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**New Theories / Is it a valid formula of mass, energy & momentum equivalence in relative motion?**

« **on:**30/10/2021 01:25:02 »

This model is based on a simple premise, that

Such statement isn't in fact in any way radical or baseless - energy/information can't propagate in space faster than c, so not only the source is as fast as the force it induces on other objects, but it also can't accelerate those objects beyond their current relative speed of c.

Now the most important questions are:

1. How does the magnitude of gravitational interaction relates to the velocity of gravitationally interacting bodies, that are already moving in relation to each other?

2. Does the strenght of gravity vary according to changing velocity of relative motion (and so it's acceleration)?

3 Is there any existing formula, that properly describes the problem of energy distribution for different velocities of gravitationally interacting bodies in relative motion?

4. Can ang of this be calculated using avaliable theories?

So, without any further delay, I can give you an answer to at least One Of those questions - sadly, it's The Last position on the list above. The answer is NO. even If there might be Some Ways around This issue, using continuous transformation of coordinates for individual frames, Bad I dont know about any possible way to matematyka deal with the absence of gravity for massive bodies moving at c.

Of course, since I'm a free spirit, capable of abstract reasoning, I had to try tackling with the problem using a completely new approach to the subject of energy distribution for moving and stationary mass.

So, first step was to know WHY a massive object moving at c won't indce any acceleration due to gravity on other bodies? I didn't have too many problems to find the most possible answer - it"s because the whole energy of that body turns at the speed of c icimpletely nto the kinetic energy (momentum) and there's no energy left for that mass, that could potentially increase the kinetic energy at (beyond) c. Following this logic, for gravitationally interacting bodies, that are initially at rest in relation to dach other, there's no kinetic energy that would be taken from the total amount of energy that a body can potentially gain by accelerating to c. Simply put, Evert body with a specific rest mass, has a specific level of energy, thai it can potentially reach, while accelerating to c, while in relative motion part of this energy is converted to kinetic energy (momentum) ofmovreal-lifeeeal-lifeee equal to 0 when the speed of c is being reached (so never in a real-life scenario)...

As for now, such depiction of energy distribution for a massive body in motion, doesn't appear to be in aby way revolutional or particularly exotic - however, it's jest an illusion, as some of more observative viewers, might notice already a teeny-tiny problem with all ofthis. You see, what you think about my idea of energy distribution in a moving body, it doesn't go well with the currently accepted description of potential energy. According to the current tgeory, level of the potential energy, is defined by the energy applied to the energy equilibrium of a body at rest and preventing the release of stored potential kinetic energy into the environment... Shortly, potential energy level is in curent model independent friom the initial level of kinetic energy and you can increase it up to theoretical infinity by continously applying external mechanical forces to that body. For example, we can change the current level of potential energy in a massive bodt, by holding it up above the surface of Earth, without changing the current level of kinetic energy induced by it on it's environment - thevsame principle goes for the mechanical energy "stored" in a fully drawed bow or for tension of a deformed metal rod with a high resistance to mechanical deformations. So, here changing the value of one doesn't necessarily affect the other, while in my model, both values are strictly dependent on each other (with the reversed proportionality).

In that case, I need to come out with a different depiction of distribution of potential and potential energy levels for a massive body in relative motion - and I can make it by using my own description of velocity of motion in relation to Constantin c - the one that can be written as a nicely looking composition of symbole: v

0≤{...}≥v1≤{...}>c<{...}≥v2≤{...}>2c

All what I have to do now, is to describe the potential energy of a massive body as energy still needed to accelerate this body to the speed of or as the kinetic energy, that this body can still gain before it reaches velocity of c... So, the total potential energy of a massive object is equal to kinetic energy required to accelerate this object from it"s rest position (v=0) to c. Alternative option is to depict it as total energy released into environment due to matter annihilation - e.g. in a direct head-on collision with itself (exact copy) moving at 100%/of c in opposite directions. Notice, that the "opposing direction" has here a crucial meaning, as collision in which one object is moving atvc and the other is stationary, won't lead to matter annihilation (that's why in the LHC particles are being accelerated almost to c in opposite directions, before they collide with dach other).

Of course, that I'm fully aware, that the last statements brutally violate the rule of relativistic velocity addition, but what to do if only this way it seems to work correctly...? Anyway, I depicted such way of describing the total energy of a massive body on the image below:

However the obvious incompatibility of my model with Einstein's relativity, is the least problematic part, because on the image above, you can swe, that in order to get a full picture of such equivalence, we need to describe the mass as a combination of square function of scalar energy with the directional vector of linear momentum - and it seems that this part is missing in the generally accepted Formula of mass / energy equivalence - the most famous formula in physics:

E=mc²

Thing is that this equation describes the total energy of a mass moving at the speed of c, but without the inclusion of oppositely directed vectors of a total momentum, it won''t give us the complete outlook on energy distribution in relative motion... So, the time came for me to także a pencil and a piece of paper and try calculating something by myself (a very uncommon practice of mine). And suprisingly, after using just two of my few remaining braincells, it didn't take me too long, to figure out this strange mathematical creature:

If you wonder from where I got the square of total potential momentum (m*c)^2, I will admit , that I'm not exactly sure - however despite my natural aversion to formulas, equations and kilometers of calculations, I know enough to tell, that this is how, I'm able to get a numerically valid result on both sides of my equation...

But don:t get too excited, as it's not even half way on the way to complete success. Now that I have the proper equation, I need to apply it to a scenario with objects in relative motion. And this is where I had to exploit the rest of mybremaining braincells.and with a pencil in my hand and a piece of paper, I've spent almost a whole week by trying all possible configirations of a wild mathematica orgy of letters and nubrers from my equation with the addition of "v" (for velocity), to figure out the way to calculate what part of the total rest mass of a body makes the kinetic energy and what part makes the remaining potential energy - and in the end I was successful... Here's how I did it

To make it simple, I've made a simple system of the necessary units based on constant c - using the metric system doesn't make sense.in this case. So..

For c=10d/t

And for rest mass

m=10 inducing acceleration of 10d/t^2 (mass of a black hole).

Let"s say that object of rest mass m=4 is moving at v=7d/t

It's total energy is E=m*c^2=4*10^2=400d/t^2 and the total momentum pt=m*c=40md/t and pt^2=1600. For a body moving at v=7d/t, p=m*v=4*7=28md/t and p^2=784

Considering the given values, the potential energy of a body of rest mass m=4 and velocity v=7d/t, potential energy can be calculated from mp=°

And there's the master equation:

And then after we put given values mt=+=1,96+2,04

Notice that potential energy is higher than kinetic energy, despite the object being further than half way to c. Let's compare it to a relative velocity of v=9d/t

p=4*9=36

p^2=1296

pt^2-p^2=304

mt=1296/400 + 304/400 = 3,24 + 0,76

For the same mass of 4 and for v=5d/t p°2=400:and 1600-400=1200

mt=1+3

For v=2d/t p^2=64 and pt^2-p^2=1536

mt=0,16+3,84

And with those coupl results, I can now conclude that there's MUCH higher efficiency for the mass/energy convesion in case of potential energy than for kinetic energy. It means that energy of the velocities between v and c are translated to much more energy than energy included in velocities from 0 to v

Ok. In next post I will show some interesting results from a reversed operatiin - where pt=p^2 is being divide by variable kinetic energy m*v^2 and potentiall energy (m*c^2)-(m*v^2) and then apply all of this, while calculating gravitational interacrions between bodies in relative motion...

TBC

**object that moves at the speed of light doesn't induce any gravitational attraction on non comoving objects.**Such statement isn't in fact in any way radical or baseless - energy/information can't propagate in space faster than c, so not only the source is as fast as the force it induces on other objects, but it also can't accelerate those objects beyond their current relative speed of c.

Now the most important questions are:

1. How does the magnitude of gravitational interaction relates to the velocity of gravitationally interacting bodies, that are already moving in relation to each other?

2. Does the strenght of gravity vary according to changing velocity of relative motion (and so it's acceleration)?

3 Is there any existing formula, that properly describes the problem of energy distribution for different velocities of gravitationally interacting bodies in relative motion?

4. Can ang of this be calculated using avaliable theories?

So, without any further delay, I can give you an answer to at least One Of those questions - sadly, it's The Last position on the list above. The answer is NO. even If there might be Some Ways around This issue, using continuous transformation of coordinates for individual frames, Bad I dont know about any possible way to matematyka deal with the absence of gravity for massive bodies moving at c.

Of course, since I'm a free spirit, capable of abstract reasoning, I had to try tackling with the problem using a completely new approach to the subject of energy distribution for moving and stationary mass.

So, first step was to know WHY a massive object moving at c won't indce any acceleration due to gravity on other bodies? I didn't have too many problems to find the most possible answer - it"s because the whole energy of that body turns at the speed of c icimpletely nto the kinetic energy (momentum) and there's no energy left for that mass, that could potentially increase the kinetic energy at (beyond) c. Following this logic, for gravitationally interacting bodies, that are initially at rest in relation to dach other, there's no kinetic energy that would be taken from the total amount of energy that a body can potentially gain by accelerating to c. Simply put, Evert body with a specific rest mass, has a specific level of energy, thai it can potentially reach, while accelerating to c, while in relative motion part of this energy is converted to kinetic energy (momentum) ofmovreal-lifeeeal-lifeee equal to 0 when the speed of c is being reached (so never in a real-life scenario)...

As for now, such depiction of energy distribution for a massive body in motion, doesn't appear to be in aby way revolutional or particularly exotic - however, it's jest an illusion, as some of more observative viewers, might notice already a teeny-tiny problem with all ofthis. You see, what you think about my idea of energy distribution in a moving body, it doesn't go well with the currently accepted description of potential energy. According to the current tgeory, level of the potential energy, is defined by the energy applied to the energy equilibrium of a body at rest and preventing the release of stored potential kinetic energy into the environment... Shortly, potential energy level is in curent model independent friom the initial level of kinetic energy and you can increase it up to theoretical infinity by continously applying external mechanical forces to that body. For example, we can change the current level of potential energy in a massive bodt, by holding it up above the surface of Earth, without changing the current level of kinetic energy induced by it on it's environment - thevsame principle goes for the mechanical energy "stored" in a fully drawed bow or for tension of a deformed metal rod with a high resistance to mechanical deformations. So, here changing the value of one doesn't necessarily affect the other, while in my model, both values are strictly dependent on each other (with the reversed proportionality).

In that case, I need to come out with a different depiction of distribution of potential and potential energy levels for a massive body in relative motion - and I can make it by using my own description of velocity of motion in relation to Constantin c - the one that can be written as a nicely looking composition of symbole: v

_{r}(relative velcity) having any value between 0 and c - or 0 and 2c in two-directions of 1D motion...0≤{...}≥v1≤{...}>c<{...}≥v2≤{...}>2c

All what I have to do now, is to describe the potential energy of a massive body as energy still needed to accelerate this body to the speed of or as the kinetic energy, that this body can still gain before it reaches velocity of c... So, the total potential energy of a massive object is equal to kinetic energy required to accelerate this object from it"s rest position (v=0) to c. Alternative option is to depict it as total energy released into environment due to matter annihilation - e.g. in a direct head-on collision with itself (exact copy) moving at 100%/of c in opposite directions. Notice, that the "opposing direction" has here a crucial meaning, as collision in which one object is moving atvc and the other is stationary, won't lead to matter annihilation (that's why in the LHC particles are being accelerated almost to c in opposite directions, before they collide with dach other).

Of course, that I'm fully aware, that the last statements brutally violate the rule of relativistic velocity addition, but what to do if only this way it seems to work correctly...? Anyway, I depicted such way of describing the total energy of a massive body on the image below:

However the obvious incompatibility of my model with Einstein's relativity, is the least problematic part, because on the image above, you can swe, that in order to get a full picture of such equivalence, we need to describe the mass as a combination of square function of scalar energy with the directional vector of linear momentum - and it seems that this part is missing in the generally accepted Formula of mass / energy equivalence - the most famous formula in physics:

E=mc²

Thing is that this equation describes the total energy of a mass moving at the speed of c, but without the inclusion of oppositely directed vectors of a total momentum, it won''t give us the complete outlook on energy distribution in relative motion... So, the time came for me to także a pencil and a piece of paper and try calculating something by myself (a very uncommon practice of mine). And suprisingly, after using just two of my few remaining braincells, it didn't take me too long, to figure out this strange mathematical creature:

m=

If you wonder from where I got the square of total potential momentum (m*c)^2, I will admit , that I'm not exactly sure - however despite my natural aversion to formulas, equations and kilometers of calculations, I know enough to tell, that this is how, I'm able to get a numerically valid result on both sides of my equation...

But don:t get too excited, as it's not even half way on the way to complete success. Now that I have the proper equation, I need to apply it to a scenario with objects in relative motion. And this is where I had to exploit the rest of mybremaining braincells.and with a pencil in my hand and a piece of paper, I've spent almost a whole week by trying all possible configirations of a wild mathematica orgy of letters and nubrers from my equation with the addition of "v" (for velocity), to figure out the way to calculate what part of the total rest mass of a body makes the kinetic energy and what part makes the remaining potential energy - and in the end I was successful... Here's how I did it

To make it simple, I've made a simple system of the necessary units based on constant c - using the metric system doesn't make sense.in this case. So..

For c=10d/t

And for rest mass

m=10 inducing acceleration of 10d/t^2 (mass of a black hole).

Let"s say that object of rest mass m=4 is moving at v=7d/t

It's total energy is E=m*c^2=4*10^2=400d/t^2 and the total momentum pt=m*c=40md/t and pt^2=1600. For a body moving at v=7d/t, p=m*v=4*7=28md/t and p^2=784

Considering the given values, the potential energy of a body of rest mass m=4 and velocity v=7d/t, potential energy can be calculated from mp=°

And there's the master equation:

mt=+=+

And then after we put given values mt=+=1,96+2,04

Notice that potential energy is higher than kinetic energy, despite the object being further than half way to c. Let's compare it to a relative velocity of v=9d/t

p=4*9=36

p^2=1296

pt^2-p^2=304

mt=1296/400 + 304/400 = 3,24 + 0,76

For the same mass of 4 and for v=5d/t p°2=400:and 1600-400=1200

mt=1+3

For v=2d/t p^2=64 and pt^2-p^2=1536

mt=0,16+3,84

And with those coupl results, I can now conclude that there's MUCH higher efficiency for the mass/energy convesion in case of potential energy than for kinetic energy. It means that energy of the velocities between v and c are translated to much more energy than energy included in velocities from 0 to v

Ok. In next post I will show some interesting results from a reversed operatiin - where pt=p^2 is being divide by variable kinetic energy m*v^2 and potentiall energy (m*c^2)-(m*v^2) and then apply all of this, while calculating gravitational interacrions between bodies in relative motion...

TBC