But it’s the standard way the luminosity distance is defined.
There is nowhere the speed of light to be seen there.
Units with c = 1 are used in the formulas.
OTOH, the “curvature of space” they mention, is not very necessary in our flat space.
Space alone is flat (within measurement uncertainties), but space-time is curved, because space expands with time.
But the Lorentz factor would be needed here.
It’s not the easiest way to treat objects moving with the Hubble flow...
Not only for the time dilatation factor, by which the energy output is to be reduced—but also for the relativistic mass increase by the same factor.
Yes, there are two (1+z) factors, one because fewer photons are emitted per unit time because “time was slower back then” (I know, not a very clear way to put it) and one because each photon is redshifted. The luminosity distance is defined with one (1+z) factor so that when you divide by its square you get (1+z)^-2.
And for the length contraction as well!
No, because we’re talking about the total luminosity of the galaxy—if its length is contracted and its luminosity density is increased by the same factor, nothing changes.
That’s the real problem, I think.
What do you mean? It’s not like this is an open question in cosmology. The implications of the FLRW metric have been well known for decades.
GBP: But it’s the standard way the luminosity distance is defined.
Still don’t like it.
Me: There is nowhere the speed of light to be seen there.
GBP: Units with c = 1 are used in the formulas.
c = 1, but v isn’t. Therefore the gamma factor is NOT a single exponential.
Me: OTOH, the “curvature of space” they mention, is not very necessary in our flat space.
GBP: Space alone is flat (within measurement uncertainties), but space-time is curved, because space expands with time.
At any moment, space has some size, a galaxy has its apparent speed, so there are mass, volume and so on, as a well defined function. Lorentz transformations of dimensions like length, clock speed and mass.
Me: But the Lorentz factor would be needed here.
GBP: It’s not the easiest way to treat objects moving with the Hubble flow...
I don’t care if it easy or not. I just want to know how it is.
Me: Not only for the time dilatation factor, by which the energy output is to be reduced—but also for the relativistic mass increase by the same factor.
Me: Yes, there are two (1+z) factors, one because fewer photons are emitted per unit time because “time was slower back then” (I know, not a very clear way to put it) and one because each photon is blueshifted. The luminosity distance is defined with one (1+z) factor so that when you divide by its square you get (1+z)^-2.
A photon is usually redshifted. Some additional redshift should occur due to the mass increase, and then some additional redshift due to the increased density, which is caused by the famous length contraction.
Me: And for the length contraction as well!
GBP: No, because we’re talking about the total luminosity of the galaxy—if its length is contracted and its luminosity density is increased by the same factor, nothing changes.
This is not true. The whole amount of emitted radiation goes down, because the escape velocity goes up. And it is more redshifted again.
Me: That’s the real problem, I think.
GBP: What do you mean? It’s not like this is an open question in cosmology. The implications of the FLRW metric have been well known for decades.
I am not sure, how well known or not well known they are. Or for how long known. I just ask a question. Do we see any relativistic effects on (far) away galaxies. If we do, fine. If we do not, also fine.
But it’s the standard way the luminosity distance is defined.
Units with c = 1 are used in the formulas.
Space alone is flat (within measurement uncertainties), but space-time is curved, because space expands with time.
It’s not the easiest way to treat objects moving with the Hubble flow...
Yes, there are two (1+z) factors, one because fewer photons are emitted per unit time because “time was slower back then” (I know, not a very clear way to put it) and one because each photon is redshifted. The luminosity distance is defined with one (1+z) factor so that when you divide by its square you get (1+z)^-2.
No, because we’re talking about the total luminosity of the galaxy—if its length is contracted and its luminosity density is increased by the same factor, nothing changes.
What do you mean? It’s not like this is an open question in cosmology. The implications of the FLRW metric have been well known for decades.
Still don’t like it.
c = 1, but v isn’t. Therefore the gamma factor is NOT a single exponential.
At any moment, space has some size, a galaxy has its apparent speed, so there are mass, volume and so on, as a well defined function. Lorentz transformations of dimensions like length, clock speed and mass.
I don’t care if it easy or not. I just want to know how it is.
A photon is usually redshifted. Some additional redshift should occur due to the mass increase, and then some additional redshift due to the increased density, which is caused by the famous length contraction.
This is not true. The whole amount of emitted radiation goes down, because the escape velocity goes up. And it is more redshifted again.
I am not sure, how well known or not well known they are. Or for how long known. I just ask a question. Do we see any relativistic effects on (far) away galaxies. If we do, fine. If we do not, also fine.
Yes. Thanks. Fixed.