The particle in the stronger gravitational field will have low energy as compared to the other particle in weaker gravitational field.Photon in stronger gravitational field will have low energy thus we'll observe reduced frequency not constant.we can't assign any change in the internal energy of a particle relative to different points, because IE is not the sum of K.E or P.E but it is the energy of the system i.e which keep the particle alive. since the mass of a particle is a measure of energy, so it is the intrinsic energy of a particle.Now when we do work to lift a particle against gravity, in this process energy is added to the internal energy of a particle,which can be converted into K.E when a particle move toward gravity.

Zeeshan,    The locally measured mass and energy of an electron do not change when an electron goes from a lower elevation to a higher elevation.  When you say that a particle in a stronger gravitational field has less energy, what exactly changes?  My question is ultimately implying that an electron and other particles must have some internal structure which undergoes a change when the gravitational potential is changed. You talk about the "internal energy" of a particle, yet the main stream physics implies that there is no such internal mechanism to give internal energy to a particle.  Part of the reason for the question is to prove that the point particle model is unworkable when addressing questions such as this.  

This is because our current understanding on gravity is based GR within the framework of classical physics. We can't explain such problems without exploring the quantum mechanics of Gravity.

Dear John,

your first question is the easiest to answer - as the potential energy is given by

E = mgh (at least for lifting here at earth)

the potential energy is stored in the larger distance from the zero point of your inertial system (in order to measure gravitational force you need at least two bodies, one of them being your testbody - this is actually the same with electric forces, etc...). These two bodies have a certain distance, which defines their potential energy with respect to each other.

For your electron: this is no pointlike particle (this is just an approximation, you have to have quantum mechnical descriptions here in most cases). But even even you treat it like a particle, the electron still has mass. Again, if you have a mass that creates your gravitational potential, this potential will act on the electron (according to Newton's actio est reactio).

So the answer to your questions is: in the distance between the particles.

Dear John,

"Local clocks at the two elevations are running at different rates of time giving the perception of a lower frequency at the higher elevation."

 Clocks run at different rates if set at different heights, in a gravitational potential. It is experimentally verified, it is confirmed every day with new "pocket" atomic clocks.... 

The perception that the frequency of the lower clocks is lower, is a correct perception . The perception that the energy of the photon gets lower is only an impression.

The force on the particle is reduced.  It could also be side that the "pressure" is reduced.

Particles ability to accelerate back to its original position changes from 0 velocity to some non-zero value depending on how far it is elevated. There is no change in its rest energy. So this is a relative phenomenon and has to do with the kinetic energy and the relativistic mass.

Dear John,

"If an electron is perceived as a point particle with no internal structure, then it is impossible to assign any change in the internal energy of an electron at two different elevations. "

The spin is the key. The spin  is strictly tied to the De Broglie frequency, which is the component of the energy of the electrons,  and to the Higg's field mechanism (PENROSE), through the Dirac Equation and Dirac spinors. The zig-zag process between a left hand zig and a righ hand zag, both of which are massless, have a coupling constant of the dirac spinors of  M*2-1/2(PENROSE the road to reality).

The view point of Peter Higgs is to consider the coupling constant  M*2-1/2 as a field, the Higgs field. It forms the mass of fermions by means of a resonance process (ZIG-ZAG) of an undefined entity (emerging from the VACUUM) with the scalar field...the HIGGS Field...

The potential energy does NOT belong to the object but to the gravitational field. Energy is conserved for an ISOLATED body: E_pot + E_kin = constant cannot refer to your object (which is not isolated), but to the ensemble object + (Earth) + Earth's gravitational field.  Indeed, gravitational interaction is like an elastic thread going from the object center-of-mass to the Earth center-of-mass:  when you stretch such an "elastic thread" by lifting your object, the energy of the gravitational field is increased (and goes back to its initial value when works for lowering the object till its previous position. Remember that the "zero" of gravitational enregy is chosen arbitrarily). Nobody knows exactly how that energy is distributed along the "elastic thread", so that noboby--as afar as I know--  can calculate the exact center-of-mass of the ensemble object + Earth. 

I broadly agree with most of the other posters - if we lift a rock away from the surface of the Earth, the energy that we'd get back by dropping the rock should be stored in the distorted shape of the combined rock-plus-Earth gravitational field, which is less spherically-symmetrical when the rock is raised than when the rock is lying on the surface.

If we assume that the gravitational force is a residue of the nuclear force then it is possible to see gravitational force as an emergent phenomenon like the elasticity. But this can change the big bang picture and raise many other issues. This will not allow any gravitational attraction between two photons or between two leptons or between two non-hadronic particles.

For a particle having mass, it is the rest energy (or equivalently the rest mass) of the particle that  increases with increasing distance from the Earth. For references please see:

1. L. B. Okun, "Photons, Clocks, Gravity and the Concept of Mass", Nucl.Phys.Proc.Suppl. 110 (2002) 151-155; arXiv:physics/0111134.

2. L. B. Okun, "Photons and static gravity, Mod.Phys",Lett.A15:1941,2000; arXiv:hep-ph/0010120.

3. L. B. Okun, K.G. Selivanov and V.L. Telegdi," On the Interpretation of the Redshift in a Static Gravitational Field", Am.J.Phys.68:115,2000;  arXiv:physics/9907017. 

I mostly agree with Okun's

The relationships all have balance.  If I have a body that is rotation the earth.  Then the gravitational potential as it is lifted to a point from the surface that will have zero potenial to fall back to earth.  This is how we put geosynchronous satellites into orbit that say in the same place over the earths surface.  The angular momentum is counters by the gravity and they are locked into a distance from the surface of the earth.  But if we look at this from a relativistic stand point there is no way to tell from the point of view of the orbiting satellite if the earth is rotating and we are following or if the object is stationary and the earth is moving around it yet the fact of the matter is the gravitational potential is reduced to zero at some point in the distance from a rotating body and past that point it will loose contact with the gravitational potential and drift away.  

I think that Gravity and Relativity are not well understood in this area.  Sure we can calculate the affects but I fail to see where we understand why.  

I would like to mention that if the dependence of mass on gravitational potential is right, then the internal structure of the particle has to change. As an example, consider the  Bohr radius of Hydrogen atom, which involves a mass term. If the concerned mass depends on the gravitational potential, then the Bohr radius has to depend on gravitational potential. This means that gravitational potential does affect the size of a Hydrogen atom, and hence the internal structure of a particle however negligible the effect may be.  In fact, any physical quantity involving a mass term (such as the spin magnetic moment of electron) has to be affected by a gravitational potential, if  the mass is dependent on gravitational potential. This is what I think on the dependence of mass on gravitational potential. But then, the effect of the dependence of mass on gravitational potential on the dynamics of a planet moving around the Sun can be shown (Please see  : arXiv:astro-ph/0410401) to have a negative contribution of 14.326 arcsec/century towards the overall non-Newtonian perihelion advance of Mercury. This is something disturbing.

It is well known that field action can deforms test bodies. The gravitational field strength depends on the distance between a massive body and a test body. The back and front of the test body have different distances from the massive body and different forces. In other words the test body is stretching by gravitational field strength. As a result we have deformation energy and additional internal pressure in the test body. If you want to calculate the gravitational energy and its distribution in space you can use the Covariant Theory Gravitation, see https://en.wikiversity.org/wiki/Covariant_theory_of_gravitation . In the theory you can find the stress-energy tensor of gravitational field, gravitational 4-potential and gravitational tensor.

 Dear Harihar Behera ·

 "In fact, any physical quantity involving a mass term (such as the spin magnetic moment of electron) has to be affected by a gravitational potential,"

The fact that absorption capabilities of atoms depends on the variation of Grav. Pot. is a fact.

The fact that spins can be affected..it is reasonable

The fact that mass depends on G.pot.. is something a bit different...

Speed of light is for certain dependent on G. Pot. (SHAPIRO DELAY) not the "proper speed" whihc is Always c, but the coordinate speed.

When an electron in the gravitational field of other body crosses the escape velocity, it just becomes a free particle after going through certain frequncy shift in quantum steps. But where is the question of storing the gravitational potential energy in this case? I think the concept of gravitational potential energy can be used only in a limited sense with in the gravitational field of the body. Out side the gravitational field, this concept has no meaning.

Dear Prof. Stefano Quattrini ,

Can you please send me your comments and criticisms on my paper arXiv:astro-ph/0410401 which explores the question of the dependence of mass on gravitational potential on perihelion advance of Mercury in particular and any planet in general ?

I am anxious to read your comments and criticisms if any for the improvement of the paper. If possible please send your valuable comments to my gmail address: [email protected]

Thanks and regards,

Hari

Energy is a convenient functional entity that is used to account for cause of an action, in mathematical analysis, where no other cause is obvious. Energy has no objective reality or positive existence. Energy, being a functional entity, can fulfill any function assigned to it by rational beings.

When a macro body is lifted away from surface of earth, we account for work-done in terms of (potential) energy, in mathematical analysis. A macro body on the surface of earth is gravitationally attracted continuously towards the centre of earth. Hence, it is continuously under acceleration and resulting motion is prevented by continuous acceleration in opposite direction, provided by the supporting mechanism. In order to raise the macro body, additional work is required to overcome work provided by gravitational attraction and displace it. While doing so, no physical entity is stored in or about the macro body. Additional work provided by lifting effort is consumed to overcome work by gravitational attraction and thereby displace the macro body.

Nainan

In periodic relativity every particle itself is its own clock. To certain extent same is the case in Quantum mechanics. But this is not the case with general relativity. Clocks have their own distinct existence in this theory. From Max Planck's quantum hypothesis we see that energy is just another name for frequency and frequency is inverse of period. So either you can describe a phenomenon in terms of time or in terms of energy but not both because they are one and the same thing. This is also understood in general relativity and therefore either you describe your equations in terms of proper time or in terms of relativistic mass (energy) but not both simultaneously.

When a particle is elevated and gains gravitational potential energy, we can use dE/dt to describe this phenomenon. This a description in terms of energy. Now if we replace E buy the quantum mechanical operator d/dt, we get dE/dt = d^2/dt^2 = acceleration. So either you talk in terms of energy or in terms of  acceleration but not both simultaneously. In periodic relativity t is replaced by period T. Therefore what physically changes in the phenomenon under discussion is just the particle frequency. Nothing else.

Dear John

“The photon appears to have lost energy but there is no change in frequency if adjustments are made for the different clock rates.”

- That isn’t so (an example – see SS post 20 days ago [to Vladimir])

https://www.researchgate.net/post/Is_there_a_solid_counter-argument_against_Dingles_old_objection_to_Relativity_Theory/53

What is rather probably happen, when a photon moves between points with different gravity potentials – see the paper “The informational model – gravity” http://vixra.org/abs/1409.0031

- it indeed changes its energy/frequency. As well as the clocks have different tick rates also, but twice lesser, than that the GR states.

That is the GR is simply non-correct, since – if the blue/red shift for photons is only because of is “Local clocks at the two elevations are running at different rates of time”, that means that – since (let - Earth) other mass must – for both also massive, of course, clocks – slow down its “tick rate” also, and so total gravitational mass defect (i.e. – [negative] gravitational energy of the system of (here) two bodies) would be twice more, then that is in reality.

“If an electron is perceived as a point particle with no internal structure, then it is impossible to assign any change in the internal energy of an electron at two different elevations.”

- Any particle has some internal structure, including the electron, or on other words, every particle is some “clock”. And every particle slows down its “internal clock rate” if, for example, it moves in the space in the absolute 4D spacetime (so maximal internal clock rate is when the particle is at rest in the space); thus, e.g., if the particle is unstable, then the moving particle – as that Pythagorean theorem states – lives longer, then at rest on Lorentz factor. That seems as the particle spends some its “internal ticks” on the steps in the space. (More - see To measure the absolute speed is possible?

http://viXra.org/abs/1311.0190)

Analogously if – say for simplicity, two particles - interact, then every of the particles spends some its “internal ticks” on the corresponding bond – at any interaction that results in a system with [negative] mass defect. The gravity is simply one of possible forces.

Cheers

Sergey, I absolutely disagree with you regarding the gravitational redshift. The redshift is entirely due to the difference in clock rates as conclusively shown in the following very good paper: L.B. Okun; Am. J. Phys. 68 (2), February 2000

Dear John,

you are touching a painful wound....very painful wound...

there are serious implications behind this paper....

I had to agree with the viewpoint of OKUN and WHEELER... but I had to carefully analyse an experiment to be convinced of their view point and discard the other....

Article Gravitation, photons, clocks

Article NASA GP-A REVIEW UPDATED VERSION

Dear John,

It seems that you have read L.B. Okun, but didn’t’ read http://vixra.org/abs/1409.0031

Where you could read, for example, that gravitational potential energy for – here is enough

– for two masses on a distance r is equal to E=GMm/r;

- this energy is divided between both masses equally Eg1=Eg2 = -GMm/2r;

- That results in the gravitational mass defect delta (M+m) = - GMm/rc2.

At that the GR in fact states that the equivalent red (or, correspondingly relative blue shift for Pound et. al. clocks) shift, which corresponds to mass defect of the clock having mass m, is equal to whole mass defect of the system; from what follows that total mass defect (or total gravitational potential energy of the system M+m) is twice larger then the experimentally observed value.

That seems quite enough to conclude, that the GR is simply wrong.

What follows, though, also, for example, from the fact that the GR states that the real spacetime is pseudo Riemannian and so it metric contains imaginary values – analogously as that the SR states for Minkowski spacetime. That seems rather strange again, because of the real 4D spacetime is Euclidian; moreover – it is “Cartesian” since the t-axis is always orthogonal to all space axes. As well as the 4D spacetime is, of course, “absolute” and, for example, the time cannot “be dilated” by any material thing – neither “reference frame”, nor “a mass”.

Again – there is nothing surprising in the gravitational clock tick rate dilation – that is simply a consequence of corresponding mass defect and such an effect takes place in any other systems of bodies when the defect is negative. For example – if a muon mu- is on a shell of an atom, it lives longer, then if it would be free. And the atom lives longer also.

Cheers

 the internal energy of the system changes.

Everything passes from a lower speed of light  to a higher speed of light . In order to let all the particles of the body  set themselves to work at a higher speed you have to give them energy (potential energy). The premise is that if I measure the speed of light locally any attempt will Always reveal "c" as the speed.

Energy is not an absolute but a relative quantity.  I perceive an object travelling at velocity v relative to me as having a kinetic energy of 1/2m.v2.  But if I am traveliing at the same speed and direction it has no energy relative to me.   Time is the key parameter.  but according to the ToR there can be no flow of time so what then is the meaning and significance of "energy"?

Stephen,

as long as you think that energy is a relative quantity according to the relative speed, then fix the coordinates. If the energy conservation is not complied, your theory is hopeless. What ever it is, unless you manage to demonstrate that you are working with coherent ensambles which have a Compton wavelengh shorter than Planck's.

Time is the key parameter???

Unfortunately I can notice that around the concept of inertial systems GRT made a total mess. The equivalence principle is at the base of this AWFUL MESS. 

Stephen I can say anything without energy conservation...physics is dead with out it because it is the intrinsic property of the spce-time,,

Stefano -  Do you reject the GRT then? Or only parts of it?

I stick to experiments, which valiate laws or falsificate them. This for me is the Science. Conjectures or Hypotheses don't interest me if they don't respect conservation laws.

If there is an experiment which shows the violation of conservation laws I surely consider it.

You see Stephen,

it is how you measure energy that it is  relative, not energy itself.

This is one of the biggest problem which I suspect prevents any unification between gravitation and quantum mechanics. Unify forces  is an ill posed problem, but only one description is necessary.

Stefano

All this talk goes back to different people having different ideas of how to define things such as vacuum, space, time, the light postulate, and much more.  There is or should be one definition for all these things and everyone understands and yet there is not.  This puzzles me.  I know that different languages have different meanings for things but we are mostly all talking the same language here and yet we have different interpretations for the same things.

Maybe we should have a base definition like Space: means the absence of everything and Space1 means the absence of everything but a gravitational field,  and Space2 means the absence of everything but a quantum field and so on.... 

The problem is the slight differences between definitions lead us to much different conclusions and thereby different theories that all have different outcomes.  So that some of these may have the correct out come for the raw data that is out there but could still not be correct.

Hi everyone,

I do not know if it has already been written in these answers by others. The object does not gain or store Grav. Pot. energy. The pot. energy always resides in the space between the objects, in the field, and not in the objects. So nothing changes for the objects themselves. It is only a loose manner of speaking that such and such object has gained/stored pot. energy.

Regards,

Rajat

Rajat: You say that "the potential energy always resides in the space between the objects". I am going to use one of Einstein’s thought experiments to disprove this. Suppose that there is a star with one planet in a highly elliptical orbit. When the planet is at its apogee it has the lowest kinetic energy and the greatest gravitational potential energy. At its perigee it has the opposite condition – the lowest gravitational potential energy and the highest kinetic energy. So, the first point is that the greatest potential energy occurs when the gravitational field is weakest between two masses. Second and most important, this is a closed system since energy is not being added or lost. Therefore, the average gravitational acceleration produced by this system does not change.  This is easiest to see at a distance large compared to the orbit.

Now, the kinetic energy of the planet clearly resides within the mass of the planet. If the internal energy of the particles that make up the planet does not change inversely to offset the change in kinetic energy, then the total energy of the planet would continuously change over its orbital path. Actually, it can be shown that the gravitational effect on the rate of time does produce many other changes. One of these changes is that a unit of energy such as 1 Joule decreases in gravity when the measurment uses an absolute scale that incorporates a constant rate of time.  

For example, the energy of an electron appears to be constant in gravity or zero gravity if the measurement is made locally. However, there is a difference if the measurement always uses the standards of zero gravity. This difference exactly offsets the change in kinetic energy of a mass in free fall in a gravitational field. The implication is that the local rate of time produces a physical change within the particles which affects internal energy.

John. As the planet in your example moves from apogee to perigee, its gravitational potential energy gets transformed into its kinetic energy and when it moves from perigee to apogee its kinetic energy gets transformed into its gravitational potential energy. Alternatively the planet motion can be described in terms of change in the frequencies of its constituent particles. The frequencies are lower at apogee and

higher at perigee. So either you can describe the phenomenon in terms of energy or in terms of frequencies, but not both simultaneously. There is no need to bring in clocks and time except for some reference.

Stephen Warren. Meaning and signifcance of energy is that it is a unifying factor of everything in the universe. Everything is reducible to energy. And another feature is that, a particular form of energy can be destroyed but as a whole, energy is indestructible.

Dear John,

This difference exactly offsets the change in kinetic energy of a mass in free fall in a gravitational field. The implication is that the local rate of time produces a physical change within the particles which affects internal energy.

The fact that the clockrates of free falling clocks is the same and is the same as the clock at infinity, is something totally unconvincing. I know this is the version of authoritative Writers and Einstein's. This is a sad consequence of the equivalence principle which is for sure falsified at least in the case of the 1911 Einstein's paper.

That in free fall the gravitational field for the free falling body is cancelled, doesn't convince me at all. The gravitational attraction looks cancelled only because I'm not resisting in order to preserve my position respect to the center of Earth. Since everything is attracted in the same way (WEP) I have the impression to cancel the gravitational field. The effect I'm experiencing  is absence of weight. 

This is totally different from the absence of weight in deep space far from masses.. a GALILEAN inertial system.

That the field gets locally  cancelled is absurd, cannot be cancelled in anyway in proximities, and the second order effect affecting the clocks is still present, in any way. I really presume that if I set two clocks along the direction of motion I will be able to reveal a time shift. Or at least I will be able to detect the direction of motion by setting properly two atomic clocks.

I know it can sound absurd, but the absurdity that free falling clocks have to have the same clock-rate brings to  violations of the NOETHER's theorem.

It seems rather strange that till now somebody states something as “...The implication is that the local rate of time produces a physical change within the particles which affects internal energy…”;

At that – as that was/is in the relativity theory always – without any explanations – what is the “time”? what is the “time rate”? how this “local rate of time produces a physical change within the particles”, etc...

Cheers

Stefano and Sergey:   It appears that both of you have misinterpreted the statement "The implication is that the local rate of time produces a physical change within the particles which affects internal energy…”; Stefano, you said "The fact that the clock rates of free falling clocks is the same and is the same as the clock at infinity, is something totally unconvincing." I agree that placing a body in free fall does not convert the rate of time to the zero gravity rate of time. In fact, in chapter 2 of my book (see link below) I specifically refute this idea. I give the example of a hypothetical cavity at the center of the earth. A clock in such a cavity would be in an inertial frame of reference (free fall) yet the rate of time would be slower than a clock on the surface of the earth which experiences gravitational acceleration.

The following statement is more difficult to explain: "The local rate of time produces a physical change within the particles which affects internal energy." I claim that this general statement has to be true and any particle model which lacks internal structure is inadequate. If both an electron and a muon are point particles, then no physical explanation can ever be devised which explains their energy, spin, charge, etc. In the link below designated "foundation" I propose a particle model based entirely on the properties of spacetime. I show why it appears to be a point particle in experiments. This particle model has quantifiable properties which allow its energy, inertia, spin, gravitational force, electrostatic force etc. to be calculated. This model also explains what changes when this model of a fundamental particle is elevated in a gravitational field. The rotational frequency changes on an absolute time scale but it tracks the local rate of time so that locally no change is obvious. A calculation shows that this effect achieves storage of the gravitational potential energy. This also achieves the necessary compensation of the kinetic energy gain in the elliptical planet example previously given.

http://onlyspacetime.com/

http://onlyspacetime.com/QM-Foundation.pdf

The rotational frequency changes on an absolute time scale but it tracks the local rate of time so that locally no change is obvious. A calculation shows that this effect achieves storage of the gravitational potential energy...

This is quite interesting...

what do you mean as rotational frequency.. something connected with the spin??

Charles. I agree.

George - i think it is a little unfair to criticise the absence of a definition of "time".  As a measure of the interval between two events in the time dimension, "chronological time" is analogous to the definition of distance in a spatial dimension (but we must remember that time has a direction defined by the entropy gradient, so the analogy is not perfect) but I'm sure others will find different definitions that they prefer.  On the other hand defining "now" in the flow of time as "the present" is, at best, circular but do you have a better suggestion?

Movement, and, therefore, kinetic energy are only possible within a flow of time so, if (pace Stefano) Godel is correct and there is no such flow, what is the meaning of potential energy if its potential can never be released as kinetic energy?

Time cannot be imaginary (it) because, if you replace t with it in, for example, the universal equation for decay,  neither the real nor the imaginary part of the result corresponds to what we always observe.  Similarly if t has the form a +ibt there are no values of a and b that give a result that corresponds to observation.

Stefano:   My proposed spacetime based model of the universe has a large number of successes including being able to see exactly where gravitational potential energy is stored when a fundamental particle such as an electron changes height in a gravitational field. The technical paper and book cited below are required to cover the entire subject, but the part relating to gravitational potential energy is as follows. Analyzing the de Broglie waves produced by moving particle such as an electron implies that the electron is surrounded by standing waves at the electron's Compton frequency. Other characteristics can also be deduced so the model of an electron that emerges is a rotating dipole wave in spacetime which possesses ħ/2 quantized angular momentum. The electron's Compton angular frequency is ωc = 7.763x1020 s-1. The rate of time gradient at the surface of the earth can be calculated from:  dτ/dt ≈ 1 + Gm/c2r. Inserting the earth’s mass and radius, results in a gradient of the rate of time of 1.092×10-16 seconds/second/meter. A 1 meter elevation change would cause a frequency change of Δωc = 84,788 s-1 on an absolute time scale. The energy change is ΔE = Δωcħ = 8.936×10-30 J. This exactly matches an electron’s gravitational potential energy difference for a 1 meter elevation change in a gravitational acceleration of 9.81 m/s2. This calculation can also be done without the numbeical example, but in the short post the numbers help. This model of the universe passes numerous other tests including the generation of gravity.

http://onlyspacetime.com/QM-Foundation.pdf

http://onlyspacetime.com/

John Macken: After multiplication of dτ/dt ≈ Gm/c2r by dr/r we have: dr• dτ/(rdt) ≈ dr• Gm/c2r2 = dr•g/ c2, where g is the free fall acceleration. The Compton frequency is: ωc = me•c2/ħ. According your notation there is: ωc •dr• dτ/(rdt) = Δωc =( me•c2/ħ) • (dr•g/ c2)= me• dr•g /ħ. If dr=1 meter, then ħ• Δωc = me• dr•g=A, where A is a 1 meter elevation work.

But the problem here why we must consider exactly ωc •dr• dτ/(rdt) = Δωc as a right equation?

For explanation of this we can use the link http://en.wikiversity.org/wiki/Covariant_theory_of_gravitation#The_principle_of_least_action.

There we find: θ1 – θ2 = ( me/ħ) ∫ Dμ dxμ, where θ2 is quantum phase without the gravitational field, and θ1 the quantum phase in the field, and the phases were synchronized at the initial time point, Dμ is the gravitational 4-potential. If there is not motion, Dμ dxμ = ψ dt, where ψ is the gravitational scalar potential.We can change the integral equation by differential equation using dθ1/dt = ω1 , dθ2/dt = ω2 : ω1 - ω2 = me ψ1 / ħ. Let’s take another point in field which is higher 1 meter for which we have: ω3 - ω2 = me ψ3 / ħ. Subtraction gives: ω3 – ω1 =Δω31 = me (ψ3- ψ1) / ħ = A / ħ . What is Δω31 here? We can suppose that ω1 is the Compton frequency at point 1, then Δω31 will be the change of the Compton frequency when the electron elevated 1 meter from point 1 to point 3.

Stephen,

Time is one of those entities that is defined in the way you describe and that is fine but most people do not define it the same way and this is were I see the problem.  If I define something by using another thing that is in question such as entropy or something that can be defined in different ways or something that could have a negative direction then I am not going to be able to always describe that same thing in the same way. 

In our most common definition of entropy it only goes in one direction.  If that always applies to the universe than that is great and we can always use this definition, however if say in a black hole that entropy is not always going in that direction then we have a problem in a large gravitational field.  Do you get my point?

Things like time need to be defined by something that has a better ability to discribe what is really going on.

I am not sure that I have the answer but we must all think the same on the definitions or it will be hard to progress in science.

What is time? – see SS post here https://www.researchgate.net/post/Is_the_flow_of_time_an_illusion#view=547a8818d11b8bb2778b4702

Including – there is no special role of the entropy relating to the time – the entropy at an evolution of some non-equilibrium state grows since the evolution goes on from the state with lesser probability to the state with greater probability; the entropy is, mostly, a measure, a “witness” of this process; not a force.

And this transition happens in most cases with [“next”] probability that is equal to one practically – analogously as with the probability that is equal [now – exactly, but that isn’t essential] to one goes on any determinate process, say – the calculation of next decimal digit of the square root of two.

Or as the process of Matter evolution in our Universe, which goes on permanently because of the energy conversation law…

Cheers

Dear John,

 "Analyzing the de Broglie waves produced by moving particle such as an electron implies that the electron is surrounded by standing waves at the electron's Compton frequency"

It is like transforming the known mass in matter waves, and then see what happens in a gravitational potential.

The De Broglie frequency of fermions is the offspring of the Dirac spinors in the ZIG-ZAG process, whose coupling coefficient is determined by the HIGGS field, what is exchanged in the process should be the HIGGS BOSON.

This process gives at rest the ħ/2 or ZPE or elementary quantum angular momentum, or half*2pi of the elementary action h.

"The rate of time gradient at the surface of the earth can be calculated from:  dτ/dt ≈ Gm/c2r"

I don't understand,

The experimental verified relation is... dτ/dt ≈ 1+Gm/c2r as far as I know...for an interval of time at r distance and an interval of time at infinite distance. Inserting the Earth's mass and radius, it comes out to be the proper time on Earth surface compared to the deep space.

Stefano:   In these short posts it is not possible to fully explain an idea. You quoted the following from my previous post, "Analyzing the de Broglie waves produced by moving particle such as an electron implies that the electron is surrounded by standing waves at the electron's Compton frequency". Your answer implies that my short statement was misunderstood. I will attempt to clarify it. In chapters 1 and 10 of my book available at the link below, I initially analyze the wave properties of photons confined in a hypothetical reflecting cavity. The analysis shows that confined photons exhibit 8 properties that we normally associate with particles. In particular, the single frequency confined photon is shown to exhibit all the properties that we normally associate with the de Broglie waves produced by a particle in a moving frame of reference. If the cavity is accelerated, there is also unequal photon pressure exerted on the walls due to different Doppler shifts. The net force created exactly matches the inertial force of an equal energy particle. If the confined photon matches the Compton frequency of a particle, (for example 1.2x1020 Hz for an electron) then both the de Broglie wave properties and the inertia of the confined photon match many of the particle's properties. This leads to a particle model which incorporates a wave with the particle's Compton frequency. This model passes numerous tests including explaining where gravitational potential energy is stored.

In your comment you also referenced the Higgs field as giving inertia to particles. I believe that the jury is still out on this point. Recent papers have been written questioning whether the particle discovered is the Higgs boson. I have several objections. 1) A confined photon achieves inertia without requiring a Higgs field. 2) The wave-based particle model described in the book achieves inertia through the same mechanism as a confined photon and precisely matches the inertia of an equal energy of confined photons. 3) The Higgs mechanism does not necessarily achieve this inertia match for an equal energy particle.

http://onlyspacetime.com/

Dear John,

I really appreciate your work and most of your point of view I share..maybe I've been misunderstood.

I was though complaining about the usage of the time dilation in a gravitational field not reporting the experimental relation..

 "I initially analyze the wave properties of photons confined in a hypothetical reflecting cavity. The analysis shows that confined photons exhibit 8 properties that we normally associate with particles. In particular, the single frequency confined photon is shown to exhibit all the properties that we normally associate with the de Broglie waves produced by a particle in a moving frame of reference."

 Are we dealing with  standing waves not being properly photons but still a Field like the ones defining atomic interactions??

 "there is also unequal photon pressure exerted on the walls due to different Doppler shifts"

It is very interesting...this would suggest that the doppler effect is at the base of inertia...

In your comment you also referenced the Higgs field as giving inertia to particles. I believe that the jury is still out on this point

I just wanted to conciliate view points. The Higgs mechanism builds the mass of particles by resonance, it is quite different from inertia... the mass-charge is the actual existance of a particle ..the inertia is its motion

 The effect of the  resonance is the spin of the particles...angular momenta... this is one of the most interesting thing I share and would like to conciliate with your point of view .

You say that no Higgs field is required for light to exibit inertia...that is fine, infact the Higgs field doesn't give inertia to anything, it gives mass by resonance not to photons. The Higgs field entraps entities initially not belonging to this 4 dimensional space-time but superior dimensions into this 4D space-time.

Dear John,

I fully agree with this from your book:

"Inertial Frame of Reference: The concept that gravity can be simulated by an accelerating frame of reference sometimes leads to the erroneous interpretation that an inertial frame of reference eliminates all effects of gravity.

Being in free fall eliminates the acceleration of gravity, but the gravitational effect on the rate of time and the spatial effects of the gravitational field remain. Another way of saying this is that the effects of the gravitational gamma Γ on spacetime are still present, even if a mass is in an inertial."

This is one of the reasons why free falling is inertial but not GALILEAN.

Nothing.

Energy is not defined in physics. It is generally understood as ability to do work. Ability is a qualification and hence a functional entity. A functional entity has neither objective reality nor positive existence in space. It exists in the minds of rational beings and mathematics. As a functional entity, energy fulfils all functions assigned to it by rational beings. There is nothing real about energy. It is an imaginary entity, usually used by us to represent cause of an action, where no logical causes are obvious.

To elevate a body from surface of earth, certain work has to be done to overcome (acceleration due to) gravitational attraction. Same quantity of work will be released, when the body is let fall. This work is done by gravitational attraction, not by stored potential energy. Potential energy stored in the body in elevated position represent this part of work, in mathematical terms.

As far as the body is concerned, no physical changes takes place. see: http://vixra.org/abs/1111.0104 

Nainan

Thank you, Nainan!  I have been wondering what energy would mean in a block-time universe and now I know.

In order to support the view poin John Macken shares, I offer you a page taken form the Feynman's lectures on Gravitation.

It is instructive to solve a purely electomagnetic analog of this problem first.  Consider two charges of the same sign.  "Where" is the energy stored?  These fields are nonlocal so the energy is indeed in the space between the particles (as already stated).  In the gravitational case one should be careful how one is defining "potential energy" so it is not identically null for any configuration in a coordinate independent description.  

 The measure of the energy might be dependent on the coordinate system, but its presence does certainly not.

Lots of posts here and i may have missed a few, but has anyone mentioned that you need to be careful about clocks and their synchronization? You have standard clocks and synchronized clocks. Two standard clocks at different elevations will not be synchronized. You could send pulses from one to the other and adjust the rate of the other clock to match that of the first. Then the clocks would be synchronized. A photon moving between lower and higher synchronized clocks will show the same frequency at both, but the frequency as shown by the standard clocks will be different: the higher clock will show a lower frequency. I hope this is not off the thread.

@Stefano, the very concept of gravitational energy in GR is a bit sketchy.  Any interesting spacetime probably does not have time translation invariance so I would like to know what quantity you are planning to use as energy.  In the PN formulation one can define as a conserved quantity and induce a kind of translation invariance relative to the coordinate time which is induced by asymptotic space.  However this is not the measured time for observers.  

Unless the gravitational field is huge, the only thing that changes is the body's position in the gravitational field. It's not a property of the body but of the body in a field. The same applies to a charged particle in a electric field that's constant in time. As far as that goes the same might be said of kinetic energy: not a property of the body but of a body in motion relative to some body at rest. And as mentioned above, none of this terminology applies in GR.

In a Universe with block time energy has no meaning because there is no motion.   Matter is distributed according to QM principles at successive instants but the instants are all simultaneous.

The momentum energy that went into raising a particle is added to the rest energy of the field between the two masses.