Elementary Differences between Energy and Mass

Elementary Differences between Energy and Mass
Rodolfo A. Frino – October 2014
Electronics Engineer
Degree from the National University of Mar del Plata
Abstract
In this paper I explain the elementary differences between energy and mass. When we
consider the famous Einstein's equation E = mc 2 these two concepts might look the same
with the only difference of a constant of proportionalyty, c 2 . However when we explore
these two concepts more closely we discover that they differ in several fundamental aspects.
1. Introduction
The celebrated Einstein's equation of equivalence of mass and energy
E = mc
2
(1)
means that energy can be converted into matter, and matter into energy. However this does
not mean than energy and matter are identical. To make things even more confusing some
people go further saying that energy is matter and matter is energy. This is a simplistic
statement aiming to explain Einstein's mass-energy relationship in simple terms. Other
people say that mass can be considered to be another form of energy. Although this is true
they don't explain the difference between these “two forms of energy”. Therefore we need to
clarify the differences between mass and energy and this is the subject of this article.
2. Rationale
i-Maximum Velocity
According to Einstein the speed of light in vacuum is the maximum speed information can
propagate through space. Also according to him massive particles obey the relativistic mass
law:
m=
m0
√
v2
1− 2
c
(2)
This formula tells us that the velocity, v, of a massive body cannot be greater (and not ever
equal) than the speed of light in vacuum, c. Mathematically
v<c
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(3)
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ii-Time
According to Feynman, particles, such as electrons, can travel backward in time. An electron
travelling backward in time is known as a positron. A positron is the anti-particle of the
electron. We also know from experiments, that when a particle and its anti-particle, such as
an electron and a positron, get in contact with each other, they annihilate. Depending on the
kinetic energy of these two particles, two or three gamma rays (photons) appear in their
place. Thus, two material particles are converted into pure energy in accordance to the
equation of equivalence of mass and energy.
The electron and the positron annihilate because these particles travel in time in opposite
directions. The electron travels forward in time while the positron, according to Feynman, is
an electron travelling backward in time.
When a particle and its antiparticle are in physical contact, they occupy the same volume of
space (or at least they are as close as they are allowed to be by the laws of physics). But the
same volume of space cannot have two different times and therefore time must cancel out.
The result of this time cancellation is the total conversion of the mass of the two particles
into energy (annihilation). Time cancellation means that energy does not travel neither
forward nor backward in time. Thus energy is timeless. In other words time does not elapse
for radiation (photons). This is a profound difference between energy and mass.
iii-Fundamental Relationships
Heisenberg showed that there is a fundamental relationship between the uncertainty of the
momentum of a particle and the uncertainty in its position. Heisenberg expressed this
relationship with an inequation known as the Heisenberg uncertainty principle (we shall use
called it the spatial uncertainty principle to distinguish it from the temporal uncertainty
principle). Thus the spatial uncertainty principle is
Δ p x Δ x≥
ℏ
2
(4a)
Δ p y Δ y≥
ℏ
2
(4b)
Δ pz Δ z ≥
ℏ
2
(4c)
Because the momentum of the particle depends on its mass
v
⃗p = m ⃗
(5)
According to equation (2) we can write
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2
⃗p =
m0
√
2
1−
v
c2
⃗v
(6)
Thus equations (4a), (4b) and (4c) tell us that there is a fundamental relationship between the
rest mass of a particle, its velocity and space.
Heisenberg has also shown that there is a fundamental relationship between the uncertainty
of the energy of a particle and the uncertainty in the duration of this energy. Heisenberg
expressed this relationship with an inequation known as the temporal uncertainty principle:
Δ E Δ t≥
ℏ
2
(7)
This inequation shows that there is a fundamental relationship between the uncertainty in the
energy and the uncertainty in the interval of time. Thus there is a fundamental relationship
between energy and time.
iv-Origin
According to my theory on the Universe [1], energy (or Meta-energy) has no origin: it always
existed (*). On the other hand, matter (and therefore mass) had a beginning and this was the
Big Bang. Thus energy is infinitely old while matter is only 13,822 billion years old.
(*) Something that has always existed has no origin so the question: Where do the Meta-laws
of physics come from? does not make any sense since this question is equivalent to asking
What is the origin of the Meta-laws of physics? However the question: Where do the laws of
physics come from? makes sense and the answer is from Meta-laws [1].
v- Ingredients
We do not know the exact difference between Meta-energy and energy. However since I
have postulated that there is no Meta-matter [1] (and therefore there is no Meta-mass), one
difference could be that Meta-energy to be truly massless. This means that its rest mass
should be zero. On the other hand, energy (photons), should have non-zero rest mass [2, 3].
We also assume that energy (or Meta-energy) has no “parts”, “components” or “ingredients”.
This means that energy is primordial and it cannot be explained in simpler terms.
On the other hand, mass has “ingredients”. Although these ingredients are more subtle than
“parts”. To find the ingredients of mass we have to look at the most celebrated equation of all
times: the Einstein's law of equivalence of mass and energy
E = mc 2
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(8a)
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Then we write this formula as follows
m=
E
c2
(8b)
According to our assumption – Energy (or Meta-energy) is primordial - and considering that
time and space were created during the Meta-transformation known as the Big-Bang, they are
not primordial (*) in this sense but they are byproducts of this Meta-transformation. We also
know that in order to propagate photons (radiation) need space and time. Therefore we
conclude that space and time are the rest of the ingredients “used” by Nature to make the
mass of all known particles. You can argue that photons are part of space-time by saying that
photons are ripples of space-time. However this would not change anything since if this were
the case then energy and space-time would still be the ingredients of mass. Thus we can
affirm that mass has three “ingredients”: energy, space and time – as shown on the second
side of Einstein's equation (8b).
(*) The word primordial in this context means that energy (or Meta-energy) existed before
the Big-Bang in its own Meta-time. Normal time, on the other hand, was created during the
Big Bang and therefore is not as primordial as energy (or Meta-energy) or as Meta-time.
Thus Meta-time is infinite while time is finite (13,822 billion years). However if Metaenergy, Meta-time and Meta-space were identical to energy, time and space respectively, our
conclusion will still hold since mass would be the result of three primordial “components”:
energy, space and time.
vi-Universal Lifetime
We shall define the universal lifetime as the time in which all mass in the Universe ceases to
exist. Thus we postulate protons, electrons and neutrinos (and any other kind of “stable”
matter may there exist) will transform into energy (or Meta-energy) at the end of time. Thus
we arrive to the following conclusion: Energy (or Meta-energy) is eternal and matter (and
therefore mass) are ephemeral. Here the term ephemeral is used as the opposite to eternal. In
other words there are no stable particles.
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3. Table of Differences between Energy and Mass
The following table shows the main differences between energy and mass.
Energy
Mass
i
Maximum velocity
( v max )
c
<c
ii
Time
does not elapse
(photons are timeless)
elapses
time
space
iii
There is a fundamental
relationship with
ℏ
2
(Temporal Heisenberg
uncertainty principle)
ℏ
2
(Spatial Heisenberg
uncertainty principle)
iv
Origin
The Meta-Universe
(Energy always existed)
The Big Bang
(Matter had a beginning)
None.
(Energy is primordial)
Energy, space and time
v
Δ E Δ t≥
“Ingredients”
E = mc 2
(Causes are on both sides of the
equation)
vi
Universal Lifetime In the end there will be
Either energy or Meta-energy
only
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Δ p x Δ x≥
m=
E
c2
(Causes are on the second
side of the equation only)
No matter
(and therefore no mass)
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4. Conclusion
In summary, we have remarked six elementary differences between mass and energy. We can
go even further by noting that, for example, when an electron and a positron annihilate, the
result of this annihilation does not contain any information about the charge of the particles
that originated the transformation. Someone observing one of the photos would not be able to
say whether it comes from an electron-positron annihilation or from another process (not
necessarily an annihilation). Thus, although charge is conserved, photons generated in an
annihilation process do not carry any information about the electric charge of the particles
involved in the annihilation. The information about the electrical charge of the particles is
lost. This is fundamental difference between matter and energy. I shall call this property of
matter distinctness. Thus if we accept that mass is another form of energy, we can extend this
concept to matter by saying that matter is energy in a distinguishable state.
REFERENCES
[1] R. A. Frino, Where Do the Laws of Physics Come From?, viXra: 1407.0103, (2014).
[2] R. A. Frino, The Theory of Massive Photons, viXra: 1409.0043, (2014).
[3] R. A. Frino, The Substitute Theory of Massive Photons, viXra: 1409.0058, (2014).
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