I actually don't feel like Mercury's perihelion precession was a good test since the theory was designed around that observation. From what I recall of the history, that's not true. Einstein already had almost all the field equations, and then applied them to the Mercury problem in his November 18, 1915 paper. He was quite excited when the result turned out to agree with the observations, precisely because he hadn't designed the theory to get Mercury right. On November 25 he modified the equations to their final, current form, but the prediction for Mercury did not change.
I think you did somewhat misread the above paragraph.
Newtonian theory predicts light bending even for zero-mass particles. (The amount of deflection is given in the article you linked.) But it does not explain why zero mass particles all have the same speed. That is where relativity differs from Newton.
By the way, I highly recommend Kevin Brown's web site (the mathpages.com site you linked). It contains many interesting calculations and musings.
I'm talking about general relativity here, so Michelson-Morley is irrelevant except insofar as validates non-gravitational portions of Einstein's theory. Special relativity was already better established. At the time of the eclipse experiment in 1919, the only other experimental evidence for GR specifically was Mercury's perihelion precession, which IMHO is not alone sufficient to declare the acceptance of the theory.
Try Science News. Short, clear articles on new scientific developments and some review articles, and when they do write about sociological or historical meta-issues in science, it's usually done so in a relatively unbiased manner and confined to separate articles.
And you think the reporting on biology has something to do with the evolution vs. creationism debate? Most biology reporting isn't about evolution.
I think the amount of biology reporting has to do with:
1. People are interested in what goes on in their own bodies. 2. Many biology stories have a direct health/medicine angle, which people are very interested in. 3. The rest of the biology stories usually have to do with charismatic animals.
and maybe:
4. Biology is often easier for people to understand or identify with than, say, physics.
(Actually, I think the opposite effect is at work in physics reporting: journalists seem to be in a competition to outdo each other in convincing people how weird and non-understandable physics is. You get the Exceptionally Simple Theory of Everything and other extremely speculative and exotic ideas, instead of the latest advances in atomic/molecular optics.)
Only a few new theories which suplant the old model do so with a really compelling single test. We can think of a few of the exceptions: General Relativity and the 1919 eclipse, Actually that one got more credit than it deserved. The error bars on that result were huge, and it's now questionable whether Eddington's experiment was able to distinguish general relativity from competing predictions, such as the Newtonian prediction of half the light bending. (To forestall possible comments from others, yes, Newtonian gravity predicts light bending for zero mass photons.) An interesting example of the opposite phenomenon: a new theory being hailed perhaps too eagerly. (On the other hand, there was also Mercury's perihelion precession.)
There's no central Usenet server. If you post an article to your own server, then it sends it off to a few more servers, who in turn send it to more, etc. So it's peer to peer in that sense. In the sense of how users get the news from their local server, though, it's client-server. (If you can say such a thing... on some systems, you don't actually make a network connection to a server to read your news, you just read articles stored on your local filesystem.)
Not to mention that the enormous changes in the speed of light that the grandparent poster is suggesting would seriously screw up all nuclear and atomic physics, to the point that nucleosynthesis, fission, and fusion wouldn't work, atomic structure would be totally different from anything we observe if it atoms existed at all, etc. You can quibble about the early universe, but we sure as hell would have noticed that if it happened within 6000 years! There's a reason why people are looking for deviations from c — or rather, to be meaningful, in dimensionless constants to which c is related, like the fine structure constant — on the order of 0.001%! Anything larger is dramatically inconsistent with the universe we see.
(He also seems to think that because that light could once travel through the universe in less time, that means it was faster. No, that means the universe was smaller.)
You are confusing time dilation due to gravity (i.e. mass) with time dilation due to velocity. No, I am not. Nowhere did I make any such claim. In fact, I gave an explicit example of gravitational time dilation (black hole event horizons) where Schroeder's argument goes similarly wrong.
Let me explain by quoting a section of the book. I know what gravitational time dilation is. I am saying that a time dilation factor — be it gravitational or velocity — is not the correct way to calculate the amount of proper time measured in the reference frame of some observer.
An observer in the modern universe sees light emitted by an early-universe observer as being time dilated. But this does not mean that an early universe observer would calculate a different value for the universe's current age! The only way for an observer to calculate a time between two events, according to his own clock, is to actually move between them. Any such observer will measure the same age as an Earth observer, assuming that observer is in the unique cosmological frame.
He later explains that the techniques used to relate the mass of the sun to the time dilation, can also be applied to the universe as a whole. This is wrong, for reasons I already explained twice.
Do understand that the fact that the rate of time being dependent on mass is established science. Schroeder is not creating anything new here, merely teaching what is already taught in physics classes around the world. Ahem. Speaking of what is taught in physics classes, I have taught general relativity at university, and what Schroeder says is NOT what GR says is the correct way to measure time.
"I have a friend who's an artist and he's sometimes taken a view which I don't agree with very well. He'll hold up a flower and say, 'Look how beautiful it is,' and I'll agree, I think. And he says, 'You see, I as an artist can see how beautiful this is, but you, as a scientist, oh, take this all apart and it becomes a dull thing.
"And I think that he's kind of nutty. First of all, the beauty that he sees is available to other people and to me, too, I believe, although I might not be quite as refined aesthetically as he is; but I can appreciate the beauty of a flower. At the same time I see much more about the flower that he sees. I can imagine the cells in there, the complicated actions inside which also have a beauty....
"Also, the processes, the fact that the colors in the flower evolved in order to attract insects to pollinate it is interesting - it means that insects can see the color. It adds a question: Does this aesthetic sense also exist in the lower forms? Why is it aesthetic? All kinds of interesting questions which shows that a scientific knowledge only adds to the excitement and mystery and the awe of a flower. It only adds; I don't understand how it can subtract."
Feynman also said, more poetically,
"Poets say science takes away from the beauty of the stars -- mere globs of gas atoms. Nothing is "mere." I too can see the stars on a desert night, and feel them. But do I see less or more? The vastness of the heavens stretches my imagination -- stuck on this carousel my little eye can catch one million year old light... What is the pattern, or the meaning, or the why? It does not do harm to the mystery to know a little about it. For far more marvelous is the truth than any artists of the past imagined! Why do the poets of the present not speak of it? What men are poets who can speak of Jupiter as if he were like a man, but if he is an immense spinning sphere of methane and ammonia must be silent?
I think that Schroeder does not use "time dilation" in the sense that you are explaining it. Just as there is a change in the time over which an observed event occurs based on the velocity of the observer, there is also a similar effect from gravity itself. Calculating time dilation factors is the WRONG way to calculate the age of anything. As I said, if you were to follow this procedure with the gravitational field of a black hole, you would conclude that because there is an infinite time dilation factor between an observer at the horizon and a distant observer, then the horizon observer experiences no time and does not age. But he does.
Similarly, if you apply this procedure to the twin paradox, it wouldn't tell you how much younger the traveling twin is when he returns. You have to know his path in spacetime (e.g., how far he turned, when he turned around). In other words, you have to integrate proper time.
Time dilation factors can be useful in calculations, but they don't tell you the amount of time experienced by a given observer between two events.
Then compare that to the sun (with its much larger mass) observing it. So Schroeder is using the fact that the rate of time is different depending on the mass of the observer. He then uses the Cosmic Background Radiation to reasonably estimate the mass of the universe. Then he applies this rate of time to the approximately 15 billion years, and finds that from the universe's perspective it is only 144 hours old (i.e. six days). But there is no ACTUAL COSMOLOGICAL OBSERVER who experienced the age of the universe as 144 hours. All cosmological observers experienced it to be 15 billion years.
Schroeder is basically making up a definition for "age of the universe" which does not correspond to the time elapsed by any observer. This contradicts relativitity, which says that time is ONLY definable by the experience of some specified observer.
He is not using "God time" as you say it, but rather universe time. As I said, there is only one, unique time in general relativity which can be called "universe time", and that is the time experienced by the "cosmological observers" who view the universe as isotropic (e.g., who are "at rest" with respect to the cosmic background).
According to this time, the universe is 15 billion years old.
Schroeder has made up a number which he may call universe time, but does not correspond to any physically meaningful (i.e., measurable) quantity in general relativity.
There is nothing preventing someone from using different references to measure time, just like someone can use different units to measure length (feet, meters, angstroms, etc). That's the problem. Schroeder hasn't used a different reference frame to measure time. He's just multiplied our time by a "time dilation factor", which is meaningless, because that doesn't actually give you the amount of time which elapses in a different reference frame.
The cosmological observers measure the same amount of time as an Earth observer, because the Earth essentially is a cosmological observer.
It is true that it's possible to construct observers who think the universe is only 144 hours old. What's not possible, in general relativity, is to construct a unique set of observers. In order to get 144 hours, you have to choose an observer who is moving with arbitrary speed with respect to a cosmological observer, and in an arbitrary direction. Then the question arises: why that speed, and why that direction? Why should anyone care about the the time measured by a randomly moving observer? It's not any kind of UNIVERSAL time: the only unique choice for that, singled out by the geometry of a homogeneous and isotropic space, is the cosmological reference frame.
Thanks for making my point. We don't know, but they claim they do. Who the hell is "they"? Certainly not cosmologists.
If they said "This phase of the universe is now known to be X billion years old" that would be at least acceptable. It's implicit in the statement, just like people often say "universe" when they mean "observable universe".
Just because the state of the universe was hot and dense does not mean it began near then. It doesn't mean that it didn't, either. We don't know.
To me, saying it 'began' at all it nonsense. That's your philosophical prejudice, not anything having to do with science. Universes with and without beginnings are both logical possibilities; it is up to experiment to decide which possibility applies to our universe (if possible, which may be doubtful).
The big bang theory is very unconvincing, mostly because there doesn't seem to be a way that matter could form out of nothing and suddenly explode in a short time too. Big Bang cosmology doesn't say that matter formed out of "nothing". (Some theories might say that, utilizing ideas analogous to quantum pair production of matter, but not all of them do.)
It also doesn't say that this matter "exploded". Rather, the space which contains it expanded.
I don't know why you say there doesn't seem to be a way that it could expand in a short time. It's a prediction of general relativity. Why don't you think that's a way?
I wonder if there was any beginning of the universe at all. Many cosmologists wonder that too. It's an open question.
Also, if there was a beginning, nothing should prevent another universe from forming again. That depends on how it happened, I suppose.
Ok, I re-read your original post... we're talking about two different aspects of Schroeder's book. I was talking about the part where he was trying to use relativity to justify a 7-day creation by playing with reference frames. I don't know about the part where he supposedly derives a 15.75 billion year age for the universe. If it's based on the above reasoning, though (e.g., starting with an assumption of 7 days and applying a time dilation factor), it's wrong.
The science is presented exactly as scientists describe it, only instead of using Earth as the basis for the rate of time, he uses the universe as a whole. There is only one kind of time which is singled out cosmologically speaking, and that's the time measured by an observer who views the cosmic background radiation as isotropic. The Earth is such an observer. (Or rather, it's within 0.002c of being such an observer, which means that the difference in elapsed times is negligible.) If you use cosmological time, you get the same answer as if you use Earth time: about 14 billion years.
It's been some time since I last looked at his arguments. But IIRC, what Schroeder does — incorrectly — is attempt to calculate a "time dilation factor" between present times and the early universe, and argue that this implies that there is a reference frame in which the major elements of the universe's evolution took only 7 days. But this is not correct: the way you calculate elapsed time according to some observer in general relativity is by integrating proper time along that observer's worldline. And when you do that, for any cosmological observer, you get the same answer, one which is essentially identical to the elapsed time according to an Earth observer.
Schroeder's reasoning is analogous to the erroneous logic which concludes that you can never fall into a black hole because the time dilation between a distant observer and the horizon is infinite. Time dilation factors between distant points do not determine elapsed proper time according to an observer's own clock (and are, in general, not even well defined; they depend on the coordinate system you choose).
Actually, Schroeder makes other errors, like pretending that there is an absolute "God's frame" in which you can measure time. In relativity, there is no such absolute frame. The closest you can get is the cosmologically preferred frame, which is singled out due to the high spatial symmetry of the universe. But as I said, the Earth is pretty much in that frame, so it essentially measures Earth time.
I have seen estimates in the 10 to 15 billion range over the last decade. Individual estimates have been in that range, with large error bars. It's when you combine them — along with other observational constraints that don't give direct age estimate but do disentangle confounding factors — that the error bars converge on the current ~14 billion years; each data set rules out a different region of parameter space. And some of the data sets are simply better than others. There are ways of estimating the age inaccurately, but we obviously favor the ways of estimating the age accurately.
Quite obviously it is not any sort of acceptable error margin. "Acceptable"? What the hell does that mean?
I got my history from a 500 page biography. My readings point to it not being a peaches and cream reception, far from it. I'm not talking about convincing the smart scientists. I'm talking about convincing the rest of the scientific community. The scientists who were actually working in that field of physics were convinced rather quickly. And frankly, who cares about the others? What a biologist or even, say, a condensed matter physicists knows about, say, cosmology isn't appreciably better than a layman.
History other than your own is written by other people, so unless you were there, you can't vouch for the authenticity of the situation any more than I can. Um, yes, it's all there in print: read the journal articles published in response to Einstein's theory. There was not massive resistance in the literature to, say, SR. This is unlike other theories that genuinely were strongly resisted by the the core researchers in that field (e.g., continental drift).
But the point of the example was that it was analogous to the previous point. I could replace the name Einstein with "foobar" and Newton with "barfoo" and it still illustrates the point. You don't have an analogy, you have an assertion about how science progresses, which is the typical layman's stereotype of daring rebels being derided or ignored by the conservative mainstream. Replacing Einstein and Newton with "foobar" and "barfoo" merely rephrases your assertion; it does not lend actual credence to it.
But you, with your ridiculous margin of error, may. Care to give an actual scientific argument why it is "ridiculous"? One that doesn't boil down to, "It seems like a small number to me, therefore I refuse to believe it"?
There are plenty of scientific results which are known to far more precision than this, as well as those which are known to far less. If you want to object to the error bars on this particular result, you have to give actual evidence why they should be larger than they are believed to be (and not smaller!).
Science that isn't bull made up by the researcher because they don't what they are doing. Statistically, 50% of the scientific community are in this boat. The other half isn't usually that much better. Yeah, why don't you support your point further with made-up facts and numbers? You're doing so well at that so far.
50% of the scientific community are below the median, by definition. That does not mean "they don't know what they are doing", and it doesn't mean that the other 50% "isn't much better".
I find it funny that the universe is now a new age. This differs from the old age figures that were spouted from people saying "it is" as well. The new age is within the error bars of the old age, so there's nothing funny about it. There would only be a discrepancy if it was outside of the error bars.
Case in hand, Albert Einstein received a cold reception to his theories. Not really true. In fact, he rather quickly found fame. Lorentz, Poincare, and Minkowski had all proposed theories that were basically Einstein's special relativity, for very similar reasons; people knew that Newton wasn't working, and the time was ripe for SR. Einstein just put the physical theory on simple conceptual grounds. And after SR, the scientific community eagerly anticipated GR. Einstein became world famous shortly thereafter with the Eddington eclipse observations. Yeah, sure, there were skeptics since there wasn't much observational evidence for GR at the time — but that's as it should be.
But hey, don't let history get in the way of your fantasies about the reactionary scientific orthodoxy.
The 2% means that the universe's mass-energy density is within 2% of the critical density that implies space is flat. (Above that critical density, space is positively curved; below, negatively.) It is possible to compare the two with general relativity, which relates geometric curvature to mass and energy via gravitational dynamics.
I'm afraid that you have a serious misunderstanding of general relativity. Considering that I've taught the subject at university, I rather doubt that.
Spacetime is indeed flat as a whole No. If it was, then we'd be in the Minkowski spacetime of special relativity, there would be no gravity, and space would not expand.
In general relativity, our universe is approximately described by the Friedmann-Lemaître-Robertson-Walker metric. This geometry demonstrably has non-zero Riemann curvature.
(besides your separation of space and time is rather nonsensical). No. There are infinitely many ways to separate spacetime into space and time (technically, a "foliation of the manifold", or a "3+1 decomposition"). In special relativity, each inertial observe singles out his/her own such separation, so that they disagree on which events are purely timelike or spacelike separated. (They agree on whether they are overall timelike or spacelike, though.)
In a generic curved spacetime, there is no unique foliation, so one's choice of what to call "space" is rather arbitrary. But in a FLRW spacetime, which is homogeneous and isotropic and therefore highly symmetric, there is: you can use the class of "cosmological observers" who view space as isotropic. The Earth is close to being such an observer (to within 0.2% of c). It is according to this foliation that cosmologists say that "space is flat".
It can be curved by mass-energy, but in the absence of ant external influence it is flat. You may have noticed that our spacetime contains mass-energy, and is therefore curved.
That's why light travels in a straight line in the absence of gravitational forces. Light travels in a straight line in the presence of gravitational forces as well, if you're talking about "straight in spacetime" (it is always a spacetime geodesic, no matter what the curvature). It can travel in a curved line in space.
Only in the presence of gravitational forces does the line appear to curve, since it is in fact traveling in a straight line along curved spacetime. To take the sheet of rubber analogy. Spacetime can be curved by a marble on the sheet, but the sheet by itself would be flat, In the rubber analogy, the sheet is not flat. But that's beside the point; in the usual "gravitational well" example, the sheet represents space, and has nothing to say about the geometry of spacetime.
really stupid question, but when was light made? I've always been under the impression that photons were emitted at the earliest stage (despite the universe being opaque/impermeable to them) but it just occured to me that I may be wrong Well, before the electroweak symmetry breaking (a few trillionths of a second after the Big Bang), the electromagnetic field didn't even exist as an independent field; it was unified with the weak nuclear force. So it's slightly ambiguous. But photons did exist, so I guess you can say that light was present. All bets are off at earlier times with potentially larger unifications, though.
(all of my non elementary physics knowledge comes from Asimov's 80s books for children)) Those Asimov science books were damn good, if sadly outdated.
also, does it not blow anyone else's mind how all the universe could fit into an infinitesimally small space. We don't know if it was "infinitestimally" small (i.e., an actual point), or just very very small.:-) And remember that new matter was created via pair-production as the universe expanded in the very early stages.
The speed of light is about 3E8 meters per second. Meters is a measure of space. If space expands, not the matter in it, the number of meters between points stays the same. No, if space expands, the number of meters between points increases. That's the definition of "space expands".
So if light takes longer to traverse it, then the speed of light relative to the space it traverses is less. You still have not defined what "the speed of light relative to space" is.
If the light is self-perpetuating in space, but its rate of perpetuation (units distance per unit time) changes, The speed of light does not change. Any observer who it passes, at any time or place, will measure it to travel at speed c.
then it seems that its speed is based on its perpetuation not in space, but in something else that's constant relative to changing space. I have no idea what that means or what it has to do with the fact that light is a self-perpetuating electromagnetic wave which is affected by the geometry of the spacetime in which it travels.
What does relativity say is the reason that light travels at the same speed while the scale of space through which it travels changes? What's the mechanism? What mechanism? Why should it be otherwise? It's not being accelerated; it travels at the same speed. The fact that space is expanding doesn't change that.
And I've been around since 1949, so my statement stands. They've only gotten accurate - we think - in the last 20-odd years. In other words, you refuse to accept that things can change.
You've missed the point entirely, however. I'm not saying the science is crap - I'm saying there's too much we do NOT know to be sure of what we think we DO know. I know what you're saying, and I think you're wrong. It's just the usual excuse that people give to pretend that we don't know anything useful about any science they have a gut feeling about. They wave their hands and say, "I don't care how much data we have, how accurate it is, how many new phenomena we are now able to explain, or how many theories we've tested and ruled out — `we don't know enough'". A total handwaving argument that neatly sidesteps arbitrarily large amounts of evidence by refusing to engage with such evidence. A favorite tactic of creationists, global warming skeptics, and so on.
Yes, there are things we don't know, but you're going to have to do better than that; you can't simply dismiss the fact that there are also a lot of things we do know, and quite accurately. We do have some idea of the errors associated with our measurements. The age-of-universe estimates in the mid-20th century had huge error bars on them precisely because we knew they were very inaccurate. Whether you admit it or not, science has progressed.
So in fact the constant speed of light is not relative even to expandable space. I have no idea what it means for the speed of light to be relative to "space".
Light takes longer to travel across "all of space" than it did, say 13.70 billion years ago. It's not traveling each meter, taking a constant amount of time. As the meters get larger over time, light takes longer to traverse each one. The meters don't get larger, space does. An actual physical meter stick made out of matter stays the same size.
Which is intriguing, because I thought light travels as a self-perpetuating disturbance in space itself, It is.
but really it looks like space can change around whatever is "waving" that we detect as light. The geometry of space can change too. This does not contradict the previous statement.
That kind of constancy does imply there's something more fundamental than space out of which the universe is made, which light does traverse as a constant speed. It doesn't imply that. It's a prediction of general relativity, which does not posit "something more fundamental than space out of which the universe is made". Therefore, there is a counterexample to your claimed implication: there exists a theory which has that kind of constancy, but does not have "something more fundamental than space".
Has anyone dusted off the "ether" yet, since more exotic models have made the old disproofs less simply clear? Yes, but "aether" theories (really, theories that break local Lorentz invariance) are not required to explain the above-described properties of light in an expanding space.
I just have a hard time accepting that from the vantage point of one planet, given our present state of (crap) technology, and given the size and (apparent) age of the universe, that some scientist can tell me a broad fact about the universe "to within a 2% error margin." Our technology isn't "crap". It's not perfect, but it's good enough to measure these things to within a few percent relative error. The era of precision cosmology started with COBE circa 1990, which found that the blackbody spectrum of the CMBR so perfectly matched theory that the error bars were smaller than the thickness of the line used to draw the curve (see, e.g., here, with the error bars magnified by 400x so they're visible). Things have only gotten better from there.
The nature of the Big Bang itself is what makes this kind of precision possible: very small deviations from flatness in the early universe get enormously magnified by the universe's expansion, to the point that they're detectable by our instruments. The expansion of the universe is a microscopic lens on the early universe.
Sorry - I expect such figures will continue to be "revised" - i.e., doubled or halved repeatedly - in what's left of my lifetime as they have been repeatedly to this point in my life. To the contrary, several independent lines of evidence have been converging on the same numbers for the last 10-20 years, in contrast to the state of cosmology at any time preceding 1990.
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I think you did somewhat misread the above paragraph.
Newtonian theory predicts light bending even for zero-mass particles. (The amount of deflection is given in the article you linked.) But it does not explain why zero mass particles all have the same speed. That is where relativity differs from Newton.
By the way, I highly recommend Kevin Brown's web site (the mathpages.com site you linked). It contains many interesting calculations and musings.
I'm talking about general relativity here, so Michelson-Morley is irrelevant except insofar as validates non-gravitational portions of Einstein's theory. Special relativity was already better established. At the time of the eclipse experiment in 1919, the only other experimental evidence for GR specifically was Mercury's perihelion precession, which IMHO is not alone sufficient to declare the acceptance of the theory.
Try Science News. Short, clear articles on new scientific developments and some review articles, and when they do write about sociological or historical meta-issues in science, it's usually done so in a relatively unbiased manner and confined to separate articles.
And you think the reporting on biology has something to do with the evolution vs. creationism debate? Most biology reporting isn't about evolution.
I think the amount of biology reporting has to do with:
1. People are interested in what goes on in their own bodies.
2. Many biology stories have a direct health/medicine angle, which people are very interested in.
3. The rest of the biology stories usually have to do with charismatic animals.
and maybe:
4. Biology is often easier for people to understand or identify with than, say, physics.
(Actually, I think the opposite effect is at work in physics reporting: journalists seem to be in a competition to outdo each other in convincing people how weird and non-understandable physics is. You get the Exceptionally Simple Theory of Everything and other extremely speculative and exotic ideas, instead of the latest advances in atomic/molecular optics.)
There's no central Usenet server. If you post an article to your own server, then it sends it off to a few more servers, who in turn send it to more, etc. So it's peer to peer in that sense. In the sense of how users get the news from their local server, though, it's client-server. (If you can say such a thing ... on some systems, you don't actually make a network connection to a server to read your news, you just read articles stored on your local filesystem.)
Not to mention that the enormous changes in the speed of light that the grandparent poster is suggesting would seriously screw up all nuclear and atomic physics, to the point that nucleosynthesis, fission, and fusion wouldn't work, atomic structure would be totally different from anything we observe if it atoms existed at all, etc. You can quibble about the early universe, but we sure as hell would have noticed that if it happened within 6000 years! There's a reason why people are looking for deviations from c — or rather, to be meaningful, in dimensionless constants to which c is related, like the fine structure constant — on the order of 0.001%! Anything larger is dramatically inconsistent with the universe we see.
(He also seems to think that because that light could once travel through the universe in less time, that means it was faster. No, that means the universe was smaller.)
An observer in the modern universe sees light emitted by an early-universe observer as being time dilated. But this does not mean that an early universe observer would calculate a different value for the universe's current age! The only way for an observer to calculate a time between two events, according to his own clock, is to actually move between them. Any such observer will measure the same age as an Earth observer, assuming that observer is in the unique cosmological frame. He later explains that the techniques used to relate the mass of the sun to the time dilation, can also be applied to the universe as a whole. This is wrong, for reasons I already explained twice. Do understand that the fact that the rate of time being dependent on mass is established science. Schroeder is not creating anything new here, merely teaching what is already taught in physics classes around the world. Ahem. Speaking of what is taught in physics classes, I have taught general relativity at university, and what Schroeder says is NOT what GR says is the correct way to measure time.
Reminds me of this quote by Feynman,
"I have a friend who's an artist and he's sometimes taken a view which I don't agree with very well. He'll hold up a flower and say, 'Look how beautiful it is,' and I'll agree, I think. And he says, 'You see, I as an artist can see how beautiful this is, but you, as a scientist, oh, take this all apart and it becomes a dull thing.
"And I think that he's kind of nutty. First of all, the beauty that he sees is available to other people and to me, too, I believe, although I might not be quite as refined aesthetically as he is; but I can appreciate the beauty of a flower. At the same time I see much more about the flower that he sees. I can imagine the cells in there, the complicated actions inside which also have a beauty....
"Also, the processes, the fact that the colors in the flower evolved in order to attract insects to pollinate it is interesting - it means that insects can see the color. It adds a question: Does this aesthetic sense also exist in the lower forms? Why is it aesthetic? All kinds of interesting questions which shows that a scientific knowledge only adds to the excitement and mystery and the awe of a flower. It only adds; I don't understand how it can subtract."
Feynman also said, more poetically,
"Poets say science takes away from the beauty of the stars -- mere globs of gas atoms. Nothing is "mere." I too can see the stars on a desert night, and feel them. But do I see less or more? The vastness of the heavens stretches my imagination -- stuck on this carousel my little eye can catch one million year old light... What is the pattern, or the meaning, or the why? It does not do harm to the mystery to know a little about it. For far more marvelous is the truth than any artists of the past imagined! Why do the poets of the present not speak of it? What men are poets who can speak of Jupiter as if he were like a man, but if he is an immense spinning sphere of methane and ammonia must be silent?
Similarly, if you apply this procedure to the twin paradox, it wouldn't tell you how much younger the traveling twin is when he returns. You have to know his path in spacetime (e.g., how far he turned, when he turned around). In other words, you have to integrate proper time.
Time dilation factors can be useful in calculations, but they don't tell you the amount of time experienced by a given observer between two events. Then compare that to the sun (with its much larger mass) observing it. So Schroeder is using the fact that the rate of time is different depending on the mass of the observer. He then uses the Cosmic Background Radiation to reasonably estimate the mass of the universe. Then he applies this rate of time to the approximately 15 billion years, and finds that from the universe's perspective it is only 144 hours old (i.e. six days). But there is no ACTUAL COSMOLOGICAL OBSERVER who experienced the age of the universe as 144 hours. All cosmological observers experienced it to be 15 billion years.
Schroeder is basically making up a definition for "age of the universe" which does not correspond to the time elapsed by any observer. This contradicts relativitity, which says that time is ONLY definable by the experience of some specified observer. He is not using "God time" as you say it, but rather universe time. As I said, there is only one, unique time in general relativity which can be called "universe time", and that is the time experienced by the "cosmological observers" who view the universe as isotropic (e.g., who are "at rest" with respect to the cosmic background).
According to this time, the universe is 15 billion years old.
Schroeder has made up a number which he may call universe time, but does not correspond to any physically meaningful (i.e., measurable) quantity in general relativity. There is nothing preventing someone from using different references to measure time, just like someone can use different units to measure length (feet, meters, angstroms, etc). That's the problem. Schroeder hasn't used a different reference frame to measure time. He's just multiplied our time by a "time dilation factor", which is meaningless, because that doesn't actually give you the amount of time which elapses in a different reference frame.
The cosmological observers measure the same amount of time as an Earth observer, because the Earth essentially is a cosmological observer.
It is true that it's possible to construct observers who think the universe is only 144 hours old. What's not possible, in general relativity, is to construct a unique set of observers. In order to get 144 hours, you have to choose an observer who is moving with arbitrary speed with respect to a cosmological observer, and in an arbitrary direction. Then the question arises: why that speed, and why that direction? Why should anyone care about the the time measured by a randomly moving observer? It's not any kind of UNIVERSAL time: the only unique choice for that, singled out by the geometry of a homogeneous and isotropic space, is the cosmological reference frame.
It also doesn't say that this matter "exploded". Rather, the space which contains it expanded.
I don't know why you say there doesn't seem to be a way that it could expand in a short time. It's a prediction of general relativity. Why don't you think that's a way? I wonder if there was any beginning of the universe at all. Many cosmologists wonder that too. It's an open question. Also, if there was a beginning, nothing should prevent another universe from forming again. That depends on how it happened, I suppose.
Ok, I re-read your original post ... we're talking about two different aspects of Schroeder's book. I was talking about the part where he was trying to use relativity to justify a 7-day creation by playing with reference frames. I don't know about the part where he supposedly derives a 15.75 billion year age for the universe. If it's based on the above reasoning, though (e.g., starting with an assumption of 7 days and applying a time dilation factor), it's wrong.
It's been some time since I last looked at his arguments. But IIRC, what Schroeder does — incorrectly — is attempt to calculate a "time dilation factor" between present times and the early universe, and argue that this implies that there is a reference frame in which the major elements of the universe's evolution took only 7 days. But this is not correct: the way you calculate elapsed time according to some observer in general relativity is by integrating proper time along that observer's worldline. And when you do that, for any cosmological observer, you get the same answer, one which is essentially identical to the elapsed time according to an Earth observer.
Schroeder's reasoning is analogous to the erroneous logic which concludes that you can never fall into a black hole because the time dilation between a distant observer and the horizon is infinite. Time dilation factors between distant points do not determine elapsed proper time according to an observer's own clock (and are, in general, not even well defined; they depend on the coordinate system you choose).
Actually, Schroeder makes other errors, like pretending that there is an absolute "God's frame" in which you can measure time. In relativity, there is no such absolute frame. The closest you can get is the cosmologically preferred frame, which is singled out due to the high spatial symmetry of the universe. But as I said, the Earth is pretty much in that frame, so it essentially measures Earth time.
There are plenty of scientific results which are known to far more precision than this, as well as those which are known to far less. If you want to object to the error bars on this particular result, you have to give actual evidence why they should be larger than they are believed to be (and not smaller!). Science that isn't bull made up by the researcher because they don't what they are doing. Statistically, 50% of the scientific community are in this boat. The other half isn't usually that much better. Yeah, why don't you support your point further with made-up facts and numbers? You're doing so well at that so far.
50% of the scientific community are below the median, by definition. That does not mean "they don't know what they are doing", and it doesn't mean that the other 50% "isn't much better".
This differs from the old age figures that were spouted from people saying "it is" as well. The new age is within the error bars of the old age, so there's nothing funny about it. There would only be a discrepancy if it was outside of the error bars. Case in hand, Albert Einstein received a cold reception to his theories. Not really true. In fact, he rather quickly found fame. Lorentz, Poincare, and Minkowski had all proposed theories that were basically Einstein's special relativity, for very similar reasons; people knew that Newton wasn't working, and the time was ripe for SR. Einstein just put the physical theory on simple conceptual grounds. And after SR, the scientific community eagerly anticipated GR. Einstein became world famous shortly thereafter with the Eddington eclipse observations. Yeah, sure, there were skeptics since there wasn't much observational evidence for GR at the time — but that's as it should be.
But hey, don't let history get in the way of your fantasies about the reactionary scientific orthodoxy.
The 2% means that the universe's mass-energy density is within 2% of the critical density that implies space is flat. (Above that critical density, space is positively curved; below, negatively.) It is possible to compare the two with general relativity, which relates geometric curvature to mass and energy via gravitational dynamics.
In general relativity, our universe is approximately described by the Friedmann-Lemaître-Robertson-Walker metric. This geometry demonstrably has non-zero Riemann curvature. (besides your separation of space and time is rather nonsensical). No. There are infinitely many ways to separate spacetime into space and time (technically, a "foliation of the manifold", or a "3+1 decomposition"). In special relativity, each inertial observe singles out his/her own such separation, so that they disagree on which events are purely timelike or spacelike separated. (They agree on whether they are overall timelike or spacelike, though.)
In a generic curved spacetime, there is no unique foliation, so one's choice of what to call "space" is rather arbitrary. But in a FLRW spacetime, which is homogeneous and isotropic and therefore highly symmetric, there is: you can use the class of "cosmological observers" who view space as isotropic. The Earth is close to being such an observer (to within 0.2% of c). It is according to this foliation that cosmologists say that "space is flat". It can be curved by mass-energy, but in the absence of ant external influence it is flat. You may have noticed that our spacetime contains mass-energy, and is therefore curved. That's why light travels in a straight line in the absence of gravitational forces. Light travels in a straight line in the presence of gravitational forces as well, if you're talking about "straight in spacetime" (it is always a spacetime geodesic, no matter what the curvature). It can travel in a curved line in space. Only in the presence of gravitational forces does the line appear to curve, since it is in fact traveling in a straight line along curved spacetime. To take the sheet of rubber analogy. Spacetime can be curved by a marble on the sheet, but the sheet by itself would be flat, In the rubber analogy, the sheet is not flat. But that's beside the point; in the usual "gravitational well" example, the sheet represents space, and has nothing to say about the geometry of spacetime.
Yes, there are things we don't know, but you're going to have to do better than that; you can't simply dismiss the fact that there are also a lot of things we do know, and quite accurately. We do have some idea of the errors associated with our measurements. The age-of-universe estimates in the mid-20th century had huge error bars on them precisely because we knew they were very inaccurate. Whether you admit it or not, science has progressed.
The nature of the Big Bang itself is what makes this kind of precision possible: very small deviations from flatness in the early universe get enormously magnified by the universe's expansion, to the point that they're detectable by our instruments. The expansion of the universe is a microscopic lens on the early universe. Sorry - I expect such figures will continue to be "revised" - i.e., doubled or halved repeatedly - in what's left of my lifetime as they have been repeatedly to this point in my life. To the contrary, several independent lines of evidence have been converging on the same numbers for the last 10-20 years, in contrast to the state of cosmology at any time preceding 1990.