Couldn't the outer part of a ring travel faster than light?

[SpeedFreek]

Heh, that was such a groundbreaking and important paper that SciAm asked the authors to do a dumbed down version for them! The article is not fully available online anymore (all the pics are missing), but the link in my sig leads to Charles Lineweavers own pdf version of the article, with diagrams intact but no webpage adverts!

The Hubble constant is not a constant in the way we usually think of the term - it is the end result of the combination of the various rates of expansion over the whole history of the universe! It tells us how much the universe has expanded in 13.7 billion years, and gives us an effective recession velocity for wherever we think everything is, "right now". It is like the "average speed" of something that has been accelerating and decelerating, as measured at the end of its journey!

70 km/s/Mpc means 70km/s per 3.2 million light-years, so that's
70,000 km/s per 3.2 billion light-years, so that's
700,000 km/s per 32 billion light-years... etc etc.

This means the edge of the observable universe (the surface of last scattering, the comoving coordinate where the CMBR we currently detect was originally emitted from), at 46 billion light-years distance, would have a recession speed of around 1 billion km/s, something over 3 times the speed of light. This makes sense as, if the universe is only 13.7 billion years old, something would have had to recede at over 3 times the speed of light to be at least 3 times that distance away in light-years by now! But at the time the CMBR was emitted, the surface of last scattering is thought to have been receding at over 50 times the speed of light!

Due to the immense but rapidly decelerating expansion rate early in the universe, combined with the long period of deceleration that followed, and only the recent and seemingly relatively slow acceleration, the Hubble constant has always been falling and will continue to do so until such a time as the accelerating rate of expansion outstrips the immense rate of expansion early on - it is highly unlikely this will happen, so we can consider the Hubble constant will continue to fall pretty much forever even in an accelerating universe, unless there is a Big-Rip caused by dark energy that grows in strength. (You might have to think about this a little bit - it is hard to describe in words!)

Not that any of this answers your actual question of course! But the way you related the Hubble constant to the expectations of what we would observe prompted me to try to describe what the Hubble constant really means.

As we look at very distant galaxies, we see them when the universe was a lot younger and was expanding a lot faster than it is at present. So, we see the universe at a time when the Hubble parameter (and thus a distant galaxy's recession speed) was a lot higher than it is today. But.... their redshift tells us how much the universe has expanded since their light was emitted, and thus allows us to work out how far away they would be today (and thus how fast they would have moved when averaged across the whole history of the universe, if everything was in the same place to begin with!).

When we look at certain types of supernova with a known brightness and duration, their apparent brightness and their duration tells us how far away they were, due to light travel time and the expansion of the universe. As our instruments got better, we started finding distant supernovae that seemed to be further away than they should have been, assuming the universe was still decelerating. They looked a little dimmer and a little more time-dilated than expected, and after collecting data for enough of these supernovae it was found that, sometime in the last 5 billion years or so, the rate expansion had levelled out and started to accelerate, meaning distant things were a little more distant than previously expected!

I hope some of this helps.

 

[csmyth3025]

Thanks SpeedFreek, that helps a lot.

What I'm a little puzzled about now is the nature of the accelerating expansion of the universe. When scientists use this term, are they saying that the rate of expansion (which, on average, has been ~70 km/sec per Mpc) was diminishing for about the first 8.5 Byr and, since then, has been diminishing at a progressively slower rate? Or are they saying that the rate of expansion leveled off and for the last ~5 Byr has actually been increasing at a progressive rate?

Chris

 

[SpeedFreek]

That's what I was trying to explain - the Hubble constant is a "proportionality constant" and doesn't relate to the changing expansion rate in the way one might think - it is a little counter-intuitive, but the rate of expansion and the Hubble constant can move in different directions.

The rate of expansion started off really fast and was decelerating for around 8 or 9 billion years when it levelled out (was "fleetingly" constant) and then started to accelerate and has been expanding at a progressive rate for the last 5 billion years or so. But the Hubble constant has been decreasing all along.

Imagine, if you will, that the universe takes a minute to expand a mile, and this lasts for a day. The next day, it takes a hour to expand a mile. The day after that, it takes a day to expand a mile, and then for the last day once again takes an hour to expand a mile. For the purposes of this example, this represents the relationship between the changing expansion rates of the universe.

On day 1, the universe expanded by 1440 miles.
On day 2, the universe expanded by a further 24 miles.
On day 3, the universe expanded by only 1 mile.
On day 4, the universe expanded by another 24 miles.

Over 4 days, the universe has expanded by 1489 miles.

At the end of day 1, the Hubble constant was 1 mile a minute, per mile (1440 miles divided by 1440 minutes)
At the end of day 2, the Hubble constant was ~0.508 miles a minute, per mile (1464 miles divided by 2880 minutes)
At the end of day 3, the Hubble constant was ~0.339 miles a minute, per mile (1465 miles divided by 4320 minutes)
At the end of day 4, the Hubble constant is ~0.258 miles a minute, per mile (1489 miles divided by 5760 minutes)


(I said it was hard to put into words! It seems that even simple figures like these make the concept easier to understand. Thank you for asking these questions as, though I sometimes know the answers in a general sense, explaining them like this helps me to crystallise things in my own mind!)

 

[csmyth3025]

I think I see what you mean. I remember a graphic that (roughly) depicted the expansion of the Universe over time. It showed a bell shaped "universe" that expanded rapidly at first (like the top of a bell), then a more gently sloping expansion (like the middle of a bell) followed by a flaring out (like the bottom of a bell). Although the proportions may not be exact, I think it's an image of what you're saying.

Chris

 

[SpeedFreek]

 

[csmyth3025]

Thanks SpeedFreek. That's the type of graphic I was talking about.

 

[dryson]

Time dialation is based on Einsteins theory of relativity which is basically the analogous thought process where devices and systems that engineers created relied primarily upon the interaction between physical forces and matter for their basic operation.

The physical force involved with time dialation would be the varrying ranges of gravity and how each wavelength of gravity would effect the upward turning motion of any of the clocks gears as well as gravity pulling down on the same gears as the gears completed their full circle which is all based upon how gravity effects the mass or the amount of matter within the atomic structure of each metal, plastic or other component material used. Ever wonder why old clocks have different sized gears that weigh differently? I just gave you the answer why.

Time dialation would not occur with digital clocks as these devices are based off of a chemical battery that produces energy that then powers the circuit board in which numbers are used to display the time. So regardless of how far away the two observers were from each other or how much gravity was present as long as there was a full charge in the battery both clocks WOULD remain in time with each other.

So ramparts your response about time dialation taking place is wrong only unless analog clocks are used which the last time I checked not very many analog clocks remain except in museums which means that time dialation like the devices and systems that were built around analog ideas are nothing more than relics from the past.

We are in the digital age which is sound waves, light intensity, forces, voltage current or charge to create numbers or digits.

The Infinity Project - Engineering our Digital Future- Devry University. Or perhaps you would like me to open up my Digital Design with CPLD Applications and VHDL book. I can also direct you to Bill Foust or Sammi Antoin at the Columbus Ohio Branch of Devry University.

 

[csmyth3025]

Time dialation is based on Einsteins theory of relativity which is basically the analogous thought process where devices and systems that engineers created relied primarily upon the interaction between physical forces and matter for their basic operation.

The physical force involved with time dialation would be the varrying ranges of gravity and how each wavelength of gravity would effect the upward turning motion of any of the clocks gears as well as gravity pulling down on the same gears as the gears completed their full circle which is all based upon how gravity effects the mass or the amount of matter within the atomic structure of each metal, plastic or other component material used. Ever wonder why old clocks have different sized gears that weigh differently? I just gave you the answer why.

Time dialation would not occur with digital clocks as these devices are based off of a chemical battery that produces energy that then powers the circuit board in which numbers are used to display the time. So regardless of how far away the two observers were from each other or how much gravity was present as long as there was a full charge in the battery both clocks WOULD remain in time with each other....

Dryson,

As has been pointed out elsewhere in this thread and in many other threads in this forum, the effect of time dilation due to the relative velocity of two atomic clocks (Special Relativity) and due to differences in the gravitational field that two atomic clocks are situated (General Relativity) has been studied and the effect has been verified.

I direct your attention to the Wikipedia article on time dilation which can be found here:

http://en.wikipedia.org/wiki/Time_dilation

The specific experiments to which I refer are contained in this article, as follows:

Hafele and Keating, in 1971, flew caesium atomic clocks east and west around the Earth in commercial airliners, to compare the elapsed time against that of a clock that remained at the US Naval Observatory. Two opposite effects came into play. The clocks were expected to age more quickly (show a larger elapsed time) than the reference clock, since they were in a higher (weaker) gravitational potential for most of the trip (c.f. Pound, Rebka). But also, contrastingly, the moving clocks were expected to age more slowly because of the speed of their travel. The gravitational effect was the larger, and the clocks suffered a net gain in elapsed time. To within experimental error, the net gain was consistent with the difference between the predicted gravitational gain and the predicted velocity time loss. In 2005, the National Physical Laboratory in the United Kingdom reported their limited replication of this experiment.[16] The NPL experiment differed from the original in that the caesium clocks were sent on a shorter trip (London–Washington D.C. return), but the clocks were more accurate. The reported results are within 4% of the predictions of relativity.

The Global Positioning System can be considered a continuously operating experiment in both special and general relativity. The in-orbit clocks are corrected for both special and general relativistic time dilation effects as described above, so that (as observed from the Earth's surface) they run at the same rate as clocks on the surface of the Earth...

Please note that the clocks in question are not mechanical clocks.

I can only imagine that you concocted your theory of time dilation as you were typing. If you're going to make up theories you should, at least, try to put more thought into the effort.

Chris

 

[csmyth3025]

To get (somewhat) back to the original subject of this thread, I'll pose this question: Is there a theoretical limit to the angular momentum (rotational speed) of a black hole?

For the purpose of this question lets use a black hole of about the size of the one that's believed to reside at the center of the Milky Way (about 4 million solar masses).

I know there is a Kerr metric which is an exact solution for the Einstein field equations of General Relativity as applied to uncharged rotating bodies. I've read about this metric but I don't pretend to understand it even a little bit.

My question stems from the Wikipedia article on the Kerr metric which can be found here:

http://en.wikipedia.org/wiki/Kerr_solut ... t_surfaces

The specific portion which prompts my question is as follows:

A rotating black hole has the same static limit at the Schwarzschild radius but there is an additional surface outside the Schwarzschild radius named the "ergosurface" given by (r − GM)2 = G2M2 − J2cos2θ in Boyer-Lindquist coordinates, which can be intuitively characterized as the sphere where "the rotational velocity of the surrounding space" is dragged along with the velocity of light. Within this sphere the dragging is greater than the speed of light, and any observer/particle is forced to co-rotate.

To me, as a layman, this portion seems to be saying that there is a theoretical exotic object that is capable of "dragging" a particle faster than the speed of light in relation to a distant observer in the "outside" universe. As I understand it the particle isn't moving faster than the speed of light relative to the spacetime of the ergosphere in which it's imbedded.

This is a far cry from the "spinning ring" scenario that started this thread. In a way, though, it's asking the same essential question.

Chris

 

[theridane]

Chris, there's a limitation imposed at least by the STR (see this thread).

 

[csmyth3025]

Chris, there's a limitation imposed at least by the STR (see this thread).

Thanks Theridane,

Since there are similar concepts discussed in in the Physics thread "Pulsar size vs frequency" to which your link is directed, I'll post my question there (hopefully with a few more numbers to work with).

Chris

 

[dryson]

Dryson,
As has been pointed out elsewhere in this thread and in many other threads in this forum, the effect of time dilation due to the relative velocity of two atomic clocks (Special Relativity) and due to differences in the gravitational field that two atomic clocks are situated (General Relativity) has been studied and the effect has been verified.
Chris

So what you are saying to be true is that if two clocks powered by a chemical cell battery process and are both digital clocks are carrierd aboard two planes that are the same design one plane coming off of the assembly line one after another and leave from the same point and travel at the same speed and altitude for the entire journey back to the point of origin as well as being kept in sync with a central clock that is timed to the atomic clock that there will be time dialation due to gravity?

Not even wrong. Gravity does play a small role in the process but it is not the defining factor that creates the time delay. What happens the farther away from the Earths surface that you travel? The atmosphere becomes colder does it not? I think it does. What happens to batteries when they become so cold? That's correct they do not produce any electrical power. This can be proven by letting a battery even a new one sit out in the freezing cold for a week and then try to use it to start your vehicle. What happens? Your vehicle will not start. So the farther out of the range of temperature that you travel that allows a batteries chemical process to work due to the temperature the less energy the battery will produce when the battery produces less and less energy even a digital clock will seem to slown down due to the battery not being able to power the systems that operate the clock. Once the battery is brought back down into the correct temperature range of operation the clock will begin to work again which in most cases will cause the clock to flash 12:00. So gravity is not the main factor in what you are trying to prove as being the main factor is the gradual loss of time. Gravity is also not the main factor involved with aging. One thing that everyone needs to remember about Einstein is that he was not involved with biology or the chemical reactions and interactions between energy and bio-matter which was a sever limiting factor in his learning about physics.

 

[dryson]

Another question that needs to be asked of the testors is did they keep the clocks in a box where the temperature of in each box was kept the same temperature as the area surrounding the central tower where they left from or did they allow the clocks to stay at a comfortable room temperature so they could manipulate the results to prove their theory?

I am assuming the latter because if the clocks were kept at the same temperature as the temperature around the tower then the batteries would have produced the collect level of electricity to keep them in sync with the point of origins tower.

 

[SpeedFreek]

So what you are saying to be true is that if two clocks powered by a chemical cell battery process and are both digital clocks are carrierd aboard two planes that are the same design one plane coming off of the assembly line one after another and leave from the same point and travel at the same speed and altitude for the entire journey back to the point of origin as well as being kept in sync with a central clock that is timed to the atomic clock that there will be time dialation due to gravity?

No, that is not what he is saying, and we have tested this using atomic clocks, not battery powered digital clocks. What you just described is an experiment where both clocks are always kept at the same gravitational potential. Now, if the two planes flew at different altitudes then there would be time-dilation due to gravity.

Not even wrong. Gravity does play a small role in the process but it is not the defining factor that creates the time delay. What happens the farther away from the Earths surface that you travel?

The gravitational potential changes - see both the Hafele-Keating and Pound-Rebka experiments.

There is no relative movement between a clock at the bottom of a mountain and an atomic clock at the top of a mountain, and yet they run at different speeds.

The atmosphere becomes colder does it not? I think it does. What happens to batteries when they become so cold? That's correct they do not produce any electrical power. This can be proven by letting a battery even a new one sit out in the freezing cold for a week and then try to use it to start your vehicle. What happens? Your vehicle will not start. So the farther out of the range of temperature that you travel that allows a batteries chemical process to work due to the temperature the less energy the battery will produce when the battery produces less and less energy even a digital clock will seem to slown down due to the battery not being able to power the systems that operate the clock. Once the battery is brought back down into the correct temperature range of operation the clock will begin to work again which in most cases will cause the clock to flash 12:00. So gravity is not the main factor in what you are trying to prove as being the main factor is the gradual loss of time. Gravity is also not the main factor involved with aging. One thing that everyone needs to remember about Einstein is that he was not involved with biology or the chemical reactions and interactions between energy and bio-matter which was a sever limiting factor in his learning about physics.

This is the physics forum, stop making up this nonsense. We are talking about atomic clocks here, not battery powered digital clocks. We are talking about the durations of processes that occur within atoms themselves. Battery powered digital clocks have a very limited temperature range in which they work, but this does not apply in anything like the same way to the processes that occur inside atoms.

 

[csmyth3025]

Dryson,

Before you try to present arguments proving why you think Special Relativity and General Relativity are wrong, it would be a good idea to research why the scientific community thinks they're right. Wikipedia and a number of other websites have a wealth of information on both of these theories, on the history of how they came to be developed, and on the many experiments that have been performed that have caused these theories to become universally accepted.

Throwing out ideas off the top of your head like mechanical clocks and cold batteries being the cause of these effects does a disservice to the many researchers who have done dozens (if not hundreds) of exacting experiments to prove (or disprove) these theories.

Chris

 

[MeteorWayne]

Somehow I doubt the head is involved. It seems more like the ideas are being pulled out of somewhere else...

 

[dryson]

Then if temperature does not play a role in the process then why does copper which is part of an octopuses blood only exhibit paramagnetic effects when the cooper has reached a certain degree of coldness? The question about the Mountain and Valley question is which clock operated at a nominal time when compared with the orbit of the Earth around the Sun? If the answer is the clock that was closer to the ground runs at the relative time of the Earths travel around the Sun and the clock on the Mountain ran slower then the determing factor is not gravity but the temperature which causes the atoms to slow down or speed up which the last time i checked involved electrons which the atomic clock is based off of.

 

[SpeedFreek]

Gravitational time-dilation.
The clock at the top of the mountain ran faster than the clock at sea level, due to the difference in gravitational potential - the clock at sea level was closer to the Earth's centre of gravity and so ran slower. It is hotter at the top of a mountain?

Time-dilation due to relative speed.
Cosmic rays hit our atmosphere, causing showers of particles called muons, which are travelling at relativistic speeds. These muons are time-dilated (time runs slower for them) than muons "at rest" in the laboratory. The muons in the laboratory decay really quickly, and if the muons coming from space decayed that quickly they would not reach the ground, but they do! Time is passing slower for the muons travelling at high speeds through the atmosphere. Considering the energies involved when travelling at relativistic speeds, are those muons caused by cosmic rays from the Sun "colder" than the muons in the laboratory?

Temperature: It is not temperature that causes atoms to become more or less energetic, it is the energy of the atoms that causes temperature.

 

[csmyth3025]

If the answer is the clock that was closer to the ground runs at the relative time of the Earths travel around the Sun and the clock on the Mountain ran slower then the determing factor is not gravity but the temperature which causes the atoms to slow down or speed up which the last time i checked involved electrons which the atomic clock is based off of.

As SpeedFreek points out, the clock at the top of the mountain runs faster than the clock at the bottom of the mountain. Now your left with trying to revise your "theory" to explain an observed phenomenon that is the total opposite of the results you've predicted.

Again, you do a disservice to the researchers who you seem to assume have overlooked such a blatantly obvious source of error in their experiment as temperature differences. Please read about these experiments before you make assumptions about how they were conducted. One good place to start is the HowStuffWorks article on atomic clocks which can be found here:

http://science.howstuffworks.com/atomic-clock.htm

Another more in-depth look at how a Cesium Fountain Atomic Clock works can be found here:

http://www.nist.gov/physlab/div847/grp5 ... ndards.cfm

And, if you're really interested in the details of the history and of the principle of atomic clocks you can download this 14 page NIST paper from this site:

http://tf.nist.gov/general/pdf/2039.pdf

Chris