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 5th January 2023, 07:10 AM #441 Ziggurat Penultimate Amazing     Join Date: Jun 2003 Posts: 53,938 Originally Posted by Mike Helland If you divide both sides by c, you get a formula for light travel time: If you divide any distance by a velocity, you will get a time. Why do you interpret it as a travel time, though? That only works if you divide a travel distance by the velocity it was traveled at. But the distance in that equation is a proper distance, ie, the distance between the CURRENT position of the source and the observer. It is NOT the distance that light has traveled between the source and the observer. So why should you interpret it as a travel distance, when it's not the distance that light traveled? You're just picking out random **** and throwing it at a wall to see what sticks. But why would you actually expect any of it to? You aren't some super genius. You have no special insights. If something isn't making sense to you, it's not because hundreds of people much smarter than you who have spent years studying the subject all missed something that you alone discovered. It's because you don't understand the subject. __________________ "As long as it is admitted that the law may be diverted from its true purpose -- that it may violate property instead of protecting it -- then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and all-absorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious." - Bastiat, The Law
 5th January 2023, 11:55 AM #442 Mike Helland Illuminator   Join Date: Nov 2020 Posts: 3,643 Originally Posted by W.D.Clinger It sounds as though Helland physics requires you to reject these parts of mainstream science:general relativity (which predicted the cosmic microwave background (CMB)) measurements of the CMB obtained by COBE, WMAP, and Planck the mainstream physics that tells us how those measurements of the CMB place tight bounds on the curvature of the universe There is more to GR than the FLRW metric and there are more practical things to do with GR than apply it to the universe as a whole. And you don't have to reject mainstream physics. Some skepticism about our understanding of the universe's beginning, a theory that's only as old as Indiana Jones and Raiders of the Lost Ark, however, is not unhealthy.
 5th January 2023, 12:00 PM #443 Mike Helland Illuminator   Join Date: Nov 2020 Posts: 3,643 Originally Posted by Ziggurat But the distance in that equation is a proper distance, ie, the distance between the CURRENT position of the source and the observer. It is NOT the distance that light has traveled between the source and the observer. So why should you interpret it as a travel distance, when it's not the distance that light traveled? If light travels for 1 billion years, at the speed of light, how far has it traveled? The distances we talked about in the expanding universe are: (1) distance between source and observer at time of light's emission (2) distance between source and observer at time of light's arrival (3) distance light actually traveled (1) and (2) are proper distances at different points in time in an expanding universe. (3) is light travel time * light speed, and works for non-expanding and expanding universes.
 5th January 2023, 12:09 PM #444 Ziggurat Penultimate Amazing     Join Date: Jun 2003 Posts: 53,938 Originally Posted by Mike Helland The distances we talked about in the expanding universe are: No ****, sherlock. But you're treating 2 and 3 as if they're the same, even though they aren't. __________________ "As long as it is admitted that the law may be diverted from its true purpose -- that it may violate property instead of protecting it -- then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and all-absorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious." - Bastiat, The Law
 5th January 2023, 12:15 PM #445 Mike Helland Illuminator   Join Date: Nov 2020 Posts: 3,643 Originally Posted by Ziggurat No ****, sherlock. But you're treating 2 and 3 as if they're the same, even though they aren't. No I'm not. In an expanding universe, a galaxy with z=11: (1) 2.66 Gly (2) 32 Gly (3) 13.2 Gly (3) is calculated by its lookback time * c.
 5th January 2023, 12:18 PM #446 Ziggurat Penultimate Amazing     Join Date: Jun 2003 Posts: 53,938 Originally Posted by Mike Helland No I'm not. Yes you are. You used distance 2 from one model, and asked why it matched a 3 from a different model, as if that was meaningful. It's not. __________________ "As long as it is admitted that the law may be diverted from its true purpose -- that it may violate property instead of protecting it -- then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and all-absorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious." - Bastiat, The Law
 5th January 2023, 12:23 PM #447 Mike Helland Illuminator   Join Date: Nov 2020 Posts: 3,643 Originally Posted by Ziggurat Yes you are. You used distance 2 from one model, and asked why it matched a 3 from a different model, as if that was meaningful. It's not. False. An expanding model has those three distances. In a non-expanding model, and assuming the galaxy in question has peculiar velocity of zero, there is just one distance. I compare distance (3) from the expanding model, to the only distance in a non-expanding model. The lookback travel times in FLRW mimic my formula: Code: `t=1/H0 * z/(1+z)` And in the case of an empty universe, they are identical. Coincidence? Last edited by Mike Helland; 5th January 2023 at 12:24 PM.
 5th January 2023, 12:36 PM #448 Ziggurat Penultimate Amazing     Join Date: Jun 2003 Posts: 53,938 Originally Posted by Mike Helland False. An expanding model has those three distances. In a non-expanding model, and assuming the galaxy in question has peculiar velocity of zero, there is just one distance. I compare distance (3) from the expanding model, to the only distance in a non-expanding model. The lookback travel times in FLRW mimic my formula: Code: `t=1/H0 * z/(1+z)` And in the case of an empty universe, they are identical. Coincidence? Oh, my mistake. This is even dumber than I thought. You constructed your own model, with no real justification, and you think it means something that one number from your made-up model matches something from a real model. It doesn't mean anything. It's not hard to make up bull **** models where one number matches a real model. __________________ "As long as it is admitted that the law may be diverted from its true purpose -- that it may violate property instead of protecting it -- then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and all-absorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious." - Bastiat, The Law
 5th January 2023, 12:42 PM #449 Mike Helland Illuminator   Join Date: Nov 2020 Posts: 3,643 Originally Posted by Ziggurat Oh, my mistake. This is even dumber than I thought. You constructed your own model, with no real justification Both: 1+z = Eemit / Eobs And: 1+b = Eobs / Eemit Are legitimate ways to quantify redshift. They lend themselves toward two different distance relationships: d = zc/H0 d = -bc/H0 We could also make these time relationships, just be removing the c. t = z/H0 t = -b/H0 But the first way, is known to be inaccurate unless z << 1. The second way produces results much closer to FLRW, and are identical when gravity doesn't affect redshift (aka empty universe). Quote: and you think it means something that one number from your made-up model matches something from a real model. It doesn't mean anything. It's not hard to make up bull **** models where one number matches a real model. One number? My model only predicts one distance (or time) per z. And it is a perfect match for the distance you get in an empty universe when you multiply the time light travel with its speed. So, for the record, this is pure coincidence? Last edited by Mike Helland; 5th January 2023 at 12:47 PM.
 5th January 2023, 01:02 PM #450 Ziggurat Penultimate Amazing     Join Date: Jun 2003 Posts: 53,938 Originally Posted by Mike Helland One number? My model only predicts one distance (or time) per z. Yes, one number: distance. And that's crap. A model should be able to do a lot more than that predict one number. Quote: So, for the record, this is pure coincidence? Probably. __________________ "As long as it is admitted that the law may be diverted from its true purpose -- that it may violate property instead of protecting it -- then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and all-absorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious." - Bastiat, The Law
 5th January 2023, 01:15 PM #451 Mike Helland Illuminator   Join Date: Nov 2020 Posts: 3,643 Originally Posted by Ziggurat Yes, one number: distance. And that's crap. A model should be able to do a lot more than that predict one number. The negative-blueshift/distance relationship predicts distance from negative-blueshift and vice versa. The negative-blueshift/time relationship predicts time from negative-blueshift and vice versa. In and of themselves, they aren't complete models. They work for non-expanding models, and an expanding model where gravity doesn't affect redshifts. So, yeah, you're right. But it's kind of non-sequitur. Depending on what model the equations are used in, you'll get different predictions. My non-expanding model predicted what JWST is showing us right now. Quote: Apparently not. Another predictable phenomenon is that people will self-gaslight themselves into believing that this was expected all along. I have been watching in real time as the community makes the transition from “there is nothing above redshift 7” (the prediction of LCDM contemporary with Bob Sanders’s MOND prediction that galaxy mass objects form by z=10) to “this was unexpected!” and is genuinely problematic to “Nah, we’re good.” This is the same trajectory I’ve seen the community take with the cusp-core problem, the missing satellite problem, the RAR, the existence of massive clusters of galaxies at surprisingly high redshift, etc., etc. A theory is only good to the extent that its predictions are not malleable enough to be made to fit any observation. As I was trying to explain on twitter that individually high mass galaxies had not been expected in LCDM, someone popped into my feed to assert that they had multiple simulations with galaxies that massive. That certainly had not been the case all along, so this just tells me that LCDM doesn’t really make a prediction here that can’t be fudged (crank up the star formation efficiency!). This is worse than no prediction at all: you can never know that you’re wrong, as you can fix any failing. Worse, it has been my experience that there is always someone willing to play the role of fixer, usually some ambitious young person eager to gain credit for saving the most favored theory. It works – I can point to many Ivy league careers that followed this approach. They don’t even have to work hard at it, as the community is predisposed to believe what they want to hear. https://tritonstation.com/2022/12/30/remain-skeptical/ Quote: Probably. So you're saying there's a chance. Let me ask you this. Is there some reason to prefer quantification of redshift as z over -b?
 5th January 2023, 01:44 PM #452 Ziggurat Penultimate Amazing     Join Date: Jun 2003 Posts: 53,938 Originally Posted by Mike Helland So, yeah, you're right. But it's kind of non-sequitur. This entire thread is basically a non-sequitor. Quote: My non-expanding model predicted what JWST is showing us right now. No, it doesn't. Your non-expanding model has basically nothing to say about any of JWST's observations. How big should galaxies be? You don't know. How dense should they be? You don't know. What temperature should they be? You don't know. Your model has no way of quantifying basically anything. You aren't actually comparing your model to JWST observations, not in any meaningful way. Quote: Is there some reason to prefer quantification of redshift as z over -b? The math will give you the same results either way, if you do it correctly. I'm not interested in looking into it any deeper than that. If you think that there's an inconsistency between the two, then you're making a math error somewhere. And if you aren't making a mistake (and so the results are identical), then the reasons for choosing one over the other aren't all that important. __________________ "As long as it is admitted that the law may be diverted from its true purpose -- that it may violate property instead of protecting it -- then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and all-absorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious." - Bastiat, The Law
 5th January 2023, 01:53 PM #453 Mike Helland Illuminator   Join Date: Nov 2020 Posts: 3,643 Originally Posted by Ziggurat The math will give you the same results either way, if you do it correctly. If z = -b, you would be right. But that's not the case. Depending on which one you decide, you will see the range of redshift changes from 0 < z < infinity to -1 < b < 0: z: b: Quote: I'm not interested in looking into it any deeper than that. If you think that there's an inconsistency between the two, then you're making a math error somewhere. And if you aren't making a mistake (and so the results are identical), then the reasons for choosing one over the other aren't all that important. There are clearly consequences for whether the observed energy is in the numerator or denominator, based on where asymptotes appear.
 5th January 2023, 02:17 PM #454 Ziggurat Penultimate Amazing     Join Date: Jun 2003 Posts: 53,938 Originally Posted by Mike Helland If z = -b, you would be right. No. If z and b are well defined, then I'm right. Quote: Depending on which one you decide, you will see the range of redshift changes from 0 < z < infinity to -1 < b < 0: So what? Why would you expect them to cover the same range? Why should they need to? The graph isn't the result. Are you familiar with inverse temperature in thermodynamics? Oh, who am I kidding, of course you aren't. Anyways, inverse temperature is actually more fundamental than temperature. You can use either one, but graphs will look different depending on which one you use. Most of the time, it's easier to work with temperature, because of things like constant heat capacity materials. But there are cases where inverse temperature is easier to work with (paramagnets in a magnetic field, where you can have negative absolute temperatures, is a classic example). But using one or the other isn't a problem, as long as you do the math right. __________________ "As long as it is admitted that the law may be diverted from its true purpose -- that it may violate property instead of protecting it -- then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and all-absorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious." - Bastiat, The Law
 5th January 2023, 02:28 PM #455 Mike Helland Illuminator   Join Date: Nov 2020 Posts: 3,643 Originally Posted by Ziggurat No. If z and b are well defined, then I'm right. They are well defined. Code: ```1 + b = 1 / (1 + z) -b = z / (1 + z)``` So the two different relationships: Code: ```t = z / H0 t = -b / H0``` When written in terms of z are: Code: ```t = z / H0 t = z / (1 + z) * 1 / H0``` Clearly, t grows without bounds in the first one, and t is bound by 1 / H0 in the second one. It makes a difference which formula you use to quantify redshift. The results contradict. Redshift is either z, or z/(1+z). Which one you choose makes a difference.
 5th January 2023, 02:44 PM #456 Mike Helland Illuminator   Join Date: Nov 2020 Posts: 3,643 Originally Posted by Ziggurat Are you familiar with inverse temperature in thermodynamics? Oh, who am I kidding, of course you aren't. Anyways, inverse temperature is actually more fundamental than temperature. You can use either one, but graphs will look different depending on which one you use. Most of the time, it's easier to work with temperature, because of things like constant heat capacity materials. But there are cases where inverse temperature is easier to work with (paramagnets in a magnetic field, where you can have negative absolute temperatures, is a classic example). But using one or the other isn't a problem, as long as you do the math right. If b = 1 / z you'd have a good point. But that's not true either. The "1+z" and "1+b" makes things less straightforward. Last edited by Mike Helland; 5th January 2023 at 02:46 PM.
 5th January 2023, 02:46 PM #457 Ziggurat Penultimate Amazing     Join Date: Jun 2003 Posts: 53,938 Originally Posted by Mike Helland They are well defined. OK then. So what's the problem? Quote: Clearly, t grows without bounds in the first one, and t is bound by 1 / H0 in the second one. It makes a difference which formula you use to quantify redshift. The results contradict. I said it would work either way, if you don't **** up the math. You ****** up the math. Let me lay it out for you. t = z/H0 is not actually correct. It is a low-z approximation to the correct function. You can get a low-z approximation of the function as follows: t(dz) ~ t(0) + t'(z)|0dz where dz indicates some small value of z, the prime indicates a derivative with respect to z and the vertical bar and subscript indicate the function is to be evaluated at z=0. t(0) = 0, and t'(z)|0 = 1/H0. This is simple Taylor expansion of the true function for t(z), or if you like, linear approximation of t(z) around zero. Now, you can do the same thing using t(b), and the two will be related to each other. In particular, t'(b) = dt(b)/db = dt(z)/dz * dz/db. But dz/db = -1 when evaluated at z=0, which is how we get the approximation t(b) = b/H0 Now, this approximation WILL NOT WORK if higher order derivatives are not zero and you go far enough away from zero. You have not found an inconsistency. What you have found is that an approximation which works at low z/low b breaks down at higher z/higher b. And it doesn't break down identically, because they aren't identical variables. The relationship between b and z is more complex than b = -z. So it's no ******* surprise that these approximations, which were only valid in the first place when b ~ -z, start failing when b != -z. You haven't discovered something new. You're just as bad at math as you are at physics. __________________ "As long as it is admitted that the law may be diverted from its true purpose -- that it may violate property instead of protecting it -- then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and all-absorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious." - Bastiat, The Law
 5th January 2023, 02:48 PM #458 Ziggurat Penultimate Amazing     Join Date: Jun 2003 Posts: 53,938 Originally Posted by Mike Helland If b = 1 / z you'd have a good point. The "1+z" and "1+b" makes things less straightforward. 1+z = 1/(1+b), so yeah, it's not quite as straight forward, but it's actually a pretty damn close comparison. Either one will work, if you don't **** up. You ****** up. __________________ "As long as it is admitted that the law may be diverted from its true purpose -- that it may violate property instead of protecting it -- then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and all-absorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious." - Bastiat, The Law
 5th January 2023, 02:51 PM #459 Mike Helland Illuminator   Join Date: Nov 2020 Posts: 3,643 Originally Posted by Ziggurat Let me lay it out for you. t = z/H0 is not actually correct. It is a low-z approximation to the correct function. Right. That's why I propose t=z/(1+z) * 1/H0. This new equation works for all z's. I came about that by quantifying redshift as 1+b=Eobs/Eemit. Which is identical to FLRW when gravity doesn't affect redshift. Which you say is "probably" a coincidence. Maybe it is. Maybe it isn't.
 5th January 2023, 04:22 PM #460 W.D.Clinger Philosopher     Join Date: Oct 2009 Posts: 5,047 Originally Posted by Mike Helland Originally Posted by W.D.Clinger It sounds as though Helland physics requires you to reject these parts of mainstream science:general relativity (which predicted the cosmic microwave background (CMB)) measurements of the CMB obtained by COBE, WMAP, and Planck the mainstream physics that tells us how those measurements of the CMB place tight bounds on the curvature of the universe There is more to GR than the FLRW metric and there are more practical things to do with GR than apply it to the universe as a whole. Although it is certainly true that there is a whole lot more to GR than the FLRW models, the FLRW models are a mathematical consequence of the fundamental field equations of GR. You can't deny the FLRW models without denying those field equations, which are the basis for everything in GR. What you can do without denying GR is to say the FLRW models are inadequate to model the universe in which we live. Everyone knows the FLRW models are idealized models. We use the FLRW models because they are exact and mathematically tractable solutions of the field equations, and there are good reasons to believe they are realistic approximations in the large scale. An even better reason to believe the FLRW models are realistic is that they predicted several physical phenomena for which we now have an impressive body of empirical evidence, notably (1) the red shifts of light from distant light sources and (2) the Cosmic Microwave Background Radiation. If you choose to argue that the FLRW models are completely unrealistic, which appears to be the corner into which you have painted yourself, then you have a responsibility to state your Helland physics explanation for red shifts and the CMB. So far, you've just been shrugging your shoulders and saying shifts happen. And you have not been able to come up with any remotely plausible explanation for the CMB. Originally Posted by Mike Helland And you don't have to reject mainstream physics. Some skepticism about our understanding of the universe's beginning, a theory that's only as old as Indiana Jones and Raiders of the Lost Ark, however, is not unhealthy. No, you don't have to reject mainstream physics. You, however, are promoting a Helland physics that runs contrary to mainstream physics in quite a few ways (which have been explained at length within this thread), so your promotion of Helland physics is an implicit rejection of mainstream physics. Originally Posted by Mike Helland The lookback travel times in FLRW mimic my formula: Code: `t=1/H0 * z/(1+z)` And in the case of an empty universe, they are identical. Coincidence? Let's not forget that the only FLRW model that can mimic your formula is a model for a completely empty universe that has hundreds of times as much negative curvature as would be compatible with observations of the Cosmic Microwave Background based on data obtained by COBE, WMAP, and Planck. Originally Posted by Mike Helland It makes a difference which formula you use to quantify redshift. The results contradict. Redshift is either z, or z/(1+z). Which one you choose makes a difference. No, it doesn't make any difference whether you choose to think in terms of the red shift z or the blue shift b. That is obvious to anyone who understands high school algebra, because the defining equations for z and b establish a simple algebraic relationship between the two, allowing any formula that uses one of the two to be converted into a completely equivalent formula that uses the other. What makes a difference is not your choice between z and b, but the equation you choose to use for d. Both of the (incompatlble) equations you have been flogging can be expressed using either z or b, so whether you choose to use z or to use b makes no difference. Originally Posted by Mike Helland That's why I propose t=z/(1+z) * 1/H0. This new equation works for all z's. I came about that by quantifying redshift as 1+b=Eobs/Eemit. Which is identical to FLRW when gravity doesn't affect redshift. Which you say is "probably" a coincidence. Maybe it is. Maybe it isn't. Let's not forget that the only FLRW model that agrees with your formula is a model for a completely empty universe that has hundreds of times as much negative curvature as would be compatible with observations of the Cosmic Microwave Background based on data obtained by COBE, WMAP, and Planck.
 5th January 2023, 04:27 PM #461 Mike Helland Illuminator   Join Date: Nov 2020 Posts: 3,643 Originally Posted by Ziggurat 1+z = 1/(1+b), so yeah, it's not quite as straight forward, but it's actually a pretty damn close comparison. Either one will work, if you don't **** up. You ****** up. You've said I messed up many times. But no one has shown the mistake. Astronomers have always been somewhat biased toward wavelength, rather than speaking of light in frequency or energy. And a positive increase in wavelength suggests redshift should be quantified as a positive number too. And initially, the redshifts were so low, that using z made more sense than using b, because b is a cramped region from -1 to 0, and z is a more spacious region from 0 to infinity. And it seems intuitive that z or -b should make no difference. But it does in the distance relationship. d = zc/H0 d = -bc/H0 If you express -b in terms of z, it's z/(1+z), so: d = zc/H0 d = z/(1+z) * c/H0 Which looks like this: Clearly there's a difference based on choice of quantifying redshift as z or -b. No one has shown the mistake. Redshift as a positive number or negative number is not an arbitrary choice, due to the asymptotes.
 5th January 2023, 04:40 PM #462 Mike Helland Illuminator   Join Date: Nov 2020 Posts: 3,643 Originally Posted by W.D.Clinger Although it is certainly true that there is a whole lot more to GR than the FLRW models, the FLRW models are a mathematical consequence of the fundamental field equations of GR. You can't deny the FLRW models without denying those field equations, which are the basis for everything in GR. Can you reject an Einstein-deSitter universe without denying GR? How about a Milne universe? Quote: If you choose to argue that the FLRW models are completely unrealistic, which appears to be the corner into which you have painted yourself, then you have a responsibility to state your Helland physics explanation for red shifts and the CMB. So far, you've just been shrugging your shoulders and saying shifts happen. And you have not been able to come up with any remotely plausible explanation for the CMB. Guilty. Quote: No, you don't have to reject mainstream physics. You, however, are promoting a Helland physics that runs contrary to mainstream physics in quite a few ways (which have been explained at length within this thread), so your promotion of Helland physics is an implicit rejection of mainstream physics. Implicit based on the assumption that one should only hold in their mind a single idea, and that two competing ideas are bad. I think two competing ideas are good. Keep in mind, this is about what happened billions of years ago billion of light years away. This isn't about deciding to poison a river or anything. Quote: Let's not forget that the only FLRW model that can mimic your formula is a model for a completely empty universe that has hundreds of times as much negative curvature as would be compatible with observations of the Cosmic Microwave Background based on data obtained by COBE, WMAP, and Planck. No one is forgetting that. Let's not forget that LCDM with different parameters makes different predictions, and my equations are based only the Hubble constant. As our ability to make measurements of distant objects improves, the discrepancy should be testable. Quote: No, it doesn't make any difference whether you choose to think in terms of the red shift z or the blue shift b. That is obvious to anyone who understands high school algebra, because the defining equations for z and b establish a simple algebraic relationship between the two, allowing any formula that uses one of the two to be converted into a completely equivalent formula that uses the other. Right. d = zc/H0 can be written as: d = -b/(1+b) * c/H0 And d = -bc/H0 can be written as: d = z/(1+z) * c/H0 While there are 4 equations there, its really a choice between 2 equations, as the other 2 are analogs. The choice between: d = -bc/H0 And: d = z/(1+z) * c/H0 Is arbitrary. There is no difference. The choice between d = -bc/H0 And d = zc/H0 Is not. There is a difference. Quote: What makes a difference is not your choice between z and b, but the equation you choose to use for d. Both of the (incompatlble) equations you have been flogging can be expressed using either z or b, so whether you choose to use z or to use b makes no difference. Yes. Of course.
 5th January 2023, 06:56 PM #463 W.D.Clinger Philosopher     Join Date: Oct 2009 Posts: 5,047 Originally Posted by Mike Helland Originally Posted by W.D.Clinger Although it is certainly true that there is a whole lot more to GR than the FLRW models, the FLRW models are a mathematical consequence of the fundamental field equations of GR. You can't deny the FLRW models without denying those field equations, which are the basis for everything in GR. Can you reject an Einstein-deSitter universe without denying GR? How about a Milne universe? The FLRW models comprise an entire family of models. It is therefore obvious that not all of those models describe the universe in which we live. It is therefore obvious that you can conclude (as most everyone has now concluded) that the Einstein-deSitter FLRW model does not accurately describe the universe in which we live. It is, however, a more accurate description of our universe than the completely empty universe with enormous negative curvature that is described by the particular FLRW model you continue to mention because its equation for distance coincides with the equation you invented for Helland physics. If, however, you deny the fact that the Einstein-deSitter model is a solution of GR's field solutions, then you are denying GR. That is an example of what I meant by saying "You can't deny the FLRW models without denying those field equations, which are the basis for everything in GR." Notice the plural in "FLRW models". In your eagerness to reject all predictions based upon FLRW models, you have often appeared to be denying the fact that the mathematical objects known as the FLRW models are a mathematical consequence of general relativity. You can't do that without rejecting general relativity.
 5th January 2023, 07:22 PM #464 Mike Helland Illuminator   Join Date: Nov 2020 Posts: 3,643 Originally Posted by W.D.Clinger In your eagerness to reject all predictions based upon FLRW models, you have often appeared to be denying the fact that the mathematical objects known as the FLRW models are a mathematical consequence of general relativity. I never said that. You reject an empty FLRW universe. Does that mean you reject FLRW? Do you reject GR? No, you don't. That'd be silly. GR is like an operating system that can run many different programs: * Minkowski * Schwarzschild * Kerr * Reissner–Nordström * Kerr–Newman * Gödel * Friedmann–Lemaître–Robertson–Walker and on and on. FLRW applies to the universe as a whole. It's not practical. And LCDM, the model based on it, has a lot of serious problems. If it does turn out to be the wrong model of the universe, GR itself has nothing to worry about.
 6th January 2023, 07:13 AM #465 Ziggurat Penultimate Amazing     Join Date: Jun 2003 Posts: 53,938 Originally Posted by Mike Helland You've said I messed up many times. But no one has shown the mistake. I just explained your mistake. And you're making it again. Quote: d = zc/H0 d = -bc/H0 Both of these are first-order approximations, only valid for small z or b. Quote: If you express -b in terms of z, it's z/(1+z), so: d = zc/H0 d = z/(1+z) * c/H0 Again, both first order approximations only valid for small z or b. And when z is small, to first order z = z/(1+z). So they match in the region where the original expressions are expected to be valid (small z). They will diverge when one or more of the original expressions are not valid. Quote: Clearly there's a difference based on choice of quantifying redshift as z or -b. No ****, Sherlock. You've got a first order approximation expressed in terms of two different variables, those approximations are going to diverge from each other. That's to be expected, because that's the nature of Taylor expansion series of a function expressed in different variables: the full functions will be identical, but each term in the expansion will not be. It doesn't mean that there's any actual difference in the true function as expressed in either variable. But you aren't working with the true function, only the first order approximation of it. Quote: No one has shown the mistake. I've explained your mistake. You don't know enough math to understand it, which is why you made the mistake in the first place. Have you even ever taken calculus? Do you know how to take a derivative? Do you know what a Taylor expansion is? It sure as hell doesn't appear that you do. Quote: Redshift as a positive number or negative number is not an arbitrary choice, due to the asymptotes. The asymptotes are where the approximations break down the most. That's exactly where you shouldn't expect EITHER expression to be valid to begin with. __________________ "As long as it is admitted that the law may be diverted from its true purpose -- that it may violate property instead of protecting it -- then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and all-absorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious." - Bastiat, The Law
 6th January 2023, 07:26 AM #466 Mike Helland Illuminator   Join Date: Nov 2020 Posts: 3,643 Originally Posted by Ziggurat Both of these are first-order approximations, only valid for small z or b. d = zc/H0 is only approximate for small z's. d = z/(1+z) * c/H0 is approximate for all z's. You can see the here they are equal at the beginning, and then clearly diverge. The first one just grows and grows. The second one approaches c/H0.
 6th January 2023, 07:35 AM #467 Ziggurat Penultimate Amazing     Join Date: Jun 2003 Posts: 53,938 Originally Posted by Mike Helland d = zc/H0 is only approximate for small z's. First off, different expansions (ie, the expansion of different possible universes) will have different functions d(z). In all cases, it is approximate for small z's by the definition of H0. It may be approximate for larger z's for certain expansions, depending on what d(z) is. Quote: d = z/(1+z) * c/H0 is approximate for all z's. No. It's approximate for small z's for all expansions, again by the definition of H0. It may be approximate for larger z's for certain expansions, again depending on what d(z) actually is. Your claim that it is approximate for all z's is unjustified. In general, it will not be. This is part of your mistake. Quote: You can see the here they are equal at the beginning, and then clearly diverge. No ****. They're first order approximations expressed in different variables, of course they agree at low z, and of course they diverge at larger z. So the **** what? That's just calculus. Which it's become clear you don't understand. __________________ "As long as it is admitted that the law may be diverted from its true purpose -- that it may violate property instead of protecting it -- then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and all-absorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious." - Bastiat, The Law
 6th January 2023, 07:39 AM #468 W.D.Clinger Philosopher     Join Date: Oct 2009 Posts: 5,047 Originally Posted by Ziggurat I've explained your mistake. You don't know enough math to understand it, which is why you made the mistake in the first place. Have you even ever taken calculus? Do you know how to take a derivative? Do you know what a Taylor expansion is? It sure as hell doesn't appear that you do. Ziggurat's questions were answered here.
 6th January 2023, 07:48 AM #469 Mike Helland Illuminator   Join Date: Nov 2020 Posts: 3,643 Why do you keep doing the "****" stuff? You want to swear, because you can't come up with other words, but you censor yourself like grade schooler. Maybe you should just chill out a bit. Originally Posted by Ziggurat No ****. They're first order approximations expressed in different variables, of course they agree at low z, and of course they diverge at larger z. So the **** what? That's just calculus. So the **** what? The z/(1+z) equation diverges away from the linear z equation, and mimics what LCDM predicts. While z/(1+z) matches exactly LCDM with ΩM=0 and ΩΛ=0, it is slightly off from ΩM=0.32 and ΩΛ=0.68. The discrepancy makes it a testable, falsifiable hypothesis. The hypothesis is that z/(1+z) is the actual redshift distance relationship, and LCDM ΩM=0.32 and ΩΛ=0.68 is the approximation.
 6th January 2023, 08:06 AM #470 Ziggurat Penultimate Amazing     Join Date: Jun 2003 Posts: 53,938 Originally Posted by Mike Helland Why do you keep doing the "****" stuff? You want to swear, because you can't come up with other words, but you censor yourself like grade schooler. I don't censor myself. The forum autocensor censors me. And it's a violation of the MA to try to bypass the autocensor. But it's not a violation of the MA to type the ******* words and just let the autocensor do its thing. And I can come up with other words. But honestly, you're not worth the effort. Quote: Maybe you should just chill out a bit. Maybe you should learn some math. Seriously, spend a year learning calculus. Get a textbook (and old one will do, calculus isn't exactly cutting edge), read it, do the problems, check solutions online to see if you're getting it. It would benefit you enormously. I had forgotten our previous exchange about integrals, the stupid was so strong it burned the memory away. Quote: The hypothesis is that z/(1+z) is the actual redshift distance relationship, and LCDM ΩM=0.32 and ΩΛ=0.68 is the approximation. Observations don't support this hypothesis. __________________ "As long as it is admitted that the law may be diverted from its true purpose -- that it may violate property instead of protecting it -- then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and all-absorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious." - Bastiat, The Law
 6th January 2023, 08:06 AM #471 Ziggurat Penultimate Amazing     Join Date: Jun 2003 Posts: 53,938 Originally Posted by W.D.Clinger Ziggurat's questions were answered here. I forgot that exchange. Yeah, that was... wow. __________________ "As long as it is admitted that the law may be diverted from its true purpose -- that it may violate property instead of protecting it -- then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and all-absorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious." - Bastiat, The Law
 6th January 2023, 08:12 AM #472 Mike Helland Illuminator   Join Date: Nov 2020 Posts: 3,643 I made this GIF to demonstrate how t = z/(1+z) * 1/H0 (black) compares to LCDM (red) with different parameters. It starts with ΩM=0 and ΩΛ=0, and you see they are exact matches. Next it adds matter by turning up ΩM to 1.0. This predicts too young of a universe and doesn't match the data. So set ΩM=0.32, and that gets you half way back to where you started, but still too low. So turn up ΩΛ=0.68, and the dark energy pushes the line back to just about where it began. But not exactly. Which means two mathematical models make two predictions which are on the verge of being testable.
 6th January 2023, 08:18 AM #473 Mike Helland Illuminator   Join Date: Nov 2020 Posts: 3,643 Originally Posted by Ziggurat Observations don't support this hypothesis. Model independent distance measures don't exist out far enough to test the discrepancy yet. When they do, we can let the observations speak for themselves.
 6th January 2023, 08:26 AM #474 Pixel42 Schrödinger's cat     Join Date: May 2004 Location: Malmesbury, UK Posts: 15,454 Originally Posted by Mike Helland Why do you keep doing the "****" stuff? I marvel at the fact he's still bothering to correct your continually repeated mistakes at all. I think he can be forgiven the occasional expletive whilst doing so. __________________ "If you trust in yourself ... and believe in your dreams ... and follow your star ... you'll still get beaten by people who spent their time working hard and learning things" - Terry Pratchett
 6th January 2023, 08:29 AM #475 Mike Helland Illuminator   Join Date: Nov 2020 Posts: 3,643 Originally Posted by Pixel42 I marvel at the fact he's still bothering to correct your continually repeated mistakes at all. I think he can be forgiven the occasional expletive whilst doing so. Do these two lines like similar to you? One blows up into the stratosphere, and one mimics LCDM. My "mistake" is not realizing they are equally wrong, apparently.
 6th January 2023, 09:40 AM #476 Ziggurat Penultimate Amazing     Join Date: Jun 2003 Posts: 53,938 Originally Posted by Mike Helland My "mistake" is not realizing they are equally wrong, apparently. No. Your mistake was expecting anyone to care that a first-order approximation which is known to only be valid at small z doesn't match at large z. That doesn't mean anything. Why should anyone care? Actually, that's only one of your mistakes. There are more. __________________ "As long as it is admitted that the law may be diverted from its true purpose -- that it may violate property instead of protecting it -- then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and all-absorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious." - Bastiat, The Law
 6th January 2023, 09:47 AM #477 Mike Helland Illuminator   Join Date: Nov 2020 Posts: 3,643 Originally Posted by Ziggurat No. Your mistake was expecting anyone to care that a first-order approximation which is known to only be valid at small z doesn't match at large z. Known to be valid at small z is d = zc/H0. Inverting the formulas and getting d = z/(1+z) * c/H0 was something I came up with in November. You think these are equally wrong?
 6th January 2023, 10:45 AM #478 Ziggurat Penultimate Amazing     Join Date: Jun 2003 Posts: 53,938 Originally Posted by Mike Helland You think these are equally wrong? I didn't say that either. But again, so what? Both are still approximations. If one is a better approximation than another, that doesn't make it exact, because it's not. It doesn't expose any sort of inconsistency either, because they're approximations derived from different Taylor expansions and obviously won't be the same. Learn some calculus, it will do you a world of good. __________________ "As long as it is admitted that the law may be diverted from its true purpose -- that it may violate property instead of protecting it -- then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and all-absorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious." - Bastiat, The Law
 6th January 2023, 10:52 AM #479 Mike Helland Illuminator   Join Date: Nov 2020 Posts: 3,643 Originally Posted by Ziggurat I didn't say that either. But again, so what? Both are still approximations. If one is a better approximation than another, that doesn't make it exact, because it's not. It doesn't expose any sort of inconsistency either, because they're approximations derived from different Taylor expansions and obviously won't be the same. t=z/H0 is a linear approximation. t=z/(1+z) * 1/H0 is not. It's literally what the lookback time function for an empty universe is. https://arxiv.org/abs/astro-ph/9306002 Notice how close an empty universe and 68% dark energy universe are: They are only off by a bit, which should be testable.
 6th January 2023, 11:11 AM #480 Ziggurat Penultimate Amazing     Join Date: Jun 2003 Posts: 53,938 Originally Posted by Mike Helland t=z/H0 is a linear approximation. t=z/(1+z) * 1/H0 is not. Yes it is. It's a linear approximation of t(b). It's not linear in z if you change the variable to z, but it's still a linear approximation in b. And conversely, if you express t=z/H0 in terms of b, it won't be linear in b, but it still comes from a linear approximation. Quote: It's literally what the lookback time function for an empty universe is. So what? The universe isn't empty, and rather obviously so. The solution to the expansion of an empty universe is of limited interest. Quote: They are only off by a bit, which should be testable. It's already been tested. __________________ "As long as it is admitted that the law may be diverted from its true purpose -- that it may violate property instead of protecting it -- then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and all-absorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious." - Bastiat, The Law

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