BiotechFusion
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Posts posted by BiotechFusion
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You have picked a unit for time, and this worries me with your argument. Really you now need to show me something mathematical.
If you want to use your own time to look at the numerous papers published, I'm not stopping you.
In fact, here, I'll even give you a head start
http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20110015936.pdf
http://www.sfu.ca/~adebened/funstuff/warpdrive.html
I also didn't "pick" a unit for time but instead generalized it to any unit, I said explicitly "mathematically, it doesn't matter how long a light-second is...as long as a photon travels one of them in a second" which is true to the extent that maxwell's equations can still be upheld. We still have a standard speed of light from which the metric deviates from in different transformations of the coordinate system. You should also note that just negative energy (which is what I was talking about) on its own will not propel an object to past the speed of light.
As long as the speed of a photon remains invariant, special relativity isn't violated.
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It is expected. We all know this... so why the attitude?
I don't think you expect it because you keep using some assumption in a physical model as a basis for a mathematical proof of some kind, not very logical.
And taking limits I would understand as part of mathematics. So?
And in that mathematics, a limit is explicitly the object or value which is apparently approached, not the value itself at the coordinate you are approaching which is why it works.
Please can you indicate where I have claimed that an infinite 'value' of anything has been measured.
I asked you multiple times if there aren't in fact infinite field tensors within any finite space, like those in the *finite* space of a gluon field, but you keep saying those objects are in fact infinite, it's your mess to clean up.
I keep on saying quite the opposite. We have never measured an infinite 'value' and we never expect to be able to do so. Do I have to keep saying this?
If that was true our discussion would have been over 8 posts ago. You're clearly a proponent that a physical infinity is measurably within our models, otherwise you would be a proponent the concept that we can only assume to have an infinity arise in reality if we start with the assumption of infinity to begin with, thus you wouldn't keep trying to debate with me.
Only claim I have made is that physical theories can misbehave and give infinite results or other results that are just not seen in nature. This usually is seen as pointing towards some new physics. We need to make better models that cover a larger parameter space.
There you go again, infinity cannot be the "result" of a model, you keep posing yourself as a proponent of a lack of infinity in nature, then you say its some result we find from a model of empirical data, even though we never ever ever ever do. Saying "we start out with infinity" to measure electro-static potential doesn't mean infinity is a result of any mathematical operation or measure of data.
What do you mean by exist? Infinity exists in the mathematical sence that I can extend the real numbers (and similar) to include an object called 'infinity'. I have some rules for dealing with this 'generalised number'.
Exist only in the sense that any other mathematical object can exist, which is to say it was defined and constructed by someone, that we have not discovered it existing on its own. There isn't a logical "extension" of a number line to infinity because you can't count to it, there is no process of succession, multiplication, exponentiation or any iterative operator that yields infinity as an actual result, but you can apply these operators to finite numbers to give you complex numbers. There is only the arbitrarily defined axiom for this mathematical object which we then attempt to derive properties of by assuming an isomorphism to number line or a set which can allow the object to be algebraically manipulated in some sense, like that infinity+1=infinity. There's no inherent proof infinity+1=infinity any more than there is a proof 1/0=infinity, it's just an axiom we define based on our own intuition of numbers, just a convenient way we like to think of infinity for taking limits and counting sets as cardinal numbers, even though again we can't actually count all the elements in an infinite set, at best we can just come up with a pattern that will give us an element for any finite input or a technical result from taking a limit. Everything about transfinite numbers is provisional, it's always "if one chooses this axiom of choice is true...then if one then chooses this axiom is true...then if one then chooses this other axiom is true...then infinity+1=infinity" we had to make an arbitrary choice of what is true and what is not along the way to deriving its properties.
If you mean do we expect to see infinity in nature, say as a result of some measurement, then the answer is no. Or at least, nobody, or almost nobody, expects infinities to be realised in nature.
Good, you're making progress. Now, I want you to take a big leap and say "infinity cannot be the result of any quantitative model of reality derived from empirical data."
The same can be said of complex numbers. We extend the real numbers to include a new 'number' which is the squareroot of -1. It is not a real number, but still we know mathematically how to deal with it. In this sense it exists.
In the sense that it exists in the realm of mathematics. Transfinite numbers have much different axioms than numbers on a number line, and again, even within that interpretation of infinity, you only have infinity when you start to infinity to begin with, you can't extend a line of finite numbers to a transfinite number.
Moreover, complex numbers seem vital in quantum mechanics. Yet we never expect to be able to measure the value of some observable to be a complex number. In this sense, nature does not realise complex numbers.
Well we never actually measure a number on its own to begin with in the first place, not even a natural number, we only measure an object that we choose to abstract the results to a mathematical system as representing a numbers, so in that sense we could be measuring complex numbers all the time without realizing it.
There are some even more exotic rings and algebras that I deal with that seem vital in building quantum field theories. However, they are more like a half-way house between the pure classical world and the quantum one. We do not expect that nature will realise these algebras in the sense that you could actually go out and measure something with values in these algebras. However, as I said, they seem vital to our overall understanding.
Vital to the accuracy of some of our predictions, not necessarily to our understanding, not yet anyway.
And again, it is generally thought that infinities will not be physically realised by nature.... shall I say it one more time?
You can say it as many times as you want, but it won't matter until you stop saying "infinity is a result of something we model reality with..."
Okay, I see what you are saying... but physics does not just use 'elementary mathematics', by which I assume you just mean the field structure of the real numbers.
Most of the most accurate models do in some sense, they typically use some kind of vector space. The standard model uses vector space for instance.
I am not thinking of a proof that infinity exists. We know within standard mathematics how to handle infinites (with some care!) and we know that they can appear in our models. That is all I have claimed and all that I and claiming.
Well, I guess that's better, but, starting with infinity with the assumption that you have infinity it is not a result, not a logical conclusion, not a deduction, not a trend fitted to empirical data, just an axiom. Transfinite cardinal numbers only have relevance if you have a set of infinite data...which we never supposedly never measure as having...thus transfinite numbers are often limited to things like abstract mathematics...combinatorics...set theory...not often physics.
Interesting question, but this is a question for philosophy.
You assume. This is why there is a debate about it, because it's not philosophy. We see nothing in the standard model that should limit the size of the universe. Does that mean the size of the universe is "infinite"? Does that mean that there is a physical manifestation of infinity in the same way that there is a physical manifestation that we assign as any finite value? We'll never measure it, yet according to our own physics, the universe should be should have no limit on its size, does that fit the definition of a transfinite cardinal number well enough? On top of all of that, changes in quantum states. Logically, if our models are correct, electrons bound to an atom (to say the least) cannot have intermediate energy states between energy levels, they can only have very specific quantum numbers. Now, this leaves us with the issue that: if an electron changes energy states, say from an S1 orbital to an S2 orbital, is it limited to only being measured in those two energy states because of the mathematical logicality that it cannot have intermediate energy states, because that would essentially nullify its existence. An electron, according to our models *cannot exist* in those intermediate energy states, so as we delve deeper into what makes the universe work, it starts to appear as though it works because of mathematical logic itself, because only certain *values* of quantum numbers, matter and energy are allowed to exist, it would be illogical for other values to exist. Even though we can't measure numbers themselves, it seems math and reality start to merge together, that there is a logical pattern to the universe, that it's not completely random.
It seems like there is more evidence for that math and more evidence for the expansion to planck length and time in a way...you might say "oh, a free electron can travel at any angle and any velocity, accelerate at any angle for any amount of time to emit any photon of any value of energy..." but what you're forgetting is that according to all of our best models, photons can only have specific frequencies. So, if an electron is free, it could only have been freed with a quantized amount of energy in the first place. Then, if that free electron that is supposedly allowed to move at any angle with any speed gets recaptured by an atom, it must, absolutely must only emit photons of certain frequencies and fall into only quantized energy states around the atom, and thus we can extrapolate that the energy the electron had in free space must have been quantized as well. Or, if an electron accelerates, it could only have emitted a photon at quantized energy levels, thus we can again extrapolate that its acceleration must in some way be quantized, and since acceleration is a function of the distance an electron travels in a given time, space and time must be quantized. In other words, speed isn't just moving meters per second, it's moving multiples of planck lengths per multiples of planck seconds. You can't mix and match continuous space and a continuous spectrum of energies with a quantized system of energy, at least not without some weird and extremely impractical models. Even doing something as simple as converting a "quantized" summation to an integral on a continuous number line gives you something like the integral of x-1/2-arctan(tan(pi*x-pi*/2))/pi which is so impractical you might as well ignore it, or you'd still have to use a flooring function or a ceiling function anyway.
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It's so convenient to say infinity is real and then to extrapolate an infinity of worlds.
Wait I don't think many worlds theory is what we're talking about...
Who knows. What do you think?
I tend to say say yes, but on the other hand we continuously show ourselves that our predictions are wrong. I'ts not to say that maybe eventually we can create a perfect mathematical model that perfectly models the observable universe. So ultimately, I just don't like when people assume either way.
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Once you realize that "intelligence" is not only unmeasurable
It's not exactly immeasurable there's plenty of models that have millions of variables and differentials that work with rates of information processing, like for instance computational theory of the mind. There is however a group of scientists, small but not irrelevant who claim a mind is non-local.
Another thing to keep in mind (no pun intended) is that pretty much every animal has some form of it, there's patterns of thought and behavior that we see across thousands of different species and all the different kingdoms of animals, so clearly there's some kind of logical pattern to it.
As for intelligence in plants, on one hand they've been around for even longer than animals, they've had more time to evolve, we really don't know anything about how they perceive the universe and they respond to stimuli and each other in different ways, and even the seemingly least intelligent animals have a lot of capacity for reacting and feeling, even tiny bugs seem capable of exhibiting emotions. But on the other hand, fish have been around for hundreds of millions of years too and they don't seem like geniuses.
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Not exactly arbitrary.
However, there is another thread on exactly this subject already so I don't see any point in rehashing it here. Infinity is well defined in mathematics (even if that is based on choosing some "arbitrary" axioms).
But that is getting off the topic of the the thread which was that infinity doesn't exist "in the real world" (whatever that means).
Well, does math exist independent from our own construction of it to model reality? Can math ever perfectly model reality or will reality always have a discrepancy from our models?
Btw I don't think you deserve a -1, it's a relevant point.
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You seem to be saying that because we can't measure an infinite value in reality that it therefore means that infinity does not exist in mathematics. That is clearly wrong. Infinities occur in many places in mathematics. When that is in a physical theory then it generally means that the theory is no longer applicable.
We can have mathematical objects which we arbitrarily label as infinity, but mathematically you cannot have infinity as a result of an operation on a finite number. Infinities don't actually "occur" anywhere in elementary mathematics, it really is that we're just arbitrarily defining it as a mathematical object and abstracting it to elementary algebra and transcendental calculus to try and reconcile some irregularities in our models and even then we still have problems when we do that, we can't ever just "have" infinity, we can only take a limit to it. In a sense, infinity is even more made up than our own number system itself and hence there are people who say "infinity doesn't exist."
So, "does infinity exist?" Well, infinity is just a mathematical object we made up, and even though within math it's not perfect, we'll assume for the sake of this point that it is perfectly abstracted to confines of elementary operations. A reasonable question would follow that,
"If there was no space, time, or anything that physically existed, would a number or mathematics still exist? Can I inherently measure a number on its own without physical representation?"
If yes, then there's a reasonable claim that infinity exists as well.
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Changing the speed of a photon.
It depends what you mean by speed. Any inertial observer will measure the local speed of light to be c. So locally all observers can considered as inertial. If we do not have an inertial observer then we can have different speeds, it does depend explcitly on the coordinates chosen.
Well essentially it comes down to a metric. As long as light travels one light second per second, as long as that ratio stays the same, a light second and a second can mathematically be any length, so all we're doing with negative energy is changing the metric of local space so that as you put it, globally we can travel faster than light but locally we cannot. In other words, to space, it doesn't matter how much distance a light second is, it just matters that a photon always only travels one of them in a second.
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Think about the electrostatic potential of a point like particle as r -> 0.
It doesn't matter for several reasons: One, you're assuming infinite distance exists to begin with. Two, we can't ever measure or test that potential is anything at infinite distance because we can't measure anything at infinite distance. Three, in our standard model, fields propagate at the speed of light, so a charged particle cannot have physical relevance at a distance beyond the length of a light second multiplied by the number of seconds that the particle has been in existence.
Fourthly, it's just a model that works with other models.
This tells you that it would take an infinite amount of energy to assemble an electron. We know this is wrong as we see electrons!
Oh no, some precious *model* wasn't a picture-perfect image of reality? How expected.
You are now lying.
I wish I was but you're not understanding that everything you're saying is just based off of another model, used to work with results from another model, that's all those tensor fields are, new models to explain other models.
In our mathematical models this is okay, which is what we are talking about.
It's actually still not "ok" in math, it's only ok to take a limit, it's really just our own arbitrary abstraction of what infinity is as an object or value that is the basis for our supposedly logical arguments, I was probably being way too generous with that compromise, I shouldn't give people false hope about obtaining infinity like that.
Nope... this was a statement about a calculation within semiclassical gravity.
Oh, so then you do admit the fallacy that we measured an infinite amount of a dimensional unit?
You seem to like to argue for the sake of it!
You seem to like assuming you solved everything for the sake of it.
Even if infinity does exist, we can never measure it as being so, we can only make assumptions from models wherein we take limits to it.
See, the problem is you're not actually proving anything. The OP may not be right, we can't really assume infinite anything does or doesn't exist not only because the concept of infinity seems to be outside of our current methodology of reasoning, but even if it did, we wouldn't know it, we wouldn't be able to measure it. The only thing we can do is assume it exists, and that's where your issue comes in: you're using the assumption that infinity exists based on some model as a proof that infinity exists.
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You are simply wrong.
It's basic math, infinity cannot be an actual result of a quantitative model, I don't know how else to break it down to you.
You are simply wrong.
For example the electron self-energy in classical theory is known to give an infinite result. It maybe that the calculation involves taking some limits, but still you can get 'infinite values' for things within a theory. This as I have said, this usually signals that you are pushing the theory beyond its scope. The curvature singularities in general relativity are also undersood in this way.Exactly, you start from infinity, you bring something from infinity which isn't a value that you can physically bring anything from and then on top of that you have to take a limit anyway, you can't actually reach infinity even in math. The field of an electron may possibly be allowed to extend indefinitely throughout space but even then it still only propagates at the speed of light. Your fallacy is that you are assuming that a few symbols on paper is reality itself, but any physicist would agree that a model is just a model, the universe is whatever it is independently from what we model it to be. But that's not even the worst of your comment, the worst is that you're ignoring that you were given infinite distance to begin with, which I said is an agreeable compromise. As long as you start with infinity as a given, you can have infinity, but if you do not start with infinity, don't expect to physically create anything remotely resembling an infinity. If you already start out considering the infinite distance of the universe, then of course you're likely going to get some kind of assumption where you are forced to assume some indefinitely large result like your boundary of integration or summation.
Like, for instance, if I start with the assumption that the universe has a non-zero density of matter and energy in proportion to volume, then I assume as a given that the universe is infinitely large, it is only then that I could conclude the universe has an infinite amount of matter and energy.
Who said anything here about empirical data?
Me, over and over again, that's the whole basis for this discussion is never actually confirming that an infinite amount of something exists in finite space which is why I said "ok, we can have infinite amount of something if we start off assuming an infinite amount of space..."
You have to look at the calculations carefully. We can and do encounter infinities when looking at various models quantum or otheriwse.
Well given a finite system to begin with, no, we encounter seeming vertical asymptotes or finite values that are assumed to occur with the indefinite growth of another value like time, even though we'll never be able to measure an infinite amount of time passing.
What?
Exactly what I said, we can *model* the relative changes in frequency of a sound wave as approaching infinity when a moving object approaches the sound barrier, but when an object actually breaks the sound barrier, even though it's a loud sound, it's not a sound of infinite frequency, even though your reasoning would suggest it has to be. Again, not only is infinity not a number, but a model is not reality, a model is just a model and it's something we use to make predictions easy.
We do not expect to ever measure something as having an 'infinite value'. Everyone here agrees... so what the heck are you trying to argue about?
Oh, so then you agree that your statement "you get infinite renormalised energy-momentum tensors of quantum fields near CTCs" is wrong? Seems like you're pretty immersed in the idea that we've measured an infinite dimensional value in physical reality despite the fact that infinity doesn't exist on a number line.
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As for the rest of your post I am not so sure.
What are you not sure about? If I start with particle A and I send something from particle A to particle A, am I sending something from particle A to particle B? No, I'm sending something from particle A to particle A, or in other words, I'm not sending anything anywhere. Entangled particles are just like the regular, every-day particles you know and teleporting photons is actually just a basic phenomena in even introductory chemistry: an electron must emit a photon when entering a lower quantum state.
So, imagine at atom with electrons around it, and imagine you shoot a photon at an electron to excite it temporarily. When the electron is recaptured by the charge of the atom and enters a lower quantum state, it emits a photon in a seemingly random direction.
Now, with entanglement, imagine I take that same electron and split it between different locations of space. When one end absorbs a photon, it has a 50/50 chance of emitting a similar photon on the other end if it enters a lower quantum state because both "ends" are the same electron, so its not actually teleporting a photon, but rather it is destroying a photon and remitting the corresponding energy it absorbed, it's no different than how an electron is prior to entanglement. The only real interesting thing that happens in entanglement is that two or more particles become indistinguishable from each other, thus in a sense becoming the same particle.
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That seems backward (or at least circular). The Planck time is defined as the time taken for light to travel one Planck length (and there is "no reason to believe that exactly one unit of Planck time has any special physical significance"):
It seems backwards but it's the way that we define space and time based on the speed of light being invariant. It also says "the Planck length is, in principle, within a factor of 10, the shortest measurable length – and no theoretically known improvement in measurement instruments could change that."
So, it doesn't have a practical application because we don't use any technology that deals with such a small scale, but in terms of physics, if it's the smallest possible unit of length, that means there are limits to how distance can be traveled by a particle, which also means there are limits to what force a particle can exert, how much energy it can have and so on. But mostly, it is the smallest amount of time that can have any measurable meaning, so why be redundant and have an necessarily complicated theory with infinitely small values below the lowest possible physically relevant value that are impossible to observe? Why don't we just explain everything with god while we're at it since he's impossible to observe too?
There is currently no evidence that space or time are quantised and my understanding is that in theories which are based on this idea the smallest lengths and times are far smaller than the Planck units.
I suppose in terms of empirical data, the real answer is that nobody really knows because there certainly isn't evidence against planck time, we certainly don't have evidence that its possible to have infinitely small mass and infinite small energy, only that they are quantized at some point. But, the possible energies associated with a standard model has a strict correlation to the propagation of electro magnetic radiation, and since the energy of light is a function of frequency, only certain wavelengths of light can exist and thus only certain energies can exist. You could do the math for interpolated frequencies, but they would be meaningless to this universe.
So at this point it's not that Planck time and Planck length have to exist, but rather that you have redundancies in physics, things which are in no way needed for the universe to function as it does when you deal with lengths smaller than a Planck length and Planck time.
Ultimately you have to ask "if matter and energy is quantized, why not space?" It's already validated that light itself is quantized, so does it really make sense to mix and match what we know for sure is a quantized system of matter and energy with another system that can have all sorts of random transcendental scalars?
When a physical theory gives an infinite result
But see that's the thing, it never, ever does that, no model does that, infinity cannot be the defined result of any mathematical operation and thus it cannot be the result of any quantitative model. Like I said, you can "approach" infinity in which case looking at empirical data, you will never find we actually obtain infinity, we never see sound wave of infinite frequency, we never see infinite repulsion in atoms, we never see photons accelerating to infinite velocity, a vertical asymtote like that just means we don't have the data to determine the correct, finite value and this is exactly why you don't want to assume that the value an asymtote approaches is the physical value at the asymtotic singularity itself, hence why mathematicians say "undefined" rather than "infinity."
You are right that one expects a quantum theory of gravity to possibily regulate the infinites that are found in semiclassical gravity, maybe not.
Again, violation of conservation laws and just common sense, you can't have infinite momentum from a finite amount of mass and force and energy, because ultimately that's what we're dealing with, we don't measure infinitely small mass, we only measure finite and even quantized mass, so any model where something like mass is allowed to become infinitely small and thus produce a vertical asymtote as mass approaches zero is inaccurate, at least if we don't assume to begin with that there are infinitely small particles of infinitely small mass that make up mass-bearing particles. The same concept is true for energy and momentum, we don't observe infinitely small momentum and energy or infinitely big momentum and energy, only finite amounts. Does it really make sense to you that a quantized system of matter and energy could ever give you an infinite amount of any dimensional vector or scalar? It if does, I refer you to the fact that breaking the sound barrier does not destroy the universe with a sound wave of infinite frequency.
From our own empirical data, not even considering any sort of mathematics, it would appear infinite anything only exists when you already start with an infinite amount of something as a given, we have never measured an infinite amount of something within a finite region of space or in a finite complexity in the mechanics of our observations.
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I don't know what believe. Well I know not to believe in God. Lol. Though you both make very valid points, and reading on bells theorem shows the theory to be wrong because it doesn't apply to the rules. So do you think mordred that the rules can never be broken.
You don't need to believe anything, you just need an understanding and logic. When two particles become entangled, they become the same particle, indistinguishable. So, if you try to "communicate" between entangled particles by altering one particle to affect the other, you're just sending information about one particle to itself so the net information sent is zero, it's like calling yourself on your own phone.
The second thing is, even if you separate particles at vasts distances, you can only do so at the speed of light. Thirdly, even though supposedly you could destroy a photon at one end the entangled pair (which isn't anything strange) and have a similar photon be re-emitted at the other end, in order to measure that anyone received that one-way piece of information and observe that they knew to send something back to you, you would have do so at a maximum of the speed of light. There's always some loop hole where even if something supposedly occurs faster than light, it can't be measured as doing so, because as soon as you say something is measured as traveling faster than light there's violations in basic causality and relativity.
Now, the trick with interstellar travel isn't traveling faster than the speed of light, it's increasing the speed of light itself so that you have a higher speed limit, thus no one actually observes you traveling "faster" than a photon in your local space. As long as nothing mass-bearing or energy-bearing travels faster than a photon. you're okay. A photon travels at about 300,000,000m/s which is invariant regardless of the frame of reference, so if you make a photon travel at 400,000,000m/s instead, the matter in that local space where that speed limit is increased could theoretically travel anywhere between 300,000,000m/s and 400,000,000m/s. In order to do that, you would have to change the metric for a Planck length and Planck time in a way that increases the amount of Planck length that you can travel in a smaller Planck time, sort of like the opposite of standard time dilation and length contraction. Supposedly this can be done with negative energy if it exists as that would cause a negative warping of space, giving the opposite of the effects that we see with positive warping due to gravity.
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What is gravitational eletricity?
I think they mean that just as with a magnetic field, a gravitational wave could be strong enough to separate an electron from an atom, thus creating a free charge that can potentially move to another atom. Not very likely, but I guess I can't rule out the possibility at some insanely high energy interaction.
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When we calculate such infinite things then the theory is understood to break down. For example, you get infinite renormalised energy-momentum tensors of quantum fields near CTCs. (In layman terms time machhines seem to break down!)
Infinity isn't a number, you can't count to it, so it's impossible for us to *count* any number of objects that total infinity. If an apparent approach to infinity arises, it doesn't necessarily (or ever) mean that there is physically an infinite amount of something in a finite region of space. Rather, it is a fallacy of the assumption firstly in the model's equivalence to the universe, secondly in the fallacious assumption that infinity is a number that can be obtained and thus thirdly the fallacy that infinity is a "result" of a model. For instance, we can *model* the increase in relative frequency of sound waves of an accelerating object as asymptotically skyrocketing towards infinity as an object approaches the speed of sound. But guess what? We never, ever, ever, ever, ever, ever, ever, ever, ever, ever, ever, ever, ever, ever, ever actually observe a sound wave of infinite frequency and we especially know we don't because the world is still here and the universe still exists, it was not destroyed by that infinite energy sound wave. Just because a function like 1/x approaches +/- infinity doesn't mean 1/0=+/-infinity and this error is exactly why mathematicians leave it as "undefined."
Another example: the inverse square law of gravity. Well, gravity might die out over distance at a rate of 1/x^2 (and something similar with charge), but guess what? Earth doesn't have infinite acceleration due to gravity at its core or anywhere around it or in it.
Yet another example: fusion. Technically, the repulsion between two protons should, according to your reasoning "be infinity" when the protons try to fuse together and come into contact with each other, thus preventing fusion. However, not only do we know fusion is possible, but we know that exact model is wrong and the reality is the repulsion isn't infinite and rather than protons tunnel through each other.
Even yet another example: Photons. Using the model that acceleration=force/mass, you'd come to the conclusion that a photon has "infinite acceleration." Well, we don't see photons accelerating past the speed of light so clearly that's wrong, we only see them being absorbed, emitted, decohered, constructed and scattered.
Even yet another example: posetive feedback loop. In certain systems of equations with solutions in the form of complex exponentials, we can see a positive feedback loop wherein the waves adding together at a certain resonance frequency supposedly producing indefinite constructive interference over time, so we should be able to bounce a few sound waves and destroy the Earth right? Well, again, even with the passage of indefinite time, a finite volume and a finite amount of matter and energy would eventually force that oscillator to become damped and you wouldn't get an infinitely large exponentially growing harmonic oscillation, just something that levels off at a finite amplitude, it's literally like the universe is built to prevent us from ever reaching infinite anything.
So, clearly, since infinity isn't an actual number, we can't measure it quantitatively. We can only assume if we choose to that an indefinitely large volume of space has an indefinitely large amount of matter and energy. Since infinity doesn't lie on a number line, it is impossible to count an infinite number of any units of any dimension, and since the basis for which we typically define physical reality is the culmination of dimensions in which space is formed and objects move within, we can't physically observe infinity in any finite region of space. "You can only have infinity if you already started with it," I think that's a pretty decent compromise like in the instance that we assume the universe is indefinitely large which allows infinity to "exist," just not measurably so.
Another thing to consider, especially in the case of the sound waves is that infinity usually gives some kind of violation in conservation laws. Just think about it: does it actually make sense that putting a finite amount of force into accelerating an object gives me a sound wave of infinite energy? I suspect the same is true with your quantum models and thus the reality is that due to the quantinization of space, time and pretty much everything, there is a finite maximum amount of energy and momentum and minimum amount of energy and momentum that a particle can have, like for instance Planck time and then dividing by Plank time. Since we can't have any time less time than Planck time and we can't travel less than a Planck length, the maximum speed of matter is probably something around 1 planck length per planck second.
Oh look, wikipedia, what a coincidence that basic logic didn't fail me
https://en.wikipedia.org/wiki/Speed_of_light
"Speed of light: Planck Length per Planck Time: 1"
The speed of light might seem like some barrier of infinity, but it's actually just the smallest possible length traveled in the smallest possible time.
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How about "it's impossible to have an infinite amount of information, mass, energy, momentum or other dimensional unit within a finite region of space-time of a non-zero metric" which also allows us to include technical conditions of the big bang where we supposedly had all the infinite mass and energy of the universe condensed into a point and also allows us to let the universe be infinite in size if it wants.
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Hmm guess it was bad intel then, not the theory I thought it was but I guess in the end they did reconcile each other to some extent.
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Gravitational waves can transfer energy to particles but the scale they would have to be for that to have any practical application is on the scale of multiple solar masses. Right now all the planets and the Sun are creating gravitational waves with their orbits and rotations and wobbles, but even at that scale, gravity is heavily weakened by distance.
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I believe the two models is LCDM vs MOND.
Hold up, why not just say dark matter itself causes variations in the gravitational constant instead of having two different theories try to predict the same kind of thing about gravity? It would give dark matter its accuracy and give MOND the mechanism.
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I can't remember what it was, but supposedly proponents of Dark Matter were challenged to predict the accuracy of Dark Matter theory by predicting where satellite galaxies around the Milky Way would be in 5 years. Their opponents were a group of scientists who claimed that dark matter didn't exist but only that the gravitational constant varied with distance.
Despite all the hype of dark matter, the gravitational constant group came out ahead with amazing accuracy while the dark matter group was very far off.
First question is: does anyone know the name of this experiment?
Second question is: I don't have a particular preference for dark matter theory, but varying gravitational constant is kind of a no-brainier almost like curve-fitting so of course its going to work if you fine tune your values. With this theory, what is the explanation for how specific, localized regions appear a lot more dense than they should be using this gravitational constant theory? Like for instance rings around galaxies that have been identified as having a higher gravity than measurable matter can account for, not the interior of the galaxy, not millions of light-years from the galaxy, a ring right around it? And what of the hubble boundary of the universe? Is it suppose to be some kind of illusion caused by how our apparent physics changes with distance, which would also affect several universal constants or is space actually still expanding with no dark model? There's so many other things that would have to vary with distance as well like Planck length, Planck time and Planck mass and Planck temperature. How does this model actually explain everything we're seeing? What's the actual explanation?
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Right, but what if there was a collection of 'points' on that plane that are the same? For example, imagine a plane with multiple points labeled as A, but on different coordinates. They are all still point A, but yet when put onto a plane occur at multiple points.
That's essentially just an intersection from a higher dimension or the warping of the coordinate system. Mathematically it would most easily be described as the severe warping of space, though that specific warping hasn't been observed in real life. To explain how that would happen, start with a plane, just a regular old square and imagine that it represents the fabric of space-time. Then, fold the plane over itself 1-6 times and poke a single hole through it.
When you unfold the plane again, you'll find that one poke made several holes in the plane at once and that's essentially how a wormhole works. It's more complicated of course because you're talking about warping 4 dimensional space, not just a plane though mostly what you're doing is just saying two different locations are brought together via the warping of space. So mathematically you could have the space of the sphere be bent and warped to allow a path through one point to lead to another part of the sphere's surface. All your doing with these points that have different spacial locations that are all connected in 4D space is the same as with a plane; folding sections sections of spacetime so they meet in one place.
You could also describe it more as the higher dimensional pathway doing the work of bending instead of space itself, like if you took a wire in 3d space and poked both ends through a 2D plane, the electricity traveling through the wire from the reference of the merely 2D plane would appear to start in one point of the plane and pop out in the other end without traveling through the intervening area as if it teleported or conservation laws were violated, even though all the electricity did was travel in a third dimension.
Not coincidentally, this higher dimensional model is exactly the sort of thing scientists use to uphold conservation laws in sub-atomic physics in new models because of the principal I just demonstrated wherein energy or a particle simply travels through another higher dimensional path rather than just a regular 4d path instead of inventing some new and unmeasured particle. Whether or not that is what's actually happening is up for debate, we don't have a strict "need" for higher dimensions beyond 4 but it's convenient to use higher dimensional models to achieve accurate results in some cases.
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Is projective geometry and cartography not a form of overlap of dimensions?
A projection is just a type of transformation, not a dimension, you're not actually moving an entire dimension when you project something, you're just seeing how one vector or set of vectors or isomorphism of a vector is mapped onto a subspace which usually is most useful when the basis of the subspace has a lower dimension than your original space.
But more than that the field of protective geometry itself doesn't use the same definitions of distance and vectors anyway, so the premise of your question is illogical to begin with since dimensions don't mean the same thing in that arrangement nor are they isomorphic to properties of dimensions defined in elementary geometry. Since it doesn't use the same definition of dimension or even use metric-based geometry, the comparison doesn't make sense.
It's like saying "a square is a rectangle" and then asking "but what if a square wasn't a rectangle?" Well who knows, a square is certainly a rectangle in any geometry of relevance here, but we could arbitrarily define any such system where it happened to be the case that a square wasn't a rectangle. There's definitely a difference between a projective space and a vector space.
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Do you at all understand why am I 'bullshitting' with these questions? These are important, imo.
Ok well if you're here to have a toxic attitude then there's no point answering your questions, so when you're ready to be act in a civilized manner again, we can talk.
That would need more information about the generators, yes. Combining several generators can be difficult.
In single and three-phase AC, synchronization is vital, both in frequency and in phase, in series connection too (when possible).
In DC and AC, if the generators give roughly a constant voltage, this voltage must match accurately, or you get worries.
Often, generators and loads are meant for some standard voltage, so series connection is seldom possible.
About fault tolerance: it depends on the expected or more probable failure mode. Many parts, including apparatuses with windings, fail as a short-circuit rather than an open circuit. But anyway, with big apparatuses, you must take corrective actions in the circuit if one fails. You can't leave a short-circuited transformer or alternator in operation nor in the circuit.
Alright then thanks, so parallel is better than series for the most part because it's easier to control each generator, that's a start. Also, from what I've been told, there are no actual "DC" generators that don't require rectifying on their own, there has to be some component that folds the waveform even if that component is an additional part of the generator itself if not within the rest of the circuit, so just assume that it's going to start AC without any additional parts.
Ok so the voltages should match or some of the energy from one generator would go into another, so make sure they match. For that to happen, it seems voltage is mostly dependent on the design. Does voltage depend at all on the angular frequency of the rotor or is that only the current that varies with frequency?
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Some general remarks.
BiotechFusion, if you want to learn some electromagnetics and electric machinery, go on. If instead you want something that works properly within a limited time, buy it. Generators are cheap, often you find some used ones for free, you'll save months of disappointment, because EM isn't trivial and takes its time to grasp. Presently you're many months away from building a usable generator.
You could acquire "Electric machinery fundamentals" by Stephen Chapman. Not more complicated than it needs, nice pictures, but it's the level of engineering students. Or accept a less numerical but much more "hands on" understanding - which has as much value to my eyes, and in my opinion should be acquired before the numerical approach - and buy yourself an experiment kit for electromagnetism.
The universal and justified choice is to build (AC) alternators and, if DC is desired, put diodes. Diodes are very cheap and reliable - much more so than the additional parts in a (DC) dynamo. Nobody would have a single diode: buy a bridge, it makes use of all alternances. 4-diode bridges for single-phase AC to (rippled) DC, 6-diode bridge for three-phase AC to (rippled) DC. Same size and price as a single diode.
Either people have the knowledge to determine if it's right or wrong or they don't, there's nothing good that can come from dancing around that fact. I talked to another 4 real electrical engineers and they all said they didn't know what the answer was, so I doubt you do which also explains why your post doesn't resolve anything. Your post really doesn't help anyone in the slightest, people already know they can buy electrical parts if they want to. I said my goal was the make something from scratch, it doesn't matter if your own personal goal is to buy something, it's not what is relevant to this topic.
In fact, no thanks to anyone here, I've determined after talking with engineers that it won't work because even though the field lines are near-perpendicular at some point, they will have to cross back down into the wire in the opposite direction, thus nullifying the force applied to the charges, so nothing moves.
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If I have multiple generators in parallel, is their synchronization important for powering a device if they have a relatively smooth current? What if they are in a series?
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no such thing as "infinity" in the real world (split)
in Speculations
Posted · Edited by BiotechFusion
Not surprised you are lost, is it's only as made up as when you say infinity is the result of a model.
I'd like to see where you stated that.
So, stop trying to divide by zero, stop trying to say we reached infinity on the real number line, stop saying infinity is a result.
Yes, we can have coordinates where the result is undefined...
A gluon field strength can be modeled as a tensor field and you already said tensor fields can have an infinite value, so I guess a gluon field can somehow have an infinite tensor.
How do you "regulate" something that isn't an actual value?
So, I'm wrong to say we can't have a model where a physical representation of infinity results? Seems like a direct contradiction to what you said earlier.
Not surprising you don't understand it, Infinity is never the "result" of a model, you never put in a piece of empirical, finite data and get in infinity as a result of predicting a value.
Please quote me where I said a given model will fit all obtained data, even though I've been arguing just the opposite.
Are we? And, are "we?" Or just you? Maybe the universe is of infinite size, but so far, we don't have a way to prove that because the way we quantify models doesn't allow us to.
Oh, so you're not making progress, my bad.
You've giving a model where people assumed that you could indefinitely approach the boundary of the universe to infinity and that somehow an electron has physical relevance at infinite distance, which logically it can't. But, you still didn't didn't show that infinity is a result, you've only showed that it can be an *assumed* *abstraction* as a basis for a deduction of the pattern of seemingly organized data.
You can assume an infinite value of something which is more or less illogical to begin with when trying to model something physical in our terrestrial physics, but infinite anything can't be the "result."
So, you can't count to infinity in a vector space, so stop saying infinity is the result of quantitative dimensional models.
Maybe we can't find proof, but I would argue about evidence. Since our standard models show no limit to the size of the universe, you could argue that is evidence for the universe somehow having an infinite size, depending on how you define infinity. Or, conversely, we could find some sort of hyper-dimensional curvature that would show the universe is a loop over some distance to show it is a finite size in a new model.
Both. Neither standard model places an upper limit on what size the universe can be. That's why the early universe is often discussed in terms of density, not volume, because in both particle physics and our own observations of cosmology, we see nothing that limits how much space there can be.
Exactly.
It actually seems like I've seen so much of your points that you can't even keep track of all your own points when I discuss them.
General relativity does not state what occurs at these singularities since the transformations that model such curvature results in a division by zero at those singularities. Some people expect these singularities to be manifested in the form of some infinite value of curvature or time dilation or length contraction, some people do not. For the people who assume it does, they are inferring that a division by zero is equal to an infinite value and thus there is much controversy about the role of infinity in our models, which, is why quantized models show promise as they get rid of a lower and upper limit that would allow an infinite value of a dimensional quantity to exist in finite space.
And you should think about how a platform that encourages the arbitrary mixing of emotions with objective logic can actually be credible. It doesn't matter if the dumbest, smartest, kindest or meanest person in the world says it, 1+1=2 in elementary mathematics, it's just logic. As far as I'm concerned, any number of reputation points is a demonstration of this platform's lack of regulation of concise scientific standards.