Understanding Gravity's Impact on Light: Beginner's Question on GM

[wofsy]

I have just started a book on GM. As motivation for the idea that gravity must affect the energy of light the following example is given.

A body of rest mass,M, falls in a gravitation field and bounces off of the ground after it has achieved velocity,v. At impact, it transforms completely into a light ray that rises upwards with energy approximately equal to m + 1/2mv^2. When it reaches the original drop height it again reflects and turns back into a body of mass equal to the photon's energy. If this energy is not m then it would be possible to create a perpetual motion machine. Why is that?

 

[tiny-tim]

Hi wofsy!

(what does "GM" stand for? )

Because it has turned back into a mass again, we can do the same experiment over and over again, gaining energy each time (or losing energy each time, in which case we simply do the experiment in reverse).

(an alternative would be to extract just enough energy to re-create the original mass, m, and to let the remaining energy escape as usable energy, like a laser!)

 

[wofsy]

Hi wofsy!

(what does "GM" stand for? )

Because it has turned back into a mass again, we can do the same experiment over and over again, gaining energy each time (or losing energy each time, in which case we simply do the experiment in reverse).

(an alternative would be to extract just enough energy to re-create the original mass, m, and to let the remaining energy escape as usable energy, like a laser!)

thanks. I don't know what GM is either.

Why is it forbidden that we could keep extracting energy for the gravitational field/ What is the postulate?

 

[tiny-tim]

thanks. I don't know what GM is either.

Why is it forbidden that we could keep extracting energy for the gravitational field/ What is the postulate?

The postulate is that energy can't be created (or destroyed) … it can only be converted, from one form to another.

Energy can be extracted from a gravitational field, in the right circumstances …

energy can be extracted from the "ergosphere" round a rotating black hole (a sort of egg-shaped region just outside the event horizon) by a sort of windmill arrangement …

but that slows down the rotation of the black hole, so the loss of energy from the gravitational field is accompanied by a change in the body producing the gravitational field …

but in the example in your book, there is (I asuume) no change in the body producing the gravitational field, and so no way of extracting energy from it.

 

[wofsy]

The postulate is that energy can't be created (or destroyed) … it can only be converted, from one form to another.

Energy can be extracted from a gravitational field, in the right circumstances …

energy can be extracted from the "ergosphere" round a rotating black hole (a sort of egg-shaped region just outside the event horizon) by a sort of windmill arrangement …

but that slows down the rotation of the black hole, so the loss of energy from the gravitational field is accompanied by a change in the body producing the gravitational field …

but in the example in your book, there is (I asuume) no change in the body producing the gravitational field, and so no way of extracting energy from it.

right - why can't the gravitational field lose energy?

 

[tiny-tim]

right - why can't the gravitational field lose energy?

I assume that the book assumes that the gravitational field is constant.

For example, it might be the gravitational field of the Earth … which doesn't change shape when you bounce things up and down on it.

Which book is this?

 

[wofsy]

I assume that the book assumes that the gravitational field is constant.

For example, it might be the gravitational field of the Earth … which doesn't change shape when you bounce things up and down on it.

Which book is this?

A first course in GR by Schutz

Not being a physicist it seems strange to me that a potential can give kinetic energy to a mass, or a charge, without expending its own energy. I know there is this idea of potential energy but it leaves me a little cold since it seems to beg the question. If a field transfers energy to something why doesn't the field lose energy?

 

[tiny-tim]

A first course in GR by Schutz

ah, that would be pages 119-120 at http://books.google.com/books?id=qh...Q6AEwAg#v=onepage&q=perpetual motion&f=false"

This is Einstein's thought experiment, specifically stated to be on Earth.

Earth's gravitational field depends on the distribution of mass, and that's not going to change during the experiment, so how could the field lose energy?

Not being a physicist it seems strange to me that a potential can give kinetic energy to a mass, or a charge, without expending its own energy. I know there is this idea of potential energy but it leaves me a little cold since it seems to beg the question. If a field transfers energy to something why doesn't the field lose energy?

We're talking about the energy being the same once the photon has returned to its original position.

In intermediate positions, there is a change of energy (between kinetic and potential energy), and it's really arbitrary to say whether the photon gains/loses energy because of its changing distance from the Earth, or the Earth gains/loses energy because of its changing distance from the photon.