Thread: Using the CMBR as a frame of reference.

1. I've been trying to figure out how well/poorly the CMBR (or rather the charged particles that emitted it at last scattering) can be used as an "inertial frame".

So far, my impression has been that it can't. I'm thinking the particles should have had every possible kinetic energy no matter what frame they are looked at from. And then their apparent velocity would be based on that, so skewed a bit toward higher speeds? (since each observer will relate the energies to velocities according to their own inertial frame.)

If there really is no base frame to measure against, then each kinetic energy level should have about the same probability for each particle, when measured from any frame of reference. That seems to clash with common sense, because one might expect two frames to have different perceptions of that. But then again.... those perceptions are modified by special relativity - so maybe it comes out even again?

- Note - remember that acceleration is what gives rise to a photon, not electron's or proton's velocity. But having a higher velocity does red shift that photon. If the acceleration is greater, the frequency of the photon will be greater, but then red/blue shifting due to velocity can further change it.

2.

3. When someone uses the CMB as a frame, they use a frame in which the CMB is (to about 1 part in 100000) isotropic.

4. Ok, so now I'm trying to figure out how it's possible that the CMBR is able to be isotropic in any frame. How could the particles have had a different average speed relative to one frame of reference, rather than another? What would have held them together like that?

If we're talking about a cloud of gas being isotropic when measured from a certain frame of reference, then gravity is what is holding them together. But gravity can't have held the particles that emitted the CMBR together because they were filling all of space, and according to BBT cosmology, the space just wraps on around so there's no outer edge for the gravity to pull inward from.

5. Originally Posted by kojax
Ok, so now I'm trying to figure out how it's possible that the CMBR is able to be isotropic in any frame. How could the particles have had a different average speed relative to one frame of reference, rather than another? What would have held them together like that?
The particles we are measuring are photons, which are always measured to have the same speed regardless of the frame of reference of the observer. If the particles that emitted those photons had random motions, this means the photons will all show a spectral shift that lies within the bounds of the upper and lower limit of those motions.

Originally Posted by kojax
If we're talking about a cloud of gas being isotropic when measured from a certain frame of reference, then gravity is what is holding them together. But gravity can't have held the particles that emitted the CMBR together because they were filling all of space, and according to BBT cosmology, the space just wraps on around so there's no outer edge for the gravity to pull inward from.
So, imagine you (as observer A) are sitting in the middle of a cloud of gas which is expanding and cooling, and that gas emits a flash of light when it reaches a certain temperature. Light will come at you from all directions, and at any given time the light that is reaching you was emitted from a certain distance away in all directions. 100 years after the flash you would be detecting photons that all took 100 years to reach you, so they were all emitted from an equal distance away in all directions.

The expansion of the cloud means that the place those photons were emitted from was receding from you at the time they were emitted, and so you measure those photons to be redshifted by that recession. If you measure those photons to be redshifted by the same amount in all directions, then you can conclude that you were at rest in relation to the body of gas they were originally emitted from. Even though there might be a range of redshifts to consider, due to the random motion of the particles that originally released those photons, that range will be the same in all directions.

Now, we look to the place where those photons we are measuring 100 years later were released from, and roll the clock back. An observer at that place (observer B) will also recede along with the expansion of the cloud, if they are at rest in relation to it. From their point of view they are also sitting in the middle of the cloud of gas and it is the position of observer A that is moving away from them. The cloud emits that flash of light in all directions, and 100 years later they will measure the redshifts of that light to be isotropic, including the light just reaching them that was emitted in the region of observer A.

So, we have two observers, A and B, starting some distance away from each other in an expanding cloud of gas, and both ending up a greater distance apart as they recede from each other with the expansion of the gas. Each measures the position of the other to be redshifted, by the same amount. To each of those observers the redshift of the CMB is isotropic, as neither of them has moved through the cloud of gas - they have moved with it.

Now we have observer C, who is in motion through the cloud of gas. They will never measure the CMB to be isotropic.

The cloud of gas has no edge, and the expansion of the cloud is the same everywhere.

6. Originally Posted by SpeedFreek
Originally Posted by kojax
Ok, so now I'm trying to figure out how it's possible that the CMBR is able to be isotropic in any frame. How could the particles have had a different average speed relative to one frame of reference, rather than another? What would have held them together like that?
The particles we are measuring are photons, which are always measured to have the same speed regardless of the frame of reference of the observer. If the particles that emitted those photons had random motions, this means the photons will all show a spectral shift that lies within the bounds of the upper and lower limit of those motions.
How would there be an upper and lower bound, though? I mean, clearly every velocity must lie between 0 and C, but why would the energies fall within any particular range, rather than covering all values from zero to infinity?

So, we have two observers, A and B, starting some distance away from each other in an expanding cloud of gas, and both ending up a greater distance apart as they recede from each other with the expansion of the gas. Each measures the position of the other to be redshifted, by the same amount. To each of those observers the redshift of the CMB is isotropic, as neither of them has moved through the cloud of gas - they have moved with it.

Now we have observer C, who is in motion through the cloud of gas. They will never measure the CMB to be isotropic.

The cloud of gas has no edge, and the expansion of the cloud is the same everywhere.
This makes sense for a cloud of expanding gas because a cloud of gas has an average velocity. If you are in the same frame as that of the average motion of the particles in that cloud, then you would observe the light it emits to have the same red shift regardless of which side of the cloud you measure from.

But, that effect is caused by gravity. The particles collide and scatter and etc.... but gravity keeps them within a range of velocities relative to one another. The particles that emitted the CMBR would not have been pulled toward any center of gravity.

So, what other effects are there that might have caused the particles to behave in a way that would make the light they emit isotropic to some frame?

7. Originally Posted by kojax
How would there be an upper and lower bound, though? I mean, clearly every velocity must lie between 0 and C, but why would the energies fall within any particular range, rather than covering all values from zero to infinity?
The photons decoupled from matter due to a universal phase transition shortly after the recombination of electrons and protons into hydrogen atoms, an event that occurred when the universe had reached a certain temperature throughout. Rather than having a range of energies between zero and infinity, everything had roughly the same energy - the energy level where the formation of hydrogen occurs.

This all assumes homogeneity and isotropy, of course.

Originally Posted by kojax
This makes sense for a cloud of expanding gas because a cloud of gas has an average velocity. If you are in the same frame as that of the average motion of the particles in that cloud, then you would observe the light it emits to have the same red shift regardless of which side of the cloud you measure from.

But, that effect is caused by gravity. The particles collide and scatter and etc.... but gravity keeps them within a range of velocities relative to one another. The particles that emitted the CMBR would not have been pulled toward any center of gravity.
Gravity is assumed to be pretty much uniform throughout in the same way as temperature, so why would any region be significantly more energetic than another region?

Everything was "smoothed out" way back in the inflationary epoch, remember?

8. Originally Posted by SpeedFreek
Originally Posted by kojax
How would there be an upper and lower bound, though? I mean, clearly every velocity must lie between 0 and C, but why would the energies fall within any particular range, rather than covering all values from zero to infinity?
The photons decoupled from matter due to a universal phase transition shortly after the recombination of electrons and protons into hydrogen atoms, an event that occurred when the universe had reached a certain temperature throughout. Rather than having a range of energies between zero and infinity, everything had roughly the same energy - the energy level where the formation of hydrogen occurs.

This all assumes homogeneity and isotropy, of course.
I'm not sure what exactly "decoupling" means in this context. My understanding of the event is that photons had constantly been getting scattered and rescattered by the free protons and electrons flying around in space, and when those protons and electrons finally combined to create neutral hydrogen, they stopped getting scattered, but otherwise were unaffected by it.

But if that is correct, then the last thing they scattered off of was a fast moving charged particle. That particle could have had any kinetic energy from zero to whatever the maximum kinetic energy they were able to reach was. I'm not aware of any mechanism that limited the maximum kinetic energy a charged particle could obtain. That's why I suggested any energy between zero and infinity.

I guess there would be a maximum, however, because if they got going too fast they'd eventually have a head on collision with another particle and do something exotic.

Originally Posted by kojax
This makes sense for a cloud of expanding gas because a cloud of gas has an average velocity. If you are in the same frame as that of the average motion of the particles in that cloud, then you would observe the light it emits to have the same red shift regardless of which side of the cloud you measure from.

But, that effect is caused by gravity. The particles collide and scatter and etc.... but gravity keeps them within a range of velocities relative to one another. The particles that emitted the CMBR would not have been pulled toward any center of gravity.
Gravity is assumed to be pretty much uniform throughout in the same way as temperature, so why would any region be significantly more energetic than another region?

Everything was "smoothed out" way back in the inflationary epoch, remember?
In a gas cloud, there would be a center of gravity.

In the case of the CMBR, there would be no center of gravity. (Plenty of gravity, but no center.) With no center, gravity has no direction to act in, and should just cancel itself out.

9. That particle could have had any kinetic energy from zero to whatever the maximum kinetic energy they were able to reach was. I'm not aware of any mechanism that limited the maximum kinetic energy a charged particle could obtain. That's why I suggested any energy between zero and infinity.
No, because if a particle had kinetic energy in excess of the energy level needed for recomination, it would not form a hydrogen atom, would remain charged, and so would not permit decoupling.

In other words, all the charged particles had the same temperature at decoupling, hence they had the same kinetic energy.

10. That depends on whether the particle was coupling to another particle headed in the same direction at the same speed. Remember kinetic energy is relative. Two bullets traveling side by side in the same direction may each perceive the other bullet to be stationary, with no kinetic energy at all.

11. So, the range of velocities for this cloud of particles would be set by whatever the maximum speed is they can obtain without colliding and shattering into smaller bits? That gives it an average velocity which particles can deviate from with statistically lower and lower probabilities. The faster they go compared with that frame, the lower the probability of continuing at that speed for long before they have a destructive collision.

Am I on the right track for arriving at an explanation?

Something had to cause this cloud of particles to conform to a proper black body, with a determinable frame of reference.

12. I think you are headed down the wrong track. The reason the CMB is isotropic is because there wasn't a range of velocities. Your cloud of particles should be more like a sea of particles.

Think in terms of thermal equilibrium, a state which any system with any temperature differential will evolve towards. The universe is thought to have been in thermal equilibrium from the first second, and would still have been so 380,000 years later, after it had cooled from a superheated plasma towards the temperature where atoms could form.

Think in terms of everything still being packed tightly together such that, although the universe was dominated by photons, none could move freely without hitting another particle.

It is often said that the universe first became transparent during the phase transition that released the CMB. This is the first time there was space enough for photons to move freely without hitting anything.

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