I am a novice that needs help with a topic that probably seems elementary to more experienced people. The case considered is a mass M sitting on Earth’s surface. Throughout this discussion, “stationary” means stationary relative to Earth’s surface at the location of M. Newtonian mechanics applied to a stationary coordinate system sees the normal force on M (the force that Earth’s surface exerts on M) and the gravitational force as real (as opposed to pseudo) forces that balance each other so M does not accelerate. Now consider a coordinate system that is initially stationary but accelerating downwards in accordance with gravity. We call this the falling coordinate system. General relativity calls this the inertial coordinate system so the real forces are the ones seen in this coordinate system. Only the normal force is real and this is the only force seen in this coordinate system. In this view, the gravitational force is a pseudo force needed by a non-inertial coordinate system (the stationary coordinate system) in order to calculate correct answers. The falling coordinate system sees M to be accelerating upwards in accordance with the normal force so M is gaining kinetic energy as seen in this coordinate system. An inertial coordinate system should have energy conservation laws so the gain in kinetic energy must be coming from somewhere. Where does it come from?
Dear L.D. Edmonds ,
I like your question, although you say that you are a novice, you don't just learn relativity, you look at the details, that's a very good sign.
In classical physics, if we derive a linear moment, we obtain its force and if we integrate between 2 distances we obtain its kinetic energy. As you well say in classical physics that moment does not arise from nowhere, it arises from a potential energy in the case of a falling stone, from a chemical potential energy in the case that you transform it into a force to throw a stone, etc. . Energy is always conserved.
The relativistic case is the same (we actually do the same because the real momentum is relativistic, the invariance of c must be conserved). We derive a relativistic moment, we obtain its force and if we integrate between 2 distances we obtain its kinetic energy (K = γ mc ^ 2 - mc ^ 2) therefore the total relativistic energy is E = γ mc ^ 2.
You will find this in any book.
But what you won't find is that for that to be true, mc ^ 2 must be a potential energy. And you will not find it because of course .. Potential energy of what?
Here you have explained and deducted that potential energy directly (the only place where you will find it, chapter 2.5):
Preprint ALL SPECIAL RELATIVITY EQUATIONS OBTAINED USING GALILEAN TRA...
Answering your question: Gravity bends space-time, there is a potential difference between the point of greatest and least curvature, that potential energy is transformed into kinetic energy exactly the same as in classical physics.
If you want to see it more clearly calculating all its forces and accelerations, look also (chapter 2.3 and 2.6):
Preprint ENERGIA FOTÓN, APROXIMACIÓN GRAVEDAD UNIVERSAL DE NEWTON Y L...
Thank you Sydney and Sergio. I have to do some more studying to understand the details but I believe that you have given the answer to my question, and provided me with the material that I need to study for a better understanding. Thanks again.
After studying the answers to my question I think I am getting the idea. First consider the hypothetical case (a case that could be imagined even if not real) in which there is a uniform gravitational field throughout the universe. A suitable coordinate transformation could make gravity completely disappear. But for Earth's surface to exert a normal force on M, gravity must come from the Earth and is not uniform. No coordinate transformation can make gravity disappear everywhere. Instead, space-time has different curvatures at different locations. Sergio pointed out that there is a potential energy associated with this curvature and changes in this potential energy supplies the kinetic energy to M.
Exactly, always think in terms of geometry and curvature.
The physics of the fields has a problem, and it is that if the value of the particle that produces it changes, the force perceived in the distance changes automatically without respecting the maximum possible speed c.
There is no medium to transmit that change.
Doesn't have much sense
L.D. Edmonds
Dear L.D.,
About General Relativity, towards the end of his life, Einstein had become adamant that gravitation follows the patterns of electromagnetism and was openly advocating that this avenue should be investigated even if this meant that his brainchildren theories of Special Relativity (SR) and General Relativity (GR) had to be abandoned as physically inapplicable, that is, even if his theories ultimately turned out to only be "a castle in the air", as he wrote in 1954.
You will find where this avenue leads to in Sections 26 and 27 of this paper published last January, and that will soon be republished upon invitation as a book chapter by Books Publishing International with complete perspective added in a book titled "New Insights into Physical Science":
Michaud, A. (2020) Electromagnetism according to Maxwell's Initial Interpretation. Journal of Modern Physics, 11, 16-80. https://doi.org/10.4236/jmp.2020.111003.
https://www.scirp.org/pdf/jmp_2020010915471797.pdf
Best Regards, André
Dear Edmonds The universe does not show us any mechanics phenomenon, therefore this Universe with billions of galaxies is not following Sir. Isaac Newton nor Mr. Einstein. Any mechanics remark needs force to move and each move has friction. The Universe is following it nature without friction under quantum physics that we do not know much about it. Thus when it comes to any force, energy, gravity, mass, color, taste, odor and so forth must have quantum origination. so the gravity. Gravity is internal not External as Newton or Einstein stated. this article is unprecedented, yet without out any error.
Article Gravity is an Internal Force
regards
Dear Edmonds,
All masses is surrounded by a neutral potential, you can find a very simple proof in "https://daontheory.com". So Einstein's relativity theories are both wrong. We have to go back to the initial thoughts of I. Newton
JES
the science of universe is not Einsteinian or Newtonian.
To understand universe we must find a new science.
Article How the Quantum Universe Works
Some of these posts are over my head so I am not participating in those discussions but my participation is not needed for other readers to share ideas or add comments.
Sydney Ernest Grimm
Dear Sydney,
You wrote: "I have read page 65 of your paper, mentioned above. The supposed "pressure" of the gravitational force is measured by Louis Rancourt and Philip Tattersall: "Further Experiments Demonstrating the Effect of Light on Gravitation". Applied Physics Research; Vol. 7, No. 4; 2015. http://dx.doi.org/10.5539/apr.v7n4p4"
Thank you so much for this reference. I will carefully study this paper.
Best Regards, André
Sydney Ernest Grimm
Dear Sydney,
Quote from the Rancourt et Al. paper: "In order to account for the observations and measurements in his pendulum experiments Louis Rancourt (2011) suggested that gravity could be conceptualized as a pushing force coming from all directions in space. Planet Earth can block some of the pushing force and the net sum of all the vectors of these forces is a downward vector pointing to the ground. That would be the cause of the weight force."
I agree that this is in complete agreement with my analysis, and consequently with Einstein's intuition about the relation between electromagnetism and gravitation.
Best Regards, André
There are some advanced discussions going on here. For the benefit of myself and other novices I wonder if an easy-to-understand answer can be given to an easy-to-understand question. If we believe the Equivalence Principle (an equivalence between acceleration and gravity as explained in detail in introductory textbooks), which leads to gravity affecting space-time geometry, it seems to me that this makes gravity profoundly different than other forces. The question is, in view of this profound difference, why do people believe in the existence of a theory (that is still being sought after) that treats all forces in the same way? I'm not criticizing this belief that is shared by brilliant people. I'm asking if it is possible to explain this in a way that is easy to understand.
L.D. Edmonds
Dear L.D.,
You write: "If we believe the Equivalence Principle (an equivalence between acceleration and gravity as explained in detail in introductory textbooks), which leads to gravity affecting space-time geometry, it seems to me that this makes gravity profoundly different than other forces."
"Space-time geometry" is a concept that belongs to the theory of General Relativity. If this theory turns out to be inapplicable in physical reality as Einstein himself suspected towards the end of his life, then this becomes a non-issue, and gravity goes back not to being such an exotic phenomenon.
You ask, speaking of the above: "For the benefit of myself and other novices I wonder if an easy-to-understand answer can be given to an easy-to-understand question."
An "easy to understand answer" may possibly be given, but only after the proper set of facts and concepts have been put in correct perspective, which is something that was usually done in older undergrad intro textbooks, but not in the current crop of chopped of intros.
If you have the patience to read through a general overview of the correctly sequenced facts and concepts presented in the following paper, then maybe you will put a finger on a possible "easy to understand answer":
Michaud, A. (2020) Gravitation, Quantum Mechanics and the Least Action Electromagnetic Equilibrium States. In: Amenosis Lopez, editor. Prime Archives in Space Research. Hyderabad, India: Vide Leaf. 2020
https://videleaf.com/gravitation-quantum-mechanics-and-the-least-action-electromagnetic-equilibrium-states/
Best Regards, André
The energy in any form comes from indomitable mind power irrespective of circumstances and junctures
Dear P. K. Karmakar
I think you just made it up. Nice.
Where the mind is coming from?
An atom without energy is dead atom.
regards
A living mind is driven by a cosmic force which is basically electromagnetic in nature
Dear Andre Michaud,
I am seeing that there are alternatives to Einstein's theory of general relativity and you have done an enormous amount of analysis on this topic. I don't have a thorough understanding of any theories so I can't answer my own question so I will ask you for the answer. Einstein's theory leads to the prediction of the precession of the perihelion of Mercury's orbit. Do any of the alternative theories make the same prediction?
The Universe is following its own nature and it does not know Einstein.
Article How the Quantum Universe Works
cheer
More sophisticated readers will appreciate details but a "yes or no" answer to my latest question (about Mercury's orbit) is good enough for me. I will wait for that answer. I need that answer before being persuaded one way or the other.
I'm wondering if we need to have more inputs for a fair discussion. We don't seem to be getting inputs from people that are pro-Einstein. A debate between experts with opposing views is much more significant than my dumb questions.
L.D. Edmonds
Dear L.D.,
You ask: "I am seeing that there are alternatives to Einstein's theory of general relativity and you have done an enormous amount of analysis on this topic. I don't have a thorough understanding of any theories so I can't answer my own question so I will ask you for the answer. Einstein's theory leads to the prediction of the precession of the perihelion of Mercury's orbit. Do any of the alternative theories make the same prediction?"
To my knowledge, the answer is no. But it must be kept in mind that his prediction was found not to be entirely satisfactory although it obviously leans in the right direction.
From my analysis, this is due to his underlying Special Relativity theory not being completely in harmony with electromagnetism, as previously analyzed.
My view is that this will be completely resolved by the upcoming generation of physicists, as electromagnetism become more deeply familiar to all in the field.
Best Regards, André
L.D. Edmonds
Dear L.D.,
You wrote: "I'm wondering if we need to have more inputs for a fair discussion. We don't seem to be getting inputs from people that are pro-Einstein. A debate between experts with opposing views is much more significant than my dumb questions."
I am pro-Einstein. Just like Einstein was pro-Newton. Einstein's aim in developing his theories was not to negate the work of Newton, but to build on it to explain further data that was not available in Newton's time. The same with Einstein's theories, that were developed 100 years ago when less data was available to him than we have now.
Time simply has come to move on, to explain more precisely what remains pending in previous theories, as always in the past.
Of course, more input would be welcome.
Best Regards, André
Dear @L.D. Edmonds,
A good theory is capable of predicting reality before it is known, a bad theory does not predict anything and changes as reality is known.
Relativity is a good theory, the standard model is not.
I think it is a mistake to try to add gravity and relativity to the physics of fundamental forces and fields (which is what almost all physicists try). I think the correct way is to add quantum physics to relativistic physics and not the other way around
Dear André Michaud
No one is against anyone. Sir Isaac Newton always stay our icon, same with Mr. Einstein. I think everyone is pro-science, like Newton and Einstein were.
You are absolutely right we have much sources to make thing more accurate.
We must be openminded use all the sources for our benefit. To my understanding both of these icons were right on their era, but they are incorrect with their theories, because they did not give universe any credibility of its creation, but both create a science (inaccurate) . Both thought universe was here, it is here and it would be here.
The fact is, our universe is not result of an accidental mechanical event with four dumb forces that we know nothing about them.
Article How the Quantum Universe Works
regards
Javad Fardaei
Dear Javad,
You wrote: "To my understanding both of these icons were right on their era, but they are incorrect with their theories,"
I would rather say that their theories are "incomplete" rather than "incorrect".
Each was "correct" as grounded on the knowledge accumulated in their respective era, but are "incomplete" with respect to the current accumulation of knowledge since they cannot explain this new knowledge.
Since the de Broglie and Marmet conclusions that were reached after the Einstein theories were developed and never amended, we now know much more about the electromagnetic nature of elementary particles of which all masses in the universe are made.
Consequently, a new and more complete model needs to be developed, all grounding elements of which have now been put at the disposal of the upcoming generation.
Best Regards, André
Dear André Michaud
You said>> Since the de Broglie and Marmot conclusions that were reached after the Einstein theories were developed and never amended, we now know much more about the electromagnetic nature of elementary particles of which all masses in the universe are made.
ME>> The problem is, we can not relay on hundred years ago which all are pro accidental of creation universe with four dumb forces. I don't know if you ever read some of my articles which all my attention to find origination of everything based on science that we know. I am presenting few thing.
1) The universe is a complete massive of organization that is working under its most accurate nature.
2) The universe is working based on duality. It's mass and energy / conservation energy all are under one ambarella.
3) Atoms are the smallest complete intelligent unit of universe.
4) Gravity is Internal, Not External as our icon stating.
5) origination of all force, energy, Information (color, taste, odors) has quantum based where all stored in the mother of all the element in periodic table HYDROGEN.
If any person agree with just one of them, then all the mechanical theories of the Big Bang is dismissed.
If anyone read these article, and find any error, I will rest my case.
Article How the Quantum Universe Works
Article Gravity is an Internal Force
best wishes.
Javad Fardaei
Dear Javad,
You wrote: "The problem is, we can not relay on hundred years ago which all are pro accidental of creation universe with four dumb forces."
I don't understand what you are talking about. The fundamental laws of nature and the electromagnetic characteristics of energy and elementary particles have nothing to do with any "pro occidental view of creation of the universe with four dumb forces", whatever this may mean. It has to do with the well understood natural properties of energy that underlie all of our successful technological achievements, whether occidental or otherwise.
From the list if issues that you mention, I see no mention of electromagnetism nor of the electromagnetic nature of energy and mass.
I can only suggest that you study electromagnetism from the pool of currently accumulated experimental knowledge.
Best Regards, André
Dear André Michaud I attached two articles that describe everything by understanding "not to follow hundred years ago scientists"
It is like we follow Alexander Graham Bell. If we were doing so, we still had old rotary phone, yet he invent the most precious tool for human.
Fundamental law is the one, I am challenging.
Where the electromagnetic is originated?
Where the energy is originated? or mass?
We have no right explanation for unit of mass, we call every mass matter, and matter mass. We think particle is floating everywhere while we never observe any free particle. Our science need help, but not from 100 yrs ago dead scientists.
If you read some of my paper you will find unprecedented origination of electromagnetic field energy, you find why earth or any planets has seismic activity and volcano, aurora and so forth.
The different between you and me is, I see a lot mistake in our text books, but you don't. Einstein GTR or principle of gravity is not science at all, it doesn't matter it is coming from icon of century.
My suggestion when you read something (electromagnetism) ask yourselves question why universe need it and where it is coming from? then you find it better than a dead scientists from 100yrs ago. I think any single person of today is much smarter than last century top scientists.
Regards
Javad Fardaei
Dear Javad,
You ask: " Where the electromagnetic is originated? Where the energy is originated? or mass?"
Well, unless you carefully study, or better yet, carry out yourself the simple experiments made by Coulomb, Oersted, Ampere, Gauss, Faraday, Biot and Savart, and verify yourself the data obtained and the conclusions that can be drawn from them and that underlie all of our modern technology, you will never know.
Best Regards, André
arriving at this point the brain will take the sights to the nature of the human abbreviation namely energy, mass, gravity, and charge ..
and the big biological mystery nature of the soul? why the end of no mass " soul " lead to death? and what is the real relation between this unknown energy and the living body?
Dear André Michaud I read all of the last four centuries icons papers. I know their perception regarding mass, energy, electron, photon, electromagnetism..and so forth. they all wrong regarding ATOM, PHOTON, UNIVERSE, GRAVITY...
I am rejecting everyone from last century icons regarding ATOM (mass) in general.
My perception of an atom is, it is the smallest intelligent complete entity that is not result of any energy. As matter of fact, it is the one conserving energy. ATOMS ARE SMART.
PHOTON ( particle) Universe can not create any mass by itself. period. All the products of universe is mass-less, volume-less, and shadow-less. i.e. photon, electromagnetic, fire, energy.
I recommend to read this article regarding Hydrogen Journey, it is rejecting all the icons that you mention.
Article Hydrogen's Journey in the Universe
just find one error I rest my case, and I know "You think mass is mechanics and create by energy " It is wrong, Our universe is much smarter than that.
regards.
Javad Fardaei
Dear Javad,
You wrote: "I read all of the last four centuries icons papers. I know their perception regarding mass, energy, electron, photon, electromagnetism..and so forth. they all wrong regarding ATOM, PHOTON, UNIVERSE, GRAVITY"
Your comment shows that you read none of the work of Coulomb, Oersted, Ampere, Gauss, Faraday, Biot and Savart on the experiments that they carried out, because none of them ever spoke of atoms, photon, universe and gravity. They discovered only the electromagnetic properties of matter.
Best Regards, André
Javad Fardaei
Well Javad, I guess we all could agree with you...
.
.
.
...but then we would all be wrong.
Relevant to the main question: Energy came from 'Time'. which is one of the main constituent of General Relativity. But Quantum mechanics only can answer its origin and conservation in to GR components.
Dear André Michaud you mention few name from last centuries, i.e. Coulomb law, it is a atomic experiment of electric charge, to my theory, it is not a mechanics, it is not result of photoelectric charge, This experiment from 1700s.and their experiment is not science that we should practice. read my paper and find an error than we can talk.
Faraday, and Ampere, electromagnetism is an atomic foundation. Electromagnetism is not a basic law. it is force that intelligent atom is providing where each atom is not capable to do so.
The perception of last centuries regarding atoms, electromagnetism (in atom), mechanical gravity, matter/anti-matter.. that we are following is wrong. period.
Atom is not mechanical as you think. there is no free electron exist to create photoelectric charge, as all mainstream think. There is no quantum mechanics, but there is quantum physics that we do not know anything about it.
you should read some of my papers, and find error.
What you read on text books, are garbage, including gravity, electromagnetism, atom...Nothing in the universe is working with the knowledge that we have. Our universe's science, we never touched it yet. not by anyone so far, even Einstein.
Article Hydrogen's Journey in the Universe
Article How the Quantum Universe Works
I can not describe everything on threat, you should read first and use your own thought, then we talk.
regards
Dear Berndt Barkholz
You already wrong with everything, you wouldn't lose anything.
Tell me ONE THING that you right. Just one. I bet you can not fine one.
regards.
Javad Fardaei
Dear Javad,
You wrote: " Coulomb law, it is a atomic experiment of electric charge"
You really are ignorant of all past discoveries that were made about physical reality.
The Coulomb law was established during experiments involving material statically charged in opposition. (static electricity). Atoms were not yet explored at the time.
You wrote: " Faraday, and Ampere, electromagnetism is an atomic foundation."
No. Faraday and Ampere were experimenting with electromagnets and electric current. Atoms were not yet explored at the time.
I read some of your papers. As Berndt so clearly highlighted, I found this in relation with real knowledge about physical processes:
.
.
.
Unfortunately, I learned nothing that I could relate to physical reality from what you explain.
I can only recommend that you study real physics from any reference work meant for engineers.
Best Regards, André
Dear André Michaud
It is okay that you didn't find anything that you know. All of my papers are unprecedented statement, any knowledgeable person can tell, it is not comparison with anything from textbook.
Faraday, electromagnetism experiment thought it is basic fundamental force (atom) wrong.
Atom is been known from thousands years ago, where they separate Gold from other metal.
I think you are good reader from past scientists where each scientists from past were bad reader (autodidactic) , because all performed new things.
my best wishes.
Dear Javad,
A theory that I would call "mature" is one that makes quantitative predictions that can be tested against observations. Einstein's theory of relativity, quantum mechanics, and Maxwell's equations are very mature theories, whether right or wrong. A theory that makes no testable quantitative predictions is not mature even if it is correct. Is your theory mature using this definition?
Dear L.D. Edmonds
Very nice mature question. You are bring many different angles.
1) Einstein theory, is not testable for whole universe with billions of galaxies, where each galaxy is carrying billions of solar system like our, while General Relativity is not working with our solar system. The origination of GR is mechanical phenomenon for one galaxy universe with indivisible atomic universe, while, the building block of universe is quantum remark, and carry trillions of solar system . it is not quantitative.
2) Quantum Mechanics : it is the science of atom, where an atom (mass) is described as a relation within energy, where both energy/mass is unknown and unmeasurable. Quantum mechanics does not exist, but quantum physics exist.
the different between these two is, one is the branch of classical physics one it has its own entity.
3) Maxwell's equation: are set of mathematical rules where partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. The equations provide a mathematical model for electric, optical, and radio technologies, such as power generation, electric motors, wireless communication, lenses, radar etc. All these set of methodical law does not representing our quantum universe.
MY THEORIES: is describing a well massive organization that is following most accurate nature phenomenon, that we do not know much about it. The science that we know is much different from science of universe. No one ever mention the sciences of universe up to this point, and I am presenting universe how it is working. The different between my theory and others is, I found how the universe is working, and others theory stating how the universe should work. these two is totally different from each other.
Article How the Quantum Universe Works
my best regards.
Dear Javad,
I don't think you answered my question. You seem to be having a conversation about something else. Let me ask it again. With "mature" as defined in my latest post, is your theory mature?
Javad Fardaei
Somebody has to "bite this sour apple" and tell you that though you sometimes say something that is true... by pure accident, like the blind chicken that incidentally finds a grain... in general, whatever you comment, you speak nonsense. It is often on your behalf toe-curling embarrassing to read you comments. So please take a rest from physics, start learning about it and come again when you know what physic is ! Here you just use space for no reason and for everybody's irritation...
Dear L.D. Edmonds
YES, VERY WELL METURE. More than you can imagine.
theory should be easy to understand for layman.
For you to understand it you should read all of my theories, many times, as you can. then, you must create questions, not judge, because, It is unprecedented, therefore there is no judgement or comparison to be made.
If you are the truth researcher ( as I believe ) then you should not think in the box, you must give yourselves a lot of time to think on them, because My theories is presenting NEW SCIENCE that never been mentioned anywhere by anyone before.
PS": My theories has been presented in many quantum physics conferences around the world, but due to virus, it is been off for next year.
This is not like any other theory that anyone can understand it, or compare it with other, thus a mature well researcher is when use his/her own mind and create many questions, and if the author could not answer your question scientifically then that theory is not matured.
When you said Einstein GR is matured, it is not, because he couldn't answer or describe his own theory.
Any open question welcome
regards.
Dear Berndt Barkholz
All of my comment is created to response to other none-sense comment that you made. I know, I know enough that I can answer any question that you have in science of physics. try it !
RG is for leaning new thing, you are ignoring this main principle.
General relativity is not science....but, you think is a science.
Some blind is much smarter than one can see, don't underestimate anyone.
try to lean new thing everyday, in the order to learn, you should read new thing every day, not write non-sense everyday.
my regards
Hi Larry: Your question sends me back into "Gravitation" by MTW and Chapter 19 "Mass and angular momentum of a gravitating system". The answer in Ch 19 comes down to "asymptotically flat spacetime" existing. Out here where geometry is flat we can measure everything gravitational in there where geometry is not flat. Ch 20 derives the laws stated in Ch 19, and the infamous section 20.4 "Why the energy of the gravitational field cannot be localized" comes down to the answer "Look at a small region on the surface of a potato. The geometry there is locally flat" ... "The over-all effect one is looking at is a global effect, not a local effect. That is what the mathematics cries out." There is one more sentence before the infamous section 20.4 comes to its glorious conclusion, but I don't need to quote it here, because we can all already conclude that mathematics rules, not physics.
I think this can be seen as an extreme case of friction. The mass M would be in a free fall were not the atoms in the surface of Earth stopping it, so the origin of the normal force in this case must be assigned to the electromagnetic interaction between M and the Earth.
Here is another possibility. As seen in the falling coordinate system we can associate a potential energy to the normal force (it is a constant force so a change in potential energy is force times displacement, which is the same as work done by the force because work done and change in potential energy both equal change in kinetic energy of M). When I first thought of this I complained that there is an unlimited potential energy because M accelerates upwards relative to the falling coordinate system forever. But that was a mistake. The falling coordinate system does not accelerate downwards relative to the stationary coordinate system forever. It oscillates between up and down motion, so M oscillates relative to the falling coordinate system. This removes my complaint about assigning a potential energy to the normal force.
Oh, I see. You are taking the notion of "falling coordinate system" literally, as a physical laboratory with mass falling through the Earth (this reminds me of a classical problem in basic courses of Physics: you dig a tunnel along an Earth's diameter and let a stone fall into it, then you are asked to compute the period of oscillations). However, consider a distant reference frame (not a physical laboratory), not affected in practical terms by the Earth gravitation, but moving with a uniform acceleration equal to g (hence, not oscillating) along a direction parallel to the local Earth's diameter on which the stationary observers is sitting. How you would interpret the potential energy in this case?
To answer your question Jose, a coordinate system moving with constant acceleration (relative to the Earth) instead of free-falling is not inertial in the context of relativity so a pseudo-force is needed. I imagine that some potential energy can be associated with this force. Also, my latest discussion is oversimplified because a free-falling coordinate system is only "locally" inertial. Equations get more complicated (and I haven't learned yet what they are because I am a novice) when such a coordinate system represents events far enough away to be in a different gravitational field. So my idea of assigning a simple potential energy to the normal force is probably oversimplified and wrong. But if some kind of potential energy can be assigned to it, even if it is more complicated than my simple suggestion, that takes care of my question of "where does the energy come from."
I understand your reasoning, but what I am trying to show is that the energy in this case cannot have its origin tied to a particular choice of a reference frame to describe the motion. The only physical reason I can see for the body on the surface to acquire energy is through its interaction with the surface... But I must admit that it is an intriguing question! :)
Why don't you ask this same question at https://physics.stackexchange.com/? It would be interesting to know the answers of people there (there are some really knowledgeable)...
I agree with Jose's objection to my latest proposal. A potential energy should have a physical origin instead of just being a mathematical construction assigned to the normal force. I think my question was already answered on ResearchGate by Sergio but some clarification might help.
The original question is unnecessarily complicated by separating a mass M from the rest of the Earth. A simpler question that has the same answer is the following. An observer O falls towards a body B in accordance with the gravitational field produced by B. O sees B accelerating so B is gaining kinetic energy. Energy conservation requires that this gain be accompanied by some other energy loss, yet O sees no gravity. What is this energy loss?
I think the answer is that O sees no local gravity, but it does see a gravitational field because free-falling objects far away from O do not travel in straight lines in O's coordinate system. So O does see a gravitational field. In an early post, Sergio pointed out that there is a potential energy associated with a given geometry of a gravitational field (I took the liberty of saying "geometry of gravitational field" where Sergio says "space-time curvature"). As O falls, the geometry of the gravitational field, as seen by O, changes in a way that is more complicated than a simple spatial translation. The reason is that the location relative to B at which the field, as seen by O, is zero at one time (which is the location of O relative to B at that time) is different than the location relative to B at which the field is zero at another time. The geometry of the spatial distribution of the gravitational field seen by O is distorting in addition to translating as O falls and this distortion causes the potential energy stored in the gravitational field to be changing as O falls. This supplies the kinetic energy of B. Do you agree?
Dear L.D. Edmonds ,
That potential energy does have a physical origin. I am going to explain it to you not using "standard" relativity, but deep down it is the same.
First, imagine that the universe is a very large hypersphere that at short distances (locally) can be considered flat. We live on your 3-dimensional hypersurface. Any movement on its hypersurface will have a centrifugal force through a 4th dimension that acts as hyperradius.
Forget about the Lorentz transformation for the moment. You can have the invariance of c with the Galileo transformation and that we are going to use.
2 point masses without velocity, will be at the same level with respect to the hyperradius.
2 point masses, one with speed, another not. They will be on a different level in the hyperradio. The one with speed will advance diagonally. Here if you do calculations you have the typical time and length contractions.
Now you see the speed increasing from time to time, you will have that typical diagonal of the speeds that is increasing in slope. The typical acceleration curve.
It can be shown that E = mc ^ 2 is a potential energy, from the center of the hypersphere to its position in the hyperradius. And also that a mass-energy curves space-time, put a point mass inside that curvature and you will have the same curve of the same acceleration that I said before (gravity).
There is a potential difference (hyperradius position) between the curved mass and the point mass that follows that curve and gains kinetic energy until it reaches the bottom of the curvature and they become equal.
If you read and above all, follow the equations of these preprints, you will understand it perfectly and you will have a tool to see relativity in a much easier way:
Preprint ALL SPECIAL RELATIVITY EQUATIONS OBTAINED USING GALILEAN TRA...
Preprint ENERGIA FOTÓN, APROXIMACIÓN GRAVEDAD UNIVERSAL DE NEWTON Y L...
OK, that looks like a plausible explanation! It would be nice to see some (at least qualitative) calculation checking its correctness, though...
Yes.. I agree with Larry's answer 100%.. I like to describe Larry's answer thermodynamically, probably because I'm an aerospace physicist? Gravitational binding-energy is well defined in the literature. The kinetic energy of the O-B interaction is converted into heat in star formation. The energy causing this heat comes from the mass of the gravitational field labeled "binding-energy". Where E(binding-energy) =: E(gravitational field) = M(c2) - E(matter) where M is the gravitational mass of the O-B system [1].
[1] Joseph Katz , "Gravitational energy", Class. Quant. Grav. 22:5169-5180, 2005
The GTR, SR. is a manmade science which it do not fit to a universe with several hundred billons of galaxies universe.
find a error in your thought, you get reward.
Article How the Quantum Universe Works
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