Redshifted light from another planet

[MikeGomez]

I observe light originating from a planet which has a much stronger gravitation field than our own earth. The wavelength of the light is recognized as having been emitted from hydrogen-1 atoms, but is red-shifted due to the higher gravitation of that planet. I have a container of some kind with which I can store the light.

Container A contains red-shifted light from the alien planet.
Container B contains light emitted by hydrogen-1 here on earth, and is not red-shifted from our perspective.

I take the two containers, some hydrogen-1, and a spectrometer, and I travel to the other planet. After I arrive at the other planet, it seems to me that…

A: When I measure the wavelength of the light from the containers, my results for each will be exactly the same as they were on Earth ( I may be in a denser gravitational field, but me and my containers and measuring devices, all share the same space-time).

Is this true or false?

B: The light from container A as measured by the inhabitants of the other planet will not appear red-shifted (or blue-shifted), because on returning to their planet it was blue-shifted the exact right amount to return it to normal from their perspective.

Is this true or false?

C: The light from container B as measured by the inhabitants of the other planet will appear blue-shifted, as it has arrived from a source of less gravitation.

Is this true or false?

I think there must be a flaw in my thinking somewhere, because if A, B, and C are all true, wouldn’t the electrons in my hydrogen-1 atoms orbit their atoms at a faster rate than the electrons in the hydrogen-1 atom from he alien planet? It doesn’t seem possible. I thought that if I enter the same space-time reference frame as the alien planet, our atoms should behave exactly the same.

 

[Ich]

Really good questions!

A: When I measure the wavelength of the light from the containers, my results for each will be exactly the same as they were on Earth ( I may be in a denser gravitational field, but me and my containers and measuring devices, all share the same space-time).

Is this true or false?

This is true as long as you and the containers are free falling. When you brake at the planet's surface, you kick the photons in the container to a higher energy, such that the light in container A is no longer redshifed, and the light in B is blueshifted.
Measured in the same state of motion (at rest at the planet's surface), Answers B and C are true, in accordance with Answer A (false).

You'd get true,false,false if you measure before braking.

 

[MikeGomez]

Thanks Ich.

I failed to mention my acceleration when departing from earth, and my deceleration when arriving. I thought they might offset each other, but if I understand it correctly based on your reply, it means the deceleration at the destination planet have a greater effect than the takeoff acceleration, due to the denser gravity?

It seems that would make everything copacetic at the destination.

 

[Ich]

I thought they might offset each other, but if I understand it correctly based on your reply, it means the deceleration at the destination planet have a greater effect than the takeoff acceleration, due to the denser gravity?

Yep, you've been falling toward the planet and have to brake trom the fall. So deceleration must be stronger than acceleration.

 

[MikeGomez]

Ok, so regarding question part A, after decelerating at the destination planet, I will actually measure the light in container B from Earth as blue-shifted, and the light from container A as non-shifted. My measurements will match the measurements of the inhabitants of the planet.

Even though I have transferred into the space-time reference frame of the heavy planet, and my measuring devices and hydrogen-1 atoms as well, the photons in my containers have not been affected by the deceleration. I read in the description of time-dilation something about time-dilation not being affected by acceleration.

“Time dilation is the factor by which an inertial observer measures another observer's clock as going slow.

Time dilation is composed of two factors:
1) a relative factor of for Lorentz time dilation, which depends only on the velocity of the clock
2) an absolute factor of for gravitational time dilation, which depends only on the position of the clock.

Time dilation does not depend on the acceleration of the clock.

Lorentz time dilation is mutual for two inertial observers, in the sense that they will each regard the other's clock as running slow by the same factor.

Gravitational time dilation is greater (the clock is slower) where gravity is stronger (and gravitational potential is higher).”


Now, in another post I inquired about the energy loss of red-shifted light (or energy gain in blue-shifted light), and I was informed that the light does not lose/gain energy, but rather it is time-dilated. However, can I not stubbornly persist in my view, and declare that my Earth photons from container B that I carried to a heavier planet have blue-shifted relative to me, and have therefore gained energy?

It seems to me as though I am free to view the light as having gained energy from the dense gravitational field, and that the energy changes in the photons from Earth are gradual (non-quantum values).

Is this fair, or have I made a mistake?

 

[Ich]

Even though I have transferred into the space-time reference frame of the heavy planet, and my measuring devices and hydrogen-1 atoms as well, the photons in my containers have not been affected by the deceleration.

Of course they have been affected. They ran into the front wall of the container, which was accelerating relative to the free-falling frame. This kick increased their energy.

I read in the description of time-dilation something about time-dilation not being affected by acceleration.

Yes. I'm not talking about time dilation, I'm talking about reflection on an incoming surface. The photons experience quite the same thing as a tennis ball at the serve.

Now, in another post I inquired about the energy loss of red-shifted light (or energy gain in blue-shifted light), and I was informed that the light does not lose/gain energy, but rather it is time-dilated.

Well, I don't know the context. There may have been reasons to suggest you look at it from that side.
Generally, I encourage people to see things from as many viewpoints as possible in relativity. The losing/gaining of energy is certainly a valid viewpoint in most circumstances.

However, can I not stubbornly persist in my view, and declare that my Earth photons from container B that I carried to a heavier planet have blue-shifted relative to me, and have therefore gained energy?

Yes, in the end they have gained energy relative to you.

It seems to me as though I am free to view the light as having gained energy from the dense gravitational field, and that the energy changes in the photons from Earth are gradual (non-quantum values).

Yes, you are free to take this viewpoint (maybe without "from the dense" gravitational field, this is non-standard terminology). It's the Newtonian point of view, where there is potential energy being converted into kinetic energy.
OTOH, in GR's philosophy it's quite clear that the containers themselves did not undergo any changes during free fall. The only thing that changed is their relation to other objects, like distance, relative velocity, and so on. You must remember that "Energy" is such a relation, too, and not something that belongs to the container alone. So their energy can easily change without anything happening to them. It changes by merely choosing a different coordinate system.

 

[MikeGomez]

Yes. I'm not talking about time dilation, I'm talking about reflection on an incoming surface. The photons experience quite the same thing as a tennis ball at the serve.

It makes sense that the wavelength of photons is affected by acceleration. I'm still confused by what scientists are talking about when they say "Time dilation does not depend on the acceleration of the clock."

 

[Ich]

I'm still confused by what scientists are talking about when they say "Time dilation does not depend on the acceleration of the clock."

The http://math.ucr.edu/home/baez/physics/Relativity/SR/clock.html" means that a clock accelerating at 10^18 g shows the same time dilation as a freely floating clock with the same velocity.