Iggy

Differences in gravity or differences in the "force of gravity" is indeed a difference in the physical environment. An observer in a windowless room can tell the difference between being subjected to a strong force of gravity and a weak force of gravity. However, the force of gravity is not a factor in time dilation. You probably imagined that clocks in a strong gravitational field tick slower than clocks in a weak gravitational field and concluded, based on that imagining, that the force of gravity changes the physical environment in a way that affects the rate of clocks. But, you have imagined relativity and time dilation incorrectly. Time dilates with gravitational potential -- not gravitational force. Two clocks which feel the same force of gravity (or no force of gravity at all) but are at different gravitational potential will tick at different rates and gravitational potential is not a physical condition of an environment. This means that the gravitational potential of a system does not affect any measurement made inside the system. Let me explain what that means, because it is key. A system could be a physics laboratory. Inside the laboratory there are various types of clocks and other physics equipment -- whatever might be needed. There is no way for a physicist in this laboratory to determine the gravitational potential of the laboratory itself, because gravitational potential is not a physical environmental condition of the laboratory the way that temperature, pressure, and composition are. Md65536 already explained why velocity isn't a physical condition of an environment, so I won't answer that part, I'll just point out that your question answers itself, If you can't tell if you are moving or if you are at rest then 'velocity' has no effect on the physical environment. If 'velocity' did have an effect on your physical environment then you could tell if you were moving or at rest. I searched the thread and this is the only explanation I could find you give for why the clocks on the rocket are wrong. You explain that the rocket's clock is incorrect because it disagrees with the earth clock and the earth clock is the correct clock. A logically identical argument is that French is incorrect and English is correct because English is the correct language and French is clearly in error, but can be corrected by translating it into English. Because this argument is circular and fallacious, can you give any other reasons why the clocks on the rocket and the age of the rocket twin are incorrect? Can you explain, in other words, why almost every clock in the visible universe is incorrect while our solar system correctly measures duration? I ask honestly -- is it because people live in this solar system and people get to decide these things?

Mpc755, if the aether is a physical entity then can you please mail me some? No, that is what the OP asserted. I disagreed with that definition of a year. Have you read the thread?

A sidereal year (the time it takes the earth to orbit once) is different as measured from the surface of the earth and as measured from a coordinate system rotating around it. Relativity does not assert that either measure is any more valid than the other. They are both correct -- they are just measures of different things. The first is a measure of proper time on the surface and the second is a measure of proper time of the astronaut. To think that the measure from the surface is somehow more valid and that all other clocks are in error is to elevate earth to some universally preferred position. To think that humans do not experience time dilation (that the astronaut would really spend a year, not a day) is pretty much the same as assuming people don't follow confirmed laws of physics.

An earth orbit is "clock time". The duration between events as measured by earth's orbit around the sun dilates just like any duration measured by any clock. The earth isn't special even if it occupies a very special place in your head. Every clock is based on cycles. Earth's cycles are not special even if you consider them "natural" -- whatever that means. Bad idea: International Astronomical Union: SI Units We would just have to be careful not to synchronize our clocks with "natural cycles" near cygnus x1, because then the human lifespan would only be a few seconds and I wouldn't mind living rather longer than that.

I'm curious what you mean by "high speed conditions"? How would a person know if they are in "high speed conditions"? Can you describe an experiment that measures "speed condition"? Is there not a "reality check" here... that a year is one orbit of earth around sun? Speeding out into space and back in a rocket does not make ten earth orbits into five just because the rocket's clock and calendar says that only five years have elapsed. In science, a year is 31.5576 megaseconds where a second is defined as "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom". A year is not defined in terms of earth orbits. In science, a clock is anything that measures duration. A mechanical stopwatch measures time by rotating a dial around a pivot point. For example, a second hand on a standard clock making a full rotation measures 60 seconds or one minute. The earth and sun likewise make a clock where one full rotation of the earth around the sun measures one year. The twin paradox is an example of time dilation. It is an example of how two twins can age differently according to relativity. A twin who makes a round trip in a rocket with a high speed relative to the earth twin can age one year while his brother the earth twin ages 60 years. Every clock -- every means of measuring proper time -- in the earth twin's frame of reference including mechanical spring watches, pendulum clocks, digital quartz clocks, atomic clocks, and biological systems will tell him that the duration of the rocket trip was 60 years. Every clock that the rocket twin has in his frame of reference (mechanical, digital, atomic, biological, etc.) will tell him that the duration of the trip is one year. The earth and the sun do not travel with the rocket -- they stay with the earth twin. The number of earth orbits is therefore not expected to measure the proper time of the rocket twin. Both twins will agree that the earth orbits the sun 60 times during the trip just like any clock measuring the earth twin's proper time will measure 60 years. Both twins will also agree that any clock measuring the rocket twin's proper time will measure one year. In other words, the point of the though experiment is to show that clocks (any method of measuring duration) in different frames of reference do not agree, so it doesn't make any sense to propose that both twins use the same clock from one of the frames. That misses the point of the thought experiment. You don't realize how apparent it is that you don't understand or aren't familiar with the concepts -- for example, of relativity and time dilation, and how much your mistaken impressions are the source of your arguments. You are imagining what relativity and time dilation might be and arguing against your own imaginings. An earth orbit is just one example of a system that can be used to keep time. It is unrealistic, and geocentric, to think that it keeps the right time and any other system of time keeping in any different frame of reference or with a different gravitational potential disagrees because of "instrument error" that somehow exactly coincides with relativity. The predictions of relativity are correct because the postulates of the theory are valid. In special relativity for example frames need to disagree about duration because they need to agree about a fixed velocity -- not because clocks in those frames are subject to instrument error.

Most things lower in temperature when they give up heat. If everything in a system is the same temperature then the system will not spontaneously segregate its temperature. A gravitationally bound system is different. It has a negative heat capacity -- if it gives up heat then its temperature can rise as gravitational potential energy is converted to kinetic energy. For this reason, a gas cloud that is homogeneous in temperature, but not density, can spontaneously turn heterogeneous in temperature without it being a violation of the second law.

Why odd? Probably not exactly because the Jeans length doesn't take into account radiation pressure and stellar winds and things like that. It is a better approximation before fusion becomes a significant factor.

Absolutely. Star clusters are the remnants of collapsing molecular clouds so you can imagine that quite a few stars form out of a collapsing cloud. I wouldn't put it quite like that, but the gas and dust between the collapsing fragments is eventually boiled away and scattered from the star's radiation. I'd again put it differently. A collapsing protostar will lower in entropy when it gets small enough. The heat it radiates raises the entropy of the surroundings to more than make up for the difference. It is something like a schwarzschild raidus. A very small volume of a gas at a certain temperature and density won't hold itself together gravitationally. It will disperse. A very large volume of the same gas at the same temperature and density will hold itself together. The Jeans length is the minimum size needed for a gas at a certain temperature and density to hold itself together gravitationally. If the volume of gas is larger than the Jeans length it will collapse. If it is smaller, it will expand.

The collapse does indeed work to raise the temperature of the cloud. Other factors work to cool it -- explained by this site: http://www.astrophysicsspectator.com/topics/milkyway/MolecularCloudCollapse.html But, as it continues to collapse the increased pressure will eventually start to increase the temperature. I'm not sure how much molecular clouds heat up before they start making a lot of protostars, but they certainly are allowed to heat up yet continue collapsing. When it gets small enough, the strength of gravity trying to collapse the cloud is overcome by the increased temperature and pressure. At that point the Jeans length is equal to the radius of the cloud and the kinetic energy of the constituent parts are equal to their gravitational potential. The pressure of the gas, which increases as the volume decreases and temperature increases, tries to expand the cloud. The strength of gravity tries to collapse it. If the pressure is stronger then the cloud will expand. If gravity is stronger then it will collapse. It stops when it finds and equilibrium. To find out if a uniform gas cloud wants to collapse or expand calculate: [math]\lambda_J\approx\sqrt{\frac{k_B Tr^3}{GM \mu}}[/math] where [math]k_B[/math] is Boltzmann's constant, T is the temperature, r is the radius, G is the gravitational constant, M is the cloud's mass and [math]\mu[/math] is the mass per particle. If the answer is smaller than r then it will want to collapse. Larger than r and it will want to expand. Molecular clouds can have a small enough T, yet large enough M/r3, for it to want to collapse.

I'm not an expert, but I might be able to answer. A gas cloud of uniform density is a gravity well. With uniform density it looks like this: http://en.wikipedia.org/wiki/File:GravityPotential.jpg or this showing one spatial dimension where a is the radius of the sphere of uniform density. If you're asking at what point the cloud would collapse, it would depend on the temperature and density of the cloud. When the gravitational potential energy of each gas molecule becomes greater than each molecule's kinetic energy it collapses... and it loses its uniform density at the very center [edited]. The Jeans length is a way to calculate. When the Jeans length is smaller than the cloud it starts collapsing. Yes, I think that is typically what happens. A molecular cloud won't be perfectly uniform. When a very large nebula in a galaxy starts to collapse, the temperature can initially stay constant or even drop because as it shrinks the cloud becomes more opaque to starlight and cosmic rays that warm interstellar space. If the cloud cools like you say, or even if the collapse causes it to heat up but only by a factor less than 1/R^1/2 where R is the scale of the cloud, then the Jeans length will shrink faster than the collapsing cloud. That means that the collapse itself can cause smaller and smaller portions of the cloud's interior to be able to collapse in on themselves. The areas inside the cloud with the highest density would self-collapse first forming stars in a developing stellar nursery for example. If the cloud were perfectly uniform and symmetrical then I don't believe it would break up into pieces when collapsing -- it would just fall in on its center. With perfect homogeneity every part of the cloud would shrink at the same rate and it would keep its uniformity except at the center where mass gathers [edited]. But, in nature it would never be perfectly uniform. It actually doesn't have to cool. So long as it doesn't heat up by a factor greater than R^-1/2 the Jeans length will remain smaller than the cloud and it will continue to collapse. The increasing temperature from the increasing pressure of the collapsing cloud can be insufficient to halt the collapse until stars start forming and warming up and clearing out the areas that surround them with radiation pressure. Would you mind posting a link to the other thread. I looked through your recent posts, but didn't see it.

He he. Ringo = pigeon. Diner = chessboard. Ringo tries to crap all over the diner, but ends up having the good sense to leave when his lunch is handed to him. It works on so many levels. Mad props

Dr. Rocket said to you some time back "the problem is that you don't know that you don't know". I'm sorry, but it's clearly true. That train sailed. The quote I gave said "exist in reality" and you interpret that "without a referent in the real world". Hopeless I'm afraid. Indeed.

No. You haven't. You have already shown that you don't understand that paper. I can quote the paper too, Your favorite paper that you keep quoting is trying to tell you the same thing we are... you're just not going to get it.

You say "two transmitters" and "no time elapsed". If the two transmitters are not in the exact same frame of reference then they will disagree about the idea of no time elapsing. If the one transmitter found that no time elapsed for the transmission of a signal the other transmitter could find that the signal landed before it was sent. If the signal had no travel time according to one of those frames then it would have a travel time according to the others -- either positive or negative. In relativity, "at the precise same time" depends on frame of reference. It is not something that everyone agrees about. If A sends a signal to B and A thinks that it takes no time for the signal to get there then B sends the signal directly back to A and B thinks that it takes no time for the signal to get back to A then A can get the return signal before he sent the original. He can get his own signal from the future. Causality is violated.

I really don't know what 'even more simultaneously' means. In relativity FTL communication would make sending signals into the past possible and pretty trivial.

You have to define "instantaneously". In relativity the present instant changes with velocity. If a transmitter, A, instantly sends a signal to another transmitter, B, and B is moving towards A and it relays the signal right back to A then A will receive the signal back before it sent the original which is a problem for causality. A gets its own signal from the future.

Seriously? Are you serious with this... again? If infinite implies unbounded then it does not necessarily follow that finite means bounded. That would be a logical fallacy called denying the antecedent. It is true that "infinite space" implies "unbounded". It is not true that "finite space" implies "bounded". If you can't think about it logically then there is no point in thinking about it. edited to add: The difference between infinite and finite space: you can only put so many ping-pong balls in a finite space, there is no limit to the number you can fit in an infinite space. A compact, finite, and unbounded space is one that only holds so many ping-pong balls. If you filled up the space with ping-pong balls the thing preventing you from adding more is that every ping-pong ball is surrounded and filled in with other ping-pong balls. There is no boundary where one side has ping-pong balls and the other doesn't. In euclidean space you would be correct. Space is either infinite and unbounded or finite and bounded. All you know is Euclidean space so you no doubt assume that what is true for Euclid is true in general. Your error is in failing to conceptualize non-euclidean space and assuming that such a space is impossible. That is your failing and your faulty assumption. Non-euclidean spaces are just as valid as euclidean. Knowing which is correct is an empirical issue. It has to be measured. Even if you really, really, really like Euclidean space -- that doesn't make the universe Euclidean. Even if you really, really, completely, fail to understand non-euclidean space and have no idea what space-time is -- that doesn't mean they are impossible. It just means that you don't understand and you don't know what you're talking about.

Finite space does not imply an end or a boundary to the space. That is the answer. It has been explained and repeated to death and you're still saying that no one has answered it like you didn't notice. It's hopeless.

Glad you are enjoying your superior perspective. But would you mind answering a few sincere questions?... A recent post of yours reminded me of Family Guy - Speaking Italian, so maybe there is something to Dr. Rocket's comment and it shouldn't be rejected as insincere. You say very definite things about concepts that you don't seem to understand at all. Like Peter not realizing that he doesn't speak Italian, I don't think you realize that you don't know what relativity is or what a closed space is.

Right. Owl actually quoted a good definition for a bounded metric: IOW, there is a bound on the distance between any two points. This article -- The Possibility of a "Finite" and yet "Unbounded" Universe -- and this statement: refer to the kind of boundary that you might run into in moving around the space. That is the meaning I was intending as well. Sorry for any confusion. Edited to add: In a closed spherical space with a diameter of 1 km, anything that travels 2 km in a straight line will end up back where it started. I really think this would help: The Possibility of a "Finite" and yet "Unbounded" Universe.

You don't seem to know what the words finite and infinite mean. You can make up your own definition, of course, but here are the definitions I have already quoted earlier. Wikipedia: Your logic may be failing you. You think that because "infinite space" implies "unbounded" then "finite space" must imply "bounded"? That would be a logical fallacy called "denying the antecedent". If "unripe banana" implies "not delicious" then you should not think that "ripe banana" must imply "delicious". If "infinite space" implies "not bounded" then you should not think that "finite space" must imply "bounded". This would help, if you read it, The Possibility of a "Finite" and yet "Unbounded" Universe

Space-time is now an established entity with intrinsic curvature? md65536 said "Similarly, we can describe a closed infinite space without the need for a 4th dimension", not me. The curvature is intrinsic. You can reference chapter 7.4 of Einstein's general theory of relativity: with modern applications in cosmology I don't believe that would be helpful. It would be helpful if you acknowledged that this is not logical, Finite space does not necessitate or imply a boundary. Closed means compact without boundary. You could imagine a creature living in a small closed three dimensional space throwing a ball in any direction. The ball would eventually hit the creature in the back. Or imagine the creature looking through a powerful telescope and seeing the back of its head.

"intrinsic curvature" means curvature without a higher dimension. Space-time has intrinsic curvature and there is no 4th spatial dimension. Your own link tells you this. So, please, just stop Owl. You are not making a coherent argument.

Acrobat creates layers like that when a scanned document is saved as an optimized pdf, and I believe some other scanning software do the same. Edited to add: Fox News -- Expert: No Doubt Obama's Birth Certificate Is Legit

There is only one assumption (i.e. postulate or axiom) that is different between Euclidean and non-Euclidean geometry. What is it? If you did read it, you didn't understand it. It says what everyone has been telling you and disagrees with your "objection" to space-time... That is not logical. Space can be finite and unbound so it is a false dichotomy between infinite space and a boundary. Assuming that space is Euclidean is also illogical. It is an empirical matter.