# Square Vector Momentum

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### #1 arkain101

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Posted 20 December 2007 - 01:42 PM

While working on some rather unadvanced equations I came across an interesting realization that had to do with momentum.

The work showed that stopping the motion of a moving body of mass (Ma) with another body of mass (Mb) was equal to reproducing the same event with the only difference being that the moving body is turned 90 degrees as opposed to stopped.

If we assume the Time (t) of deceleration is of a value of 1 (where 1 can be 1 second or 1 nanosecond) the forces of each event are equal.

In the case where the moving body of mass (Ma) is brought to a stop, and the two bodies unite as a single body the momentum is applied to the sum of their total mass.

In the case where where the moving body of mass (Ma) is turned 90 degrees, all the forces 'should' be the same but in this case the original moving body (Ma) continues on a new course with the same momemntum.

So the conclusion I gathered was that Momentum is a dual or twin vector event that operates with square vector behavior.

If we were to apply this rule of thumb to Energy, or light if you will, using the existing knowledge we have of light. That is, Light has no mass but contains "momentum". We could conclude that light IS momentum as much as we conclude it is Energy.

If we can do so, then light would have to be described as a dual natured entity, with 90 degree split vector qualities and characteristics.

We may possibly conclude it is neither particular vector of a 90 degree opposing set, but both at the same time.

As for showing my work and equations I have not got this far yet, and it was awhile ago that I was working on this.

Is it possible that what I have said is an accurate statement?

### #2 snoopy

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Posted 21 December 2007 - 07:49 AM

That is, Light has no mass but contains "momentum". We could conclude that light IS momentum as much as we conclude it is Energy.

If we can do so, then light would have to be described as a dual natured entity, with 90 degree split vector qualities and characteristics.

We may possibly conclude it is neither particular vector of a 90 degree opposing set, but both at the same time.

As for showing my work and equations I have not got this far yet, and it was awhile ago that I was working on this.

Is it possible that what I have said is an accurate statement?

A massless particle can have energy E and momentum p because mass is related to these by the equation m2 = E2/c4 - p2/c2

Im not sure, but what you describe in the rest of your post sounds like the polarization of light.

But light necessarily must have both Energy and momentum.

Maybe you could post further ideas on exactly what you mean ?

Thanks

### #3 arkain101

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Posted 22 December 2007 - 01:59 PM

One purpose in this is to apply a kind of understanding of a property to EMR in its free independent state.

The properties we understand today have been produced from physical interactions with Energy in order to get some understandings of it. However, as we have learned, as you interact with Energy it produces some remarkable results. These are things such as wave-particle duality and a constant velocity.

(What we know less about, as far as I understand, is how to describe energy when it has not interacted, or is not interacting with anything.

What I intend to do is exactly that. Which is, apply a property to energy in its un-disturbed state. At least in a theorectical manner with mathematical support.

So we begin with comprehending bodies of mass interacting together.

Without getting back into the examples I will just state the following:

Bringing an object to a stop requires the same amount of work as turning an object 90 degrees from its course of trajectory.

In the case of the object being brought to a halt the momentum is conserved and transfered in the direction of trajectory to the object doing the blocking. (with some exceptions)

In the case of the object being redirected 90 degrees, the momentum is conserved and remains with the original moving object.

In these scenarios the object that is doing the blocking experiences the same net forces in either case. (assuming time, t is equal).

To add to this. If the blocker object attempted to redirect the moving object in the opposite direction. That is, to stop the object and send it off from which it came the circumstance is not the same.

It is only the square relationship that shares these equalities.

So far quite simple right?

Now, if we take this knowledge and apply it to Energy (EMR) is there anything we can learn?

Energy (ie massless photon) for starters contains no mass. Also, Energy can neither be created or destroyed.

With physics we continually see a give and take relationship of conservation. For example, if you give an object velocity it gains kinetic energy.

So if we remove the quality of 'mass' from a particle one would expect this to create an exchange, such as applying some kind of new attribute to the particle.

My question is what would this new attribute be?

A massless particle can not be contemplated to interact with other massless particles in a physical way, because mass is the key to having physical interaction.

My assertion is that a massless particle would be required to take on the square relationship of mass to its own particular characteristic.

One way to imagine this is to consider that this object always moves two directions at the same time two perpendicular directions. This is because, if we consider what the source of squaring is all about it is the perpendicular juxt opposing directions.

So if we were to imagine a massless particle, we must imagine a kind of duality be applied to that particle.

If the particle is moving north for example, I assume to say it also moves East or West, or East and West. For each incriment this object moves north it spreads out to a larger area east and west and thus its total quantity is spread over a larger area. Basic practical physics would suggest it to be less energetic on a given consistent area as it grows in volume(or area) when taking a measurement.

By the above I mean to relate to pressure and pounds per square inch. So, a small object and a large object of equal mass apply a different value of force and energy to a given and equal target.)

What I personally find remarkable is that light (energy) behaves very similar to this assertion I bring forth here.

I am afraid I need a refresh course on the $latex$ commands to show more work.

Hopefully this clarifies any confusion and likewise adds none..

### #4 arkain101

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Posted 22 December 2007 - 02:41 PM

I was taking a shower and something hit me for another layer to help explain this and well, support it I hope as well.

Lets talk dimensions..

When we are dealing with mass we are dealing with macoscopic relative observation of compound interactions of supposedly fundamental objects.

As far as I understand,

Mass can only move in 1 dimension. So this is also to say it can only be in one dimension at any give time. Secondly it can only follow this path in one direction, which is also the hypothechical direction of time and its dimension.
(One rule is that for this to make sense you NEED a minimum of Two seperate existing bodies of mass.)

If we consider anything fundamental, such as energy, it can not connect to itself. For example, A hypothetical fundamental particle has no connections to the universe around it and thus it is the universe, its own universe. It does not have its own means of fundamental particles to interact with other fellow fundamental particles.

This realm is thus infinite in nature. This is because it does not have a minimum of two interacting bodies, and to be an observer in this realm from this reference point is dimensionless.

So moving along here, we consider the transition of Mass into Energy. A 1 dimensional property into a ___ dimensional property of Energy. I suppose what I suggest is that the blank two (two dimensional).

How to go about describing this and or showing this transition I am not so sure.

But for starters I suppose we could imagine A squared vector of mass...

example --->$^2$ reforming into a geometry as this.

^
|
|
|----->

This of which is Energy (light) a 2D particle.. may be the right way to explain this.

### #5 snoopy

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Posted 23 December 2007 - 04:50 AM

My assertion is that a massless particle would be required to take on the square relationship of mass to its own particular characteristic.

Yes it does given by the equation

$m^2 = \frac{E^2}{c^4} - \frac{p^2}{c^2}$

Im just learning latex so I know what you mean about needing a course in it as for the rest of your post Im in agreement with you up until

So if we remove the quality of 'mass' from a particle one would expect this to create an exchange, such as applying some kind of new attribute to the particle.

My question is what would this new attribute be?

I have no idea what your talking about here the massless particle would still have energy and momentum and be therefore related to mass while not possesing any rest mass of its own.

But interesting ideas though

### #6 arkain101

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Posted 23 December 2007 - 04:47 PM

Interesting Snoopy and I thank you for your responses!

I enjoy discussing ideas and now I can rest easily knowing I have gotten this out of my mind lol.

### #7 snoopy

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Posted 24 December 2007 - 05:50 AM

I was thinking about this further and thought of GEM or Gravito electro magnetism I think you would find this interesting
Gravitomagnetism - Wikipedia, the free encyclopedia

I too enjoyed our conversation have a nice christmas.

Peace