# Thread: What causes Red shift?

1. The space expansion between object and observer

OR

The motion of the object away from the observer

I know both means the same in case of galaxies, they are speeding away from us due to space expansion.
Does space time really stretches the wave length of light along with it or is it it's(object's) speeding away that causes the shift in color.

If a rocket is speeding away from us with sufficiently high velocity , the light from it will be red shifted due to Doppler effect even if the space between us and the rocket is too small for space expansion to have any effect.

Q2) How far can wavelength of light be stretched? Light from far away galaxies can be stretched beyond radio wavelengths? We just need larger dishes to detect them?
Light from infinity(moving away with infinite velocity) will reach us in infinite time...it's wavelength will become infinite and frequency be zero.But is not possible for an object to have infinite velocity, so theoretically what is the maximum wavelength?

2. Does space time really stretches the wave length of light along with it or is it it's(object's) speeding away that causes the shift in color.
It's the same thing, there is no difference between the two in this instance. What happens is that very remote objects appear to recede from us rapidly because space is exanding between us and that object. The object itself is locally ( approximately ) at rest in its own frame of reference.

If a rocket is speeding away from us with sufficiently high velocity , the light from it will be red shifted due to Doppler effect even if the space between us and the rocket is too small for space expansion to have any effect.
Yes, correct. This is due to the Doppler effect.

How far can wavelength of light be stretched
Well, the limit would be a redshift that corresponds to a time when the first galaxies appeared, because before that there were no objects which emitted enough light to be observable now. Observationally, the highest redshift ever recorded was at z=8.6, which corresponds to a period about 500-600 million years after the BB event.

3. Originally Posted by Markus Hanke
Well, the limit would be a redshift that corresponds to a time when the first galaxies appeared, because before that there were no objects which emitted enough light to be observable now.
Cough, cough, CMBR, cough, cough.

4. Originally Posted by MaxPayne
The space expansion between object and observer

OR

The motion of the object away from the observer

I know both means the same in case of galaxies, they are speeding away from us due to space expansion.
Does space time really stretches the wave length of light along with it or is it it's(object's) speeding away that causes the shift in color.

If a rocket is speeding away from us with sufficiently high velocity , the light from it will be red shifted due to Doppler effect even if the space between us and the rocket is too small for space expansion to have any effect.
In both cases, the objects are further away from us now than they were in the past, and this increasing distance produces the redshift. But there is a difference between these two cases. In the case of objects speeding away from us in flat spacetime, the three-dimensional space of constant age is hyperboloidal. By contrast, in cosmology, the expanding three-dimensional space of constant age is flat (to within measurement error). To put this in a more familiar context, note that in ordinary (flat) three-dimensional space, the two-dimensional surface that is constant distance from a single point is a sphere. For this surface to be flat, the embedding three-dimensional space would have to be curved. Thus, the flatness of the three-dimensional space of constant age tells us that the embedding four-dimensional spacetime is curved.

5. Thanks mark & KJ...You guys are great!

the flatness of the three-dimensional space of constant age tells us that the embedding four-dimensional spacetime is curved.
What if we are in a 5(say) dimensional spacetime? 2 dimensions of time??..What makes us think that there is only one dimension of time?5 dimensional spacetime should also be curved right?There could be hidden dimensions of time also?Right?

the embedding four-dimensional spacetime is curved.
Does this mean that we are going to end up in a big crunch?Again??

Well, the limit would be a redshift that corresponds to a time when the first galaxies appeared, because before that there were no objects which emitted enough light to be observable now
.
Cough, cough, CMBR, cough, cough.
Forget about the big bang,If I give you infinite time...can wave length become infinite.At infinite wavelength the energy would be zero?right?what will happen to this photon?will it stand frozen in time?

6. Originally Posted by MaxPayne
What if we are in a 5(say) dimensional spacetime? 2 dimensions of time??..What makes us think that there is only one dimension of time?5 dimensional spacetime should also be curved right?There could be hidden dimensions of time also?Right??
It doesn't matter. The four-dimensional spacetime that we observe will be curved.

Originally Posted by MaxPayne
the embedding four-dimensional spacetime is curved.
Does this mean that we are going to end up in a big crunch?Again??
No. I didn't say in what way the spacetime is curved. That depends on how the universe is expanding.

Originally Posted by MaxPayne
Forget about the big bang,If I give you infinite time...
The biggest problem with "infinite time" is that stars only have a finite amount of fuel which would run out after a finite amount of time.

7. Originally Posted by KJW
Cough, cough, CMBR, cough, cough.
Yes, but didn't he ask about visible light ? That's how I understood the question.

What if we are in a 5(say) dimensional spacetime? 2 dimensions of time??
I don't think a universe with 2 dimensions of time would be stable.

8. Yes, but didn't he ask about visible light ? That's how I understood the question.
No
The biggest problem with "infinite time" is that stars only have a finite amount of fuel which would run out after a finite amount of time.
..lol,that was a nice dodge.

What if we are in a 5(say) dimensional spacetime? 2 dimensions of time??
I don't think a universe with 2 dimensions of time would be stable.
My point there was that the nature of 3D Universe should not change, no matter how many dimensions of time we add to it.

9. Originally Posted by MaxPayne
My point there was that the nature of 3D Universe should not change, no matter how many dimensions of time we add to it.
It would, because time and space dimensions aren't freely interchangeable. There are both mathematical and physical differences. If you add more more time dimensions, the universe changes quite fundamentally. This is a good introductory article, which I recommend reading, especially the last section :

Spacetime - Wikipedia, the free encyclopedia

10. Originally Posted by Markus Hanke
It would, because time and space dimensions aren't freely interchangeable. There are both mathematical and physical differences. If you add more more time dimensions, the universe changes quite fundamentally. This is a good introductory article, which I recommend reading, especially the last section :

Spacetime - Wikipedia, the free encyclopedia
The point I was making (and I think it was the point being made by MaxPayne in agreement) is that hidden extra dimensions wouldn't affect the dimensions we observe (although there may be some topological restrictions imposed by the embedding).

11. Originally Posted by KJW
The point I was making (and I think it was the point being made by MaxPayne in agreement) is that hidden extra dimensions wouldn't affect the dimensions we observe (although there may be some topological restrictions imposed by the embedding).
If you are referring to compactified extra dimensions ( as e.g. in String theory ), then yes, that's true.

12. Originally Posted by Markus Hanke
If you are referring to compactified extra dimensions ( as e.g. in String theory ), then yes, that's true.
I was just referring to simple embedding. However, I meant what I said in a particular way. That is, nothing within the higher-dimensional space can affect the lower-dimensional space (spacetime) in a way that is not admissible in the lower-dimensional space that is not embedded in a higher-dimensional space.

13. Originally Posted by KJW
I was just referring to simple embedding. However, I meant what I said in a particular way. That is, nothing within the higher-dimensional space can affect the lower-dimensional space (spacetime) in a way that is not admissible in the lower-dimensional space that is not embedded in a higher-dimensional space.
That's true. It may still give some interesting physics though - for example brane cosmology gives a simple answer as to why gravity is ( in comparison ) so much weaker than the other interactions.

14. That's true. It may still give some interesting physics though - for example brane cosmology gives a simple answer as to why gravity is ( in comparison ) so much weaker than the other interactions.
But isn't electromagnetic force a lot weaker than strong nuclear force. We will think that since the range of nuclear force is so tiny it must be operating in small hidden dimensions as well. That means EM force is the only force that is operating only in our 3D World. Is it just a mere coincidence that,out of all 4 fundamental forces it is EM that we have mastery over.

15. When the wave length goes beyond the red shift it is no longer light and becomes microwaves. There have been tests performed to identify Cosmic Microwaves that are believed to be galaxies far far away and very old.

Cosmic microwave background - Wikipedia, the free encyclopedia

16. hi, Valtiz
Thus true! By light I mean the complete electromagnetic spectrum.Also by red shift, I meant elongation of wavelength?
After the reading that page I found that the Cosmic Microwave Background Image is not the picture of any galaxy, it's the picture of the aftermath of the big bang.

17. Originally Posted by MaxPayne
But isn't electromagnetic force a lot weaker than strong nuclear force.
True in a sense, but then again, the two are hard to compare since they work in completely different ways.

18. Originally Posted by MaxPayne
If I give you infinite time...can wave length become infinite.At infinite wavelength the energy would be zero?right?what will happen to this photon?will it stand frozen in time?
If it has zero energy then it no longer exists.

19. If it has zero energy then it no longer exists.
OMG..violation of first law?
Does that mean time isn't infinite?

20. Originally Posted by MaxPayne
OMG..violation of first law?
Photons already "lose" energy as they get red-shifted. Conservation of energy is only defined locally; energy is dependent on the frame of reference. My understanding is that there is no good definition of energy on cosmological scales.

21. Photons already "lose" energy as they get red-shifted. Conservation of energy is only defined locally; energy is dependent on the frame of reference. My understanding is that there is no good definition of energy on cosmological scales.
Yes, we don't know the definition yet.

22. Originally Posted by MaxPayne
Yes, we don't know the definition yet.
No, it's deeper than that. It basically stems from the fact that only for a restricted set of quantities can one even sum the quantities if they are at different locations, and the energy-momentum tensor isn't one of those quantities. Thus, the conservation of the energy-momentum tensor can only be covariantly applied locally. In other words, even though the energy-momentum tensor is conserved at every location within some region, it may not conserved for the region as a whole.

23. Originally Posted by KJW
In other words, even though the energy-momentum tensor is conserved at every location within some region, it may not conserved for the region as a whole.
That's interesting, I thought initially that you made an error with this statement; however, on closer inspection you are of course absolutely correct. We know that T is locally conserved in the sense that in Minkowski space-time; we can integrate this over some larger region and still get

since space-time is globally flat. Not so in cases where space-time is no longer Minkowskian, because now we have to replace the partial derivative with a covariant derivative - locally, this still vanishes : . However, if we integrate this up over a region of space-time we now get

The first ( partial derivate ) term under the integral still vanishes, but the other two terms are sums of products with the components of the connection coefficients, and will not, in the general case, vanish since neither all the coefficients nor the components of stress-energy vanish. Hence in curved space-time, even though the SEM tensor is conserved locally, it is not generally conserved globally, by factors which are the direct result of curvature.

24. For vector quantities, one can define global conservation because:

and therefore Stokes' theorem can be applied to the covariant divergence. But for symmetric second-order tensors (such as the energy-momentum tensor), one has:

where the second term involving the connection prevents Stokes' theorem from being covariantly applied. On the other hand, for antisymmetric second-order tensors, the second term involving the connection vanishes if the connection is symmetric (zero torsion), and therefore Stoke's theorem can be covariantly applied.

25. Originally Posted by KJW
Shouldn't there be two correction terms involving the connection coefficients here, since this is a rank-2 tensor ? Or does the other one drop out due to the tensor being symmetric ?

26. Originally Posted by Markus Hanke
Shouldn't there be two correction terms involving the connection coefficients here, since this is a rank-2 tensor ? Or does the other one drop out due to the tensor being symmetric ?
No, there is only one connection for the second-order tensor for the same reason that there is none for the vector: one is absorbed by the partial derivative of .

27. Originally Posted by KJW
one is absorbed by the partial derivative of .
Ok, I see. Thanks

28. Originally Posted by KJW
No, there is only one connection for the second-order tensor for the same reason that there is none for the vector: one is absorbed by the partial derivative of .
Alternatively, if is a weightless tensor, then is a tensor of weight . Therefore:

Note that the third connection term comes from the weight. Interchanging the and dummy indices of the third connection term:

where is the (contracted) torsion tensor. Thus, for a symmetric connection :

29. Hmmm. looking at the derivation in my previous post, I noticed something interesting, though the significance is unclear to me. Considering that derivation for a vector, one has:

Interchanging the and dummy indices of the torsion term and applying the antisymmetry of the torsion tensor:

For :

The point is that once the torsion tensor is contracted, the resulting vector has no "memory" of its origin, and therefore can be some arbitrary vector. Note that I'm regarding:

as an operator in its own right, and could even notate it as:

Anyway, that is just a consideration. I can't say what the significance is.