Astronomy Seminar 5

TRANSCRIPT:  Astronomy Seminar 5. VIHE Seminar: Towaco, NJ - c. 1990 / (209)

Today there are some other topics that I could cover. Thus far we have been talking about essentially the solar system. So one may raise the question that: Well, even if you can interpret various features of the universe described in the Fifth Canto as corresponding to certain features of the solar system as understood in modern terms, still what about the universe as a whole, because the brahmāṇḍa described in the Fifth Canto is supposed to be the entire universe and yet according to modern science the universe as a whole is utterly enormous. It extends out for like 20 billion light years or so if you go out to quasars. So what can one say about that! 

So there’s a chapter in the book here, Chapter 7, in which I discuss modern cosmology. So I thought I would go over that so as to give you an idea of the kind of foundation which modern cosmological thinking has. Now in this chapter I only discuss one particular aspect of modern cosmological theory, although it is an important aspect. But there are many other things that could also be discussed. So what I am talking about there is the idea of the expanding universe. So probably everyone has heard of this concept that the universe is expanding. This is connected today with the Big Bang theory of the universe. According to this idea, at a certain point in time, which would be about 20 billion years ago – 15 or 20, it varies depending on different estimates – all of the matter within the universe was compressed literally into a point, and it exploded. What this means in effect is that there was a mathematical singularity at the beginning of the formation of the universe because when everything is compressed into a literal point, then all the mathematics breaks down, laws of physics are no longer meaningful. So in mathematics that is called a singularity.  

So the idea is that somehow or other, beginning with a singularity, everything expanded out; and initially as the expansion began the universe was in the form of a super-heated plasma of subatomic particles with temperatures of billions and billions of degrees. And it then expanded and as it expanded it cooled, and as it gradually cooled off different forms of particle combinations now became stable as the temperature was low enough for them to form. And so at a certain point, well, protons and neutrons and so on formed, and then they began to form helium nuclei. Gradually when the universe cooled off sufficiently electrons were able to combine with these nuclei to form atoms. So you finally had an expanding cloud of atoms which are mostly hydrogen and helium, almost exclusively hydrogen and helium according to this idea, and the expansion continues and somehow or other these masses of atoms coalesce into clumps which later form galaxies.

Question:  Somehow or other? 

Answer:  Somehow or another, because that is a great mystery. No one has yet even come up with a, an even partially adequate theory of how that is supposed to have happened. It’s a real problem because the expansion tends to drive things apart and yet gravity has to be able to take over and pull them together into clumps. And all of the models people have tried to make for this thus far have failed. In any case, somehow it’s supposed to happen. So galaxies form initially as clouds of gas. Then within the galaxies, due to contraction under the influence of gravitation, these clouds of gas coalesce into stars. So you have millions upon millions of stars forming within the galaxies. And then planets form around the stars, and this earth is one such planet, and then life forms on the earth and so on. This is the story they present.  

[5:00]

So one key ingredient in this whole picture is the idea that the universe is expanding. Now when they say that the universe is expanding they specifically mean that it is expanding in the manner of explosion. So you might ask: Well, how does an explosion expand? Well, if you think about an explosion you’ll see that, let’s say one second after the explosion one object may be, let’s say, 100 feet from the center of the explosion, and another object may be 200 feet. The object that is 200 feet away has gone as twice as fast as the object that’s 100 feet away because it’s gone twice as far. So in an explosion, the rate at which an object is moving away from the center is proportional to how far away from the center it is. That’s the basic rule. So it is claimed on the basis of observation that the galaxies in outer space are moving apart from one another at a rate which is proportional to how far away they are from one another. From our own point of view that means all the galaxies that we see out there on an average are rushing away from us. Among nearby galaxies there are some exceptions to this but on the whole, as you go out, the idea is that they are all rushing away and the further they are the faster they’re going.  

So this is related to a method for determining the distances of galaxies. And according to this method, if you can measure how fast the galaxy is moving away from us then you can tell how far away it is, because the speed is proportional to the distance. So that’s the basic picture of the expanding universe. The Big Bang theory is based on this because if it’s true that the universe is expanding as though it were an explosion, then you can argue: Well, maybe it really is an explosion. In that case, at some point in time, it was then compressed into a small volume from which it exploded. So that’s how the argument goes.  

Q:  I hate to harp on this point, but the universe as a whole is expanding according to the modern idea, but there are so many localised areas of contractions… but no explanation as yet.

A:  Right, that’s what they propose. They cannot explain, as yet, how those contracted regions got started. You see, once you have local contracted regions then you can see why they should remain stable because gravity keeps them clumped together, and then the clumps just continue moving apart from each other. But the problem is: imagine you have an elastic sheet and you are stretching it. The elasticity represents the force of gravity that tends to pull things together. So you are stretching it. What would cause the elastic sheet to break into little clumps which would then contract? Or you might say: Well, it rips in certain ways. But you have to explain how it would rip in such a way as to form clumps of one basic size. So if you actually take a sheet of elastic and do that, you may get it to break, but it will tear in one place or something like that. The question is, how do you get it to tear into a whole series of roughly equal fragments evenly distributed across the whole elastic sheet?  

Q:  The galaxies are more or less uniformly sized?  

A:  More or less. There is considerable variation, but still more or less. Just like people, there is considerable range and size if you look at people, but still there is a certain basic theme and size. So it’s like that with galaxies.  

Q:  Is their distribution in space more or less equal…?

A:  Well, people used to think that their distribution in space was pretty uniform, not perfectly uniform. For a long time they recognised that galaxies tend to form groups. But the idea... well recent observations are tending to show that there’s a whole hierarchy of sizes and clumps, and this is really hard for the people to understand. There are clumps, and there are clumps made of clumps, and clumps made of clumps of clumps, and in between these clumps there are areas called voids in which you don't find anything. This is what they claim. And this is hard for them to explain, you know, why it should do that.  

So they have this basic idea of the expansion. Now what we want to look into is what is the evidence for this, for this expansion.

Q:  Is the earth and the sun and the planets that are visible now, are they moving away from each other…?

[10:14]

A:  The idea is that the earth and the planets in the solar system, they’re bound together by gravity, so they’re not moving away from one another. For that matter, the stars in one galaxy are bound together by gravity. So they’re staying in a clump, but all the clumps are moving away.  

Q:  How long do they move away for – until they stop?

A:  Well, that’s another area of speculation. There are basically two views on that. According to one view, the whole thing is expanding; but as it expands it slows down and at a certain point it will come to it furthest point and then reverse and starts pulling in on itself. And then you’ll have what they call the Big Crunch. So Big Bang is followed by the Big Crunch. 

Q:  Didn't you say that the Vedas don't talk of gravity at all?

A:  No. Gravity of course is a wonderful subject. They talk about gravity; I am going to say some things about it here also.  

The other theory that they have is the expansion just goes on forever. According to that theory our ultimate fate is the galaxies go expanding out, gradually all the suns will die out, they will burn up their nuclear fuel, and be reduced to black, cold embers. All temperatures will gradually fall down to absolute zero, and all you would have would be a few black rocks hurtling through the void forever. And this is the future!

Q:  How does this crunch theory, what does it do [unclear] ...it would no longer be random.

A:  Yeah, there are great problems with the laws of thermodynamics when you apply it to the universe as a whole. The whole idea of the second law of thermodynamics – entropy and so forth – practically you have to restructure these laws when you talk about the universe as a whole. And there are different theories that people have. So that’s another whole area of theoretical…

Q:  [unclear]

A:  Well, one idea is that the entropy does get reversed; they do go back to a state of greater order…

Q:  ...when it turns around the direction of time shifts or something?

A:  Not exactly that. There are different theories. You see entropy is a very artificial concept anyway. It’s only introduced into physics by postulating very special initial conditions, because the laws of physics are time reversible. And the law of entropy says you have irreversible processes. So how do you have irreversible processes if the basic laws are time reversible? So the way to get around that is by postulating very special initial conditions.

So there are many topics to go into there, then it gets very complicated, and it’s really the area of theory. So what I wanted to talk about was this question of: why do they think the universe is expanding anyway? What’s the basis for that? Yeah?

Q:  How is a galaxy defined?

A:  Well, it’s basically defined on the basis of observation. Through telescopes you see these little glowing patches in the sky. Initially they were called nebulae which means clouds – now they’re called galaxies. So they observed these and speculated about what they are. So their present idea concerning what they are is that a galaxy is a huge cloud of stars and gas, floating in a region in which you don’t have so many stars and as much gas. So that’s what they think it is. Yeah?

Q:  Can the individual stars in the galaxies be resolved under present telescopes?

A:  They can be in the Andromeda galaxy. That one is the closest galaxy to us according to them. I think it’s about 1.5 million light years away.  

Q:  [unclear]

[15:00] 

A:  Right. You can see stars there. I have seen photographs of the stars in the Andromeda. It’s a fact, though, in most galaxies you can’t resolve the stars. You just see a milky, cloudy kind of light. So I should point out by the way that, you’ve probably seen pictures of what galaxies look like, you know, usually the picture you see most frequently is what they call the spiral galaxy; it looks something like that, sort of like a pinwheel. There are others though. There are elliptical galaxies which are basically either circular or elliptical with just a sort of central mass of brilliance fading out towards the edges. You will see descriptions to the effect that we are in a galaxy like this, and the sun is out on the edge of one of its spiral arms like that. The point should be made, though, that no one sees that with telescopes. What we actually see through telescopes is a band of stars in the sky, and that’s actually, if you want to see what that’s like, if you look on page 60 and 61 you can see the Milky Way as it actually looks in the sky. It’s a bit dim in these pictures but you can see it. In figure 11 you see this band here – that’s the Milky Way; and in figure 12 it’s a little bit hard to see, but I think it must be this band right here.  

Q:  [unclear]

A:  So it’s interesting, by the way, that according to the Vedic literature the Milky Way corresponds to the celestial Ganges. So that is described.  

Q:  It’s a more concentrated area of stars?

A:  Yeah, the Milky Way is a more concentrated area of stars. That is how it actually looks.  

Q:  [unclear]

A:  I am not aware of any specific reference to galaxies in the Vedic literature except for the Milky Way. But of course there it’s described as this band of stars and it’s identified with the celestial Ganges.  

But anyway, the question is, why do they think that the universe is expanding? So here is the history behind that. As I mentioned previously, there’s a whole series of ideas as to how to measure distances of things. It’s called the "cosmic distance ladder," as you work your way up step-by-step. So when you get out to the area of galaxies, the basic theory they have is that among all galaxies of a given type, the brightest in given group of these should have a fixed value of brightness. That’s a theory.

Q:  Could you say that again?

A:  Among all galaxies of a given type, say an elliptical galaxy, classed according to their shape, if you look at a group of those then the brightest one amongst, in that group... Let’s say in space, in this region, there’s a bunch of them, and there may be other things there, but there are a bunch of galaxies of a given type.

Q:  How do you know they are actually close to each other? I mean you can’t tell for sure.

A:  You see, this is how they reason: They are probably all in a group because, after all, they are one area of space.

Q:  They could be in any distance from you…..

A:  Yeah, one could be close, the other could by [unclear] and so on.

Q:  [unclear]

A:  Assuming that, you say the brightest one amongst them, on the average such a clump has a certain degree of brightness. Now we then take the measured degree of brightness and we apply the inverse square law for diminution of light intensity, and on that basis we calculate the distance. That’s an example of the way they calculate distances. It’s pretty shaky, I mean there are so many things...

Q:  [unclear]

A:  The idea, it’s just like, they are speculating. What they want to do is to get some sort of grasp on how bright the thing is.  

Q:  But compared with what?

A:  You see, the idea is this: there is a  cosmic distance ladder. So suppose they apply this method. Let’s suppose you have some fairly nearby groups of galaxies. So this clump is nearby and using another method that you have, you can tell how far.

Q:  [unclear]

A:  You see it’s a ladder. It’s a ladder, so I am just describing one step in the ladder, that’s the key thing. If you’ve already figured out the distance of this group, one way in which they do that is to use what they call Cepheid variable stars. They are stars that vary in brightness, and they argue the rate at which they vary in brightness is related to how bright they are. So you can do a curve in which you have here a rate of variation, let’s say, and here you have brightness.

Q:  You mean to say how individual stars will vary in brightness over period of time.

[21:11]

A:  Yeah, these stars have the property that they get brighter, then dimmer, brighter and dimmer in a cycle, and the rate at which they do that is related to how bright they are. This is their idea, by some curve, maybe it’s like that. So according to this idea, if you look at a Cepheid variable star and you measure its rate of variation, say here, and then you go up to the curve and go over and that tells you how bright it is.

Q:  [unclear]

A:  It’s the cosmic distance ladder.

Q:  What is the first rung?

A:  Well the first rung, as I mentioned, was stellar parallax.

Q:  That one I can accept.

A:  The second rung was statistical parallax, which I mentioned the other day. And there are a couple of rungs, I have to review it myself to see exactly what they are.

Q:  It’s getting more and more speculative…..

A:  Yes, I think so. I mean to be honest, actually I studied some of this material before I became a devotee and I thought it was doubtful then. Till then I was a true believer in all these things, but I thought it was doubtful back in those days. But in any case, what they do is, suppose you have a bunch of stars in this kind called Cepheid variables; and you have determined by some method how far away they are, then you can measure their rate of variation, and from how far away they are and how bright they seem to be, you can figure out how bright they really are. And then in this one you’ve got this curve, you say, “Well, let’s assume this curve applies everywhere.” And then you say, “Ok, here we have identified this Cepheid variable and we have measured its rate of variation. So we look on this curve – that’s how bright it is. So knowing that, we calculate how far away this is.”  

Q:  By brightness, do you mean, like the average brightness?

A:  Well yeah, because it varies – we measure, say, the midline of the variation. They have the definitions worked out as to how to handle this. So that’s the method used in Cepheid variables. Then it turns out there is another kind of variable star, Lyrae variables. They also vary in brightness and that’s related to how bright they are but the relationship is different than the Cepheid variables. So if you mistake one of these stars as the Cepheid variable and apply this curve it would be the wrong curve. You will get the wrong answers. You have to be careful to determine what type of variable star you are looking at. So there are many complexities in all of this.  

Q:  Is there a desire to…

A:  Their aim is to find out how far away things are. The basic principle behind it is that as things move further away they get dimmer. Yeah?

Q:  ...do they even have one object they know for sure how far away it is?

A:  Yeah well, you see, you have two problems. One is you are not sure how far things are. The other is that objects can be of different intrinsic brightness. In other words, a search light at vast a distance would seem just as bright as a flashlight from a much closer distance. So all you can see is this little point of light. How do you know if it’s a distant searchlight or a nearby flashlight? How can you tell? So this is the problem that they are facing. Yeah?

Q:  [unclear]

[25:25]

A:  Well, they’re trying to find the distance. Of course the basic problem is that no one has been out there. So all we have is light coming down, and they use radio waves – they are coming down also. So from looking at that light you have to figure it all out. That’s difficult. So this is just the beginning of the story. This is how you get the idea that you take some pretty speculative shaky steps that pile on top of one another in order to get an idea of how far away these galaxies are.

So, but let’s suppose you have done that. Now you know how far away they are. Now here is the next step, and this involves what is called the ‘redshift.’ So the basic idea here, you know, light is a wave and it has wavelength and frequency. Wider and longer wavelength we say is red light, as the wavelength gets shorter it goes down the spectrum through yellow, green and so forth, towards the blue end.

Q:  ROYGBIV?

A:  Pardon me? ROYGBIV?

Q:  Red, orange, yellow...

A:  Oh yeah, yeah, ok. If the wavelength is really long, you get into infrared and then you get to microwaves and radio. Going the other way you get the ultraviolet and x-rays and gamma rays and so on.  

So it turns out that if you have something emitting light and is moving towards you then the light shifts in its wavelength towards the blue end of the spectrum. That is, the wavelength becomes less. Now the same thing happens with the sound. So this is often illustrated with sound. Say if you hear a train going by blowing its whistle, you will hear this characteristic sound which is high pitched and when the train goes by it drops in pitch. So it goes… [makes a train sound] ...like that. So the idea is that the whistle is producing sound at a given frequency. As the train is going towards you, the waves are compressed because the train is moving ahead a little bit as it produces each wave. So they are closer together. So they are compressed and have a higher frequency, and so it’s a higher tone. Then as it goes away from you it’s the opposite effect and has a lower frequency. So this is called the Doppler effect. So this can be used to measure the speed of automobiles and so forth, with radar and so on also.   

So some astronomers noted that the light from certain stars has shifted towards the red end of the spectrum. Now I have to explain what is involved here. If you heat a gas, this is a bit of a technical point, if you heat a gas of a particular element and then look at the spectrum of that, that is you take the light from that gas, put it through a prism and that prism will divide it into light of different colors. If you do this with sunlight you’ll get a full spectrum of light. If you do it with a particular element such as sodium, if you have sodium gas, if you heat that in a tube you will see that it looks yellow. And you’ll see in fact that particular bands of light are there in the yellow region of the spectrum. And that’s characteristic of sodium… [break in recording] ...because it’s moving away, the wavelength has shifted towards the red – they call that a redshift. They interpret it as due to the Doppler effect; and they interpret it as meaning that the object is moving away, and the greater the degree of shift, the greater the velocity with which it is moving.

Q:  And at what speed does this become noticeable? Presumably it’s a lot bigger than with sound waves.  

A:  Yeah, it has to be bigger but it depends on the sensitivity of your measuring apparatus. If something is moving away from you and velocity is at the rate of miles per second or kilometres per second it’s easy enough to measure.  

Q:  [unclear]

A:  A few miles per second, you can easily measure it. I am just describing the idea of measuring the speed with which something is moving along your line of sight based on this idea of the shift of the spectral lines of the light, because the whole expanding universe idea depends on this. Apart from this there is no basis for the idea of the expanding universe, so I’ll explain why that is.

[30:34]

So given this basic idea, some people began to observe different galaxies and they said: Well, it seems that the further away a galaxy is, based on our method of measuring distances, the greater the degree of redshift in the light from that galaxy. There’s a fellow named Huddle who originally came up with this idea. In the 1930s he measured distances and redshifts of many galaxies and he said: Well, we see this proportionality that the further away the galaxy is, the greater the redshift. So then he said: Aha, the universe has expanded, and it’s expanding in this manner of an explosion. This was his conclusion. So this was a revolutionary idea because until then nobody had thought of such a concept. Yeah?

Q:  So this redshift is kind of the last rung on the ladder of measuring distances?  

A:  Well you see he was using measurements he made of distance using these other techniques that I alluded to. But, and then he began observing the redshifts and he said there is a correlation. Now later people said: Aha, there is this correlation. So therefore if we want to measure the distance of something it becomes very easy. We just measure the redshift and we know there’s a correlation between the distance and the redshift, so we can get the distance. And that’s what they do, it’s a very widespread method.  

Q:  So they don’t use the other things anymore?

A:  Well, for the really distant things they don’t.  

Q:  Is there any other way to account for the redshift besides the distance thing?

A:  Well that’s what we are coming to. Now according to standard physical theories you are pretty limited in ways of explaining a redshift. For example, a very intense gravitational field will cause the light to shift towards the red. But this isn't a very good explanation because for an incredibly intense gravitational field, if the light of that galaxy has shifted towards the red, then that gravitational field has to apply to that whole galaxy. And no one has any idea how to make that theory work.  

So basically the Doppler effect is their main idea, how to explain the redshift. Yeah?

Q:  Has redshift been measured experimentally on a scale that people can manage?

A:  Yeah that works, that’s not a problem. So this is their basic idea. Now that’s the theory they believe in. Now I can tell you what’s wrong with this after that introduction. Now I should point out that most astrophysicists and astronomers fully accept this theory at the present time. But there are some professional astronomers who have found quite a bit of evidence that completely goes quite against it. So to give you one example, one of these people is a fellow named Halton Arp (wherever he got that name, I don’t know), but he’s an astronomer who worked for many years at Mount Palomar Observatory. He began making a lot of rather disturbing observations. What he would do is to observe galaxies and some objects next to the galaxy called quasars, and even connected to the galaxy by some luminous material. And unfortunately the galaxy would have a redshift indicating, say, it’s a few million light years away, maybe twenty million or something like that. But the quasars would have a redshift indicating they are billions of light years away, radically different distance.  

Now he said: Well this seems to create a bit of a problem. The immediate reply of course was: Well, the quasar is much further away from the galaxy and they just happened to be in the same location in space.

Q:  [unclear]

A:  Yeah, right, but they would make that argument here. But then Arp would come back to them and say: Well what about this luminous bridge which connects them? And they would say: Well there just happens to be a luminous bridge there that may be coming out from the galaxy and just happens to overlay the quasar. So they are actually at vastly different distances. So then Arp would say: Well, I can give you a hundred examples of this. Are you saying this happens by chance over and over again and they just lined up on our line of sight in this way?  

So he has presented this kind of evidence. Basically this would seem to indicate that you can have redshifts that are not related to cosmic distance because if his argument is correct, both the quasar and the galaxy are at nearly the same distance being physically linked and yet they have completed different redshifts. So that creates a problem with the theory. So that’s one example.  

Q:  What was his conclusion then as to why that was happening?

[36:30] 

A:  Well, to give you an idea of what he eventually came up with, I’ll give you another example of something he has pointed out. He pointed out that you can have a series of galaxies lined up on a straight line and this line is really straight. They are almost on the exact straight line as closely as you can measure it, and they have successively increasing redshifts. He gives quite a few examples of this phenomena. So if you say: Well, how are we to explain that? He proposes that it looks at though one galaxy is emitting another galaxy which in turn is emitting another galaxy. Galaxies are shooting out galaxies and when they first come out they have a higher redshift. This is how he interprets it.  

Now that would be bizarre because if galaxies are clouds of gas and stars, then how does one galaxy emit another galaxy? How can one clump of stars and gas throw out another clump of stars and gas? And why would the redshifts be there? So this would indicate, I mean his interpretation would require some kind of radical revision of our ideas of galaxies. But the worst is yet to come. I will sum this up quickly, we are running out of time. So these are some of the observations of Arp.

Then there’s the fact that Hubble's constant – the relation between redshifts and expansion and distance is called Hubble’s constant – and Hubble’s constant has varied incredibly over the years. It had values ranging over... well, some people would call it Hubble’s variable. Like once it was 550, once it was 55, once it was 260, 75, 130. It gets around quite a bit, but that’s not the worst thing.

One astronomer observed that if you measure Hubble’s variable in a direction in which there are a lot of nearby galaxies you will get one value and if you measure it in a direction in which there are not so many nearby galaxies you get a different value. And this works consistently. In other words, the degree of redshift as varying with distance changes depending on whether or not there are any nearby galaxies. So how do you account for that? Well, he proposed what he called the tired light theory. According to this idea, light gets tired out as it travels along long distances and it gets redder as it becomes tired. So according to this idea the redshift is not due to the fact that the things are moving away, it’s caused by the fact that the light gets tired as it goes across space. And then he argued that: Well, if there are a lot of foreground galaxies there must be a kind of particle associated with them, which is floating in space. So there are more of those particles near areas where there are a lot of foreground galaxies. So the light in the distant galaxies goes through more of those particles on its way here so it’s reddened more. And that’s why the Hubble’s constant takes on a different value if you measure it through a cloud of foreground galaxies than it does if it’s measured in another direction. So the whole thing has nothing to do with the expansion of the universe, things moving away from us. It has to do with light changing its wavelength as it moves through space. So that’s another whole theory.

[40:42] 

Well, one may say: Well we don’t like this theory. But what can you say about his data, namely the expansion rate varies depending on whether there are foreground galaxies or not. So this isn't the worst thing. I think I have got four minutes to do the worst thing. The real interesting thing is the redshifts turn out to be quantized. This was observed by a man named Tifft. I have talked to him actually, he is an astronomer. For twenty years he has been publishing papers on this in the Astrophysical Journal, and he told me on the phone that they publish his papers because nobody can find anything wrong with them technically. But he said there is a sort of tacit agreement that nobody talks about them – sort of a barrier of silence technique. What he has observed is that redshifts from distant galaxies come in groups. Now how to explain this. The basic idea is that the redshifts are multiples of a certain basic value of 72 of the units that they use. So that means you can have a redshift of value 72 or close to that. It could be you know 71, 73 or so, or it could be 144 or you know like 142 or 147 or so. Or it could be, what’s the next one, around that, with some range around that. So these are all multiples of this basic unit. So he said if you make these measurements you will find that the redshifts form groups like this in multiples of this unit.

Q:  [unclear]

A:  Everywhere. So he said, “Well now, what does this mean?” Well if things are moving away from us and their velocity of recession is what determines the redshift, which is the Doppler effect, does that mean that the things are moving away from us in multiples of these different speeds. That doesn't make sense. We’d expect a continuous variety of speeds for things moving away, not that they would come in these clumps, and there are things even worse than that. This is the last point that I will sandwich in.

Q:  Is that the fifth shift?

A:  If you look at two galaxies which are orbiting one another in space – you see, if the galaxies are nearby, supposedly by gravity they must orbit around one another – so if you measure the redshifts of these relative to one another, that is you take the redshift from the first one and subtract it from the redshift of the second, that should tell you the relative velocity of those things as they are orbiting around. So if you look at a lot of galaxies orbiting, you should get a whole variety of relative velocities depending upon where you can catch them in their orbits, but those are also quantised...