# Lorentz Transformations (split from why nothing >c)

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Lets do simple math.

Speed of light in vacuum in km/sec is 300,000 km/sec.

70 km/sec/Mpc multiplied be 4400 units. is 308,000 km/sec Oh were already faster than c recessive velocity.

If you devide c by 70 you will get 4286 Mpc. This is the point where recessive velocity equals c.

How much simpler can you get. A little understanding and grade 4 math.

There is your Hubble horizon using 70 km/sec/Mpc precisely 4286 Mpc away. Simple mathematics.

$v_{recessive}=H_o d$

Where $H_o =70 km/sec/Mpc$ good ole Hubbles law.

$70 km/sec/Mpc*4286$ Mpc is 300,020 km/sec.

No conflict here just simple math

Edited by Mordred

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If you devide c by 70 you will get 4286 Mpc. This is the point where recessive velocity equals c.

How much simpler can you get. A little understanding and grade 4 math.

There is your Hubble horizon using 70 km/sec/Mpc precisely 4286 Mpc away. Simple mathematics.

$v_{recessive}=H_o d$

Where $H_o =70 km/sec/Mpc$ good ole Hubbles law.

$70 km/sec/Mpc*4286$ Mpc is 300,020 km/sec

Thanks

That was very clear to me.

However, this doesn't answer my question.

Do I need to explain the question?

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Your question on what causes expansion has been answered in numerous other threads that you started. Including a rather lengthy one on what causes expansion. The answer is thermodynamic relations that can be equated to kinetic vs potential energy relations via the equations of state for each particle contributor of their own self gravity vs their inherent kinetic energy.

Geordiof posted a section where I showed the scalar field modelling of Higgs inflation. In the universe today tbe dominant contributor is the cosmological constant.

I recall supplying all the gritty details before with you. I'm not into repeating previous efforts to teach the same individual the same lessons from his own previous threads on more than one occassion. Look over those previous threads you were involved in.

Edited by Mordred
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Thanks, but that isn't my question.

The questions are as follow:

As SPECIAL relativity applies locally in flat space – please specify the distance range which is considered as locally. Is it 1 Mpc? 100 Mpc? or xMpc?

On the other hand, from which distance we consider it as SPECIAL relativity?

There is no "distance range".

I can't understand why there is no distance range?

Edited by David Levy
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Thanks, but that isn't my question.[/size]

The questions are as follow:[/size]

As SPECIAL relativity applies locally in flat space – please specify the distance range which is considered as locally. Is it 1 Mpc? 100 Mpc? or xMpc?[/size]

On the other hand, from which distance we consider it as SPECIAL relativity?[/size]

Your question was answered: SR applies in flat space, GR in other situations; distance is not the proper way to assess the situation. Asking the same question isn't going to change the response.

.

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Depends on the size of the anistropy region. SR as applied to gravitational potential variation. SR does not apply via gravity relations in a homogeneous and isotropic global metric.

Lets explain that. You need a change in gravitational potential in a given volume to apply SR. Event A will be at a different gravitational potential than event B.

Example stars, Galaxies, etc. For cutoff distance on the range of local from a galaxy the scientific community afiak still accept a cutoff where the effective force or amount of action due to gravity is 100 times that of the citical density. Critical density in joules is roughly

$7.2*10^{-10}$ joules per cubic metre. (I ran the calcs previous with you on how to calculate that number).

The cutoff itself is due to effective action in a given region. (action equates to kinematic motion.)

That will be your region where gravitational SR relations takes effect and is considered local. The global being homogeneous and isotropic will have no effective differences in gravitational influence between any two event coordinates. (that's your global metric) ie FLRW metric.

You require a Difference in gravitational potential to apply SR relations due to gravity

Edited by Mordred
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With regards to - homogeneous and isotropic global metric.

https://physics.stackexchange.com/questions/24881/what-is-meant-when-it-is-said-that-the-universe-is-homogeneous-and-isotropic

"A sufficiently large scale (greater than about 100 Mpc), the universe can be treated as homogeneous and isotropic then a uniform density."

So, just as a brief estimation - can we assume that up to 100 Mpc it is considered SR, and above that it is GR?

Edited by David Levy
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In essence yes though GR is more applicable as you will have numerous variations within that region. Its simply more accurate to map multiple variations via GR than in SR in this instance.

Edited by Mordred
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In essence yes though GR is more applicable as you will have numerous variations within that region. Its simply more accurate to map multiple variations via GR than in GR in this instance.

Thanks

Because Lorentz Transforms are part of SPECIAL relativity that only applies locally in flat space.

The expansion of space is described by GENERAL relativity.

So can we claim that Lorentz Transforms works up to 100 Mpc? (Which means velocities don't add linearly)

While above 100 Mpc we need to use GR:

Every individual Mpc expands at the same rate 70 km/sec/Mpc. that is the expansion rate at every point in space. It is only when you add up a large number of individual Mpcs that you accumulate to greater than c recessive velocity.

Edited by David Levy
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Don't get your heart set in stone on a set distance. The key is when you have sufficient difference in potential to cause action.

Edited by Mordred
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Don't get your heart set in stone on a set distance. The key is when you have sufficient difference in potential to cause action.

I just want to get a brief estimation for: Up to what distance Lorentz Transforms is applicable?

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I just want to get a brief estimation for: Up to what distance Lorentz Transforms is applicable?

FFS, you've had three people tell you there is no answer to this question.

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I just want to get a brief estimation for: Up to what distance Lorentz Transforms is applicable?

A few centimetres, currently. As the accuracy of measurements increases, this distance will decrease.

Take the example of GPS satellites at an altitude of 20,000 km, in this case, you cannot just use velocity and the Lorentz transform to work out the difference in clock rates. You have to use GR.

So SR is an approximation. When and where that approximation can be used depends on the accuracy of the measurements you need to make, and the environment you are making them in.

Currently, the most accurate clocks we have can detect a difference in gravitational potential equivalent to a few centimetres of altitude.

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Well, it seems that I was not clear with my message as I look on Mpc.

Therefore, I would like to summarize our discussion as follow:

GR works at homogeneous and isotropic global metric, which is estimated for above 100 Mpc.

SR works below 100 Mpc (also estimated).

Expansion has a linear speed and works for GR, while Lorentz Transforms has a non linear speed and works for SR.

Hence:

Linear speed based on expansion works for GR at above 100 Mpc.

Non Linear speed based on Lorentz Transforms works for SR at below 100 Mpc.

A galaxy which is moving at a speed of 0.6 c, should be located above 100 Mpc.

Therefore, we shouldn't operate Lorentz transforms formula on a galaxy which is located at above 100 Mpc.

Just a brief calculation:

$70 km/sec/Mpc*4286$ Mpc is 300,020 km/sec.

0.6 c = 0.6 * 300,000 = 180,000 km/sec

180,000 / 70 = 2571 Mpc

Therefore, in order to gain a speed of 0.6 c a galaxy should be located at a distance of 2571 Mpc from us.

That is far above the estimated 100 Mpc for SR.

Edited by David Levy
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Space is not a substance, just the distance between objects. It turns out that in a universe described by the equations of general relativity (as ours appears to be) that objects will tend to get further apart (*) over time if no force acts on them (and if there is an even distribution of matter). This is slightly counterintuitive, as we tend to a some that things will just stay "where they are". But this is the reason for expansion.

Locally, things are held together by gravity and other forces, and so the expansion only occurs over very large scales, where these forces become insignificant.

There is no "drag" from space. But it was generally assumed that gravity would gradually slow the expansion and start a process of collapse. But then it was found that the expansion is accelerating. This acceleration is attributed to "dark energy" - something unknown, but that can be modelled as an extra energy throughout the universe.

(*) Or get closer together. Depending on energy density, initial conditions, etc.

Thanks Strange, but still don't follow the explanation for the expansion of the universe.

Dark energy seems to be the most common answer when searching on Google, but here are three options as far as I understand their merit / issues...

1) If the expanding universe were to be due to space expanding literally, then that would suggest that things are pegged to their position in space while space in between increases, causing them to drift apart. But since we are able to move through space unimpeded and are not pegged to a position, that explanation doesn't work.

2) If the expanding universe were to be due to the things in the universe shrinking in size - then the distances between them would appear to be increasing - so that would be an alternative way to get the above to occur. But if that were the case, then distance objects would not occur any red shift - and that contradicts what is observed.

3) If the expanding universe were to be due to dark energy pushing things apart, then that seems to be a better fit to what is observed. But a couple of questions.

3a) If dark energy is the explanation, wouldn't distant galaxies be constrained to move apart within the speed of light?

So although at this moment, light from the most distant galaxies hasn't had time to reach us, eventually all galaxies would come into view?

3b) If dark energy is the explanation, how is it able to push against things, and yet when those things move due to local forces, those things do not experience a drag through the dark energy?

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I really think the ant on the balloon is a good analogy. The balloon is expanding under its feet, and if there is another ant along the balloon, the distance the ants have to walk to get to each other along the surface increases, but they are not "pegged" to their position on the balloon. They can move around freely as the balloon continues to expand under their feet. That is essentially what happens with us and space.

So it's 2, but it doesn't require anything being permanently fixed to its location.

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I really think the ant on the balloon is a good analogy. The balloon is expanding under its feet, and if there is another ant along the balloon, the distance the ants have to walk to get to each other along the surface increases, but they are not "pegged" to their position on the balloon. They can move around freely as the balloon continues to expand under their feet. That is essentially what happens with us and space.

Thanks Delta1212. The difficulty with the ant on the expanding balloon analogy and bearing in mind we are in a 3D world, is that it requires our 3D world to expand into the 4th dimension. That introduces the issue of what is dragging us in that direction? In the analogy, the rubber of the balloon is pushing the ant into the third direction. What are we 'standing on' that pushes us into the 4th dimension?

Edited by robinpike
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Thanks Strange, but still don't follow the explanation for the expansion of the universe.

Dark energy seems to be the most common answer when searching on Google, but here are three options as far as I understand their merit / issues...

Firstly, dark energy is NOT the cause of expansion. It is placeholder for whatever causes the apparent accelerating expansion. (That should be put in a sticky post.)

1) If the expanding universe were to be due to space expanding literally, then that would suggest that things are pegged to their position in space while space in between increases, causing them to drift apart. But since we are able to move through space unimpeded and are not pegged to a position, that explanation doesn't work.

They are not "pegged" to their locations, but they will stay in those locations unless some force acts on them. Thus, in the absence of any force, they will drift apart.

2) If the expanding universe were to be due to the things in the universe shrinking in size - then the distances between them would appear to be increasing - so that would be an alternative way to get the above to occur. But if that were the case, then distance objects would not occur any red shift - and that contradicts what is observed.

You can describe things in that way (it is a "coordinate transformation"). But it isn't used because it ends up being more complicated (there are complications like the speed of light changing over time, etc) and it is unintuitive (for most people - although there are a regular individuals with their "personal theories" based on the idea).

As for the red-shift, in this model, it comes from the fact that the atoms (or whatever) were larger and hence the wavelength of the light was longer (redder) in the past.

As it is a coordinate transform, anything that exists, or can be described, in one system also has an equivalent in the other. So, for example, you still need an equivalent of dark matter to explain the "accelerating shrinking of matter".

3) If the expanding universe were to be due to dark energy pushing things apart, then that seems to be a better fit to what is observed. But a couple of questions.

3a) If dark energy is the explanation, wouldn't distant galaxies be constrained to move apart within the speed of light?

So although at this moment, light from the most distant galaxies hasn't had time to reach us, eventually all galaxies would come into view?

3b) If dark energy is the explanation, how is it able to push against things, and yet when those things move due to local forces, those things do not experience a drag through the dark energy?

Dark matter doesn't really push things. It just changes the energy density so that the expansion rate increases (the details of that are somewhat over my head).

The difficulty with the ant on the expanding balloon analogy and bearing in mind we are in a 3D world, is that it requires our 3D world to expand into the 4th dimension. That introduces the issue of what is dragging us in that direction? In the analogy, the rubber of the balloon is pushing the ant into the third direction. What are we 'standing on' that pushes us into the 4th dimension?

There is no higher dimensional space that we are embedded in (if there were, it would be fifth dimension, as the fourth is time ).

To understand why, means getting your head round the tricky concept of intrinsic curvature.

It is probably easier to think of the universe as being infinite. And then you don't have to worry about what it is expanding into, because it is already everywhere!

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I assume that by now we all agree that the following formula isn't relevant for GR

$\frac{0.6c+0.6c}{1+ \frac{0.6c(0.6c)}{c^2}} = 0.88235... c$

Due to the expansion, at that range (2571 Mpc) the speed should be linearly.

Therefore, the relative speed between A and C is 1.2 c.

Edited by David Levy
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... Therefore, the relative speed between A and C is 1.2 c.

You sneaky sneaky thing, you!

Don't you remember:

...

Hence, instead of using the word "moving" away, we need to use the word "recede" away.

I have no problem with that.

Now we can be friend again.

No more war!

One simple word, same meaning - bring peace to our universe.

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Sorry

This isn't the main issue.

We discuss on linearly speed at GR.

Therefore, the following example of rockets over rockets should work O.K.

At t=1 we get:

A-B-C-D-E-F-G-H-I-J-K-L-M

At t=3 we get:

A---B---C---D---E---F---G---H---I---J---K---L---M

Edited by David Levy
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I assume that by now we all agree that the following formula isn't relevant for GR

$\frac{0.6c+0.6c}{1+ \frac{0.6c(0.6c)}{c^2}} = 0.88235... c$

Due to the expansion, at that range (2571 Mpc) the speed should be linearly.

Therefore, the relative speed between A and C is 1.2 c.

This doesn't really make any sense.

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This doesn't really make any sense.

Why?

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Why?

Because, if there is expansion of space and the galaxies are far enough away that this is significant, then you cannot compare their velocities without using GR to take the expansion into account. Therefore you cannot add velocities as you are doing.

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Therefore, the following example of rockets over rockets should work O.K.

As soon as you bring rockets into it, you're really talking about something quite different to the apparent motion of galaxies due to expansion.

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