Domain of relativistic mechanics

[07PRADEEP]

1.
Domain of relativistic mechanics

.
Consider the simple formula 4AB=(A+B)-(A-B)² or AB=(A+B)²/4 -(A-B)²/4
We proceed like this If A+B>A-B ,Then B>0
Because mc>mv in all cases
We are going to check whether the numerical values are satisfied
Let us assume above simple formula is analogous to either (m₀ c)²=(mc)²-(mv)²,where L.H.S represents product of rest mass and velocity of light squared,
Or m₀²=(square of m )-(mv/c)², Case 1 (m₀ c)²=(mc)²-(mv)²
Let A=c,B=(c-mv)We get 4(c) (c-mv)=(2c-mv)²-(mv)²
B>0 gives mv<c
For m₀<2kg,mc < 2c units, we obtain m< 2Kg
for (mv)less than(c),Maximum of m=2,minimum of or atmost v=c, m=2 kg,m₀=2kg,
Case-2
Consider the simple formula 4AB=(A+B)²-(A-B)² orAB=(A+B)²/4 -(A-B)²/4
Analogous formula
m₀²=m²-(mv/c) ²,Putting A=c,B=(c-mv/c) and
comparing with (c) (c-mv/c)=(c-mv/2c)²-(mv/2c)²,B>0 implies
mv< c² and mv<2c²hence conclusion is mv< c², in m₀²=m²-(mv/c) ²
m₀<c kg
mc<c²,m<c
Now mv< c²/2
therefore maximum of v=c/2 units
Case-3
Consider the simple formula 4AB=(A+B)²-(A-B)²orAB=(A+B)²/4 -(A-B)²/4
Analogous formula,m₀²=m²-(mv/c) ²,Putting A=k,B=(k-mv/c) and
comparing with (k) (k-mv/c)=(k-mv/2c)²-(mv/2c)²,we get
mv<ck,
B>0 givesmv<2ck,
m₀<k where k stands for any fixed value,it can assume any value ,
maximum of v=c/2,m<k Since mv<ck,mv<2ck conclusion is mv<ck Also since
mv/2c leads to k/2,Comparing it with the analogous equation,
k/2=kv/c,leads to v=c/2


Conclusion

Maximum of v=c/2 units, in RELATIVISTIC MECHANICS DOMAIN namely Case2 and Case3
Case1 mv<c , rest mass m₀ element of ( 0 to 2)kg , m<2 kg
Case 2 mv <c²,rest mass m₀ element of (2 to c)kg , m<c kg
Case3 mv<kc ,rest mass m₀ element of (c to k)kg m<k kg
Where k stands for any fixed value ,however large

[SteveA]

1.
Domain of relativistic mechanics

.
Consider the simple formula 4AB=(A+B)-(A-B)² or AB=(A+B)²/4 -(A-B)²/4
We proceed like this If A+B>A-B ,Then B>0

...

I already like your post (I've built some rather fast electronic hardware for multiplication using this algorithm and I think there are some interesting physical correlations as well)

Yes, we can reduce a two dimensional multiplication to a squaring operation in a single dimension (though this can raise the question of whether or not higher dimensional spaces can inversely be constructed by operations performed within a single dimension! I think this is true and that the dimensionality of a space arises from quantities and the inherent diversity of qualities in the context of which information is presented)

Anyway, with regard to your specific example, if we detect energy in discrete units and there are not fundamentally fractional units of things, then we should be operating with natural numbers.

Notice that subtraction and division are in many ways more fundamental than addition and multiplication. We can construct addition by two subtractions, whereas we can't construct subtraction from addition and similarly, a multiplication can be performed by two divisions, whereas we can't construct division from multiplication.

x/(1/y)=x*y
x-(0-y)=x+y

We could even construct 0 and 1 using division and subtraction and remove the constants like this:

x/((x/x)/y)=x*y
x-(x-x-y)=x+y

The parenthesis aren't even required, as we could use reverse polish notation http://en.wikipedia.org/wiki/Reverse_Polish_notation and that would be an interesting physical system in which discrete "quantum units" could actually be constructed by relative comparison between two unknown, by identical quantities as a ratio of 1:1 (and notice that physical measurements are made in relative terms of ratios).

You comment that B>0 I agree with. Normally division by 0 is considered illegal but this is only a symptom of a dicontinuity in the information that arises from a multiplication by 0. Calculus gets around this problem in an approximate manner, but it's not a precise solution and it misses many interesting infinitesimal and/or infinite structures.

And requiring B>0 is also addtionally beneficial in that information is retained regarding the sign of the result (thank you for your post as this wasn't something I had considered before, but your comment stimulated the insight for me ).

Notice that if we had something like:

A*B=-3

Well we know if A and B are integers that there would be 4 possible solutions {1,-3},{-1,3},{-3,1},{3,-1}, but this is not necessarily optimal from the perspective that, given a result of -3, we can't determine specific values for A and B.

If we required B>0, this would then limit us to only the 2 possibilities of {-1,3} or {-3,1}.

I've found some reasons to believe that there should exist a rigid ordering to fundamental physical units as there should exist some "objective" timeline in which events occur sequentially and we have a continual growth, n, n+1, n+2, ...

We could additionally place some requirement like |B|>|A| and then further restrict this to a unique solution of {-1,3} or A=-1, B=3 if A*B=-3. Of course that would no longer be a typical multiplication but a special multiplicative class. Notice that this requirement to have quantities sorted in space would then also allow the possibility of quantities appearing to move in space as they undergo mathematical transformations.

A couple more brief comments regarding the implicit physical context of negative and rational numbers:

Measurements of zero or negative quantities of things don't occur directly. A measurement of zero indicates that we at least could construct a reference for what it was that we specifically found nothing of within some selected component of space and time.

Negative numbers or zero are constructed by differences between quantities A-B, where B>=A.

Also fractions or rational numbers imply a relative comparison between two quantities, though we have information potentially lost when these ratios are reduced and do not indicate the original quantities. For example, knowing that half of some set of samples are of some specific result doesn't indicate the confidence (or an equivalent entropic energy of uncertainty) that could exist in those samples. If only two tests were performed, there's little reason to believe that this should be very repeatable, whereas if it was precisely 500 out of 1000 samples, there's a large probability that another 1000 samples would results in some comparable quantity of results (these statistical methods I believe are where we move from the quantum/discrete and more immediately present realm into that of macroscale observations).

I'd enjoy posting some more regarding some correlations between the squaring operation and a stretching of space with chaotic properties (if we trace out how information "flows" within the digits of the number - if basically "stretches" the number of digits to twice the width and shifts this space as well and can create the appearance of chaotic cross interactions. Multiplication has close physical correlations to physical reverberations/echoes as well). A related subject is the chaotic properties of a Logistic Mapping http://en.wikipedia.org/wiki/Logistic_map.

I began posting some details, but it got a bit too complex and I don't want to sidetrack your post much (I apologize for going off on a personal tangent but I saw some correlations in your post with things I'd previously thought about and your comments helped clear up a couple ideas for me as well. Thanks again ).

[plsnt]

I took a different approach with a simpler equation. I don't know how to insert equations in the browser. Hence please check the word document attached.

[SteveA]

Hi there, "plsnt". I tried viewing your doc file but I only have WordPad and could only view a small amount of text. Do you have a text version or other link?

[plsnt]

Hi Steve,

The file has equations and it won't work in text or rich text programs. I have converted and attached the PDF version. Hope that helps. It is nothing great. Just two or three simple equations. But the point is, I don't understand the co-relation between them and the range of values specified by Pradeep sir in his post. I hope you can help.

Regards,

Pleasant

[SteveA]

Hi again, Pleasant

See if this is what you're looking for.

I'll use text and define

p=((c/v)^2-1)^(1/2)

m=m0*y

In all your cases it appears you want to rescale your equations like this:

v*y*m0<c
m0<p

On the left, you're rescaling by a factor 1/(v*y) and so the ratio of p/c should also be 1/(v*y).

(v*y*m0)/m0=c/p
v*y=c/p

Resubstituting for p, we get:

v*y=c/(((c/v)^2-1)^(1/2))

I'll square both sides (though there's a potential issue with signs and/or imaginary values, but I'll ignore that):

(v*y)^2=c^2 / ((c/v)^2-1)
(v*y)^2=c^2 / (c^2/v^2-1)
v^2*y^2=c^2 / (c^2/v^2-1)
y^2=c^2 / (v^2*(c^2/v^2-1))
y^2=c^2 / (c^2-v^2)
y^2=1 / (1-v^2/c^2)

And then we can take the square root:

y=1/(1-v^2/c^2) ^ (1/2)

or similarly:

y=(1-v^2/c^2) ^ (-1/2)

I didn't double check the math, but I assume that's basically what you were looking for.

[plsnt]

Hi Steve,

I am sorry, but that is not what I was looking for. I was not trying to derive gamma. In each of the cases, the value of m0 goes from "0 to 2", "2 to c" and "c to k" respectively. Now my problem is that I am not able to co-relate between my values of m0 which are delta, c*deta and k*delta and the values derived by Pradeep sir.

Pleasant

[SteveA]

Hi again, Pleasant.

My earlier reply to Pradeep was not as much regarding the derivations as it was about the treatment of multiplication. My views on how mass arises is not conventional, though his restrictions placed upon the physical equivalent of multiplication appear applicable and "waste less" information.

I don't believe the "speed" of light is a speed in the conventional sense at all and believe that an individual photon is effectively infinitely fast. In the end, there's nothing but information and how it is interpreted.

There are basically 3 components that are being physically measured in the above cases and we can see these as position, velocity and mass.

If we have a binary stream of information sampled to represent information about an object and we do not keep track of how these events are ordered in time, but simply add up the quantities of 1s and 0s (which can be seen as equating to photons and "time", which is just another form of photon detection).

If we're making measurements in a single dimension and consider one polarity of detection to imply a unit of motion in one direction and the alternate polarity to be a unit of motion in the other direction, then we could summarize a measurement as a quantity of velocities in opposing directions.

If we have 100% detection of events in one direction, then we have maximal velocity in that direction and 100% detect in the opposing direction would be -100% velocity.

A "stationary" state in this case would be a 50/50 distribution, but though we have only 1 unique sequence each for +100% to -100%, we have a larger number of possible "slower" motions and the distributions of these are according to Pascal's Trangle.

Atomic Structure and Pascal's Triangle
http://milan.milanovic.org/math/engl.../electron.html

Though the origin of a measure would be required to be a 50/50 distribution over a complete measurement, it can be in "motion" during a complete measurement (i.e. a sequence of 10101010, would be a measurement over 4 cycles of a binary motion, but a sequence of 00001111, would be a complete "orbit" that encompassed a measurement over all 4 of the previous cycles).

"Matter" in this case arises from the possible statistical distributions of these forms and we can see that over vaguely "large" measurements (which is the "macroscopic" realm of Relativity), of we're not "moving" at light speed, then we can have Poisson distributions describe objects moving at various velocities http://en.wikipedia.org/wiki/Poisson_distribution.



For a "stationary" object, this would specifically be of a Gaussian form (a "Bell Curve" or "Normal Distribution"): http://en.wikipedia.org/wiki/Normal_distribution

If the velocity of light is effectively infinite, then obviously any motion within space will not appear to alter its velocity, hence the speed of light appears to be constant (not due to the reasons ascribed in physics). The issue here is that we measure time in a relative and secondary manner and do not measure a fundamental form of time. The time we physically measure is a secondary and dependent construction of a more fundamental version of time, which has no specific duration at all but instead is a serial process that's applied to all elements in the universe. This allows "spacetime" to remain coherent and assures time, throughout the universe is synchronized, though our secondary physical version of time can vary as the distributions of the measured polarities of motion differ.

If we're making measurements from matter, then we're measuring quantities of opposing and "diffusive" pairs of complimentary motions. In this case, our measured version of time "slows" when we approach light speed because the measurements of energy in this state approach maximal + or - values.

Making observations from a "stationary" state means assuming we're at a 50/50 distribution. Deviations from this are probabilistic for mass (for light we're measuring the repetitive wavelengths - matter arises from the equivalent of chaotic "wavelengths") and if we look at their distributions, it's a Gaussian:



Notice that the peak of this "falls off" as a parabolic function (this is why gravity appears locally to be a 1/d^2 function), but then the slope transitions toward a linear region and then becomes and exponentially decaying function. There are similar classes of observations of galaxies (and we should be able to determine their fundamental distance, not by redshift, but by their observed shape).

In this case, we do not have a light speed limit for velocities (notice that in Relativity there is time dilation and effectively nothing denying travelling across a galaxy in what could appear to be a very short time), but instead we have a statistical restriction that arises from the lack of knowledge regarding chaotic functions of matter (notice that the only atom that a decent model exists for is the very simplest - hydrogen and that the n-body problem doesn't (yet) have a general solution).

Anyway, sorry for the long reply, but my first reply to Pradeep was really with regard to the fact that we're making measurements using a single positive quantity of informational units and though I didn't follow through his rewrite, it does appear quite useful to isolate the components of a physical measurement that can only be positive, as these should be quantities of fundamental units of time/information that are being measured. The bipolar values arise when we're making differential measurements across these informational states. Also, fractional quantities arise when we're making ratiometric measurements relative to a quantity of information - the individual units themselves are not fractional (this also tells us when we're making measurements over time and not an instantaneous measurement - non-instantaneous measurements require the addition what would conventionally be considered faster-than-light correlations or in other aspects memory or space. At any moment, nothing more than a single unit of information should be measured, and its maximum information is 1 of n possible detection sources - my comments above were just regarding binary polarities in a single dimension, but we have more "dimensions" of information available to physical perceptions and due to the fact that two different measurements made from 1 of n and 1 of m different possible states can have n and m contain relatively prime factors, then we can't precisely describe the information acquired via. one such "channel" of information in terms of another and this is how different wavelengths and conscious qualities of experiences can arise as well as the coherent features observed in quantum mechanics).

Anyway, I can't give you much more details regarding how anything more correlates with conventional physics because things appear to diverge (I'm work mostly with mechanical systems, software, electronics and and prefer discrete, combinatorial or statistical representations and tend to avoid continuous field theories and "real" numbers as I think these have many indeterminant aspects that allow for quite arbitrary derivations to be arrived at, though they do allow for simpler and more intuitive representations so a final version of these ideas may end up as field approximations, but they you can't rederive quantum features once that approximation has been used).

Sorry, if my post isn't very helpful in what you're looking for but there might be some details you can find correlations with in your own pursuits.

Steve

[SteveA]

As another potenially applicable concept. It's quite possible that kinetic energy and various physical representations of temperature and pressure are derived from higher order "statistical moments" of the distributions of these informational units.

As you either bias things toward less Gaussian and more Poisson distributions are have information conveyed in a higher number of dimensions, then these measurements could help isolate those components into unique statistical properties. This could also give information regarding the quantity of units being measured for some specific physical property:

Statistical Moments
http://geography.uoregon.edu/geogr/topics/moments.htm

That would allow you to distinguish between a wider range of statistical distributions, such as:



Though I believe more fundamentally these can arise perceptually as just pattern matching over a small window of information (i.e. a short term subconscious/physical memory).

[plsnt]

Dear Steve,

I appreciate your effort to explain the concept to me. But I am still skeptical about what you told regarding light speed. I have learned that light speed is similar to any established law of physics in that it remains constant no matter what the observer's speed is or where he is located. Also I have learned that even gravity waves travel at the same speed and that space-time warps in order to accommodate this limiting factor. Now if light photon can travel at infinite speed, how do we explain the warping of space-time?

Pleasant