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 Elementary Differences between Energy and Mass - v2 Copyright © 2012-2014 Rodolfo A. Frino. All rights reserved. (3) 1 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 Elementary Differences between Energy and Mass - v2 Copyright © 2012-2014 Rodolfo A. Frino. All rights reserved. 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 Elementary Differences between Energy and Mass - v2 Copyright © 2012-2014 Rodolfo A. Frino. All rights reserved. (8a) 3 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. Elementary Differences between Energy and Mass - v2 Copyright © 2012-2014 Rodolfo A. Frino. All rights reserved. 4 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 Elementary Differences between Energy and Mass - v2 Copyright © 2012-2014 Rodolfo A. Frino. All rights reserved. Δ p x Δ x≥ m= E c2 (Causes are on the second side of the equation only) No matter (and therefore no mass) 5 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). Elementary Differences between Energy and Mass - v2 Copyright © 2012-2014 Rodolfo A. Frino. All rights reserved. 6