Johanluus

i say neither, Now if that molecules electron(s) absorb an photon and jumps to a higher orbital ( if that is correct) has the molecules "mass" increased ? "There is no mechanism by which the lone atom would emit thermal radiation" post #10 Further when it falls back to the lower orbital emmiting a photon , could that not be accepted as "thermal radiation" or is that something else .

Time cannot run "backwards" but a set of equations can be time invarient.Surely there is a difference?

i was wondering if schrodingers cat (paradox) would be classified as consciousness.. just classifying consciousness is the real question

"I don't think two is enough, but if two is the ensemble, or system of interest, the mass of that system could be considered greater than the sum of it's parts, (as you would consider in a gas cloud which would certainly have a temperature) as you could include the kinetic energies with respect to the center of mass." It sounds like temprature is only well defined using Maxwell-Boltzmann statistics, which implies that temprature is "emergent " . As we increase the number of atoms in a vacuum box the temprature increases using the relation PV= nRT. Similarly the as the Mass increases gravity "emerges" causing additional potential energy. This is how I interpret it , does it make sense? Merged post follows: Consecutive posts mergedSimilarly the mass the Mass increases gravity "emerges" causing additional potential energy. oops typo error apologies!

"it won't even emit an IR signal that you can measure while a collection of atoms will." is this just because we dont have a sensitive enough measuring apperatus yet or is there a more fundametal property of an ensemble of atoms that is different from a single atom, s mass.

The photon is created traveling at c. even so "Would it not make more sense to say that redshift /blueshift. is a result of gravitation , and not the speed of recession of the two objects in question"

event1 1. A photon is created when object(1) of mass release energy through radiation.. event2 2. The Photon is destroyed when it is absorbed by another object(2) absorption. Between event 1 and event 2 this PHOTON must be accellerated from rest ( WRT object1) resulting in redshift and Decellerated to rest ( WRT object2) resulting in blueshift. This is directly atributable to Gravitation of both objects as i understand it. If the photon does not change its speed i.e always c IN ALL INHERTIAL FRAMES. Would it not make more sense to say that redshift /blueshift. is a result of gravitation , and not the speed of recession of the two objects in question. For light , velocities of objects, have no physical meaning if its velocity is constant for ALL objects i.e c .Velocities and time are of no importance between linking two events that are not in contact due to gravitation. Why do we always then relate redshift => hubbles constant => expansion of universe. Are these effects on photons , not predominantly due to Gravitational effects e.g LENSING ETC.

"Hotter objects have more mass than when cooler" would this also be true for a single atom say hydrogen? Is this mass increase dm only attibutable to the absorbtion of the photon by the electron?

Ive started on "Carroll's lecture notes on general relativity" so far so good , thanks all.

1. "What is invariant is the "length in space and time", the so called space-time interval" I've had diffaculty understanding this . How does one define this "interval" and prove that it is invariant under all inhertial frames. (This is my theoretical question) But this led me to another consideration:(philisophical consideration- not sure if it belongs here , but here goes) 2. Is GR not just a manipulation of variables to fit our model of how we would like to percieve space and time with our current measurments? I know it works very well in general relativity but so did Newtons gravitational law for 300 years, until we found slight discrepancies with our planetary orbits, moving clocks etc. What i'm mabey asking is , how complete is an equation, is there a "limit". How accurate can one go, to get more precise measurment of events and observations, it is an endless cycle.. My analagy of this is the car decellerating to a "stand still". At what "point" in space-time does it come to a stand still. if it goes slower, and we measure a speed , we can always divide that speed by two and measure again, there is always a point slower than the last.At what point will we be satisfied that the transition from motion- to rest has occured. I can continue to do this until my instrument does not give a reading , but that does not mean it can't decellerate more, it may be we just cant measure it. Their may be a "limit" in mathematics , but could this just be a manipulation of differentiation , of our definition of decelleration. In reality we are limited to our instruments and measurments until we cannot measure more precicely. Where does this space-time interval begin and end, what defines its boundries? So we formulate a new set of equations that suit our new set of instruments and then manupulate to suit our better measurments.Which now stop at Heisenbergs uncertainty principal , FOR NOW .. OR NOT? Are we not missing the point. Is there really a formula for the "theory of everything ". Does the formula preceed everything we percieve today. Or do we manipulate/ define a formula base on how we all collectively percieve something today with our measurments. Does PERCEPTION -> PROOF -> TRUTH ? OR does truth exist always , no matter what our current perception is there is only one truth.

Can anybody help , with a basic tutorial for the introduction to tensors - with a workable example , perhaps. My algebra and calculus , is ok but slightly rusty.

"What you seem to be asking is how there can be an Event Horizon with lower surface acceleration than we have here on Earth and still have an escape velocity higher than speed of light." Yes that is exactly right "A lightray that leaves Earth don't have to struggle against an acceleration of 9.82 m/s2 very far, but a lightray escaping from close above the hypothetical Black Hole's Event Horizon will have to struggle against that acceleration during a very long distance" Agreed. "If the gravitational well gets bigger, it does not only get deeper it gets wider too." This was the information that i was missing !! -{1} I believe the area under such a (slope/function) would be the total amount of energy needed to escape the gravity well. But what determines the shape of such a slope, or topology. What information / equation relates the "DEPTH" of the gravitational well to its "WIDTH". Conclusion: Black Holes remains Black Holes even if the surface acceleration at the Event Horizon tends to zero when the mass approaches infinity. Based one {1} i can finally understand this. Thanks spyman for your persistance.

While special relativity constrains objects in the universe from moving faster than the speed of light with respect to each other, there is no such theoretical constraint when space itself is expanding. It is thus possible for two very distant objects to be moving away from each other at a speed greater than the speed of light (meaning that one cannot be observed from the other). There is a very fundamental difference in the two statments highlighted above when they are isolated , which leads to confusion for many people including myself. The first implies that the OBJECT has a momentum relative to a force and energy, measured by both observers. The second first implies that the OBJECT is being "moved" by the expansion of space , rather like two boats on the ocean drifiting apart due to ocean currents. Not quite the momentum energy required in the former statment.Where a reference inhertial frame is required. Hence special relativity.

"Yes, if there was an alien on a planet close to the center and it had the proper balance between the pull of the blackhole to it's perception of the space between them expanding(due to this deceleration theory)... it would measure itself as orbiting the blackhole and not falling in." So assuming we have just witnessed (with our new super telescope ) the Aliens planet falling into the black hole and being pulled apart , with our Super telescope today. Theoretically the Alien from his perspective on his planet, is still orbiting that black hole?

"So why do you think that "there would be a point in time where photons and matter would , then have enough escape velocity to reach outside observers" if the Black Hole is allowed to grow sufficient enough?" Thanks for your input spyman: The above statment is the crux of my question. The equation for [math]a_{EH}}[/math] (the accelleration at the event horizon (which we made equal to its Schwarzschild radius for simplicity) is given by:(post #12) [math]a_{EH}=\frac{c^4}{4Gm}[/math] We also deduced that "surface acceleration decreases when mass increases " for this equation , the reason being(post #10): "Is this perhaps because the distance between the "centre" of the black hole and the event horizon i.e the Schwarzschild radius, has also increased due to the mass increase and this affects the force ( accelleration) in Newtons gravitational law, with a inverse square relationship? Reducing the accelleration." So my logic says that: As time goes by and the Black hole swallows more and more mass , the accelletation [math]a_{EH}}[/math] which is just outside our Schwarzschild radius from our assumption, will tend to zero. So at some point in time , this accelleration [math]a_{EH}}[/math] will eventually be comparable to say earths gravitational pull on its surface ( 9.8 ms^2) at which photons can easily escape, which implies no more black hole?

"A comet outside the frame would not perceive this expansion and would instead see the Earth spiraling in towards the Sun, getting closer with each revolution. We may have evidence of this spiraling already. The most common type of Galaxy as far as I know is a Spiral Galaxy." Would your theory imply then ,that the Andromeda Galaxy to US here on earth , is spiraling into its black hole . But to An Alien on some planet relatively close to the centre of Andromeda , be in a constant elliptical orbit around its centre?

" at which amount of mass in a Black Hole, the calculated escape velocity at its Event Horizon would go below c" That point is always the Schwarzschild radius no matter what the mass is inside it , not so? My assumption in (post #8) was "when the radius in eq2 is equal to its Schwarzschild radius (eq1)" [math]r_{s}=\frac{2Gm}{c^2}[/math] -eq1 [math]g=\frac{Gm}{r^2}[/math] - eq2

To summarize then [math] a_{EH}=\frac{c^4}{4Gm} [/math] Given the initial mass M of the black hole already there. The accelleration [math]a_{EH}[/math] can only decrease with time , as matter (energy) is sucked into the EH , with the EH growing proportionately relative to its Schwarzschild radius.(Assuming Hawkin radiation does not exist). One could possibly deduce that a black holes "maximum" [math]a_{EH}[/math] would be at the instant of creation i.e at the collapse of the large star forming the black hole. And as it sucks in matter, the space curvature outside the event horizon would try and "renormalize" as it tends back to flat ecludian space. [math]a_{EH}[/math] tends back to zero. Surely then, there would be a point in time where photons and matter would , then have enough escape velocity to reach outside observers, and not fall into the EH?? What am i missing here?

I think I follow your reasoning , I like the idea of decellerating mass , causing a "time" and "Length" expansion , which follows from special relativity. I always however have a problem percieving " rest mass". To me rest mass can only have meaning , when the two objects ( observer/ object with mass) are in the same inhertial frame.More precicely the distance between them is constant. If the objects are say moving apart each object will percieve the other object to have different masses due to relativity . And both will be right in their inhertial frame! "however since both the Earth and the Sun both contain rest mass(which is what I believe to be decelerating, not mass-less particles, but particles with rest mass). the effects of the deceleration cause the distance between the two to expand" This would only be with respect to eachother(sun -earth) , again same inhertial frame. When we introduce another observer say on Halleys comet , their perception will be totally different. And again if we introduce another observer , say on a photon propergating through space at c . All events and time are simoultaneous and at the same place WRT the photon.But WRT us it has travelled for billions of years. Perhaps your "decelleration" is the wrong choice of word. Rather the creation of energy levels that cannot overlap(fermions- requiring individual spaces) from Bosons (massless and at constant speed - at all points in space).

Your idea is very interesting to me "I'll start with the distances. If distances are increasing from the decelerating matter's perspective, than objects not being pulled towards it fast enough by gravity, will appear to be moving away at an accelerated rate and the unaffected light(since it has no rest mass and is not decelerating) appears to be stretched as it crosses this increasing distance in space... appearing as a red shift(no need for dark energy). Now in this scenario the earth for instance would be on a balanced downward spiral towards the sun, but as they are both decelerating the effects of this stop them from reaching each other, because the distance appears to be increasing at a similar rate. " When you say "but as they are both decelerating the effects of this stop them from reaching each other" How do you define ( or percieve) this deceleration, is it only with respect to c(massless particles) ?

[math] a_{EH}=\frac{c^4}{4Gm} [/math] yes of course , my apologies. "surface acceleration decreases when mass increases " This is suprising , because with Newtons gravitational law , force(hence accelleration) between objects increases with increased mass. [math] F_{EH}=\frac{G M_{1}m_{2}}{r^2} [/math] Is this perhaps because the distance between the "centre" of the black hole and the event horizon i.e the Schwarzschild radius, has also increased due to the mass increase and this affects the force ( accelleration) in Newtons gravitational law, with a inverse square relationship? Reducing the accelleration.

"That is some region of space-time for which no information can escape. You can of course enter such a region." very much like the entropy of our universe and the arrow of time.

"It is commonly believed that if FTL objects were to exist, they would be invisible, because photons would go the wrong way". Would it not be more correct to say that " light goes in all directions at c at the instant the photons leave the FTL moving object" So when we absorb the photon some time later dt , the object has moved further than dtc.

"but it must be emphasized that the light from the surface of the frozen star becomes redshifted very fast, turning the black hole black very quickly" But from our point of view as an observer outside , the light is still just outside the event horizon is still "frozen there"? Will we continue to see it forever?

[math] r_{s}=\frac{2Gm}{c^2} [/math] - EQ1 math]g=\frac{Gm}{r^2}[/math] - EQ2 Thanks Spyman I am trying to digest all the info . Would it be correct to say that when the radius in EQ2 is equal to its Schwarzschild radius in EQ1 then the accelleration g just outside the radius would have a value of ( c^4/4)? This would be the "minimum" value that g may be at the surface(horizon) of the black hole? I deduce this from the fact that if the gravitating body's raduis were greater than its Schwarzschild radius photons would have enough escape velocity to reach us. (with the assumption that the body is not rotating).