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originally posted by: Kashai
a reply to: chr0naut
I have always had a problem with the idea that radiation results from a random event. The fact that anything emits radiation is the result of a process, as in the case of a clockwork perspective.
No field has yet been discovered that is responsible for this inflation. However, such a field would be scalar and the first scalar field proven to exist was only discovered in 2012 - 2013 and is still being researched.
So it is not seen as problematic that a field responsible for cosmic inflation and the metric expansion of space has not yet been discovered. The proposed field and its quanta (the subatomic particles related to it) have been named the inflation. If this field did not exist, scientists would have to propose a different explanation for all the observations that strongly suggest a metric expansion of space has occurred and is still occurring (much more slowly) today.
en.wikipedia.org...(cosmology)
thought?
originally posted by: Kashai
a reply to: TrueBrit
The way I am considering this in relation to a really massive MA event like in the early Universe. This could then have generated massive gravity waves that would affect spacetime in such a way as to result in cosmic inflation.
The mass would have then had a chance to clump forming not only black holes but matter as we understand it.
I looked into what you were saying and then, in that case, more like the Big Stretch.
Have a discussion about the origins of the Universe and, ere long, someone will inevitably use the term “the Big Bang” to describe the initial moment of expansion of everything that was to everything that is. But in reality “Big Bang” isn’t a very good term since “big” implies size (and when it occurred space didn’t technically exist yet) and there was no “bang.” In fact, the name wasn’t ever even meant to be an official moniker, but once it was used (somewhat derisively) by British astronomer Sir Fred Hoyle in a radio broadcast in 1949, it stuck.
The big bang is the foremost model that scientists use to describe the creation of the universe. This theory proposes that the universe was created in a violent event approximately 12 to 15 billion years ago.
In 1926, Oskar Klein gave Kaluza's classical five-dimensional theory a quantum interpretation,[3][4] to accord with the then-recent discoveries of Heisenberg and Schrödinger. Klein introduced the hypothesis that the fifth dimension was curled up and microscopic, to explain the cylinder condition. Klein suggested that the geometry of the extra fifth dimension could take the form of a circle, with the radius of 10−30 cm.[5] Klein also calculated a scale for the fifth dimension based on the quantum of charge
an·i·so·trop·ic
[anˌīsəˈtrōpik, -ˈträpik]
ADJECTIVE
(of an object or substance) having a physical property that has a different value when measured in different directions. A simple example is a wood, which is stronger along the grain than across it.(of a property or phenomenon) varying in magnitude according to the direction of measurement.
i·so·trop·ic
[ˌīsəˈträpik, ˌīsəˈtrōpik]
ADJECTIVE
(of an object or substance) having a physical property that has the same value when measured in different directions. Often contrasted with anisotropic.(of a property or phenomenon) not varying in magnitude according to the direction of measurement.
originally posted by: Kashai
a reply to: chr0naut
"The 'smoothness' of the cosmic background (CMB) microwave energy of the universe when looking in different directions (it's anisotropy), indicates that there were likely very few black-hole to black hole mergers in the early universe and hence there were few, or none of, gravitational wave generating events in the early universe. The expansion of the universe, in fact, was less like a bang and more like a fast even expansion."
an·i·so·trop·ic
[anˌīsəˈtrōpik, -ˈträpik]
ADJECTIVE
(of an object or substance) having a physical property that has a different value when measured in different directions. A simple example is a wood, which is stronger along the grain than across it.(of a property or phenomenon) varying in magnitude according to the direction of measurement.
i·so·trop·ic
[ˌīsəˈträpik, ˌīsəˈtrōpik]
ADJECTIVE
(of an object or substance) having a physical property that has the same value when measured in different directions. Often contrasted with anisotropic.(of a property or phenomenon) not varying in magnitude according to the direction of measurement.
Perhaps you could be more specific?
originally posted by: Kashai
a reply to: chr0naut
The idea that FTL is impossible is an oversimplification.
Thoughts?
We propose here two new transformations between inertial frames that apply for relative velocities greater than the speed of light, and that are complementary to the Lorentz transformation, giving rise to the Einstein special theory of relativity that applies to relative velocities less than the speed of light. The new transformations arise from the same mathematical framework as the Lorentz transformation, displaying singular behaviour when the relative velocity approaches the speed of light and generating the same addition law for velocities, but, most importantly, do not involve the need to introduce imaginary masses or complicated physics to provide well-defined expressions. Making use of the dependence on relative velocity of the Lorentz transformation, the paper provides an elementary derivation of the new transformations between inertial frames for relative velocities v in excess of the speed of light c, and further we suggest two possible criteria from which one might infer one set of transformations as physically more likely than the other. If the energy–momentum equations are to be invariant under the new transformations, then the mass and energy are given, respectively, by the formulae and where denotes the limiting momentum for infinite relative velocity. If, however, the requirement of invariance is removed, then we may propose new mass and energy equations, and an example having finite non-zero mass in the limit of infinite relative velocity is given. In this highly controversial topic, our particular purpose is not to enter into the merits of existing theories, but rather to present a succinct and carefully reasoned account of a new aspect of Einstein's theory of special relativity, which properly allows for faster than light motion.
originally posted by: Kashai
a reply to: chr0naut
We propose here two new transformations between inertial frames that apply for relative velocities greater than the speed of light, and that are complementary to the Lorentz transformation, giving rise to the Einstein special theory of relativity that applies to relative velocities less than the speed of light. The new transformations arise from the same mathematical framework as the Lorentz transformation, displaying singular behaviour when the relative velocity approaches the speed of light and generating the same addition law for velocities, but, most importantly, do not involve the need to introduce imaginary masses or complicated physics to provide well-defined expressions. Making use of the dependence on relative velocity of the Lorentz transformation, the paper provides an elementary derivation of the new transformations between inertial frames for relative velocities v in excess of the speed of light c, and further we suggest two possible criteria from which one might infer one set of transformations as physically more likely than the other. If the energy–momentum equations are to be invariant under the new transformations, then the mass and energy are given, respectively, by the formulae and where denotes the limiting momentum for infinite relative velocity. If, however, the requirement of invariance is removed, then we may propose new mass and energy equations, and an example having finite non-zero mass in the limit of infinite relative velocity is given. In this highly controversial topic, our particular purpose is not to enter into the merits of existing theories, but rather to present a succinct and carefully reasoned account of a new aspect of Einstein's theory of special relativity, which properly allows for faster than light motion.
rspa.royalsocietypublishing.org...
Related article.
gizmodo.com...
I am fascinated with considering what happens if one were achieved infinite density. I consider that as one approaches the singularity of a black hole the same thing happens in that the mass archives infinite density.
originally posted by: Kashai
a reply to: chr0naut
Invariably you're making a good point but the problem of infinity is that it does pertain in general to the idea that anything can happen. Not necessarily jumping for joy over this myself but given that nature in so far as we know does calculate to infinity. Under such circumstances, as we are discussing, brings up the issue of potentials beyond current comprehension, at least mathematically.
Its conceivable that what we today define today scientifically and otherwise as infinity is not infinity.
This is another common use of l'Hôpital's Rule. If you are finding a limit of a fraction, where the limits of both the numerator and the denominator are infinite, then l'Hôpital's Rule says that the limit of the fraction is the same as the limit of the fraction of the derivatives. For example,
Most students have run across infinity at some point in time prior to a calculus class. However, when they have dealt with it, it was just a symbol used to represent a really, really large positive or really, really large negative number and that was the extent of it. Once they get into a calculus class students are asked to do some basic algebra with infinity and this is where they get into trouble. Infinity is NOT a number and for the most part, doesn’t behave like a number. However, despite that we’ll think of infinity in this section as a really, really, really large number that is so large there isn’t another number larger than it. This is not correct of course but may help with the discussion in this section. Note as well that everything that we’ll be discussing in this section applies only to real numbers. If you move into complex numbers, for instance, things can and do change.
The modern development of calculus is usually credited to Isaac Newton (1643–1727) and Gottfried Leibniz (1646–1716), who provided independently[8] and unified approaches to differentiation and derivatives. The key insight, however, that earned them this credit, was the fundamental theorem of calculus relating differentiation and integration: this rendered obsolete most previous methods for computing areas and volumes,[9] which had not been significantly extended since the time of Ibn al-Haytham (Alhazen).[10] For their ideas on derivatives, both Newton and Leibniz built on significant earlier work by mathematicians such as Pierre de Fermat (1607-1665), Isaac Barrow (1630–1677), René Descartes (1596–1650), Christiaan Huygens (1629–1695), Blaise Pascal (1623–1662) and John Wallis (1616–1703). Regarding Fermat's influence, Newton once wrote in a letter that "I had the hint of this method [of fluxions] from Fermat's way of drawing tangents, and by applying it to abstract equations, directly and invertedly, I made it general."[11] Isaac Barrow is generally given credit for the early development of the derivative.[12] Nevertheless, Newton and Leibniz remain key figures in the history of differentiation, not least because Newton was the first to apply differentiation to theoretical physics, while Leibniz systematically developed much of the notation still used today.
Since the 17th century, many mathematicians have contributed to the theory of differentiation. In the 19th century, calculus was put on a much more rigorous footing by mathematicians such as Augustin Louis Cauchy (1789–1857), Bernhard Riemann (1826–1866), and Karl Weierstrass (1815–1897). It was also during this period that the differentiation was generalized to Euclidean space and the complex plane.
Painter's paradox[edit]
Since the horn has a finite volume but infinite surface area, it seems that it could be filled with a finite quantity of paint, and yet that paint would not be sufficient to coat its inner surface – an apparent paradox. In fact, in a theoretical mathematical sense, a finite amount of paint can coat an infinite area, provided the thickness of the coat becomes vanishingly small "quickly enough" to compensate for the ever-expanding area, which in this case is forced to happen to an inner-surface coat as the horn narrows. However, to coat the outer surface of the horn with a constant thickness of paint, no matter how thin, would require an infinite amount of paint.[2]
In reality, paint is not infinitely divisible, and at some point, the horn would become too narrow for even one molecule to pass. But the horn to is made up of molecules and so its surface is not a continuous smooth curve, and so the whole argument falls away when we bring the horn into the realm of physical space, which is made up of discrete particles and distances. We talk therefore of an ideal paint in a world where limits do smoothly tend to zero well below atomic and quantum sizes: the world of the continuous space of mathematics.
Gabriel's horn (also called Torricelli's trumpet) is a geometric figure which has an infinite surface area but finite volume. The name refers to the tradition identifying the Archangel Gabriel as the angel who blows the horn to announce Judgment Day, associating the divine, or infinite, with the finite. The properties of this figure were first studied by Italian physicist and mathematician Evangelista Torricelli in the 17th century.
originally posted by: Kashai
Painter's paradox[edit]
Since the horn has a finite volume but infinite surface area, it seems that it could be filled with a finite quantity of paint, and yet that paint would not be sufficient to coat its inner surface – an apparent paradox. In fact, in a theoretical mathematical sense, a finite amount of paint can coat an infinite area, provided the thickness of the coat becomes vanishingly small "quickly enough" to compensate for the ever-expanding area, which in this case is forced to happen to an inner-surface coat as the horn narrows. However, to coat the outer surface of the horn with a constant thickness of paint, no matter how thin, would require an infinite amount of paint.[2]
In reality, paint is not infinitely divisible, and at some point, the horn would become too narrow for even one molecule to pass. But the horn to is made up of molecules and so its surface is not a continuous smooth curve, and so the whole argument falls away when we bring the horn into the realm of physical space, which is made up of discrete particles and distances. We talk therefore of an ideal paint in a world where limits do smoothly tend to zero well below atomic and quantum sizes: the world of the continuous space of mathematics.
Gabriel's horn (also called Torricelli's trumpet) is a geometric figure which has an infinite surface area but finite volume. The name refers to the tradition identifying the Archangel Gabriel as the angel who blows the horn to announce Judgment Day, associating the divine, or infinite, with the finite. The properties of this figure were first studied by Italian physicist and mathematician Evangelista Torricelli in the 17th century.
en.wikipedia.org...