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Author Topic:   Purple dosn't beleve in relativity
RAZD
Member
Posts: 19816
From: the other end of the sidewalk
Joined: 03-14-2004
Member Rating: 10.0


Message 91 of 114 (167936)
12-14-2004 12:34 AM
Reply to: Message 85 by teratogenome
12-13-2004 4:32 AM


Re: What about 0 gravity at the bottom of the well?
would you fall to the center? or would you be able to stand on the inisde? you would have to integrate all the dM/dd2 increments but I suspect that you would get a net force holding you to the underside, and you might find the ring analogy holds ... in 3D.

enjoy.


we are limited in our ability to understand
by our ability to understand

RebelAAmerican.Zen[Deist
{{{Buddha walks off laughing with joy}}}


This message is a reply to:
 Message 85 by teratogenome, posted 12-13-2004 4:32 AM teratogenome has not yet responded

Replies to this message:
 Message 92 by Sylas, posted 12-14-2004 3:55 AM RAZD has not yet responded

  
Sylas
Member (Idle past 3368 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


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 Message 91 by RAZD, posted 12-14-2004 12:34 AM RAZD has not yet responded

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contracycle
Inactive Member


Message 93 of 114 (167993)
12-14-2004 5:53 AM
Reply to: Message 88 by Raymon
12-14-2004 12:15 AM


Re: What about 0 gravity at the bottom of the well?
quote:
This fact has a neat little corralary- If you had a hole that went from one place on the surface of the earth and followed a straight line to another hole on the surface of the earth, and you dropped a ball down the hole, it would have a period of occilation of 84 minutes- even if the hole was through the center of the earth.(I'm a physisist, so I'm considering a spherical earth of uniform density)

Actually I was kinda working from that - the sphere of the earth must exert gravity at the point of the wall you are passing, no? Nevertheless, you fall toward and through the centre of the sphere and oscillate around that.


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Raymon
Inactive Member


Message 94 of 114 (168129)
12-14-2004 2:13 PM
Reply to: Message 90 by jar
12-14-2004 12:22 AM


Sorry
:-)

Yes. And yes, presuming your hole goes through the center of the earth. It doesn't have to.


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Raymon
Inactive Member


Message 95 of 114 (168137)
12-14-2004 2:22 PM
Reply to: Message 93 by contracycle
12-14-2004 5:53 AM


Re: What about 0 gravity at the bottom of the well?
Actually I misspoke. Sylas is right. You don't feel gravity inside a uniform shell. So you can only oscilate around the center if you have enough velocity to go through the other side of the shell. If you could use a rocket to reduce your speed to zero inside the shell, you would just float there, never moving.
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teratogenome
Inactive Member


Message 96 of 114 (168220)
12-14-2004 6:00 PM
Reply to: Message 92 by Sylas
12-14-2004 3:55 AM


Re: What about 0 gravity at the bottom of the well?
Sylas, the real reason I asked that question was because I was trying to use the earth's matter shell as sort of an analogy for the matter of the visible universe. If Earth was close to the center of this visible universe, could the greater amounts of red shift from distant galaxies be caused by the type of time dilation/compression you just mentioned? Could they in fact be expanding more slowly but because of their time being compressed in relation to us, APPEAR to be moving away faster?

The only other thing I can think of is some sort of dark matter crap. Even that would preclude a big bang unless it's repulsive force (per "mass" or "amount" ) diminishes over distance at a different rate than gravity and thereby overcomes it when normal matter becomes significantly diffused. Even then I don't see how it could come to be incorporated into the initial big bang material.


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 Message 97 by The Dread Dormammu, posted 12-15-2004 4:55 AM teratogenome has responded

  
The Dread Dormammu
Inactive Member


Message 97 of 114 (168408)
12-15-2004 4:55 AM
Reply to: Message 96 by teratogenome
12-14-2004 6:00 PM


The Milky way IS in the "center"
If Earth was close to the center of this visible universe, could the greater amounts of red shift from distant galaxies be caused by the type of time dilation/compression you just mentioned? Could they in fact be expanding more slowly but because of their time being compressed in relation to us, APPEAR to be moving away faster?

First of all the milky way DOES appear to be in the center of our hubble volume (meaning observable universe) ALL the other galaxys seem to be moving away from US at increasing speed depending on their distance.

This is due to the fact that space itself is expanding.

I do not understand your question about their time being compressed relative to us, please elaborate.


This message is a reply to:
 Message 96 by teratogenome, posted 12-14-2004 6:00 PM teratogenome has responded

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PurpleYouko
Member
Posts: 713
From: Columbia Missouri
Joined: 11-11-2004


Message 98 of 114 (168625)
12-15-2004 3:49 PM
Reply to: Message 97 by The Dread Dormammu
12-15-2004 4:55 AM


Re: The Milky way IS in the "center"
Dormamu writes:

This is due to the fact that space itself is expanding.

I don't understand this statement. I have never really got this part of it at all.

If space is made of nothing then how can it expand?

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.
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.

It must take a lot of energy to accelerate a galaxy. Where is that energy coming from? I don't understand how exapnading nothingness can drag real things with it.

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?

Confused? I sure am.

PY


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 Message 97 by The Dread Dormammu, posted 12-15-2004 4:55 AM The Dread Dormammu has not yet responded

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Sylas
Member (Idle past 3368 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 yet responded

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

  
JonF
Member
Posts: 4560
Joined: 06-23-2003
Member Rating: 4.4


Message 100 of 114 (168717)
12-15-2004 8:11 PM
Reply to: Message 99 by Sylas
12-15-2004 7:04 PM


Re: The Milky way IS in the "center"
Surely for something to expand, it would have to have something there which is actually doing the expansion. ... 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.

PurpleYouko initially thinks that there must be some "thing" expanding, and follows that thought to a logical conclusion which is suspiciously like aether, and is then puzzled because either the initial thought is wrong or there must be an aether ... neither possibility seems attractive.


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 Message 99 by Sylas, posted 12-15-2004 7:04 PM Sylas has not yet responded

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PurpleYouko
Member
Posts: 713
From: Columbia Missouri
Joined: 11-11-2004


Message 101 of 114 (168861)
12-16-2004 9:15 AM
Reply to: Message 100 by JonF
12-15-2004 8:11 PM


Re: The Milky way IS in the "center"
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.

JonF writes:

PurpleYouko initially thinks that there must be some "thing" expanding, and follows that thought to a logical conclusion which is suspiciously like aether, and is then puzzled because either the initial thought is wrong or there must be an aether ... neither possibility seems attractive.

Thanks Jon. That summed it up perfectly.

I guess my difficulty in understanding all this is that (like most people) I think intuitively and that appears not to jazz with the explanations given by people who are obviously much more knowledgable about the actual mechanics and mathematics of the situation.

I think my biggest non-understanding has to be the bit about local forces overcoming expansion of space.
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.

Does any of this logic make sense?

Hopefully Sylas or someone else can shed some light here.

PY


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Sylas
Member (Idle past 3368 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


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NosyNed
Member
Posts: 8842
From: Canada
Joined: 04-04-2003
Member Rating: 7.4


Message 103 of 114 (169146)
12-16-2004 7:18 PM
Reply to: Message 102 by Sylas
12-16-2004 6:43 PM


Broken first two links?
The first two links don't work for me.

Btw Thanks to all for this, I had never thought to ask the question about local effects of cosmic expansion. I just arm waved it away as "small".

ABE
Fixed the first one, couldn't find the second.

This message has been edited by NosyNed, 12-16-2004 07:29 PM


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JonF
Member
Posts: 4560
Joined: 06-23-2003
Member Rating: 4.4


Message 104 of 114 (169147)
12-16-2004 7:20 PM
Reply to: Message 102 by Sylas
12-16-2004 6:43 PM


Re: The Milky way IS in the "center"
Interesting. I don't get the last line of the table.

(I don't know why I get a large space above my table.)

Happens to me, too, whenever I do a table. I bet it's a bug/feature.


This message is a reply to:
 Message 102 by Sylas, posted 12-16-2004 6:43 PM Sylas has not yet responded

  
sidelined
Inactive Member


Message 105 of 114 (169177)
12-16-2004 9:56 PM
Reply to: Message 102 by Sylas
12-16-2004 6:43 PM


Re: The Milky way IS in the "center"
Sylas

(I don't know why I get a large space above my table.)

Blame it on the expansion of space upon local computers.


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