I don’t like this solution. There is nowhere the speed of light to be seen there.
OTOH, the “curvature of space” they mention, is not very necessary in our flat space.
But the Lorentz factor would be needed here. 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. And for the length contraction as well!
That’s not a very useful concept, because it’s nothing but the total energy measured in different units. It only has a name of its own for hysterical raisins. A much more useful concept is the invariant mass, which is the square root of the total energy squared minus the total momentum squared (in suitable units), which (as the name suggests) is the same in all frames of references; in particular, it equals the total energy in the frame of reference where the total momentum is zero. Nowadays when people say “mass” they usually mean the invariant mass, because it makes more sense to call the relativistic mass “total energy” instead.
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.
z is defined based on frequency change but the frequency change must also be the amount it appears to be slowed down, since e.g. you could measure the number of peaks in a light wave coming from a galaxy as a measure of time.
For the benefit of others: in making this post Thomas is I expect motivated by my responses to his post here:
you must get an apparent slowdown proportional to the ratio of frequencies, because the frequency is itself a measurement of time.
That is NOT true AT ALL! Time dilatation IS NOT linear. NOT AT ALL.
And what about blue shift galaxies? Do you think they speed up their internal clock?
I will not approve such comments anymore. You have to know the basic stuff.
In reply about the blue shift galaxies: they will indeed appear to be sped up from our perspective. Something moving toward us is slowed down in our reference frame by time dilation, but also appears sped up because light takes less and less time to get here. As with redshift, both of these effects are baked into z, so the final (apparent) speedup is what you get from z.
You can use a light wave as a clock. The ratio of frequency that the light wave is emitted at to the frequency we perceive is 1+z. Thus, the ratio of the time we observe a galaxy for to the amount of time that elapsed in the galaxy’s proper time is also 1+z.
For non-relativistic motion, the speed is approximately proportional to the redshift, but as speeds get higher, that breaks down. Apparent slowdown in terms of v will involve a Lorentz factor, but in terms of z it will not, because of the definition of z being in terms of apparent slowdown (of light).
Not directly. You have to square the velocity of a galaxy, then you must divide it by c (light speed). Then you must divide it by c once again. Then you have to subtract 1, change the sign, compute the square root.
Regardless of the direction of the galaxy in question.
You are very wrong here, I am sorry.
But that’s beside the point. We want the right solution and that solution should be in a good agreement with all those Hubble pictures.
Imagine there are aliens in the high-z galaxy. They produce a laser beam with a particular frequency, pointed at us. There are also other events occurring in their galaxy, for simplicity at the beam source. The aliens measure the time between two events as a particular number of cycles of the laser light.
Now when we observe the laser light and the events, we must also measure the time between the events as the same number of cycles of the laser light apart. But, we see the cycles at a lower frequency by a factor of 1+z, so we also see the two events an increased time apart by a factor of 1+z.
Now, it seems to me that maybe the issue is disagreement on what exactly we are measuring. What I am talking about is what we see when we look through a telescope. But it seems to me that maybe what you are talking about is what is “really” there in “our” reference frame. Unfortunately that latter thing is ambiguous since you can extend our reference frame to the other galaxy in different ways.
It’s true that you can view far away galaxies as actually moving away from us rather than stationary in an expanding universe—both are valid ways of looking at reality in general relativity. But, there’s a reason most astronomers use metrics in which galaxies are (almost) stationary: it’s much simpler and less confusing.
z represents frequency differences which is the same as apparent slowdown (or speedup for blueshift). Note, this is apparent slowdown in the sense of what we see through a telescope, not how much it is “really” slowed down in “our” reference frame.
Now, when we imagine an extending our reference frame to that other galaxy in a particular way such that in that particular extension of our reference frame the slowdown is caused by motion rather than by universe expansion, then we use the relativistic doppler shift formula to get a speed. That formula involves a Lorentz factor (or rather a sqrt ((1+v/c)/(1-v/c)) factor).
Edit: for clarity, the relativistic doppler formula I think should be better represented as (1+v/c)/sqrt(1-(v/c)^2). This makes it more clear that it’s a Lorentz factor (the denominator) representing the relativistic time dilation in combination with the numerator which represents the non-relativistic doppler effect (due to the time it takes light to get here increasing as the thing moves farther away).
Another later edit: We actually don’t want to just use a doppler formula, at least if in the standard picture the expansion rate of the universe is changing. That’s because the expansion rate changes via a gravitational effect that would also be expected to have a gravitational doppler effect. So in a no-expansion picture we want a combination of doppler effect and gravitational redshift (at least for a changing expansion rate), just nothing from stretching of space.
Because of relativistic invariance (or Lorentz covariance or whatever the official term is), the dynamics will not change if we calculate something in a reference frame in which an object is moving, as compared to if we calculate something in the reference frame in which it is stationary, then translate to that reference frame in which it is moving.
In particular neutron stars will not change to black holes, we will see things moving around in the same way despite the differences in density between the reference frames, etc.
Something moving in our reference frame has a mass increase from the kinetic energy it has in our reference frame. It just doesn’t turn into a black hole. I don’t yet intuitively understand why (without doing the work of calculating it which might be a lot of work), but:
Lorentz covariance is a property of our current theories of physics, so a calculation according to our current theories must return that result (that whether an object is a black hole or not is independent of speed).
So, it does no good to sarcastically say that that our current theories must return some other result, and then try to use that claim of what you think the calculation would return as evidence against current theories.
This question can be potentially be interpreted in two ways:
1) “are” the galaxies “really” deformed due to relativistic effects?
2) do the galaxies appear deformed when viewed in a telescope?
The answer to the first question depends on how you extend our reference frame out to them.
If you do it in the standard way then they aren’t “really” length contracted (or actually in a sense they’re expanded, since in the past the same size of galaxy would occupy a larger portion of the universe). If you do it in a way that views the redshift as due to motion (e.g. you go back in time along the light beam reaching us from the galaxy, at each point laying down a space and time coordinate system such that a “stationary” observer according to that coordinate system sees the light beam as having the same redshift that we see) then it is “really” length contracted.
(Edit: as good burning plastic pointed out in a response below, it’s better not to think of it as a real effect. Rather I think it’s better to regard this as definitional—is the galaxy deformed according to the coordinate system we are using.)
The answer to the second question is readily observable. So we should calculate the same answer no matter how you extend the reference frame to the other galaxy, if it’s correct that they are both valid pictures.
Now, since our telescopes see a 2-d picture, the easy answer, that I gave in response to the post on your blog, is that since the motion is almost directly away from us any distortion is along our line of sight and thus is not visible as a deformation in the telescope.
Now I also wanted to do a calculation for 3d telescopes, but I found it difficult to do the calculation for the motion-only-no-expansion picture so am dropping that part of this comment. For a brightness-based distance measure, I think it’s actually an increase, not contraction, of apparent size of a galaxy in the depth direction that you get (as calculated in the standard picture at least).
(edit: I may have messed that up. I imagined an expanding shell of light starting from the far end of a galaxy, then as that shell reaches the near end a new shell expands from the near end. When both shells reach us the shell from the far end the difference in shell sizes is more than the diameter of the galaxy due to universe expansion. So I figured that this would result in some extra dimming of the far and of the galaxy. But I forgot to account for the fact that the ends of the galaxy aren’t stationary in the standard expanding-universe picture—one is moving slightly towards us, the other slightly away if the galaxy as a whole is stationary—which result in the light energy not being evenly distributed across these shells considered in the standard picture. I don’t know which effect will dominate.)
2) do the galaxies appear deformed when viewed in a telescope?
Even in flat Minkowski space-time and even with stereo vision, no they wouldn’t, because the fact that the light from the far side of an object left it earlier than the light from the near side compensates the length “contraction”. If anything, if the object is moving perpendicularly to the line of sight you would see it rotated.
(And I find “length contraction” a pretty misleading name. It’s a purely kinematic effect due to the geometry of spacetime, and no more of a “contraction” than the fact that the height of a pencil is less if it’s askew than if it’s upright.)
No, if an object is moving away from you in Minkowski space time, the time difference of light coming from the far side and from the near side doesn’t compensate the “contraction”—it actually increases the apparent contraction (assuming 3-d perception). For an object moving toward you, it counteracts as you say (and in fact makes the object appear (with our 3-d, but still light-based, camera) longer, just as it also appears to be sped up).
Also what you see when observing a perpendicular motion isn’t actually a rotation. Imagine a cube with opaque edges but otherwise transparent, running at high speed along tracks that are touching and aligned with the edges. The edges must remain touching and aligned with the tracks from any observer’s point of view. So it’s not a rotation but some kind of skew. A sphere will still look circular from a moving observer’s point of view though.
And I find “length contraction” a pretty misleading name. It’s a purely kinematic effect due to the geometry of spacetime, and no more of a “contraction” than the fact that the height of a pencil is less if it’s askew than if it’s upright.
Agreed. I would in fact go further, in that it’s not so much the effect of the geometry of spacetime, as an effect of how we choose to define a coordinate system on that geometry.
No, there is a relativistic mass increase in the galaxies-moving-away picture, and I expect deformation along our line of sight (so not visible in our photographs).
No superluminal galaxies. In the galaxies-moving-away picture, you get the speed by applying the relativistic redshift formula to get the speed from the redshift, which will always come out less than the speed of light while they’re still visible to us. In the conventional picture the galaxies are almost stationary wrt the coordinate system used; you can come up with a superluminal speed by asking “how quickly is the distance between us and that galaxy increasing” where distance is referring to the distance the standard picture would say they are apart from us currently. But that isn’t motion but a change of a distance due to expansion of the universe.
They are “defining ” in a way, that no galaxy is bound to any visible relativistic effect. Everybody does that, albeit on at least two different ways.
How convenient!
We have superluminal galaxies, not bound to relativity. We have nearly light speed galaxies, free of any observable relativistic effect. Our hypothetical ancient space ship sent there (to a nearly light speed away moving galaxy), would slow down all its clocks, the surrounding galaxy wouldn’t.
Unimportant answer: No, it will appear to have slowed down clocks (as was explained to you at the beginning of this thread) and the ancient ship, if it is now at the same distance and stationary with respect to that galaxy, will appear to have the same slowdown.
The more important answer: at this point, this discussion as it is going now is looking pointless.
You have intuitions, backed up by some argumentation, but without a complete mathematical picture, that general relativity produces predictions that don’t match observations.
I have intuitions, backed up by other argumentation, also without a complete mathematical picture, that general relativity produces predictions compatible with observations.
I think my intuitions are better supported, but that’s not what it important.
What is important: general relativity is a physical theory, published long ago and available to anyone, such that this argument can be resolved once and for all by actually doing the math. I am too lazy to do it for the purposes of a comment debate (I might possibly do a blog post though, if it turns out not to be too much work). You come across as probably smart enough to learn how to do the math, so get a general relativity textbook and work it out. You should subjectively estimate a much bigger gain than I do from doing the math, given your subjective assessment that GR gives false predictions and my subjective assessment that it gives true predictions: whoever disproves general relativity will probably get a Nobel prize.
I don’t think, that my intuition should be backed by, or crushed by (doesn’t matter which, really) - more mathematics.
I think my intuition should be backed or crushed by some experimental evidence. Which we probably have.
It seems to me, that no relativistic time slowdown is observed in distant galaxies. What are implications for the GR I really don’t care very much. Theories in Physics are downstream of how the reality is.
It seems to me, that no relativistic time slowdown is observed in distant galaxies.
If you are correct then cosmologists either (1) are very stupid or (2) are knowingly in possession of strong evidence against a pretty much universally accepted, and central, part of physics but haven’t said anything about it.
I am extremely confident that #1 and #2 are both false.
Of course this isn’t scientific evidence that you’re wrong, and if for some reason anything of substance hung on this then it would be appropriate to look more carefully at the evidence and the theory and the mathematics and see what’s going on. And if you really think you’ve got good evidence that relativity is wrong then you should do the work and collect your Nobel prize. For my part, simply on the basis of #1 and #2 (plus the absence of any reason to think you’re so astoundingly smart that it would be unsurprising for all the world’s cosmologists to have simply missed something that you see intuitively) I am confident enough that you’re wrong that I feel no inclination to go to that effort to confirm that the received wisdom hasn’t just yet been overthrown.
I am not very eager to fight against, or for the GR. I don’t care that much about this. It’s a low priority suitable maybe for my occasional blog post and a crosslink to here, where debates are quite long.
Still, no apparent time slowdown in those fast moving galaxies, or some apparent time slowdown—is a bit interesting topic.
As I mentioned earlier, you could count the number of cycles of a laser light beam between two events. For this reason, the apparent slowdown has to be proportional to the redshift. This is a fairly general argument that should work for more theories than just general relativity.
In order for there not to be an apparent slowdown, something really wierd would have to be going on.
At one moment, nothing can be faster than light, the next moment there is a billion of faster than light galaxies.
The next moment, it’s okay, they are not faster than light, only the space is replicating itself between us an them.
Exactly. If you have two ants on a rubber band and you stretch the rubber band, the time derivative of the distance between the ants may be larger than twice the maximum speed at which an ant can walk, but that’s not due to the ants walking so there’s no paradox.
I am not that sure, that there is no paradox. As I see, it can easily be. There is a smaller chance that there isn’t any paradox, after all. Still possible.
I wish, I could find an internet site, which would address those problems. I can’t.
I don’t like this solution. There is nowhere the speed of light to be seen there.
OTOH, the “curvature of space” they mention, is not very necessary in our flat space.
But the Lorentz factor would be needed here. 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. And for the length contraction as well!
That’s the real problem, I think.
That’s not a very useful concept, because it’s nothing but the total energy measured in different units. It only has a name of its own for hysterical raisins. A much more useful concept is the invariant mass, which is the square root of the total energy squared minus the total momentum squared (in suitable units), which (as the name suggests) is the same in all frames of references; in particular, it equals the total energy in the frame of reference where the total momentum is zero. Nowadays when people say “mass” they usually mean the invariant mass, because it makes more sense to call the relativistic mass “total energy” instead.
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.
It’s all baked into z.
z is defined based on frequency change but the frequency change must also be the amount it appears to be slowed down, since e.g. you could measure the number of peaks in a light wave coming from a galaxy as a measure of time.
For the benefit of others: in making this post Thomas is I expect motivated by my responses to his post here:
https://protokol2020.wordpress.com/2013/09/06/embarrassing-images/#comments
In an edit to my last comment, Thomas wrote:
In reply about the blue shift galaxies: they will indeed appear to be sped up from our perspective. Something moving toward us is slowed down in our reference frame by time dilation, but also appears sped up because light takes less and less time to get here. As with redshift, both of these effects are baked into z, so the final (apparent) speedup is what you get from z.
Yes. You were my inspiration for this problem.
How exactly is everything baked into z?
The mass is increased and volume is decreased by factor gamma.
So the density is increased by gamma squared.
Do we really see that?
You can use a light wave as a clock. The ratio of frequency that the light wave is emitted at to the frequency we perceive is 1+z. Thus, the ratio of the time we observe a galaxy for to the amount of time that elapsed in the galaxy’s proper time is also 1+z.
For non-relativistic motion, the speed is approximately proportional to the redshift, but as speeds get higher, that breaks down. Apparent slowdown in terms of v will involve a Lorentz factor, but in terms of z it will not, because of the definition of z being in terms of apparent slowdown (of light).
Not directly. You have to square the velocity of a galaxy, then you must divide it by c (light speed). Then you must divide it by c once again. Then you have to subtract 1, change the sign, compute the square root.
Regardless of the direction of the galaxy in question.
You are very wrong here, I am sorry.
But that’s beside the point. We want the right solution and that solution should be in a good agreement with all those Hubble pictures.
Let me try to explain more clearly.
Imagine there are aliens in the high-z galaxy. They produce a laser beam with a particular frequency, pointed at us. There are also other events occurring in their galaxy, for simplicity at the beam source. The aliens measure the time between two events as a particular number of cycles of the laser light.
Now when we observe the laser light and the events, we must also measure the time between the events as the same number of cycles of the laser light apart. But, we see the cycles at a lower frequency by a factor of 1+z, so we also see the two events an increased time apart by a factor of 1+z.
Now, it seems to me that maybe the issue is disagreement on what exactly we are measuring. What I am talking about is what we see when we look through a telescope. But it seems to me that maybe what you are talking about is what is “really” there in “our” reference frame. Unfortunately that latter thing is ambiguous since you can extend our reference frame to the other galaxy in different ways.
It’s true that you can view far away galaxies as actually moving away from us rather than stationary in an expanding universe—both are valid ways of looking at reality in general relativity. But, there’s a reason most astronomers use metrics in which galaxies are (almost) stationary: it’s much simpler and less confusing.
Do you think, the Lorentz factor id somehow present in z, or not?
z represents frequency differences which is the same as apparent slowdown (or speedup for blueshift). Note, this is apparent slowdown in the sense of what we see through a telescope, not how much it is “really” slowed down in “our” reference frame.
Now, when we imagine an extending our reference frame to that other galaxy in a particular way such that in that particular extension of our reference frame the slowdown is caused by motion rather than by universe expansion, then we use the relativistic doppler shift formula to get a speed. That formula involves a Lorentz factor (or rather a sqrt ((1+v/c)/(1-v/c)) factor).
Edit: for clarity, the relativistic doppler formula I think should be better represented as (1+v/c)/sqrt(1-(v/c)^2). This makes it more clear that it’s a Lorentz factor (the denominator) representing the relativistic time dilation in combination with the numerator which represents the non-relativistic doppler effect (due to the time it takes light to get here increasing as the thing moves farther away).
Another later edit: We actually don’t want to just use a doppler formula, at least if in the standard picture the expansion rate of the universe is changing. That’s because the expansion rate changes via a gravitational effect that would also be expected to have a gravitational doppler effect. So in a no-expansion picture we want a combination of doppler effect and gravitational redshift (at least for a changing expansion rate), just nothing from stretching of space.
Good. So we see a galaxy going away with the 99% c − 7 times dimmer plus Doppler red shift?
49 times denser as well? Some neutron stars are apparent black holes?
Because of relativistic invariance (or Lorentz covariance or whatever the official term is), the dynamics will not change if we calculate something in a reference frame in which an object is moving, as compared to if we calculate something in the reference frame in which it is stationary, then translate to that reference frame in which it is moving.
In particular neutron stars will not change to black holes, we will see things moving around in the same way despite the differences in density between the reference frames, etc.
Splendid. So a fast receding neutron star is “invariant” to the relativistic mass increase.
Good to know.
A neutron is sensitive to it, a neutron star isn’t.
Something moving in our reference frame has a mass increase from the kinetic energy it has in our reference frame. It just doesn’t turn into a black hole. I don’t yet intuitively understand why (without doing the work of calculating it which might be a lot of work), but:
Lorentz covariance is a property of our current theories of physics, so a calculation according to our current theories must return that result (that whether an object is a black hole or not is independent of speed).
So, it does no good to sarcastically say that that our current theories must return some other result, and then try to use that claim of what you think the calculation would return as evidence against current theories.
I don’t understand you.
Are those galaxies relativistically “deformed” or not?
This question can be potentially be interpreted in two ways:
1) “are” the galaxies “really” deformed due to relativistic effects?
2) do the galaxies appear deformed when viewed in a telescope?
The answer to the first question depends on how you extend our reference frame out to them. If you do it in the standard way then they aren’t “really” length contracted (or actually in a sense they’re expanded, since in the past the same size of galaxy would occupy a larger portion of the universe). If you do it in a way that views the redshift as due to motion (e.g. you go back in time along the light beam reaching us from the galaxy, at each point laying down a space and time coordinate system such that a “stationary” observer according to that coordinate system sees the light beam as having the same redshift that we see) then it is “really” length contracted.
(Edit: as good burning plastic pointed out in a response below, it’s better not to think of it as a real effect. Rather I think it’s better to regard this as definitional—is the galaxy deformed according to the coordinate system we are using.)
The answer to the second question is readily observable. So we should calculate the same answer no matter how you extend the reference frame to the other galaxy, if it’s correct that they are both valid pictures.
Now, since our telescopes see a 2-d picture, the easy answer, that I gave in response to the post on your blog, is that since the motion is almost directly away from us any distortion is along our line of sight and thus is not visible as a deformation in the telescope.
Now I also wanted to do a calculation for 3d telescopes, but I found it difficult to do the calculation for the motion-only-no-expansion picture so am dropping that part of this comment. For a brightness-based distance measure, I think it’s actually an increase, not contraction, of apparent size of a galaxy in the depth direction that you get (as calculated in the standard picture at least).
(edit: I may have messed that up. I imagined an expanding shell of light starting from the far end of a galaxy, then as that shell reaches the near end a new shell expands from the near end. When both shells reach us the shell from the far end the difference in shell sizes is more than the diameter of the galaxy due to universe expansion. So I figured that this would result in some extra dimming of the far and of the galaxy. But I forgot to account for the fact that the ends of the galaxy aren’t stationary in the standard expanding-universe picture—one is moving slightly towards us, the other slightly away if the galaxy as a whole is stationary—which result in the light energy not being evenly distributed across these shells considered in the standard picture. I don’t know which effect will dominate.)
Even in flat Minkowski space-time and even with stereo vision, no they wouldn’t, because the fact that the light from the far side of an object left it earlier than the light from the near side compensates the length “contraction”. If anything, if the object is moving perpendicularly to the line of sight you would see it rotated.
(And I find “length contraction” a pretty misleading name. It’s a purely kinematic effect due to the geometry of spacetime, and no more of a “contraction” than the fact that the height of a pencil is less if it’s askew than if it’s upright.)
No, if an object is moving away from you in Minkowski space time, the time difference of light coming from the far side and from the near side doesn’t compensate the “contraction”—it actually increases the apparent contraction (assuming 3-d perception). For an object moving toward you, it counteracts as you say (and in fact makes the object appear (with our 3-d, but still light-based, camera) longer, just as it also appears to be sped up).
Also what you see when observing a perpendicular motion isn’t actually a rotation. Imagine a cube with opaque edges but otherwise transparent, running at high speed along tracks that are touching and aligned with the edges. The edges must remain touching and aligned with the tracks from any observer’s point of view. So it’s not a rotation but some kind of skew. A sphere will still look circular from a moving observer’s point of view though.
Agreed. I would in fact go further, in that it’s not so much the effect of the geometry of spacetime, as an effect of how we choose to define a coordinate system on that geometry.
Can you just answer either:
A—Yes, they are deformed and this is visible on our pictures.
B—No, there is no deformation to be seen on our pictures.
B—No deformation to be seen in our pictures.
Okay. Thank you for this straight answer.
No deformations. No relativistic mass increase. Which should also be visible via orbital velocities inside those galaxies.
But that wouldn’t be a problem at all, we have the dark matter for such cases. Even here at home.
In any case, some galaxies are superluminal, what’s the use of relativistic effects for them? No use.
No, there is a relativistic mass increase in the galaxies-moving-away picture, and I expect deformation along our line of sight (so not visible in our photographs).
No superluminal galaxies. In the galaxies-moving-away picture, you get the speed by applying the relativistic redshift formula to get the speed from the redshift, which will always come out less than the speed of light while they’re still visible to us. In the conventional picture the galaxies are almost stationary wrt the coordinate system used; you can come up with a superluminal speed by asking “how quickly is the distance between us and that galaxy increasing” where distance is referring to the distance the standard picture would say they are apart from us currently. But that isn’t motion but a change of a distance due to expansion of the universe.
You are mistaken.
https://arxiv.org/abs/astro-ph/0011070
There are superluminal galaxies. Quote:
They are defining distance based on the conventional picture, then asking how fast it is increasing with time, as I mentioned in my above comment.
They are “defining ” in a way, that no galaxy is bound to any visible relativistic effect. Everybody does that, albeit on at least two different ways.
How convenient!
We have superluminal galaxies, not bound to relativity. We have nearly light speed galaxies, free of any observable relativistic effect. Our hypothetical ancient space ship sent there (to a nearly light speed away moving galaxy), would slow down all its clocks, the surrounding galaxy wouldn’t.
Funny.
Unimportant answer: No, it will appear to have slowed down clocks (as was explained to you at the beginning of this thread) and the ancient ship, if it is now at the same distance and stationary with respect to that galaxy, will appear to have the same slowdown.
The more important answer: at this point, this discussion as it is going now is looking pointless.
You have intuitions, backed up by some argumentation, but without a complete mathematical picture, that general relativity produces predictions that don’t match observations.
I have intuitions, backed up by other argumentation, also without a complete mathematical picture, that general relativity produces predictions compatible with observations.
I think my intuitions are better supported, but that’s not what it important.
What is important: general relativity is a physical theory, published long ago and available to anyone, such that this argument can be resolved once and for all by actually doing the math. I am too lazy to do it for the purposes of a comment debate (I might possibly do a blog post though, if it turns out not to be too much work). You come across as probably smart enough to learn how to do the math, so get a general relativity textbook and work it out. You should subjectively estimate a much bigger gain than I do from doing the math, given your subjective assessment that GR gives false predictions and my subjective assessment that it gives true predictions: whoever disproves general relativity will probably get a Nobel prize.
I don’t think, that my intuition should be backed by, or crushed by (doesn’t matter which, really) - more mathematics.
I think my intuition should be backed or crushed by some experimental evidence. Which we probably have.
It seems to me, that no relativistic time slowdown is observed in distant galaxies. What are implications for the GR I really don’t care very much. Theories in Physics are downstream of how the reality is.
If you are correct then cosmologists either (1) are very stupid or (2) are knowingly in possession of strong evidence against a pretty much universally accepted, and central, part of physics but haven’t said anything about it.
I am extremely confident that #1 and #2 are both false.
Of course this isn’t scientific evidence that you’re wrong, and if for some reason anything of substance hung on this then it would be appropriate to look more carefully at the evidence and the theory and the mathematics and see what’s going on. And if you really think you’ve got good evidence that relativity is wrong then you should do the work and collect your Nobel prize. For my part, simply on the basis of #1 and #2 (plus the absence of any reason to think you’re so astoundingly smart that it would be unsurprising for all the world’s cosmologists to have simply missed something that you see intuitively) I am confident enough that you’re wrong that I feel no inclination to go to that effort to confirm that the received wisdom hasn’t just yet been overthrown.
I am not very eager to fight against, or for the GR. I don’t care that much about this. It’s a low priority suitable maybe for my occasional blog post and a crosslink to here, where debates are quite long.
Still, no apparent time slowdown in those fast moving galaxies, or some apparent time slowdown—is a bit interesting topic.
Isn’t it?
As I mentioned earlier, you could count the number of cycles of a laser light beam between two events. For this reason, the apparent slowdown has to be proportional to the redshift. This is a fairly general argument that should work for more theories than just general relativity.
In order for there not to be an apparent slowdown, something really wierd would have to be going on.
We have seen weirder things going on. A superluminal galaxy is quite weird, isn’t it?
At one moment, nothing can be faster than light, the next moment there is a billion of faster than light galaxies.
The next moment, it’s okay, they are not faster than light, only the space is replicating itself between us an them.
The next moment the space is growing exponentially. What is not that weird, we are accustomed to exponentials when replicating is involved.
Nothing is really weird, except the logic must not be violated. Everything else can be weird as it wants to.
Exactly. If you have two ants on a rubber band and you stretch the rubber band, the time derivative of the distance between the ants may be larger than twice the maximum speed at which an ant can walk, but that’s not due to the ants walking so there’s no paradox.
I am not that sure, that there is no paradox. As I see, it can easily be. There is a smaller chance that there isn’t any paradox, after all. Still possible.
I wish, I could find an internet site, which would address those problems. I can’t.
Can you?