Daedalus

Thank you AJB for stepping in and showing how this concept does have some merit. I realize that [math]l[/math] probably has a lot more mathematics behind it, but at leasts it is a start.

Continuing with this discussion, let us see how this modification effects relativistic mass. The original equation is: [math]m_{r}=\frac{m_{0}}{\sqrt{1-\frac{v_{r}^{2}}{c^{2}}}}[/math] Substituting this hypothetical correction to gamma we get (I am going to ignore our relative temporal velocity because it will always be zero for all observable objects moving with us through time): [math]\gamma=\frac{1}{\sqrt{1-\frac{(v_{r}+v_{r} l)(v_{r}-v_{r} l)}{c^{2}}}}[/math] [math]m_{r}=m_{0}\gamma=\frac{m_{0}}{\sqrt{1-\frac{(v_{r}+v_{r} l)(v_{r}-v_{r} l)}{c^{2}}}}[/math] When relative velocity is equal to the speed of light we get: [math]m_{r}=\frac{m_{0}}{l}[/math] If [math]l=0[/math] it would take an infinite amount of energy to reach the speed of light. However, I have shown that we do move at the speed of light in my thread on Temporal Uniformity (Time) and AJB showed me that the four vector of a massive particle in the rest frame is equal to the speed of light. Since we move at the speed of light through space-time, then it seems as though [math]l[/math] does exist and that it does not require an infinite amount of energy to reach the speed of light. This actually makes sense because it seems improbable that the universe has an infinite amount of physical space and mass-energy. If you do believe that there is an infinite amount of mass-energy and space, then my argument for temporal uniformity would be true because the universe would still be exploding at time zero at the center of the big bang as I type these words. So my theory suggests a finite universe. But we shouldn't get our hopes up of reaching light speed as it would probably take all of the energy in our universe to do so.

Because of the law of balance, I believe that it may be true that length cannot by reduced to zero as a result of a mathematical tranformation of actual physical space. There must always exist some distance in between any two points. Anyone who has taken calculus knows this because of having to calculate integrals using the Riemann sum. Applying the same concept to deriving points in space, shows that there will always exist some distance in between any two infinitesimal points. The universe implements this abstract mathematical concept, of a physical distance always existing between two points, using mechanics that drive the cosmological constant. This would explain the anti-gravitational effects we observe for these things. This is why I posed the question here on this site, "Quantization of Length? Heresy or Merit?". These questions are important because they affect the underlying space-time metric. The Lorentz transformation affects all aspects from length contraction to time dilation. If we know that the current metric that we use does not properly describe all apsects of physical space, then we must consider such questions and hypotheses that affect this attribute to space-time. Combining all of my proposed ideas allows us to redefine gamma as: [math]\gamma=\frac{1}{\sqrt{1-\frac{v_{r}^{2}}{c^{2}-v_{w}^{2}}(1-l^{2})}}=\frac{1}{\sqrt{1-\frac{(v_{r} + v_{r} l)(v_{r} - v_{r} l)}{(c + v_{w})(c - v_{w})}}}[/math] Where [math]v_{r}[/math] is the relative velocity perpendicular to the temporal axis, [math]v_{w}[/math] is the temporal velocity relative to time zero at the center of the big bang (equals zero with respect to the time-normal and time-relative frames of reference), [math]l[/math] is the length quantization number (which could actually be zero), and [math]c[/math] is the speed of light.

It does seem as though he has. But there could be any number of reasons why he has not replied.

Tar, I think the true nature of this is that the spheres are different in size. The repulsion forces of like charged particles would keep certain spheres from touching each other. From this we could obtain tightly packed clusters. We can also pack more spheres together using higher dimensional spaces.

Dimensional Collapse A Thought Experiment on Obtaining Light Speed When dealing with the construct of the universe it is necessary to use the microscope of the mind to gain insight into the problem at hand. We will take a journey on a spaceship that is designed to test how light speed affects our vision. Our scientists have invented a device that, for the purpose of this discussion, allows two astronauts to defy relativity and reach the speed of light. Taking into account the dangerous nature of this mission, the two astronauts prepare their estates, take care of any last minute business, and say their good byes to their friends and family. Because according to relativity, if the anti-relativity device fails, they could end up being crushed into a singularity as a result of having infinite mass. The day finally arrives and the two astronauts pilot the spaceship to the location where the test is to begin. After some time of acceleration along their flight path, the two astronauts finally obtain light speed. At the point in time they obtained light speed, both astronauts looked at the other in anticipation of celebrating the moment. It is at this moment, the anti-relativity device malfunctions. For sake of discussion, we will not be so cruel as to crush our astronauts into a singularity by observing the effects of relativity. However, the view has changed entirely for our astronauts. According to special relativity it takes an infinite amount of energy to reach the speed of light. We must also conclude that the reverse is true and, unless the anti-relativity device begins to function properly, our astronauts are now forever trapped going the speed of light in the direction they are traveling. We must also conclude that all motion, in the direction the spaceship is traveling, has been restricted to a plane perpendicular to the direction of forward motion. This is because special relativity states that nothing can go faster than the speed of light. So our astronauts can only move in the direction of up, down, left, or right. All forward and backward motion would be impossible and because our astronauts were looking at each other, they would also notice that each appear to the other as a vertical strip. This is because we have two eyes and since our astronauts are traveling at the speed of light, they can only see light perpendicular to the direction they are moving. Since the brain combines the images from our eyes to form a single image with the perception of depth, our astronauts would really see each other as a single vertical strip. For all intents and purposes, both astronauts actually appear to be two dimensional in how they view each other and how they are restricted to movement along a two-dimensional plane. They are experiencing dimensional collapse in the direction of motion and because of the definitions in relativity, they also appear two dimensional to observers on Earth. The consequence of dimensional collapse is a reality of the Lorentz contraction and combined with the constancy of the speed of light, we can explain how we experience time. Even if the astronauts could move around freely, they would not be able to see the light from anything behind them in the direction of motion. And if everything else in the universe was also moving at the speed of light parallel to and in the direction of their motion, they would not be able to see the light from anything in front of them. Due to dimensional collapse from the Lorentz contraction, they would be restricted to only being able to view the universe along dimensions that are perpendicular to their motion. The speed of light accounts for why we cannot see objects in the future or past, and the Lorentz contraction collapses the dimension of time to where it is no longer perceived to have any length and restricts us by no longer allowing us to traverse forward or backward in the direction of motion. This means that the future and past would be nothing more than physical points along the spatial dimension of time where all observable phenomena co-exists at a definite point along with all other non-observable phenomena existing at different points along the temporal dimension, all traveling with uniform direction at the speed of light. If we apply the same scenario as explained above to a four dimensional space where all matter and energy are co-moving at the speed of light along a spatial dimension, such as the dimensional axis the astronauts are traversing, then we can account for having three spatial dimensions and one temporal dimension. Since the astronauts are now traveling at the speed of light through four-dimensional space, the temporal axis collapses and we are left with three observable spatial dimensions. This is logical because mathematics defines that all spatial dimensions share a common origin point and must be perpendicular to each other regardless of number. The previous statement only holds for Euclidean space as it is not referring to projected or transformed spaces. Since the speed of light is constant, both astronauts would forever be at rest with each other along the temporal axis and could only perceive their forward motion through time by observing motions through dimensions perpendicular to the temporal axis. And because they would no longer be able to observe objects in front of them or behind them, they would no longer be able to measure their forward velocity in the traditional sense as they would not have a reference point to measure their motion against along the collapsed temporal dimension. If for some reason both our astronauts developed amnesia and could not remember their initial velocity, they would have to derive a new way to measure their forward motion as they can no longer physically move or see along the dimensional axis they are traversing at the speed of light. This is identical to how we experience time, as a perceived forward motion, with no reference to the velocity, distance traveled, or physical size along the temporal axis, while existing in three-dimensional space. Thus we are restricted to only being able to see and interact with the objects that co-exist with us at our point in time. The only way we could measure our forward motion through time, is by using a device with a mechanism that can oscillate with intervals of known length along the dimensions perpendicular to the forward motion. If the astronauts recovered from their amnesia, they could remember that they are traveling at the speed of light. And even though they can no longer perceive the dimension in the direction of their forward motion, they could use an oscillator of specified interval, along with the rediscovered knowledge of their velocity, and calculate the distance they traveled. We can also deduce why our space is nearly flat. This is because if the entirety of space is curved, as shown in the image from an earlier post visualizing the big bang, then light would travel along this larger curvature of space. We can only percieve this large curvature as straight lines due to the nature of light. The gravitational lensing from super massive bodies that bends light and show us that space is curved, warps the existing topology of this larger curvature comprising the entirety of space allowing us to see that space is warped. But this does not mean that we should be able to look out through the entirety of space and see this larger curvature. Another way to think about this is from the stanpoint of space being shaped as a sphere. Since light must follow the shape of space and we use light to measure lines, then we would be able to see galaxies and stars on the other side of this sphere. If space didn't expand faster than the speed of light, we would eventually and "theoretically" be able to see the entire history of Earth from start to end (as long as we weren't on the planet when it ended : ) This shows how the universe deals with infinity using a finite amount of space and mass-energy. Law of Balance We can also argue that the primary law of the universe is balance in the form of opposition. Even though we cannot completely prove assumptions based on the law of balance, we can still determine if our thought process is balanced. From this I can state, "The opposite of dimensional axes where I have the freedom to change my speed and direction and where I can perceive size in the form of width, height and length, is a single dimensional axis of space where I do not have the freedom to change speed or direction and where I cannot perceive any physical length along the restriced axis. Therefore, space and time are balanced through opposition. Space gives rise to time and time gives rise to space. They are one and the same no different than how up is the same as down. I understand that this view is more a philosophical one, but the logic can also be applied to science and religion. Science and religion are both philosophies which are opposite in nature. Science demands belief by evidence and religion demands belief by faith. Therefore science and religion are balanced through opposition. Religion gives rise to science which in turn gives rise to religion. But even if the law of balance cannot directly prove a statement, we can show that it holds true for all things. This can be demonstrated in the fact that if there was no up, there would be no down. If there was no religion, a philosophy where belief is governed by faith, then how could science exist? The fact that science demands belief based on evidence shows that its opposite, belief based on faith, must also exist. Because, we could not define one without the other. This is why the law of balance is so important. It provides us with a way to do consistency checks on our logical pathways no different than that of a computer. Swansont could use the law of balance to argue that motionless physics, QM, is balanced by opposition in relation to classical physics where motion is realized. He would be partially correct in that definition. But this is also where balance can be misinterpreted by thinking in opposites and explains why we cannot use it for the basis of a proof. Physics is based on mathematics and from this fact it would be better to say, "Mathematical space, being a set of motionless points, is opposite in nature from motion that moves through these points in space. Therefore, space and motion are balanced by opposition and are one and the same. Space gives rise to motion which in turn gives rise to space. You cannot have one without the other. This may not seem logical to most people. But the truth is that we move through space because all points in space have distance between them. You may try to argue that space can exist without motion but then how could you explain the big bang from the standpoint of a singularity? It is a dimensionless point. There are no other points one could move to and if motion did not exist, there would be no distance between the points in any metric space. Motion can only exist if there are distances between points, so a space that has distance between points implies motion because we now have a distance to move through. It is the same paradox relating to, "What came first? The chicken or the egg?". The only truth is that the chicken and the egg are opposite in nature. Therefore the egg gave rise to the chicken which in turn gave rise to the egg. You can't have one without the other. We call the science the explains how the egg derived the chicken, evolution, and the science of biology explains how the chicken derives an egg. We can infer that if there exists opposites that must simultaneously exist, such as up and down, then there are also opposites that are not simultaneous (one must come before the other). But you still cannot have one without the other. This is what I meant by stating that [math]f(x)[/math] implies motion along the [math]x[/math] or [math]y[/math] axis. This explains "why" the space in our universe is actually expanding. Balance is a binary mathematical relationship that stores information about the existence of any and all things and It would be impossible to store any type of information if the law of balance did not exist or hold true. This is as stated before, without up you cannot have down. The fact that up and down does exist, adds an informational bit to the structure of the universe. But it does not tell us "how" a physical system works or allow us to make statements about the accuracy and precision of the measurements we can make within the physical system. You cannot have physical space with distances between points without motion extending these points, and according to Swansont, QM works without motion in regards to atomic clocks. I asked him to remove all "motion" from the physics for which QM is based on and show that we can still have QM. Even though he may be completely 100% correct in his definitions for QM, if we removed all physical motion, even time, then QM would not exist. Therefore this idea of QM requiring no motion at all to measure time, is not balanced.

An excellent point Bignose. Except we must always consider that the path to living in a hell like North Korea, or any other communist country as such, is paved with good intentions.

Considering that my theory deals with time from the point of view of SR / GR, that it is improper to compare such theory to QM when the theory does not make any assertions to QM. To this date no one person has proved a link between SR / GR and QM that would allow us to make such assertions. Furthermore, the mathematics complements the framework as defined in SR and does not conflict with relativity in any way. Unless the mathematics or the logic can be proven wrong, I recommend that we elevate this speculation to the status of being a valid scientific theory for which will be the basis for the "Principle of Temporal Uniformity". This theory will suffice for the attainment of a simple and consistent theory of the temporal uniformity of rigid bodies as pertaining to temporal displacement which would result in altering the past in any way that would affect the present or allow the transmission of information from either the future or past into the present. The notion of temporal displacement in regards to being able to travel forwards or backwards through time to alter the present is impossible as the view here developed will not allow one to travel through time in such a way that would allow them to view or interact with the same matter and energy from their original point in time. It shows that the notion of being able to travel to any time, that only exists as a memory of the past, or will exist as a memory in the future, is impossible. I must also ask you to consider the attached image I provided earlier. This view of the universe aligns itself with all aspects of mathematical spaces. We can see that the image demonstrates a relationship between three dimensional space to a fourth dimensional time axis. The birth of our universe is centered at the origin of the coordinate system and there is an imaginary psudeo-fifth dimensional axis that goes through the positions of the closed universe singularities due to space-time curvature. The true nature of mathematics is one of recursion and not that of heuristic shortcuts which simplify the equations. We cannot construct a universe from math without including all aspects of which is entailed in mathematics. This can be logically deduced as follows: "Mathematics cannot exist without the universe and the universe cannot exist without mathematics. Therefore the universe gave rise to mathematics which in turn gave rise to the universe. In short, the proof comes from the fact that if it was impossible to do mathematics in a universe no different than ours, then this universe would exist as a paradox unto itself because the beings that inhabit it would still be able to group, identify, count and measure objects that exist in their universe. If the true laws of physics were known by these beings, then they would be able to deduce the existence of other universes and therefore these other universes are observable even if they are void of life. This is a complicated way of saying that every mathematical property and relationship must have existed at time zero or before the birth and expansion of our universe and because life exists in our universe, then the laws that govern life also existed at the creation of the universe. Who am I to say what form this life took before my universe was created when I do not know the mathematics which govern it? The only truth I can derive is that the universe is so perfectly balanced that it is also unbalanced." When you begin to consider all the possible options, whether you believe in a big bang that was created as M theory proposes or any other theory, you have to consider black holes as the source for the big bang. I am working on the mathematics that shows the shape of the universe from the point of view of a spherical shaped singularity, based on the Schwarzschild radius, that exploded along an arbitrary spatial dimension simliar to gamma ray burts, quasars, and pulsars. This arbitrary spatial dimension is the axis of space we call time and the outer edge of the sphere to the center represents the length of the temporal segment. I have already worked out the mathematics that shows the field lines of each layer radiating away from the singularity. Oddly enough this idea is based on mathematics that I have been developing that shows the field lines that light from an image form to reach an observer. I've transfered this concept to the shape of a sphere where we consider the inverse of the mathematics as shown in the image I have attached to this post and allows for the cosmological constant to govern the expansion. The green vectors are all of equal length, the blue lines represent the photon fields, and the purple arcs represent the light we see instantaneously. The triangle represents the observer's field of view. The photon fields extend from negative infinity to positive infinity and have a horizontal asymptotic relationship with the dimension along the width of the screen, or any other geometrical shape that emits / reflects an image. Once I am done, I should have a good estimate for the geometry of space because the photon field lines would represent the space we exist in and I can substitute any geometrical shape in place of the singularity. I will post the mathematics once I am done. The following parametric equation is incomplete but does allow us to produce the image below: [math]x_{\{t,u\}}=t-(I_{y}-u) \frac{t}{\sqrt{t^{2}+I_{y}^{2}}}[/math] [math]y_{\{t,u\}}=I_{y}-(I_{y}-u) \frac{I_{y}}{\sqrt{t^{2}+I_{y}^{2}}}[/math] The variables [math]t[/math] and [math]u[/math] are the parameterized inputs, [math]I_{y}[/math] is the screen's [math]y[/math] position with the [math]x[/math] position being located at zero, and the observer is at the origin.

You are welcome Theresa. I will definitely check out those MIDI instrument packs. I also enjoyed the video and the music. Thank you for sharing!

I'm starting this topic so that we can all share music that we have created and discuss music theory and composition. I play guitar and piano. I use Ableton and Cakewalk to record MIDI and compose my music. I record the guitar audio with a Korg Pandoras Box. I mainly play classical on piano and metal on the guitar. But not the type of metal that most people relate with the genre. I'm not the best musician in the world, nor do I claim to be. I figured that since I know a lot of engineers that play music, that some of you may also and would like to have a thread to share and discuss the science of music. My influences are: On the metal side: Michael Angelo Batio, Yngwie Malmsteen, Joe Satriani, Steve Vai, Eric Johnson, Randy Rhoads, Zakk Wylde, etc... On the classical side: Johann Sebastian Bach, Wolfgang Amadeus Mozart, Ludwig Van Beethoven, etc... Here are a few links to some of the music I have posted on the internet (I must appologize ahead of time for the lack of quality in both the recording and MIDI instrument sounds that I have at my disposal): - This is one of my warmup riffs - This is a song that my brother and I wrote. I'm the guy in the white shirt playing on my Dean Razorback Explosion series axe.A Father's Love - I wrote this lullaby for my two sons, Maxximus and Adam. In The Dark of Night - I wrote this song right after my divorce. I love how emotion drives the music we create. Bewtiched - I wrote this for a chick I know ; ) I am working on recording the metal version of this song. The arpeggios are awesome!!! Enjoy!

My original point can be summarized as follows: When we measure motion, we are actually making a statement about a rate of change in the measurement of distance travelled. For example, to state that we are traveling at 100 m/s, is to declare that one hundred meters will be measured for each second of time measured. This defines a relationship between distance and time in terms of speed. It is a relationship that is expressed as the physical measurement of the distance traveled within an interval of oscillation of known length as provided by a clock. This leads us to the conclusion, that motion in terms of velocity or acceleration, is actually a statement of directional motion compared to a rotational or cyclic motion. This allows us to mathematically redefine motion in terms of frequency times distance traveled per unit cycle, [math]f \times m / cycles[/math], which is exactly what we are doing when we measure motion using clocks. This can be demonstrated using dimensional analysis as follows: [math]v = \frac{m}{s}=f \times \frac{m}{cycles}[/math] [math]f = \frac{cycles}{s}[/math] [math] \frac{m}{s}=f \times \frac{m}{cycles}=\frac{cycles}{s} \times \frac{m}{cycles}=\frac{m}{s}[/math] [math]time=s=\frac{cycles}{f}[/math] Where [math]v[/math] is velocity, [math]cycles[/math] is the number of oscillations, [math]f[/math] is the frequency of the oscillation, [math]m[/math] is meters, and [math]s[/math] is seconds. Before we can interpret our motion through time as having a velocity, we must understand what it means to have velocity. This is because we measure our motion through space with respect to our motion through time. Therefore, when we try to measure our velocity through the temporal dimension we can only obtain a normalized velocity of one. This is a result of how we measure speed as a change in space over a change in time and, according to relativity, is the same as measuring a change in space over a change in fourth dimensional space. We could use any dimensional axis as a replacement for time. The only difference is that we have the ability to change our speed and direction in the other spatial dimensions, creating consistency issues with this pseudo-temporal dimension. This leads us to the conclusion that, even though motion through time is the same as motion through space, we cannot measure our speed through time in the same manner that we do for space as a result of [math]dt / dt[/math]. This is why we are forced to measure motion through time using constant oscillations of known intervals. Oscillation allows us to normalize our measurements of motion through time. The fact that we measure time in seconds is irrelevant because this unit of measurement is just an interval of oscillation that we have created to measure the passage of time. A second could have lasted for any length of duration. However, it is the relationships imposed on these measurements which are important as they define the mechanics that describe the universe. The mathematics I posted near the beginning of this thread supports this notion of time as demonstrated in the attached image from my post above yours: We can see from the attached image that the observers, at [math]\tau_{1}[/math] and [math]\tau_{2}[/math], would radiate away from the big bang frame of reference at the speed of light frozen in place along the temporal segment. We can show that the space-time vectors, with the head at each observer's position and the tail remaining at the center of the singularity at time zero, is equal in magnitude. This means that no matter how fast each observer moves in directions perpendicular to the axis of time, each observer will remain "radially" frozen along the temporal segment radiating outward from the big bang frame of reference at the speed of light, with a relative temporal velocity of zero with respect to each others frame of reference as shown by the mathematics. The result of which does not refute the possibility of temporally displaced mass-energy. This is because the magnitude of the space-time vectors as defined from the big bang frame of reference to the observer's frame of reference, can be used to determine which "universe" the observer is located in. Furthermore, because I related all three frames of references to each other we can use the following relationship to show that even though both observers experience time differently, they are moving through time equally from the big bang frame of reference. From the big bang frame of reference, both observers place themselves in the time-normal frame of reference placing the other in the time-relative frame of reference. So from the big bang frame of reference both observers have a zero relative velocity, [math]V_{r}=0[/math], and experience the time equally: [math]\Delta t_{b} \sqrt{1-\frac{V_{w}^{2}}{c^{2}}-\frac{0^{2}}{c^{2}}}=\Delta t_{b} \sqrt{1-\frac{V_{w}^{2}}{c^{2}}}[/math] However, I do not imply that this proves that mass-energy is temporally displaced. Therefore, I have provided science with a way to test this hypothesis: Have I not followed the scientific method? I base my claims on existing characterizations of the subject matter being discussed as SR and GR deals with space and time. I stated a hypotheses about a theoretical notion to the nature of time. I derived mathematics from which lead to a prediction which can prove the hypotheses true or false. And, I have submitted my theory for peer review so that scientists, astronomers, and cosmologists can conduct experiements based on my predictions.

If we look at the second half of my hypothesis in regards to temporally displaced mass-energy, we must consider the big bang and the metric expansion of space. The following image from wikipedia inadvertently demonstrates temporally displaced mass-energy: From this view of the universe we can see our own unique history radiating away from time zero of the big bang. The vertical slices in the image above are different points through the fourth dimension, time. We can also view the vertical slices as temporally displaced parallel "universes" all co-moving at the speed of light in a uniform direction through time. These "universes" would just be different views of our single universe. Each universe would have its own unique history because any observer located along the temporal axis could record events using space-time coordinates that would be unique to their view of the universe. We could also show that time should be bi-directional. Even though SR may not perfectly describe the metric of space, we know that it involves functions that specify a rate of change that includes square roots. Mathematically, square roots have two solutions. However, it is customary to choose the solution that satisfies the physical system. If we make a conjecture that the big bang expanded space in a similiar manner that a gamma ray burst, or quasar radiates energy into space along both directions of an arbitrary spatial dimension, then we can interpret the results of the mathematics by introducing positive and negative time as shown by an image I produced to visualize the concept:

I am assuming that all of this takes place in three dimensional space. The next question is, am I allowed to increase the number of spatial dimensions?

Am I restricted to using identically sized spheres? And by densly packed are you refering that all spheres must make contact with adjacent spheres or can they just touch spheres located near each other?

For anyone wondering what started this debate in regards to the inference of motion, I have pasted the hypothesis from the original post below:

Sure it is when you consider that you cannot, with 100% certainty, measure the length or position of such object. This can be shown with the laws of thermodynamics. Since a body's temperature affects the QM state of the atoms, the matter either contracts or expands. So the length of the body is in motion with respect to temperature. You would not only have to calculate the length and trajectory of the body from your choosen frame of reference, but you would also have to account for QM affects to even be able to determine the center of mass for the body to be able to tell me the object's true position or size in relation to your choosen coordinate system. I have not described motion using any form of classical physics. I never said that position, length, or any other quantity can be determined absolutely. That is an assumption you made by not clearly reading my posts. It may be that I have not properly explained myself. Regardless of your stance, you cannot dismiss my claims by stating such things without demonstrating why or how I have used such notions in physics in a classical, non-modern way. Also, you have not shown any mathematics to support your claims. Am I to believe that you are free from the burden of proof and that this only applies to me or anyone else that proposes theories that might not necessarily fit within your current views on Physics? My point is simple in that QM uses a metric mathematical space which represents our physical universe. Because physics makes assertions and claims using the abstraction of mathematics, you cannot say that [math]f(x)[/math] does not imply physical motion. This is because the input [math]x[/math] implies motion along the [math]x[/math] axis of the mathematical space that QM uses to describe its processes. Therefore we can infer motion from functions operating in mathematical spaces that represent our physical world. I could use any physical process, classically defined or accepted by modern science, and still arrive at the same conclusion regarding motion. Motion is still infered even from your own arguments of the deBroglie matter wave as you cannot describe the deBroglie Matter Wave without velocity or any other form of motion. This implies that motion is still an integral part of QM from which you cannot ignore or get rid of by dismissing my comments. And, the Heisenberg uncertainty principle is only true because motion exists. We cannot relate such simple HS mathematics to the mechanics which describe the laws of nature. When dealing with abstract notions of a definite static length, position, or any other classically defined notion, we must accept that these are pure mathematical abstractions and cannot be used to describe the universe with 100% certainty. Plus any mathematical functions you choose to describe a physical system are inherently bound to describing the rate of change for such functions with respect to the input or output of the function. Let me clarify a relevant point on the topic of rates of change. When looking at any form of [math]d?/d?[/math] with the concept that this rate of change represents a physical process, then the mathematical construct which represents the rate of change becomes a description of physical motion whether it is related to time, temperature, or any other physical quantity. I understand that you are referring to motion as defined below: However, I must ask you to consider that we can infer motion in relation to time even when stating rates of change that do not describe its motion or change with respect to time. This is because, as mentioned in Wikipedia, motion signifies any temporal change in a physical system. Therefore I can imply that any physical rate of change is motion in relation to time regardless if the physical rate of change uses time or not. Because you relate motion with respect to time is irrelevant. I can relate my displacement along the [math]x[/math] axis to any other physical quantity because the physical system from which this quantity is defined relates such quantity to time. This means that I could use the rate at which a given species of bacteria reproduces as the basis for my time keeping device. Therefore I can relate my [math]x[/math] position to the number of bacteria in my time keeping device. I can also relate any other physical quantity to the [math]x[/math] position of a car that I am riding in instead of using time. I could state that for every meter I travelled along the [math]x[/math] axis, that I measured a displacement of two meters along the [math]y[/math] axis. The reason why we do not do this is because we cannot derive consistent relationships which can describe such mechanics in an accurate and precise way. This is why time works for our purposes and gives us an explanation as to why we can always describe rates of change with respect to time. This is because regardless of our frame of reference, we cannot choose a coordinate system where motion through time can no longer be implied. If you claim that you can, then by all means go live at a position defined by that coordinate system. You will live longer : ) So my statement regarding motion still stands: Unless you can show that you can define the wave function without using any form of metric space and functions from which we can infer motion through that space, then the above statement holds true. Time can be considered as motion through a spatial dimension no different than the other three observable spatial dimensions. The only reason why we relate motion to time is that we are expanding with the big-bang through all spatial dimensions. We can deduce that we move at the speed of light through the fourth dimension. I explained this near the top of this thread. Plus, AJB was nice enough to demonstrate how we can arrive at my same conclusion using physics that I have yet to learn. From the big-bang frame of reference, a coordinate system that is always positioned at time zero in the center of the big-bang, we can deduce that we move at the speed of light through the dimension of time. If we choose this coordinate system, we can state that the space we are moving through is stationary or vice-versa. This means that the Lorentz contraction would have collapsed the dimension of time to having no perceivable length. This explains why we are unable to see the objects temporally displaced from our position in time. It also gives us a reason for why it is nearly impossible to displace our position temporally due to the constancy of the speed of light. Plus, if mass-energy is temporally displaced it would move at the same rate as we do through this fourth dimension of space. There is one way to test this theory. If we observe a star that wobbles as if locked into a binary star system and we cannot detect this other star, then based on the wobble of the star to rule out any other cosmic possibilities we can determine if mass-energy is truly displaced temporally. Otherwise, it will either require a consistent theory of quantum gravity or solutions in cosmology that solves the dark matter, energy, and flow problems, to prove or disprove this notion. Even though my knowledge of physics may not be equivelant to yours, you cannot deny the logic in the statements I have made in regards to motion and mathematics. I know that you all do not know me very well and, as such, I must prove myself. When I find some extra time, I will post some of the mathematics that I have derived. I mainly work in game theory, probability and statistics, and finite calculus and numerical analysis as required by the industry for which I have based my career. You are more than welcome to read about it in my profile. On a seperate matter, how often do you get a theory proposed in the Speculation group where there is math to support it and the author provides a way for you to check to see if the second half of his hypothesis, temporally displaced mass-energy, is true or false by observing the motions of stars in the heavens?

Plus you have to be able to show why this is false The short hand version is that [math]\frac{dx}{dt}[/math] is no different than [math]\frac{dx}{dy}[/math], or [math]\frac{dx}{dx}[/math], and you cannot define a function, [math]f(x),f'(x),f''(x)[/math], etc... such that I am unable to infer motion as a rate of change along the axes of the specified mathematical space. This would mean that you would have to be able to describe QM without a mathematical space and use functions from which I would not be able to infer motion.

The input variable [math]x[/math] implies motion along the [math]x[/math] axis. Remove the motion of [math]x[/math] from the equation and you lose the input for which you are relating to the [math]y[/math] axis. Therefore, [math]sin[/math] looses meaning. It not a matter of physics at this point, but one that specifies motion is nothing more than a measure of a rate of change.

It is his repsonsibility to uphold his end of the debate. I showed mathematically how we can infer motion when he insists that motion is not inherent. I have upheld my responsibility to defend my statements. Now he must also defend his statements. I am not repsonsible for proving him right. Or are we to just take one persons word, without evidence, as scientific fact? It may be that you do not fully realize the scope of my statements concerning mathematical spaces or you would have posted a counter argument showing how I would be incorrect. Since you responded in such manner as to infer that I do not understand mathematics or have not defended my statements, then I suggest that you read the entirety of this thread.

This time I will sit back and see if you can respond to my previous post. I have provided more than a fair share of math to support my theory when you have not even provided any that supports your claims. Plus you seem to be ignoring any factual statement I've made about motion. So I'm still waiting for you to explain QM to me without using a mathematical space or any function from which we could infer motion. Good luck! You know that you cannot, which is devastating to any counter argument you may present. Otherwise, you would have posted a reply regarding such notion dealing with mathematical spaces.

As long as you can define the wave function mathematically, then yes it is in motion. Refer to the explanation below as explained from the previous post. If you read through my posts carefully you would realize that I never stated that electrons are particles and the fact that you refer to oscillation infers motion. Remove said motion from your system and I guarentee you that your system will collapse into meaningless results.

Then please by all means, explain how processes in QM can be driven such that motion is not part of these processes. I do not claim to understand all of QM. So I would be more than happy to learn how QM handles physics without motion of any kind. If you claim that state changes are what drives this system, then wouldn't the changes in such states be considered motion of state vectors? Otherwise, if this motion of changing state also did not exist, then how could QM describe its processes? You are referring to a wave right? How could such wave even exist if motion was not inherent in the process. You might as well try to convince me that waves do not exist. It's not as though I stated that these electrons could be found easily and must be particles. I was just making a point towards why the Heisenberg Uncertainty Principle is true. A standing wave is one that oscillates in place, no different than that of the head of a drum. Try convincing a drummer that a wave has no motion to it and he'll ask you if you can feel the beat from his double-bass drums. This is not true. Read the entirety of this thread. I provide mathematics that supports my theory. Plus, it is simple to deduce four dimensional velocity as AJB was so nicely able to demonstrate for me in conjunction to my own method: I also mean no disrespect to your views on QM. You may very well be completely correct in your argument. If so, I only ask for proof so that I may align my way of thinking towards the facts. Otherwise, it will be quite difficult to convince me that motion does not exist or that it is not inherent in time. I will also require time to take in whatever mathematics that you have in support of this. Once I can pose an educated response to your theories and that of QM, we can take the debate further. After a little thought, I managed to come up with a way to show that motion is in integral part of any mathematical space. For any function that takes at least one variable as its input, infers motion through the space for which such function is defined: [math]f(x)=c[/math] [math]f'(x)=0[/math] or [math]f(x)=x^{2}[/math] [math]f'(x)=2x[/math] This is because any such space that the function operates within, must allow the function the ability to at least change position with respect to the either the input or the output. Thus a change in space versus a change in time, [math]\frac{dx}{dt}[/math], is no different than a change in space versus a change in fourth dimensional space, [math]\frac{dx}{dw}[/math]. And even if you claim to only operate in one dimensional space, I can still infer motion through [math]\Delta x[/math]. Since you cannot derive mathematics for QM that uses no inputs and has no mathematical space, I say that you must concede or provide an explanation of how QM can operate without any form of mathematical space and does not make use of deltas [math]\Delta[/math]'s, derivatives, or any other form of function from which we can infer motion.

Nicely done swansont. However, I still stand by my statements for motion. Even if inferring motion is a naive interpretation of physics, we still cannot deny that it is motion that drives these processes. One clue to this is that you state, "During the oscillation, it is in a superposition of the two spin states". You are refering to oscillation which is nonetheless motion. How would the state of such QM systems progress if motion did not exist? If there were no spin, orbits, oscillations, or motion of any kind. To say that motion can be dismissed would seem to lack foundation as well. I am aware of timeless physics. But even here we have motion being described on how we perceive the snapshots of time that we progress through. Which goes back to my clarification: It is because of the reasons stated above that the Heisenberg Uncertainty Principle is true. Otherwise, we would be able to measure such things both accurately and precisely.

If you are referring to how a particle can seem to be in two places at once, then refer to the definition of motion as provided by the Merriam-Webster dictionary: Definition of Motion Particularly that motion is an act, process, or instance of changing place. Nothing was mentioned about the final location(s) of the body in motion or that it must do so in respect to time. If this is not what you meant, then please be clear as to what you mean by your statement, "that is doesn't work like that". How else are we to debate the subject matter if we are to make vague statements without showing how the other is incorrect with a valid argument or proof. If you are suggesting that motion does not exist in QM, then I would have to refer you to: Wikipedia - Motion So my statement about the motion of the electron still stands. Because if the electron was not in motion at all, and even if it was expressed as a wave without a definite location, then we would still be able to easily find them. The fact that the motion of the electron is such that it is impossible to measure both location and momentum, shows that motion is at the heart of the internal workings of QM. This can be viewed from the point that if electrons were not in motion, then I would be able to infer their location and momentum based on the process I used to measure the motion of the electron. However, since electrons are in motion, I am unable to make this determination because the process I use to measure such motion will affect both, the location and momentum of the electron. Therefore making it impossible to simultaneously know both the location and momentum of the particle.

Good point. However, if the electrons did not move, they would have a specific location and be easily found. Since this is not the case, we can infer that they are in motion.