/sci/ - Science & Math

>>6584995
Oops, I meant km/s. change all hours to seconds please! Not that it really matters, the point still sort of remains intact.

>>6584995
The absence of an ether sort of proved it indirectly
>nothing tells me that time should stop at light and light only
its implied by the lorentz factor

>>6585034
Can you explain Lorentz factor in layman's terms? Google was pretty complicated

>>6585045
Try this visualization
http://www.youtube.com/watch?v=C2VMO7pcWhg

>>6585045
Different anon here. Observe this equation taken directly from Einstein's book on his theory. Notice how a velocity equal to c results in a zero in the denominator.

>>6585066
Shit... wrong image. Sorry.

>>6584995
>What factor behind Einstein's idea decides that light is the fastest?
There's a whole history behind the development of special relativity.

First came Maxwell's equations. They predicted an absolute speed of light.

In order to make physics work with an "absolute reference frame", people invented the concept of a luminiferous aether.

However, experiments failed with this. Also, some mathematicians and physicists figured out that that although Maxwell's equations aren't Galilean-invariant, they were invariant under a new kind of transformation called Lorentz transformations.

Einstein figured out that this wasn't just some quirk of the equations, that this was really how space and time behave. From this he figured out all of special relativity.

>>6585059
WOW!!!! THANKS!

>>6585066
The math is what I struggle with. I will be looking at this for awhile now. Thank you.

>>6585083
This is your answer OP

>>6585087
Can you provide a site that describes Maxwell's equations in ways that someone who may not be well attuned to math may understand? Whenever I use google they immediately bombard me with the heavy-duty stuff and never begin from the beginning. They always assume that I have been equipped with the knowledge up to that point where it is discussable.

Thank you.

>>6585094
>Can you provide a site that describes Maxwell's equations in ways that someone who may not be well attuned to math may understand?
Nope.

If you want to learn this stuff and actually understand it, you have to do the math. There's no way around it.

>>6585094
Physics is understood through the math, not the stories.

>>6585094
Maxwells equation sum up a wave equation, with a non variable wave velocity, the speed of light.

Aka speed of light is a constant no matter where u are

>>6585094
Maxwell's Equations are difficult to understand without understanding the underlying mathematics... but I'll try and break them down a little.

<span class="math">
\nabla \cdot \bar{E}~=~\frac{\rho}{\epsilon_0}
[/spoiler]
<span class="math">
\nabla \cdot \bar{B}~=~0
[/spoiler]
<span class="math">
\nabla \times \bar{E}~=~-\frac{\partial \bar{B}}{\partial t}
[/spoiler]
<span class="math">
\nabla \times \bar{B}~=~{\mu}_{0}\bar{J}~+~{\mu}_{0}{\epsilon}_{0}\frac{\partial \bar{E}}{\partial t}
[/spoiler]

#1 is Gauss's Law for an Electric Field. It states that the <span class="math">divergence[/spoiler] of an electric field is proportional to the <span class="math">charge~density[/spoiler] of the source. That is to say - how much electric field comes from a source depends on how much charge there is and how it's distributed.

#2 is Gauss's Law for a Magnetic Field. The divergence of the field is zero - which means that the amount of magnetic field coming out of a source has to equal the amount flowing back in, or to put it another way - magnetic fields are not monopoles. Magnetic fields start at one point and form a loop that returns to that point (imagine the North and South poles of a bar magnet for example, a magnetic dipole)

#3 is Faraday's Law. It states that the <span class="math">curl[/spoiler] of an electric field is proportional to the rate of change of a corresponding magnetic field. That is to say - a changing magnetic field produces an electric current.

#4 is Ampere's Law (with a little adjustment). The first part of the equation (<span class="math">{\mu}_{0}\bar{J}[/spoiler]) states that the an electric current can produce a magnetic field. And the second term (<span class="math">{\mu}_{0}{\epsilon}_{0}\frac{\partial \bar{E}}{\partial t}[/spoiler]), added by Maxwell says that even if you don't have a current, as long as there is a changing electric field you can still produce a magnetic field.

>>6585392
If we do some math and make a few assumptions, like assuming there's no electric current (<span class="math">J = 0[/spoiler]), we can derive these equations:
<span class="math">
{\nabla}^{2}\bar{E}~=~-{\mu}_{0}{\epsilon}_{0}\frac{{\partial}^{2} \bar{B}}{{\partial t}^{2}}
[/spoiler]
<span class="math">
{\nabla}^{2}\bar{B}~=~-{\mu}_{0}{\epsilon}_{0}\frac{{\partial}^{2} \bar{E}}{{\partial t}^{2}}
[/spoiler]

These are <span class="math">wave~equations[/spoiler], they describe how a wave behaves relative to changes in space and time. These could be sound waves, water waves, or in this case, electromagnetic waves.


In general, a wave equation looks something like:
<span class="math">
{\nabla}^{2}f~=~-\frac{1}{{v}^{2}}\frac{{\partial}^{2}f}{{\partial t}^{2}}
[/spoiler]
Where the way the behavior of the wave depends on a velocity, v.

In the case of electromagnetic waves, we get that

<span class="math">{v}^{2}~=~1/{\mu}_{0}{\epsilon}_{0}~=~1/{c}^{2}[/spoiler]
or simply
<span class="math">v~=~c[/spoiler]


Electromagnetic waves travel through empty space at a constant velocity c, the speed of light.

>>6585392
If we do some math and make a few assumptions, like assuming there's no electric current (<span class="math">J = 0[/spoiler]), we can derive these equations:
<span class="math">
{\nabla}^{2}\bar{E}~=~-{\mu}_{0} {\epsilon}_{0} \frac{{\partial}^{2} \bar{B}}{{\partial t}^{2}}
[/spoiler]
<span class="math">
{\nabla}^{2}\bar{B}~=~-{\mu}_{0} {\epsilon}_{0} \frac{{\partial}^{2} \bar{E}}{{\partial t}^{2}}
[/spoiler]

These are wave equations, they describe how a wave behaves relative to changes in space and time. These could be sound waves, water waves, or in this case, electromagnetic waves.


In general, a wave equation looks something like:
<span class="math">
{\nabla}^{2}f~=~-\frac{1}{{v}^{2}} \frac{ {\partial}^{2}f }{ {\partial t}^{2} }
[/spoiler]
Where the way the behavior of the wave depends on a velocity, v.

In the case of electromagnetic waves, we get that

<span class="math">{v}^{2}~=~1/{\mu}_{0}{\epsilon}_{0}~=~1/{c}^{2}[/spoiler]
or simply
<span class="math">v~=~c[/spoiler]


Electromagnetic waves travel through empty space at a constant velocity c, the speed of light.

>>6585105
>>6585120

>>6585410
>appeal to authority
Irrelevantly quoted, as always. I doubt whether Einstein actually said that.

The point is that you may be able to explain it simply, not that you can explain it simply enough so that others will understand it. To what do you attribute all of Feynman's students failing his class when he's regarded as one of the best physics teachers of all time?

>>6585420
if all students fail is it not bad teaching?

>>6585422
I don't think there's an answer to that question.

The point is that whether or not his students failed he was noted for being able to explain things simply.

both he and einstein are dead so make up some new rules

>>6585410
He anon, haven't been following this thread really but I think about that quote sometimes and here's my view.

I agree with the idea that a good gauge to see if you understand something is whether or not you can explain it simple. But the thing is, (parts of) mathematics can be seen as actually the result of this philosophy adhered to by people over many centuries, trying to understand nature. In other words, it's the accumulation and current consensus of what people think is the least ambiguous, most complete and simplest form to express our understanding of the world.

For example, people have long wondered about stuff like infinity and movement (or change in general), for example in Zeno’s paradox. Before Cantor, Newton, Leibniz and some other smarty-pants, people used to think about infinity as ‘that which is greater than all finite things’. Such a definition may look simple, but the fact that it lead to so many paradoxes when considered more closely shows it isn’t. The development of calculus and set-theory made things a lot simpler, because the theories became more precise, and the concepts better defined. But the consequence is that the theories become richer as well.

The moral here is that you shouldn’t conflate simple with easy and fast to understand. Particularly, advanced topics in science, especially math-heavy stuff, take a long time to understand.

Say for example you are studying at some university. You wouldn’t go to your professor and ask if he could explain his own research in half an hour to you, and go on claiming he doesn’t understand his own research if he says it can’t be done without a proper long road of education.

(cont)

>>6585578
Compare it to explaining how to build a house. You could say: build a foundation, then a wall and put a roof on top. Although very easy and fast to understand, you wouldn’t say that the person you are explaining it to then understands how to build a house.

The thing is, lots of science and math are accumulative, so that understanding higher concepts is only possible by understanding the lower ones. For example relativity theory, as you have seen, rests on other equations, which rest on mathematical concepts, which rest on other mathematical concept, so on until you end up at the high-school level (simply put). But this sequence of steps is very long and it takes years to understand on average. This precisely because all the steps are as simple as possible at the present state of our knowledge.

>>6585410
Just a troll who never tried to explain universal extra-dimensions to laymen.
Brotip: You can't.

>>6585392
>>6585400
Awesome breakdown, thanks!

>>6585045
>Can you explain Lorentz factor in layman's terms? Google was pretty complicated
The faster you travel through space the slower you travel through time (relative to another observer).


So let's say you're travelling in your super awesome spaceship that can go 0.5 c. You want to get to a start that's 10 light years away.
<span class="math">{t}_{me} = \gamma~{t}_{you}[/spoiler] , where
<span class="math">\gamma = \frac{1}{\sqrt{1 - {\beta}^{2}}}[/spoiler] , where
<span class="math">\beta = \frac{v}{c}[/spoiler]


From my frame on Earth, it takes you 20 years. But for you, travelling at 0.5 c:
<span class="math">\gamma = \frac{1}{\sqrt{1 - {0.5}^{2}}}=1.155[/spoiler]
<span class="math">{t}_{you} = \frac{{t}_{me}}{1.155}[/spoiler]
so your trip takes almost three years less from your point of view than from mine

>>6586046
There's 3 things you need to know about special relativity, OP:

1. relativity of simultaneity
2. time dilation
3. length contraction

These are the 3 main "effects" of special relativity.

>>6585595
That pic is hilarious.

In his defense, the meals are where his characters do most of their interactions.

>>6586067
I'm also pretty sure the original caption of that was about deaths

If I have 4 electromagnetic waves; we will call them black, red, green, blue; and I shoot them like this picture shows... and if black passes through red, green, and blue... then does it take (from my perspective) black a slightly longer time to reach the same distance as red?

That is, red was only interfered with 1x so it can go X distance in 1 second while black was interfered with 3x so it can go X distance in slightly more than 1 second.

What do you think?

>>6586082
Photons are non self interacting, meaning no transfer of energy between them as they pass one another.

>source
http://en.wikipedia.org/wiki/Standard_Model#mediaviewer/File:Elementary_particle_interactions_in_the_Standard_Model.png

>>6586143
I'll add something

http://en.wikipedia.org/wiki/Electromagnetic_field_tensor#Properties

>Inner product: If one forms an inner product of the field strength tensor a Lorentz invariant is formed

Since the plane waves are orthogonal, no matter where they interfere in their phase their inner product is zero. This can be seen from the fact their wave functions are components of orthogonal hilbert space basis vectors.

>>6586143

>photons are non-self interacting

The double slit experiment suggests otherwise.

>>6586165
That is not "self-interaction". That's just wave interference.

The interference between two different components of a superposition state of a photon. A "self-interaction" would be an interaction between 2 distinct photons.