The finitude of the universe makes a prior to the Big Bang almost inevitable

Conclusion of Con's rebuttal Con conceded (A 0); the wording "or even prior to the Big Bang" was only chosen to stress my introduction's validity for both debaters' stances, not as an argument itself. Since Con conceded (A 1.1) (and (A 1.3) if being supported by (A 1.2)), I interpret Con's statements as agreeing with the whole resolution for the case* that there were particles at the Big Bang* that their velocity must have been ill defined if it was the beginning of time and* that this conflicts with current observations Rebuttal of Con's objections(R 1) "[. .. ] there would be no particles at t=0 as no matter would exist [. .. ], just energy. " - Con. First of all I have to point out, that Con's sources neither support his negating claims, nor his stance. Con claims particles did not exist at t=0 according to his source #4, but his source says nothing about the existence of particles at t=0 at all. Con's source #2 solely addresses atoms being the building blocks of matter, but in mentioning particles I didn't refer to atoms in the first place. Talking of particles, I meant all particles in general as known in the Standard Model of particle physics [1], which are all assumed to have been present at all times of the universe [2.1][2.2][2.3]. Con further claims that only energy was present at t = 0, but his source #3 actually supports my position, as the formula E=mc^2 applies for particles only [3]. The most important objection to my opponent's argument is that particles are not analogous to matter, as he states. All forms of energy can only exist in the states of particles: Matter and antimatter are being composed of so-called hadrons and leptons [4], electromagnetic energy such as radio waves, light and radioactive gamma radiation are being composed of photons [5] and the gravitational interaction and gravitational energy are generally being assumed to consist of gravitons [6]. The physical definition of energy itself is only possible with respect to particles [3], be it kinetic energy or potential energy. Thus, if there was energy at the beginning of time (as Con arguments), there must have been particles to carry it. (R 2) "[. .. ] all particles have had an undefined velocity at t = 0 [. .. ] remains as an unjustified assumption. " - Con. Con raised doubts about my deduction of the concept of velocity being undefined at a beginning of time (t=0). I admit, I could have been a bit clearer in my argumentation, which I will now make up for. But I have to stress, that contrary to what was said, all necessary sources have been present in Round Two. As stated in my source #4 of Round Two, the velocity of any particle is defined as dx/dt, which is a mathematical formula representing the distance dx a particle travelled divided by the time dt needed. More precisely, it is a derivative, which makes this definition meaningful even for infinitely small intervals of time or movement [7]. This is the definition used in both general relativity and quantum field theory [8]. However, as stated in my source #3 of Round Two, a derivation can in principle only be performed, if differentiability of a function is given. A derivation with respect to time can not happen at an alleged beginning of time (see Fig.1, compare to [9]). Thus, a definition of velocity is impossible at a beginning of time - all velocities must be undefined. (R 3) "Pro did not defend his position regarding how this conflicts with observation. " - Con. Con conceded that according to conservation laws, if all particles at t=0 had undefined velocities, they must have kept them until today. He however challenges my claim, that this is not obviously contrary to observation. But had all particles an undefined velocity even today, velocity measurements wouldn't be possible, as they would logically yield undefined values. Thus, every velocity measurement on any present particle yielding a result would be a contradiction to undefined velocities at t = 0. Defined velocities are constantly measured [10]. By this, a beginning of time at t=0 would conflict with observation. Fig. 1) Plotting the position of a particle as a function of time, the velocity is always defined as a tangent to that function. However, at an alleged beginning of time (t = 0) velocities are completely undefined, as there is no tangent. Argument 2 (A 2) Noether's theorem will most likely hold at the beginning of the universe. If there was a first state of time at t = 0, according to the theorem an unbounded amount of energy should have been produced. This conflicts with the current model of inflation [expansion of the early universe]. Thus, judging on current physics a first state of time is impossible and a period of time preceding the Big Bang must have existed. (A 2.1) Noether's theorem will most likely hold at the beginning of the universe. Noether's theorem is valid in both general relativity and quantum field theory [11] and is as such, according to the introduction (A 0) Con agreed on, one of the best candidates to hold even for a description of earliest universe development. (A 2.2) If there was a first state of time at t = 0, according to the theorem an unbounded amount of energy should have been produced. According to Noether's theorem, energy conservation (and a concept of energy) can only exist, if time is differentiable [11]. As demonstrated in (Fig.1), this is however not the case. Therefore at t = 0 no law of energy conservation could be applied - and as there is no other bound to regulate a creation of energy - an unbounded amount of energy should have been produced. (A 2.3) This conflicts with the current model of inflation. While this may not seem as a problem first, as the beginning of the universe is commonly associated with a creation of energy, the implications are in fact disastrous for any model of the Big Bang:The current model of inflation, governing the expansion of the early universe, only has finite expansive power for finite regions of spacetime [12][13]. It follows logically, that if an unbounded amount of energy should have been created, inflation would not have been able to counteract its immense gravity, thus inflation shouldn't have occurred. (A 2.4) Thus, judging on current physics a first state of time is impossible and a period of time preceding the Big Bang must have existed. But inflation occurred [12], and therefore the creation of an unbounded amount of energy is contradicted by evidence. Thus, a beginning of time at t = 0 is almost impossible and a period of time prior to the Big Bang almost inevitable. Argument 3 (A 3) All current approaches to quantum gravity refuse a beginning of time itself [14][15][16]. In conclusion I successfully negated all of Con's doubts on my argument (A 1). Moreover, since both (A 1) and (A 2) are valid, and (A 3) is a strong support for my stance, I see the burden of proof met and the resolution to be established. Sources [1] . http://en.wikipedia.org...[2.1] . http://www.physicsoftheuniverse.com... ('Unification' existed at Big Bang)[2.2] . http://en.wikipedia.org... ('Unification' is equivalent to existence of particles)[2.3] . http://science.howstuffworks.com... (specifically states quarks existed at the Big Bang)[3] . http://hyperphysics.phy-astr.gsu.edu...[4] . http://hyperphysics.phy-astr.gsu.edu...[5] . http://en.wikipedia.org...[6] . http://en.wikipedia.org...[7] . http://www.math.uni-bremen.de... (a bit technical)[8] . http://en.wikipedia.org...[9] . http://www-math.mit.edu... (especially point 5)[10] . http://www.sciencedirect.com... (only one random example)[11] . http://www.mathpages.com... (especially the last paragraph)[12] . http://en.wikipedia.org...(cosmology)[13] . http://ned.ipac.caltech.edu... (modelling a finite inflational potential)[14] . http://science.psu.edu...[15] . http://phys.org...[16] . http://en.wikipedia.org... (states a temporal singularity is questionable in any quantum gravity approach)