspot.com/-174aisbYlQg/TdsmidIfHGI/AAAAAAAAAJQ/WcebCxyczdc/s400/nerd.jpg) will answer all your questions.


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## Polednice

Are there any promising ideas yet for a 'theory of everything'?


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## Vaneyes

Polednice said:


> Are there any promising ideas yet for a 'theory of everything'?


****** has been lingering around TC for a while. Just kidding.


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## Scarpia

Polednice said:


> Are there any promising ideas yet for a 'theory of everything'?


Short answer, nope.


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## Polednice

And if there aren't any yet, is there any feeling about which current areas of research might give us some clues?


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## aleazk

Polednice said:


> Are there any promising ideas yet for a 'theory of everything'?


Yes, "string theory" (the mysterious M-theory) is a candidate for a 'theory of everything', supported mainly by the particle physics community. However, the very idea of a 'theory of everything' is currently on debate. Let alone the idea that string theory is that theory...


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## HarpsichordConcerto

Is string theory physics or philosophy?


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## aleazk

HarpsichordConcerto said:


> Is string theory physics or philosophy?


Neither of the two. String theory is "protophysics", i.e., a set of ideas that, in the future, could be relevant to physics, but in this moment are speculative.


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## Fsharpmajor

How can neutrinos travel at the speed of light (or even faster) when they are supposed to have mass?


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## aleazk

Fsharpmajor said:


> How can neutrinos travel at the speed of light (or even faster) when they are supposed to have mass?


Well, according to the Special Theory of Relativity they can't travel at the speed of light. The recent experiment realized on the CERN laboratories is far from conclusive.


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## Philip

HarpsichordConcerto said:


> Is string theory physics or philosophy?


it is physics... although i'm sure you could argue that all physics is actually just very rigorous philosophy.

but please don't believe that new age bullcrap supposedly motivated by quantum mechanics and string theory, for instance the ideas of your dead relatives living in a parallel universe, the physical action of conscience in observation, etc. these topics are complete fabrications intended to capture the imagination and sell books.


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## aleazk

Philip said:


> it is physics... although i'm sure you could argue that all physics is actually just very rigorous philosophy.
> 
> but please don't believe that *new age bullcrap supposedly motivated by quantum mechanics* and string theory, for instance the ideas of your dead relatives living in a parallel universe, *the physical action of conscience in observation*, etc. these topics are complete fabrications intended to capture the imagination and sell books.


I strongly agree with this, I too think it's bullcrap.


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## Dodecaplex

With a minimum of 800 words, please explain in detail why Newtonian mechanics is incompatible with Maxwell's equations.


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## Scarpia

Dodecaplex said:


> With a minimum of 800 words, please explain in detail why Newtonian mechanics is incompatible with Maxwell's equations.


Why impose a minimum? If it can be explained in 10 words, that wouldn't be boring enough?


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## Trout

Ah, physics. I used to know about physics, but then I took an arrow to the knee.


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## HarpsichordConcerto

Philip said:


> it is physics... although i'm sure you could argue that all physics is actually just very rigorous philosophy.
> 
> but please don't believe that new age bullcrap supposedly motivated by quantum mechanics and string theory, for instance the ideas of your dead relatives living in a parallel universe, the physical action of conscience in observation, etc. these topics are complete fabrications intended to capture the imagination and sell books.


Yes, I agree. Even a non-physicist like me can sense that's just popular-industry trying to make a buck. It would be too shocking to think there is another Andrea Rieu in another parallel Universe (or in the Multiverse)!

*Next question, which is probably more astrophysics, just tell us what the current thinking is: does information ever leave the blackhole?*


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## starthrower

I have Brian Greene's books. Are they worth reading? The only book I read on physics was The Dancing Wu Li Masters.


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## HarpsichordConcerto

Great thread, by the way! Many thanks!


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## Philip

Dodecaplex said:


> With a minimum of 800 words, please explain in detail why Newtonian mechanics is incompatible with Maxwell's equations.


i don't know why you keep asking this question... it really isn't that difficult to answer


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## aleazk

Dodecaplex said:


> With a minimum of 800 words, please explain in detail why Newtonian mechanics is incompatible with Maxwell's equations.


hard answer: special relativity asserts that spacetime is a fourdimensional, hausdorff, paracompact, real manifold. Tensor fields are the only fields defined on a manifold. If you want that Maxwell's equations behave as true tensor equations in that manifold, then you have to put a metric of lorentzian signature in the manifold. Diffeomorphism invariance of the manifold model of spacetime implies certain equations of motion for the stress-energy-momentum tensor of the matter fields. For a perfect fluid (together with the lorentzian signature thing) , these equations are precisely the relativistic mechanics equations of motion for particles.


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## aleazk

HarpsichordConcerto said:


> Yes, I agree. Even a non-physicist like me can sense that's just popular-industry trying to make a buck. It would be too shocking to think there is another Andrea Rieu in another parallel Universe (or in the Multiverse)!
> 
> *Next question, which is probably more astrophysics, just tell us what the current thinking is: does information ever leave the blackhole?*


well, this is an open question in today's physics, we need a theory of quantum gravity to answer it.


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## Chrythes

Are black holes essential to our universe?
What are the best guesses for what dark energy and dark matter might be?


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## aleazk

Chrythes said:


> Are black holes essential to our universe?
> What are the best guesses for what dark energy and dark matter might be?


what do you mean by "essential"?


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## Chrythes

I mean, what is their purpose?
What the universe would look like without them?


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## Dodecaplex

Philip said:


> i don't know why you keep asking this question... it really isn't that difficult to answer


I'm currently studying special relativity. What can I say?


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## aleazk

Chrythes said:


> I mean, what is their purpose?
> What the universe would look like without them?


 well, haha, certainly it will look different!, stellar mass black holes are the result of the gravitational collapse of a very massive star. Supermassive black holes are in the center of galaxies.


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## Chrythes

OK, I know that, but what would happen without them?
I know it's essentially because of them we have spiral galaxies, but other than that - what would be different in our universe without black holes?
Would material exist forever without black holes sucking it?


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## aleazk

Chrythes said:


> OK, I know that, but what would happen without them?
> I know it's essentially because of them we have spiral galaxies, but other than that - what would be different in our universe without black holes?
> Would material exist forever without black holes sucking it?


black holes don't suck everything. They have a thing called "the event horizon". This event horizon is (in the most simple case) a spherical surface. Now, for a Black hole of mass M, the gravitational field outside the event horizon is exactly the same as the field of an ordinary star of mass M. So, if you are outside the horizon, you can escape from the black hole influence. If you enter the horizon, then you can't escape outside it never. Even more, in a finite amount of time, you will be confronted with the singularity that lies in the center of the black hole. So, black holes are not wild animals that suck everything.


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## Chrythes

I know that as well, I guess my question was not clear enough - as far as I know supernovas provide our galaxy with a lot of new material for galaxies/star formations, but black holes seem to do the opposite - they suck the material that enters their event horizon. Now, what is the ESSENCE OF BLACK HOLES?
How would the universe would look without black holes? Would it lose something that is fundamental for its existence?
By sucking the material that reaches the event horizon - are they the destructive forces of our universe?
I truly am just trying to understand the most fundamental effect of a universe with and without black holes - how would a universe without black holes look? etc.


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## Dodecaplex

*How come good ol' Albert had 10 mistresses? Just . . . just how did he have the time to solve physics problems while having all of that sex?*


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## Chrythes

Dodecaplex said:


> *How come good ol' Albert had 10 mistresses? Just . . . just how did he have the time to solve physics problems while having all of that sex?*


Maybe sex helped him to solve physical problems.
In fact we might thank his mistresses for inspiring him!


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## Scarpia

aleazk said:


> hard answer: special relativity asserts that spacetime is a fourdimensional, hausdorff, paracompact, real manifold. Tensor fields are the only fields defined on a manifold. If you want that Maxwell's equations behave as true tensor equations in that manifold, then you have to put a metric of lorentzian signature in the manifold. Diffeomorphism invariance of the manifold model of spacetime implies certain equations of motion for the stress-energy-momentum tensor of the matter fields. For a perfect fluid (together with the lorentzian signature thing) , these equations are precisely the relativistic mechanics equations of motion for particles.


How easy to conceal a lack of insight behind a lot of jargon!


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## Philip

Dodecaplex said:


> I'm currently studying special relativity. What can I say?


i forgive you


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## Dodecaplex

Chrythes said:


> Maybe sex helped him to solve physical problems.
> In fact we might thank his mistresses for inspiring him!


*Can you imagine Albert having sex with one of his mistresses while simultaneously contemplating physics?* Just think about it:
"Ohhh, baby, ohh, Lorentz transformation! Ah, yes, time dilation! Oh, length contraction!"


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## aleazk

Dodecaplex said:


> *How come good ol' Albert had 10 mistresses? Just . . . just how did he have the time to solve physics problems while having all of that sex?*


i know that he put his schizophrenic son into an asylum, and he never went to visit him. there you have some saved time.


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## Philip

Dodecaplex said:


> *Can you imagine Albert having sex with one of his mistresses while simultaneously contemplating physics?* Just think about it:
> "Ohhh, baby, ohh, Lorentz transformation! Ah, yes, time dilation! Oh, length contraction!!"


in other words Einstein is telling us that velocity during sexual activity may cause time to slow down, while lengths may shrink... this is a difficult compromise indeed


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## aleazk

Philip said:


> i forgive you


the Tintin avatar softened you?


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## Dodecaplex

aleazk, are you getting hundreds of notifications or is my experiment failing?


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## aleazk

Dodecaplex said:


> aleazk, are you getting hundreds of notifications or is my experiment failing?


i'm not going to answer...


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## aleazk

Chrythes said:


> I know that as well, I guess my question was not clear enough - as far as I know supernovas provide our galaxy with a lot of new material for galaxies/star formations, but black holes seem to do the opposite - they suck the material that enters their event horizon. Now, what is the ESSENCE OF BLACK HOLES?
> How would the universe would look without black holes? Would it lose something that is fundamental for its existence?
> By sucking the material that reaches the event horizon - are they the destructive forces of our universe?
> I truly am just trying to understand the most fundamental effect of a universe with and without black holes - how would a universe without black holes look? etc.


The percentage of matter that black holes suck is very small. So, for the quantity of matter in the universe, they are not a really big influence. The enormous black hole in the center of our galaxy is inactive. Back holes are of supreme importance theoretically because of the remarkable analogy between the laws of black hole mechanics and the ordinary laws of thermodynamics. In fact, the laws of black hole mechanics are simply the ordinary laws of thermodynamics applied to a system containing a black hole!!


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## TrazomGangflow

I'm not sure if this is a physics questions but how fast would you have to be traveling for it to make time accelerate significantly? Ex. 1:2 ratio, 1 day of "time travel" equivalent to 2 earth days.


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## aleazk

TrazomGangflow said:


> I'm not sure if this is a physics questions but how fast would you have to be traveling for it to make time accelerate significantly? Ex. 1:2 ratio, 1 day of "time travel" equivalent to 2 earth days.


tv=te.sqrt (1-v^2/c^2). tv=1/2.te, then: 1/2=sqrt (1-v^2/c^2) --> 1/4=1-v^2/c^2 --> v^2/c^2=1-1/4=3/4 --> v^2=3/4.c^2 --> v=sqrt (3)/2.c !! v=0,86.c


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## HarpsichordConcerto

Why is there so "few" antimatter compared with matter?


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## Chrythes

aleazk said:


> The percentage of matter that black holes suck is very small. So, for the quantity of matter in the universe, they are not a really big influence. The enormous black hole in the center of our galaxy is inactive. Back holes are of supreme importance theoretically because of the remarkable analogy between the laws of black hole mechanics and the ordinary laws of thermodynamics. In fact, the laws of black hole mechanics are simply the ordinary laws of thermodynamics applied to a system containing a black hole!!


/
So they are more of theoretical significance than practical (to the universe)?
Why aren't they inactive? Isn't the form of our galaxy (spiral) determined by the black hole that lies in its centre?
To my former question - what are currently the best guesses for what might dark matter and dark energy be?
In what state does string theory stand in these days? 
A few months ago i remember watching a show with Neil deGrasse Tyson and at one point he said that when black holes emerge it's possible to find a space where time becomes distorted, making time travel possible - if it's true, why such effect would take place? 
What would neutrinos moving faster than light essentially mean? And just out of curiosity - what is the second fastest particle after the photon?


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## aleazk

Chrythes said:


> /
> So they are more of theoretical significance than practical (to the universe)?
> Why aren't they inactive? Isn't the form of our galaxy (spiral) determined by the black hole that lies in its centre?
> To my former question - what are currently the best guesses for what might dark matter and dark energy be?
> In what state does string theory stand in these days?
> A few months ago i remember watching a show with Neil deGrasse Tyson and at one point he said that when black holes emerge it's possible to find a space where time becomes distorted, making time travel possible - if it's true, why such effect would take place?
> What would neutrinos moving faster than light essentially mean? And just out of curiosity - what is the second fastest particle after the photon?


well, black holes are in the center of galaxies, so it's obvious that they will define the form of the galaxies, because of their gravitational influence.
With respect to the dark matter-energy question, these are open questions today. Some people thinks that dark matter could be composed of neutrinos.
string theory is protoscience right now.
The only way you can travel backwards in time is if you create a CTC (Closed Timelike Curve) in spacetime. Hawking proved that in all the cases designed so far for creating such curves, you will need matter of "negative mass". It's not clearly know if this kind of matter can really exist, at least in the quantity needed for creating those CTCs.
the faster than light thing is a very complicated matter, i think the neutrino experiment it's plain wrong, because of the contradiction with previous results in the same subjet.


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## science

This is pretty awesome. 

My first question is: I had one year of calculus in high school, which I should of course review. But from there, what specifically would I need to study in order to understand 

a) Laplace's celestial mechanics?
b) Maxwell's equations?


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## Chris

This is a puzzle I saw some time ago. I remember the answer (which I will not reveal) but not the reasoning behind it. The question is: If the universe was made entirely of water, but with air bubbles scattered throughout it, under the influence of gravity would those bubbles tend to:

1. converge
2. move further apart
3. neither


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## Scarpia

science said:


> This is pretty awesome.
> 
> My first question is: I had one year of calculus in high school, which I should of course review. But from there, what specifically would I need to study in order to understand
> 
> a) Laplace's celestial mechanics?
> b) Maxwell's equations?


I would start with Einstein's own book, _Relativity_. It is public domain by now so there are various Kindle editions that are free or almost free (can be read on any PC or Mac using a web browser, even if you don't have a Kindle). It was written for non-scientists and assumes familiarity with high-school level math.

Here is one edition, there are others.

http://www.amazon.com/Relativity-Sp...?s=digital-text&ie=UTF8&qid=1323788754&sr=1-8

You will need no calculus to understand relativity and the Lorenz transformation.

However, the Lorenz transformation was formulated as a response to problems with the Maxwell Equations. You will only need to understand the Maxwell Equations if you want to know the motivation for the theory of relativity, not its implications. Maxwell equations require rather advanced calculus.

However, the crux of it can be expressed quite simply.

Maxwell figured out that light is a wave. If you have a string, you can get waves to propagate down the string, and the speed of the waves will depend on the tension in the string and the density (think of a guitar string). The basic physical principle is that if you pull on the string, it wants to return to its original state. Similarly, sound is a wave that propagates in air, and the speed depends on the density of the air and the pressure. As in the string, if you compress some air, it wants to return to its equilibrium state. But if light is a wave, what is the medium that light propagates in? What is the analog of pressure or tension that describes the tendency of this medium to return to its equilibrium distribution? Light can propagate in empty space, so it seems to imply that empty space is full of some sort of 'stuff' that light propagates through. (There is no sound if there is no air, and no waves on the string if there is no string.) But it gets worse. Sound has a fixed speed with respect to the air. Waves on a string have a fixed speed with respect to the string. If you are moving with respect to the air, or the string, the wave that propagates in the air or string will appear to move at a different velocity from your frame of reference. What is the 'stuff' with respect to which the speed of light is defined? It seems to imply that 'space' itself has to be at rest to measure the proper speed of light. Scientists postulated and 'ether' that fills space, through which light propagates.

Michaelson tried to detect this ether and failed. He observed that light seems to propagate at the same speed, no matter what frame of reference you observe it from. This is the central idea of relativity. You have to screw around with time and space to get the result that light has the same velocity no matter what reference frame you are in. The rest you will find in Einstein's book.


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## aleazk

science said:


> This is pretty awesome.
> 
> My first question is: I had one year of calculus in high school, which I should of course review. But from there, what specifically would I need to study in order to understand
> 
> a) Laplace's celestial mechanics?
> b) Maxwell's equations?


from the mathematical point of view, you will need a rather good knowledge of multivariable calculus (differential and integral), ordinary and partial differential equations. man, those topics you want are rather advanced, i.e., college level physics and math.


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## science

aleazk said:


> from the mathematical point of view, you will need a rather good knowledge of multivariable calculus (differential and integral), ordinary and partial differential equations. man, those topics you want are rather advanced, i.e., college level physics and math.


Thank you!

So -

1. Multivariable Calculus 
2. Linear Algebra
3. Differential Equations
4. Introduction to Partial Differentiation

Would that do me? I think I can handle 4 semesters of study. I might even be able to teach myself multivariable.

Is that just to get to Laplace, or does that get me to Maxwell?


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## jalex

Chris said:


> This is a puzzle I saw some time ago. I remember the answer (which I will not reveal) but not the reasoning behind it. The question is: If the universe was made entirely of water, but with air bubbles scattered throughout it, under the influence of gravity would those bubbles tend to:
> 
> 1. converge
> 2. move further apart
> 3. neither


Layman's guess: move farther apart?


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## Philip

science said:


> Thank you!
> 
> So -
> 
> 1. Multivariable Calculus
> 2. Linear Algebra
> 3. Differential Equations
> 4. Introduction to Partial Differentiation
> 
> Would that do me? I think I can handle 4 semesters of study. I might even be able to teach myself multivariable.
> 
> Is that just to get to Laplace, or does that get me to Maxwell?


to get to the Maxwell equations, you need to take an Electricity and magnetism class. the prerequisites are usually Advanced calculus and Ordinary differential equations. i'm not familiar with the Laplace celestial mechanics, but i'd take this on more as a historical topic rather than a current theory.

instead i'd look into the Laplace transform, which is a generalization of the Fourier transform, since it might help you if you ever feel the urge to tackle Signals and systems or quantum mechanics.


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## Chris

Just thinking again about that puzzle. If the universe was made of water I suppose you couldn't have it starting from a Big Bang theory. Everything would have just got soaked.


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## science

Philip said:


> to get to the Maxwell equations, you need to take an Electricity and magnetism class. the prerequisites are usually Advanced calculus and Ordinary differential equations. i'm not familiar with the Laplace celestial mechanics, but i'd take this on more as a historical topic rather than a current theory.
> 
> instead i'd look into the Laplace transform, which is a generalization of the Fourier transform, since it might help you if you ever feel the urge to tackle Signals and systems or quantum mechanics.


Thank you. I might actually do this. I like math and I love history, and I've found that my students like them more together than separate. But sadly, I really can't do much in the 19th century.


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## TrazomGangflow

aleazk said:


> tv=te.sqrt (1-v^2/c^2). tv=1/2.te, then: 1/2=sqrt (1-v^2/c^2) --> 1/4=1-v^2/c^2 --> v^2/c^2=1-1/4=3/4 --> v^2=3/4.c^2 --> v=sqrt (3)/2.c !! v=0,86.c


Ok. Just give me some time to mull it over. I'm still on the first letter.


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## Dodecaplex

aleazk said:


> tv=te.sqrt (1-v^2/c^2). tv=1/2.te, then: 1/2=sqrt (1-v^2/c^2) --> 1/4=1-v^2/c^2 --> v^2/c^2=1-1/4=3/4 --> v^2=3/4.c^2 --> v=sqrt (3)/2.c !! v=0,86.c
> 
> 
> TrazomGangflow said:
> 
> 
> 
> Ok. Just give me some time to mull it over. I'm still on the first letter.
Click to expand...

You should have been informed that aleazk suffers from Physicsitis, a deadly disease that forces physicists into showing off their ultra-magnificent-physics-solving abilities. But worry not, faithful acquaintance, for I shall explain it to you. What aleazk wanted to say was:

(time) (velocity) = (time) (2.718) (sqrt (1-velocity^2 / speed of light^2) )
(time) (velocity) = (1/2) (time) (2.718), then: 1/2 = sqrt (1-velocity^2 / speed of light^2)
1/4 = 1-velocity^2/speed of light^2
velocity^2/ speed of light^2 = 1- 1/4 = 3/4
velocity^2 = (3/4) (speed of light^2) 
velocity = sqrt (3) / (2) (speed of light) !!
velocity = (0.86) (speed of light)

I'm just translatin'.
Edit: Forget about _e_. I was gravely mistaken, indeed.


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## Chrythes

TrazomGangflow said:


> Ok. Just give me some time to mull it over. I'm still on the first letter.


I believe only the last letters count - you'll need to travel around 86% of C (light speed) to reach such a ratio of time difference (1:2). You'll be needing to travel around 257k Km/h if i understand correctly.


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## aleazk

TrazomGangflow said:


> Ok. Just give me some time to mull it over. I'm still on the first letter.


tv is the time elapsed for the guy traveling at the velocity v and te is the time elapsed on earth. tv=te.sqrt (1-v^2/c^2) is the standard relativistic time delay formula


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## pjang23

Which area of mathematics caused you the most nightmares? 

Functional analysis, differential geometry, topology, algebra, measure theory, etc...

Also, what was most helpful?


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## aleazk

pjang23 said:


> Which area of mathematics caused you the most nightmares?
> 
> Functional analysis, differential geometry, topology, algebra, measure theory...
> 
> Also, what was most helpful?


well, differential geometry and topology are the basics for general relativity, i found them very fun to learn. For a physicist, the exposition of both topics given in Wald's "general relativity" (1984), is a good introduction, for the former specially. The most subtle details of functional analysis require a very good disposition from the student. All these topics are essential for a theoretical physicist.


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## Couchie

I'm kind of uncertain about the Uncertainty Principle. What is that about?


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## Igneous01

Couchie said:


> I'm kind of uncertain about the Uncertainty Principle. What is that about?


I think i can explain this:

Uncertainty principle states that you cannot know both the momentum and position of a particle (electron) at the same time. This is because when trying to measure the particle, you need photons to hit it in order to be able to track it. When the photons collide with the electron, they change the electrons velocity and momentum, causing the electron to change its "flight path".

If you measure the momentum of the particle, you cannot get its position because it has changed because of collision. If you measure the position of the particle, you cannot get its momentum because it has been changed because of collision.

you cant measure both at the exact same time.

btw, if I am wrong, enlighten us further


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## Couchie

That begs the question: what is momentum?


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## Igneous01

product of mass and velocity - kg*m/s or better known as Newtons*s

I cant really explain it further (as I forgot, havnt taken physics in a year or so)

you can extrapolate the velocity from an objects momentum assuming its mass remains constant (mass is constant in classical mechanics for particles I THINK)

Im not sure how this translates in quantum mechanics, as an electron can loose its mass to certain phenomena

if you know the velocity of the particle and its position at the same time, you can predict the particles "line" of travel and easily locate it and do much more. Hence why uncertainty principle exists, because you cant predict where an electron will be nor can you find its "line" of travel. Theres a chance the electron will go somewhere random. hence Einstein's famous response to Heisenberg "God does not play dice".


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## mmsbls

Momentum is simply the mass times the velocity of any object.

Igneous01's answer is basically correct. The uncertainty principle states that there are pairs of observables (like position and momentum) that can never be known to better than a specific precision. More accurately, in any observation the product of the uncertainty of these observables must be greater than a fixed number. That number is extremely small so you would never notice this effect without extraordinary instruments. Another pair of observables is energy and time. Their uncertainty has the same constraint.

This uncertainty is not something that we can overcome with better and better instruments. It is a fundamental feature of reality.


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## Couchie

Is that fixed number related to the Planck constant?


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## mmsbls

It is indeed! It is exactly Planck's constant divided by 4*pi.


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## Philip

Igneous01, what you're saying is true, but it is not the reason for the uncertainty principle. Even if you don't measure anything, the uncertainty still holds... thus the implications are much deeper.

The uncertainty principle is actually quite easy to understand... once you wrap your mind around the premise of quantum mechanics: the particles are also waves, hence the "wave-particle duality". The interpretation of the wave function is that its square modulus (value to the power of 2) represents the probability density of the particle's position. In 3D, eg. in the hydrogen atom, an electron forms a probability cloud around the nucleus.

With that in mind, it is quite obvious that probability and uncertainty are an intrinsic part of quantum mechanics. The uncertainty principle comes into play when you relate the particle's position to its momentum. The momentum is simply the rate of change of the position (velocity) times its mass. From there, we note that if the position is non-deterministic, the momentum will also share this nature.

So... what is the relation between the position and momentum wave functions? The Fourier transform! The FT of the position wave function is precisely the momentum wave function. To anyone familiar with the FT, this reveals the behaviour of both functions in relation to one another: the more precise the position, the more imprecise the momentum, and vice versa. Therefore, the uncertainty principle has nothing to do with measurement, nor the precision of the measuring apparatus.


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## Igneous01

Couchie said:


> Is that fixed number related to the Planck constant?


Planck's Constant is the physical size of energy quanta (also called 'packets') it is believed that particles like photons cannot be reduced to smaller particles, and so a cluster of photons is the smallest unit in reality, this cluster is called a 'packet' or quanta.

so, planck's constant states that energy quanta (smallest unit of energy) is constrained to be a certain size and that this size is always constant.


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## Igneous01

Philip said:


> Igneous01, what you're saying is true, but it is not the reason for the uncertainty principle. Even if you don't measure anything, the uncertainty still holds... thus the implications are much deeper.
> 
> The uncertainty principle is actually quite easy to understand... once you wrap your mind around the premise of quantum mechanics: the particles are also waves, hence the "wave-particle duality". The interpretation of the wave function is that its square modulus (value to the power of 2) represents the probability density of the particle's position. In 3D, eg. in the hydrogen atom, an electron forms a probability cloud around the nucleus.
> 
> With that in mind, it is quite obvious that probability and uncertainty are an intrinsic part of quantum mechanics. The uncertainty principle comes into play when you relate the particle's position to its momentum. The momentum is simply the rate of change of the position (velocity) times its mass. From there, we note that if the position is non-deterministic, the momentum will also share this nature.
> 
> So... what is the relation between the position and momentum wave functions? The Fourier transform! The FT of the position wave function is precisely the momentum wave function. To anyone familiar with the FT, this reveals the behaviour of both functions in relation to one another: the more precise the position, the more imprecise the momentum, and vice versa. Therefore, the uncertainty principle has nothing to do with measurement, nor the precision of the measuring apparatus.


interesting, so these two functions share an inverse relationship to each other?

question: do these functions only show (prove) uncertainty on paper (calculated)?

Perhaps im not thinking about this clearly, but if you are to increase precision on the position of a wave function, how does it make the momentum wave function loose precision? Is there a physical example or phenomena (besides measuring) that shows this?

Thanks for the insight, my knowledge of UP is not very large, so thanks for sharing


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## Couchie

I scratched the surface of this stuff in 2nd year university where we did a bit of computational quantum chemistry, predicting the structures of compounds and so forth, so it's ringing very distant bells. Of course, the computers did all the heavy lifting, I just had to drop atoms into the program and examine the molecular orbitals. Are what I know as molecular orbitals the square modulus of this wave function (is that the Schrödinger equation?) for the entire molecule?


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## Igneous01

one more question:

what is the field of cymatics? I have seen experiments on youtube showing matter form geometric shapes and patterns when vibrating at a specific frequency - but does it provide insight/relate to anything in quantum mechanics or general relativity?


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## Philip

Igneous01 said:


> interesting, so these two functions share an inverse relationship to each other?
> 
> question: do these functions only show (prove) uncertainty on paper (calculated)?
> 
> Perhaps im not thinking about this clearly, but if you are to increase precision on the position of a wave function, how does it make the momentum wave function loose precision? Is there a physical example or phenomena (besides measuring) that shows this?
> 
> Thanks for the insight, my knowledge of UP is not very large, so thanks for sharing


Yes, in fact you can visualize what the minimum uncertainty waves look like by thinking in terms of Fourier transforms: they are normalized Gaussians, or "bell" curves. Incidentally, the FT of a Gaussian is another Gaussian, together they form the minimum total uncertainty possible.

You can develop your instinct of FTs by looking at graphs of standard curves, and see what their FTs look like. The application of these principles is quite revealing in signal theory, hence audio and music.


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## Couchie

Philip said:


> Yes, in fact you can visualize what the minimum uncertainty waves look like by thinking in terms of Fourier transforms: they are normalized Gaussians, or "bell" curves. Incidentally, the FT of a Gaussian is another Gaussian, together they form the minimum total uncertainty possible.
> 
> You can develop your instinct of FTs by looking at graphs of standard curves, and see what their FTs look like. The application of these principles is quite revealing in signal theory, hence audio and music.


Is a Fourier transform like a Laplace Transform?

We use Laplace Transforms to determine whether process control schemes will be stable or blow up, I still have no idea what the hell they are.


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## Philip

Igneous01 said:


> one more question:
> 
> what is the field of cymatics? I have seen experiments on youtube showing matter form geometric shapes and patterns when vibrating at a specific frequency - but does it provide insight/relate to anything in quantum mechanics or general relativity?


I'm not familiar with the field, but the most insightful analogy of wave functions that i can think of, at least for myself, is an experiment that almost anyone who has taken a HS physics class has done: take a long rope, give the other end to a partner, and... agitate the rope until it forms a standing wave, with nodes. The more energy you input into rope, the more nodes appear. These are the quantized energy levels. Depending on the energy, the rope "jumps" from one stationary state to another.

There are requirements, for example the ends must stay put, ie. the wave function is _a priori_ continuous, and since it is null beyond your hands, it must also be zero at your hands. There are other requirements (eg. normalization), but i don't wish to take this analogy any further...

At this point, you have to interpret the wave as a probability density (when squared). Therefore you know that the particle is between the two ends... but you can't tell exactly where it is... take the FT of this function, you get the momentum function of the particle described by that position wave function.

This is a one dimensional example, which is pretty much the same thing as the particle in a 1D box example. In 2D, the wave functions look like vibration patterns on a drum. In 3D, they look like the density clouds in an atom.

Note that the quantized energy levels only appear when the particle is restrained, or bounded, eg. like the rope in our example is bounded by two hands, the drum by the attached circumference, and the electron by the limited surface area of the nucleus. A free particle can have any energy level.


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## Philip

Couchie said:


> Is a Fourier transform like a Laplace Transform?
> 
> We use Laplace Transforms to determine whether process control schemes will be stable or blow up, I still have no idea what the hell they are.


The Laplace transform expresses a function in terms of exponentials, sines and cosines; the Fourier transform expresses it only in terms of the sines and cosines. Practically, the FT is useful to show a signal's frequency content. As opposed to the LT which describes a system's behavior more generally.


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## Scarpia

Igneous01 said:


> Planck's Constant is the physical size of energy quanta (also called 'packets') it is believed that particles like photons cannot be reduced to smaller particles, and so a cluster of photons is the smallest unit in reality, this cluster is called a 'packet' or quanta.
> 
> so, planck's constant states that energy quanta (smallest unit of energy) is constrained to be a certain size and that this size is always constant.


This is not quite right. Planck's constant is not an energy. Energy is quantized, but the unit of energy is not the same in all situations. For a photon, the energy is Planck's constant times the frequency of the light, so that blue photons have more energy than red photons. For particles such as electrons the formulae for energy involve Planck's constant but also involve the mass of the particle and geometry of the state.


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## Scarpia

Philip said:


> So... what is the relation between the position and momentum wave functions? The Fourier transform! The FT of the position wave function is precisely the momentum wave function. To anyone familiar with the FT, this reveals the behaviour of both functions in relation to one another: the more precise the position, the more imprecise the momentum, and vice versa. Therefore, the uncertainty principle has nothing to do with measurement, nor the precision of the measuring apparatus.


I you don't know the math of Fourier transforms, an analogy with sound can be effective, since to some approximation the ear performs a Fourier transform.

If a waveform has a well defined frequency (pitch) it has to go on for a long time (like a note from an organ pipe). If a note is very short (like a whack on a snare drum) is can't have a very well defined frequency (pitch). In quantum mechanics the position of a particle in spaces is represented by a wave. Position is analogous to the duration of the sound wave and momentum analogous to frequency. If a particle has an exact position the momentum is ill-defined (the snare drum whack) and if the momentum is well defined, it is not well located in space (the organ pipe tone).


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## Igneous01

Scarpia said:


> This is not quite right. Planck's constant is not an energy. Energy is quantized, but the unit of energy is not the same in all situations. For a photon, the energy is Planck's constant times the frequency of the light, so that blue photons have more energy than red photons. For particles such as electrons the formulae for energy involve Planck's constant but also involve the mass of the particle and geometry of the state.


thanks for the correction 

i meant to say that Plancks constant is a number that is used to calculate quanta - did not mean it as defined unit of energy quanta


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## aleazk

Igneous01 said:


> interesting, so these two functions share an inverse relationship to each other?
> 
> question: do these functions only show (prove) uncertainty on paper (calculated)?
> 
> Perhaps im not thinking about this clearly, but if you are to increase precision on the position of a wave function, how does it make the momentum wave function loose precision? Is there a physical example or phenomena (besides measuring) that shows this?
> 
> Thanks for the insight, my knowledge of UP is not very large, so thanks for sharing


in quantum mechanics, observables are represented mathematically by linear operators in a hilbert space. the commutator of two operators is defined as (for operators x and p here) [x, p]=xp-px . if the commutator between the two is zero, then the measurement of one of the observables does not affect the value of the other (compatible observables). In the case of the spin, S^2 commutes with Sz, so you can measure both quantities simultaneously, and they will be well defined (mathematically, if the commutator is zero, both operators have the same eigenstates). if the commutator is not zero, then the measurement of one of the observables _does_ affect the value of the other (they don't have the same eigenstates). taking the spin example again, Sz and Sx don't commute, so if you measure Sz first, and you get say "up", and then Sx, and then Sz again, you can get both up or down , the measurement of Sx destroyed the previous information about Sz! (incompatible observables). The UP is a consequence of this last situation, and can be proved mathematically that this is the case.


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## Couchie

Can our physicist friends recommend a good introductory book/textbook on particle physics (standard model)? Ideally this book would not be too "layman" but be at about the undergraduate physics level, would go into the math assuming a basic foundation in linear algebra, calculus, etc, but would also assume the reader is entirely unfamiliar with the math so as to present a good explanation? Thanks.


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## aleazk

Couchie said:


> Can our physicist friends recommend a good introductory book/textbook on particle physics (standard model)? Ideally this book would not be too "layman" but be at about the undergraduate physics level, would go into the math assuming a basic foundation in linear algebra, calculus, etc, but would also assume the reader is entirely unfamiliar with the math so as to present a good explanation? Thanks.


_An Introduction To Quantum Field Theory_, by _Michael E. Peskin, Daniel V. Schroeder_ is a standard basic introduction (at the graduate level). I particularly liked the first chapters about canonical quantization. You need only a standard undergraduate background in physics for that book (although you must be very well versed in that background; special relativity and classical field theory, nonrelativistic quantum mechanics and linear algebra, fourier transforms and dirac delta functions, integration on the complex plane, some group theory).


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## Philip

Couchie said:


> Can our physicist friends recommend a good introductory book/textbook on particle physics (standard model)? Ideally this book would not be too "layman" but be at about the undergraduate physics level, would go into the math assuming a basic foundation in linear algebra, calculus, etc, but would also assume the reader is entirely unfamiliar with the math so as to present a good explanation? Thanks.


I think there's only a couple books that are in comprehensible language...


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## Couchie

aleazk said:


> _An Introduction To Quantum Field Theory_, by _Michael E. Peskin, Daniel V. Schroeder_ is a standard basic introduction (at the graduate level). I particularly liked the first chapters about canonical quantization. You need only a standard undergraduate background in physics for that book (although you must be very well versed in that background; special relativity and classical field theory, nonrelativistic quantum mechanics and linear algebra, fourier transforms and dirac delta functions, integration on the complex plane, some group theory).


As I have but a simple engineering undergrad, that definitely sounds like running before walking. A good book on "nonrelativistic quantum mechanics"?


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## aleazk

Couchie said:


> As I have but a simple engineering undergrad, that definitely sounds like running before walking. A good book on "nonrelativistic quantum mechanics"?


well, Quantum Field Theory is really very advanced physics, even for physicists, in QTF you use all your background as a graduate physicist. I'm really starting in QFT now, since I went to General Relativity first. But anyway, your background as an engineering undergrad is a good start. You will need also some physics. Some of the topics are:

-Lagrangian formulation, in classical mechanics (Analytical Mechanics). The Lagrangian formulation is a mathematical reformulation of the classical laws of mechanics, a good book is _H. Goldstein, C. Poole, J. Safko, Classical Mechanics_.
-Electromagnetism and Special Relativity. You will need to know some basic Special Relativity and how to formulate Maxwell's equations in Special Relativity. Once you have that, you need to formulate Maxwell's equations (in the context of Special Relativity) in the Lagrangian formulation. This is known as 'classical field theory'. Standard references for all this are _Classical Electrodynamics, John David Jackson_, _Introduction to electrodynamics, David Jeffery Griffiths_ and _Classical electromagnetic radiation, Jerry B. Marion_. Also in Goldstein's book you will find some Special Relativity.
-Standard, nonrelativistic, Quantum Mechanics. Of course, since we want to quantize something . A nice, 'first principles', introduction is _Modern Quantum Mechanics, J. J. Sakurai_. Although you may want to supplement that with some advanced linear and multilinear algebra (Hilbert space, operator theory, etc.). Almost any mathematics book which is relatively rigorous in these topics is useful (the problem with Sakurai's introduction is that some of the mathematics presented are not very rigorous, the physics is fine, however). Some 'wave function approach' to Dirac's equation is sometimes covered, but I think that is not really necessary and can be conceptually misleading.


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## Petwhac

As a complete layman who likes to read popular science books I have a question regarding radiation.

As I understand it, the smaller the wavelength/higher frequency the more damage it can cause to cells, tissues or organs. Ultra- violet, X-rays, Gamma. So, if microwaves are at the bigger end of the spectrum are they less harmful than visible light and infra-red. How do microwave ovens work (I know it's something to do with vibrating water molecules) is it to do with intensity rather than wavelength?
I always poo-poo people when they say not to stand too close to a microwave oven or to let the food rest for a minute which is surly nothing to do with radioactivity but merely to let the heat spread evenly.


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## emiellucifuge

Microwaves work by producing a magnetic field. Polar molecules such as water will try to align with the field and in the process they will collide with eachother producing heat energy.


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## aleazk

Petwhac said:


> As a complete layman who likes to read popular science books I have a question regarding radiation.
> 
> As I understand it, the smaller the wavelength/higher frequency the more damage it can cause to cells, tissues or organs. Ultra- violet, X-rays, Gamma. So, if microwaves are at the bigger end of the spectrum are they less harmful than visible light and infra-red. How do microwave ovens work (I know it's something to do with vibrating water molecules) is it to do with intensity rather than wavelength?
> I always poo-poo people when they say not to stand too close to a microwave oven or to let the food rest for a minute which is surly nothing to do with radioactivity but merely to let the heat spread evenly.


So, your question is why microwaves and no other waves?. It has to do with the _frequency-dependent response of water molecules._ From an online source:



> Under low frequency irradiation, the dipole may react by aligning itself in phase with the electric field. Whilst some energy is gained by the molecule by this behaviour, and some is also lost in collisions, the overall heating effect is small. Under the influence of a high frequency electric field, on the other hand, the dipoles do not have sufficient time to respond to the field, and so do not rotate. As no motion is induced in the molecules, no energy transfer takes place, and therefore, no heating.
> 
> Between these two extremes, at frequencies which are approximately those of the response times of the dipoles, is the microwave region. The microwave frequency is low enough that the dipoles have time to respond to the alternating field, and therefore to rotate, but high enough that the rotation does not precisely follow the field. As the dipole reorientates to align itself with the field, the field is already changing, and a phase difference exists between the orientation of the field and that of the dipole. This phase difference causes energy to be lost from the dipole in random collisions, and to give rise to dielectric heating.


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## Petwhac

@ aleazk and emiel,
So microwaves are as harmless? A microwave oven can only hurt you if you are in it? Food heated that way is harmless even straight away? I have been assuming the answer to be yes but thought I'd run it by some experts.


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## brianwalker

Where are the selectrons?


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## Philip

Petwhac said:


> @ aleazk and emiel,
> So microwaves are as harmless? A microwave oven can only hurt you if you are in it? Food heated that way is harmless even straight away? I have been assuming the answer to be yes but thought I'd run it by some experts.


Put a body part or an animal test subject in a microwave oven and you will find out... but if you stand outside, the amplitude of the microwaves decrease exponentially beyond the metal mesh window. In other words, it may heat up your face if you stick it right in the door.


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## aleazk

Adding to Philip's comment. Microwaves are not an _ionizing radiation_, they are not sufficiently energetic as to ionize your atoms. Ionizing radiation (like gamma rays) can even break DNA molecules, which is catastrophic, since this can lead to cancer and all those well known effects. Microwaves are going to heat you only, because you have water in your body. But careful, since excessive heat can also alter the body chemistry.


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## Petwhac

OK thanks phillip and aleazk, got it.
Next....
Do mobile phones (cell phones) use microwaves and are there any dangers or just scare stories.


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## aleazk

According to the WHO, there's no risk:

http://www.who.int/mediacentre/factsheets/fs193/en/


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## Crudblud

Nah, it's the internet that'll kill you.


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## Petwhac

Crudblud said:


> Nah, it's the internet that'll kill you.


It kills time that's for sure. But it's pretty cool that I can sit in my living room and have real live physicists answer my questions.


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## Petwhac

aleazk said:


> According to the WHO, there's no risk:
> 
> http://www.who.int/mediacentre/factsheets/fs193/en/


Thanks for that.


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## EddieRUKiddingVarese

My head hurts now


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## Becca

EddieRUKiddingVarese said:


> My head hurts now


Then either take it out of the microwave or turn off same.


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## EddieRUKiddingVarese

Will a tin hat help


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## EddieRUKiddingVarese

Does Physics answer why Donald's hair looks like it does?


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## EddieRUKiddingVarese

How does on Pardon ones self without disappearing in a puff of hypocrisy?


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## Richannes Wrahms

Which are the best books for introductory level physics and math?


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## Guest

See if I can get an answer to this. In my field, I use a flow cytometer, which utilizes lasers to excite fluorescent molecules to characterize small particles (cells, bacteria, etc.). Most lasers have a gaussian profile of energy emission - the most energetic part of the beam is in a very narrow range, and so laser alignment is constantly a concern as you want the fluorescent molecules to receive maximum excitation. The cytometer I use, though, has what are called "flat-top lasers" where the range of maximum excitation is broadened - to about 50 microns. How is that accomplished?


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## philoctetes

DrMike said:


> See if I can get an answer to this. In my field, I use a flow cytometer, which utilizes lasers to excite fluorescent molecules to characterize small particles (cells, bacteria, etc.). Most lasers have a gaussian profile of energy emission - the most energetic part of the beam is in a very narrow range, and so laser alignment is constantly a concern as you want the fluorescent molecules to receive maximum excitation. The cytometer I use, though, has what are called "flat-top lasers" where the range of maximum excitation is broadened - to about 50 microns. How is that accomplished?


Solid state lasers can be very adaptable, that might be your answer. Your use of dimensions is confusing not sure if you mean beam width or wavelength...

solid-state lasers can also be tunable using several intracavity techniques, which employ etalons, prisms, and gratings, or a combination of these.[5] Titanium-doped sapphire is widely used for its broad tuning range, 660 to 1080 nanometers. Alexandrite lasers are tunable from 700 to 820 nm and yield higher-energy pulses than titanium-sapphire lasers because of the gain medium's longer energy storage time and higher damage threshold.

https://en.wikipedia.org/wiki/Solid-state_laser


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## philoctetes

Enlightening books on physics would include Feynman's lectures and his Theory of Fundamental Processes...


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## KenOC

Question: I more or less understand the relativity thing, special relativity anyway. There’s no absolute velocity or even absolute direction except in relation to other objects and frames of reference. But I imagine that if I were somewhere in empty space with a weight on a rope, it might simply drift. But if I fired my spacesuit’s thrusters to rotate me, it would rise and make a circle around me, pulling on my arms even in the absence of gravity – just as it does on Earth.

If so, it seems that rotation must be “absolute”. So my question is, “absolute” in relation to what?


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## senza sordino

KenOC said:


> Question: I more or less understand the relativity thing, special relativity anyway. There's no absolute velocity or even absolute direction except in relation to other objects and frames of reference. But I imagine that if I were somewhere in empty space with a weight on a rope, it might simply drift. But if I fired my spacesuit's thrusters to rotate me, it would rise and make a circle around me, pulling on my arms even in the absence of gravity - just as it does on Earth.
> 
> If so, it seems that rotation must be "absolute". So my question is, "absolute" in relation to what?


Yes, relativity is a challenge. Has your question something to do with the equivalence principle? That rotation is indistinguishable from a gravitational field. From here, I can't help. I'm just a humble high school teacher.


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## aleazk

KenOC said:


> Question: I more or less understand the relativity thing, special relativity anyway. There's no absolute velocity or even absolute direction except in relation to other objects and frames of reference. But I imagine that if I were somewhere in empty space with a weight on a rope, it might simply drift. But if I fired my spacesuit's thrusters to rotate me, it would rise and make a circle around me, pulling on my arms even in the absence of gravity - just as it does on Earth.
> 
> If so, it seems that rotation must be "absolute". So my question is, "absolute" in relation to what?


In any of the relativity theories, 4-acceleration is absolute. That is, you either follow a spacetime geodesic or not (in that case, you have a non-zero 4-acceleration.) Given your spacetime trajectory, what determines if it's a spacetime geodesic is the spacetime metric g, which is the same entity that determines or models the gravitational field. You don't need anything else, like, e.g., a reference frame, hence the "absolute".


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## KenOC

aleazk said:


> In any of the relativity theories, 4-acceleration is absolute. That is, you either follow a spacetime geodesic or not (in that case, you have a non-zero 4-acceleration.) Given your spacetime trajectory, what determines if it's a spacetime geodesic is the spacetime metric g, which is the same entity that determines or models the gravitational field. You don't need anything else, like, e.g., a reference frame, hence the "absolute".


Thanks! Your explanation was a bit opaque to me, so I checked Wiki's entry on "absolute rotation", which was interesting. It discusses Mach's principle: "The idea is that the local motion of a rotating reference frame is determined by the large-scale distribution of matter in the universe. Mach's principle says that there is a physical law that relates the motion of the distant stars to the local inertial frame. If you see all the stars whirling around you, Mach suggests that there is some physical law which would make it so you would feel a centrifugal force. The principle is often stated in vague ways, like 'mass out there influences inertia here'." To me, that seems unsatisfying.

The entry concludes by discussing general relativity and says, "In general relativity, no external causes are invoked. The rotation is relative to the local geodesics…" I'm not sure I fully understand that, but it seems to have at least the flavor of what you wrote…


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## aleazk

Well, rotation is a tricky subject in GR. The first thing you must have in mind is that "(locally) inertial" motion is defined by your spacetime trajectory being a spacetime geodesic. But in the vicinity of heavy rotating objects, like a rotating black hole or even Earth, you have an effect called "frame dragging" in which the geodesics themselves are dragged in the direction of rotation. But, how can we even know when geodesics rotate if (usually) one thinks of rotation as something defined with respect to the geodesics. And, again, the answer is that in GR you can define the rotation of a congruence of geodesics in an absolute and intrinsic way: https://en.m.wikipedia.org/wiki/Raychaudhuri_equation (called "vorticity" there.) It's a central notion that is used in many results in GR.


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## KenOC

aleazk said:


> Well, rotation is a tricky subject in GR. The first thing you must have in mind is that "(locally) inertial" motion is defined by your spacetime trajectory being a spacetime geodesic. But in the vicinity of heavy rotating objects, like a rotating black hole or even Earth, you have an effect called "frame dragging" in which the geodesics themselves are dragged in the direction of rotation. But, how can we even know when geodesics rotate if (usually) one thinks of rotation as something defined with respect to the geodesics. And, again, the answer is that in GR you can define the rotation of a congruence of geodesics in an absolute and intrinsic way: https://en.m.wikipedia.org/wiki/Raychaudhuri_equation (called "vorticity" there.) It's a central notion that is used in many results in GR.


Thanks (again) for that. I'm pretty sure I understand this at least a little better than I did!


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## Sad Al

This isn't a question but a drop of the endless ocean that is my wisdom.
Light is outside time because it is always new. However, it is also inside spacetime. Therefore light is inside space but outside time.


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## Guest

philoctetes said:


> Solid state lasers can be very adaptable, that might be your answer. Your use of dimensions is confusing not sure if you mean beam width or wavelength...
> 
> solid-state lasers can also be tunable using several intracavity techniques, which employ etalons, prisms, and gratings, or a combination of these.[5] Titanium-doped sapphire is widely used for its broad tuning range, 660 to 1080 nanometers. Alexandrite lasers are tunable from 700 to 820 nm and yield higher-energy pulses than titanium-sapphire lasers because of the gain medium's longer energy storage time and higher damage threshold.
> 
> https://en.wikipedia.org/wiki/Solid-state_laser


Sorry, just getting back to you.

So the 50 microns refers to the beam width, not the wavelength. We do have 4 different solid-state lasers - a blue, a red, a yellow, and a violet, that are coupled to fiber optics that deliver the excitation light to an interrogation point where cells are streamed. But there is a beam-shaping optic in between that is able to, as I understand it, convert the laser beam from having a gaussian profile in terms of maximal energy, to a flat-top gaussian profile where the beam width for maximal energy is increased to 50 microns (not sure what the standard width is in a normal gaussian profile. Just wondering how that is accomplished.


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## philoctetes

DrMike said:


> Sorry, just getting back to you.
> 
> So the 50 microns refers to the beam width, not the wavelength. We do have 4 different solid-state lasers - a blue, a red, a yellow, and a violet, that are coupled to fiber optics that deliver the excitation light to an interrogation point where cells are streamed. But there is a beam-shaping optic in between that is able to, as I understand it, convert the laser beam from having a gaussian profile in terms of maximal energy, to a flat-top gaussian profile where the beam width for maximal energy is increased to 50 microns (not sure what the standard width is in a normal gaussian profile. Just wondering how that is accomplished.


Lens design voodoo, you can stack enough lenses to do anything... but It's not cheap

https://www.edmundoptics.com/f/flat-top-beam-shapers/15036/

A simple lens acts like a Fourier transform, a more complex one redistributes the radial energy to form a different shape...

In audio... to get that kind of flatness (see the beam profile) means that the odd-order harmonics are being boosted over the even-order ones... not sure how that's done optically but there is a lot of tech info on this site....

Edit: I think the optical solution would be to use a filter in the fourier domain that blocks the even spatial harmonics, in audio it's done with op amp or tube clipping ...

Either way some power may be lost but I assume that the ends justifies the means... just use a more powerful laser...

getting a major hailstorm as I type...


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## philoctetes

In addition to lenses, mirrors can be especially useful for shaping wavefronts... so they may be part of the system... I'm not an optics person but I designed algorithms for optical systems my whole career... one of the best references is Introduction to Fourier Optics by Goodman

I'm thinking about mirrors maybe being used to flip even orders to odd orders... or some kind of phase delay...


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## philoctetes

Sad Al said:


> This isn't a question but a drop of the endless ocean that is my wisdom.
> Light is outside time because it is always new. However, it is also inside spacetime. Therefore light is inside space but outside time.


As they say, light is on the spacetime cone... and we live inside it, like Maxwell Smart


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## philoctetes

philoctetes said:


> In addition to lenses, mirrors can be especially useful for shaping wavefronts... so they may be part of the system... I'm not an optics person but I designed algorithms for optical systems my whole career... one of the best references is Introduction to Fourier Optics by Goodman
> 
> I'm thinking about mirrors maybe being used to flip even orders to odd orders... or some kind of phase delay...


So... I think they can delay phase simply with different refraction indices... they can probably engineer glass to their specs... so with a lens that uses phase delays, shifting even spatial components into odd, the beams can be flattened without energy loss... and that's my answer off the top o my head...


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