Albert Einstein's Theory Of Gravity

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Albert Einstein introduced his theory of General Relativity in 1915 (New Site). This theory includes a field equation for gravity, which consists of three terms: two tensors that represent space-time and the energy-momentum tensor. The energy momentum tensor represents the matter and energy in the universe which bends space-time to produce gravity (lecture 1). His equation is seen in Figure 1. Figure 1 On the right side of the equation is the matter and energy tensor and, on the left, are the two space-time terms (lecture 1). Despite the incredible paradigm shift this equation and the rest of General Relativity had, it also had a profound implication that tremendously bothered Einstein (New Site). Einstein’s field equation implies that …show more content…
That means every collection of energy and matter in it are steadily growing farther apart (New Site). The energy that is producing this effect has become known as dark energy and the cosmological constant as the vacuum energy density (Dynamics Paper). When setting the energy-momentum tensor to zero, removing all matter and energy from the universe, the negative cosmological constant remains as a left over energy. This implies that a vacuum will inherently possess energy (Lecture 1). Thus, vacuum energy density is the value that this energy has at any point in space, and cosmological constant theories predict that this value is “constant” (Dynamics Paper). But, where does this energy originate from? Currently, there are two prominent theories in the physics community that predict a vacuum energy. These are Quantum Field Theory and Supersymmetry, referred to as QFT and SUSY respectively. Each of these theories predicts a different value for the constant vacuum energy density (Lecture 1). According to Quantum Field Theory, in every point of space, there is a small harmonic oscillator of every possible frequency. When these oscillators are excited with an influx of energy, a particle will appear in space (Lecture 1). The energy of these harmonic oscillators is represented by Figure 3. Figures 3, 4, 5, and 6 feature the zero point energy …show more content…
Figure 5
∫_0^K▒(ⅆ^3 k)/(3π^3 ) (1/2 √(k^2+m^2 ))
Since it is known that E=ℏω –energy equals frequency times Planck’s Constant–, E^2=p^2+m^2 –the energy momentum relationship from relativity–, and p=ℏk –the linear momentum of a particle, or the number of waves that will occur within a certain distance, equals the reduced Planck’s constant multiplied by the wave number of a particle (New cite for each equation). Figure 5 can then be reduced to Figure 6, according to Parikh, because m can be disregarded at sufficiently high temperatures:
Figure 6
∫_0^K▒(4πk^2 dk)/(2π^3 ) (1/2 k)  K^4/(16π^2 )
The upper limit value of K is a value at which it is known that Quantum Field Theory breaks or no longer holds true. The Planck Scale Energy at 1028 electron volts is a limit at which it is known that QFT can, as stated by Parikh, “…no longer be trusted”. Therefore, it is a reasonable choice for K. Substituting this value into the integral returns a value of about 10110 eV4, which is the Quantum Field Theory prediction of vacuum energy density (Lecture

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