Mordred

Different locations on Earth can have different gravitational potentials even at sea level. Same problem. Next definition of importance. Potential energy is the energy due to field location. (Applies to all field treatments) Obviously kinetic energy is due to the objects motion. (This stress tensors employ thus through the full Einstein field equatioms) so does QFT (QED etc) Side note test of GR. They have measured time dilation at 1/2 foot difference.

Excellent answer +1. A good example of imprecise verbal descriptives is spacetime curvature. When you study the math itself without wordplay you learn it means the freefall paths become curved. Example the worldline of a photon

Place that same weighed object and weigh it on the moon. The weight will be different but the mass would be the same. Edit I should be more precise here the invariant mass would be the same. Under GR graviton all mass is identical to inertial mass. [math] m_g=m_i [/math] the subscript i denotes inertial mass (relativistic mass or variant mass ) with last being modern usage. rest mass and relativistic mass caused too much confusion. Those terms are replaced with invariant and variant respectively. (Also works better with tensors in gauge group theories such as relativity)

Well that is certainly true a lot of confusion arises in simply not realizing our models describes our Observable universe which in itself is finite and had a hot dense state as far back as we can model. Unfortunately space as in outer space and the physics/geometric definition of space often get confused. As far as the universe in its entirety beyond our observable universe it could be finite or infinite. We have no way of knowing and are likely to never have a means of knowing.

Well space is simply volume that is correct however belief in whether a volume can end or be created is pretty much meaningless and irrelevant to the universe creation scenario. What the BB model under LCDM describes is our observable portion which amounts to our shared causality region. Reverse expansion and that shared causality region is smaller than an atom. Prior to that is speculative

Lol I didn't know nothing was a killer 😆

You would need a mechanism of collapse to get a new BB. The energy density may only be equivalent to zero point energy with total energy being huge but there would be no reason for a new BB. You would be as close to the lowest energy density state as possible. The state above would be as close to zero K as possible under zero point energy. You also wouldn't have a false vacuum state as per the inflationary models (false vacuum by Allen Guth was the first inflationary model) Here is a related question.. Under thermodynamics of an ideal gas. Why does a gas uncontained expand ? Now treat your universe as an ideal gas. Our universe follows the ideal gas laws. (The fluid equations of the FLRW metric employs those laws)

Well not constant when you consider flow of charge under vectors. However an average current could be considered constant

On that point there is some new representations that has been hitting papers with regards to Dirac notation. Ie statements with more than one ket and bra statement.

Judging from the question regarding the candle it occured to me that we should clarify a detail. Mass doesn't mean weight. Mass is the resistance to inertia change. Just wanted to add this point just in case as that is a common misconception.

Sounds good for a quick and dirty rough order age of the universe that assumes constant expansion. There is a quick calculation, to account for evolution of matter radiation and Lambda takes a considerable more work.. With the Hubble value given by Planck 2015 this will give an age of 14.4 Gyrs. However when you employ the full equation you can narrow that down. For starters lets just do the rough order calculation (initial estimate. [math]V=frac{d}{t}[/math [math]t=d/t[/math] [math] H_0=v/d[/math] [math]v=d*H_O[/math] combine those two and substituting for velocity [math]t=\frac{d}{v}=\frac{d}{d*H_o}=\frac{1}{H_o}[/math] now as you know Hubble parameter isn't constant which is one reason for the discreptancy however this is a quick and dirty estimate. Practice this with the conversions first before we get into the more complex equations for the evolution of the density parameters. a true critical flat universe would be [math]t=\frac{2}{3}\frac{1}{H_o}[/math] were not quite a true critical flat and we have a cosmological term to deal with but practice those first. You could use[math] 3.16*10^7 s/year[/math] its not quite accurate as your not accounting for leap years lol. just a side note no method I show you will get precisely the Planck value for age as Planck does a best fit over several different datasets including type 1A supernova measurements.

Can energy exist on it own ? The answer is no it can't. It is a property defined as the ability to perform work. You can't have momentum without having something that moves can you ? When you put particles in a box those particles can exert pressure on the container walls. Answer this question how can a laser propel a solar sail if light cannot gain mass through the relation I posted ?

Try the full energy momentum formula when discussing the mass of the photon it has no rest mass (invariant mass). However the photon can have the variant mass or inertial mass. If you think about solar sails this provides an application where this is used. See here https://en.m.wikipedia.org/wiki/Energy–momentum_relation The problem is not realizing that mass can and does refer to different mass terms (invariant) rest mass and (variant ) inertial mass under GR. See here how the mathematical proof comes about in SR https://www.google.com/url?sa=t&source=web&rct=j&url=https://pdfs.semanticscholar.org/7c91/d1f7979c0f0fb4348e3b00e21abc6f2ce80a.pdf&ved=2ahUKEwjUzqOgp7bkAhXGrJ4KHa54AD0QFjAAegQIBRAB&usg=AOvVaw1Y2SJGPsxC4-m5zov6Da9p It would be far easier to understand this than understanding how all forms of energy contribute to mass via the energy/momentum stress tensor of GR. (That includes the Stress tensor for the EM field under Maxwell equations.)

Close to the beginning it's in the right ball park. I will get you the correct formula to calculate universe age though if you look at the advanced user guide to the cosmocalc that I previously linked I believe it's there.

Wouldn't you consider that to be problematic considering your involving Hubble parameter ?

That is far older than the age of the universe.

You might want to study what a vector gauge boson entails. (Virtual boson) Did you ever stop to think why all the experts in quantum mechanics will tell you the same thing ? There is a difference between the photon as per a quanta of light and the photon as per the mediator of an EM field. VP's have less than a quanta of energy/mass. Here is a quick run down of the virtual photon https://en.m.wikipedia.org/wiki/Virtual_particle The part on the Feymann diagrams where it mentions the internal lines this is where the VP operate. They are not observable due to their mass/energy being too low. Even with an idealized perfect detector it would be impossible to detect individual VP. Though we can detect their collective effects. The external lines on Feymann diagrams however have an excess of a quanta of action. They are observable under measurement. Yes I know it's a lot to take in but the quantum theories take a considerable study to get a handle on the topic. Though relativity is also a lengthy topic to learn. You will come across a lot of theories which will be difficult to apply in a strictly classical understanding. In some cases there is no classical means to explain.

There is no easy explanation for how mass curves spacetime in terms of freefall paths. It takes a considerable amount of study to follow Euler Langrene equations for the path of least action just to get a feel for it. Unless your already familiar with calculus of variations. In essence at each infinitesimal there is a relation between a particles kinetic energy and the fields potential energy. The path taken at each spacetime coordinate will involve the path with the least action which will equate to the shortest path. The mass term is synonymous to how strongly particles couple to a field this is true of spacetime as well. The path of least action also works under Newtonian gravity

Gravitons don't create curvature they would if they exist simply act as a mediator much like photons mediate an EM field.

Your expression should be mass tells spacetime how to curve. As all forms of energy and matter can contribute to the mass term. It would help if you think of mass as resistance to inertia change and curvature as the freefall paths. In this you can use parallel laser beams. If you have no curvature the beams are parallel. If you have positive curvature the beams will converge. If negative they diverge.

While I don't know squat about the American health care system. As a married man to a wife with serious health issues. I can appreciate the health care system in Canada. I priced out the medications my wife has to take daily to the tune of a little over 800.00 per month. With the medical plan I have through my company I pay a flat zero dollars for her prescriptions. All I can say is I am thankful for that plan and the Canadian health care system without it I would likely be bankrupt trying to keep my wife healthy

Yes unfortunately that is true and oft times it's even in the physics peer reviewed papers. The term superposition actually originates in statistics and the word entanglement is a replacement term for correlation. If you can make a correlation between two states those states are effectively entangled by that correlation. One of the premises of QM and the Schrodinger equation is the following. https://en.m.wikipedia.org/wiki/Quantum_superposition The many paths of Feymann diagrams also fall into this lemma. (principle of least action ) you have the probability of all possible paths but the particle will only take one path the path of least action. +1 on last response one should dispense with belief when examining models. Once you believe too strongly in one model you close the book on other possibilities.

Observation is a rather misleading term. Any act of measurement is an observation. When you measure a quantum state you interfere with that state. In entanglement you have determined a wavefunction thus collapsing a superposition state. Superposition being a probability of all possible states. With any particle under QM the wavefunction is a probability function that the square of the amplitude gives the highest probability of locating the energy/momentum terms of a particle. Ie locating the particles position. Once you make a determination you no longer require a probability function as you have made a determination via observation/measurement. The entanglement scenario is also of this case, for example when you entangle two electrons there is only two possible states one being the opposite of the other. Until you make a measurement you have no way of knowing the individual states but can establish a probability correlation function that describes the superposition of states and the strength of how correlated the two states are to the experimental apparatus. Once you determine one state you automatically know the other state which collapses the probability superposition state as well as the correlation function which is also a statistical probability function. Little side note on entangled particles. Measuring one particle doesn't affect the actual particle state of the other particle. It only affects the superposition state which is a probability state. Once determined there is no longer any probabilities involved. There is no action at a distance nor hidden variables. Nor do the two particles communicate FTL. No locality of the two particles involve the detail that the superposition wavefunction applies to both particles simultaneously. When you measure you collapse that wavefunction by making a localized determination of one of the pairs which allows you to determine the non localized state of the other particle state. Unfortunately pop media articles don't sell well talking about probability functions puts readers to sleep so they typically romanticize what is involved with regards to the observation effect. https://en.m.wikipedia.org/wiki/Observer_effect_(physics) You should be able to better understand several of the lines in this link with that in mind. In particular

You can simplify it by treating the Earth frame as the rest frame under Lorentz then run a comparison to each twin relative to the Earth frame. Have both twins run the same path along the x axis, they both have the same turnaround but at different instantaneous velocities during turnaround due to both twins having different velocities for the main flight paths. Yes each reference frame will have its own time dilation factor but we only need the ratios of differences to the Earth reference frame of the two twins. The Earth triplet being the only reference frame that doesn't undergo acceleration.

The turnaround is useful in the twin paradox as part of its solution. It shows the symmetry breaking aspects of the Lorentz transforms. Recall in SR you can arbitrarily set any observer in any inertial frame to zero.