Re: Gravity waves

[agrayson2000]

On Saturday, January 13, 2018 at 6:03:07 AM UTC-7, Lawrence Crowell wrote:
>
> On Friday, January 12, 2018 at 10:33:29 PM UTC-6, agrays...@gmail.com 
> wrote:
>>
>>
>>
>> On Friday, January 12, 2018 at 5:40:27 PM UTC-7, Lawrence Crowell wrote:
>>>
>>> On Friday, January 12, 2018 at 12:33:51 PM UTC-6, John Clark wrote:



 On Fri, Jan 12, 2018 at 11:06 AM,  wrote:

 For me, the problem is space vs spacetime. In LIGO, the recombined 
> waves of light show offsets due to different path lengths. So this seems 
> to 
> be a differential distortion of *space *as the wave passes. So what 
> has *time* got to do with the phenomenon? AG
>

 ​
 The gravity wave changes the *time* it takes for light to go down 
 those different paths, that's how we know the length i
 ​n​
 *space* must have changed because the one thing that nothing can do, 
 not even a gravity wave, is change the speed of light in a vacuum.
 ​ So its best not to think of space and time as 2 seperate things, 
 there is just spacetime.  ​


 John K Clark

>>>
>>> The metric components that vary are the spatial parts of the metric. In 
>>> the weak field limit the metric may be written as g_{ab} = η_{ab} + h_{ab}, 
>>> where η_{ab} is the flat spacetime metric the h_{ab} are the perturbation 
>>> terms on the flat space metric. The elements h_{11} = h_{22} and h_{12} = 
>>> h_{21} are the + and x polarization directions of the helicity = 2 
>>> field-wave. Then for technical reasons one takes the traceless part of this 
>>> metric and runs it through the Einstein field equations. Since the field is 
>>> weak these field equations are linear and the wave equation is a standard 
>>> EM-like wave equation. 
>>>
>>> LC
>>>
>>
>> *I was going to post that since the metric field is a function of space 
>> and time, and we can speak of space-time, the same can be said of any field 
>> dependent on space and time, such as the EM field. AG *
>>
>
> The difference is that with an ordinary field φ = φ(r,t) a derivativea are 
> ∂φ/∂t, ∂φ/∂r. If φ is a vector field this still holds. However, with 
> spacetime physics you have the frame a local field operator is on also 
> being dynamical. Then for a vector field V^μ a derivative ∂V^μ/∂x^ν, for 
> the Greek indices running over (t, r, y, z) is modified to 
>
> ∂V^μ/∂x^ν → DV^μ/∂x^ν = ∂V^μ/∂x^ν - Γ^μ_{να}V^α.
>
> This is the covariant derivative that contains the connection term 
> Γ^μ_{να}involving derivatives of the metric tensor. Since this is from a 
> covariant derivative of the metric tensor we have
>
> Dg_{μν}/∂x^ρ = ∂g_{μν}/∂x^ρ + Γ^α{μρ}g_{αν} + Γ^α_{νρ}g_{μα }.
>
> The covariant derivative of the metric is zero, this is a consequence of 
> the equivalence principle, and so one can then derive what the connection 
> terms are according to derivatives of the metric. 
>
> The equivalence principle tells us that no observer in a local frame can 
> determine whether they are falling or in a free region of flat spacetime. 
> This means their motion is not dependent on any direction so the covariant 
> directional derivative of a vector must be zero or ∇_uU = 0, and because 
> the metric defines the interval ds^2 = g_{μν}dx^μdx^ ν, and U^μ = dx^μ/ds, we 
> then also have ∇_ug = 0 or Dg_{μν}/∂x^ρ = 0. Just write 
>
> 1 = g_{μν}(dx^μ/ds)(dx^ ν/ds)
>
> and use the fact the derivative of 1 is zero.
>
> LC
>

I've been studying Roahn's videos on GR and other related topics for which 
I was the inspiration, enough to see you are fairly expert in these 
subjects. Maybe in a year or more I'll catch up. Not so easy, particularly 
GR. Appreciate your input. If anyone is interested, the link to the videos 
is, 

https://www.youtube.com/channel/UCn88wjHSqECSbgrakivJjjg

AG
 

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Re: Gravity waves

[Lawrence Crowell]

On Friday, January 12, 2018 at 10:33:29 PM UTC-6, agrays...@gmail.com wrote:
>
>
>
> On Friday, January 12, 2018 at 5:40:27 PM UTC-7, Lawrence Crowell wrote:
>>
>> On Friday, January 12, 2018 at 12:33:51 PM UTC-6, John Clark wrote:
>>>
>>>
>>>
>>> On Fri, Jan 12, 2018 at 11:06 AM,  wrote:
>>>
>>> For me, the problem is space vs spacetime. In LIGO, the recombined waves 
 of light show offsets due to different path lengths. So this seems to be a 
 differential distortion of *space *as the wave passes. So what has 
 *time* got to do with the phenomenon? AG

>>>
>>> ​
>>> The gravity wave changes the *time* it takes for light to go down those 
>>> different paths, that's how we know the length i
>>> ​n​
>>> *space* must have changed because the one thing that nothing can do, 
>>> not even a gravity wave, is change the speed of light in a vacuum.
>>> ​ So its best not to think of space and time as 2 seperate things, there 
>>> is just spacetime.  ​
>>>
>>>
>>> John K Clark
>>>
>>
>> The metric components that vary are the spatial parts of the metric. In 
>> the weak field limit the metric may be written as g_{ab} = η_{ab} + h_{ab}, 
>> where η_{ab} is the flat spacetime metric the h_{ab} are the perturbation 
>> terms on the flat space metric. The elements h_{11} = h_{22} and h_{12} = 
>> h_{21} are the + and x polarization directions of the helicity = 2 
>> field-wave. Then for technical reasons one takes the traceless part of this 
>> metric and runs it through the Einstein field equations. Since the field is 
>> weak these field equations are linear and the wave equation is a standard 
>> EM-like wave equation. 
>>
>> LC
>>
>
> *I was going to post that since the metric field is a function of space 
> and time, and we can speak of space-time, the same can be said of any field 
> dependent on space and time, such as the EM field. AG *
>

The difference is that with an ordinary field φ = φ(r,t) a derivativea are 
∂φ/∂t, ∂φ/∂r. If φ is a vector field this still holds. However, with 
spacetime physics you have the frame a local field operator is on also 
being dynamical. Then for a vector field V^μ a derivative ∂V^μ/∂x^ν, for 
the Greek indices running over (t, r, y, z) is modified to 

∂V^μ/∂x^ν → DV^μ/∂x^ν = ∂V^μ/∂x^ν - Γ^μ_{να}V^α.

This is the covariant derivative that contains the connection term 
Γ^μ_{να}involving derivatives of the metric tensor. Since this is from a 
covariant derivative of the metric tensor we have

Dg_{μν}/∂x^ρ = ∂g_{μν}/∂x^ρ + Γ^α{μρ}g_{αν} + Γ^α_{νρ}g_{μα }.

The covariant derivative of the metric is zero, this is a consequence of 
the equivalence principle, and so one can then derive what the connection 
terms are according to derivatives of the metric. 

The equivalence principle tells us that no observer in a local frame can 
determine whether they are falling or in a free region of flat spacetime. 
This means their motion is not dependent on any direction so the covariant 
directional derivative of a vector must be zero or ∇_uU = 0, and because 
the metric defines the interval ds^2 = g_{μν}dx^μdx^ ν, and U^μ = dx^μ/ds, we 
then also have ∇_ug = 0 or Dg_{μν}/∂x^ρ = 0. Just write 

1 = g_{μν}(dx^μ/ds)(dx^ ν/ds)

and use the fact the derivative of 1 is zero.

LC

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Re: Gravity waves

[agrayson2000]

On Friday, January 12, 2018 at 5:40:27 PM UTC-7, Lawrence Crowell wrote:
>
> On Friday, January 12, 2018 at 12:33:51 PM UTC-6, John Clark wrote:
>>
>>
>>
>> On Fri, Jan 12, 2018 at 11:06 AM,  wrote:
>>
>> For me, the problem is space vs spacetime. In LIGO, the recombined waves 
>>> of light show offsets due to different path lengths. So this seems to be a 
>>> differential distortion of *space *as the wave passes. So what has 
>>> *time* got to do with the phenomenon? AG
>>>
>>
>> ​
>> The gravity wave changes the *time* it takes for light to go down those 
>> different paths, that's how we know the length i
>> ​n​
>> *space* must have changed because the one thing that nothing can do, not 
>> even a gravity wave, is change the speed of light in a vacuum.
>> ​ So its best not to think of space and time as 2 seperate things, there 
>> is just spacetime.  ​
>>
>>
>> John K Clark
>>
>
> The metric components that vary are the spatial parts of the metric. In 
> the weak field limit the metric may be written as g_{ab} = η_{ab} + h_{ab}, 
> where η_{ab} is the flat spacetime metric the h_{ab} are the perturbation 
> terms on the flat space metric. The elements h_{11} = h_{22} and h_{12} = 
> h_{21} are the + and x polarization directions of the helicity = 2 
> field-wave. Then for technical reasons one takes the traceless part of this 
> metric and runs it through the Einstein field equations. Since the field is 
> weak these field equations are linear and the wave equation is a standard 
> EM-like wave equation. 
>
> LC
>

*I was going to post that since the metric field is a function of space and 
time, and we can speak of space-time, the same can be said of any field 
dependent on space and time, such as the EM field. AG *

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Re: Gravity waves

[Lawrence Crowell]

On Friday, January 12, 2018 at 12:33:51 PM UTC-6, John Clark wrote:
>
>
>
> On Fri, Jan 12, 2018 at 11:06 AM,  
> wrote:
>
> For me, the problem is space vs spacetime. In LIGO, the recombined waves 
>> of light show offsets due to different path lengths. So this seems to be a 
>> differential distortion of *space *as the wave passes. So what has *time* 
>> got to do with the phenomenon? AG
>>
>
> ​
> The gravity wave changes the *time* it takes for light to go down those 
> different paths, that's how we know the length i
> ​n​
> *space* must have changed because the one thing that nothing can do, not 
> even a gravity wave, is change the speed of light in a vacuum.
> ​ So its best not to think of space and time as 2 seperate things, there 
> is just spacetime.  ​
>
>
> John K Clark
>

The metric components that vary are the spatial parts of the metric. In the 
weak field limit the metric may be written as g_{ab} = η_{ab} + h_{ab}, 
where η_{ab} is the flat spacetime metric the h_{ab} are the perturbation 
terms on the flat space metric. The elements h_{11} = h_{22} and h_{12} = 
h_{21} are the + and x polarization directions of the helicity = 2 
field-wave. Then for technical reasons one takes the traceless part of this 
metric and runs it through the Einstein field equations. Since the field is 
weak these field equations are linear and the wave equation is a standard 
EM-like wave equation. 

LC

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Re: Gravity waves

[K E N O]

I guess this visualisation is at least fine to imagine how light has to travel 
through spacetime: 
http://www.esa.int/var/esa/storage/images/esa_multimedia/images/2015/09/spacetime_curvature/15576375-1-eng-GB/Spacetime_curvature.jpg
 
.


> Am 12.01.2018 um 19:33 schrieb John Clark :
> 
> 
> 
> On Fri, Jan 12, 2018 at 11:06 AM,  > wrote:
> 
> For me, the problem is space vs spacetime. In LIGO, the recombined waves of 
> light show offsets due to different path lengths. So this seems to be a 
> differential distortion of space as the wave passes. So what has time got to 
> do with the phenomenon? AG
> 
> ​The gravity wave changes the time it takes for light to go down those 
> different paths, that's how we know the length i​n​ space must have changed 
> because the one thing that nothing can do, not even a gravity wave, is change 
> the speed of light in a vacuum.​ So its best not to think of space and time 
> as 2 seperate things, there is just spacetime.  ​
> 
> John K Clark
> 
> 
> 
> 
>  
> 
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Re: Gravity waves

[John Clark]

On Fri, Jan 12, 2018 at 11:06 AM,  wrote:

For me, the problem is space vs spacetime. In LIGO, the recombined waves of
> light show offsets due to different path lengths. So this seems to be a
> differential distortion of *space *as the wave passes. So what has *time*
> got to do with the phenomenon? AG
>

​
The gravity wave changes the *time* it takes for light to go down those
different paths, that's how we know the length i
​n​
*space* must have changed because the one thing that nothing can do, not
even a gravity wave, is change the speed of light in a vacuum.
​ So its best not to think of space and time as 2 seperate things, there is
just spacetime.  ​


John K Clark

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Re: Gravity waves

[Brent Meeker]

The spacetime metric field.

Brent

On 1/12/2018 1:10 AM, agrayson2...@gmail.com wrote:

What exactly is waving? Space-time? What is that? TIA, AG


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Re: Gravity waves

[agrayson2000]

For me, the problem is space vs spacetime. In LIGO, the recombined waves of 
light show offsets due to different path lengths. So this seems to be a 
differential distortion of *space *as the wave passes. So what has *time* 
got to do with the phenomenon? AG

On Friday, January 12, 2018 at 3:13:37 AM UTC-7, K E N O wrote:
>
> For all those speaking German: This is a quite sophisticated podcast 
> episode about gravitational waves: 
> https://raumzeit-podcast.de/2016/02/18/rz061-gravitationswellenastronomie/
> .
>
> Am Freitag, 12. Januar 2018 10:10:52 UTC+1 schrieb agrays...@gmail.com:
>>
>> What exactly is waving? Space-time? What is that? TIA, AG
>>
>

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Re: Gravity waves

[K E N O]

For all those speaking German: This is a quite sophisticated podcast 
episode about gravitational waves: 
https://raumzeit-podcast.de/2016/02/18/rz061-gravitationswellenastronomie/.

Am Freitag, 12. Januar 2018 10:10:52 UTC+1 schrieb agrays...@gmail.com:
>
> What exactly is waving? Space-time? What is that? TIA, AG
>

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