Time

• Dinesh Bhagwan Hanchate asked a question:
New
Which are the various methods of multiplication and their time complexities?

New
Raster plot representation for neural spikes ?

I am analysing some neural spike data. It is in an array, with each value being the time at which a spike event occurred, I want to be able to display an x-axis of times,and draw a raster plot when a spike occurred Does anyone know how I might achieve this using  MATLAB? Thanks in advance

4
Are there any publications operationally defining a limp according to a cutpoint in the difference between left and right foot stance times?

For example a >10% difference in left vs. right stance time = limp

This question was initiated relative to a potential retrospective study utilizing a large sample of barefoot walking plantar pressure measurements from an Emed (Novel) system collected from a variety of patients in a clinical setting.  We want to exclude people from the study that had a significant limp and use the pressure data to do so.  However, I have not seen a specific threshold (X% difference in stance time, peak force, etc) used previously for discriminating people with vs. people without a limp.  Although the question was initially posed relative to stance time, many other variables could be used (peak force, force-time integral...).  We're just looking for an established level of asymmetry for categorizing people as to whether they did or didn't have a limp.

5
How to calculate LC50 and LD50 value of different concentration with different time interval?

while using fish for mortality studies

As said probit analysis helps you to calculate LC 50. SPSS is of helpful in this kind

92
What caused space and time?

Space and time don't exist obviously without matter. The assumption is incorrect respectively wrong that space and time are objective present or existing and the matter only overmoulding or modelling space and time. Space and time are products or effects of the objective existing matter. Insofar Einstein was putting the cart before the horse.

In mathematics you can assume or conceive an objective and infinite space and time. But nowhere in universe you can find the same conditions or properties for the space and nowhere is a clock that shows an universe-time. If you could leave the earth, space and time would modify and you couldn't perceive because you take part on the changes.

Our thoughts are determined by terrestrial clearness, mathematical ideas and many unproven theories. I can't share the view that the reality is nearly recognized.

January 30, 2016, is the deadline to submit your keyword search (see linked article). I do not have anyone from the research community who has submitted an entry yet? I wonder why?

If you wish to participate in this quick and easy keyword phrase search, here are some links to get you started. Pick some, all, or from the many other available resources online, your choice:

http://education.iseek.com/iseek/home.page
http://www.ojose.com/
http://www.scirus.com/
http://www.dmoz.org/
http://www.dogpile.com/
http://yippy.com/
http://www.metacrawler.com/
http://www.mamma.com/
http://www.info.com/
http://www.msfreckles.com/index.php?lang=en
http://www.infotopia.info/
http://www.educationworld.com/a_tech/tech001.shtml
http://tools.niehs.nih.gov/srp/publications/highimpactjournals.cfm
http://www.scimagojr.com/journalrank.php?country=US
http://www.sciencegateway.org/rank/
http://iopscience.iop.org/
http://ips-search.thomsonreuters.com
http://www.refseek.com/
http://eric.ed.gov/
http://citeseerx.ist.psu.edu/
http://www.getcited.org/
http://www.bioline.org.br/
http://www.doaj.org/
http://www.plosone.org/
http://www.bioone.org/
http://iopscience.iop.org/1468-6996/
http://www.sciencedirect.com/
http://www.virtuallrc.com/
http://www.refseek.com/
http://libguides.com
http://www.citeulike.org/
http://www.base-search.net/
http://www.archives.gov/research/catalog/
http://www.sweetsearch.com/

• Source
Article: How Students And The General Public Can Confirm If Quantum Mechanics Is A Fundamental Theory Without Opening A Book
[Hide abstract]
ABSTRACT: Abstract: Grade school, high school, and college students as well as the general public are invited to verify if the scientific method needs an overhaul by simply doing searches for the keywords "direct selection" and "indirect selection" in peer-reviewed scientific papers. In doing so, the public will be able to confirm if experiments used to validate quantum mechanic theories are based on a fundamental omission error or not. The attached "Flawed Scientific Method" document was designed to go with the public invitation to help science self-correct. In essence, this one page document illustrates the mechanics of the discovery of Einstein's nonlocal hidden variables which in turn revealed how the scientific method is flawed and how to fix it.
Full-text · Article · Sep 2015
• Hemamala Krishnan asked a question:
New
Looking for some help in resolving a bug in my System Dynamics Model. Could anyone help?

I use iThink software for modeling. I need some help in resolving a DT issue. Would like to discuss through mail. Looking for someone very comfortable modeling using this software with some time to spare. Please help.

• Nguyen Minh Dien asked a question:
New
Find estimate for $u_x$ on nonlinear heat equation?

We are studying nonlinear heat equation: $u_t=u_{xx}+f(x,t,u,u_x); (x,t)\in (0;\pi)\times(0;T)$ on the conditon $zf(x;t;z;0)\le az^2+b$ or $f(x;t;p;q)\le a(|p|+|q|)+b$. I want to know that $|u_x|<M \forall (x,t)\in (0;\pi)\times(0;T)$ or not?

2
Is it possible to intercept a time reversal RF communication ?

Time Reversal (TR) is often used in RF communication as it enables space time focusing of EM waves. Time focusing is an interesting property because it  reduces intersymbol interference. Spatial focusing on the intended receiver is also interesting because it implies that the communication has a low probability of intercept (LPI) by another receiver located nearby.

My question is: is it nevertheless possible to intercept and decode a TR communication?

In TR communication, the emittors encode their signals using the complex conjugate of the time reversed impulse response of the communication channel between them and the receiver. Interception means that a spy may catch these signals at a different space-time place than the receiver. The code will then not be suited for this spying receiver and the arrival times of all the signals from all the emittors will be altered, implying additional distorsion.

If the spy is close to the receiver, then the spy's channel is not so different from the normal channel, and its impulse response may be a simple small variation from it.

But what if the distance is larger? Is it possible, knowing the relative positions of the emittor, the receiver and the spy, for the spy to reconstruct the signal?

Amrit says: "Time is not reversal........time does not run at all. Changes run and time is their numerical order."

Finally, I heard somebody saying that which I have been shouting for three hundred years!

More about my view of time can be found in my paper "On the Nature of Time" (on RG). Needless to say, my paper was rejected (in a hostile way) by several journals to which I submitted it.

Somebody recently wrote (somewhere on web) the following statement: "The best treatment of time I have seen is by Mario Radovan of the University of Rijeka, Croatia. I suggest you read him. Do a google search for his essay "On the Nature of Time".

However, a huge majority of "experts" refuse to think in the way Amrit suggests, and which I advocate in my paper

Anyway, I rounded up my story about time; I now write about communication, which is part of my professional activities. Time was a matter of passion & curiosity.

99+
Is the flow of time an illusion?
This has been discussed on ResearchGate in a rather ad hoc way in relation to another question about the absolute immutability of some physical laws but it really deserves its own separate discussion. Below I summarise the arguments in favour.
The philosophers
The nature of time has been the subject of discussion by philosophers for 2000 years or more. In the last two decades their views have crystallised. If time flows - (1) How do we know? and (2) How do we measure its speed? In other words - what frame of reference can we use to measure time?
The philosophers' conclusion is that they would have to invent another time dimension for the purpose but this would then need a third time dimension and so on ad infinitum. This would be absurd and so they conclude that the flow of time is an illusion.
Relativity, Einstein and Godel (A World Without Time - Palle Yourgrau - Penguin Books, 2005)
According to the theories of relativity two observers can never agree on the simultaneity of two events that both witness and neither has a "preferred" position that makes one of them correct. This implies that all events already exist and that what we perceive as the flow of time is an illusion.
Godel showed that rotating universes were consistent with relativity and proved that in them it was possible to travel back in time. He immediately realised that this implied that the past must still exist and that what he called "intuitive time" is therefore an illusion. In 1949 he published a formal proof that time (in our intuitive sense) cannot exist in any universe. This uncomfortable discovery was ignored for nearly half a century but was revived by Julian Barbour in "The End of Time" and is now widely discussed and accepted by many physicists.
The Laws of Physics
The fundamental laws of physics describing the forces are time-symmetric.
What can we say about the time dimension?
Time still exists but only as a chronological map in which events are located;
Time is not in any way like the spatial dimensions because:
It is anisotropic and contains an entropy gradient;
If we exist in more than one location in any of the spatial dimensions then we will also always then be in different locations in the time dimension;
Separations in 4 dimensions are extensions of Pythagoras's Theorem but have the form:
separation = √[x2 + y2 + z2 - (ct)2], which means that time measurements are imaginary (ict) where i=√(-1), as Hawking suggests in "A Brief History of Time".
Consequences
Free will is also an illusion
We live all our lives all the time but every instant feels like "now"
Time travel is impossible because (a) there is no dimension in which travel is possible, (b) we occupy all the spacetime of our lives and cannot take back to an earlier time our memories of a later time.

@ Steven: As far as I can see (I have read a paper entitled Is there an alternative to the Block Universe View'' by Petkov, no more). there seems to be a misunderstanding concerning what the past is: it appeared to me that some philosophers argued that, whenever the time coordiinate of one event A is less  than that of another event B, then A is in the past of B. A paradox then arises from the fact that, depending on viewpoint, A may lie both in B's past, and its future, according to that definition.

Hence my post: I argued that the correct definition of past and future should involve the past and future light cones. This distinction *is* observer independent, and thus leads to no paradoxes. The past and future are then separated by events of which it makes no sense to say that they are either in the one or in the other, since they may have no kind of influence whatever on the present. We thus need not, and in my opinion should not, include them in any kind of future/past dichotomy. This was also the origin of my argument, that the possibility of influencing the present causally should characterise the past, and the opposite should define the future.

I have said rather explicitly that I am wary of making existential statements, as I have no  clear idea of what existence means. But we are aware of the slap in the face we are experiencing right now in a qualitatively different way than we are of that of yesteryear, or of the one we anticipate receiving tomorrow. If such a difference in the awareness level may be taken to mean a different existential status, then I would assume that the present (approximate, say within a few seconds) exists in a different way from either past or future (let alone the unattainable region).

The past, however, does have its own objective mode of being. We may not live the past, but we also cannot change it. In that sense, it is what it is, and cannot be made otherwise. I am reluctant to call it wholly inexistent. This is surely a reflection on my inability to deal coherently with such issues.

As to Godel's Universe, it concerns a Universe with rotation and with cosmological constant. It is a well established experimental fact that our Universe does not rotate and that the cosmological constant has an extremely small value. Further, it should be added that Godel's Universe contains no timelike closed geodesics: free particles do not travel in time. It is possible to travel in time, but one needs to use forces.

Summarising, Godel's Universe is a mathematically consistent one, but there is no reason to assume that this potentiality is actually realised in fact. Even if it is, it need not follow that conscius beings could ever travel in time. Further, I somehow doubt that a complex universe, like ours is, in which the entropy concept makes sense, could allow for closed timelike curves. I should, by the way, correct my earlier statement: Godel's Universe is, in fact, rather realistic, since it corresponds to a Universe with constant matter density.

@ Sergei: I was answering the initial question, and remain content with such a limited understanding of time as I happen to have. I apologise somewhat for not reading your paper. However, I do not promise I shall do so any time soon.

4
Can anyone help me get the list of ISO-14001 certified companies in the UK?

I am collecting Data from ISO-14001 Certified Companies in the UK. If you know the source where i can get that list or if you have any list of ISO-14001, please do let me know.

I appreciate your time and help.

Sincerely Yours,

Abdul Ali

Dear Hannes Krieg,

10
Is the time derivative associated with a system is always the same as that associated with a cotrol volume?

control volume,Reyonld transport theorum

That link is on audio. The question in on fluid dynamics.

Aziz

2
How can I find out the expression for rate of propagation for a particular reaction?

I need to find out rate of propagation in the expression of time for the following reaction-

P(i) + M   = P(i+1)    where rate constant is Kp

P(i) - Polymer chain attached with 'i' monomer

M - monomer

uSE THE EXPRESSION:

Rp= Kp[M][P(i)]

7
How can I get the time (hour:minute:second) that MODIS image was captured for an area?

I work on MODIS data, and want to know the time for the scene i work on, i found the day only, but couldn't deduce the time.

Ha, sounds good. You are welcome~

3
Can someone suggest review literature and mentions about time discretization?
I would like to get basic knowledge in this topic at least basics. Because I'm new in this field I don't know what is a better way to start. Could anybody suggest any reviews and books on such a topic, or at least where it was mentioned and discussed?

A new approach to the correction of Galilean transformation.

8
Why did authors still concentrate on difference equations and differential equations instead of dynamic systems on time scales ?

Why did authors still concentrate on difference equations and differential equations instead of dynamic systems on time scales ( As a generalization of both of them) ?

There are alternative approaches appart from time scales calculus. There are mathematical techniques allowing to combine (relatively) slow and fast processes in a single sistem, that means a time scales model. Please, find below references related to difference and differential equations (ODE - autonomous/nonautonomous and PDE).

Reduction of discrete dynamical systems with applications to dynamics population models. Mathematical modelling of natural phenomena. Vol 8(6). 2013. 107–129

Aggregation of variables and applications to population dynamics. In: P. Magal, S. Ruan (Eds.), Structured Population Models in Biology and Epidemiology, Lecture Notes in Mathematics, vol. 1936, Mathematical Biosciences Subseries. Springer, Berlin, 2008, p. 209-263.

Reduction of nonautonomous population dynamics models with two time scales. Acta biotheoretica. DOI 10.1007/s10441-014-9221-0

2
What are the method for conservation of cyanobacteria for a long time?

What are the method for conservation of cyanobacteria for a long time?

Dear Soumia

I have attached some valuable papers, might be useful for you.

1. Algae and cyanobacteria: isolation, culture and long-term maintenance by J. Acreman in Journal of Industrial Microbiology; May 1994, Volume 13, Issue 3, pp 193-194. (link: http://link.springer.com/article/10.1007%2FBF01584008)

2. An Efficient Protocol for Long-Term Preservation of Cyanobacteria by Mayashree B Syiem* and Amrita Bhattacharjee in Journal of Advanced Laboratory Research in Biology; Volume I, Issue I, July 2010.

3. H. K. Park, “Long-Term Preservation of Bloom-Forming Cyanobacteria by Cryopreservation,” Algae-Inchon., Vol. 21, 2006, pp. 125-132.  http://dx.doi.org/10.4490/ALGAE.2006.21.1.125

Regards

Abhishek raj

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4
Can we consider " Time " as an assemblage? and how can it be discussed in the area of technofanatsies and posthuman?

An detailed perspective of how "time" could be talked in these areas is needed, and some possible examples for understanding is also pleased.

How we can image time or speak about it without using a clock?
Time is only the name of ticking of clock. Does time has arrow? yes, it has, but time gets arrow from clock.

1
P300 based speller design - Is Row column information necessary ?

Is it possible to classify the character without knowing the row-column information?

p300 signal is generated when human are looking at flashing light. From the EEG signal correctly detection of p300 is important. After detection of p300 our job is to find what time this p300 signal generated and at that time instant which row or column flashed. From this row-column combination we can get the original character.

Now if I don't have the row-column information. Is this possible to detect the character from EEG signal?

Sourav ,if  Row column information works, learn from it. However, you can also try ellipses, hyperbolas, and the form of the Spirals of the Milky Way. Since I am totally ignorant of your way, All I can and will do is to  encourage you to answer your question yourself and become in the process a successful Scientist! It worked for me and many others. Cheers, Ingo H. Leubner Dr. rer. nat.

10
Why does my silver nanoparticles wavelength decreases after 120 days from 455nm to 435nm?

I prepared silver nanoparticles and I checked UV-Visble spectroscopy at that time I found absorption maximum for silver nanoparticles at 455nm after 120 days again I checked at that time I found the absorption band at 435nm. For this solution zeta potential is 35mV. Reason for wavelength decrease? Generally wavelength increases means new particles formation takes place but decrease means?

You can check the particles stability by either DLS or TEM to be sure.

3

I have to apply a displacement on frame which is varying with time and it is cyclic. I have midas FX+ Modeller

I have applied cyclic loading as a base function command (displacement varying with time). I did nonlinear analysis, so i used time steps. But after analysis, the displacement is not showing to and fro motion. I have attached the pictures for reference

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99+
How you organize your work and time?
Do you plan things out in microdetails or you are a spontaneous person?

When we know what the priorities in our specific conditions are, we will see how to organize our work and time, which can change for the same person, from a time to time.

63
A question on Time as an emergent property
Time can be viewed as an emergent property : whenever any change occurs anywhere in the universe - in other words whenever the state space of the universe undergoes any change - then Time itself happens and 'notches up' one tick (at least in the 'neighbourhood' of the change, which is a separate discussion.)

But isn't this circular reasoning ? For a change in state space to be able to occur in the fist place, isn't the pre-existence of something like time a prerequisite ?

The only way out of this conundrum is that all elementary state space changes must happen out of time, i.e. instantaneously (with a delta time = 0.) But this would then require the superimposed coexistence of 2 elementary state spaces. Can this happen ? We could probably engineer a situation where the Pauli exclusion principle would then be violated. This would tend to prove that Time as an emergent property cannot be the whole story?

Matts,

"You need not agree with him".

Of course, I only ask for comments as it is an interesting hypothesis of the origin of "time" and such an hypothesis, if true, would mean that it is quite possible to envisage a timeless world (lets' think of the "big bang" state).

32
Before the big bang, did time exist? If it did, is time invented by man or God's creation?
I believe time is a measure of duration, and man invented clock to measure time. Therefore there should be an empiricism that explains the time that dark matter and dark energy existed before the big bang

Hi,

Yes indeed,

Time has been invented by man. However, we can replace the time indicator of Universe dynamic by the matter density. In some sense the density correlates with time. Therefore, we can assume that in the beginning the density was equal to zero (no matter existed), and the singularity problem disappears. It can be like some energy field existed before the density in some point in energy field suddenly transforms into matter of positive density – known as initial inflation phase of the Big Bang. Thanks

3
Does anybody know about recent good articles on the changing perception of time and space in the digital world (interdisciplinary welcome!)?
I am looking for different approaches from neuroscience, philosophy, communication science, sociology etc.

Miriam: Not sure if it is of any use to you, but I have explored the limited information rate for perceiving novel information, from the perspective of information science, i.e. bits per second:

3
How can I analyse correlation in Panel data analysis?

Can anyone help or guide on how to analyse correlations of variables in Panel data analysis  I have to remove few variables(both time variant and  time invariant)  to improve Adjusted R(square). I am using R .

I would start with a pooled matrix, which would basically look at the fixed effects variables of your model. You could certainly go beyond that, but I am not sure how easy it would be to interpret the correlations at various time points in the broader context.

6
A mental time travel?
There is connection between thoughts past, present and future?
15
Could gravitation have affected evolution of DNA ?

Hi, I am wondering whether evolution of DNA molecule would have been influenced by the gravitational curvature of space-time continuum giving DNA molecule a double helical shape. Any comments are welcome.

Dear Professor A. Sepehri ,

Thank you very much for your lively, interesting and valuable discussion. Some fields of science particularly related to cosmology/astronomy are largely ignored. One of my research paper entitled ' EVOLUTION AND RELATION OF MICROCOSM AND MACROCOSM' showing correlation between Genetic Code and Solar System is posted on ResearchGate. I am sending you the Link

• Source
Article: EVOLUTION AND RELATION OF MICROCOSM AND MACROCOSM
[Hide abstract]
ABSTRACT: ( Excerpts from my research paper "EVOLUTION AND RELATION OF MICROCOSM AND MACROCOSM" with edition ) The present study implies that the two parts of nature, biological universe and physical universe, are intimately correlated, a fact which has always been overlooked. The investigation points out a definite correlation between the organizational plan of DNA molecule and cell during organic evolution and the organizational plan of our Solar System during inorganic evolution. The following equation showing the correlation between the genetic code and the apparent motion of the Sun, due to Earth’s revolution around the Sun, has been derived by me during the present investigation. (64 – As) / 20 = 339 / 107.65 Where, 64 = Number of codons 20 = Number of amino acids As = Astromolecular constant i.e. 1.013, derived during the present Investigation 339 = Number of disks of Sun to measure its apparent path along the ecliptic in Celestial sphere between the two equinoxes . 107.65 = Average distance of the Sun in terms of its own diameter All living organisms on the earth share the same 64 codons and 20 amino acids. The above equation correlates the molecular data with the astronomical data implying a common organizational plan of the DNA molecule and our Solar System probably due to the influence of a common governing force i.e. Sun’s large gravitational force.Also the nebula shaped like DNA and biomolecule DNA both might have been formed and shaped under the influence of universal gravity. The genetic code made up of DNA, acts as an intracellular computer for the structure and physiology of the cell and governs the embryonic development leading to the formation of the body plan of the organisms. The data of the present investigation clearly show that the microscopical numbers i.e. the number of codons of the genetic code, number of amino acids which are common to all organisms, are functions of the astronomical numbers as shown in the above equation derived. The genetic code works as an intracellular computer which governs the organization of the cell and nucleus and the phylogenetic evolution of living organisms. This intimate correlation found between the biological and physical universe during the present investigation, and the electron microscopic structures of different types of cells and tissues observed during my studies and their comparison with telescopic pictures of the universe taken by me and many astronomers, have led me to hypothesize that the physical universe is like a living system or organism. The phenomenon of accretion of gas onto a massive black hole at the galactic center and the jets of material ejected from the accretion disc around a black hole, which expand and decay over a few days, or the explosion of supernovae and their remnants may be analogous with the biological phenomena inside living organisms like secretion of substances used by the body. The process of stellar nucleosynthesis and formation of stars in the nebulae may be analogous to the synthesis of substances in the living organisms. Pulsating system and phenomenon of pulsations observed in the universe like stellar pulsations are analogous to pulsating system in the body like pulsations of arteries in tune with the heartbeat. These analogies existing on the two different scales of space and time might appear unrelated initially. So, in my opinion all the activities observed in the universe are its life activities like vital activities of our bodies. The universe has two coordination systems like human body which brings integration in the whole universe. The two systems – Neural Coordination and Chemical Coordination which controls and integrates the different activities and structures of human body, may also be controlling and integrating various structures and activities in the universe. The telescopic pictures of the universe observed by me and many astronomers very much resemble the microscopic pictures of the nervous system particularly brain, observed during my present investigation. Astronomers have taken the pictures of interconnecting filaments of star clusters and clusters of galaxies that form the texture of the universe and connect our Galaxy to the vast expanse of the universe. One of these filaments of groups of galaxies and star clusters surrounded by immense voids is considered like the umbilical cord that fed our Galaxy during its youth. These filaments of clusters and superclusters of galaxies, arms of spiral galaxies and other such trabecular strand structures in the universe resemble the branches (dendrites and axons) of the nerve cells of brain in particular and of nervous system in general. DNA, the blueprint of all living organisms on the earth, is involved in all vital functions like protein synthesis and production of energy. The ultimate result of these vital activities is consciousness. Similarly the blueprint of the universe may be producing matter & energy which along with other activities of the universe might result in large scale consciousness i.e. super-consciousness. In my opinion, this super-consciousness is the driving force of everything in this universe. From tiny world of atom to the vastness of universe, there are integrated levels of organization including all living organisms. The whole universe is a living entity or organism and we are like microorganisms or micromolecules or macromolecules. Evolution of life is progressing through different levels of dimensions and the universe is the highest dimension of life with super-consciousness which drives and shapes everything. We are all small and ephemeral part of greater and eternal living entity, the ultimate living universe. The organization of life is key to the organization of physical universe. The correlation of the genetic code (DNA) with the Solar System in particular and with the universe in general observed during my present investigation clearly implies that coding of DNA molecule has been very meticulously planned and regulated, because DNA has evolved in a four dimensional space-time continuum which is influenced,curved and distorted by gravity. I propose that knowing the biology better will solve the mysteries of the universe better. Sometimes it is Big-bang hypothesis and sometimes Contraction hypothesis; redshift and blueshift. My alternative hypothesis is that the universe is living, conscious and it has a thinking mind, and so follows the rules of life including growth and decay. Because the universe is a living system, it is aging naturally. The abnormal activities observed in the universe indicates its senility. Like living organisms the universe will one day die down. The advent of new generation of astronomical instruments opens new windows for the astronomers and may call for major revisions in the standard view of cosmology. My proposition is that an extensive and well co-ordinated work between different types of microscopes and telescopes could be able to reveal more mysteries enveloping the microcosm and macrocosm and thus bridging further the gaps between the disciplines like biology, chemistry, physics and astronomy.
Full-text · Article · Sep 2009
99+
How did Schrodinger concluded that adding a complex number to wave function is important? What's the physics behind that?

The wave function is complex, Why? Can the time and position for elementary particles have a complex relation (transformation) relative to our time and position?

Bushan,

Briefly, one may start with probabilities for the results of measurements of position. Gleason's theorem enables one to put the probability density functions into direct correspondence with states in Hilbert space, and Stone's theorem enables one to establish that states in Hilbert space satisfy a Schroedinger equation.

Momentum states are defined by by superposition of position states, using the Fourier Transform. The Heisenberg uncertainty principle follows directly.

You may find the mathematical details on my website and in my papers. This is not a new approach to quantum mechanics, but I have tried to clarify an established approach which many physicists find obscured by mathematical formality.

http://www.rqgravity.net/RelativisticQuantumTheory