Age of the Universe

Actually, the page is explicit that using general relativity is a bad case of overkill in this problem, because it is not about curved spacetime, or gravitation.General relativity, being the more general theory, is certainly able to handle the turnaround, but the "gravity" involved in the accelerated frame is a kind of "flat" gravity pervading all of space, which is an exceptionally simple case that does not really require all the tensor maths and limits used in the more general curved case that results from a gravitational attractions and massive bodies.The page itself puts it like this:

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Some people imagine that you need General Relativity to handle accelerated observers — but you don't. General Relativity has to do with gravitation, and with curved spacetime. The centrifugal field on a playground merry-go-round is not caused by spacetime curvature, and similarly the time-shift that Moe sees during the turnaround is not caused by spacetime curvature. Using GR to solve such problems would be like using a gold-plated jackhammer to crack open a pistacio. It would work, but it's waaaay more than you need.

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I may be being a bit pedantic about this; but it is a very common mistake to think that you need general relativity to handle accelerated motions. It is a mistake I used to make myself, which is perhaps why I more aware of it. I wanted to nip that notion in the bud.(By the way; what is the best way to quote an extract from an external page? I've used the "quote" tags; but that is normally used to quote another article in the board...)Cheers -- cjhs[This message has been edited by cjhs, 10-26-2003]

I'm a bit confused. It seems to me that the reason you don't need GR is that the accelerations are so small as to produce negligable effects on the flow of time. Isn't that all there is too it?

Special relativity is perfectly adequate to handle accelerations, of any magnitude.You only need the more general theory when working with spacetime curvature and gravitational fields. Relativity does make an equivalence between gravitation and inertial forces in an accelerated from; but that does not mean you need the general theory to handle accelerated frames.In fact (and I am not an expert in relativity, so take this with caution) I am given to understand that a good way to start learning about general relativity is to do the derivations for accelerated motions in the special relativistic framework, and then see how that can be generalized for gravitational forces.Cheers -- cjhs

The amount of acceleration has nothing to do with it. The fact that the reference frame of one observer changes is enough, it does not matter how this is achieved.Gravity and acceleration are indeed indistinguishable. This can be illustrated by a centrifuge. If it would be spinning in empty space in such a way that a person would experience 1g, this would be exactly the same as standing on the earth. The same goes for standing in an elevator in the middle of space that is accelerating at 1g. However, one can be described with special relativity, as it can be expressed in simple vectors, but space-time and its curvature need more difficult mathematics. The great breakthrough of general relativity as I understand it is exactly equating gravity to acceleration, via the space-time curvature effect.

That is how I understand it.So here is an interesting puzzle. Despite my agreement, it turns out that there is a difference between the elevator accelerating at 1g, and standing on the surface of the earth. What observations could someone perform if they were trapped in an elevator and needed to tell whether they were located on Earth, or accelerating uniformly through empty space? You may assume whatever measuring equipment you need, but you can't look outside the elevator.Cheers -- chjs

Do i have instruments of unlimited precision?

cjhs,Apart from some obvious effects (arrow of gravitational acceleration need not be perpendicular to the earth’s surface, earth is spinning, a sphere does not give a linear field etc), there would be nothing to distinguish them as I understand it.[This message has been edited by Taco, 10-26-2003][This message has been edited by Taco, 10-26-2003]

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I think you're right that there's a terminological and conceptual conundrum involved. We have neither the terminological nor conceptual tools with which to properly express such things as the beginning of time. Perhaps someone else has a better answer, but all I can say suggest is that you attempt to go with the spirit of what is meant and not worry too much about the precision of the available terminology nor the lack of an appropriate pre-existing conceptual framework.

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Yeah, I'm not trying to start a semantics game or anything. I'm just discussing the Cosmological Argument somewhere else; and besides the obvious flaws in its construction, I can't seem to accept that the universe 'began' to exist. Does saying time stretches back 14 billion years imply that it began to exist? If so, I think it is legitimate to ask, when?JustinC

JustinC,According to the BB theory, for everyone in our reference frame the universe came into existence about 14 bln years ago. As time is part of the universe that is also when time came into existence. It makes no sense to ask what there was before the universe, since there was no time and therefore no way to define "before". The moment of the big bang is t(0) as it were. Another thing to keep in mind is that time is, according to general relativity, not substantially different from space. Together they form the 4-dimensional space time. If you can imagine space coming into existence at the moment of the BB, then time can be treated in much the same way.There are some new theories around that have some more to say on this subject, among others superstring theory. However, for all practical purposes the BB theory explains matters very well.

Your instruments must be within the limits of existing technology. I am pretty sure that will be enough. Assume a good sized freight elevator able to fit the instruments you need.Cheers -- cjhs

Hello Percy,
As you say, the time dilatation is the same for both observers, and each sees the other's clock running at half speed. But relativistic effects apply to space and time, and Joe and Moe have different views of the distance travelled. If the distance is 3.48 ly in the static observers frame, then it will be 1.74 ly in the moving observers frame (from his point of view, he is stationary, and the distance is moving past him. They agree on their relative speed, and so the turnaround point reaches him in half the time (his time), and his clock says 2 years have passed, fully in agreement.The Joe and Moe story correctly describes the three reference frames involved, but does not describe Moe's experience as he hops off one reference frame onto another. Special relativity handles the three frames pefectly, and Moe1 can synchronise his watch with Moe2 at the turnaround point. But Moe1 and Moe2 have very different views of the time back home, and special relativity does NOT handle this problem for an observer who changes reference frames.In General Relativity, gravity and acceleration are the same thing. Special Relativity does NOT handle the observations of accelerated observers. It makes no difference whether the gravitational field is linear and uniform, as in our case, or radiating and following the inverse square law, as in the case of space distortion by a mass. The time dilatation caused by a difference in gravitational potential (or an acceleration) is not described by Special Relativity.Getting back to Joe and Moe, when Moe gets home, Joe looks at Moe's clock and sees it reading 4 years, while his own reads 8 years. But Moe saw Joe's clock running slow while he was travelling, so at some stage he must have seen Joe's clock jump ahead to make up the difference. This time jump is required by Special Relativity, and has to happen when Moe changes reference frames. But Special Relativity can only insist that it happens. General Relativity is required to explain it.1. Moe cannot change reference frames without accelerating.
2. General Relativity says Moe will experience the acceleration as if a gravitational field had been switched on.
3. General Relativity states that a clock higher in a gravitational field will run faster than one lower.In our example, if it takes Moe a time t to turn around, the gravitational force will be 2v/t. The difference in altitude in the field will be 1.7 ly in Moe's reference frame. This adds up to a tremendous gravitational time dilatation - almost like Humphries sitting near a black hole and watching the rest of the universe evolve around him. So Moe WILL see Joe's clock speed up as he turns around.MikeSorry all this is off the track of the age of the universe, but I feel it needs clearibng up before we can talk about the time scales of different observers.

I"m guessing that NosyNed was asking about instrument precision to see if it was possible to detect a difference in the force of gravity between the top and bottom of the elevator. If they're the same you're in an accelerating RF, if not you're in a gravity well.--Percy

That is the method I was thinking of. The effect was first detected forty years ago, by measuring gravitational time dilation in a height of about 70 feet, in the Harvard Tower Experiment. I'm assuming that the accuracy of instruments has improved since then. It should be possible to detect differences in gravity at the top and at the bottom of a freight elevator.To make this relevant, this can be thought of as measuring curvature of spacetime. General relativity needs to use tensors and so on to handle this curvature. Special relativity does not. An accelerating elevator is indistinguishable from an elevator in a field from a very massive object a long long way away, so that the distance from top to bottom of the elevator is negligible by comparison with the distance to the bottom of the gravitational well. But Earth's field gives sufficient curvature to detect over those distances.Special relativity works fine in the limiting case of no detectable curvature, and that is why it works with accelerated motions.There is another point of relevance to this forum here, which others have remarked upon. This effect, which has been measured, means that photons from the roof of the elevator in a gravitational well are very slightly blue shifted.In Russell Humphrey's ridiculous Starlight and Time model, the blue shift would be enormous, and starlight and background radiation would be shifted into a rather more deadly radiation. We can tell that we are not at the bottom of Humphrey's well very effectively.Cheers -- cjhs[This message has been edited by cjhs, 10-26-2003]

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According to the BB theory, for everyone in our reference frame the universe came into existence about 14 bln years ago. As time is part of the universe that is also when time came into existence.

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"Came into existance" seems to imply that time already exists, since "came" is a verb, and all verbs imply time.

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It makes no sense to ask what there was before the universe, since there was no time and therefore no way to define "before". The moment of the big bang is t(0) as it were.

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Just as it makes no sense to ask what was before the BB, it seems to make no sense to say the BB 'began to exist'(or came into existance) because it seems to imply time.

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Another thing to keep in mind is that time is, according to general relativity, not substantially different from space. Together they form the 4-dimensional space time. If you can imagine space coming into existence at the moment of the BB, then time can be treated in much the same way.

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The only reason I can think of space coming into existance is because I can reference "coming" (as in coming into existance) with time, i.e. it came into existance at time x. But when consider all dimensions, it doesn't seem you can say it "began to exist" or "came into existance".I really have no solid background in physics (only 1 college level physics class and internet), so that's probably why I can't grasp these concepts too well. I just bought "A Brief History of Time" and "Schrodinger's Kittens", so hopefully once I get through those I'll be able to understand better.JustinC

JustinC,
The difficulty with words is that it is easy to get confused by the terminology. This is why formulas are so handy.I used "came into existence" to avoid using "created". The most popular visual image of the BB is of empty black space, with a sudden explosion. This makes no sense, as space is part of the universe. The same goes for time. Even if there was something before the BB (until it was discovered recently that it appears that the universe expands at an accelerating rate one theory was of a periodically expanding and contracting universe) it will have no effect on us and can therefore be ignored. For all intents and purposes, the axis of time starts at the BB, the moment of the BB being t(0). What I claimed earlier was that depending on what reference system you're in (stationary or travelling at the speed of light), you will have different ages of the universe. But both will still agree that it was at t(0), since they are at different locations on the time-axis.BTW, if you think relativity stretches the imagination, quantum mechanics (Schrodinger's book) will do that even more. QM has weirdness in it that even Einstein couldn't accept.[This message has been edited by Taco, 10-27-2003]