Dear Sofia,

Certainly the proper time (tau) doesn't flow the same in flat spacetime ( Minkowski metric) than in a curved one (pseudo-Riemann metric). If the spseudo-Riemann space is created by the gravitational interaction with a Schwarzschild solution both times are related by

dτ=dt(1- 2GM/rc2)1/2

being M the mass creating the gravitational field, G constant of gravitation, r radial coordinate and c the velocity of light. The time t is assumed to be the one where the metric is flat, while tau is the time measured by one observer in a system under the gravitational field created by the center of the mass M. Therefore we can see that the time flows more slowly within a high gravitational potential than other weaker.

Dear Sofia,

in the script below it is what is predicted by the Einstein FE (1915) in the symmetric spherical homogeneous mass configuration of the exact solution of Schwartzschild (1916) , also shown by Daniel

Preprint Frequency shifts of moving oscillators in gravitational potentials

the prediction of SR in regards to time dilation are generally recognized to be only due to dynamics...

It is interesting in regards some experimental facts of TIME DILATION/REDSHIFT like:

Article NASA GP-A REVIEW UPDATED VERSION

I will rewrite this paper which is quite old...I did not know infact at that time that in 2001 they re-made similar calculations to find the right model for the doppler cancelling system..

My dear Stefano, and all the users,

I am not competent in calculi with Einstein's FE, but I found in Wikipedia a statement which is quite clear for me,

https://en.wikipedia.org/wiki/Gravitational_time_dilation#Outside_a_non-rotating_sphere

"A common equation used to determine gravitational time dilation is derived from the Schwarzschild metric, which describes space-time in the vicinity of a non-rotating massive spherically symmetric object. . . . . . . . without accounting for the effects of rotation, proximity to Earth's gravitational well will cause a clock on the planet's surface to accumulate around 0.0219 fewer seconds over a period of one year than would a distant observer's clock. In comparison, a clock on the surface of the sun will accumulate around 66.4 fewer seconds in one year."

So, I understand that in a gravitational field the clock beats at a slower rate. To be clear, all the clocks are stationary, none is falling in the gravitational field. That means, if we have a pair of twins, one living in a gravitational field and the other far from that field, and they meet sometime, the one who lived in the field would be younger.

This is not the twins' effect with one of the twins traveling and one remaining at rest. The effect with the gravitational field is due to the change of the space-time metric in a field of forces.

The time dilatation due to the field was tested

"Gravitational time dilation has been experimentally measured using atomic clocks on airplanes. The clocks aboard the airplanes were slightly faster than clocks on the ground. The effect is significant enough that the Global Positioning System's artificial satellites need to have their clocks corrected. Additionally, time dilations due to height differences of less than one metre have been experimentally verified in the laboratory. Gravitational time dilation has also been confirmed by the Pound–Rebka experiment, observations of the spectra of the white dwarf Sirius B, and experiments with time signals sent to and from Viking 1 Mars lander."

Now, my question remains, in base of the equivalence principle, can the time dilatation due to gravitation be obtained in an accelerating frame? And also, electromagnetic fields change the space-time metric too; do they produce any time-dilatation?

Dear Sofia

Proper time is the time recorded by a clock at rest in an inertial reference frame that itself may be subject to external forces. The effects of time dilation are observed by an observer in a reference frame external to the reference frame in which the clock is situated. The airplane experiment compared the passage of time of clocks at two different gravitational potentials where the observer's clock was fixed in the gravitational potential at a point on the Earth's surface. The airplanes flew in different gravitational potentials but the overall passage of time on the airborne clock was slower than that observed on the fixed earth-based clock. Had the airborne clock been the reference clock it would have been the earth-based clock whose time keeping would have appeared discrepant. There is no absolute measure of time's passing because to measure time requires recording time at two points in time. This defines an "interval" of time that may be different when compared in different reference frames. But to an observer fixed with his/hers clock in a given reference frame time marches on at its inscrutable pace.

Dear Dwight,

I don't think that Wikipedia falsifies reports of experiments. The passage of time on the airplane clock was quicker, not slower, than that observed on the fixed earth-based clock. In short, the pilot grew older than the observer on the Earth.

The experiment was done also in the lab, please read my citation again, or, read the experiment.

As to reading two fixed clocks at the same lab-time, why should it be a problem? Can't you place two cameras and take pictures of the two clock readings?

Dear Sofia,

this topic was initially treated by Einstein in 1907 as the extension of the Newton equivalence between gravitational and intertial mass (like EOTVOS type experiments). It remains quite controversial and unclear ...it has been criticized ever since by eminent Physicists (including Vladimir Fock and Synge) although it is still used and supported, by some indicated as fundamental.

The Equivalence Principle is enunciated as follows: ”a frame at rest in a (uniform) gravitational field and a uniformly accelerated frame, free from gravitational fields are equivalent for all physical processes”.

The previous sentence has one main implication: experiences in acceleration within a lab, EA, and experiences in static gravitation, EG, cannot be distinguished, from within the lab.

This is usually broken in two parts for the measure of forces and times

a) accelerations in EA and EG have to be identical

b) differences of times in EA and EG have to be identical (otherwise from within a lab, by means of two clocks, one could distinguish the two configurations, hence the equivalence would fail)

In regards to a) If in EG the measured acceleration is g directed downwards and in EA the measured acceleration has the same module and direction, (a) is verified and this is not difficult to conceive and experience as well (hence no particular issue), provided that the lab is sufficiently small to prevent to appreciate with the measuring devices the second order effects (TIDAL effects of the gravitational field, which is never homogeneous).

In regards to b) we have to measure difference of times in the lab having at disposal two clocks in a lab in the case of EA and EG.

for EA, ***Special relativity affirms, according to the relativity of simultaneity (never experimentally verified):

two equally accelerated clocks A and B set at distance H, where B is in the rear position along the direction of acceleration g, having departed from an inertial frame in sync, manifest a time dilation such that:

TB=TA(1+gH/c2), such that the period TB of the rear clock is larger

For EG, it has been verified that, at the first order, in case of gravitation (Pound and Rebka) , two clocks set in a gravitational field at distance H, the relation between the period of the clocks, TB=TA(1+gH/c2), where H is the height in between them and B is in the lower position (on the surface of a planet with acceleration g).

following a) and b) there should be no way at the first order (LOCALLY) to distinguish the two fields, hence the EP should hold....

-------------------------------------------------------------------

So far it has been described what story tellers, tell about the EP : Equivalence of acc and grav at the first order.

Unfortunately though the ***result of special relativity has never been verified experimentally (although somebody affirms that such result is a consequency of the twin effect). It is based on the only substantial difference which Special Relativity shares with Lorentz ether theory (LET) (equally valid in accelerators) , the concept of simultaneity which for SR it is relative and for LET it is absolute.

All is based on the assumption of SR that c is the same one-way (not only two-way) for every IRF.

On the contrary LET, assumes a preferred frame of reference, in which only the two-way (experimentally verified) an only there it is possible to measure c.

The paper of Schiff and its revisitation in 2013 can be illuminating. The time dilation in electrodynamics is treated consistently although the equivalence principle is misapplied...

yes they contribute to the stress tensor...a strong magnetic field of a pulsar gives a contribution to gravitation as well...

My dear Stefano,

First of all thanks for the clear explanation. Now, I'd like to stress an issue: consider a body without electromagnetic properties, i.e. non magnetized and electrically neutral. Does it feel in an electromagnetic field a gravitational effect?

It seems to me impossible. If the body doesn't feel the electromagnetic field, how can it be influenced by this field gravitationally? I mean, how could it feel that the space-time metrix is curved?

But there is much more! If the non-magnetic and electrically neutral body does not feel the curved metrix of the space-time, while another body, say, with magnetic properties, yes feels the curved metrix, then, the space-time is TWO-FOLD. It would be a blow for those who claim that the space-time is some sort of fabric. As a consequence, it won't be simple to say that the space-time is extending because it won't be clear WHAT is extending, WHAT is this space-time. (In fact, I believe than anyway we don't have a clear idea of what is the space-time, but with a two-fold metrix the situation would be even worse.)

What you say?

With kind regards

Dear Sofia,

Proper time is the time registered by a clock as measured along its worldline. In flat space, if the clock is moving inertially, the worldline will be straight. The presence of mass, or energy of any other form including EM, the manifold becomes curved (also known as "gravity") and a body moving under its own inertia follows a curved path (a geodesic). The curvature is determined by the stress energy tensor and for EM that is:

https://en.wikipedia.org/wiki/Electromagnetic_stress%E2%80%93energy_tensor

Mass is a much more compact and simple means of creating gravity.

Proper time remains that measured along the clock's path. Time dilation is just the ratio of that between two events to the coordinate separation of those events, or more generally in differential form, the limit as the separation goes to zero of the advance of proper time to the advance of coordinate time. Clearly then, it depends on your choice of coordinate system.

Dear Sofia,

Dear Sofia,

your question is very important for understanding of physical nature of gravitation.The curvature of space-time is determined by 3 factors: 1) curvature of 3-dimensional space:; 2) rotation of 3-space; 3-dimensonal gravitation force. Interval of observed time T depends on the velocity of rotation of 3-space v_i (i = 1,2,3) and 3-dimensional gravitational potential w: dT = (1 - w/c^2)dt + v_i dx^i/c^2, where t is ideal time. If w = 0 and v_i = 0, then dT = dt^ the space does not rotate and gravitate. Contemporary cosmologists use for calculations Friedman models where dT = dt, because 3-space in these models possesses 3-dimensional curvature but does not rotate and gravitate. Because the explain observed results only through expansion of the Universe. The 3-space of de Sitter model does not rotate but it gravitates. If cosmological constant is positive, we obtain the force of attraction. The temp of observed time in this case decreases and it is stopped at horizone of events/ Conclusion: gravitational force determines the temp of the observed time. With best wishes, L. Borissova

Dear Larissa,

Thanks for your explanations.

Now, there are some notations and terms I didn't understand. For instance you write: dT = (1 - w/c^2)dt + v_i dx^i/c^2. T is unidimensional, while, as you say, w should be a vector. Do you mean that w is the modulus of that vector? Also what you mean by "ideal time"? Is it the time in the flat space?

"The temp of observed time in this case decreases and it is stopped at horizone of events"

What do you mean by "temp" and in which direction decreases? I gues that the direction is from outside the horizon inwards, toward the horizon. Am I right?

But, above everything I repeat the question that I asked Stefano and for me is a MAJOR one: could it be that an electromagnetic field has gravitational influence on a body which is electrically and magnetically neutral?

With kind regards

Dear Stefano, George, Larissa, Daniel, Dwight, and all the other users,

As I am not a specialist in general relativity I acknowledge that my questions can be naive. Though I am asking two top questions:

1) Consider the following experiment. An object magnetically and electrically neutral is placed in an electromagnetic field. Would the object feel a gravitational force? If I understand correctly Stefano's explanation, the answer is positive. But, even more significantly, could the electromagnetic field be configured in such a way as to act on the object with a force opposite to the local gravitational field?

2) Consider another experiment, involving two twins Adam and Bob. Adam is mounted on a rapidly rotating disk. After some time the disk is stopped, and Adam meets again his brother Bob. Would Adam be younger than Bob?

According to Larissa's explanation the answer seems to be positive. Am I right?

The significance of the fact that the proper time is a function of other parameters, is that an additional dimension, the proper time, is added to the space-time. The relativistic interval equation would look as follows:

(1) (Δx0)2 - (cΔτ)2 - (Δx1)2 - (Δx2)2 - (Δx3)2 = 0,

where Δτ depends on the field of forces in which the experiment is carried.

Shortening the proper time for a passenger traveling between two points in space may represent a substitute of a worm-hole.

With best regards

Dear Sofia,

Dear Stefano,

Sofia: "But, even more significantly, could the electromagnetic field be configured in such a way as to act on the object with a force opposite to the local gravitational field?"

Stefano: "not the gravitational effect of the EM field as mass/energy."

Why not? If there is a gravitational-like force resulting from the presence of the EM tensor, the direction of the force depends on the configuration of the EM field, doesn't it? Why should the direction of this force copy the direction of the true local gravity force?

Anyway, the 10-20 factor makes the issue impractical.

Dear Sofia,

In General Relativity the Gravitation doesn't do a force on bodies directly, Einstein's equations (EE) only change the geometry (the metrics are the solutions). Therefore what changes for a given body is its geodesic. On the other hand the source of the EE are only the tensor energy-momentum without distinguishing its origen, i.e. it doesn't matter if it is due to charges, quarks, pressure, etc...

Dear Sophia,

My dear Stefano,

I agree with you, however, the issue is whether the space-time curvature produced by the EM field can cancel part of the curvature produced by gravity. In my understanding there are differences in order of magnitude. It would be interesting to know how much should one intensify the EM field for obtaining a significant reduction of the gravity curvature. Of course, it may be that the answer would be enormous, totally non-realistic.

(By the way I read some material about levitation. It it currently used, but it is pure matter of electomagnetism, having no obvious connection with EFE.)

SW: the issue is whether the space-time curvature produced by the EM field can cancel part of the curvature produced by gravity.

First, gravity is geometric curvature, EM exerts force, so you can lift a pin from a table using a magnet.

If you want to cancel gravitational curvature due to mass using gravitational curvature due to EM energy, it would be like placing the pin half way between two equal masses in deep space, the effects would be balanced. For an order of magnitude comparison, the energy released in the Hiroshima bomb was the equivalent of 0.6 gm of mass. Using half an aspirin would be easier and safer.

Ah, George,

why don't you read attentively what I write?

". . . gravity is geometric curvature, EM exerts force, so you can lift a pin from a table using a magnet."

You can't lift the pin with a magnet if the pin is made of wood. I said explicitly that I consider only objects without EM properties (no electric charge, no possibility of magnetization) as staying in the field. (As to gravity, it is also a force, it depends on which picture you adopt.)

"If you want to cancel gravitational curvature due to mass using gravitational curvature due to EM energy, it would be like placing the pin half way between two equal masses in deep space, the effects would be balanced. For an order of magnitude comparison, the energy released in the Hiroshima bomb was the equivalent of 0.6 gm of mass. Using half an aspirin would be easier and safer."

I have no idea what you talk about. The EM field is not confined to a volume, like a mass, it is spread over the space (unless it is produced by an electric charge, and no magnertic field - which I didn't say). You can't place the pin half way between a mass and a field. The EM field has to spread over the space in which you have also the gravitational field, and the pin has to be placed inside this space. As to the Hiroshima bomb, it was based on nuclear energy, not EM energy.

I pobably should stay out this discussion but at the moment gavitation and EM have not been linked; Yes, you can lift a pin off a table with EM but remove the table and the pin falls - that's gravitation. The two forces are very similar in their manifestations but we have no idea of what they are or why they are but if they weren't there neither would we.

Dear Sofia,

You said earlier "As I am not a specialist in general relativity I acknowledge that my questions can be naive." so I am trying to keep the answers at a fairly high level, just an overview.

SW: You can't lift the pin with a magnet if the pin is made of wood.

You can't make a magnet from wood.

What I was trying to do there was show that there is an ambiguity in the way you asked the question. You can cancel the effect of gravity using the effect of a magnet, but that isn't the same as cancelling spacetime curvature.

That is reflected in your comment that "the issue is whether the space-time curvature produced by the EM field can cancel part of the curvature produced by gravity. In my understanding there are differences in order of magnitude.". The point was that the magnetic effect of a small magnet could more than cancel the gravitational effect of the whole planet, that's the only interpretation in which your words "differences in order of magnitude" make sense.

GD: If you want to cancel gravitational curvature due to mass using gravitational curvature due to EM energy, it would be like placing the pin half way between two equal masses in deep space, the effects would be balanced. For an order of magnitude comparison, the energy released in the Hiroshima bomb was the equivalent of 0.6 gm of mass. Using half an aspirin would be easier and safer.

SW: I have no idea what you talk about. The EM field is not confined to a volume,

In order to cancel curvature locally, that is what you have to do. For example, light is EM in nature so suppose you make a small sphere perfectly reflective on the inside and you release a large quantity of light into it. That EM energy is then contained inside the fixed volume. The mass-equivalent of the contained EM energy will then create spacetime curvature equal to the curvature produce by a mass of E/c2. If you hold that above the pin, it will partly cancel the curvature caused by the Earth. It would of course be simpler and more effective to hold a bowling ball over the pin.

To put it into context, if you could contain all the energy released at Hiroshima, it would produce the same spacetime curvature (gravity) as half an aspirin.

I didn't want to go into so much detail because there are secondary effects that get in the way, putting that much light into the sphere creates radiation pressure on the sphere and pressure creates gravity so a full analysis becomes much more complex, but as an overview the simple picture is that energy creates gravity in the same way as mass.

Dear Sofia,

GD:>

George is right you cannot cancel the curvature, you can only locally counterbalance its effects...and the curvature produced by an EM field, being this energy, just adds up in the total curvature produced by the Stress tensor.

George,

"the magnetic effect of a small magnet could more than cancel the gravitational effect of the whole planet"

Yes, that's true. I believe that I'd better tell you my thoughts in a private message.

With kind regards

Dear Sofia D. Wechsler

"Now, my question remains, in base of the equivalence principle, can the time dilatation due to gravitation be obtained in an accelerating frame?"

Frames are irrelevant - you are free to use whatever frame (better, whatever system of coordinates) you like. In every system of coordinates you will obtain the same result for the time along a given trajectory.

The "proper time" (which is simply the time shown by a clock) depends only on the gravitational field (the metric gmn(x)), not on the electric, magnetic, or whatever other fields. The SR line element will simply be replaced by the generalization to GR, which depends on the gravitational field:

(Δs)2 = gmn(x) Δxm Δxn

but on no other fields.

No, Ilja Schmelzer,

That's not true. Any field that contributes to the source-tensor Tμν in EFE, contributes to the metric tensot gμν. The magnitude of the contribution may be big or low - that's another question and depends on the field intensity - but theoretically, the field is part of the Tμν .

Sofia, what Ilja said is true, proper time is obtained from gμν. What you said is also true but describes what contributes to gμν.

Yes, the EM field can modify the gravitational field, and in this indirect way influence the clocks too. But there is no other way. "the magnetic effect of a small magnet could more than cancel the gravitational effect of the whole planet" is fine about the influence on the trajectory of some other magnet, but makes no sense in relation to the proper time.

There is an influence, to be clear: The small magnet has a mass too, thus, contributes to the mass of the Earth, thus, influences the time dilation by slightly increasing it. Similarly, there will be also an influence on an uncharged piece of matter - it will also gravitationally attracted by the mass of the small magnet. But all this is so small that you can ignore it FAPP.

Yes, Ilja Schmelzer , that's absolutely true!

The magnetic field acts directly on a body that also has magnetic properties. If the body is no magnet and no magnetizable, then the only effect on it is through gμν obtained from EFE. This one may be indeed extremely small.

I agree with the other effects you mentioned.

The proper time doesn’t change because is the time measured in the reference frame of the particle, it supposes that the particle is free from interactions of any kind. It is a Lorentz invariant, gravitational and EM deforms and modulates, respectively, the spatial and temporal component of space-time in such a way that the proper time remains invariant.

It exists a unified geometrodynamical description of gravity and EM which must be taken very seriously, unfortunately academic physicists seem to have very high inertial with respect to new ideas that really work.

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