Sapient and the "Eternal Universe"

akolutheo
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Sapient and the "Eternal Universe"

Sapient,

If you could take the time to answer this, I would greatly appreciate it. I know you are busy running this website, so, if you do not have time, I understand.

My question is about your claim that the universe is eternal, meaning it always existed. This is the claim you made on Night Line to Kirm Cameron. I have a question for you about the second law of thermodynamics. I understand that the second law of thermodynamics DOES NOT mean evolution cannot happen. Many Christians have tried to state this before and they misunderstand the concept altogether and they misuse the word "disorder" in doing so.

Yet, I do understand that, according to the second law of thermodynamics, the universe is being brought forth to a state of entropy, meaning that while there is energy, it is reaching a state of being unusable.

My question for you is this: if there is an infinite amount of time behind this point in time, how do we still have useable energy in stars and in other places in the universe?

Some secondary questions are these: Doesn’t the mere presence of useable energy mean there cannot be infinitel time in the past? Should not all hydrogen have morphed into heavier elements by now?

Thank you for your time.  


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Quote:My question for you is

Quote:

My question for you is this: if there is an infinite amount of time behind this point in time, how do we still have useable energy in stars and in other places in the universe?

I think you misunderstand the basic physics behind this issue. Many theists try to get away with saying that the Big Bang was a point of "creation", or ex nihilo. But it was not. By absolutely all accounts of everything we know from every discipline in physics, the concept of literal "creation" is nonsense. The Big Bang describes a transition.

Theists typically assert that there is an inherent contradiction between the laws of the thermodynamics and our observation that the universe had a beginning, or rather, was what they call ex nihilo. The first two laws, henceforth referred to as FLOT and SLOT, are under consideration. For their lack of understanding of said laws, theists imagine that a deus ex machina, a creator "outside" such laws, is the solution to our apparent conjecture, without justification as to the mechanism by which this creator may be considered a "solution" in any sense of the word. So we should consider the first two laws of thermodynamics first:

In simple terms, FLOT refers to the nature of matter and energy as interchangeable between states, but indestructible. Since energy, in essence, refers to a scalar unit of the potential of a material body, it can only be transited between different forms. SLOT in essence (there are an uncountable number of ways to state it) refers to the fact that regardless of how hard we try, all things fall towards their lowest energy states, where the inequalities in the potential of material bodies necessary to generate any process begins to dissipate, as energy is virtually unable to be recaptured once converted into the irretrievable form of heat, as a result, energy, over time, becomes more equally distributed and in a lower state. The result is that all things become more disordered. the ashes of a burned piece of paper, after all, do not reconstitute themselves into paper. Here is the supposed contradiction. While FLOT implies that there is an infinity associated with matter and energy (that it was always here), SLOT and our empirical knowledge imply that the universe necessarily had a moment of creation. And hence, theists postulate that a "God" who can violate such laws created matter and energy from a supernatural origin. This reflects ignorance on modern cosmology and the Big Bang. We don't consider the universe to have "come from nothing" in the literal sense. In fact, science regards the term "nothing" as generally incoherent.

 All the Big Bang theory states is that the universe expanded outwards 13.7 billion years ago from what we now believe to be a symmetrical state. Many theists miscontrue the Big Bang as ex nihilo, "out of nothing". It is not the case. There are certain models postulating pre-Big Bang occurances, the boundary condition in Hartele-Hawking, brane cosmology, etc. But the BB itself says nothing about the creation of the universe. It simply describes an expansion occurance 13.7 billion years ago from a prior state, and the model describes occurances from the Planck time onwards from this prior state, that we can describe events from the Planck Time until the end of BB nucleosynthesis.

To understand this, it is necessary to be familiar with the mass-energy equivalence: E=mc^2, which is more accurately stated: (Delta)E=c^2(delta)m

Now, with respect to the mass-energy equivalence, it is inaccurate to say that energy is conserved. Only mass-energy is conserved. Consider fusion. At the point where the internal gravity of a protostar is such that the kinetic energy of protons in the proton-proton cycle is enough to overcome the mutual repulsion of protons, the nuclei fuse. At this point, they lose kinetic energy, at which point they gain potential energy from the transfer, and a small amount of mass is interconverted into energy when the nuclei fuse, called the mass deficit. The opposite effect occurs when the binding energy is input into a nucleus to break it into its constituency. Part of the work is converted into mass, and at the point where the strong nuclear force is broken, the protons have zero potential energy (which means they had a negative potential after fusing. This is called a well in physics). This means the sum of the constituents per se of any nucleus will always have more mass than the nucleus, which leaves us with a more accurate restatement of Einstein's equations:

The energy required to break every bond in the nucleus=[(Mass of sum of constituents)-(Mass of nucleus)]x(c^2)

So, the first principle we must understand is this: The Big Bang describes a transition event. The sum entropy of all the matter that formed from energy interconversion at the moment of the Big Bang was the lowest entropy, and hereafter has been steadily increasing. This has several consequences for the prior state of the Big Bang. Firstly, it has no entropy. How could it? Entropy is always with respect to temperature, by this formula: delta(G)=(delta)H-T(delta)S.

According to this formula: Tp=mpc^2/k=r(hr)c^5/Gk^2, matter breaks down at the Planck Temperature, 10^32K. It is nonsense to speak of matter being "hotter" since temperature is a measure of particle kinetics. In the low-entropy state, there wasn't any matter, it becomes interchangeable with energy. And energy does not have temperature. We speak of probability in thermodynamics always in terms of matter, firstly because of temperature, and secondly because equations in statistical mechanics is always given as a function of the probability of certain states occuring, and that is always with respect to particles. Thermodynamics literally means "movement of heat". It does not apply to energy per se. It is a study of matter. Matter did not exist until 13.7 billion years ago.

At the moment of transition, the interconversion of energy to mass spawned both matter and antimatter. As Einsten explained, there was an infintesmally larger amount of matter which, when the matter-antimatter pairs annihlated, was left, forming everything we see around us. The energy released by the annihlation is what is left today, and as explained, the sum entropy of the matter in the universe at the point where the annihlation released the energy in question would have been the lowest point in the history of the known universe.

The second thing we must consider is time. You are trying to combine the modern notion of Big Bang with the Aristotilean notion of time as a flowing river and it won't work.

The laws of General Relativity break down as you approach the prior entropy state, until Planck Time. According to BB theory, nothing can be known about the pre-Planck Time existence, all we know is that the universe expanded outwards from some prior entropy-less state when presumably the symmetry in the four disngaged forces were unified. There was no matter, it would have been too excited and broken down, due to Planck's Temperature. This system was extremely unstable and collapsed into our present system. Remember, when one intuitively speak of "time" you are speaking of time as a progression. I am referring to the Lorentz Manifold, the causal structure. This applies to Minkowski and Non-Minkowski space. So, it is unhelpful to say that time "did not exist" before BB. If we start to suggest time is a flowing river, we get endless paradoxes (a supposed God would be one of them, since it would necessitate postulating a causal agent to explain why the necessary substrate for causality exists). According to the Lorentz Matrices, time, strictly speaking, is invariant, it has no direction and there is no reason it should. This is demonstrated by the light-cone experiments, which can be causal-chronological or chronological-causal. Time is not a thing unto itself, being relative to the observer, but absolute space-time is. The concept of time as we understand it is quite simple to begin with. In a 2D Euclidean manifold, with two vectors, the square of the displacement of a body will be equal to the squares of the sum of the vectors. This is Pythagoras' theorom: x^2+y^2=h^2. This can be extended to incorporate a Z axis: x^2+y^2+z^2=h^2. Minkowski realized that if a 3D body displaced a 3D Euclidean manifold, than (and this fit perfectly into the contradiction Einstein found between Maxwell's equations and the Galilean Transformations), time could be included as being displaced as well, along a 4D manifold called Minkowski space. In this scenario, time simply becomes another unit of measurment, the same of length, width and breadth, which can be displaced. THe equation derived for this simply follows the same rule of transformation: x^2+y^2+z^2+(ict)^2=h^2. This works tidily since c is constant in all frames of reference, although it needs some righting since it is unhelpful to vector something to an imaginary number, i which is formally r(-1), and since squared, becomes: x&2+y^2+z^2-(ct)^2=h^2. In this scenario, time has no direction, although it still has causality (since it is a part of a topological structure instead of an abstraction), that causality, described by the causal manifold, an extensive topic in Relativity, can go, as the experiment demonstrated, both ways. Time is very much a structure of the universe as opposed to a flowing river of Aristotilean mechanics. It is necessary to take this into account.

The gist is that all the BB says is that the universe expanded from a symmetrical entropy-less state which may have been a false vacuum which inflated, via which the force disengagement could have been created and matter could form since it is no longer too excited below Planck temperature. This circumvents SLOT because the system in question could not have had entropy. .

Now I must go, I am pressed for time.

 

 

 

"Physical reality” isn’t some arbitrary demarcation. It is defined in terms of what we can systematically investigate, directly or not, by means of our senses. It is preposterous to assert that the process of systematic scientific reasoning arbitrarily excludes “non-physical explanations” because the very notion of “non-physical explanation” is contradictory.

-Me

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Wow.   Fly. Meet Bazooka. 

Wow. 

 

Fly. Meet Bazooka.

 


akolutheo
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Deludedgod:Wow. Thank you so

Deludedgod:

Wow. Thank you so much for this response. I admit, I will have to read it many times before I even begin to comprehend it! lol. I am not being sarcastic; I am dead serious. I really, really appreciate your help and I ask that you please be patient with me as I try to wrap my mind around your comments. Would you care to help me out a little more and, if possible, to put this in "laymen’s" terms for me?

Here are some questions I have for you.

You said:

You are trying to combine the modern notion of Big Bang with the Aristotilean notion of time as a flowing river and it won't work.

 

My questions / comments:

Okay. So, I am claiming that time exists now. This moment in time I am in now will cease and another will arrive. This is true and is true all over the planet. Yet, prior to the BB, this was not happening. Is this correct?

 

You said:

According to BB theory, nothing can be known about the pre-Planck Time existence, all we know is that the universe expanded outwards from some prior entropy-less state when presumably the symmetry in the four disngaged forces were unified.

My questions/comments:

Once again, your answer to why the universe has not entered into the state of unusable energy is that it use to exist in a far different state prior to the BB; yet, we can no nothing about this previous state, yet, we do know something, it did not exist as it does now and this explains why there is still useable energy. Did I interpret this correctly out of your comment?

You said:

Time is very much a structure of the universe as opposed to a flowing river of Aristotilean mechanics.

My questions / comments:

Once again, time, the cessation of one moment and the start of another, exists but DID NOT ALWAYS EXIST. There use to be a time before the BB when everything was different. We have no idea what it was like, yet, we know now that time is not the cessation of moments but is a structure of the universe like mathematical dimensions. Did I interpret this correctly out of your comment?

 

You said:

This circumvents SLOT because the system in question could not have had entropy.

My comments:

Okay please help me out here. It seems you are saying, the universe prior to the BB was totally different. You can’t figure out what it was like, none-the-less, it proves why we still have energy. Entropy is present now and used to not be prior to the BB. I don’t get this. The answer to why there is energy is the unknowable state of the universe prior to the BB?

It still seems logical to me that time DOES exist now and is experienced by our relative experience here on earth and by the relative experience of stars in space. If infinity is behind us, it seems to me energy should be in a unusable state. I am not convinced that the solution is, "The universe prior to the BB was totally different, you can’t know what it was like, but just accept it." It seems to me this is the gist of what you said, if I am wrong, please help me to understand.

One last question. If the universe began at the content, if you can call it that, of the BB, what was outside the content that experienced the BB?

 


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Yup, yeah to the DG, and the

Yup, yeah to the DG, and the BIG bang (transition), as if it is big !  That's some mighty  small thinking. Big my ass. The "see able, detectable" universe is but a clue of the "infinite eternal",  our intuition suspects ??? ...... Awesome aye ! ummm, how many multiple other, way out there bangs? What is big / small ? .... We are stuck in this bang .... Black Holes? Anti matter?  ..... did someone say gawed ! 

    "Fly. Meet Bazooka."     

  (me is a fly, yet I am god too)

 

 


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Quote:Okay. So, I am

Quote:

Okay. So, I am claiming that time exists now. This moment in time I am in now will cease and another will arrive. This is true and is true all over the planet. Yet, prior to the BB, this was not happening. Is this correct?

Only under Newtonian mechanics in which time is simply a variable in a differential equation: dv/dt or ds/dt or da/dt. When describing the physical universe, it is false. Under Relativitic Kinematics, it is not the case. If you were a light beam wearing a wristwatch, it would not tick. Because of this principle, where time simply becomes an extra dimension in a 4D set of axes, at some spatial point sufficiently far away enough, the events being described are with respect to what is occuring in the far future of the spatial and temporal points that it is being described with respect to us. This means the notion of "moment of time" is ficticious, because if we introduced the concept of a "moment in time" then we would find that a "moment in time" now would be 500 years in the future at a sufficiently far away body moving towards us at a sufficient speed. So, it cannot be the case that there are "moments of time". We might say that as conscious agents we percieve the structure of the relationship between objects in such a way as if time flowed like a river, but really, the notion you are describing came and went with Newton's differential equations with respect to rate of change of distance. There are multiple paradoxes this spawns. In Relativistic Kinematics, time and space can be described under the same manifold, and under the Planck constants, we can speak therefore of "smallest possible" units of time and space. This would not be possible under a differential equation in which we described time in terms of a sequence of "moments". Consider imputing that into Newton's differential quotient.

Suppose time did behave in this way, then we could do what Newton did (because he believed it did) and impute it into a quotient which derives the differential equation of a line for some function which describes it. Suppose we are measuring speed, then your displacement (s) is a function of the time passed (t):

f(t)=s

Put that into the quotient where h is a gap between two points in time:

ds/dt=f(t+h)-f(t)/h

As the limit h approaches zero, then we have a slight problem. All very well and good for mathematics, where the accuracy of differentiation allows us to perfectly calculate the gradient of a non-linear function with respect to the x-variable. Not so good for physics, where it spawns twenty-odd paradoxes. Like I said before, suggesting God as the solution happens to spawn an extra paradox which I already mentioned. The whole problem can be gotten rid of by abandoning the notion that time is a variable which can be differentiated with respect to some y-variable, implying that we can have a sum of a set of infinitesmal moments of time. The notion of time being a series of moments worked on paper, for Newton, 400 years ago, when differentiation was revolutionary. Not anymore.

If you read my previous post, you'll realize I've already demonstrated all of this mathematically and therefore I am repeating myself. Refer back to the Minkowski transforms.

Quote:

Once again, your answer to why the universe has not entered into the state of unusable energy

As I told you before, entropy has only been decreasing for a finite amout of time. Refer back to the previous post.

Quote:

Did I interpret this correctly out of your comment?

No. When I said "nothing can be known about the prior state" I meant not empirically. In terms of BB theory, we can say that the transition event was in terms of energy to matter and matter-antimatter annihlation. So I suppose we do know something about it. The reason thermodynamics does not apply is because there is no matter in this prior state. Please refer to the above post.

Quote:

Once again, time, the cessation of one moment and the start of another, exists but DID NOT ALWAYS EXIST.

No. Basic Relativity. See above. Time is not a squence of moments. There is no such thing as a moment. Stop talking about moments. It works only in the quotient differential equations for velocity and acceleration. If time were a sequence of moments, what I described above would not be possible. I invite you again to refer to the above post, where I demosntrated that time is indeed a topological structure of the universe, or part of one.

Quote:

You can’t figure out what it was like

No. We can infer the aforementioned points about the transition event. We cannot investigate the event empirically. There is no way to empirically investigate the point before the BB. But we can know things about it. THat is what I meant. Stop misinterpreting my comment. Focus on the points at hand. Time is not a series of moments. Time cannot possibly be a series of moments. We percieve time as a series of moments, but then again, we percieve a lot of things about the universe that our science has told us is false. Forget your perception of time. It has nothing to do with "time" in modern physics. That is what I am trying to describe to you. You will not be able to follow unless you ditch the notion that time can be described by the Newtonian quotient equation. It can't. If it could, what I described above would be impossible. Entropy is with respect to temperature and matter. As such it has been increasing for a finite amount of time. The matter-antimatter annihlation that resulted from the spawning of matter from energy during the transition event we call the Big Bang produced the matter in the universe today. The event described by the Big Bang indicates that there was only energy, from which matter spawns via the above equation. That is your answer. Focus on that. Now you are interested in a different topic: How the BB relates to space-time. This is a much more complex topic. Since I am writing in spare time, I cannot possibly introduce a whole subdiscipline of theoretical physics. Just don't fall into the trap of thinking the BB "created" the space-time manifold. THere are countless theories explaining the current space-time manifold. In fact, just forget the whole notion of "created". By absolutely all accounts of modern physics, "created" is an incoherent term. Physics is about describing transition events, and the Big Bang was a transition event.

Quote:

"The universe prior to the BB was totally different, you can’t know what it was like, but just accept it."

I did not say any of that. I explained precisely why the laws of thermodynamics implied that entropy has been increasing only since the transition event. All the Big Bang describes is a transition event in which the mass-energy equivalence produced matter-antimatter pairs from energy, which annihlated, leaving a small excess of matter and the energy of annihlation. That is the universe. Absolutely nowhere did I say "it's just different, just accept it". Entropy has been increasing after this event since entropy is always with respect to matter and temperature. Entropy is the only variant unit with respect to time, known to all of physics. Forget the single line I mentioned about "nothing can be known about this prior state" and focus on the answer: The Big Bang describes a transition event from a state of energy to one of matter. The interconversion of energy to matter produced annihlating pairs which left a small amount of matter and the energy from annihlation. At the point of transition, we can now speak of entropy since we can now speak in terms of probability states. That is not possible when there is no matter. Please read the above post again, carefully. I told you precisely why entropy increase has only been occuring since the Big Bang, because entropy is a description of matter, and there was no matter until 13.7 billion years ago. Entropy is not a function of energy by itself, because energy does not have temperature. As such, whatever state before the transition event occured would not have had entropy.

To put it simply, the whole notion of entropy and probability in statistical mechanics can only be understood in the context of this diagram:

When you study entropy for very long, you will get to know and love this diagram. Every single concept and equation in statistical mechanics refers to this diagram. That's what entropy is. It's a measure of probability states. Probability states are given in terms of possible arrangements. That in turn is a function of number of particles, by this equation:

 

S=klogW

Or rather:

e^S/k=W

 

 

"Physical reality” isn’t some arbitrary demarcation. It is defined in terms of what we can systematically investigate, directly or not, by means of our senses. It is preposterous to assert that the process of systematic scientific reasoning arbitrarily excludes “non-physical explanations” because the very notion of “non-physical explanation” is contradictory.

-Me

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deludedgod wrote:Entropy is

deludedgod wrote:
Entropy is not a function of energy by itself, because energy does not have temperature. As such, whatever state before the transition event occured would not have had entropy. How hard is this to grasp?

Dude, pass my crayons...

 

{Seriously, I get it.... barely...}

 

LC >;-}>

 

 

Christianity: A disgusting middle eastern blood cult, based in human sacrifice, with sacraments of cannibalism and vampirism, whose highest icon is of a near naked man hanging in torment from a device of torture.


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Maybe a metaphor will

Maybe a metaphor will help.

Think of time as an orange. The size of the orange is time, and the inside and surface of it is space. The big bang is essentially the moment when we could call the fruit an orange, with space and time expanding outward as it grows. Following along on this metaphor, we could ask "what happened before the big bang?" This would be equivalent to asking how big the orange was before it began to grow. There is no good answer for this; rather we ask things like "what processes produced the orange?"

Of course we turn or attention then to the plant. The plant in this case represents the underlying physical foundations that require the universe to arrive. This foundation requires that through any number of possible means our universe must come into being, just as the plant cannot help but produce oranges any more than we can halt our hair growth through sheer mental will.

 


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(lol) Is that fair ?

  (lol)  Is that fair ? (religion and god!!!)    


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Check out this Sean Carroll

Check out this Sean Carroll clip, it is pretty informative and deals partly with the idea of the universe being eternal.

Sean Carroll is a Senior Research Associate in Physics at the California Institute of Technology. He previously worked at MIT, UC Santa Barbara, and the University of Chicago. He studies topics in theoretical physics, focusing on cosmology, field theory, particle physics, and gravitation. He is currently studying the nature of dark matter and dark energy, connections between cosmology, quantum gravity, and statistical mechanics, and scenarios for the beginning of the universe. He is a contributor to the blog Cosmic Variance

“Fear is the path to the dark side. Fear leads to anger. Anger leads to hate. Hate leads to suffering.” Yoda


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Really, thanks HeyZeus for

Really, thanks HeyZeus for those links. That video is so in tune with what I've been trying to say and "feel" about the universe. I will be mailing that out.

   Some good articles too. The private "Media" and TV really angers me, as I often rant.

 Archives, 

http://cosmicvariance.com/archives/

 

  Media,

http://cosmicvariance.com/category/media/


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Glad you liked it man. I

Glad you liked it man. I just checked out the tremulous punditosphere...pretty good read. Its great when Scientists can comment coherently and insightfully on things that are not completely relegated to their own fields. I like to read Pharyngula as well, lots O'Science with dashes of liberal politics, and just the right amount of Atheistic ranting. Most things on scienceblogs are a good mix of science an opinionated semi-journalism.

“Fear is the path to the dark side. Fear leads to anger. Anger leads to hate. Hate leads to suffering.” Yoda


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Hey, cool .... and Pat

Hey, cool .... and Pat Condell in that site too, who finally has a DVD ....

http://scienceblogs.com/pharyngula/2008/04/solid_condell.php#comments


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Response to many

 Response to many people  

Deludedgod:

I am checking over your last post. I have a lot going on at work right now, but I am very interested in your comments and I really appreciate your help. Please be patient with me. You are obviously highly trained in this area and I am a novice with this topic; yet, it seems you are on here to help educate people or you would not have written such a comprehensive response. I hope you will stick around this post and guide me through this material. I will do my best to respond by this weekend.

 

Oh, and by the way, you claimed I was "misinterpreting you" and you asked me to stop. I am sorry if it came off that way; I was trying to clarify to see if you thought I understood what you said. Once again, I apologize for my ignorance in this area; I will probably misinterpret many things you say upon a first read. Feel free to correct me.

 

daedalu

Thanks for the introduction!

Louis_Cypher:

My favorite colors are yellow and blue J

Inspectormustard:

Thanks for the analogy! It really helped out a lot. Illustrations like that are great in helping me to understand this topic. Thanks for your authentic, polite response.

I am God as you.

I don’t mean to be rude, but many of your posts are a bit incoherent. You throw ellipses all over the place and sometimes your content barely follows a sentence structure or logical expression. Once again, I am not trying to be rude, I am just trying to understand the humor of your insults and it is difficult in such sloppy grammar. You apparently want to insult me, so I will just take it as an insult.

For instance:

The "see able, detectable" universe is but a clue of the "infinite eternal",  our intuition suspects ??? ...... Awesome aye ! ummm, how many multiple other, way out there bangs?

 

HeyZeusCreaseToe

Thanks for the video! I will check it out ASAP!   

 


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No insult to you ako at all.

No insult to you ako at all. I just don't like dogma in any form, even science.

And yeah, I AM a hard read for many .... but most often I don't know why. Maybe being god is part of it .     Also my writing is often more of what I'd call speech writing .... Friends read me and say what?, then I simply read it to them and they say, oh I understand perfectly now ... (whether they agree or not)  Language is often strange.  IE, I'd rather hear a poet than read them .....

  As for this,

The "see able, detectable" universe is but a clue of the "infinite eternal", our intuition suspects ??? ...... Awesome aye ! ummm, how many multiple other, way out there bangs?

  That's damn simple. I will re-write here in more common form,

  Intuition suspects this entire universe of ours is but one clue of a larger reality of many other Big Bangs, so far away that we have, as yet, been unable to detect them, and maybe never will.

  More simple yet; Why would this be the only universe? 

   Here again is that cool 12 min video .... in that direction of thought, 

http://thesciencenetwork.org/BeyondBelief2/watch/carroll.php

  P.S. I love you ! 

  

    

 


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In hindsight I realized that

In hindsight I realized that I explained all of that terribly. I am sorry, I was writing very quickly and under time pressure. Let me try to clarify. Tell me if I am clear:

The first concept we should understand is the fundamental theorom of calculus. Calculus is all about rates of change. In Newtonian mechanics, speed is defined as the distance displaced per time period. Acceleration is defined as the rate of change of distance per unit time period. Suppose we had a graph determining how your distance changed per unit time. On the x-axis, we would plot time, and on the y-axis, we would plot distance. Since speed is defined as the change in distance per unit time, it is determined by the gradient of the graph. The gradient is better characterized as the "steepness" of the graph. The steeper the graph, the greater the change in distance over a period of time, hence the greater the speed. If someone was moving at a constant speed, then the graph would give a straight diagonal line. The amount of distance displaced over one unit of time is constant throughout. Hence the gradient does not change. The change in distance per unit time is constant throught. This means that the gradient is constant, a single number. If the gradient is 6, it means that the person is moving 6 distance units per unit time (I am using arbitrary units for distance and time to demonstrate that the units don't matter. We could be talking in km, miles, meters, whatever). Graphs such as this are said to be linear functions because they are constant.

So we should characterize what a function is before continuing. A function takes an independant variable, inputs it into mathematical machinery, and delivers an output called the dependant. For a variable x, a function of x is given as f(x). If f(x)=5x, this means that the function of x takes whatever constant is assigned to it, multiplies it by five, and delivers the output. So, if f(x)=5x, then f(6)=30. Notice how, in this function, there is a linear relationship between x and y. y is always five times x. This is a linear function, as such it produces a linear graph like the one described above. In this case, x is time, and f(x), which is plotted on the y axis, is distance. This means that distance is a function of time. If you input a value of time into the function, then you get distance out. This is what the graph represents.

Things get more complicated when the change in distance per unit time is not constant. If the rate of change of distance over time is not constant, that means the speed of the person on the distance-time graph is changing. This cannot be handled by linear functions, because a linear function always delivers and independant variable which is always in a directly proportional relationship with x. This means that there is no change in in the gradient. But on a displacement-time graph, when speed is changing, it means the gradient is changing.

The problem can be considered like this. In these cases, we can use non-linear functions. Instead of saying there is a constant of proportionality between x and y, there is now a change

Let us take a classic non-linear function. Say that the function of x, f(x) (plotted on the y axis), is

f(x)=x^2 (x squared)

This is interesting. There is no longer a constant relationship between x and f(x). Try yourself. If x=2, then y=4. This means y/x=2. If x=6, y=36, meaning y/x=6. The relationship between x and y changes. This is why it is called a non-linear function. Non-linear functions are the basis of calculus.

Consider this function in a displacement time graph. This means that the for every unit time, the change in distance is the square of that unit of time. This is not a linear relationship because the gradient is changing. There is no constant linking y and x. If the function is linear, then the constant of proportionality is some constant. If f(x)=6x, then the constant is 6. f(x) is always six times x, and six is a constant. But in this function, we can see that what links x and y together is x, since x times x is y. So every time we divide y/x, we get x. But x is not a constant, it is a variable, so the function is not linear. This is a problem.

How are we supposed to calculate the speed from a displacement-time graph is the relationship between distance and time is not with respect to a constant but respect to the variable time, as in f(t)=t^2? A simple method we could use is to look at the whole graph, and find the average gradient. Take the distance at the very end of the graph, minus the distance at the very beginning (which will be zero). This gives the overall change in distance. Then divide that by the overall change in time. This gives the average gradient. The gradient is defined as the rate of change of y with respect to x. In linear functions, this is a constant, but in non-linear functions, it is defined in terms of the variable x, so it changes. Taking the average gradient is not accurate.

Consider linear functions again. If f(x)=6x, then the gradient is given in terms of of f(x)/x. This is 6. For a line which is represented by y=f(x), the gradient is a "function of a function". We take the function of x, put it into the "gradient function" and that tells us how f(x) changes with respect to x. With a linear function, this is just some number. For non-linear functions, the function of a function will be given in terms of x. So, for any x value we are given, we can take it, put it into our function of a function, and get the gradient out. This is the basis of differentiation.

Recall the example where we derived the average gradient. How did we do it? We took the change in distance, and divided it over the change in time. We defined this in terms of the change in x-value. In this case, the change in x-value happened to be the span of the whole graph. We'll call this change in x-value h. We'll call the x-value at the starting point, which happened to be the start of the graph, x. This means that the change in distance is given as

f(x+h)-f(x).

This means that the gradient is given is that difference divided by the difference in x value:

f(x+h)-f(x)/h

This is the same formula I provided above. I hope it makes sense now. This is called Newton's quotient. This quotient allows us to calculate the average gradient between any two points on the graph. The closer that the two points on the graph are, the more accurate the average between those two points will be. This means, as x gets smaller, the gradient for the line between the two points gets more accurate. If we were to draw two points, P and Q on the graph with a non-linear function, and we were to draw a straight line which connected them, this line would be called the secant line. The closer P and Q get, the closer the secant line gets to the tangent. The tangent is a straight line drawn at any point on a non-linear function which is directly perpindicular to the point and therefore gives the gradient. Since the straight line has a constant gradient, the gradient of a non-linear function at that point is given by the gradient of the tangent. As the difference in X value between two points, shrinks, then the secant tends towards the tangent. As h approaches zero, the gradient approaches the tangent of a given point. This is the concept of a limit. At this point, we are measuring a change in an infinitesmal difference of change of x and y values. This is symbolized like this:

dy/dx

Or, since we are talking about distance and time

ds/dt

This means:

ds/dt=(lim h>0) f(x+h)-f(x)/h

From this formula, it is possible to derive a formula which tells us how to differentiate any function with polynomials f(x)=x^2 is an example of a polynomial. Polynomials are very easy to differentiate, much easier than trigonometrical functions or logarithms. To know the derivation, it is necessary to go into binomial theorom, which I really can't otherwise this post will stretch on for hours. The important thing to take away is this:

For any function where f(x)=ax^n, then:

dy/dx= nax^(n-1)

Note that the little "hike" symbol means "to the power of".

This means that if (fx)=x^2 then dy/dx=2x. This means that the rate of change of y with respect to x is 2x. The gradient of any given point is the x-value of that point multiplied by two. On a graph of y=x^2, if we took x=4, this would mean that y=16, and dy/dx=8.

This is in essence what you meant when you talked about a "series of moments". In calculus, we divide some function into an infinitsemally small set of quantities and take the sum of these quantities. In the opposite process of differentiation, integration, we find the area under the curvev by dividing the area into a set of infinitesmally thin rectangular bars, which more accurately represent the area as the width of each bar approaches zero, and use the integration quotient to derive a formula similar to the one above (just in reverse, since integration is the opposite), which allows us to describe the area in terms of x for a function y=f(x).

With respect to time, this works very well when considering acceleration, velocity, and rate of acceleration in Newtonian mechanics. We send rockets to the moon with this mathematics. Unfortunately, it does not work when describing the nature of reality. In modern physics, we do not describe time in terms of a differential quotient. It is not a series of moments. It is time to consider Relativity.

Now we should consider Relativity.

The problem of Relativity springs forth from the well known Relativitiy of motion problem. It was first formalized by Newton with his bucket experiment. Consider this. Chances are you are sitting down at your computer reading this. You think you are not moving. You are at rest. But what does this mean? You are sitting on the chair. The chair is not moving. But the chair is on the Earth, which is moving around the sun at millions of miles per hour. What about the Sun? The sun is moving, like all stars it has a recessional velocity, since the universe is expanding. But to us, it certainly does not appear that the sun is moving. The sun is moving because the whole galaxy is moving, and the sun is part of the galaxy. We define motion as relative. You are at rest with respect to the Earth. The Sun is not moving with respect to the galaxy. If two trains are parallel and moving at exactly the same speed next to each other, they are not moving with respect  to each other. The last one might seem a little counterintuive. How could the trains be not moving? But why not? If you can stand on a large planetary object which moves at millions of miles an hour and claim "I am not moving", so too, two passangers on the adjacent trains staring directly at each other would conclude "he is not moving". And he isn't, from their perspective. This is the basis of the Galilean transforms, which, for 400 years before Einstein, described motion. If two cars are travelling adjacent, one at 40 miles per hour, the other at 50, then within the frame of reference of the slower car, as the faster one overtakes, the faster one is travelling at 10miles per hour within the moving frame of reference of the slower car.

This is well and good, but it fails completely. The problem comes when we consider light. According to the Maxwell equations, a photon is an electric field oscillating at 90 degrees to a magnetic field. Einstein asked what would happen if someone raced a light beam, travelling closer and closer to light speed (by the way, light speed is 3x10^8 meters per second). Well, according to Galilean transforms, the observer should see a light beam at rest, without oscillation. Maxwell's equations do not allow this. The oscillation of a magnetic field to an electric one cannot be "at rest". If somebody moves towards you at some velocity v, then according to the Galilean transforms, the light should arrive at a velocity of (v+c) where c is the speed of light in a vacuum (already given). This never happens. The speed of light is always c, in all frames of reference. This is the fundamental postulate of special Relativity. This is a problem. So, what would happen if the observer reached light speed? The asnwer is, he wouldn't. This is another fundamental postulate of special Relativity. Under the Galilean Transforms, we would say that the velocity of light within a moving frame of reference is merely the sum of the vectors. In Relativity, that is not possible. Instead, Einsten realized, of saying that velocity of light changes, another quantity changes at such a velocity.

Time.

Essentially, as you reach closer and closer to light speed, if you were wearing a watch, it would tick slower and slower. As I said above, if you were a light beam wearing this watch, it would not tick. This is called the time dilation effect. At first this may seem confusing to you. How is this possible? But again, why not? Time is just a unit in physics, there is no "constant" of time the same way there is a constant speed of light. Consider a thought experiment central to Relativity, the light clock. A light clock is a hypothetical device where a light beam is continually reflected between two mirrors which stand opposite each other. The amount of time it takes for the light to reflect from one mirror and reach the other is called a tick. It is a single tick of the light clock. Now, what if the light clock has two mirrors which are vertically in parallel (one on top of the other), with the light clock moving horizontally. Then, the distance travelled by the light in the clock will be given as a perpindicular vector. Let us say that the light clock has a height h. If the light clock was not moving, or rather, was in the stationary frame then the time between ticks is simply h/c. Now consider the clock moving along a horizontal distance. Since distance is simply velocity x time, the horizontal distance is given as vt'. then the distance travelled by the light is given as a pythagorean vector, like a right angled triangle. Hence

Sqrt [(vt')^2+(h^2)]/c

Sqrt is square root.

This can be rearranged to give:

t'=1/(r{1-(v^2/c^2)) x t

t is the time for a tick in the stationary frame. r is square root.

This formula gives time dilation. It will give the difference taken for a tick on a moving clock versus a stationary clock. The factor by which the stationary tick is multiplied above is called the Lorentz factor.

Einstein and Lorentz realized that if time changed, that means other quantities change with velocity as well, length contracts by the same proportion that time dilates. This is called the Lorentz contraction. A bullet fired near light speed would start to flatten into a disc, it would also gain mass, which is why it is impossible for any massive body to achieve light sped. This means that space and time are both relative to the observer. So, this prompts the question: What is the absolute referent in all frames of reference? This is where we really start to shred the notion of time the flowing river. Up until this point, we've been discussing Special Relativity. Now we can talk about General Relativity.

The first thing we should consider is what gravity is. Newton said that gravity is a force. As a force, Gravity was proportional to the inverse square of the distance between the two objects which exerted gravity on each other. This is given by the Newton Inverse Square law, which says:

F=Gm1m2/r^2

m1 and m2 are the mass of the objects. r is the distance between them. G is the Gravitational constant. F is the force exerted.

Under Newton's laws, the force required to accelerate an object by a certain amount is proportional to mass. THe more massive, the more force is needed to accelerate a body by the same amount. This is given like this:

F=Ma

In this case, therefore, m is the inertial mass. Inertia is a property which determines how the object responds to an equal amount of force. A ship has greater inertia than a baseball. More force is needed to accelerate a ship than is needed to accelerate a baseball by the same amount. This is given like this:

m=F/a

Gravitational mass is a property which determines how much force of gravitation a body feels with respect to another massive object. The less massive the object, the more force other objects exert on it. The Earth exerts a lot of force on me. I do not exert a lot of force on the Earth. As it turns out, inertia and gravitational mass are the same thing. This may be suprising, but consider that without air resistance, a feather and a bowling ball will fall towards the Earth at the same rate. We've known that since Galileo. This means, totally counterintuitively, that gravity is not a force. In fact, gravity is caused by the curvature of space-time by matter. Time and space themselves may be relative, but space-time is an absolute referent in Relativity. This is another fundamental postulate of General Relativity. Two observers will agree not only on the speed of light, but also the 4D coordinates of an event in terms of space and time, just not space and time seperately, since those are relative. But space-time is absolute. This is the fundamental postulate of General Relativity. This principle follows directly from special Relativity. The two are fundamentally linked. Consider a black hole. A black hole is a collapsed star so massively dense that the curvature of space time is so warped that it captures light, which is why it is black. At a particular distance from the center of the black hole is the point where light is captured. This is the point where the escape velocity (the velocity required to escape from the black hole) is equal to light speed. This radius around the black hole is where nothing can escape, even light, and is called the Schwarzchild radius. At a distance just outside the SR, photons are massively deflected around the black hole (in a manner similar to how the curvature allows planets to orbit stars). This causes a thin belt of light just outside the SR called the photon sphere. This is important because our discussion is about the nature of time. Now, what will happen when an observer crosses the event horizon. Let's forget about the fact that the poor observer will immediately be stripped into subatomic particles and just consider space and time. Since light is captured by a black hole, nothing can get out of a black hole, which is why in thermodynamics it is sometimes called an information sink because no information can leave a black hole. An observer watching an unfortunate crossing the event horizon (this is the SR) will see time slowing down for that object for this reason. They will never see the object cross the horizon, because of the information sink.

I do hope I've more or less shredded your previously conceived notions of time. But I suppose this is what physics does to intuition. We must accept that space-time is the arbiter of reality. This must be considered independantly of the concept of time as we percieve it as conscious beings, only as a topological structure of the universe which governs the causal-chronological structure. This is demonstrated by a thought experiment called a light cone. The time you are describing is not an innate structure of reality. It cannot be for the reasons just mentioned.

Finally we should consider thermodynamics:

The first thing we should consider is a fundamental question similar to Newton's question about gravity. Newton's question was why apples fell. We need a similar problem to kick off thermodynamics. The question at hand shall be this: Why do eggs break?

This seems like an odd question. If I push an egg off a table, it will break. Why will it break? We might say in terms of Newton's laws, because the egg was under the influence of gravity, so the Earth exerted a force on the egg, and the floor exerted an opposing force on the egg, etc. But this is not what we are looking for. We want to know why it breaks. It may be helpful to flip the question around. Well, if we leave it for long enough, why doesn't it unbreak? Why, when we burn paper, does it always produce ash and gas, but that the ash and gas never reconstitute paper? These questions cannot be answered by Newton's laws. They must be answered by turning to thermodynamics. To answer this necessitates that we abandon physics and look at some chemistry:

 

Let us imagine a box, a system closed off from the universe, with a cell inside it. The cell in a box is a closed system with a fixed amount of free energy. This system will have a total amount of Energy denoted E. Let us suppose the reaction A to B occurs in the box and releases a great deal of chemical bond energy as heat. This energy will increase the rate of molecular motions (transitional, vibrational and rotational) in the system. In other words it will raise the temperature.

However, the energy for these motions will soon transfer out of the system as the molecular motions heat up the wall of the box and then the outside world, which is denoted sea. Eventually, the cell in a box system returns to it’s initial temperature, and all the chemical bond energy released has been transferred to the surroundings. According to the first law of thermodynamics, the change in energy in the box (denoted ∆Ebox or just ∆E) must be equal and opposite to the amount of heat energy transferred out, denoted as h. Therefore ∆E=-h.

E in the box can also change during a reaction due to work done in the outside world. Suppose there is a small volume increase in the box (∆V) which must decrease the energy in the box (∆E) by the same amount. In most reactions, chemical bond energy is converted to work and heat. Enthalpy(H) is a composite function of work and heat, (H=mc∆T). Technically it is the Enthalpy change (∆H) is equal to the heat transferred to the outside world during a reaction, since Enthalpy is the composite function in question. In the equation above “c” simply refers to the specific Heat Capacity of the Material in question, such that the SHC is the amount of energy required to be inputted into the system to raise the temperature of one gram of the substance in question by one Kelvin (note that we can also measure this in terms of moles instead of mass, termed molar heat capacity). In the language of the First Law of Thermodynamics, we would express such like this:

Where Q=∆U-Wo, Q=mc∆t or (for molar heat capacity) Q=nc∆T

So, ∆H is a quantity expressing the SHC multiplied by the temperature change and by the mass of the substance in question. Since SHC is simply a measure of Energy change per Kelvin per Gram (or per mole), ∆H is simply a quantity expressing the change in energy of a system in question, where ∆H is roughly equivalent to the heat energy lost in a reaction.

Reactions with a +∆H are endothermic, and ones with -∆H are exothermic. Therefore –h=∆H. The volume change in reactions is so negligible that this is a good approximation.

-h≈∆H≈∆E

The Second Law of Thermodynamics allows us to predict the course of a reaction.

Let us consider 1000 coins in a box, all facing heads. It is a closed system, which, by definition, does not exchange energy input or output with the rest of the universe. States of high order have low probability. For instance, if we imagine a box with 1000 coins lying heads up, and we shake it twice, it is vastly more probable that we will end up with a chaotic arrangement of coins than the arrangement that we had previously. Thus, the law can be restated closed systems tend to progress from states of low probability to high probability. This movement towards high probability in a system where the energy is E, is progressive. In order for the entropy (the progression towards high probability) to be corrected, there must be periodic bursts of energy input, which would break the closed nature of the system. In this case, it would require someone to open the box and rearrange the coins. The second Law of thermodynamics is a probability function dictating that energy, regardless of how hard we try, always “spreads out” by which we mean that it becomes converted into less useful forms that are probabilistically very, very difficult to retrieve back into ordered states. This governs our lives. Eggs do not unbreak, glasses do not unshatter, entropy is highly directional, for it predicts, in any given system, there to be only one ordered state and a vast amount of disordered states, such that the probability of a disordered state is logarithmically greater than those of ordered states. Specifically, heat, being random hubbub of molecular motion, is the most singularly chaotic and disordered form of energy, and ultimately, therefore, almost impossible to retrieve into ordered states. There is a critical equation governing this to be described below.

 

We need a quantitative unit to measure entropy, and to measure the degree of disorder or probability for a given state (recall the coins in a box analogy). This function is entropy (denoted S) The change in entropy that occurs when the reaction A to B converts one mole A to one mole B is

∆S= R log PB/PA

PA and PB are probabilities of states A and B. R is the gas constant ∆S is measured in entropy units (eu). But that equation is normally used for chemical reactions which change the entropy of a system because they change the energy distribution, from highly ordered packets of free energy in reactive chemical bonds to vastly more disordered, improbable heat energy released. On Boltzmann’s tomb there is a famous epitpath:

S=klogW

This, as you can see, is my signature and tribute. That equation is simply a rewording of the one above, where the entropy of a system is the gas constant multiplied by the natural logarithm multiplied by W, the number of possible microstates in question.

Once we begin to consider the nature of ordered systems, the probabilities in question become mind boggling. Consider a book with 500 pages, if unbound, and tossed into the air, what is the entropy change associated? The 500 pages all in correct order represent a single ordered state. 1/W. The number of disordered states is vast, truly and utterly beyond comprehsion, for the number in question is (500!) or 500 factorial, which means 500 x 499 x 498 x 497....x 1, where n! is expressed as n x (n-1) x (n-2) x (n-3)...This number is 1.2 x 10^1134, or to make it more visually holding:

 

12201368259911100687012387854230000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

000000000

 

Entropy therefore is a measure of the probability associated with a system, and an increase in entropy in invariably a tend towards more probable states, by which we mean less ordered states. When we consider entropy in relation to Enthalpy, we realize that highly disorderd states are vastly more probable than highly ordered states, since there are simply so many more than there are ordered states. At any rate, when we consider that it is the nature of all things to head probabilistically towards the lowest energy state, one might ask why, in fact, all things do not immediately do so. Why does paper not spontaneously combust? Paper is an ordered state. Ash and gas, disorded and vastly more probable. The oxidized ash and the escaping carbon dioxide never reconstitute themselves into paper. Clearly, there is vast favorability associated with this combustion? So why do we not all spontaneously combust. The answer is activation energy, for a reaction to occur requires a certain energy level be reached that systems in their stable state normally do not attain unless prompted to do so, such as by being supplied by a fire, in this case. Activation energies are the principles upon which enzymes work. Most reactions in the body could only take place inside an oven without catalysis. Occurances into lower-probability states still need energy inputs into the system in order to coax the reaction to fall towards the lower probability state. In the case with a bound book, the book will not spontaneously disorder itself, but once given the necessary energy (unbind it and toss it into the air). For any reaction where the Free-energy change is positive, which thence cannot proceed with spontaneity, not only a vault over an energy barrier required, but also then, state B is less probable than state A, as opposed to a favourable reaction, where upon the completion of an energy barrier, the free energy drops such that the reaction proceeds spontaneously, hence, if I toss a book, unbound, into the air, I have provided the activation energy, and the rest proceeds spontaneously. If I drop an egg off a table, I have provided that activation energy such that the reaction may proceed spontaneously, but I cannot do the same for attempting to reconstruct the shattered egg, for such is expressly forbidden by the laws of probability.

In an example with a box containing one thousand coins all facing heads, the initials state (all coins facing heads) probability is 1. The state probability after the box is shaken vigorously is about 10^298. Therefore, the entropy change when the box is shaken is R log 10^298 is about 1370eu per mole of each container (6.02x10^23 containers). ∆S is positive in this example. It is reactions with a large positive ∆S which are favorable and occur spontaneously. We say these reactions increase the entropy in the universe.

Heat energy causes random molecular commotion, the transfer of heat from the cell in a box to the outside increases the number of arrangements the molecules could have, therefore increasing the entropy (analogous to the 1000 coins a box).The release of X amount of heat energy has a greater disordering effect at low temp. than at high temp. therefore the value of ∆S for the surroundings of the cell in a box denoted ∆Ssea is equal to the amount of heat transferred divided by absolute temperature or

∆Ssea =h/T

So, now we know what entropy is. Now we understand why entropy is a function of temperature and of number of particles, hence probability states. Hopefully, now this graph should make sense to you:

All this means is that the probability distribution for a set of particles in a system is given as that most particles do not have enough energy to complete a chemical reaction. This graph, called the Maxwell-Boltzmann Distribution, is central to chemistry and statistical mechanics. The number of particles that have a certain range of energies is given by integrating the area between the two values we want to measure. That's it. This is thermodynamics in a nutshell. I hope with all of this, that the above post now makes sense. If you need more, please ask.

Phew.

 

 

"Physical reality” isn’t some arbitrary demarcation. It is defined in terms of what we can systematically investigate, directly or not, by means of our senses. It is preposterous to assert that the process of systematic scientific reasoning arbitrarily excludes “non-physical explanations” because the very notion of “non-physical explanation” is contradictory.

-Me

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akolutheo
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I am God as you:Wow, that

I am God as you:

Wow, that did make more sense. Thanks man. If there are other universes, could not God be in one of the other ones? BUT lets chase that rabbit another time, I am really interested in the second law of thermodynamics.

 


akolutheo
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Deludedgod:Thanks! I will

Deludedgod:


Thanks! I will read this as soon as possible. It will probably be this weekend sometime. I want to give it may full attention. Thanks again for your help. I look forward to talking about this stuff again after I have read this. Wish me luck in trying to even comprehend half of it! ha ha ha.


Brian37
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The problem with laymen and

The problem with laymen and theists, especially laymen theists, is that they do not understand the difference when they use a word vs the different meaning in science language.

"Law" in laymen's terms is a concept whereby a agent (person, or group) make a law.

In science, "Law" does not mean the same thing. In science, "Law" means that the scientist, in using method, must follow the "law" formula, in order to maintain the quality control of the data, in order to properly describe an event.

"eternal" is also another bastardized term that theists jump on and say "AH HA" therefor magic!"

The sideways figure 8 is the scientific definition of infinity. But it is NOT the same thing the theist thinks of and in no way implies a greater power nor is the use of it intended to favor theism over atheism. It is simply a scientific definition.

Where people go wrong is when they equate social language to be equal to the language in science. Scientific method is not a social agenda. It is merely a tool used to make observations about events. As such the language of science should not be treated as being the same as social language.

It would be like equating "love" in tennis, to "love" in a relationship.

"We are a nation of Christians and Muslims, Jews and Hindus -- and nonbelievers."Obama
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ctressle
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What is your educational

What is your educational level, akolutheo? I ask b/c I was trying to correct some very simple mistakes in deludedgod's latest post, but I wasn't for sure if they were mistakes you could get by on and understood what he meant or if my corrections might insult your intelligence.

You've most likely taken algebra, geometry and trig and perhaps pre-cal; taken calculus?


akolutheo
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BA in History Education

I have a BA in History Education. You will not instult at all by making the math more simple. Trust me I need it!  I made it up to pre-cal in highschool; but I don't remember any of it. Your clarification would be great.

 

 

Deludedgod, I am sorry I didn't get a chance to respond this weekend. I teach and we are pretty busy here at the end of the year. I should get some time soon to respond. I will respond ASAP.


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Ok here are corrections

 

Ok here are corrections and deeper explanations hopefully this will help. deludedgod’s post has some mistakes and much backtracking, though it is much shorter you may have to take a lot of time to stop and think about what he is saying. On the other hand, mine is much longer going into details but you won’t have as much trouble either. Take your pick. There were other mistakes I did not care to bother correcting, in that what was said was just to illustrate some other point and so their accuracy made no difference in understanding his essay.

By the way, this part does not address his section on thermodynamics. I am less familiar with it though his explanation looks simple I will spend some time on it too. Since all the quoted words are italicized, I will embolden words and special symbols of deludedgods’ post that were already italicized, and I will also take the liberty to underline once-italicized words or other words I pick out for special emphasis.

deludedgod wrote:

In hindsight I realized that I explained all of that terribly. I am sorry, I was writing very quickly and under time pressure. Let me try to clarify. Tell me if I am clear:

The first concept we should understand is the fundamental theorom of calculus. Calculus is all about rates of change. In Newtonian mechanics, speed is defined as the distance displaced per time period. Acceleration is defined as the rate of change of distance per unit time period. Suppose we had a graph determining how your distance changed per unit time. On the x-axis, we would plot time, and on the y-axis, we would plot distance. Since speed is defined as the change in distance per unit time, it is determined by the gradient of the graph. The gradient is better characterized as the "steepness" of the graph. The steeper the graph, the greater the change in distance over a period of time, hence the greater the speed. If someone was moving at a constant speed, then the graph would give a straight diagonal line. The amount of distance displaced over one unit of time is constant throughout. Hence the gradient does not change. The change in distance per unit time is constant throught. This means that the gradient is constant, a single number. If the gradient is 6, it means that the person is moving 6 distance units per unit time (I am using arbitrary units for distance and time to demonstrate that the units don't matter. We could be talking in km, miles, meters, whatever). Graphs such as this are said to be linear functions because they are constant.

So we should characterize what a function is before continuing. A function takes an independant variable, inputs it into mathematical machinery, and delivers an output called the dependant. For a variable x, a function of x is given as f(x). If f(x)=5x, this means that the function of x takes whatever constant is assigned to it, multiplies it by five, and delivers the output. So, if f(x)=5x, then f(6)=30.

Just to clarify, the given variable x is right now the independent, and usually y = f(x) is the dependent. And the mentioned "whatever constant" is assigned to x (not the function), and is multiplied by five (this is the function).

 

deludedgod wrote:

Notice how, in this function, there is a linear relationship between x and y. y is always five times x.

Anyways, the point being is that y is now deemed the dependent variable, which should have been mentioned as soon as x was, so now y = f(x).

deludedgod wrote:

This is a linear function, as such it produces a linear graph like the one described above. In this case, x is time, and f(x), which is plotted on the y axis, is distance. This means that distance is a function of time. If you input a value of time into the function, then you get distance out. This is what the graph represents.

Things get more complicated when the change in distance per unit time is not constant. If the rate of change of distance over time is not constant, that means the speed of the person on the distance-time graph is changing. This cannot be handled by linear functions, because a linear function always delivers and independant variable which is always in a directly proportional relationship with x.

Linear functions deliver dependents, in said relationship with the independent (in this case, y and x, respectively).

When deludedgod mentioned ‘graph’ above with say y = 5x, you should picture something approximate to the following (ignore the red, horizontal line for the moment):

 

Points anywhere on a graph are labeled (x, y), and points on a function that is graphed, with y = f(x) specified, are labeled (x, f(x)). The independent variable x is horizontal and the dependent y is vertical. His numbers, f(6) = 5*6 = 30, are not shown. However, the point (1, 5) = (1, f(1)) is where the red line goes through the purple line.

deludedgod wrote:

This means that there is no change in in the gradient. But on a displacement-time graph, when speed is changing, it means the gradient is changing.

The problem can be considered like this. In these cases, we can use non-linear functions. Instead of saying there is a constant of proportionality between x and y, there is now a change

Let us take a classic non-linear function. Say that the function of x, f(x) (plotted on the y axis), is

f(x)=x^2 (x squared)

Note that the little "hike" symbol means "to the power of". x*x*x*…*x = x^n, if there are ‘n  x’s being multiplied. This was later typed in deludedgod’s post, just thought it made more sense when the symbol first appeared.

deludedgod wrote:

This is interesting. There is no longer a constant relationship between x and f(x). Try yourself. If x=2, then y=4. This means y/x=2. If x=6, y=36, meaning y/x=6. The relationship between x and y changes. This is why it is called a non-linear function. Non-linear functions are the basis of calculus.

Consider this function in a displacement time graph. This means that the for every unit time, the change in distance is the square of that unit of time. This is not a linear relationship because the gradient is changing. There is no constant linking y and x. If the function is linear, then the constant of proportionality is some constant. If f(x)=6x, then the constant is 6. f(x) is always six times x, and six is a constant. But in this function, we can see that what links x and y together is x, since x times x is y. So every time we divide y/x, we get x. But x is not a constant, it is a variable, so the function is not linear. This is a problem.

How are we supposed to calculate the speed from a displacement-time graph if the relationship between distance and time is not with respect to a constant but respect to the variable time, as in f(t)=t^2? A simple method we could use is to look at the whole graph, and find the average gradient. Take the distance at the very end of the graph, minus the distance at the very beginning (which will be zero). This gives the overall change in distance. Then divide that by the overall change in time. This gives the average gradient. The gradient is defined as the rate of change of y with respect to x. In linear functions, this is a constant, but in non-linear functions, it is defined in terms of the variable x, so it changes. Taking the average gradient is not accurate.

Again this is probably easily understood but to clarify: one can, on the outset, choose whatever letters one wishes for the dependent and independent variables, as long as one sticks with them. If we choose y = f(t) = t^2, then the gradient is the rate of change of y with respect to t. Similarly so if x replaces t, all throughout (obviously stick with x for now until otherwise specified).

deludedgod wrote:

Consider linear functions again. If f(x)=6x, then the gradient is given in terms of of f(x)/x. This is 6. For a line which is represented by y=f(x), the gradient is a "function of a function". We take the function of x,  f(x), put it into the "gradient function" and that tells us how f(x) changes with respect to x. With a linear function, this is just some number. For non-linear functions, the function of a function will be given in terms of x. So, for any x value we are given, we can take it, put it into our function of a function, and get the gradient out. This is the basis of differentiation.

Recall the example where we derived the average gradient. How did we do it? We took the change in distance, and divided it over the change in time. We defined this in terms of the change in x-value.

Yes, if x is currently representing our independent variable, time. deludedgod used t for time for the independent before defining gradient way above. Again, doesn’t matter as long as one is consistent, so we’re still sticking with x in general explanation for now.

deludedgod wrote:

In this case, the change in x-value happened to be the span of the whole graph. We'll call this change in x-value h. We'll call the x-value at the starting point, which happened to be the start of the graph, x. This means that the change in distance is given as

f(x+h)-f(x).

This means that the gradient is given is that difference divided by the difference in x value:

f(x+h)-f(x)/h

Likely obvious but:    (f(x+h) – f(x))/h

deludedgod wrote:

This is the same formula I provided above. I hope it makes sense now. This is called Newton's quotient. This quotient allows us to calculate the average gradient between any two points on the graph. The closer that the two points on the graph are, the more accurate the average between those two points will be. This means, as x gets smaller, the gradient for the line between the two points gets more accurate.

It’s h that we’re concerned with getting smaller, x can be anything and thus the gradient can be anywhere along the graph at x and x+h.

And, more accurate to what? This is the ‘secant/tangent’ stuff, below.

deludedgod wrote:

If we were to draw two points, P and Q on the graph with a non-linear function, and we were to draw a straight line which connected them, this line would be called the secant line. The closer P and Q get, the closer the secant line gets to the tangent. The tangent is a straight line drawn at any point on a non-linear function which is directly perpindicular to the point and therefore gives the gradient.

No, not perpendicular, and not to a point. ‘Tangent’ is either the said line itself (a noun), or describes the straight line to the curve (adjective). A straight line that touches a curve at one point and does not go through the curve (see example below) is called tangent to the curve, or the straight line itself is called a tangent or tangent line.

To relate what might be seemingly different ideas in his essay thus far:

Now, when he mentioned P and Q, what he was referring to was this:

 

Ignore where it says "slope = ..." (not accurate anyways).

 


P = (x, f(x))    and      Q = (x+h, f(x+h))

Deludedgod brought in P and Q without mentioning their relevance, here now is that relevance right above. The line going through P and Q is the secant, and the line going through only P in the dark image is the tangent. Here is another example of tangent:

deludedgod wrote:

Since the straight line has a constant gradient, the gradient of a non-linear function at that point is given by the gradient of the tangent. As the difference in x value[s] between two points, shrinks, then the secant tends towards the tangent. As h approaches zero, the gradient approaches the tangent of a given point. This is the concept of a limit. At this point, we are measuring a change in an infinitesmal difference of change of x and y values. This is symbolized like this:

dy/dx

Or, since we are talking about distance and time

ds/dt

deludedgod never mentioned s before, but essentially what he has now done was to replace the dependent y with the dependent s, and the independent x with the ind. t. So now, s is for distance and t for time. Probably obvious and understood but just to make sure.

deludedgod wrote:

This means:

ds/dt=(lim h>0) f(x+h)-f(x)/h

ds/dt = (lim h>0) (f(s+h) – f(s))/h

h>0” just means that h is shrinking toward 0, and ‘lim’ means the end of this process.

deludedgod wrote:

From this formula, it is possible to derive a formula which tells us how to differentiate any function with polynomials. f(x)=x^2 is an example of a polynomial. Polynomials are very easy to differentiate, much easier than trigonometric functions or logarithms. To know the derivation, it is necessary to go into binomial theorom, which I really can't otherwise this post will stretch on for hours. The important thing to take away is this:

For any function where f(x) = ax^n, then:

dy/dx= nax^(n-1)

Note that the little "hike" symbol means "to the power of".

This means that if f(x)=x^2 then dy/dx=2x. This means that the rate of change of y with respect to x is 2x. The gradient of any given point is the x-value of that point multiplied by two. On a graph of y=x^2, if we took x=4, this would mean that y=16, and dy/dx=8.

This is in essence what you meant when you talked about a "series of moments". In calculus, we divide some function into an infinitsemally small set of quantities and take the sum of these quantities. In the opposite process of differentiation, [which is] integration, we find the area under the curve by dividing the area into a set of infinitesmally thin rectangular bars, which more accurately represent the area as the width of each bar approaches zero, and use the integration quotient to derive a formula similar to the one above (just in reverse, since integration is the opposite), which allows us to describe the area in terms of x for a function y=f(x).

With respect to time, this works very well when considering acceleration, velocity, and rate of acceleration in Newtonian mechanics. We send rockets to the moon with this mathematics. Unfortunately, it does not work when describing the nature of reality. In modern physics, we do not describe time in terms of a differential quotient. It is not a series of moments. It is time to consider Relativity.

Now we should consider Relativity.

The problem of Relativity springs forth from the well known Relativitiy of motion problem. It was first formalized by Newton with his bucket experiment.

deludedgod didn’t elaborate on the bucket experiment, but with everything that’s been said don’t worry about the specifics.

Summary thus far: with the above mathematics, in conjunction with using time as the independent variable, we were able to express the laws of physics as discovered by Newton. Now we can no longer use time as the independent variable, here’s why:

 

deludedgod wrote:

Consider this. Chances are you are sitting down at your computer reading this. You think you are not moving. You are at rest. But what does this mean? You are sitting on the chair. The chair is not moving. But the chair is on the Earth, which is moving around the sun at millions of miles per hour. What about the Sun? The sun is moving, like all stars it has a recessional velocity, since the universe is expanding. But to us, it certainly does not appear that the sun is moving. The sun is moving because the whole galaxy is moving, and the sun is part of the galaxy. We define motion as relative. You are at rest with respect to the Earth. The Sun is not moving with respect to the galaxy. If two trains are parallel and moving at exactly the same speed next to each other, they are not moving with respect to each other. The last one might seem a little counterintuive. How could the trains be not moving? But why not? If you can stand on a large planetary object which moves at millions of miles an hour and claim "I am not moving", so too, two passangers on the adjacent trains staring directly at each other would conclude "he is not moving". And he isn't, from their perspective. This is the basis of the Galilean transforms, which, for 400 years before Einstein, described motion. If two cars are travelling adjacent, one at 40 miles per hour, the other at 50, then within the frame of reference of the slower car, as the faster one overtakes, the faster one is travelling at 10miles per hour within the moving frame of reference of the slower car.

“within the [moving] frame of reference of slower car” essentially means “with respect to the slower car”.

 

deludedgod wrote:

This is well and good, but it fails completely. The problem comes when we consider light. According to the Maxwell equations, a photon is an electric field oscillating at 90 degrees to a magnetic field. Einstein asked what would happen if someone raced a light beam, travelling closer and closer to light speed (by the way, light speed is 3*10^8 meters per second). Well, according to Galilean transforms, the observer should see a light beam at rest, without oscillation. Maxwell's equations do not allow this. The oscillation of a magnetic field to an electric one cannot be "at rest". If somebody moves towards you at some velocity v, then according to the Galilean transforms, the light should arrive at a velocity of (v+c) where c is the speed of light in a vacuum (already given). This never happens. The speed of light is always c, in all frames of reference. This is the fundamental postulate of special Relativity. This is a problem. So, what would happen if the observer reached light speed? The asnwer is, he wouldn't. This is another fundamental postulate of special Relativity. Under the Galilean Transforms, we would say that the velocity of light within a moving frame of reference is merely the sum of the vectors. In Relativity, that is not possible. Instead, Einsten realized, of saying that velocity of light changes, another quantity changes at such a velocity.

Time.

Essentially, as you reach closer and closer to light speed, if you were wearing a watch, it would tick slower and slower. 

The slowing of ticks only appears to someone else (if they’re able to even see it) who is moving at a different velocity. You would not see any difference if you’re traveling with the time-keeping technology (of any kind be it watch clock… ). And expressions such as “at rest” and “stationary frame” are euphemisms for the person measuring other objects that happen to be moving. With deludedgod’s explanation above, you will probably figure that one man’s rest is another man’s movement, and vice versa, always. Unless they’re moving at the same speed with each other, of course.

deludedgod wrote:

As I said above, if you were a light beam wearing this watch, it would not tick. This is called the time dilation effect. At first this may seem confusing to you. How is this possible? But again, why not? Time is just a unit in physics, there is no "constant" of time the same way there is a constant speed of light. Consider a thought experiment central to Relativity, the light clock. A light clock is a hypothetical device where a light beam is continually reflected between two mirrors which stand opposite each other. The amount of time it takes for the light to reflect from one mirror and reach the other is called a tick. It is a single tick of the light clock. Now, what if the light clock has two mirrors which are vertically in parallel (one on top of the other), with the light clock moving horizontally. Then, the distance travelled by the light in the clock will be given as a perpindicular vector. Let us say that the light clock has a height h. If the light clock was not moving, or rather, was in the stationary frame then the time between ticks is simply h/c. Now consider the clock moving along a horizontal distance. Since distance is simply velocity multiplied by time, the horizontal distance is given as vt'. then the distance travelled by the light is given as a pythagorean vector, like a right angled triangle. Hence

Sqrt [(vt')^2+(h^2)]/c

Sqrt is square root.

This can be rearranged to give:

t'=1/(Sqrt{1-(v^2/c^2)}) x t

t is the time for a tick in the stationary frame.

Here is a picture for the last section:


The two horizontal blue bars are the mirrors, and the two mirrors are moving at speed v. Never mind the large vertical bar, except that it’s height, the distance between the two mirrors, is h. Obviously for the light to hit the moving mirrors, it would have to be angled just the right way so that as the light moves from mirror to mirror and as the two mirrors move horizontally, the light still bounces back between them.

Remember one of the postulates of relativity? It’s that you measure the speed of light as the same, no matter if you’re moving with the mirrors or if you’re “at rest”. This is supposed to imply two different measurements of time, which is why deludedgod has both a t and a t’ (read “t prime” ). t is the duration of time from someone who is “at rest”, and t’ is the duration of time of someone moving with the mirrors. Accordingly, they’re allegedly not the same. Let’s see why:

If you’re measuring the duration of time t of how long the moving mirror has been moving, then the distance it has traveled is vt, and the distance that light travels is ct, from your rest perspective. In this perspective, light moves at an angle from mirror to mirror, just like I described two paragraphs above.

If instead you’re moving with the mirrors,

then the duration is t’, the speed is v’ but that is 0 since the mirror is at rest with respect to you, so now the distance the mirror is moving away from you is also v’t’ = 0. But light still moves at the same speed, c, so now the distance the light travels on its way to a mirror is now ct’. But from your new perspective, the light moves back and forth straight from one mirror to the other, not at an angle. Remember, if you’re moving with the mirror, then it’s as if you and the mirror are at rest. So, that distance light moves from one mirror to the other is nothing more than the height, ct’ = h!

Remember the Pythagorean theorem? c^2 = a^2 + b^2, here ‘c’ is the length of the side away from the angle that is the right angle, where the right angles are always drawn with a square (see below). Not to be confused with the speed of light c.


Above in the moving – mirror illustration, try to imagine two right triangles “back to back” touching, similar to the following


where ‘a’ = h, ‘b’ = vt, and ‘c’ is the distance traveled by the light from one mirror to the other. That distance is now thus

‘c’ = Sqrt(a^2 + b^2) or now Sqrt(h^2 + (vt)^2), which is similar to deludedgod’s expression above. He got the t’s mixed up, which is why you don’t see a prime ‘ in my expression. And we’re measuring distance, so we’re not yet dividing by c to get time. The distance traveled by light is ‘c’ = ct, ‘c’ is the length of the line away from the right angle and c is the speed of light. So,

(vt)^2 + h^2 = (ct)^2





c2t2 - v2t2 = h2

(c2 - v2)t2 = h2

(1 - v2/c2)t2 = h2/c2 = t'2

t*[Sqrt(1 - v2/c2)] = t'

The last expression is also similar to deludedgod’s last expression, but again I have the t’s different from his. Remember that h = ct’ which is the distance the light travels if you’re moving with the mirrors, and ct is the distance if you’re at rest seeing the mirrors move.

So now you see why time can be different to two different people. First, note that t’ is smaller than t,   t’ < t. So, if you move, you age less than others. So, why don’t we ever “feel” or observe these effects?

It’s because v in everyday life is very small compared to c. If v << c (read, v is much less than c), then v/c ≈ 0, also note v/c < 1. In other words, ≈ is “approximately equal to”. When squaring numbers smaller than 1, you get an even smaller number i.e. 0.52 = 0.25. Then, 1 – (v/c)^2 ≈ 1, so that tt’. This approximation is so close for everyday small speeds that we can’t observe this difference unless we have high tech equipment.

deludedgod wrote:

This formula gives time dilation. It will give the difference taken for a tick on a moving clock versus a stationary clock. The factor by which the stationary tick is multiplied above is called the Lorentz factor.

Einstein and Lorentz realized that if time changed, that means other quantities change with velocity as well, length contracts by the same proportion that time dilates. This is called the Lorentz contraction. A bullet fired near light speed would start to flatten into a disc, it would also gain mass, which is why it is impossible for any massive body to achieve light speed. This means that space and time are both relative to the observer. So, this prompts the question: What is the absolute referent in all frames of reference? This is where we really start to shred the notion of time the flowing river. Up until this point, we've been discussing Special Relativity. Now we can talk about General Relativity.

Lorentz contraction occurs only in the direction of motion and only to the object’s length moving in that direction, not to its position. For the mirror illustration above, we were not concerned with the length of the mirrors, only the distance they traveled. Thus, it did not factor into the math.

When the bullet flattens into a disk, remember only the length in the direction of motion is affected. Thus, all other dimensions of the bullet stay the same.

Summary thus far: with calculus (mathematics before first summary) in conjunction with using time as the independent variable for everything, we were able to express the laws of physics as discovered by Newton (which is approximately good why? Because v<<c). Now we can no longer use time as some universal independent variable, and the above is why:

There is no “universal time” i.e. there is no “flow”.

deludedgod wrote:

The first thing we should consider is what gravity is. Newton said that gravity is a force. As a force, Gravity was proportional to the inverse square of the distance between the two objects which exerted gravity on each other. This is given by the Newton Inverse Square law, which says:

F=Gm1m2/r^2

m1 and m2 are the mass of the objects. r is the distance between them. G is the Gravitational constant. F is the force exerted.

Under Newton's laws, the force required to accelerate an object by a certain amount is proportional to mass. THe more massive, the more force is needed to accelerate a body by the same amount. This is given like this:

F=Ma

In this case, therefore, m is the inertial mass. Inertia is a property which determines how the object responds to an equal amount of force. A ship has greater inertia than a baseball. More force is needed to accelerate a ship than is needed to accelerate a baseball by the same amount. This is given like this:

m=F/a

Gravitational mass is a property which determines how much force of gravitation a body feels with respect to another massive object. The less massive the object, the more force other objects exert on it. The Earth exerts a lot of force on me. I do not exert a lot of force on the Earth. As it turns out, inertia and gravitational mass are the same thing. This may be suprising, but consider that without air resistance, a feather and a bowling ball will fall towards the Earth at the same rate. We've known that since Galileo. This means, totally counterintuitively, that gravity is not a force. In fact, gravity is caused by the curvature of space-time by matter. Time and space themselves may be relative, but space-time is an absolute referent in Relativity. This is another fundamental postulate of General Relativity. Two observers will agree not only on the speed of light, but also the 4D coordinates of an event in terms of space and time, just not space and time seperately, since those are relative. But space-time is absolute. This is the fundamental postulate of General Relativity. This principle follows directly from special Relativity. The two are fundamentally linked. Consider a black hole. A black hole is a collapsed star so massively dense that the curvature of space time is so warped that it captures light, which is why it is black. At a particular distance from the center of the black hole is the point where light is captured. This is the point where the escape velocity (the velocity required to escape from the black hole) is equal to light speed. This radius around the black hole is where nothing can escape, even light, and is called the Schwarzchild radius (SR). At a distance just outside the SR, photons are massively deflected around the black hole (in a manner similar to how the curvature allows planets to orbit stars). This causes a thin belt of light just outside the SR called the photon sphere. This is important because our discussion is about the nature of time. Now, what will happen when an observer crosses the event horizon. Let's forget about the fact that the poor observer will immediately be stripped into subatomic particles and just consider space and time. Since light is captured by a black hole, nothing can get out of a black hole, which is why in thermodynamics it is sometimes called an information sink because no information can leave a black hole. An observer watching an unfortunate crossing the event horizon (this is the SR) will see time slowing down for that object for this reason. They will never see the object cross the horizon, because of the information sink.

This is not too precise, but: What is meant by information, or rather sending info, is anything that can move. Light sends information, and is actually the fastest form of sending information. If the escape velocity from the gravity of an object is c, then nothing can escape from the gravity of said object. Thus, information can’t be sent from said object, which is why the black hole is called the information sink.

If you want something more precise about this and this link with thermodynamics I honestly don’t have it unless I did some research, deludedgod would probably know and even be willing to help. I say if because it’s just more to talk about to extend this already-long thread, maybe best in another thread though that’s not my call.

deludedgod wrote:

I do hope I've more or less shredded your previously conceived notions of time. But I suppose this is what physics does to intuition. We must accept that space-time is the arbiter of reality. This must be considered independantly of the concept of time as we percieve it as conscious beings, only as a topological structure of the universe which governs the causal-chronological structureThis is demonstrated by a thought experiment called a light cone. The time you are describing is not an innate structure of reality. It cannot be for the reasons just mentioned.

He brings things up but sometimes doesn’t elaborate (maybe he expected you to do research for light cone and I’m spoiling your fun? Go ahead and give it a shot  ). What is meant by light cone and topology and causation is this: the “shape” of all movement, and thus every interaction in the universe, is restricted to speeds less than light. If you want to cause something to happen, the speed with which you can do so is less than light. But not only that, but imagine turning on a light bulb right when and where you start to initiate such a causal event. When the bulb is first turned on, there is a spherical surface of light that grows out at the speed of light in all directions. So we have a “space-time limitation” on causation: from the moment you attempt to cause something, you can only do so within this “sphere” and no faster than the light going out from the moment you make that attempt. Just like a cone is like a circle growing bigger in a direction from a point, so too is the light cone not a circle but sphere growing bigger in “a direction” from a point, and that “direction” is time.

Now if anyone would like to correct my corrections lol…

If/when I have the time I will attempt to do more later.