Gravitational Time Dilation

[GoodKat]

A YEC I have been debating for some time has recently made a video claiming that because according to general relativity, time is slowed by gravity, earth may be only ~10,000 years old while most of deep space is several billions, allowing enough time for light from very far away stars to reach us. I know that his idea of how much gravity affects time is WAYYY off, but I need to know how much, this is an excellent opportunity for me to show him that he forms conclusions far too rapidly without adequate research. So, I need to know how much time is slowed by gravity on earth(as compared to an area with essentially no gravity), and how to calculate it. I've never worked much with relativity, so the more in depth the explanation, the better.

 

[ImprobableJoe]

I'm not an expert, and I'm not claiming to be... but if time was apparently 10,000 years on earth but 14 billion years to the rest of the universe, wouldn't relativity require that it LOOK like 10,000 years from our reference point, by all measurements including the age of the universe?

 

[GoodKat]

I'm not an expert, and I'm not claiming to be... but if time was apparently 10,000 years on earth but 14 billion years to the rest of the universe, wouldn't relativity require that it LOOK like 10,000 years from our reference point, by all measurements including the age of the universe?

It would require that the earth appear to be 10,000 years old, but not the rest of the univers(I don't think). It would require that earth's gravity make time pass 1.3 million times slower than in dead space, which is why I know he is WAYYY off.

 

[ImprobableJoe]

It would require that the earth appear to be 10,000 years old, but not the rest of the univers(I don't think). It would require that earth's gravity make time pass 1.3 million times slower than in dead space, which is why I know he is WAYYY off.

What I'm saying is that for only 10,000 years to pass on earth, it would look like only 10,000 years had passed everywhere FROM EARTH. The Earth would appear to be 10,000 years old to people on earth, but so would everything else FROM earth.

 

[GoodKat]

What I'm saying is that for only 10,000 years to pass on earth, it would look like only 10,000 years had passed everywhere FROM EARTH. The Earth would appear to be 10,000 years old to people on earth, but so would everything else FROM earth.

Would it? So if an observer is under the affect of time dilation, it appears to him that everything else is under the same effect?

 

[ImprobableJoe]

[Would it? So if an observer is under the affect of time dilation, it appears to him that everything else is under the same effect?

How could it be otherwise?

 

[GoodKat]

How could it be otherwise?[/quote]
Hmm, like I said, I have very little experience in dealing with relativity.

 

[ImprobableJoe]

Hmm, like I said, I have very little experience in dealing with relativity.

The point of it, as I understand it, is to do with frames of reference. Time dilation occurs when you are accelerated from a given point of reference, and it can only be noticed from the initial point of reference. The so-called "twin paradox" as an example? It only occurs and is noticed when someone is accelerated to near the speed of life, and then turns around and returns to that original reference point.

Therefore, the only way for the earth to experience time dilation would be for it(and the rest of the solar system) to be accelerated separately from the rest of the universe, and then returned to its original location relative to the rest of the universe.

 

[GoodKat]

The point of it, as I understand it, is to do with frames of reference. Time dilation occurs when you are accelerated from a given point of reference, and it can only be noticed from the initial point of reference. The so-called "twin paradox" as an example? It only occurs and is noticed when someone is accelerated to near the speed of life, and then turns around and returns to that original reference point.

Therefore, the only way for the earth to experience time dilation would be for it(and the rest of the solar system) to be accelerated separately from the rest of the universe, and then returned to its original location relative to the rest of the universe.

I think you're talking about velocity induced time dilation, I am talking about gravitational time dilation. I did some more research, and it seems that the dilation caused by an object's gravity can be found by plugging its escape velocity into the velocity time dilation equation.

 

[ImprobableJoe]

I think you're talking about velocity induced time dilation, I am talking about gravitational time dilation. I did some more research, and it seems that the dilation caused by an object's gravity can be found by plugging its escape velocity into the velocity time dilation equation.

Same thing. Gravity IS velocity, in a "negative direction"... again, unless I'm totally missing something.

 

[e2iPi]

You should tell this idiot that his theory is not only bullshit, but epic bullshit. However, this will give you a good enough approximation to let your YEC know he should probably stick with what he can dredge up at answersingenesis.org rather than attempting to think on his own.

In order to calculate time dilation, the equation is:
sqrt (1 - (v^2 / c^2))

where
v = velocity (To solve for a gravitational field, set v = escape velocity, approximately 11000 m/s on Earth)
c = speed of light (2.99 x10^8 m/s)

Let's plug in those numbers and see what it gets us:
(11000 m/s)^2 / (2.99 x10^8 m/s)^2 = 1.35x10^-9
taking the square root, we come up with .99999999998 (at least on my calculator)
Anyway, this tells us that the clocks will differ by about a nanosecond.
About 1 second every 31 years
about 330 seconds 10,000 years

This form of the equation involves an inertial mass (which is equivalent to a gravitational mass) which is not curved, rather it is flat. If you REALLY want to get into the Schwarzschild (sp) solutions for spherical bodies, let me know.


-1

 

[aeroeng314]

Same thing. Gravity IS velocity, in a "negative direction"... again, unless I'm totally missing something.

Gravity is equivalent (for the most part) to acceleration, not velocity. That's sort of the starting point for GR (the thought experiment has something to do with an accelerating elevator in space that has a window with light shining through; this can be used to derive some basic results from GR). This is not a symmetric result since you can measure an absolute acceleration where you can't measure an absolute velocity (velocities are relative, accelerations are not). This means you would indeed observe a clock at a higher altitude to tick faster than a clock at a lower altitude, regardless of where you actually are.

 

[ImprobableJoe]

Gravity is equivalent (for the most part) to acceleration, not velocity. That's sort of the starting point for GR (the thought experiment has something to do with an accelerating elevator in space that has a window with light shining through; this can be used to derive some basic results from GR). This is not a symmetric result since you can measure an absolute acceleration where you can't measure an absolute velocity (velocities are relative, accelerations are not). This means you would indeed observe a clock at a higher altitude to tick faster than a clock at a lower altitude, regardless of where you actually are.

Crap... yeah. That's what I meant.

 

[Pulsar]

I've always thought that creationists are shooting themselves in the foot by using this time dilation argument. After all, the age of the universe is derived from observations on earth, therefore the universe is 13.7 billion EARTH-years old. So, if one year on earth, in our local gravitational field, is longer than a 'cosmic' year in 'empty space', then the actual age of the universe in a gravitationless frame of reference would be even more than 13.7 billion 'cosmic' years! But maybe I'm wrong... Joe, was this what you meant?

Anyway, you can indeed use the escape velocity approximation to calculate the dilation. As e2iPi derived, the dilation cause by the gravitational field of the earth is 7x10^-10. This corrected time is called Geocentric Coordinate Time, and it's used for satellites. Likewise, there a dilation caused by the Sun: both a gravitational correction (Sun's escape velocity: 42.1 km/s) and a correction due to the earth's orbital velocity (30 km/s) which can be approximated by the same formula. Combined with the gravitational field of the earth, you get a factor 1.6x10^-8, called Barycentric Coordinate Time, used for spacecraft.

It's far more difficult to estimate the influence of our Galaxy, it depends on the distribution of stars, gas and dark matter. But for first approximation, it's escape velocity is ~1000 km/s (although less where we are, since we're not on the edge), and the orbital velocity of the Sun is 220 km/s. I get a factor of ~6x10^-6. But other effects should be incorporated: the path of light is bent near stars, so it travels longer to reach us, which gives an additional delay (see Shapiro delay). And then our Galaxy travels in a cluster (I don't know the escape velocity), with a velocity of ~600 km/s...

Still, adding everything, the combined effect is extremely small.