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Author Topic:   Purple dosn't beleve in relativity
Sylas
Member (Idle past 5260 days)
Posts: 766
From: Newcastle, Australia
Joined: 11-17-2002


Message 70 of 114 (166825)
12-10-2004 12:59 AM
Reply to: Message 63 by NosyNed
12-09-2004 8:06 PM


Re: Which ends up older?
NosyNed writes:
One minor; you'd have to travel at near .99c to have time slow down by half. It is not linear and it is not time moving at half speed if you do half light speed. Doesn't really matter to the overall question it is just a nit.
Strictly speaking, the factor for time dilation is sqrt(1-v2/c2). This means you can travel at about 0.87c, and time slows down by half.
That is when the shuttle returns (at some speed so that it's clock runs at half the rate when observed from earth) then it will show less time passing.
I don't actually know if this is a purely special relativisitc effect (which I think is the case) or if general relativity is involved.
You want numbers... we got numbers!
Both velocity and gravity effects contribute to time dilation of an astronaut, but by comparison with ground control the velocity effects dominate, because a shuttle orbit is not that much higher than the surface, by comparison with Earth's radius. Hence the shuttle astronauts age fractionally less than ground controllers, simply because they move faster.
But astronauts in a very high orbit will age fractionally more, since the relative velocity has little effect, and ground controllers are deep inside a gravitational well, so their clocks run more slowly.
The effect of gravity is sqrt(1-2GM/Rc2). M is mass of the Earth, and R is distance from the center. For a circular orbit, velocity is sqrt(GM/R). When you put it all together, the time dilation for a body in circular orbit is sqrt(1 - 3GM/Rc2).
For the ground controller, the effect of velocity can be ignored, and they experience only sqrt(1 - 2GM/Rc2). This means that the orbit clock matches the ground clock at an orbit with a radius of 3/2 times earth's radius; an altitude of 3200 km. Astronauts at that orbit experience no time dilation with respect to ground control; those above age more.
We can try some numbers here. G is 6.7e-11, M is 2e30, c is 3e8 and R is 6.4e6. (R being radius of the earth.)
We can approximate sqrt(1-x) by (1-x/2) for small x. Hence the factor sqrt(1-2GM/Rc2) is close enough to running slower by GM/Rc2 seconds every second. This is about 7e-10
Put another way, time dilation for a ground controller with respect to an observer way out in space is a bit more than two hundredths of a second every year. A shuttle astronaut, at an orbit of 200 km, is a bit more than three hundredths of a second per year younger with respect to the distant observer. Hence the shuttle astronauts age about one hundredth of a second less than the ground controller over a year, or about 200 micro seconds in a one week mission. This effect is measurable, and confirms the relativistic calculations.
Hi gang. I'm back... for a bit anyway.
Cheers -- Sylas

This message is a reply to:
 Message 63 by NosyNed, posted 12-09-2004 8:06 PM NosyNed has replied

Replies to this message:
 Message 71 by NosyNed, posted 12-10-2004 1:09 AM Sylas has replied
 Message 77 by Hangdawg13, posted 12-10-2004 4:41 PM Sylas has not replied

  
Sylas
Member (Idle past 5260 days)
Posts: 766
From: Newcastle, Australia
Joined: 11-17-2002


Message 72 of 114 (166843)
12-10-2004 1:31 AM
Reply to: Message 71 by NosyNed
12-10-2004 1:09 AM


Re: Which ends up older?
Here are four individuals, given in order of age, from oldest to youngest. The first person on the list experiences the greatest elapsed time, and has the largest readings on her watch at the reunion party when they all get together again.
  • Oldest is the one riding on a geosychronous orbit, at about 36,000 km altitude.
  • Next oldest is the ground controller who is not in orbit at all; and also the astronaut orbtting at an altitude of 3,200 km. These two are the same age.
  • Youngest is the shuttle pilot, orbiting at 200 km altitude.
You age more slowly by moving faster, and also by being deeper down in a gravitational well. Both effects contribute to making your watch and also your body clock run more slowly, and as a result you end up being younger than those who moved more slowly or lived at higher altitudes.
Cheers -- Sylas (who always wanted to live in the mountains anyway)
PS. I had a special hello for you in my original post Ned! But it somehow got lost before I posted it. Nice to see you again!
This message has been edited by Sylas, 12-10-2004 01:35 AM

This message is a reply to:
 Message 71 by NosyNed, posted 12-10-2004 1:09 AM NosyNed has not replied

Replies to this message:
 Message 73 by The Dread Dormammu, posted 12-10-2004 6:04 AM Sylas has replied

  
Sylas
Member (Idle past 5260 days)
Posts: 766
From: Newcastle, Australia
Joined: 11-17-2002


Message 74 of 114 (166897)
12-10-2004 7:09 AM
Reply to: Message 73 by The Dread Dormammu
12-10-2004 6:04 AM


Re: What about 0 gravity at the bottom of the well?
The Dread Dormammu writes:
What about someone in the center of a massive object (like the earth)? It's 0g so there should be no dialation right?
What about someone in the center of mass between two nutron stars orbiting eachother? (I think frame dragging might influence this one) the net is still 0g's or am I making a mistake somewhere?
This is out of my league; I'm reduced to guessing.
Time dilation should always be measured as a difference between two observers; not as a comparison against an absolute. I am pretty sure that the center of the earth would have time synchronous with an observer at infinite distance from the earth. I have no idea about frame dragging, however.
Cheers -- Sylas

This message is a reply to:
 Message 73 by The Dread Dormammu, posted 12-10-2004 6:04 AM The Dread Dormammu has replied

Replies to this message:
 Message 79 by The Dread Dormammu, posted 12-10-2004 6:28 PM Sylas has not replied

  
Sylas
Member (Idle past 5260 days)
Posts: 766
From: Newcastle, Australia
Joined: 11-17-2002


Message 92 of 114 (167976)
12-14-2004 3:55 AM
Reply to: Message 91 by RAZD
12-14-2004 12:34 AM


Re: What about 0 gravity at the bottom of the well?
It is a fairly standard result that there is no net gravitational force anywhere inside a uniform spherical SHELL of matter.
This means that if you are inside a uniformly dense SPHERE of matter, then you only experience a force related to the amount of mass in the sphere that is closer to the center than you are.
That is, drill a tunnel right through the Earth. Let g be the force you experience on the surface, and R be the radius of the earth.
Then the force you feel when you are in the tunnel at a distance of r from the center of the Earth should be g*r/R. The effective mass is proportional to r3, and the normal distance relation scales the force as r-2.
However, I have been persuaded by comments from others that the gravitational time dilations at a certain depth are not directly related to the force you experience at that point. A thought experiment. A photon falling into a gravitational well will change wavelength; and this can be related to time dilation. But on passing through a shell of matter into an interior cavity, the photon should not suddenly chance frequency, but will remain at the frequency it had just prior to pentrating the shell. This implies that a clock at the center of the Earth will indeed run more slowly than one at a great distance. I think.
Thanks all for the input on this; I've learned something.
Cheers -- Sylas
This message has been edited by Sylas, 12-14-2004 03:57 AM

This message is a reply to:
 Message 91 by RAZD, posted 12-14-2004 12:34 AM RAZD has not replied

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Sylas
Member (Idle past 5260 days)
Posts: 766
From: Newcastle, Australia
Joined: 11-17-2002


Message 99 of 114 (168693)
12-15-2004 7:04 PM
Reply to: Message 98 by PurpleYouko
12-15-2004 3:49 PM


Re: The Milky way IS in the "center"
PurpleYouko writes:
If space is made of nothing then how can it expand?
You can have different amounts of nothing. We call this "distance".
Consider two objects, at rest, which are a certain distance from each other. If space expands, then the distance between them increases. This is what we observe galaxies doing.
Of course, if the two objects are held together by, say, a piece of string, then they will remain at the same separation (although there will be some tension in the string). Same applies for objects held together by gravity. Hence the Milky Way galaxy itself is not expanding. It is gravitationally bound, and does not expand. Put another way; motions and forces in space can overcome the expansion of space to hold things together in a local association.
PurpleYouko writes:
Surely for something to expand, it would have to have something there which is actually doing the expansion. Vacuum can't exert a pressure to accelerate anything.
Curiously, a vacuum does exert pressure; though this has nothing to do with the expansion of space. It is called the Casimir Effect, predicted from quantum mechanics in 1948 and measured in 1996 to confirm the prediction.
To measure this pressure, we need two plates very very close together in a vacuum. They experience an attractive force, because there is, in a sense, less vacuum between the plates, and the vacuum on the otherside pushes them together. Actually, the pressure is due to the existence of so-called virtual particles which pop in and out of existence continually in the vacuum. The very small space between conducting plates) limits the possibilities for virtual particles.
The point of this example is that modern physics turns out to be rather unintuitive. Out intuitions about "nothing" and "space" and so on are frequently a poor guide to how the world actually works at the most fundamental levels of physical laws.
The vacuum pressure has nothing to do with the expansion of space. (Actually, that may not quite be true; but the connection is indirect. Expansion of space is a consequence of general relativity, and the energy bound up in the vacuum, which is expressed as virtual particles, makes a difference to the equations and the rates of expansion or contraction of space.)
Expansion of space is not about any material objects being accelerated by forces. A force accelerates objects in space. The expansion of space merely increases the distance between things at rest. Note that it makes perfect sense to speak of an increasing distance between things at rest, but only if you consider the space between things to be increasing. That is exactly what is predicted by general relativity. What we observe in the universe is consistent with those predictions.
PurpleYouko writes:
This also suggests that the media through which bits of the universe are travelling would have to have a profound effect on those bits of the universe (planets stars etc.).
Sounds a lot like the Aether theory to me.
I don't understand this paragraph. No media or aether is involved.
One of the things which is inconsistent with the notion of an aether is that the expansion of space means that every point sees the rest of the universe moving away from it, at a speed that is proportional to distance. I'm using "speed" here advisedly; bearing in mind that this is not a rate of motion through space, but a rate at which separation distances are increasing.
The Hubble constant, which measures the rate of expansion, is H0 = 71 km/sec/Mparsec
This means that the distance between two objects that are a MegaParsec apart from each other is increasing at a rate of 71 kilometers every second. The speed of light is 3*105 km/sec. Hence if two objects are about 4200 MegaParsecs apart, then the rate at which their separation distance is increasing is the speed of light. If objects are 5000 MegaParsecs apart, then the distance between them increases by more than the speed of light. This would be a violation of relativity, if expressed as a motion of objects in space.
However, there is no violation, because the increasing separations is not motion, but expansion of space. I'm not kidding; this really is the basics of general relativity in an expanding space.
A parsec, by the way, is about 3.26 light years, so 4200 MegaParsecs is 13.7 billion light years; the age of the universe. That is, the measured rate of expansion of space, extrapolated backwards, means that 13.7 billion years ago there was no space. This is the famous singularity at the start of the Big Bang.
If by an expanding universe you mean something like an equal increase in the the size of all space then wouldn't that mean that an observer would be expanding at the same rate as everything that he observed? Wouldn't this also make it impossible for him to actually observe the expansion? Or is the universe only expanding at the edges?
This is a very good question. The short answer is that things can be held together over small regions of space, so that they remain the same volume. You are probably about 1.7 meters tall. A parsec is 3.1*1016 meters, so you are about 5.5*10-23 MegaParces tall. The expansion of space means that the distance from head to toe will tend to increase by 71000*5.5*10-23 = 3.9*10-18 meters every second. That is not much, and the forces that hold your body together overwhelm this expansion to keep you from expanding.
So no, the universe is not expanding only at the edges. It is expanding throughout all of space. The expansion of space means that the distance between objects at rest tends to increase. For objects that are close together, this increase in separation distance is very small, and is overwhelmed by forces and local motions in space. But for objects that are very far apart, the rate of increase in separation distance is far too great for any local motions or forces to overcome it.
Cheers -- Sylas
This message has been edited by Sylas, 12-15-2004 07:18 PM

This message is a reply to:
 Message 98 by PurpleYouko, posted 12-15-2004 3:49 PM PurpleYouko has not replied

Replies to this message:
 Message 100 by JonF, posted 12-15-2004 8:11 PM Sylas has not replied

  
Sylas
Member (Idle past 5260 days)
Posts: 766
From: Newcastle, Australia
Joined: 11-17-2002


Message 102 of 114 (169127)
12-16-2004 6:43 PM
Reply to: Message 101 by PurpleYouko
12-16-2004 9:15 AM


Re: The Milky way IS in the "center"
PurpleYouko writes:
Thanks for the explanation Sylas. There are still some parts I don't quite get though. I am not arguing that you are wrong here, just trying to get an explanation that I can understand so please bear with me.
No problem; I quite understand. It's the same for me as I continue to try learning about aspects of this. I am not a physicist, so I quickly get out of my depth when attempting to explain, and I'm still reading and trying to get to grips with various aspects of the matter. I have read fairly widely on the subject, both technical and popular literature; but I still don't really get the maths of general relativity; so I still need to deal with that qualitatively. This is all amateur explanation; and I will try to give a feel for where I am unsure and extrapolating beyond what I really know of the models.
The way I see it is that if all space is expanding then the space between and within atoms should expand at the same rate. (ie . 10 microns expands to 10 microns + 2% and 10 MegaParsecs expands to 10 MegaParsecs + 2%)
If local forces can prevent this expansion then there has to be a further factor involved or else the large and small forces, gravity etc. would all change proportionally to the expansion and no expansion would ever be detectable due to the change in the frame as a whole. Gravity (for example) is a function of mass and distance so if distance changed then the local gravity would have to become greater in order for the change to be locally resisted. This means that small objects would actually have to be shrinking with respect to actual distances which are increasing. What factor other than actual distance can we measure this by? Surely if this is true then local gravity must be increasing.
My understanding is that local forces do not prevent expanding. They just act, as they have always done, to move things around. Don't think of the local force as preventing expansion of space, but of moving things through an expanding space so that they remain at about the same separation.
The Earth itself is a ball of matter. Its size is balanced between the attraction of gravity holding it together, and the primarily electromagnetic forces at the levels of atoms to hold particles apart from each other. If somehow space expanded very rapidly, so that the space within which the Earth resides expanded by 2% over about a minute, then you would suddenly have Earth being 2% larger. But it would then very quickly collapse again back to about its present size, due to the forces of gravity. Hence the expansion of space does not change the size of the Earth.
As a minor mathematical aside, the current cosmological expansion is roughly linear (measured as 71 km/sec/Mparsec). This means that as the universe gets large, it takes correspondingly longer to get a certain proportionate increase in size. At present, it takes 274 million years to get a 2% increase in size; but as time passes it will take longer to get a 2% increase. The kind of expansion in which space expands by a fixed proportion per unit time is very different; an exponential expansion. Most cosmologists believe that there was this kind of expansion very briefly and very early in the history of the universe; it is called inflation.
The case for the orbit of the Earth is a bit more subtle; but it can be calculated. The expansion of space has effects analogous to a kind of pseudoforce acting to increase the radius of the Earth's orbit. The effect is much more complex than simply increasing orbit size by an amount relating to the amount of increased space, because the Earth is in constant motion. We have to calculate some rather hairy differential equations to combine the force of gravity with the expanding space. The calculations are available here:
The influence of the cosmological expansion on local systems,
by F. I. Cooperstock, V. Faraoni, D. N. Vollick,
in Astrophys.J. 503 (1998) 61 (astro-ph/9803097)
Basically, the effect of expansion is to perturb an orbit to increase the radius and decrease the orbital period. The effect on the scale of the Earth-Sun system is small, to say the least. Over the life span of the solar system, the Earth orbit should be expected to increase by a fraction of about 10-24. This is less than than changes in orbit due to tidal effects.
The effects of cosmic expansion can really only be detected at scales beyond that of our galaxy. On smaller scales, bodies are in constant motion under forces of gravity that hold them together against the expansion of the space in which they are embedded. The space still expands, but bodies move through space under the influence of gravitational forces to maintain the same separation to within the bounds of measurement.
See also the usenet physics FAQ answer to this question: If the universe is expanding, does that mean atoms are getting bigger? Is the Solar System expanding? Here is the introduction. (I love the quotes from Annie Hall!)
Mrs Felix: Why don't you do your homework?
Allen Felix: The Universe is expanding. Everything will fall apart, and we'll all die. What's the point?
Mrs Felix: We live in Brooklyn. Brooklyn is not expanding! Go do your homework.
(from Annie Hall by Woody Allen)
Mrs Felix is right. Neither Brooklyn, nor its atoms, nor the solar system, nor even the galaxy, is expanding. The Universe expands (according to standard cosmological models) only when averaged over a very large scale.
This FAQ also points out that the actual metrics for expansion of space are fantastically complicated. The basic FRW solution for the universe as a whole is a very simple approximation, that gives a uniform rate of expansion through all of space. This same uniform expansion is assumed in the calculated orbit perturbations to which I allude above; but in a local mass concentration rates of expansion will vary; and calculating this completely is intractible. I do not know if the rate of expansion is locally greater or smaller; but in any case it is still bound to have insigificant consequences at the scale of our solar system.
And finally, just for fun to really blow your minds. There is a speculative theoretical model for an accelerating expansion of the universe, in which the rate of acceleration increases. Let me introduce to you all the Big Rip; a model developed last year by Robert R. Caldwell, Marc Kamionkowski, and Nevin N. Weinberg. This has a singularity in the future; but not by a collapse back to infinite density. The future singularity involves an expansion so rapid that eventually atoms themselves cannot hold together against its effects. Here is a timeline from the formal paper at Phantom Energy and Cosmic Doomsday (astro-ph 0302506).

The history and future of the Universe with ω = −3/2 phantom energy.
TimeEvent
~10−43 sPlanck era
~10−36 sInflation
First Three MinutesLight Elements Formed
~105 yrAtoms Formed
~1 GyrFirst Galaxies Formed
~15 GyrToday
trip − 1 GyrErase Galaxy Clusters
trip − 60 MyrDestroy Milky Way
trip − 3 monthsUnbind Solar System
trip − 30 minutes Earth Explodes
trip − 10−19 sDissociate Atoms
trip = 35 GyrsBig Rip
Cheers -- Sylas
PS. Fixed the first two links in edit. Thanks Nosy; I have removed your comment from the previous fixed, and applied the fix also the the second link. Also got rid of spacing problem.
This message has been edited by Sylas, 12-19-2004 04:30 AM

This message is a reply to:
 Message 101 by PurpleYouko, posted 12-16-2004 9:15 AM PurpleYouko has not replied

Replies to this message:
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 Message 105 by sidelined, posted 12-16-2004 9:56 PM Sylas has not replied
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Sylas
Member (Idle past 5260 days)
Posts: 766
From: Newcastle, Australia
Joined: 11-17-2002


Message 108 of 114 (169475)
12-17-2004 3:28 PM
Reply to: Message 107 by teratogenome
12-17-2004 10:04 AM


General questions on gravity
teratogenome writes:
Well, if you still experience time dilation at the center of a gravity well but no longer experience the gravitational effects, could it be possible for us to be (or have been during a big bang, for example) at the center of a very large gravity well and be experiencing time dilation effects? Is there any way for us to calculate what the time dilation might approach if we are very near the middle of a very massive part (or the entire) universe?
Would that explain why bodies farther away from us appear to be accelerating outwardly? The farther out they are, the more distant they might be from the center of the universe's gravity, and therefore their time would be more compressed in relation to ours.
No, not possible. That would have effects the opposite of what we observe.
We observe that distant galaxies are red-shifted, with the red shift increasing in proportion to distance.
When you are deep in a gravity well, the light from the rest of the universe is blue-shifted; not red-shifted. This blue shift is how gravitational time dilation was first observed in a series of experiments at Harvard in the early sixties, based on the gravity well of the Earth.
Sylas, regarding the expansion of space, how could the force of empty space be measured on anything? How does a virtual particle spring into existence without ceasing to be virtual?
Bear in mind the comment I made in the first place; the pressure of a vacuum, which is the force of empty space due to virtual particles, has nothing to do with expanding space.
The force is measured the same way you measure any force. The first detection of this effect used a kind of torsion pendulum. A description of various ways in which the force has been measured is available at PhysicsWeb.
What makes a particle virtual is that it springs out of existence almost as soon as it springs into existence. It is usually explained with reference to the uncertainty principle; they borrow a bit of energy from the universe and give it back again so quickly that it all fits within uncertainty limits. For that brief instant, however, they can still push other particles.
Exactly how much mass per cubic meter does it take before gravity overcomes the force of nothing that is pushing it apart, and begins to coalesce? Wouldn't it interfere with star formation?
If you have a mass M all contained within a sphere of radius 2MG/c2, then the gravity overcomes any other force, and the matter compresses without limit. This is called a black hole.
Hyperphysics has a black hole calculator that lets you find the radius required for a given mass. For example, the mass of the Sun within a sphere of radius 3 kilometres would become a black hole. The mass of the Earth within a sphere of radius just under 1 cm would become a black hole.
Yes, it interferes with star formation to have too much mass involved.
Cheers -- Sylas
This message has been edited by Sylas, 12-18-2004 12:17 AM

This message is a reply to:
 Message 107 by teratogenome, posted 12-17-2004 10:04 AM teratogenome has not replied

  
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