Time dilation on a Neutron Star

[Alan McDougall]

If we use a thought experiment and supposed an entity on a neutron star, could look out at the outside universe, would the enormous gravity field of such a massive neutron star skew time so that the outside universe would appear to move faster relative to it?

 

We could take this further and suppose two entities on different neutron stars could look at each other, what effect would time dilation then have on each of the entities?

[Arnaud Antoine ANDRIEU]

We could take this further and suppose two entities on different neutron stars could look at each other, what effect would time dilation then have on each of the entities?

 

 

 

The x-rays/light can create a "piece of matter" with it opposite ?

 

interesting

Edited November 18, 2012 by Arnaud Antoine ANDRIEU

[timo]

If we use a thought experiment and supposed an entity on a neutron star, could look out at the outside universe, would the enormous gravity field of such a massive neutron star skew time so that the outside universe would appear to move faster relative to it?

Yes. You can evaluate the time dilatation factor yourself: Plug the mass and the radius of your Neutron star into the 00-Component of the Schwarzschild Metric (readily found on Wikipedia or via Google); the square root of (the magnitude of) the component is the time dilatation factor. This value X will be smaller than one, in some sense (that I don't want to specify to keep the post sufficiently simple) meaning that for each second passed in the "outside world" only X seconds passed on the neutron star.

 

We could take this further and suppose two entities on different neutron stars could look at each other, what effect would time dilation then have on each of the entities?

Just look at the ratios of the time dilatation factors. For identical neutron stars it is one, meaning there is no relative effect.

[Moontanman]

If we use a thought experiment and supposed an entity on a neutron star, could look out at the outside universe, would the enormous gravity field of such a massive neutron star skew time so that the outside universe would appear to move faster relative to it?

 

We could take this further and suppose two entities on different neutron stars could look at each other, what effect would time dilation then have on each of the entities?

 

 

Try this book, it is fiction but written by a scientist...

 

http://en.wikipedia.org/wiki/Dragon's_Egg

 

Forward was the scientist and Larry Niven the author in a tutorial on science fiction writing, and later that evening Forward and Niven agreed to collaborate on a novel on aliens on a neutron star. However, Niven soon found himself too busy with Lucifer's Hammer, on which he was already co-writing with Jerry Pournelle. Forward wrote the first draft himself, but several publishers suggested the story should be rewritten by Niven or Pournelle – who were still busy. Finally editor Lester del Rey provided comments that guided Forward through two rewrites, and del Rey then bought the novel.[7] Forward described the work as "a textbook on neutron star physics disguised as a novel".[8]

[Greg H.]

Try this book, it is fiction but written by a scientist...

 

http://en.wikipedia.org/wiki/Dragon's_Egg

 

 

 

I was going to suggest this. I've read the book twice myself, and it's actually quite interesting, especially in the time differences between the humans and the cheela (the aliens on the neutron star). Well worth the read.

 

Forward also included some appendixes (at least in my copy) that delve more into the science behind the book.

[Alan McDougall]

I was going to suggest this. I've read the book twice myself, and it's actually quite interesting, especially in the time differences between the humans and the cheela (the aliens on the neutron star). Well worth the read.

 

Forward also included some appendixes (at least in my copy) that delve more into the science behind the book.

 

Thanks guys just when I thought I had an original idea I find out it is old hat, I will get the book if I can.

[Delta1212]

Yes. You can evaluate the time dilatation factor yourself: Plug the mass and the radius of your Neutron star into the 00-Component of the Schwarzschild Metric (readily found on Wikipedia or via Google); the square root of (the magnitude of) the component is the time dilatation factor. This value X will be smaller than one, in some sense (that I don't want to specify to keep the post sufficiently simple) meaning that for each second passed in the "outside world" only X seconds passed on the neutron star.

 

Just look at the ratios of the time dilatation factors. For identical neutron stars it is one, meaning there is no relative effect.

This is almost certainly asking you to desimplify that 'in some sense' comment, but how would that work with the constancy of the speed of light?

 

Let's say for the sake of simple numbers that X is 1/2. So for every second on the neutron star, two pass outside. The neutron star observer sees the outside observer conduct an odd test. The outside observer hits a button that fires a small beam of light at a mirror two light seconds away. Five seconds later, he pushes a button that places a mirror in the path of the returning light, however, the light would have only taken four seconds to return and so has already passed the mirror.

 

On the neutron star, the observer would count only 2.5 of his own seconds between the outside observer hitting the light button and hitting the mirror button. For the light to have already passed the point at which the mirror is placed, it would need to have traveled more than four light seconds in 2.5 seconds as counted by the neutron star. If the light had not yet reached the mirror because it had only traveled 2.5 light seconds, then when it reached the mirror, the neutron star observer would see it reflect off despite the fact that the outside observer had already seen it pass by the mirror.

 

I can see how this is resolved if either the speed of light is not constant in an accelerated reference frame or distances outside become shortened to observers in a gravitational field as well as time appearing to speed up, but these both seem vaguely counter-intuitive. I suppose the latter would be my guess if I had to pick one of the two, but I'm not entirely sure how that would work.

 

Anyone up for clarifying?

[Spyman]

I am not an expert on relativity but if time passes half as slow on the neutron star than for the outside observer, then an observer on the neutron star only measures one second for the small beam of light to reach the mirror at 'two light seconds away' and two seconds for it to also return back.

 

 

Is The Speed of Light Constant?

 

/.../

 

General Relativity

 

Einstein went on to discover a more general theory of relativity which explained gravity in terms of curved spacetime, and he talked about the speed of light changing in this new theory. In the 1920 book "Relativity: the special and general theory" he wrote: . . . according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity [. . .] cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position. Since Einstein talks of velocity (a vector quantity: speed with direction) rather than speed alone, it is not clear that he meant the speed will change, but the reference to special relativity suggests that he did mean so. This interpretation is perfectly valid and makes good physical sense, but a more modern interpretation is that the speed of light is constant in general relativity.

 

The problem here comes from the fact that speed is a coordinate-dependent quantity, and is therefore somewhat ambiguous. To determine speed (distance moved/time taken) you must first choose some standards of distance and time, and different choices can give different answers. This is already true in special relativity: if you measure the speed of light in an accelerating reference frame, the answer will, in general, differ from c.

 

In special relativity, the speed of light is constant when measured in any inertial frame. In general relativity, the appropriate generalisation is that the speed of light is constant in any freely falling reference frame (in a region small enough that tidal effects can be neglected). In this passage, Einstein is not talking about a freely falling frame, but rather about a frame at rest relative to a source of gravity. In such a frame, the speed of light can differ from c, basically because of the effect of gravity (spacetime curvature) on clocks and rulers.

 

If general relativity is correct, then the constancy of the speed of light in inertial frames is a tautology from the geometry of spacetime. The causal structure of the universe is determined by the geometry of "null vectors". Travelling at the speed c means following world-lines tangent to these null vectors. The use of c as a conversion between units of metres and seconds, as in the SI definition of the metre, is fully justified on theoretical grounds as well as practical terms, because c is not merely the speed of light, it is a fundamental feature of the geometry of spacetime.

 

Like special relativity, some of the predictions of general relativity have been confirmed in many different observations. The book listed below by Clifford Will is an excellent reference for further details.

 

Finally, we come to the conclusion that the speed of light is not only observed to be constant; in the light of well tested theories of physics, it does not even make any sense to say that it varies.

 

Reference:

 

C.M. Will, "Was Einstein Right?" (Basic Books, 1986)

 

http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/speed_of_light.html

Edited November 26, 2012 by Spyman

[BlackRock]

On 25/11/2012 at 3:04 PM, Delta1212 said:

This is almost certainly asking you to desimplify that 'in some sense' comment, but how would that work with the constancy of the speed of light?

 

Let's say for the sake of simple numbers that X is 1/2. So for every second on the neutron star, two pass outside. The neutron star observer sees the outside observer conduct an odd test. The outside observer hits a button that fires a small beam of light at a mirror two light seconds away. Five seconds later, he pushes a button that places a mirror in the path of the returning light, however, the light would have only taken four seconds to return and so has already passed the mirror.

 

On the neutron star, the observer would count only 2.5 of his own seconds between the outside observer hitting the light button and hitting the mirror button. For the light to have already passed the point at which the mirror is placed, it would need to have traveled more than four light seconds in 2.5 seconds as counted by the neutron star. If the light had not yet reached the mirror because it had only traveled 2.5 light seconds, then when it reached the mirror, the neutron star observer would see it reflect off despite the fact that the outside observer had already seen it pass by the mirror.

 

I can see how this is resolved if either the speed of light is not constant in an accelerated reference frame or distances outside become shortened to observers in a gravitational field as well as time appearing to speed up, but these both seem vaguely counter-intuitive. I suppose the latter would be my guess if I had to pick one of the two, but I'm not entirely sure how that would work.

 

Anyone up for clarifying?

I think you could view it as the pathway of light...it curves to make an object in space seem smaller, and for the person in space, it curves to make the object on the neutron star seem bigger(self magnification)...?