Tuesday, February 17, 2015

Proof that E=mc2

PressureVolumeExpInstruments
Figure1: Experimental apparatus for determining relationship between Pressure (P) and Volume (V). Image is obtained from http://galileo.phys.virginia.edu

Figure 1 is an image of an instrument used to determine the relationship between Pressure (P) and Volume (V)-(Boyle’s Law). Pressure is inversely proportional to Volume ie P ∝ (1/V). Pressure is created by particles bumping into a 2 dimensional surface as shown in Figure 1. Repeated below...
P ∝ (1/V)
P = Pressure
V = Volume
∝ means proportional

This same model was used by Einstein to derive is very famous model equation E=mc2.

Einstein modeled the cause of the photoelectric effect (ie he basically shone a light on a surface and measured the force caused by that light) as mass impacting a 2 dimensional surface which then moved electrons and hence caused a flow of electrons ie a current. The mass impacting the 2 dimensional surface is viewed like a pressure (in electrical terms a voltage). This is shown in Figure 2 below.

PhotoelectricExperimentIntrument
Figure 2: Photoelectric effect experiment instrument that is used to determine Planck's constant as well as used as the model to derive E=m.c2. Image is obtained from http://imgarcade.com

Newton's theory of Force and momentum is shown in equation 1 below
Equation 1:
F.Δ t = (Δ m . v)
where
F=Force
Δ means difference eg A2 - A1 = ΔA
t = time
Δ t = amount of time (ie time at end - time at start eg 10sec - 5 sec = 5 sec)
v = velocity

Pressure by definition is measured as amount of Force (F) given within specific area A and the relationship is shown in equation 2 below:
Equation 2:
P = F / A
P = Pressure
F= Force
A = Area

therefore
Equation 3:

P = pressure
m = mass
v = velocity
t = time
F= force
A = Area


Since velocity v = c the velocity of light - about 300 x 106 ms-1 (since the things causing the pressure [P] is light itself and light can only travel at the speed of light)
therefore
Equation 4:

P = pressure
m = mass
c = speed of light which is about 300 x 106 ms-1
t = time
F = force
A = area


Mass [m] can be obtained by multiplying the density of a volume by the number of volumes. Density is given by m/V and V is volume so
Equation 5:

Where
m = Mass
V = Volume
density = m/V


A volume V is defined as the multiplication of 3 dimensions, width, height and Length (L).

We also can define the region that the particles collide with as an Area (A) as it has 2 dimension only.
This can be visualized as the blue part of the rectangle and is found by multiplying the height and the width
Equation 6:
(Height . Width) = Area (A)

We can obviously define Volume V as Area (A) multiplied by Length (L)
Equation 7:
V = A . L
V = Volume
A = Area
L = Length

VolumeArea
Figure3: Definition of Area (A) and Volume (V). Image is obtained from http://www.advancedaquarist.com

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Putting all the above together:

Therefore
Equation 4


can have Equation 5 inserted into it giving


-Mass is the same as saying the average density of all the virtual particles multiplied by the known volume.

This is sometimes called the mass density of energy.


Using Equation 7 this is the same as saying (I just moved the variables around)


Volume is then converted to Area (A) multiplied by Length (L). In this case the Area means the surface of the light sensor and where light impinges on (see Figure 2) multiplied by the Length that light travels in a known (constant) time eg 1 second.
or
v = (ΔL/Δt)
v = Velocity
ΔL = Distance travelled (actually length of vector to get in correct in physics terms)
Δt = amount of time taken
v = c since, as mentioned before, the thing causing the pressure is light itself which can only travel at the speed of light (commonly annotated as c).

giving

As you can see by the missing component above I am unfortunately being hacked by Fruitcake so I have added a Google Drawing in place of the Google Doc that has been corrupted.
MC2Eq04+05+07_Reworked

Link to this equation in Google Docs can be found here:
https://docs.google.com/document/d/1PETJ85YDxBb-vplJOqnAeXxSbyha09UJY7YXffC_ASk/edit?usp=sharing

-The A in the numerator (top part of the division sign) and in the denominator (bottom part of the division sign) can cancel as they are both the same. We make it the same as the size of the surface of the part of the experiment's apparatus that the light shines on.

If we use a constant light source with a constant frequency then the amount of mass delivered by a light pulse per second on the experiment's receiver (see figure 2 above) will be the same for each volume V.

Anyway by rearranging the equation above we get the following
Equation 8


This result only gives the relationship between pressure (P) and the mass delivered by a constant volume of light which is at a constant frequency.

Notice I write light instead of electro-magnetic pulse. Its the same thing.

The relationship E=mc2 is obtained by the relationship Pressure (P) and Temperature (T) and Temperature (T) and Energy (E).

Energy (E) is proportional to Temperature (T).

Pressure (P) is proportional to Temperature (T).

This relationship is shown below:

T ∝ E ie the more energy inputted the hotter something becomes
Where
T = Temperature
E = Energy

Since Pressure multiplied by Volume (P.V) is proportionally related to Temperature (T) then we can say
PV ∝ T. (Google Gas Laws eg Boyle's Law)
In fact to be even more correct we should say
ΔPV ∝ ΔT
P = Pressure
V = Volume
T = Temperature

If we hold volume V constant then we can say that Pressure (P) is proportional to Temperature (T).
ΔP ∝ ΔT
P = Pressure
T = Temperature

Since
ΔPV ∝ ΔT
And if Volume is constant then
ΔP ∝ ΔT

and since
ΔPV ∝ Δm.c2
and if Volume is constant then
ΔP ∝ Δm.c2

then
ΔT ∝ Δm.c2

and since
ΔE ∝ ΔT

then it also implies that

ΔE ∝ Δm.c2
where
P = Pressure
V = Volume
T = Temperature
c = velocity of light
m = mass
E = Energy

We can get rid of the Δ symbol if we say that we start at a value of 0 for amount of energy (E).

This all implies that
E ∝ m.c2
where
c = velocity of light
m = mass
E = Energy

The idea here is that a mass of virtual particles (see later for an explanation of this) impacts a surface and transfers its momentum.

If all of the available momentum is not transferred then the equation will look something like
Equation 9
E = k.m.c2
c = velocity of light
m = mass
E = Energy
k = some constant with a value between 0 (no momentum transferred) and 1 (all momentum transferred).

We assume that all the momentum is transferred from a light pulse that impinges the experiment's receptor in a constant time. This means that from Equation 9 we get
E = k.m.c2 = 1.m.c2
which is the same as saying
Equation 10
E = m.c2
c = velocity of light
m = mass
E = Energy

Energy in the experiment (Figure 2) will be measured as Voltage difference across the experiment circuit.

An analogy to this experiment would be to hit a single stationary pool ball (ball A [m2,v2'] - the receiving mass or photoreceptor) once every second with another pool ball [m1,v1'] (ie the light, mass-density of a volume, virtual particles etc).

It (Ball A [m2,v2']) is then hit again with another pool ball over and over again. The pool balls that are used to hit pool ball (A - [m2,v2']) are always precisely the same mass and collide with ball A [m2,v2'] at the same velocity. The balls [m1,v1'] that hit pool ball (A - [m2,v2']) lose all their energy and stops moving.

PoolBallAnalogy
Figure 4: Conservation of Momentum: Pool ball analogy. Image is obtained from http://www.sparknotes.com

The Youtube vid below shows a similar model. Ball-1 is the mass of virtual particles and Ball-2 is an electron on the photoreceptor. Notice that Ball-1, the mass of virtual particles lose all energy. If this video was fully representative of what happens then Ball-1 should also disappear entirely as it is only virtual ie a flexing of whatever space is and not a particle like a proton or electron.


In fact this analogy is the reasoning for electron cooling see http://www.nist.gov/pml/div686/chip_scale_042105.cfm.

In summary energy such as heat, light etc acts on the electrons in a lump of metal (commonly called an heat sink). We can then use the same principles as normal refrigeration, the principles derived from the kinetic theory of gases, to cool the heat sink. The electrons are seen as a electron gas much the same way as the coolant molecules or atoms in a mechanical and gas system.

Electron cooling is also very efficient compared to the mechanical and gas refrigeration systems we use today (which also is modeled by the kinetic theory of gases). For instance a electron cooling solid state refrigerator can cool an equivalent size room as a standard mechanical-gas air-conditioner with less power then a fan.

The kinetic theory of gases is also the underlying model for quantum theory. It is a simple theory that explains by model how a mass of particles that are in a gas state will act. It is modeled using probability theory and hence can be calculated mathematically. This is useful if you want to test something that has parts where the kinetic theory of gases applies by computer instead of having to build it. A lot cheaper then building the thing to test it.

The 'Schrondinger's cat of quantum theory' thing is actually a falsity to make impossible to understand what is actually very simple.

--------------------------

What I found interesting about this whole exercise was how it said light can be modeled as some mass colliding with a surface like Pressure (P). This seemed strange because I never thought of light having mass.

It turns out that gravity does warp or bend space. But this bending of space also results in that warped space forming its own gravity field. Done sufficiently strongly space itself forms particles. I discovered this fact from Halton Arp’s book "Quasars, Redshifts and Controversies". I believe the price is USD20.00 and can be purchased from Amazon.

If large amounts of gravity can act on a thing with mass ie matter then then it goes to reason that even small amounts of gravity can do the same thing to some extent.

Light appears to form gravity because it is formed of warped space ie a wave. Bent space forms gravity like a particle ie a virtual particle.

It appears that light waves act almost like a particle such as an electron or proton. However light is not made up of particles. The wave is I guess visualized easily as 'warped' space. This warping of space somehow has a gravitational field and mass. As such it is also attracted to other gravitational fields, the larger the other mass the greater the attraction. This explain things like gravitational lensing ie the fact that light can be bent (lensed) around large gravitational masses. The word “virtual particles” seemed to be quite apt although I wouldn’t read the very badly written Wiki’s on what this word means.

A final thing.

Conservation of Momentum is a fundamental principle in physics and we have almost made the mistake, actually probably have made the mistake, of assuming this to be like a 'law' ie immutable. However the Universe has proven once again things tend to be flexible contingent on the context and that maybe anything and everything is possible.

The proof of this can be found in high energy physics where they collide particles against each other. It has been shown that Conservation of Momentum to be untrue and can be visibly violated - and if it happens at all then it probably happens all the time but just less often and less visibly.

An example of this is the decay of Δ- particle into an electron (e). The decay process for instance is as follows:
Δ- → Π- + n → μ- → e
Δ- Delta negative particle
Π- Pion particle
μ- Muon particle
n = neutron
e = electron

The breaking of the Conservation of Momentum occurs at μ- → e where the μ- particle has a mass 105.7MeV and the electron (e) particle has a mass of 0.51MeV (about a 200 times difference in mass change).

What seems to have happened is that the μ- particle is actually an electron (e) but something about it has changed straight after a high velocity collision.

I hypothesize and think maybe the particle has changed its surface area and/or volume as it recovers into a stable shape and configuration that is the electron (e).

Here are a couple of very good explanations of measuring mass by motion of a charged particle through a magnetic field, in other words using energy which momentum is derived from to measure mass of a particle ie eV (electron volts).
-What is an electron volt (eV) etc
-Obtaining energy and momentum (hence mass) from radius of curvature for a charged particle moving through a known magnetic field.


April 17, 2015
I think the circular motion of a charged particle in a magnetic field is actually an artifact of the machine that we are using to measure particle's mass.

One of the outcomes of understanding this science is that we should be able to manufacture unlimited quantities of atoms and probably manufacture atoms that are not able to exists in this Universe without some kind of scaffolding.

This leads to unlimited and cheap quantities of material eg gold, platinum etc as well as opening the doors to possibly new kinds of machines with these new materials. For instance virtual machines made up of virtual particles. Taking it even further down the track I can see the probability of virtual machines that manufacture real things ie the Star Trek replicator device.

These virtual machines will be better than the replicators on Star Trek in that they will be able to fit in a device the size of a smart phone and be able to make other machines and anything else that we desire.

It will make Star Trek quite dated apart from the fact that Star Trek has teleporters. The industrial, scientific and technological foundations already exists. The industrial foundations slightly less so but I think the advantages of this kind of technology will result in this being a short term issue.

Some of the industrial foundations we see today are the shift to the use of design technologies and techniques for manufacturing eg CAD → 3D-Printing → Manufacturing is an example and early implementation of this concept.

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