Special And General Relativity Time Dialation

[Endercreeper01]

What would the time dialation equation be when you combine both special and general relativity's effects?

[xyzt]

You do not need to "combine both GR and SR effects", GR gives the COMPLETE prediction , all by itself. It falls out straight from the Schwarzschild solution.

Edited October 5, 2013 by xyzt

[swansont]

The gravitational term is GM/rc² and the kinetic term is v²/2c² (using and expansion ignoring higher orders of c)

[Endercreeper01]

You do not need to "combine both GR and SR effects", GR gives the COMPLETE prediction , all by itself. It falls out straight from the Schwarzschild solution.

General relativity time dialaion is t(1-Rs/r)^(-1/2) and special relativity time dilation is t(1-v^2/c^2)^0.5

[xyzt]

General relativity time dialaion is t(1-Rs/r)^(-1/2) and special relativity time dilation is t(1-v^2/c^2)^0.5

First off, it is called "dilation", not "dialation". Second off, GR gives you all the components, including the effects due to both linear and rotational motion. Third off, both your t(1-Rs/r)^(-1/2) and t(1-v^2/c^2)^0.5 formulas are incorrect. If you do not understand the subject, just ask and I will explain.

Edited October 6, 2013 by xyzt

[Endercreeper01]

First off, it is called "dilation", not "dialation". Second off, GR gives you all the components, including the effects due to both linear and rotational motion. Third off, both your t(1-Rs/r)^(-1/2) and t(1-v^2/c^2)^0.5 formulas are incorrect. If you do not understand the subject, just ask and I will explain.

First, i meant ^(1/2), second, I meant t as proper time. Rs is 2Gm/rc²

 

Sources:

http://scienceworld.wolfram.com/physics/TimeDilation.html

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/gratim.html#c4

 

And also if t=t'/(1-Rs/r)^0.5, where t' is the relative time, then t'=t(1-Rs/r)^0.5.

The gravitational term is GM/rc² and the kinetic term is v²/2c² (using and expansion ignoring higher orders of c)

Actually, it is 2Gm/rc² and v²/c²

Edited October 6, 2013 by Endercreeper01

[swansont]

 

Actually, it is 2Gm/rc² and v²/c²

 

I think you've put in a factor of 2 from elsewhere. If you expand gamma to first order, the term is definitely v²/2c²

[Endercreeper01]

 

I think you've put in a factor of 2 from elsewhere. If you expand gamma to first order, the term is definitely v²/2c²

Then why is it that in the equations for time dilation, we use v²/c² instead of v²/2c²

[swansont]

Then why is it that in the equations for time dilation, we use v²/c² instead of v²/2c²

 

There is also a square root involved in the original equation. The factor of 2 comes from the binomial expansion, which is explained in your second link.

[Endercreeper01]

 

There is also a square root involved in the original equation. The factor of 2 comes from the binomial expansion, which is explained in your second link.

Yes, but in the equations, we use Rs/r and v²/c²

[xyzt]

First, i meant ^(1/2), second, I meant t as proper time. Rs is 2Gm/rc²

 

Sources:

http://scienceworld.wolfram.com/physics/TimeDilation.html

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/gratim.html#c4

 

And also if t=t'/(1-Rs/r)^0.5, where t' is the relative time, then t'=t(1-Rs/r)^0.5.

Actually, it is 2Gm/rc² and v²/c²

Obviously you are more interested in persisting in your errors than learning the answer.

[Endercreeper01]

Obviously you are more interested in persisting in your errors than learning the answer.

I gave you the sources that I got m equation from, so therefore general relativity time dilation does not include both.

Show me an equation and a source for a general relativity equation that includes both.

Edited October 7, 2013 by Endercreeper01

[xyzt]

I gave you the sources that I got m equation from, so therefore general relativity time dilation does not include both.

Show me an equation and a source

You quoted (incorrectly) separate sources for separate effects. You cannot combine them in order to get a correct answer. Like I said, the Schwarzschild solution produces all the effects in one equation. You can give me all the negatives you have available, you will still not have learned anything.

[Endercreeper01]

You quoted (incorrectly) separate sources for separate effects. You cannot combine them in order to get a correct answer. Like I said, the Schwarzschild solution produces all the effects in one equation. You can give me all the negatives you have available, you will still not have learned anything.

Show me a source that shows the swartzchild time dilation solution with both effects

[xyzt]

Show me a source that shows the swartzchild time dilation solution with both effects

First take your gratuitous negs back. BTW: it is "Schwarzschild", not "swartzchild".

[Endercreeper01]

First take your gratuitous negs back.

You first.

Edited October 7, 2013 by Endercreeper01

[xyzt]

You first.

I didn't give you any negs.

[CaptainPanic]

!

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xyzt, Endercreeper01,

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[Toffo]

Let's say I hit my watch with a hammer, which causes the clock's ticking rate to increase to 1.1 times the correct rate.

 

Then I descend into a gravity well wearing the watch, which causes the ticking rate to halve.

 

Then I run around in a circle at speed 0.86 c, which causes the ticking rate of my wach to halve again.

 

 

At what rate is the watch ticking now?

 

Answer: 1.1 * 0.5 * 0.5 * the original rate

[xyzt]

Let's say I hit my watch with a hammer, which causes the clock's ticking rate to increase to 1.1 times the correct rate.

 

Then I descend into a gravity well wearing the watch, which causes the ticking rate to halve.

 

Then I run around in a circle at speed 0.86 c, which causes the ticking rate of my wach to halve again.

 

 

At what rate is the watch ticking now?

 

Answer: 1.1 * 0.5 * 0.5 * the original rate

GR makes a different prediction than the one you have, the changes are much more complicated than you think. A good synopsis can be found in the description of the Hafele-Keating experiment. The effects are additive, not multiplicative.

Edited October 7, 2013 by xyzt

[Toffo]

GR makes a different prediction than the one you have, the changes are much more complicated than you think. A good synopsis can be found in the description of the Hafele-Keating experiment. The effects are additive, not multiplicative.

For some reason I'm confident my simple idea is correct.

 

Let's see now ... Oh yes, the instantaneous frequency of a clock can be deduced in my simple way.

 

On the other hand the average ticking frequency during the whole watch malteatment episode would indeed be complicated thing to calculate.

[xyzt]

For some reason I'm confident my simple idea is correct.

 

Let's see now ... Oh yes, the instantaneous frequency of a clock can be deduced in my simple way.

 

On the other hand the average ticking frequency during the whole watch malteatment episode would indeed be complicated thing to calculate.

Multiplying the effects is a common mistake. It turns out that the effect is (heavily) non-linear , so you cannot resort to multiplication. The Schwarzschild solution provides you all the information necessary for performing the correct calculation. The Hafele-Keating experiment has been reprised with a much higher precision. Incidentally, the additive effect is also at the foundation of the GPS relativistic corrections.

The overall effect is derived from the Schwarzschild solution:

 

[math](c d \tau)^2=(1-r_s/r)(cdt)^2-dr^2/(1-r_s/r)-r^2(d\theta)^2[/math]

 

giving:

 

[math]\tau=\int{\sqrt{1-r_s/r-(v/c)^2/(1-r_s/r)-(r/c)^2 \omega^2} dt}[/math]

 

For small values of [math]r_s, v/c, r \omega /c[/math] the above can be simplified to:

 

[math]\tau=\int{(1-0.5(r_s/r+(v/c)^2/(1-r_s/r)+(r/c)^2 \omega^2)) dt}[/math]

 

...recovering the explanation from the wiki article on Hafele-Keating.

Edited October 7, 2013 by xyzt

[swansont]

For some reason I'm confident my simple idea is correct.

 

Let's see now ... Oh yes, the instantaneous frequency of a clock can be deduced in my simple way.

 

On the other hand the average ticking frequency during the whole watch malteatment episode would indeed be complicated thing to calculate.

 

No, the fractional frequency terms add together.

You quoted (incorrectly) separate sources for separate effects. You cannot combine them in order to get a correct answer.

 

I'm wondering why you claim this, when you have shown links and just posted an equation that does this very thing — combine the separate effects.

[xyzt]

 

No, the fractional frequency terms add together.

 

I'm wondering why you claim this, when you have shown links and just posted an equation that does this very thing — combine the separate effects.

1. Have you looked at the formulas he's posted?

2. You do realize that all the components are derived from GR, not from a combination of GR and SR, right? There is no SR involved in the derivation.

Edited October 7, 2013 by xyzt

[swansont]

1. Have you looked at the formulas he's posted?

2. You do realize that all the components are derived from GR, not from a combination of GR and SR, right?

 

The correct response is that the equations are wrong, not that they can't be combined. And you link to the H-K experiment page, which shows/uses separate kinematic and gravitational terms, so while it's true these are all part of GR, it contradicts your claim.