Mordred

Purpose of life to live and experience life.

Man. One reason to never trust Quora. I know of several banned members on this forum that constantly post there LMAO. No dark matter does not equal gravity. One can cause spacetime curvature without DM Here is a real world example. LIGO calibrates it's detectors using lead weights placed near the detector of sufficient mass to cause a slight curvature. Planets, stars etc cause curvature.

Hrrm under GR the above doesn't follow. You and I reside in coordinate time the only proper time (invariant time=same for all observers) is along the worldline. This is different than the older SR definition where proper time was the observer at rest. Convention now follows the GR definition. Also acceleration induces rapidity under rapidity you change world lines. Lorentz transforms apply constant velocity. An acceleration causes a rotational translation. (Rapidity). This is the key to solving the twin paradox.

That is fine in an of itself, but maybe a better way of expressing this would have been better. So let's get to the last comment. Yes there was contention for years on the nature of particles. The wave particle duality met with strong resistance in both camps for years . Some stressed particles were corpuscular and didn't like the wave explanations and vise versa. Eventually research showed that particles display both charactistics as U explained in an earlier post. I don't know if you will read this but there is an excellent paper on the topic. It is an Arxiv article "There are no particles, there are only fields" In essence it explains how wave particle duality works with the double slit experiment. https://www.google.com/url?sa=t&source=web&rct=j&url=https://arxiv.org/abs/1204.4616&ved=2ahUKEwj7o_CNhPDjAhXUo54KHQEwBGIQFjAAegQIBBAC&usg=AOvVaw27uWB6T-rNUVN6PSSrQiFO On phone it is an Arxiv article.

Not sure I understand what your trying to express here but the order of spatial coordinates and time axis isn't important. The importance is the symmetry basis between them for example I can write x,y,z,t or place time as the first coordinate which is the current accepted convention of the four momentum. (t,x,y,z). All four coordinates are othogonal 90 degree to each other in Cartesian coordinates. I can't say anything about your application of three time dimensions as you haven't really defined this yet. I myself use an important definition of dimension (that definition applies to both mathematics and Physics) an independent variable\value or other mathematical object that can vary without varying any other mathematical object. In essence a degree of freedom. Studiot has commented before that I follow and oft stress proper definitions. LOL.

What makes you believe he didn't

Your claim better have a VERY strong defense because I can easily dispute the last post. Simply by the conservation laws.

Let's start with this question. Ok we will start with the Lorentz transformations rules. [latex] \acute{x}=\gamma(x-vt),\acute{y}=y, acute{z}=x, \acute{t}=\gamma(t-vx/c^2)[/latex] With inverse note sign change [latex]x=\gamma(\acute{x}+v\acute{t}), y=\acute{y}, z=\acute{x},t=\gamma(\acute{t}+v\acute{x}/c^2)[/latex] Where [latex]\gamma=(1-v^2/c^2)^{\frac{1}{2}}[/latex] This shows that both time and space is relative to the observer. Under Galilean relativity only space was relative so the only transformation was on the x axis [latex]\acute{x}=x-vt,\acute{y}=y, \acute{z}=z,\acute{t}=t[/latex] Inverse( I will only do the x axis as rest is just which y,z,t is prime) [latex]x=\acute{x}+v\acute{t}[/latex] Now we will set each inertial frame up in the same manner. [latex]S:(x,y,z,t), \acute{S}:(\acute{x},\acute{y},\acute{z},\acute{t})[/latex] Now under Galilean relativity it was meaningful to talk about the relative velocity of inertial frame to the other. The laws of physics are the same in each inertial frame. The transform rules under Newtonian mechanics are covariant. (Of the same form) thus forms the Galilean group in which the laws of mechanics are the same. If you have another frame Let's denote this [latex]\acute{S}\prime[/latex] moving relative along the x axis to [latex]\acute(S)[/latex] with speed [latex]\mu[/latex] along their common axis x. Then the speed of [latex]\acute{S}\prime[/latex] to S is [latex]w=\mu+\nu[/latex] Thus is the law of velocities in the Newtonian-Galilean Principle of Galilean relativity Now in the Lorentz case one must use the law of relativistic velocity addition rules. Now the consequence of the relativistic velocity addition https://en.m.wikipedia.org/wiki/Velocity-addition_formula This link has both forms the form below has a third observer described above. [latex]w=\mu+\nu[/latex] It is the velocity addition rules that sets the speed limit at c. If you exceed c the time coordinate changes sign. It sets the limit of times arrow forward. Now recall I mentioned mass is resistance to inertia change ? All massive particles couple to their fields us is the strength of that coupling that determines its mass. Massless particles do not couple. They have no rest mass as a consequence. So they are not delayed in going from a to b. It is very similar to propogation delay when a signal goes past a magnet it gets delayed by its coupling strength Photons and gluons do not couple hence no rest mass hence delay in getting from a to b. However still limited by c (speed of information exchange) Massless particles therefore follow null geodesics while massive particles follow spacetime geodesics. Different spacetime paths. Now entangled particle states don't exchange information. The correlation function is already set by how the entangled pair is prepared and the experimental apparatus used in there measurement. The superposition state applies to the two bags (apple,orange) just as it does under QM probability functions. All particles entangled or not,virtual or not are limited by c. There is no FTL information exchange under spooky action at a distance as one must know how the particles are correlated to even determine the state of the other particle. The particle state does not contain this information. The correlation function is a seperate probability function.

Nothing wrong with the above however the Schrodinger equation is not Lorentz invariant. The equation that takes the Schrodinger equation and adapts it to Lorentz invariance is the Klein Gordon equation. I am still gathering the information I need to answer your post previous to this one as you have two very important questions that need to be addressed properly and as complete as viable.

True but I can tell you Swansont has been accurately answering your posts. Wave particle duality simply means that all particles display both wavelike and pointlike characteristics. Pointlike is described by the particles Compton or DeBroglie wavelength. All particles are field excitations that are described by a wavefunction. Not all wavefunction are probabilistic there are also physical wavefunctions. Particles are not little bullets or balls. They are field excitations with no corpuscular (material structure) component's. I also have a degree in particle physics so can confirm the accuracy in Swansonts posts. Neither one of us has any issue correcting each other should we make a mistake. We actually appreciate such corrections should mistakes arise.

Let's address this statement all three is part of the same state, if you have a fequency you automatically have a wavelength and the frequency will have momentum. They are all properties of the same state not separate states. Gluons also propogators at c all massless particles do so Mass is resistance to inertia change massless particles have no resistance to inertia change so they all propogators at the same speed as photons. We keep telling you there is nothing special about entangled particles. Not in so far as spacetime. It has a predictable nature simply due to probability statistics. The spooky action at a distance is simply part of the statistical nature. They do not communicate with one another, nor does one alter the other at a distance. In essence there is no Action when you determine one and know the state of the other. You can do the same with an apple, an orange and two paper bags. Get someone else to put the apple and orange into separate bags. You can formulate the statistics of 50% chance bag a has an apple. You now have a correlation function the bags are in superposition as each bag can have either or. Once you open bag A and see it has am orange you automatically know bag b has an apple. Particle entanglement is the same.

Better qualified well Swanson does have a PH.D I say he's qualified enough.

Let's clarify a few things in the last post. All mass less particles are invariant at c. Particles do not store gravitational potential energy regardless of being entangled or not. That is the job of the spacetime field itself. That field applies the mass or energy density at each region. All particles contribute to the mass density. The propogator can be the field itself which can contain the virtual particles though these are a convenient label. In QFT it's never referenced as virtual particles. They simply define it as the propogator state. All particles are field excitations described as wavefunction states. Your terminology is getting much better and it's evident your listening and learning keep it up +1 HiAn entangled pair is nothing more special than two states that one has prepared to assign a statistical correlation function to. For example you create two electrons as a consequence one must be spin up the other spin down to maintain conservation of spin. So you also have a statical probability that if you measure one of the two the other particle must be the opposite spin.

Well different perspectives on interpretation of the mathematics has its uses. I prefer that to straight metaphysics that most times never want any math lol. The Schodingrr equation has its uses but the Klein Gordon upgrades it to incorporate Lorentz invariance. This is a primary equation in QFT so you can relax it's already taken care of.

Yes it undefeated speculation, with the Alcubierre drive however they have performed the main calculations. As Beecher noted it isn't antigravity but it is manipulating spacetime to your advantage. Now here is the thing quantum entanglement won't help. It's actually extremely easy to entangle particles. They have diodes that can do just that. They won't contribute anything that single particle states can do. Two single particle states have the same energy/mass as two entangled particles.

Spacetime field differentials is how Alcubierre drive works. It theorizes two different curvature region's one in front and one behind the craft at two different energy densities. It's theoretically viable but requires extreme energy requirements. Here https://en.m.wikipedia.org/wiki/Alcubierre_drive

Look I know how to mathematically describe Spacetime curvature both positive and negative. I also know how to describe mathematically spin 1 or spin 2 gravitons in a path integral. We suspect spin 2 but haven't confirmed spin two. I also know how other fields affect spacetime as well as what is really involved in entangled states beyond pop media. Pictures don't count for much. Trust me even if you generate negative curvature or even anti gravitons. It's stil not antigravity. In antigravity Newton's laws literally reverse. The good news is you don't require antigravity to use spacetime to generate thrust. Google Alcubierre drive.

Has literally nothing to do with belief. I know the mathematics involved and the physics.

Claiming isn't the same as proving.

Invariance of c is covered in the to first few chapters of any GR textbook. You can't learn GR without first learning that lesson.

It's not a prerequisite to space travel. Regardless of propulvise method you still have time to deal with. The worse being time dilation. Look let's keep this straight fotward. You need far more than anything you have written in your article and on this forum. All forms of known energy/mass systems generate spacetime curvature but never to an antigravity effect. As you always have a positive energy density. Entanglement definitely does nothing to change that truth.

He is trying to account for two simultaneously varying values under constant thrust. That's not what these equations are designed for. If you have constant thrust and fuel consumption varying the mass the acceleration also changes.

How is that a mistake with regards to the rocket ship scenario ? The original equation is for constant mass how is that different describing Newton's laws of inertia ? You adapt the original equation for two varying values.

Good catch thanks was distracted by wife lmao corrected above

If gold became readily available in a cost effective manner it would certainly drop market price. Good ole supply and demand