Subspace Physics

8/12/2019 Subspace Physics

1/35

Subspace Physics, v.2.0

By Jason Hinson

HTML by Joshua Bell, converted from a USENET posting with the permission of the author.

Last (seriously) modified: Sat Nov 19 23:31:11 1994

This is the version 2.0 of this post. It has changed from version 1.0 in that I have added three

new sections and change a few things in some of the other sections accordingly. Two of these

new sections deal with subspace itself as well as how one might fictionally produce subspacefields. The other added section (Section 7) deals with the question of angular momentum

conservation, which is ignored elsewhere in the post. I hope you enjoy it.

[Jump to the Contents]

So, what's all this then?

The following is a mixture of concepts mentioned in canon and semi-canon sources combinedwith a healthy dose of physical reasoning and a big spoonful of personal speculation to help it all

go down. It looks at the properties that subspace fields and warp fields are supposed to possess,

and examines how these properties might live in harmony with certain physical laws(specifically, with conservation of energy and momentum).

The discussion is mainly written as if it were addressing a twenty-fourth century audience, and

so the concepts I have developed for explaining various aspects of subspace physics are stated asfacts. In reality, even though the main properties of the subspace and warp fields come directly

from canon sources, many of the other aspects of these fields are developed from physicalreasoning with a spattering of my own personal tastes.

For example, we know that to sustain a subspace or warp field, it is necessary to continually feedit energy. So, where does this energy go? Does the field continually build up energy, storing all

of the energy being poured into it. Even if this were the case, what happens to all that energy

when the field is shut off. The best answer to me seems to describe the field as "unstable" in thatit doesn't stick around if you stop feeding it energy. Instead, we might say that it continually

"bleeds" this energy back into normal space in the form of heat in the field coils, electromagnetic

radiation, and/or (perhaps) subspace radiation which can couple its energy back to normal space(like the shock wave in Star Trek VI).

Please let me know if you find any problems with the explanations I give (either problems

related to the physics or problems with contradicting canon sources). I tried to keep in mind allthe various aspects given by canon sources, but I could have trampled over a few. For example,

one part of the Technical Manual (page 49) mentions symmetric fields as non-propulsive

(indicating that a propulsive field could be created by producing an asymmetric field). However,
http://www.physicsguy.com/subphys/SubspacePhysics.html#contentshttp://www.physicsguy.com/subphys/SubspacePhysics.html#contentshttp://www.physicsguy.com/subphys/SubspacePhysics.html#contents


2/35

in another section (page 54) it indicates that the key to "non-Newtonian" propulsion (which

would seem to me to be a propulsive warp field) "lay in the concept of nesting many layers of

warp field energy." I therefore tried to incorporate both ideas into my explanation of warppropulsion.

Oh, one other thing before we get to the discussion. I have assumed in writing this that the readerhas read my monthly "Relativity and FTL Travel" post. In the discussion below, I assume

concepts discussed in the Relativity post (specifically, the idea of subspace providing a special

frame of reference for the purpose of faster than light travel such that warp fields "plug into" thatframe of reference). The Relativity post should be posted at approximately the same time as this

discussion, so if you haven't read it, you may want to give it a look.

So, I hope you enjoy this fairly lengthy discussion of subspace and warp fields. Even if you

disagree with the way some of the concepts are explained, at least understand that a lot of

thought has gone into them in order to make the abilities of subspace and warp fields fit in with

the concepts of momentum and energy conservation.

Okay, prepare to take a little excursion. As always, your thoughts and criticisms are welcome.

A Discussion of Subspace and Warp Fields

Especially as they Apply to Momentum and Energy Conservation

Contents

1. Introduction2. Subspace and its Frame of Reference3. Creating Subspace Fields

1. Creating a Simple Subspace Field2. Creating a Warp Field

4. General Aspects of Subspace Fields5. Simple Subspace Fields

1. Momentum and Energy Conservation with Simple Subspace Fields1. Momentum conservation2. Energy Conservation3. Some Examples

2. Technical Notes for this Section (Simple Subspace Fields)6. Warp Fields

1. Warp Propulsion1. Single-Layered Warp Fields2. Multi-Layered Warp Fields3. Development of Modern Warp Propulsion Fields4. Modern Warp Propulsion Field Generation
http://www.physicsguy.com/subphys/SubspacePhysics.html#1http://www.physicsguy.com/subphys/SubspacePhysics.html#1http://www.physicsguy.com/subphys/SubspacePhysics.html#2http://www.physicsguy.com/subphys/SubspacePhysics.html#2http://www.physicsguy.com/subphys/SubspacePhysics.html#3http://www.physicsguy.com/subphys/SubspacePhysics.html#3http://www.physicsguy.com/subphys/SubspacePhysics.html#3.1http://www.physicsguy.com/subphys/SubspacePhysics.html#3.1http://www.physicsguy.com/subphys/SubspacePhysics.html#3.2http://www.physicsguy.com/subphys/SubspacePhysics.html#3.2http://www.physicsguy.com/subphys/SubspacePhysics.html#4http://www.physicsguy.com/subphys/SubspacePhysics.html#4http://www.physicsguy.com/subphys/SubspacePhysics.html#5http://www.physicsguy.com/subphys/SubspacePhysics.html#5http://www.physicsguy.com/subphys/SubspacePhysics.html#5.1http://www.physicsguy.com/subphys/SubspacePhysics.html#5.1http://www.physicsguy.com/subphys/SubspacePhysics.html#5.1.1http://www.physicsguy.com/subphys/SubspacePhysics.html#5.1.1http://www.physicsguy.com/subphys/SubspacePhysics.html#5.1.2http://www.physicsguy.com/subphys/SubspacePhysics.html#5.1.2http://www.physicsguy.com/subphys/SubspacePhysics.html#5.1.3http://www.physicsguy.com/subphys/SubspacePhysics.html#5.1.3http://www.physicsguy.com/subphys/SubspacePhysics.html#5.2http://www.physicsguy.com/subphys/SubspacePhysics.html#5.2http://www.physicsguy.com/subphys/SubspacePhysics.html#6http://www.physicsguy.com/subphys/SubspacePhysics.html#6http://www.physicsguy.com/subphys/SubspacePhysics.html#6.1http://www.physicsguy.com/subphys/SubspacePhysics.html#6.1http://www.physicsguy.com/subphys/SubspacePhysics.html#6.1.2http://www.physicsguy.com/subphys/SubspacePhysics.html#6.1.2http://www.physicsguy.com/subphys/SubspacePhysics.html#6.1.3http://www.physicsguy.com/subphys/SubspacePhysics.html#6.1.3http://www.physicsguy.com/subphys/SubspacePhysics.html#6.1.4http://www.physicsguy.com/subphys/SubspacePhysics.html#6.1.4http://www.physicsguy.com/subphys/SubspacePhysics.html#6.1.5http://www.physicsguy.com/subphys/SubspacePhysics.html#6.1.5http://www.physicsguy.com/subphys/SubspacePhysics.html#6.1.5http://www.physicsguy.com/subphys/SubspacePhysics.html#6.1.4http://www.physicsguy.com/subphys/SubspacePhysics.html#6.1.3http://www.physicsguy.com/subphys/SubspacePhysics.html#6.1.2http://www.physicsguy.com/subphys/SubspacePhysics.html#6.1http://www.physicsguy.com/subphys/SubspacePhysics.html#6http://www.physicsguy.com/subphys/SubspacePhysics.html#5.2http://www.physicsguy.com/subphys/SubspacePhysics.html#5.1.3http://www.physicsguy.com/subphys/SubspacePhysics.html#5.1.2http://www.physicsguy.com/subphys/SubspacePhysics.html#5.1.1http://www.physicsguy.com/subphys/SubspacePhysics.html#5.1http://www.physicsguy.com/subphys/SubspacePhysics.html#5http://www.physicsguy.com/subphys/SubspacePhysics.html#4http://www.physicsguy.com/subphys/SubspacePhysics.html#3.2http://www.physicsguy.com/subphys/SubspacePhysics.html#3.1http://www.physicsguy.com/subphys/SubspacePhysics.html#3http://www.physicsguy.com/subphys/SubspacePhysics.html#2http://www.physicsguy.com/subphys/SubspacePhysics.html#1


3/35

2. Momentum and Energy Conservation with Warp Propulsion1. Some Examples

3. Technical Notes for this Section (Warp Fields)7. Angular Momentum Conservation -- for the 20th Century reader8. Conclusions9.

Author's Note: Some final words

1. Introduction

In this discussion we will examine some of the basics of both simple subspace fields as well as

warp fields. In particular, we wish to look at how momentum and energy conservation come into

play with the use of these fields.

Before discussing the subspace fields, we first want to talk in general about subspace and itsframe of reference. We will then see how the definition of the frame of reference of subspaceallows for the creation of subspace fields (both simple subspace fields and warp fields).

After mentioning some general aspects that both types of fields possess, we will lookindividually at each type of field. In each case, we will first go over some of the major

characteristics of the particular field of interest. We will then discuss how momentum and energy

conservation come into play with that particular type of field. Finally, we will look at examplesto further examine the conservation of momentum and energy with each type of field.

In addition to this, there are also a few technical notes at the end of some sections (specific to

each section) which will be referred to at various times. These will go into more technical detailconcerning specific topics.

(A note to the 20th century reader:The final sectionbefore the conclusion deals with the

question of angular momentum conservation. Throughout the other sections of the discussion,

"momentum" is used to refer to linear momentum only. This section will discuss for the 20thcentury reader why angular momentum has been left out everywhere else.)

2. Subspace and its Frame of ReferenceSubspace is a continuum that exist in conjunction with our own space-time continuum. Every

point in our universe has a corresponding point in subspace. Also, at every point in our universe,subspace has a particular frame of reference. One could imagine subspace to be vaguely similar

to a huge cloud-like field that pervades the known universe. The particles in one area of such a

cloud would be moving at some particular velocity, while the particles in another area may be
http://www.physicsguy.com/subphys/SubspacePhysics.html#6.2http://www.physicsguy.com/subphys/SubspacePhysics.html#6.2http://www.physicsguy.com/subphys/SubspacePhysics.html#6.2.1http://www.physicsguy.com/subphys/SubspacePhysics.html#6.2.1http://www.physicsguy.com/subphys/SubspacePhysics.html#6.3http://www.physicsguy.com/subphys/SubspacePhysics.html#6.3http://www.physicsguy.com/subphys/SubspacePhysics.html#7http://www.physicsguy.com/subphys/SubspacePhysics.html#7http://www.physicsguy.com/subphys/SubspacePhysics.html#8http://www.physicsguy.com/subphys/SubspacePhysics.html#8http://www.physicsguy.com/subphys/SubspacePhysics.html#authorhttp://www.physicsguy.com/subphys/SubspacePhysics.html#7http://www.physicsguy.com/subphys/SubspacePhysics.html#7http://www.physicsguy.com/subphys/SubspacePhysics.html#7http://www.physicsguy.com/subphys/SubspacePhysics.html#authorhttp://www.physicsguy.com/subphys/SubspacePhysics.html#8http://www.physicsguy.com/subphys/SubspacePhysics.html#7http://www.physicsguy.com/subphys/SubspacePhysics.html#6.3http://www.physicsguy.com/subphys/SubspacePhysics.html#6.2.1http://www.physicsguy.com/subphys/SubspacePhysics.html#6.2


4/35

moving at another particular velocity. Similarly, at every point in our space, subspace has a

particular "velocity" or frame of reference.

This fact is very important, because this feature of subspace is what allows us to travel faster

than light without having to worry about such things as traveling back in time to meet ourselves

every time we jump into warp. The reason this is so will not be covered in this discussion, butthere are texts available which explain why this is.

So, what is the frame of reference of subspace at a particular point in our universe? Well, theframe of reference is defined by the local distribution of mass. More specifically, it is defined by

the distribution of mass and energy which is mathematically defined by what is known as the

stress-energy tensor of local energy distributions. However, for our purposes here, we willexplain how the subspace frame of reference is approximately defined by using the less

complicated concept of mass distribution.

There is one other note that needs to be made before we get into defining the subspace frame of

reference. In subspace physics, there are three meanings to the word mass. Classically, there aretwo "types" of mass theoretically believed to be equivalent. They are gravitational mass and

inertial mass. With subspace physics, there is also the concept of subspace-equivalent mass. Thisis the mass subspace "sees" which defines its frame of reference. Generally, this mass is

equivalent to the gravitational and inertial mass; however, it can be different under certain

circumstances. Similarly, there is also a concept of the subspace-equivalent stress-energy tensor.

Now we will describe how someone can find the speed of the frame of reference of subspace

with respect to their own frame of reference.

First, imagine dividing all the mass in the universe into sufficiently small chunks of mass "dm".

We then number each chunk so that the "i-th" chunk would have a mass of "dm_i". We also notethat for objects in the universe which are basically spherical and uniform, we can define the

whole object as one of our chunks of mass (provided the object isn't a spherical shell which we

might happen to be inside of).

So, we will be in one particular frame of reference (call it O). We want to find the speed of the

frame of reference of subspace (in our frame of reference) at some point in the universe. Well, inour frame of reference, the i-th chunk of mass (dm_i) has a particular velocity in the x direction

(Vx_i). It also has a particular distance away from the point of interested (R_i). For each chunk,

we then calculate the quantity:

dm_i * Vx_i-------------

(R_i)^2

Once we calculate this quantity for every chunk of mass, we then sum up all the various

quantities and call this sum "S":+---\ dm_i * Vx_i

S = / ------------ .+--- (R_i)^2

i


5/35

Now, we want to consider another frame of reference which is moving with respect to our own.

We could figure out what velocities and distances would be measured for each chunk of mass in

that frame, and we can calculate the sum, S, in that frame as well. If we continue to do this forvarious frames of reference, then we will eventually find the frame of reference in which the

absolute value of S is minimized. The x velocity of that frame of reference will then be the x

velocity of the of the subspace frame of reference as measured in our frame. We could then dosimilar calculations to find the y and z components of the velocity of the subspace frame ofreference.

A note to the 20th century reader: For now, this is only a preliminary way for determining the

frame of reference of subspace. There may be unforeseen problems in this definition, and I'llhave to take some time to consider various aspects of this definition to see if it is really what we

want to use.

So, what does all that mean? Well, consider a bit of matter that is very close to the point of

interest in the frame of reference you are considering (i.e. R_i for that bit of matter is quite smallin that frame of reference). That means that bit of matter provides a fairly large contribution to

the sum, S, UNLESS the velocity of that bit of matter is very small in the frame of reference you

are considering. So, the speed of the subspace frame of reference will likely be close to the speedof that nearby bit of matter. (Note: this is why we say that the subspace frame depends on the

local distribution of mass. For chunks of matter that are very far from you, their contribution to S

is generally negligible.)

However, also note that if there are many chunks of matter at some average distance from youwhich are all traveling at the same speed (like all the chunks of matter in a nearby star, forexample) then all that mass provides a large contributes to the sum. This means that the subspace

frame of reference will be close to the frame of reference of those chunks (so that Vx in that

frame of reference is small in order to canceling the large contribution created by the large

mass).

Obviously, we could discuss the determination of the frame of reference of subspace for some

time; however, for our purposes, it is only important to remember a couple of things about thisdetermination: In the simplest idea, the subspace frame of reference is determined by the nearby

distribution of mass. However, in actuality, it is the distribution in the more complex structure

known as the stress-energy tensor that determines the subspace frame of reference.

3. Creating Subspace Fields

The creation of simple subspace fields as well as warp fields is closely related to the way in

which the subspace frame of reference is defined (as described above). Here we will look first at

the creation of a simple subspace field and second at the creation of a warp field to show howthese fields are produced.

3.1 Creating a Simple Subspace Field


6/35

Inside of a subspace field generator, generally a plasma stream is used to create a particular

stress energy tensor within the generator. Within the area of space where this stress-energy

tensor is strongest, the frame of reference of subspace defined by the tensor is made to beradically different from the subspace frame of reference just outside of this area. Thus, when

produced correctly, the stress- energy tensor creates a large change in the frame of reference of

subspace over a small area of space.

One might think that this could have the effect of "tearing" subspace in that area if it weren't for

the fact that subspace has a natural mechanism for preventing this. It creates what we call asubspace field which surrounds the offensive stress-energy tensor. This field reduces the effect

that the tensor has on the definition of the subspace frame of reference. Basically, this reduces

the effects of the subspace-equivalent stress-energy tensor. However, at this point the subspace-

equivalent stress energy tensor is still directly related to the real-space stress-energy tensor. So,the field also lowers the effects of the stress-energy tensor as viewed in normal space (outside of

the subspace field) as well.

By correctly producing the stress-energy tensor, one can create a subspace field which extendswell beyond the localized area of the tensor (large enough, in fact, to surround a ship). If we

replace the concept of the stress-energy tensor for a moment with the simpler concept of mass,we see that this has the effect of lowering the apparent mass of anything within the subspace

field. In essence, the subspace field "submerges" a fraction of the mass into subspace so that it

does not have to be considered as real-space mass when defining the subspace frame of

reference. Details on how momentum and energy remain conserved with this apparent massreduction will be covered in a later section.

So, we see that by correctly manipulating the normal space effects which dictate the local frameof reference of subspace, we can create a simple subspace field.

3.2 Creating a Warp Field

The creation of the warp field isn't all that different in principle from the creation of a simple

subspace field. The major differences are in the energy and configuration of the plasma streamand the exotic nature of the stress-energy tensor needed.

For the purposes of illustration, we will concentrate here on producing a warp field which is usedfor propulsion. Other warp fields are produced in a similar manner by producing different stress-

energy tensors. Here we discuss the most basic components of warp field production; however,

in section 6 we will mention a few more aspects that can come into play when producing warp

fields.

Generally, to create a warp field, the plasma is injected into warp field coals which are made of

an appropriate material. The material in the warp field coil is important because as the plasma isinjected, the combination of the configuration of the plasma stream and the coil through which

the plasma passes is what creates the exotic stress-energy tensor needed to produce the warp

field.


7/35

The energizing of the field coil material with a properly configured plasma stream creates a

stress-energy tensor that produces a much more violent change in the frame of reference of

subspace over a much smaller area than is needed to produce a simple subspace field. Tocounteract this violent change, subspace produces what we call a warp field, shifting the energy

frequencies of the plasma deep into the subspace domain. This shift has the effect of completely

removing the significance of the stress energy tensor from the determination of the subspaceframe of reference.

As with subspace fields, it is then possible to produce a warp field which extends far beyond thelocal area effected by the exotic stress-energy tensor. When such a field surrounds an entire ship,

everything within that ship can be removed from the determination of the subspace frame of

reference. This brings up two points to be discussed:

First we consider the frame of reference of the ship. Because of the warp field, subspace and

outside observers no longer consider the frame of reference of the ship when determining the

subspace frame. Instead, they considers all other "bits of matter" and determine the frame of

reference from them. Does the ship then nothave a frame of reference from the point of view ofsubspace and outside observers? Not exactly. The frame of reference of the ship instead becomes

the frame of reference of subspace as it is defined without the ship's contribution. Then,obviously subspace does not have to consider the ship when determining the subspace frame,

because the ship's frame of reference perfectly matches the subspace frame of reference as it is

determined from all other factors in the universe. In other words, the ship's frame of reference is

made to be such that it does not contribute to the sum, S, discussed earlier. The only way this ispossible is if the ship's frame of reference seems to be exactly the frame of reference of subspace

defined as if the ship were not there.

Therefore, a warp field couples the frame of reference of everything inside the warp field to the

frame of reference of subspace. This becomes true regardless of what the frame of reference ofthe ship would be without the warp field there (i.e. it is true regardless of the actual speed of theship with respect to subspace). Thus, while the warp field is active, the ship's frame of reference

remains the frame of reference of subspace and is notdependent on the ships speed. This is what

places the ship outside of the realm of relativity and allows it to travel faster than light withoutgross violations of causality.

Second, we note that this sounds like the warp field is completely removing the mass of the shipas viewed from outside of the warp field; however, this isn't the case. Theory tells us that in

order to completely remove the effects of a ship's mass from the universe, one would have to

expend an infinite amount of energy. What the warp field does is to de-couple the relationship

between subspace- equivalent mass/stress-energy and normal space mass/stress-energy. Thesubspace-equivalent mass becomes zero, while the normal space mass is reduced (in the eye of

the outside observer) much like it is in the case of simple subspace fields.

So, this is how simple subspace fields and warp fields are formed by manipulating normal space

material to produce desired effects on the frame of reference of subspace. Next we will discuss

certain aspects of these fields.


8/35

4. General Aspects of Subspace Fields

All forms of subspace fields (be they simple subspace fields or warp fields) have certain generalaspects. For example, all subspace fields have effects in both space and subspace and form an

interaction between the two. We thus talk about such things as the shape of the field as it exists

in the normal space domain or the subspace domain. The two shapes can be different, and aparticular mapping will exist that maps one shape to the other. The shape of the field in subspace

will be mentioned later, but for other aspects of subspace fields, we will generally discuss only

the effects they have in normal space.

All forms of subspace fields have three basic layers -- the interior layer, the exterior layer, and

the interaction layer.

The interior layer is generally surrounded by the interaction layer. Though the interior layer isusually normal space, there are some cases in which the field changes the characteristics of thespace within the interior layer (such as the subspace fields used with today's faster than light

computer cores which will be discussed later). More often, the interior layer is basically a

"bubble" of normal space surrounded by the interaction layer of the field.

The exterior layer is the part of the field which extends beyond the interaction layer. This layer is

generally filled with normal space with certain aspects of the interaction layer spilling over andmixing in with the normal space.

In the interaction layer, space and subspace combine. The interaction of space and subspace

within this layer is what gives subspace fields their unique capabilities. For example, observersoutside of the subspace field see various effects (such as a reduction of mass) when viewing

objects within the subspace field. The outside observers see these effects because they areviewing the objects through the influence of the interaction layer. Also, the effects of the

interaction layer are what causes subspace to ignore (to some extent) masses (or more

appropriately, stress-energy tensors) which are inside of a subspace field, as mentioned earlier.

Subspace does this because it too is "viewing" those objects through the effects of the interactionlayer.

With these common basics in mind, we can now discuss specific aspects of simple subspacefields and warp fields independently.

5. Simple Subspace Fields

A subspace field which is symmetric in the subspace domain causes subspace to (in essence) actas an energy reservoir. Such a field is referred to as a simple subspace field (or just "a subspace


9/35

field"). To outside observers, anything within such a field will appear to "loose" some of its mass

energy to subspace while the field is active (as discussed earlier. (Equivalently, one could say

that the field masks out part of the mass of objects inside the field as they are viewed fromnormal space.) The amount of interior mass energy "placed" into subspace is dependent on the

strength of the subspace field. For all practical purposes, while the field is active, this mass

energy disappears from normal space (seeTechnical Note 1for this section). However, it shouldbe noted that when one compares the normal-space energy and momentum of a closed systembefore a subspace field is activated with that of the system after the field is deactivated, energy

and momentum conservation must apply. We will now look at momentum and energy

conservation considerations with respect to simple subspace fields.

5.1 Momentum and Energy Conservation with Simple

Subspace Fields

Here we will look separately at momentum conservation and energy conservation as they apply

to subspace fields. At the end of this section, examples will be considered to illustrate theseconservation considerations.

5.1.1 Momentum Conservation

Consider a ship of mass M which surrounds itself in a simple subspace field. To outside, normalspace, the mass of the ship becomes m < M once the field is active. This new, lower mass is

called the apparent rest mass of the ship (or simply its "apparent mass"). If the normal space

manifestation of the subspace field can be shaped so that the ship's fuel is kept outside of the

field, the ratio of fuel mass to ship mass will be greatly increased. In accordance with momentumconservation, fuel expelled with a given momentum will cause the ship to have an equivalent

momentum in the opposite direction (thus conserving momentum). However, with the subspacefield activated, the speed this momentum gives to the ship would be calculated using the

apparent (lower) rest mass of the ship. Thus, with the use of a subspace field one can achievegreatly improved acceleration rates as well as greatly lowered energy costs for reaching a given

speed.

As long as the field is active, kinematic considerations of the ship will be calculated with theship's apparent mass. However, when the subspace field is deactivated, the masked mass of the

ship returns. The results of this returning mass as it applies to momentum conservation will beconsidered in the examples given after the energy conservation considerations have been

discussed.

5.1.2 Energy Conservation

Once a subspace field is activated, energy conservation can be realized only if one includes the

mass energy which is "submerged" into subspace. This will be demonstrated in examples givenat the end of this section.
http://www.physicsguy.com/subphys/SubspacePhysics.html#5tn1http://www.physicsguy.com/subphys/SubspacePhysics.html#5tn1http://www.physicsguy.com/subphys/SubspacePhysics.html#5tn1http://www.physicsguy.com/subphys/SubspacePhysics.html#5tn1


10/35

There are, however, energy considerations other than kinematic ones. Some of the energy that is

internal to the ship must go into producing the subspace field. Currently, subspace field

generators produce unstable fields which continually "bleed" their energy back into normalspace. (This energy generally manifests itself as a combination of heat within the subspace

generator, electromagnetic radiation, and/or subspace radiation which can couple its energy into

normal space. Also, this energy bleeds off symmetrically so that momentum is conserved.)Because of this bleed off, subspace field generators must continually supply energy to thesubspace fields. The same amount of energy supplied to the field is eventually bled back into

regular space, thus conserving energy.

The final energy consideration involves internal ship energy which remains internal (producing

life support, etc.). Because the ship is within the interior of the subspace field, it appears to itself

to be in a normal-space "bubble." This means, for example, that to the ship's crew, the matter andantimatter on board do not loose any mass. Objects on board the ship only seems to loose mass

into subspace when the observer views the ship through the masking of the subspace field's

interaction layer. Inside the ship, the available energy does not change, and energy conservation

goes on as it always did.

We can, however, show that even when viewed from normal space outside the subspace field,the energy released by the interaction of matter and anti-matter on board the ship is the same as if

the matter and anti-matter hadn't "lost" mass to subspace. It is true that once the field is activated,

the matter and anti-matter aboard the ship will seem to "loose" some of its mass energy to

subspace in the point of view of the outside observer. For the outside observer to realize thatenergy has been conserved, he must remember that this mass energy did not actually disappear

from existence, but has simply been submerged into subspace. However, as the matter and anti-

matter interact, their mass is turned into other forms of energy. Since this energy is no longer inthe form of mass, the subspace field no longer masks part of that non-mass energy from the

outside observer. So, as the matter and anti-matter interact, the outside observer not only sees the

reduced masses of the matter and anti-matter turn into other forms of energy, he also sees mass

energy that had been masked by subspace being converted into normal, non-mass energy. Theresult is that he sees as much normal, non-mass energy being produced as any inside observer

would see, thus conserving energy from all points of view.

5.1.3 Some Examples

To analyze the conservation of energy and momentum involved with subspace fields, we willlook at two examples. In each example we will consider a ship which encloses itself within a

subspace field and then expels fuel in order to take a trip. At each step of the trip we will show

that energy and momentum are conserved.

Example 1

In these examples, the ship of mass M begins in one particular frame of reference. All energies

and momentums will be calculated in this frame. Initially, the ship's energy consists of its mass

energy (M*c^2) and internal energy (E(int) -- which will be used for various purposes). Duringthe trip, part of the internal energy will be used for on-ship purposes, and while this energy may


11/35

change form (becoming heat and eventually being radiated into space, for example) we know

that this energy is always present in some form. Thus this part of the internal energy is preserved.

The rest of the energy involved will be considered at each step to show that it is also conservedalong with momentum.

Step 1

The ship uses part of its internal energy to create a subspace field. As explained above, this

energy is bled back into space, thus this energy is conserved. As the field is turned on, part of theship's mass is masked from outside observers, and the apparent mass of the ship becomes m. To

realize the conservation of energy, we must remember that this mass energy is still "present", but

is submerged in subspace. This submerged energy is the difference between the mass energy of

the ship initially and its mass energy now -- (M - m)*c^2. This makes it obvious that the energy

is conserved (since the submerged energy of the ship plus its energy now is the same as its initialmass energy).

Step 2

The ship uses part of its internal energy to produce a high energy photon (as fuel) with a certain

momentum in a particular direction. In accordance with conservation of momentum, the shipmust gain an equivalent momentum in the opposite direction. In accordance with conservation of

energy, the internal energy used must be equal to the energy given to the photon plus the change

in energy of the ship (which now has more energy since it is moving in the original frame ofreference). (SeeTechnical Note 2for this section.) The change in energy of the ship is calculated

with the ship's apparent mass (m), and the energy submerged in subspace is still equal to (M -

m)*c^2.

So, part of the internal energy goes into the energy of the photon and increases the energy of the

ship, while the energy submerged in subspace is still the same. Meanwhile, the momentum of thephoton is canceled out by the momentum of the ship. Thus, energy and momentum are

conserved.

Step 3

As the ship travels, it may experience "collisions" with other objects. As long as these collisionsdo not collapse the subspace field, the ship's apparent rest mass will still be m as far as the

collisions are concerned.

This is no violation of energy or momentum, because for all intents and purposes, the missing

mass of the ship has been "left" sitting still in the original frame of reference by keeping itsubmerged in subspace. Thus the ship should interact with other objects as if its mass is m.

Step 4

Part of the internal energy is used to produce another photon for fuel which brings the ship backto rest in the original frame of reference. Energy and momentum are conserved here in the same

way they were conserved in step 2.


12/35

Step 5

The subspace field is disengaged, and the energy which had been submerged in subspace is

returned to the mass energy of the ship. This is just the reverse of the first step, and energy isobviously conserved.

Example 2

This example is identical to the first example up to and including Step 3. We will begin here witha new Step 4.

Step 4

In the previous example, the ship "decelerated" to get back to the original frame of reference and

then shut off its subspace field. Here we examine what happens if the subspace field is shut off

(intentionally or accidentally) while the ship is still moving in the original frame of reference.

As the field is deactivated, the mass energy which was submerged in subspace will be addedback to the ship. This mass energy can be modeled as actual mass which is sitting at rest in the

original frame of reference. In this model, as the field dies, it is as if the ship runs into a portion

of matter with a mass of (M - m). This is not as harmful as it may seem. A ship which actuallyruns into a chunk of matter with significant mass will be crushed because the force applied to the

front of the ship will have to be transferred to the back of the ship before the back will stop

moving. This produces the crushing effect. In our case, the mass is "added" throughout anyobjects within the subspace field at the same moment as the field is deactivated. All particles

throughout the interior of the subspace field are decelerated at the same time and at the samerate.

It is not that obvious what exactly takes place in this case to allow for the conservation ofmomentum and energy. We can deduce what would happen by considering the model of the

situation in which a ship runs into a mass of (M - m). In this case, a ship of mass m andmomentum p inelastically collides with an object of mass (M - m) which is at rest. After the

collision, the combined clump of ship plus object has a mass of M and a momentum p (to

conserve momentum). But, the energy of a mass m with momentum p plus the energy of a mass

(M - m) does not generally equal to the energy of a mass M with a momentum p. In order toconserve energy in this case, the final system must have internal energy in addition to its mass

energy and kinetic energy. (SeeTechnical Note 3for this section.) In our model, the collision

will generally cause heating to produce this internal energy. In the actual situation, the system

after the subspace field has died will include electromagnetic radiation, and/or subspace

radiation, and/or heat inside the ship to make up the extra energy needed for energyconservation.

In short, we have shown energy and momentum conservation in these examples with the

following comparisons. Turning on the subspace field is compared to a situation where the shipremoves part of its mass, leaving it at rest in its original frame of reference. The ship then

continues along its trip, just as if it had a lower mass. Turning off the subspace field can then be

compared to adding back on the previously removed mass which is still at rest in the original


13/35

reference frame. With these comparisons, one can see how energy and momentum are conserved

in the use of simple subspace fields.

5.2 Technical Notes for this Section (Simple Subspace Fields)

Technical Note 1

We say that when a subspace field is activated, part of the mass energy of objects within the field

disappears from normal space for all practical purposes (as seen by outside observers). We

should note, however, that other aspects of this matter (charge, baryon number, lepton number,etc.) are unaffected.

For example, an electron sitting within a subspace field will still seem to outside observers tohave a charge of -1, a lepton number of 1, etc. However, it will seems as if the normal rest massof the electron has been reduced.

So, when a ship in a subspace field seems to loose part of its mass as seen by outside observers,it is not as if the ship has lost some of its particles. Instead, it is as if all the particles individually

became particles of lower rest mass.

Technical Note 2

Here we examine the amount of energy needed to propel a ship with a reduced mass of m to avelocity v by expelling a photon. We will be using regular relativistic equations for momentum

and energy with the following notations:

c = the speed of light

v = the velocity of the shipbeta = v/c

1gamma = ---------------

____________\/ 1 - beta^2

Now, at some point the ship (whose reduced mass is m) uses part of its internal energy to expel aphoton in a particular direction. If the photon is created correctly, afterwards the ship will be

moving with the desired velocity v. Its momentum and energy will thus be given by the

following:p(ship) = gamma*m*v (the relativistic momentum of the ship)E(ship) = gamma*m*c^2 (the relativistic energy of the ship)

Now, in order to conserve momentum, the photon's momentum will have to be equal andopposite to that of the ship. The energy of the photon can then be calculated from its momentum.We can thus write the following:

p(photon) = p(ship) = gamma*m*vE(photon) = p(photon)*c = gamma*m*v*c


14/35

It is now possible for us to calculate how much of the internal energy of the ship would have to

be used to expel this photon. Before the photon was expelled, the energy of the system included

the mass energy of the ship (m*c^2), the internal energy of the ship which would be used toexpel the photon (E(fuel)), and some other internal energy which wouldn't be changed. After the

photon is expelled, the energy of the system includes the larger energy of the ship

(gamma*m*c^2), the energy of the photon (gamma*m*v*c), and that part of the internal energywhich wasn't changed. The energy used to expel the photon must make up for the difference inenergy between these two situations. We can thus write the following:

E(fuel) = (gamma*m*c^2 + gamma*m*v*c) - (m*c^2)= [gamma*(1 + beta) - 1]*m*c^2.

The interesting thing to note here is that if the subspace field hadn't been used to lower the

apparent mass of the ship, this energy would be calculated with the same formula, except m

would be replaced by M. This means that the subspace field allows a savings of energy given byE(saved) = [gamma*(1 + beta) - 1]*(M - m)*c^2.

As long as the energy needed to produce and maintain the field is less than this energy, thenthere is an overall savings in energy for this particular example.

It should also be noted that for significantly high velocities, the E(fuel) could still beimpractically high unless the apparent mass (m) is significantly small. As it turns out, mass

masking by subspace fields can provide the needed lowering in mass to make large changes in

the velocity of the ship a practical ability.

Technical Note 3

Here we examine the momentum and energy considerations of a collision between a mass m

with momentum p and a mass (M - m) at rest. Consider the following diagrams of the situationsbefore and after the collision:

Before:

m O M - mO----------> p O O P = 0

O

(The total internal energy of these systems = E(int-before).)

After:

O MOOO---------->pO

Internal energy = E(int-after).

The momentum of the larger mass M (after the collision) will be equal to the momentum of themass m (before the collision) in order to conserve momentum. We are interested in the difference


15/35

in the Energy between the two situations. We will calculate this energy using the following

notations:

gamma = the relativistic gamma factor for the mass mGAMMA = the relativistic gamma factor for the mass M

We can then write the difference in energy as follows:E(After) - E(Before) =[E(int-after) + GAMMA*M*c^2] - [E(int-before) + gamma*m*c^2 +

(M-m)*c^2]

Conservation of energy requires this difference to be zero. Using this, we will isolate the internal

energies of the systems on one side of the equation. This will be the difference in the internalenergies before and after the collision (Delta(E-int)). We thus write the following:

Delta(E-int) = E(int-after) - E(int-before)= gamma*m*c^2 + (M-m)*c^2 - GAMMA*M*c^2= [(M-m) - (GAMMA*M - gamma*m)]*c^2

Now, we can rewrite the gammas by remembering that for any system of mass m and momentum

p, the energy can be written as___________________E = gamma*m*c^2 = \/p^2*c^2 + m^2*c^4

We can thus write gamma for such a system as the following:___________________

gamma = \/ p^2/(m^2*c^2) + 1

Since the momentum of both m and M are the same in our example, we can rewrite the change in

internal energy as the following:_______________ _______________

Delta(E-int) = [(M-m) - (\/ p^2/c^2 + M^2 - \/ p^2/c^2 + m^2 )]*c^2

Now, since M > m, and both momenta (p) above are the same, we can draw the followingdiagram representing the relationships between M, m, and p as follows:

+ - +/| | /|/ | | / |

/ | | / | M-m/ | |M / |H + - | => H +/ / | | | / // h | |m | / h

/ / | | | / /// | | | //

o---p/c---+ - - o

_______________ _______________Note: H = \/ p^2/c^2 + M^2 and h = \/ p^2/c^2 + m^2

Looking at the right hand diagram, it's simple to show thatH = H - h


16/35

or_______________ _______________

(M-m) >= (\/ p^2/c^2 + M^2 - \/ p^2/c^2 + m^2 ).

(where ">=" denotes greater than or equal to). Thus,_______________ _______________

[M-m - (\/ p^2/c^2 + M^2 - \/ p^2/c^2 + m^2 )]*c^2is always greater than or equal to zero.

So, we see that the change in internal energy is always positive. That means that in order for

energy and momentum to be conserved in this type of collision regardless of the masses and

momentum involved, the overall system must increase in internal energy. Generally, this wouldmean that the collision would cause heating and this additional heat would allow for energy to be

conserved.

6. Warp FieldsThere is one major difference between simple subspace fields and warp fields. A field is labeledas a warp field when it produces a reference-frame coupling. The reference frame of objects

within the real-space manifestation of the warp field must be coupled in some way to the

reference frame of subspace, as discussed in section 3.

In section 3 we mentioned that we would discuss other aspects of warp field production in thissection. What we want to consider is the difference in the "exotic" nature of the stress-energy

tensors needed to produce simple subspace fields and those needed to produce warp fields. There

are essentially two ways in which one could imagine changing a subspace-field-producing stress-energy tensor so that it becomes a warp-field-producing stress-energy tensors.

As it turns out, the easiest way to do this is to change the exotic nature of the tensor so as to skew

the subspace manifestation of the subspace field until it is no longer symmetric in that domain.Interestingly, manipulating a subspace-field-producing tensor in this way creates an exotic

enough effect to produce a reference-frame coupling at the interaction layer of the field.

Observers in the interior of such a field will measure space and time outside of the field as if they

were viewing it from within the subspace frame of reference -- regardless of the velocity of theseobservers. This feature is what allows for the faster than light travel on which we so depend.

Another useful features of skewed subspace fields is that the depositing of mass energy intosubspace which occurs is not symmetric. This asymmetric placing of energy into subspace

manifests itself as momentum transfer, and this causes subspace to act as a momentum reservoir

as well as an energy reservoir. Momentum is essentially deposited within subspace, and to

conserve overall momentum, the combination of all objects within the warp field will gain anequivalent momentum in the opposite direction. Only when the momentum transferred into

subspace is taken into account can momentum conservation be realized. At the time the ship's

momentum is changed, no actual fuel is expelled to produce this momentum, and normal-space-


17/35

only momentum conservation is essentially ignored as long as subspace is masking the

momentum. Therefore, this method of warp travel is labeled as non-Newtonian propulsion. The

use of warp propulsion will be discussed in a later subsection.

It is also possible to change the exotic nature of the stress- energy tensor in order to produce

warp fields which are non- propulsive. This is generally done simply by intensifying the exoticnature of the tensor by increasing its strength alone, and without skewing the subspace field.

Such tensors are generally called subspace-symmetric warp tensors, and they produces a field

which provides a reference frame coupling while the subspace manifestation of the field is stillsymmetric. By changing the characteristics of such tensors, one can produce many different

varieties of these fields, and even though they are technically warp fields (because they produce

a reference frame coupling) certain varieties are sometimes still referred to simply as subspace

fields (because of they are in fact symmetric within the subspace domain.)

Perhaps the most useful non-propulsive warp fields in use today are ones which provide a

subspace reference frame coupling to every point within the interior of the field as views by

every other point within the interior of the field. Unlike the warp propulsion field, this fieldallows objects within its interior to travel faster than light with respect to one another. These

fields are the ones in which modern shipboard computer cores are placed so that signals can besent faster than light between various computer components.

Another type of symmetric, non-propulsive field which has been studied with interest are knownas static warp bubbles. These have been known to have the odd effect of coupling people inside

the field not back to real space-time, but to a virtual space-time created within the bubble.

There are, as mentioned, many different types of non-propulsive warp fields, and we will not

consider them all here. What we wish to stress here is that the one major component which all

warp fields share (propulsive/asymmetric or non-propulsive/symmetric) is a reference framecoupling of one type or another.

6.1 Warp Propulsion

Producing a warp propulsion field causes subspace to act as both an energy and a momentum

reservoir. The ship within the warp field will have a lower apparent mass, and it will gain a

momentum equivalent to and in the opposite direction of the momentum placed into subspace.Because there is also a reference frame coupling, the relationship between the momentum and

the velocity of the ship is not calculated using Einsteinian physics. This allows the ship to have a

real (non-imaginary) momentum and energy even though its apparent speed is greater than the

speed of light. Energy and momentum conservation will be discussed in a later subsection.

6.1.1 Single-Layered Warp Fields

First we will consider warp propulsion produced with a single- layer warp field. As such a field

is activated, the momentum of the ship (and thus its speed) will increase. At first, the ship will be

traveling at slower than light speeds, and the energy of the ship increases dramatically as itsspeed approaches that of light. Only after the jump to faster than light speeds occurs will the


18/35

reference frame coupling take full effect, and the energy of the ship be completely outside of the

realm of Einsteinian physics.

Once the reference frame coupling takes effect, all measurements with respects to the ship are

done as if the ship is in the frame of reference of subspace. That means that at any particular

moment, properties such as distances, times, etc. are measured just as if the ship were sitting stillfor that moment in the frame of reference of subspace. As in illustration, one could imagine

taking a snapshot of a ship in warp and finding that it is indistinguishable for that one moment

from a ship who is not moving with respect to the subspace frame of reference. Yet, we attributekinetic energy (energy of motion) to such a ship, even if we view it from the subspace frame of

reference. This is because the kinetic energy of the ship is actually held within the warp field

itself.

Thus, to keep the ship at a certain speed, one must keep the warp field at a constant energy level

which is seen as the energy of the ship itself. But, today's warp field generators produce unstable

fields (similar to subspace field generators.) Thus, warp fields also bleed off there energy back to

the normal universe (in the form of heat in the field coils, electromagnetic energy given offnearby the ship, etc.). Therefore, the warp field must be given a constant supply of energy from

the ship. (This, too, will be discussed in a later subsection. The important thing to understandhere is that the warp field does need a constant supply of energy).

To increase the speed of the ship, one must increase the energy level of the warp field. However,at higher energy levels, a warp field becomes much less efficient (bleeding off its energy at much

larger rates). Therefore, the power output of the ship must increase dramatically to hold the warp

field at a higher energy level (thus holding the ship at a large velocity).

For our examples, we will use a model which approximates warp field energy levels in certain

geometries. The power (the amount of energy given to the field per unit time) given to a fieldlayer depends on the energy of that layer, and in our model that dependence is as follows:

Power = P_0*(E/E_0)^3

Where E is the energy of the layer (and thus the energy of the ship) and P_0 & E_0 are a power

level and an energy level intrinsic to the model.

For example, a ship traveling at a particular warp velocity may have an energy of 2*E_0associated with its motion. In order to keep the warp field up, the ship would have to output

energy at a particular rate, providing a power of 8*P_0. If the ship increases its speed so that its

energy is now 4*E_0 (twice as much as before), the ship will have to provide a power of 64*P_0

(8 times as much as before) in order to keep the warp field up. The energy of the ship itself(associated with its velocity) has only increased by a factor of 2, while the warp engines are now

having to output eight times as much power into the warp field because the higher energy warp

field is much less efficient (quickly bleeding its energy back into normal space).

6.1.2 Multi-Layered Warp Fields


19/35

As the ship's speed increases, the correlation between space and subspace at the interaction layer

becomes greater and greater. More and more of the ship's mass energy is masked by (or

submerged into) subspace, and more and more momentum is placed into subspace. We thus saythat the ship is submerged to a deeper subspace level as its speed increases. (We should,

however, remember that the interior of the warp field is essentially still normal space. It is only

the relationship between the interior and exterior of the field that becomes deeper interlaced withsubspace.) We can use this analogy to understand why multi-layer warp fields are used today forwarp propulsion.

By correctly setting up the geometry of the stress-energy tensor within a warp field generator,

one could produce a double layered warp field which conceptually divides subspace into two

levels (an "upper" level and a "lower" level). This is basically done by creating a two stage stress

energy tensor which when both stages are active looks like the usual warp-field-creating stressenergy tensor. However, when only one stage of the tensor is active, its effects would not be able

to "submerge" a ship deeper than the "bottom" of the upper level of subspace, regardless of how

much energy was provided to the tensor. For our purposes we will say that if the ship were

"submerged" as deep as this first stage could take it, it would have an energy of E_th (thethreshold energy between the two subspace levels). Then, when the first layer of the warp field

was active, the ship's energy would be between zero and E_th. For illustration, we can assumethat E_th is a particular value, say 4*E_0 (where E_0 comes from our model mentioned above).

With the first warp layer active, one can supply it with more and more power up to the point

where the energy in that layer is 4*E_0. At that point, one would be supplying a power of64*P_0 (as seen earlier). This is no different from having a single-layer geometry to the warp

field rather than a double-layer warp field. The difference will be evident if one attempts to

supply even more power to the first layer of the double-layer warp field. With only the first layeractive, the energy of the warp field can be no higher than 4*E_0 (the energy associated with

being "half way deep" into subspace). Any power supplied to the layer above 64*P_0 will be

instantly bleed back into normal space rather than pushing the warp field to a higher energy.

In order to push the ship deeper into subspace and further increase its energy, the second warp

field layer needs to be activated. One therefore turns on the second stage of the stress- energytensor, creating the second warp field layer. This can only happen once the first layer has taken

the ship deep enough into the first level of subspace to "jump" into the second level as the second

layer is activated. This is due to the fact that if one tries to energize the second stage of a two-

stage stress-energy tensor before the first stage is sufficiently energized, the overall tensor willnot have the geometry needed to sustain a warp field. However, once the first stage is sufficiently

energized, the second stage will complement the overall geometry of the tensor, producing the

second field layer. Once the second layer is activated, the total energy of the warp field is

_divided_ among the two stages of the tensor, and thus among the two layers of the subspacefield.

In our example, one could hold the ship just above 4*E_0 (close enough for us to estimate it with4*E_0) with each layer holding 2*E_0 of energy apiece. This means that the power needed by

each of the two layers is only 8*P_0 apiece (as calculated in our model) for a total of 16*P_0

rather than 64*P_0. This is a substantial savings in power consumption.


20/35

To sum up... As one pushes one layer of a warp field to higher and higher energies, the efficiency

of that layer drops dramatically. However, one can use multi-layer warp fields to divide subspace

into many levels. By adding enough energy to the warp field while N layers are active, one cango deeper and deeper into level N of subspace. Once one is close enough to level N + 1, one can

activate the next warp field layer and "jump" into the next subspace level. This divides the

energy of the warp field among more layers, lowering the energy level of each individual layer.This in turn increases the efficiency of each individual layer (thus increasing the overallefficiency of the warp field as a whole).

The actual calculation of the power requirements for a warp field is more complicated than in our

simple model. However, the principle is the same, and multi-layer warp fields do increase power

efficiency. When this discovery was made, it had a profound effects on the future of Warp

Propulsion.

6.1.3 Development of Modern Warp Propulsion Fields

Just after the discovery of increased efficiency with the use of multi-layer warp fields, manyresearch teams started working to produce various multi-layer strategies and maximizing there

efficiencies. One particular team jumped ahead of the rest and fairly easily developed a 9 layer

warp field design (the first layer beginning at the speed of light). While work started onmaximizing the efficiency of this new 9 layer design, still other teams moved on to try and

produce strategies with even higher numbers of layers. However, no such attempts were

successful.

Work done to maximize the 9 layer design soon lead to theories which suggested that the success

of the 9 layer strategy wasn't simply luck or coincidence. These theories suggested that subspaceactually possessed an intrinsic 9 level nature -- that there really were 9 preexisting subspace

levels. Such theories correctly predicted the proper method for maximizing the 9 layer warp fielddesign, and they suggested that it was impossible to produce warp fields with more than 9 levels.

Today, many aspects of these theories are widely accepted, and the 9 layer warp field is the

standard by which warp factors are defined. The full development of the first warp field layer(Warp 1) in today's warp systems constitutes the entrance into the first level of subspace. Each

consecutive warp factor constitutes the entrance into the next consecutive subspace level. As one

approaches warp 10, one presses deeper towards the "bottom" of the ninth subspace level, and

warp 10 corresponds to being fully submerged into subspace. Thus, fully submerging a vesselinto subspace theoretically gives the vessel infinite velocity, requires an infinite amount of

energy to get the vessel there, and requires an infinite output of power to hold the ship there.

Unfortunately, the 9 levels of subspace (which is theoretically natural and cannot be bypassed) is

the limiting factor of the speeds maintainable by today's warp vessels. Past warp 9 the power

requirements for higher warp speeds continues to increase without another power threshold likethose found at the integer warp factors. The fact that current theory rules out the possibility of

producing a tenth highly efficient warp factor is generally referred to as the "warp 10 barrier."

(Note: Sometimes this phrase is used to refer to the infinite speed one would theoretically obtainat warp 10. However, this is a less proper use of the phrase. Thus, the statement "perhaps one


21/35

day we will break the warp 10 barrier" would more likely refer to the possibility of finding an

efficient means for traveling much faster than warp 9 rather than referring to the possibility of

traveling faster than infinite speed.)

Though our current technology still supports the theories behind the warp 10 barrier, certain

brushes with advanced non-federation technology suggests that some linking of warp fieldproduction and strong gravimetric distortion may hold the key to producing fantastic speeds

through energy and power outputs easily attainable by today's starships. Still, skepticism

abounds, and only time will tell whether we will ever be able to "break" the warp 10 barrier.

6.1.4 Modern Warp Propulsion Field Generation

There was one very important problem with multi-layered warp fields that we have yet tomention. The geometry of a multi-stage stress-energy tensor inherently produces a warp field

which is symmetric in the subspace domain. That means that the multi-layered warp field

produced by such a tensor cannot be propulsive.

In order for propulsive fields to gain the benefits which multi- layered warp fields possess, a new

way to produce multi-layered fields needed to be found. As it turns out, the key to regaining thenon- Newtonian drive came in nesting many layers of warp field energy within one another. In

today's warp engines, a series of single-stage tensors are activated in a particular way to produce

a warp field which has the desired effects. We will now examine how the "trick" of producingmulti-layered, propulsive warp fields is performed by considering an example using 3 single

layer field generators.

The 3 field generators are placed in a row with a particular distance between each of them. The

generators are then activated in sequence, one after the other, at a particular frequency. This

means that plasma is ejected for a moment into each field coil, and then it is quickly shut off.Each coil then produces its own warp field layer which dissipates energy as it expands andeventually disappears once it has lost all its energy. Before the field layer produced by the first

generator dies, the second field generator is activated, and so on.

Because the tensors used to create the 3 fields are each single- stage tensors, the three fields

themselves do not form a three layer warp field like we have previously described. Instead, they

act as three separate, nested layers of warp field energy. However, when the frequency at whichthe three fields are produced is just right (the actual value depends on the precise geometry of the

situation) the nested field layers form at just the right spacing so that they interact to produce a

single warp field. At that point, the three nested field layers appear to subspace to be one warp

field which consists of the first layer of a multi-layer design. If the tensors used to produce thefields have the correct geometry (which in part depends on the number and placements of the

field coils), then this multi-layer design seen by subspace will be the natural 9 layer design which

we want. Also, because the nested layers that make up this field are produced at different pointsin space (and thus at different corresponding points in subspace) the overall warp field appears to

be asymmetric in the subspace domain. Thus, this "first-level" warp field will be a propulsive

field.


22/35

At this point, we could increase the energy input to each of the field coils in order to make the

field press deeper into subspace. However, when we do this we increase the energy of the overall

warp field being created, thus lowering the efficiency of the overall field. This means that eachnested field layer will dissipate its energy more rapidly, thus expanding and dying more rapidly.

Remember that the key to having the 3 nested layers act as a single warp field was that they were

created with just the right spacing to interact properly. Thus, because the higher energy fieldlayers are expanding more rapidly, we must produce the layers at a higher frequency if we stillwant them to interact properly and form a single warp field.

At some point, the energy in the overall warp field will be enough to press the ship into the

second level of subspace. When this happens, we will have a second-level warp field -- subspace

will see the three nested field layers as a single warp field consisting of 2 un- nested field layers.

Conceptually we can then think of the total energy of the field being divided among these two"virtual" un-nested field layers, thus increasing the total efficiency of the warp field as discussed

earlier. With the efficiency increased, each layer now dissipates and expands more slowly.

However, in the second level of subspace, each field layer needs to interact more strongly with

the next, and thus they must be created closer together. The combination of slower expansionand the need to create the fields closer together exactly cancel each other out such that the

frequency just before interring the second level is approximately equal to the frequency just afterinterring the second level.

This process can be continued--increasing the energy of the warp field and increasing the

frequency at which the nested layers are created--in order to press deeper into subspace and passthrough the higher efficiency points at the integer warp values.

And there we have it--the effects of a multi-layered warp field design which is produced withsome number of nested layers of warp field energy, each created at a different point in space and

subspace such that the field is asymmetric (and thus propulsive). We should note that this meansthat the asymmetry of the field (and thus the direction of propulsion) is not controlled bychanging the complex geometry of the tensor used to create the field, but rather by sequencing

the field coils in a particular way. With modern ship design, an optimal number of field coils are

placed within two warp nacelles on either side of the ship. This means that by properlysequencing the coils in the two nacelles, the ship will be able to maneuver in various directions

during warp. We could also produce maneuverability in a single nacelle design by changing the

geometry of the tensors used such that they give a left-right asymmetry. However, this has been

found to be much less efficient and much more difficult than simply using two nacelles andsequencing the field coils properly to produce the desired effects.

Finally, we should note that in this modern design, the momentum coupling (the placement ofmomentum into subspace as mentioned earlier) manifests itself as a force coupling between the

various layers of warp field energy. During the coupling, part of the mass energy of the ship

becomes masked by (or submerged into) subspace in an asymmetric way (because of the

geometry of the field) to produce the momentum masking which creates the non-Newtonianpropulsion.


23/35

6.2 Momentum and Energy Conservation with Warp

Propulsion

In this section we will consider the conservation of momentum and energy as it applies to warp

propulsion. When we did this with normal subspace fields, we looked separately at each issue(energy and momentum), however, here they are so integrated that it will be easier to consider

them both at once.

Again, we look at two types of energy separately--the internal energy of the ship, and the energyassociated with the mass of the ship and its motion. The momentum is, of course, closely related

to the energy of the ship and its motion, so we will look at the two together. For the internalenergy of the ship, the conservation of energy takes place much the same way it did with

subspace fields. The mass of any matter/anti-matter is lowered, but energy is seen to be

conserved by all observers, just as it is with subspace fields. Part of the internal energy will go to

produce the warp field, and this will eventually be bleed back into real space.

(Note: Since the warp field produces the motion of the ship in real space, and this bleeding off of

energy makes it necessary to output energy at a constant rate in order to keep moving, one canalso explain this as "continuum drag." This is done by associated the motion of the ship to the

motion of a classic vessel moving through the use of friction. In this model, subspace is said to

provides a constant force against the ship while the ship provides a constant force in order tokeep moving at a constant velocity. (SeeTechnical Note 1for this section.))

Just as it was with simple subspace fields, a warp field masks part of the mass of the enclosedship from outside observers. This leaves a ship of mass M with a new "apparent mass" of m.

Again, overall energy conservation can be realized only when one takes into account the mass

energy submerged into subspace.

Now, it is the kinematic energy of the ship that is associated with its momentum. They both

increase as the actual velocity of the ship increases. However, the velocity increases as the warpfield increases, and this reduces the ship's apparent mass. All of this can be accounted for with a

simple association. We associate the actual, faster than light velocity of the ship (v) with a

slower-than-light, "energy-equivalent" velocity (v'). We then use the actual mass of the ship (M)and the energy-equivalent velocity (v') in conjunction with normal, relativistic equations to

calculate the momentum and energy of the ship. (Note: the relationship between v and v' is

discussed inTechnical Note 2.) This association allows us to easily calculate the momentum and

energy of the ship, and all the complexity of increasing the actual velocity while decreasing theapparent momentum are all rolled into the association.

So, where does this energy and momentum of the ship come from, and how are they conserved?Well, remember that part of the internal energy goes into maintaining the warp field at a constant

energy level. That means that part of the internal energy must go into the warp field to raise it to

that constant energy level in the first place. As mentioned earlier, this constant energy level ofthe warp field IS the energy of the ship's motion. They are one and the same.
http://www.physicsguy.com/subphys/SubspacePhysics.html#6tn1http://www.physicsguy.com/subphys/SubspacePhysics.html#6tn1http://www.physicsguy.com/subphys/SubspacePhysics.html#6tn1http://www.physicsguy.com/subphys/SubspacePhysics.html#6tn2http://www.physicsguy.com/subphys/SubspacePhysics.html#6tn2http://www.physicsguy.com/subphys/SubspacePhysics.html#6tn2http://www.physicsguy.com/subphys/SubspacePhysics.html#6tn2http://www.physicsguy.com/subphys/SubspacePhysics.html#6tn1


24/35

The momentum comes directly from the fact that a propulsive warp field causes subspace to act

as a momentum reservoir. There is a momentum being masked by subspace which is equal but

opposite to the momentum of the ship. Only when this masked momentum is taken into accountcan conservation of momentum be realized. One could think of this situation as equivalent to a

Newtonian drive situation by equating the momentum masked by subspace to the momentum of

the expelled fuel in a Newtonian drive situation. However, there is a major difference--anythingin normal space which has momentum also has energy, and the energy of the expelled fuel in theNewtonian drive situation must come from the ship's internal energy. However, the momentum

masked by subspace has no energy associated with it, and so it doesn't take away from the ship's

internal energy.

The fact that subspace takes up for the momentum of the ship (momentum which seems to come

from nowhere in the eyes of outside observers who only consider normal-space momentum) hassome rather interesting effects, as we will see in examples below.

6.2.1 Some Examples

To analyze the conservation of energy and momentum involved with warp propulsion fields, we

will look at two examples (similar to what we did when considering simple subspace fields). In

each example we will consider a ship which takes a trip using warp. At each step of the trip wewill show that energy and momentum are conserved.

Example 1

In these examples, the ship of mass M begins in one particular frame of reference. All energiesand momentums will be calculated in this frame. Initially, the ship's energy consists of its mass

energy (M*c^2) and internal energy (E(int)--which will be used for various purposes). During

the trip, part of the internal energy will be used for on-ship purposes, and while this energy maychange form (becoming heat and eventually being radiated into space, for example) we knowthat this energy is always present in some form. Thus this part of the internal energy is preserved.

The rest of the energy involved will be considered at each step to show that it is also conserved.

Step 1

The ship uses part of its internal energy to create a warp field. As discussed above, part of thisenergy is bled back into space, while the rest accounts for the kinematic energy of the ship, thus

this energy is conserved. As the field is turned on, part of the ship's mass is masked from outside

observers, and the apparent mass of the ship becomes m. To realize the conservation of energy,

we must remember that this mass energy is still "present", but is submerged in subspace. Thissubmerged energy is the difference between the mass energy of the ship initially and its mass

energy now--(M - m)*c^2. This makes it obvious that this energy is conserved (since the

submerged energy of the ship plus its energy now is the same as its initial mass energy).

The warp field also causes subspace to act as a momentum reservoir, and so a certain momentumbecomes masked by subspace. As mentioned above, this momentum has no energy associatedwith it. To conserve overall momentum, the ship gains an equivalent momentum in an opposite


25/35

direction. The motion of the ship gives the ship kinematic energy. Again, this energy is part of

the energy contained in the warp field, and thus it comes from part of the internal energy.

We have thus shown overall conservation of momentum and energy in this step.

Step 2

As the ship travels, it may experience "collisions" with other objects. Though these collisions

may not collapse the warp field, they would have interesting effects. We will wait to considerthese effects in example 2.

Collisions which do collapse the warp field can have very damaging effects. (SeeTechnical Note3for this section.)

Step 3

As the ship comes to its destination, it shuts down its warp field. As this is done, the momentum

masked by subspace becomes unmasked, and the ship in turn looses its momentum. The energycontained in the warp field is bleed back into normal space as the warp field collapses.

Remember that this energy also accounts for the energy of the ships motion, thus as the ship

looses momentum, it also loses its kinematic energy which is bleed back into normal space.Finally, the mass energy that was masked by subspace returns to the ship, bringing its mass back

to the original M.

So, here we again see that the overall energy and momentum are conserved.

Example 2

The first step in this example is identical to the previous example. We will thus start with thesecond step and more closely examine the collisions mentioned in step 2 of example 1.

Step 2

During the travel, the ship encounters a large object. For convenience, we will assume that the

object is at rest in the original rest frame of the ship so that it must be deflected away from the

path of the ship. As the object is deflected, the ship's momentum is effected as if it were a shipwith a momentum calculated by using its energy-equivalent velocity (v'). That is, the ship acts no

different (kinematically speaking) from a ship of mass M and velocity v'.

Deflected the object will give it energy and momentum. The energy can come in part from thekinematic energy of the ship and in part from the internal energy of the ship (if a tractor beam is

used to deflect the object, for example). But, in addition, internal energy must be transferred to

the warp field in order to keep it from collapsing during the interaction with the object. Howmuch internal energy needs to be expended and why will be explained as we look at momentum

conservation.
http://www.physicsguy.com/subphys/SubspacePhysics.html#6tn3http://www.physicsguy.com/subphys/SubspacePhysics.html#6tn3http://www.physicsguy.com/subphys/SubspacePhysics.html#6tn3http://www.physicsguy.com/subphys/SubspacePhysics.html#6tn3http://www.physicsguy.com/subphys/SubspacePhysics.html#6tn3http://www.physicsguy.com/subphys/SubspacePhysics.html#6tn3


26/35

To conserve momentum, the total change of the ship's momentum will be equal and opposite to

the change in the momentum of the object. The deflection of the object will cause the warp field

to become imbalanced in the direction of the ship's change in momentum. This happens as theadditional energy is feed to the warp field to keep it from collapsing. After the interaction, the

ship can do one of two things. First, it could continue on its changed course, coming out of warp

at some later point in time; or, second, it could use its warp field to adjust its momentum (and itscourse) to get to its original destination.

In the first case, the ship will continue its journey along its changed course until step 3. In thesecond case, the ship will use the warp field to readjust its course. As this readjustment is made,

the imbalanced warp field deposits actual momentum into space (generally in the form of

photons) rather than "putting" the momentum into subspace. This means that the real change in

momentum of the object will be counteracted by the real momentum of the expelled photons--thus conserving normal space momentum.

The energy needed to produce these photons comes from the energy placed into the warp field

(to keep it from collapsing) as the interaction with the object took place. Also note that as thephotons are emitted, the ship gains back the momentum it lost during the collision. That means

that it must also gain back the kinetic energy that it lost. This energy must also be supplied by theenergy stored in the warp field while the interaction took place. Since this energy is exactly the

energy lost to the object during the interaction, the object's energy eventually comes from the

internal energy of the ship. Therefore, as the object is deflected, the energy feed into the warp

field is just enough to produce photons (whose momentum will be equal and opposite to thechange in the object's momentum) and to restore the kinematic energy lost by the ship.

(Note: The ship could continually adjust its warp field during the collision so that its momentumand velocity don't change. In this case, energy is still feed to the warp field during the

interaction, but the continually adjusting warp field will continually use that energy toimmediately create the photons necessary to conserve momentum. The end result is the same--the ship has changed the momentum of the object, a momentum equal and opposite to that of the

change becomes real in the form of photons, and the ship's momentum remains unchanged.

Meanwhile, the internal energy of the ship has been used to produce the photons and to give theobject its energy.)

So, energy and momentum in real space are conserved during and after a "collision" with anobject.

Step 3

The ship reaches its destination and shuts off its warp field. What happens here will depend on

which of the two cases (mentioned above) was chosen. If the ship changed its course after thecollision (thus completely making up for the collision), then as the ship comes out of warp it willcome back to rest in its original frame of reference (just as it did in example 1). However, if the

ship did not change its course, then it will have to make up for the collision as it comes out of

warp. As the imbalanced warp field collapses, the energy that was placed in the warp field duringthe interaction will produce the photons necessary to make up for the real momentum given to

the object. As the momentum of these photons gives momentum back to the ship, the ship will


27/35

gain energy which must also come from the energy stored in the warp field during the

interaction. Then the re- balanced warp field can completely collapse, bringing the ship to rest in

its original frame (just as it did in example 1).

Note, that if the energy needed to create the photons and restore the ships lost kinetic energy

were not stored in the warp field during the collision, then they would have to be supplied by theinternal energy of the ship as the warp field collapses. That means that one would actually have

to expend energy just to shut off the warp field (which makes no sense because the warp field

must collapse when you stop feeding energy to it, even if you have no more energy left to createphotons, etc.). This is why it is important that all the energy needed to make up for the collision

is stored in the warp field during the collision.

So, we see conservation of energy and momentum in all the stages of this example as well.

6.3 Technical Notes for this Section (Warp Fields)

Technical Note 1

Here we consider the model of warp travel which involves the concept of continuum drag. In this

model, the constant power supplied to the warp field to keep the ship at a constant speed isrequired because a constant force (continuum drag) is said to be applied to the ship. To examine

this, we consider a classical case of supplying a constant force against a friction force in order to

maintain a constant velocity.

In this situation, a vehicle which has already reached a particular velocity (v) continues to supply

a constant force equal and opposite to an opposing frictional force to maintain its velocity. So wewrite

_ _F(vehicle) = -F(friction) = constant (in, say, the x direction).

Now, if the vehicle starts at a position x = 0 and at some point the vehicle has traveled to theposition x, then we can calculate the amount of work done by (and thus the amount of energy

supplied by) the vehicle during the trip:x/

E = | F(x') dx' (the integral from 0 to x of F(x'), dx')./0

But since the force is constant over time (and thus over distance), this reduces to the following:

E = F*x

Finally, we can calculate the amount of power output one would need to keep supplying thisforce during the whole trip:

dE dxP = -- = F*-- = F*v


28/35

dt dt

Under normal circumstances, the vehicle wou

Documents

Subspace Physics