# When to use Special versus General Relativity?

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I've read various accounts of the GPS that invoke both SR and GR in making required adjustments, but this use of both SR and GR confuses me. SR applies only in inertial frames and GR in all frames. Inertial frames don't actually exist in nature b/c there's always some kind of gravitational field present, even in empty space, so strictly speaking SR should never apply in the real world. But we still use it as a useful tool even though we know it doesn't strictly apply. That said, I'm confused why both SR and GR are invoked when it comes to the GPS system b/c it seems that any adjustments that would have to be made would require GR only. Or is SR being used for some adjustments b/c its math is so much easier? Any help clarifying these issues would be appreciated.

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Special Relativity is used in high energy physics, quantum physics, nuclear physics (decay of unstable isotope) etc. etc.

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1 hour ago, aramis720 said:

I've read various accounts of the GPS that invoke both SR and GR in making required adjustments, but this use of both SR and GR confuses me.

This is not completely accurate.

What they really mean is that adjustments have to be made for both the speed of the satellite (relative to the receiver) and the difference in gravitational potential. The first could be described purely by SR, the latter needs GR. But, in fact, SR is just a special case (the clue is in the name) of GR so GR would handle both the relative speed and the gravitational difference.

However, that would require a full treatment using the rather complex math of GR. So from what I remember (it is decades since I worked on GPS systems) they use a GR-based approximation to handle the gravitational side of things and the (simple) Lorentz transform from SR for the relative speed.

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Strange, thanks, that's what I figured but good to hear you confirm it. So, strictly speaking, only GR should be used. But for ease of application both SR and GR are used? And do you agree that SR will never apply strictly in the real world b/c grav fields are always present?

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5 minutes ago, aramis720 said:

Strange, thanks, that's what I figured but good to hear you confirm it. So, strictly speaking, only GR should be used. But for ease of application both SR and GR are used?

That's it. (If I remember correctly.)

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And do you agree that SR will never apply strictly in the real world b/c grav fields are always present?

Remember it is the difference in gravitational potential that is important. So if we are considering two bodies on the surface of the Earth, the difference will be nearly zero. In many other cases, the difference may be negligible.

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Hmm, even if the difference in fields is minimal SR won't strictly apply, correct? Of course, in physics small quantities are ignored regularly, but I'm just asking about strict applicability. And by the same token, no where in the universe will SR strictly apply because there are always grav fields. So SR is an idealized case.

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15 minutes ago, aramis720 said:

Hmm, even if the difference in fields is minimal SR won't strictly apply, correct? Of course, in physics small quantities are ignored regularly, but I'm just asking about strict applicability. And by the same token, no where in the universe will SR strictly apply because there are always grav fields. So SR is an idealized case.

I suppose. But it is a pretty pointless distinction.

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Maybe not pointless if there are better approaches that do strictly apply and are simpler. Have you read Beckmann's book Einstein Plus Two, detailing his ether-based theory that is strictly applicable and simpler and encompasses both SR and GR? I'm not at this point equipped to say it's a superior approach but I'm working through it and it seems promising.

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3 minutes ago, Strange said:

I suppose. But it is a pretty pointless distinction.

Wouldn't a freefalling body come under SR and GR can be ignored? There's no acceleration.

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3 minutes ago, aramis720 said:

Have you read Beckmann's book Einstein Plus Two, detailing his ether-based theory that is strictly applicable and simpler and encompasses both SR and GR?

If this were true, he wouldn't be publishing it in a book (self-published by any chance?) but submitting it to peer-review. But of course it would fail and so...

7 minutes ago, aramis720 said:

I'm not at this point equipped to say it's a superior approach but I'm working through it and it seems promising.

Unless you are already thoroughly familiar with GR (and you don't give that impression) then you are not in a position to judges work.

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No, my OP had no ulterior motive But since the discussion went this way I asked. Anyway, if you're curious check out the book or Bethell's much more accessible overview that includes Beckmann's work (Questioning Einstein). Don't you agree that if a theory is strictly applicable and much simpler it would be worth looking at? The use of both SR and GR in the GPS is a good illustration of the complexity that Einstein's approach has led to.

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1 minute ago, aramis720 said:

Don't you agree that if a theory is strictly applicable and much simpler it would be worth looking at?

It obviously isn't.

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16 minutes ago, StringJunky said:

Wouldn't a freefalling body come under SR and GR can be ignored? There's no acceleration.

The definition of free fall is that the body is moving under the influence of no other force than gravity.

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2 minutes ago, aramis720 said:

No, my OP had no ulterior motive But since the discussion went this way I asked. Anyway, if you're curious check out the book or Bethell's much more accessible overview that includes Beckmann's work (Questioning Einstein). Don't you agree that if a theory is strictly applicable and much simpler it would be worth looking at? The use of both SR and GR in the GPS is a good illustration of the complexity that Einstein's approach has led to.

Of course, and by the way Einstein is questioned every day by the experts in the field, which obviously Beckmann is not. As has already been conveyed to you, if anyone did have a hypothesis that either invalidated an incumbent theory, or explained more then the incumbent theory, that "anyone" would not be publishing it in a book...If he seriously had a workable hypothesis that did what he claimed, he would proceed by writing a proper scientific paper, for proper professional peer review.

I mentioned it the other day in another thread, that in my time on another forum, we had over a couple of years , four "would be's if they could be's" each claiming to have overthrown Einstein's GR, and each after much questioning and probing by other members, were found to have agendas...in three of those it was a closeted ID/religious agenda that finally surfaced. The impetus that drives these type is the fact that science has pushed back any need for any deity into near oblivion, and they are driven to try and expose the science, particularly SR,GR and general cosmology as in error. The fourth was just a down and out anti science nut. You may not have an ulterior motive, but as you have been informed, there is a proper procedure for anyone to go through, if they had anything of any consequence and were fair dinkum. Let me say that I see that chance as vanishingly small, as  relativity and the mathematical validation that goes with it, is rather complicated.

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16 minutes ago, studiot said:

The definition of free fall is that the body is moving under the influence of no other force than gravity.

I know but the freefalling object is not 'feeling' gravity so its frame is inertial, is it not?

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5 minutes ago, StringJunky said:

I know but the freefalling object is not 'feeling' gravity so its frame is inertial, is it not?

This is true. But there can still be differences in gravitational potential (between the floor and roof of the free-falling box, for example).

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45 minutes ago, Strange said:

It obviously isn't.

Why do you say that? Have you reviewed this alternative theory?

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2 minutes ago, Strange said:

This is true. But there can still be differences in gravitational potential (between the floor and roof of the free-falling box, for example).

Right.Thanks.

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22 minutes ago, beecee said:

Of course, and by the way Einstein is questioned every day by the experts in the field, which obviously Beckmann is not. As has already been conveyed to you, if anyone did have a hypothesis that either invalidated an incumbent theory, or explained more then the incumbent theory, that "anyone" would not be publishing it in a book...If he seriously had a workable hypothesis that did what he claimed, he would proceed by writing a proper scientific paper, for proper professional peer review.

I mentioned it the other day in another thread, that in my time on another forum, we had over a couple of years , four "would be's if they could be's" each claiming to have overthrown Einstein's GR, and each after much questioning and probing by other members, were found to have agendas...in three of those it was a closeted ID/religious agenda that finally surfaced. The impetus that drives these type is the fact that science has pushed back any need for any deity into near oblivion, and they are driven to try and expose the science, particularly SR,GR and general cosmology as in error. The fourth was just a down and out anti science nut. You may not have an ulterior motive, but as you have been informed, there is a proper procedure for anyone to go through, if they had anything of any consequence and were fair dinkum. Let me say that I see that chance as vanishingly small, as  relativity and the mathematical validation that goes with it, is rather complicated.

It is sometimes the case that theories become pedestalized to such a degree that anyone who tries to go through the normal channels is effectively shut down. Hence Beckmann's alternative approach. There are also a number of dissident physics journals created to mitigate this problem. Unfortunately, science isn't always entirely rational and funding, careers, groupthink, etc., can often prevent the most reasonable solutions from coming to the fore. Have you read Smolin's book The Trouble With Physics, looking in detail at why string theory is in his view a dead end, and yet consumed many physics careers for some time?

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If gravity is there how can you ignore GR?

And how can you say a body doesn't 'feel' the gravity?

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Wikipedia

In Newtonian physics, free fall is any motion of a body where gravity is the only force acting upon it. In the context of general relativity, where gravitation is reduced to a space-time curvature, a body in free fall has no force acting on it and moves along a geodesic. The present article only concerns itself with free fall in the Newtonian domain.

An object in the technical sense of the term "free fall" may not necessarily be falling down in the usual sense of the term. An object moving upwards would not normally be considered to be falling, but if it is subject to the force of gravity only, it is said to be in free fall. The moon is thus in free fall.

In a uniform gravitational field, in the absence of any other forces, gravitation acts on each part of the body equally and this is weightlessness, a condition that also occurs when the gravitational field is zero (such as when far away from any gravitating body).

No the abscence of gravity is called weightlessness.

If gravity is present, space is 'warped' and GR is required.

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2 minutes ago, studiot said:

If gravity is present, space is 'warped' and GR is required.

If spacetime is sufficiently flat graviational effects can be ignored. We do this all the time.

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59 minutes ago, Strange said:

If this were true, he wouldn't be publishing it in a book (self-published by any chance?) but submitting it to peer-review. But of course it would fail and so...

I was impressed by how quickly you deduced the book was self-published.

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Petr Beckmann (1924-1993) was an electrical engineerphysicist, and major crank. He was a prolific technical writer, churning out a huge number of works on engineering, statistics, and nuclear power. He also wrote a history of the calculation of pi, appropriately titled A History of Pi.

He then defected to the US from Czechoslovakia in the 1960s and met Ayn Rand, soon becoming a total Randroid. When he wasn't doing his own scientific work, he was attempting to undo the work of others, most notably Albert Einstein. The Objectivists' disdain for modern physics seemed to have rubbed off on him and he became a "skeptic" of the Theory of Relativity. He set up his own vanity press to publish this work.[1] He called his alternative theory conjecture "Galilean Electrodynamics."[2] Other topics Beckmann wrote about at length in Rand's publications and on his own were libertarianism, the virtues of the free marketanti-environmentalism, and other various "problems" with modern physics. He started the newsletter Access to Energy to promote nuclear energy, which is now run by Arthur Robinson.

Edited by zapatos

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17 minutes ago, aramis720 said:

Why do you say that? Have you reviewed this alternative theory?

If you tell me which peer reviewed journals it has been published in, I will take a look.

15 minutes ago, studiot said:

If gravity is there how can you ignore GR?

Because it may be insignificant. We do it all the time.

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And how can you say a body doesn't 'feel' the gravity?

Ask the people on the ISS if the feel Earth's gravity.

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No the abscence of gravity is called weightlessness.

As is being in free fall.

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If gravity is present, space is 'warped' and GR is required.

GR is not necessarily required. We use Newtonian theory all the time.

Edited by Strange

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16 minutes ago, swansont said:

If spacetime is sufficiently flat graviational effects can be ignored.

Is spacetime flat for a free falling observer? Locally.

Edited by StringJunky

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6 minutes ago, StringJunky said:

Is spacetime flat for a free falling observer?

No. This looks like a good explanation: http://www.einstein-online.info/spotlights/geometry_force

See the section "Remains of gravity" where it discusses tidal forces.

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