How Does Acceleration Affect the Relativistic Mass of Particles?

[Frame Dragger]

The apple does not simply appear to accelerate it does accelerate and because it accelerates then it seems obvious that the increasing force of gravity acting upon it is more than sufficient to overcome the apple's increasing inertial resistance.



As you effectively point out - the particle appears, to a distant observer, to be slowing down as it approaches the event horizon but assuming that he is aware of the fact that as the particle moves closer to the black 'hole' the light that the particle emits reaches him at progressively slower velocities he should be capable of realizing that what appears to be taking place is nothing more than a visual illusion.



He falls off a cliff and at that very instant 'is' of the opinion that not only the cliff but also the entire universe is accelerating in a particular direction!

Presumably being scientifically inclined he might perhaps ask himself what (greater-than-infinite and increasing) force could cause an infinite universe to accelerate.

Uhhh... doppler shifting isn't "illusory", it's a real effect, and it's also very real that the observer will NEVER be able to see the 'astronaut' falling past the horizon. In the same way, the issue of the scientist you propose requires that he be aware of initial conditions to make his judgement, otherwise... still relative. The fact that he'll fall to his death doesn't change the nature of relative motion or Relativity.

 

[utesfan100]

I think I found Starthaus' objection to the long monorail example. Compare the velocity described for the train to the escape velocity of the Earth and consider which way the force must go.

Now, suppose a thin ring is supported by a stand and then spun to a speed where its mass is moving at v=0.6c along the ring. Would the stand feel more weight to support the ring?

 

[yuiop]

I think I found Starthaus' objection to the long monorail example. Compare the velocity described for the train to the escape velocity of the Earth and consider which way the force must go.

Sure, if the train is exceeding orbital velocity on a spherical massive body then it will take off, but I would like to consider a very localised version on a very large flat earth, to give us an idea of what happens when considering situations like the one you describe below.

By the orbital argument, a mass moving with orbital velocity parallel to the surface of the Earth experiences zero or negative gravity. Now consider a helicopter with masses on the end poles instead of lifting blades on a gravitational body with no atmosphere. What will happen if the rotor rotates with relativistic tip velocities that exceed the escape velocity of the massive body? Will the helicopter be able to hover or ascend in no atmosphere just using the rotational velocity of its rotor tip weights? I think the answer is no.

Now, suppose a thin ring is supported by a stand and then spun to a speed where its mass is moving at v=0.6c along the ring. Would the stand feel more weight to support the ring?

Most of the things I have read would say the answer is yes.

 

[utesfan100]

By the orbital argument, a mass moving with orbital velocity parallel to the surface of the Earth experiences zero or negative gravity. Now consider a helicopter with masses on the end poles instead of lifting blades on a gravitational body with no atmosphere. What will happen if the rotor rotates with relativistic tip velocities that exceed the escape velocity of the massive body? Will the helicopter be able to hover or ascend in no atmosphere just using the rotational velocity of its rotor tip weights?

In this case the rotor provided the force to keep the tips in place, circling above to no effect, other than to keep the helicopter grounded by the increase in mass caused by their rotation.

 

[yuiop]

In this case the rotor provided the force to keep the tips in place, circling above to no effect, other than to keep the helicopter grounded by the increase in mass caused by their rotation.

OK, we are in agreement here.

 

[cos]

Uhhh... doppler shifting isn't "illusory", it's a real effect,

My comment had absolutely nothing whatsoever to do with doppler shifting!

If a far distant observer is looking at a beam of light that is heading directly toward a black 'hole' that beam will accelerate! (He cannot, of course, actually see that beam - it is only a hypothetical situation.)

Similarly if he is looking at a beam that is moving directly away from that object the velocity of that beam, relative to him, will be dependent upon the distance of its source from that black star (assuming that the source is external to the event horizon).

and it's also very real that the observer will NEVER be able to see the 'astronaut' falling past the horizon.

Irrelevant. I made no reference to an [object] falling past the horizon.

In the same way, the issue of the scientist you propose requires that he be aware of initial conditions to make his judgement...

I specifically wrote that the scientist falls off a cliff! He cannot fall off a cliff unless he is initially located on that cliff ergo is presumably aware of the initial conditions - assuming mental competence/awareness of course.

He could, of course, have been rendered unconscious and thrown off the cliff but I prefer to stick with relevance.

 

[yuiop]

I think I found Starthaus' objection to the long monorail example. Compare the velocity described for the train to the escape velocity of the Earth and consider which way the force must go.

I found another article http://www2.warwick.ac.uk/fac/sci/physics/teach/module_home/px436/notes/lecture16.pdf that has equations similar to those of Rindler. Starthaus is obviously talking about "effective potential" where the effect of centrifugal potential due to orbital velocity around the massive body is subtracted from the gravitational potential. For a circular orbit the potential gradient is zero. In the case of the weight of a small spinning ring, orbital velocities are not relevent.

 

[starthaus]

I found another article http://www2.warwick.ac.uk/fac/sci/physics/teach/module_home/px436/notes/lecture16.pdf that has equations similar to those of Rindler.

Yes, this is good but not as good as Rindler. In essence it is an abstract of Rindler's chapter 11, minus the proofs.

Starthaus is obviously talking about "effective potential" where the effect of centrifugal potential due to orbital velocity around the massive body is subtracted from the gravitational potential.

Rindler is talking about particle orbits in Schwarzschild space. This describes exactly the motion of particles at LHC, i.e. it answers the OP.
As an aside, the Jonsson paper is pure nonsense, AmJPhys publishes a lot of bad papers when it comes to relativity. The other paper (Matsas?) is not even peer-reviewed.

 

[Frame Dragger]

My comment had absolutely nothing whatsoever to do with doppler shifting!

If a far distant observer is looking at a beam of light that is heading directly toward a black 'hole' that beam will accelerate! (He cannot, of course, actually see that beam - it is only a hypothetical situation.)

I either stand corrected, or deeply confused. Actually, the latter regardless of the former.

Similarly if he is looking at a beam that is moving directly away from that object the velocity of that beam, relative to him, will be dependent upon the distance of its source from that black star (assuming that the source is external to the event horizon).

That I understand, but I'm not grasping why this is significant in this situation. I don't mean that sarcastically, I just (clearly) don't get it.

I specifically wrote that the scientist falls off a cliff! He cannot fall off a cliff unless he is initially located on that cliff ergo is presumably aware of the initial conditions - assuming mental competence/awareness of course.

Agreed, but given all of that, how is this a question which touches on Relativity at all? You have your initial and final velocities of the hapless scientist (the final being most upsetting to him), and all other conditions set; you have your IRF of the scientist established.

He could, of course, have been rendered unconscious and thrown off the cliff but I prefer to stick with relevance.

Well, relevant, but genuinely cruel,

If there is a single source of my confusion here, it would be that what you're ascribing to an illusory effect, seems more to do with gravity as fictitious force, than relative motion. I wouldn't argue that we can establish IRFs, or that at the end of the fall distant observers will agree on the end result (thud), but I don't see what it is you're illustrating.

 

[cos]

If a far distant observer is looking at a beam of light that is heading directly toward a black 'hole' that beam will accelerate! (He cannot, of course, actually see that beam - it is only a hypothetical situation.)

I either stand corrected, or deeply confused. Actually, the latter regardless of the former.

You wrote that you understand that if a far distant observer is looking at a beam that is moving directly away from that object the velocity of that beam, relative to him, will be dependent upon the distance of its source from that black star.

In accordance with that concept - the light emanating from a source that is at a (hypothetically) fixed location relative to a black star will travel toward the distant observer at a slower rate than the light from an object that is located further away from the star.

Similarly, the light emitted by both sources toward the star will accelerate.

Imagine that you are at a vast distance from a light source that emits beams of light to your right hand side and to your left. Obviously (although you cannot actually see those beams) they will both be moving at identical speeds away from the source however if the source starts accelerating in the same direction as one of those beams that beam will be moving away from the source at a slower speed than the other beam (but only whilst the source is accelerating).

In accordance with the principle of equivalence - if a source is at a fixed distance from a black star the beam that is projected toward the star will accelerate whilst the other beam will travel away from the source at a (slower) velocity that is dependent upon the source's distance from the star (however only from your, far distant, point of view not from that of an observer located alongside the source).

I specifically wrote that the scientist falls off a cliff! He cannot fall off a cliff unless he is initially located on that cliff ergo is presumably aware of the initial conditions - assuming mental competence/awareness of course.

Agreed, but given all of that, how is this a question which touches on Relativity at all?

If you fail to see how this touches on relativity and mass dilation I cannot clarify the situation.

You have your initial and final velocities of the hapless scientist (the final being most upsetting to him), and all other conditions set; you have your IRF of the scientist established.

We do not have our IRF of the scientist!

He is accelerating hence is not in an inertial reference frame!

If there is a single source of my confusion here, it would be that what you're ascribing to an illusory effect, seems more to do with gravity as fictitious force, than relative motion. I wouldn't argue that we can establish IRFs...but I don't see what it is you're illustrating.

My description of an illusory effect is that it is the fact that the speed of the light traveling toward a distant observer from an object that is falling into a black star slows down as the object enters stronger gravitational tidal areas giving the distant observer the impression that the object's rate of travel toward the star is decreasing but in reality (and the distant observer should be fully aware of this fact) the object is accelerating.

The illusory effect is analogous to when a person sees a mirage; the scene is not actually where it appears to be in the same way that if we see a star that seems to have changed locations as its light bypasses a massive body (e.g. during an eclipse) that star has not physically moved; this is only a visual illusion.

 

[Frame Dragger]

You wrote that you understand that if a far distant observer is looking at a beam that is moving directly away from that object the velocity of that beam, relative to him, will be dependent upon the distance of its source from that black star.

In accordance with that concept - the light emanating from a source that is at a (hypothetically) fixed location relative to a black star will travel toward the distant observer at a slower rate than the light from an object that is located further away from the star.

Similarly, the light emitted by both sources toward the star will accelerate.

Imagine that you are at a vast distance from a light source that emits beams of light to your right hand side and to your left. Obviously (although you cannot actually see those beams) they will both be moving at identical speeds away from the source however if the source starts accelerating in the same direction as one of those beams that beam will be moving away from the source at a slower speed than the other beam (but only whilst the source is accelerating).

In accordance with the principle of equivalence - if a source is at a fixed distance from a black star the beam that is projected toward the star will accelerate whilst the other beam will travel away from the source at a (slower) velocity that is dependent upon the source's distance from the star (however only from your, far distant, point of view not from that of an observer located alongside the source).



If you fail to see how this touches on relativity and mass dilation I cannot clarify the situation.



We do not have our IRF of the scientist!

He is accelerating hence is not in an inertial reference frame!



My description of an illusory effect is that it is the fact that the speed of the light traveling toward a distant observer from an object that is falling into a black star slows down as the object enters stronger gravitational tidal areas giving the distant observer the impression that the object's rate of travel toward the star is decreasing but in reality (and the distant observer should be fully aware of this fact) the object is accelerating.

The illusory effect is analogous to when a person sees a mirage; the scene is not actually where it appears to be in the same way that if we see a star that seems to have changed locations as its light bypasses a massive body (e.g. during an eclipse) that star has not physically moved; this is only a visual illusion.

As I understand it, light does not "slow down" or accelerate as it approaches black hole (Black Star if you prefer), but that its degrees of freedom become increasingly limited, until all possible paths lead past the Event Horizon.

At no point is light's velocity changing except in regards to the medium it is passing through. A mirage is the result of refraction, and while I'm not contesting the notion of gravitaitonal lensing, it doesn't have a thing to do with why an observer will simply see the scientist grow dimmer, and dimmer, redder, and redder.

You seem to think that light is "sucked" into a black hole, rather than following a geodesic into it. That has nothing to do with a geometrical view of gravity, nor does "accelerating light". I'm sorry cos, but if the light accelerated, there would BE no relativity. Using sceintists falling off cliffs, or black holes isn't materially different from trains. Light's speed in a given medium is CONSTANT, and the gravity of a "black star" simply restricts possible geodesics that would lead to an escape. At no point is "c" changing, at least, until you get past the EH, then who knows.

 

[cos]

As I understand it, light does not "slow down" or accelerate as it approaches black hole (Black Star if you prefer),

To clarify the situation - I made no suggestion that light slows down as it approaches a black star; it speeds up!

(I prefer the title 'black star' on the basis that there is no 'hole' - that this is nothing more than a fanciful description aimed at impressing the general public).

(Incidentally - to set the record straight - my references are to beams of light that are moving radially toward or away from a black star not tangentially relative to same.)

Light does not slow down as it departs a black star; its velocity is determined by the location of its source in the star's gravitational tidal area i.e. its distance from the star.

In a previous message I wrote -

Similarly if he is looking at a beam that is moving directly away from that object the velocity of that beam, relative to him, will be dependent upon the distance of its source from that black star (assuming that the source is external to the event horizon).

To which you responded -

That I understand...

I take it that you understood but did not accept it?

Were you able to understand my depiction of your looking at a distant source that emits beams of light to your right hand side and your left hand side then the source accelerates?

Are you of the opinion that the beam that is moving in the same direction as the source will not be moving away from the source at a slower rate than the other beam or are you of the opinion that the principle of equivalence does not apply to this concept?

I sincerely hope that with your comment "light does not 'slow down' or accelerate as it approaches black hole..." you are not resorting to the dubious practice of referring to a determination made by a local observer.

but that its degrees of freedom become increasingly limited, until all possible paths lead past the Event Horizon.

All of my postings apply to events that take place this side of the event horizon so it would be appreciated if you did not refer to this obfuscatory material.

At no point is light's velocity changing...

I reiterate - In a previous message I wrote -

Similarly if he is looking at a beam that is moving directly away from that object the velocity of that beam, relative to him, will be dependent upon the distance of its source from that black star (assuming that the source is external to the event horizon).

To which you responded -

That I understand...

I assume that you understood but did not accept it.

except in regards to the medium it is passing through.

Please do not introduce obfuscatory material. Light approaching or departing a black star may well be passing through a medium that is accelerating toward the star however this should not be taken into account in relation to a hypothetical situation of light moving through a vacuum.

A mirage is the result of refraction, and while I'm not contesting the notion of gravitaitonal lensing, it doesn't have a thing to do with why an observer will simply see the scientist grow dimmer, and dimmer, redder, and redder.

It would be very much appreciated if you did not twist my words!

I said nothing about the observer seeing the scientists image becoming dimmer and redder! My comment was in relation to the claim that a distant observer will see the scientist slowing down as he approaches that object not accelerating!

The fact that the distant observer will see the light emitted by the scientist slowing down as he enters progressively stronger gravitational tidal areas may give him the impression that this is taking place however assuming that the observer is of reasonable intelligence he should be able to realize that whilst the scientist appears to be slowing down this is nothing more than a visual illusion and that the scientist, just like all other forms of matter, is accelerating!

You seem to think that light is "sucked" into a black hole, rather than following a geodesic into it.

Your deprecatory remark verges on a personal insult and further applications will terminate this discussion. I would be appreciated if you did not try to put words in my mouth or make accusations!

As does all other matter, light falls into a gravitational field. It is not 'sucked' by gravity.

A beam of light that is traveling directly (radially) toward a black star is not following a geodesic (i.e. following the shortest possible line between two points on a sphere or other curved surface).

That has nothing to do with a geometrical view of gravity, nor does "accelerating light". I'm sorry cos, but if the light accelerated, there would BE no relativity.

In his book 'Relativity' http://www.bartleby.com/173/ Einstein wrote (76) -

"...our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuuo...cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity (more correctly - the speed) of light varies with position...[SR's] results hold only so long as we are able to disregard the influences of gravitational fields..."

The speed of a beam of light varies depending on its position (i.e. its location) relative to a gravitational source and in the case of a black star a massive, virtually infinite, source of gravity.

Einstein continues that whilst some people are of the opinion that GR overthrows SR (that in your words 'there would BE no relativity') he points out that SR 'lives on' in GR 'as a limiting case' in other words - when there is no gravitational effect but to the best of scientific knowledge there appears to be no such thing as a totally zero gravitational location.

Light's speed in a given medium is CONSTANT, and the gravity of a "black star" simply restricts possible geodesics that would lead to an escape.

What does the fact that light's speed in a given medium is constant have to do with a beam of light that is moving toward or away from a black star? At that instant the star may have already absorbed any medium in the vicinity of the beam.

At no point is "c" changing...

"[SR's] results hold only so long as we are able to disregard the influences of gravitational fields." (Albert Einstein)

SR's 'results' include the theory that the speed of light does not change yet according to Einstein we should disregard SR's results when gravity is involved.

 

[yuiop]

To clarify the situation - I made no suggestion that light slows down as it approaches a black star; it speeds up!

To local observers, the speed of light is constant (always equal to c). To a distant observer the coordinate speed of light slows down as it travels deeper into the gravitational well. It is necessary to state the location of the observer when making statements about the speed of light in a gravitational field and both you and FD are guilty of not doing this.

How do I arrive at the conclusion that the speed of light slows down as it falls according to the distant observer? First consider a clock that is lowered to radius r in a gravitational well and then at r for a period and then brought back up. The time that elapses on the lowered clock is less than the time that elapses on a clock that remains high up. The time dilation effects during the traveling phase of the lowered clock while being lowered and raised can be eliminated by comparing to the results to a control clock that is lowered and raised without the dwell time t. The results show that gravitational time dilation is real. Clocks really do run slower deep in a gravitational well, relative to a distant clock. An observer deep in the well considers the distant clock to be running faster than his own clock and the distant observer considers the deep clock to be running slower than his own clock. Both observers agree that the deeper clock runs slower. There is no ambiguity of reciprocal clock rate measurements as in SR.

Now if you agree that clocks near a gravitational source really do run slower relative to distant clocks, then if a local observer measures the local speed of light with a slow clock to be the same as the local speed of light as measured by a distant observer using a faster clock, then the speed of light must be different at the different locations in a relative coordinate sense. The only way this can be avoided is by having vertical rulers that get longer by a factor of gamma = 1/(1-2GM/r) to cancel out the effect of slower clocks, but the Schwarzschild metric says exactly the opposite and rulers get shorter by a factor of gamma deeper in the well. In fact the vertical coordinate speed of light measured by the distant observer gets slower by a factor of gamma squared, the deeper you go into the well.

(I prefer the title 'black star' on the basis that there is no 'hole' - that this is nothing more than a fanciful description aimed at impressing the general public).

Black star implies a body with a solid surface, while the "surface" of a black hole is an event horizon rather a solid surface and the event horizon encloses a region that is a vacuum except for a point with infinite density at the centre of the region. The conventional view in GR is that a body with greater than the Schwarzschild density does not have a solid surface and so it is not described as a black star.

Light does not slow down as it departs a black star; its velocity is determined by the location of its source in the star's gravitational tidal area i.e. its distance from the star.

You are right that light does not slow down as departs a black hole. It speeds up as it rises, from the point of view of a distant observer and is constant from the point of view of the local observers that the light passes on the way up.

I sincerely hope that with your comment "light does not 'slow down' or accelerate as it approaches black hole..." you are not resorting to the dubious practice of referring to a determination made by a local observer.

There is nothing dubious about FD referring to the measurements made by a local observer. The only dubious practice is not making it clear what observer makes the measurement, when making statements about the speed of light.

 

[Frame Dragger]

To clarify the situation - I made no suggestion that light slows down as it approaches a black star; it speeds up!

I have the same problem with "speed-up" as "slow-down".

(I prefer the title 'black star' on the basis that there is no 'hole' - that this is nothing more than a fanciful description aimed at impressing the general public).

Whereas "black star" is what.. less fanciful? It's not a star anymore, and "hole" is a decent approximation for an inescapable region of spacetime. To be honest, "Black Star" sounds a hell of a lot more fanciful that "Black Hole" in terms of capturing the public imagination; not that I believe for a second that is the point, but you're entitled to your opinion.

(Incidentally - to set the record straight - my references are to beams of light that are moving radially toward or away from a black star not tangentially relative to same.) Light does not slow down as it departs a black star; its velocity is determined by the location of its source in the star's gravitational tidal area i.e. its distance from the star.

Let me pose this to you: Take your light beams and have them at orbital distance from the BH/BS, but now make it the original star. Do you still believe that the velocity of light is determined by its distance from the star?

<snip> Were you able to understand my depiction of your looking at a distant source that emits beams of light to your right hand side and your left hand side then the source accelerates? Are you of the opinion that the beam that is moving in the same direction as the source will not be moving away from the source at a slower rate than the other beam or are you of the opinion that the principle of equivalence does not apply to this concept?

I think you need to explain how it applies, and how that squares with GR.

I sincerely hope that with your comment "light does not 'slow down' or accelerate as it approaches black hole..." you are not resorting to the dubious practice of referring to a determination made by a local observer.
All of my postings apply to events that take place this side of the event horizon so it would be appreciated if you did not refer to this obfuscatory material.

I am saying that outside of an Event Horizon, the speed of light is constant in a given medium, including a vacuum. My understanding of how light "falls" into a gravity well is due to restriction of its degrees of freedom, and possible escape routes, not by altering its speed. That is the ONLY reason I mentioned event horizons at all. I don't believe that clarifying my point is obfuscating anything.

Please do not introduce obfuscatory material. Light approaching or departing a black star may well be passing through a medium that is accelerating toward the star however this should not be taken into account in relation to a hypothetical situation of light moving through a vacuum. It would be very much appreciated if you did not twist my words!

See previous, I'm not twisting anything, anymore than I am secretly editing your posts. I was saying clearly (I thought) that light's speed is CONSTANT unless you DO invoke a medium.

I said nothing about the observer seeing the scientists image becoming dimmer and redder! My comment was in relation to the claim that a distant observer will see the scientist slowing down as he approaches that object not accelerating![/quoter]

You do realize that every time I respond to you, I'm not trying to reframe the argument, I'm actually trying to make a point as well? Slowing down, gravitational redshifting, slower apparent tick rates on clocks... I'm making the point that it's not an "illusion", but a real effect. If an infalling astronaut (my model this time) manages to escape a Black Hole before passing through the EH, they will experience very REAL effects of differential aging/time dilation, much as they would in the twin paradox or The Planet of The Apes!

The fact that the distant observer will see the light emitted by the scientist slowing down as he enters progressively stronger gravitational tidal areas may give him the impression that this is taking place however assuming that the observer is of reasonable intelligence he should be able to realize that whilst the scientist appears to be slowing down this is nothing more than a visual illusion and that the scientist, just like all other forms of matter, is accelerating!

... See previous.

Your deprecatory remark verges on a personal insult and further applications will terminate this discussion. I would be appreciated if you did not try to put words in my mouth or make accusations!

Taking something as an insult is not the same as being insulted. I made an observation which reflects how I see this discussion trending. You have been curt to the point of rudeness, and I have not been. There is a difference between being insulted, and being pissed off, and I think right now you're the latter. What did I accuse you of? What words did I put in your mouth? I said, "You seem to think that light is "sucked" into a black hole, rather than following a geodesic into it." I still think that, and nothing you've said makes me think otherwise. I don't mean that as an insult, or an accusation.

Meanwhile you've grown increasingly hostile, so I am going to leave this to others to either correct my errors, yours, or both. You either want a fight, or seem unable to have a civilized discussion ONLINE. You don't have to worry about "terminating the discussion"; you fired it up after a 4+ day break, and I frankly wouldn't have even known you'd commented other than the auto-notify feature. My investment here is 0 + mild interest - your hostility = "Me gone until/unless a mentor/advisor decides to correct me, you, or both." I simply don't care about this enough to deal with someone who takes an observation as an accusation.

If I'm wrong, I can learn on my own or with others, and if you're wrong I no longer care about your possible misconceptions in the slightest. I'm not trying to be insulting, but enough of this nonsense. You've made a discsussion into a contest with only one participant. Bravo.

@Kev: Thanks, and you're right about not making clear who's making the measurement, but I'm arguing that the effect is not "illusory".

 

[cos]

To local observers, the speed of light is constant (always equal to c).

To local observers the speed of light is only determined to appear to be constant due to the fact that their measuring rods and clocks are distorted by that gravitational field.

To a distant observer the coordinate speed of light slows down as it travels deeper into the gravitational well.

It is noted that neither of you responded to my analogy so I will repeat it in the hope that you will answer.

You are looking at a light source that is some distance from you and contained within your reference frame - it is stationary. External to and concentric with the light source is a semi-transparent sphere.

The source simultaneously projects beams of light to your right hand side (A) and to your left (B). Those beams will, according to light speed constancy, reach the sphere at the same instant from your point of view (assuming no influence by any gravitational field) as well as from the point of view of an observer standing alongside the source.

The source starts accelerating to your right but the sphere remains stationary. Beam B will reach the sphere before A ergo beam B is traveling away from its sourcefaster than A.

Now imagine that a source and its associated semi-transparent sphere are (hypothetically) located at a fixed distance from a black star . According to the principle of equivalence this is analogous to the source accelerating in the above depiction.

From your point of view, the beam (B) that is moving toward the star travels a greater distance in one of your seconds than a beam (A) that is moving in the opposite direction! Beam B will arrive at the semi-transparent sphere before A reaches the sphere.

The rates of travel of those beams away from their source, from your point of view, are not identical!

Those beams, relative to you are moving at different speeds.

You now move to the source's location ergo becoming a local observer. You have witnessed one beam moving faster than another beam however your, now, gravitationally distorted measuring rod and clocks indicate otherwise.

Some people may be able to realize that because their measuring devices are distorted due to gravity they are not providing 'true' readings.

An observer is located on a mountain top. He finds that a clock at that location is ticking over at precisely the same rate as his own clock.

He moves to sea level where he finds that a clock at that location is also ticking over at the same rate as his own clock but looking back at the mountain-top clock he notes that it is ticking over at a faster rate than his own clock.

He could either conclude that for some reason the rate of operation of the mountain top clock has increased or (via a Confucian proper application of knowledge) that it is his clock, now located in a stronger gravitational tidal area, that is ticking over at a slower rate than it was when he was atop the mountain.

Some people may be able to realize that his clock is affected (changed, 'distorted') by his location in a gravitational field whilst others insist that the mountain-top clock's rate of operation physically changes.

When you change your location from a far distance and become a local observer you, too, may be able to realize that your rods and clocks have been physically affected (changed, 'distorted') due their present location in an intense gravitational field.

It would be very much appreciated if you did not edit this analogy and if you responded to same!

It is necessary to state the location of the observer when making statements about the speed of light in a gravitational field and both you and FD are guilty of not doing this.

I have endeavored to make every attempt to state the location of the observer however when I write that a beam of light will accelerate toward a black star I am talking about from every observer's point of view on the basis that a local observer should be able to realize that his rods and clocks are distorted by that intense gravitational field.

Now if you agree that clocks near a gravitational source really do run slower relative to distant clocks, then if a local observer measures the local speed of light with a slow clock to be the same as the local speed of light as measured by a distant observer using a faster clock, then the speed of light must be different at the different locations in a relative coordinate sense. The only way this can be avoided is by having vertical rulers that get longer by a factor of gamma = 1/(1-2GM/r) to cancel out the effect of slower clocks, but the Schwarzschild metric says exactly the opposite and rulers get shorter by a factor of gamma deeper in the well. In fact the vertical coordinate speed of light measured by the distant observer gets slower by a factor of gamma squared, the deeper you go into the well.

You write "..the Schwarzschild metric says exactly the opposite and rulers get shorter by a factor of gamma deeper in the well."

Imagine that a ship is at a fixed distance from a black star. The astronaut, using equipment on the ship, manufactures steel rods of identical lengths one of which (A), fixed to the ship, extends toward the black star whilst the other one (B) extends in the opposite direction. As the result of spaghettification, rod A will be physically longer than B which is compressed in length irrespective of the fact that the stamp on the ends of both rods indicate identical manufacture lengths.

Black star implies a body with a solid surface, while the "surface" of a black hole is an event horizon rather a solid surface and the event horizon encloses a region that is a vacuum except for a point with infinite density at the centre of the region. The conventional view in GR is that a body with greater than the Schwarzschild density does not have a solid surface and so it is not described as a black star.

Your 'point with infinite density at the centre of the region' is presumably what is also known as a singularity - a totally hypothetical concept that has never been located. I cannot accept that it has 'infinite density' i.e. that it has a density equivalent to that of the entire universe.

If a massive star collapses to the size of a basketball it obviously has a solid surface; if it collapses to the size of a pea it obviously has a solid surface; if it collapses to the size of an atom it obviously has a solid surface.

When somebody actually trips over a singularity or a point with infinite density and returns to inform us that it has no solid surface I might be persuaded to accept this pronouncement.

You are right that light does not slow down as departs a black hole. It speeds up as it rises, from the point of view of a distant observer and is constant from the point of view of the local observers that the light passes on the way up.

Light travels away from such an object at precisely the same speed as its escape velocity. It has no access to any form of energy that would generate an increase in its speed and has no inherent energy that it can expend in order to do so.

The only way that light can speed up as it moves away from a gravitational source is if the source is surrounded by, for example, an atmosphere.

There is nothing dubious about FD referring to the measurements made by a local observer. The only dubious practice is not making it clear what observer makes the measurement, when making statements about the speed of light.

FD did not make it clear, and made no attempt to do so, as to which observer he was referring. I agree with you that this is a dubious practice which is what I suggested he may have been guilty of doing!

 

[yuiop]

Rindler is talking about particle orbits in Schwarzschild space. This describes exactly the motion of particles at LHC, i.e. it answers the OP.

You seem to be saying that particles in the LHC are effectively orbiting the Earth. You also made it clear earlier that you do not think relativistic mass (or a term that looks like it) plays no part in calculating the gravitational force acting on a particle. There appears to be a fundamental difference in opinion between the memebers of this forum which can be encapsulted in the answer to this this simple question. "Does a spinning brick weigh more than a non spinning brick?" I think most people here would say yes and you seem to be saying that no, the spinning brick will weigh less (or the same?) as a non spinning brick. More extremely, you seem to be saying that if parts of the spinning brick had orbital velocity (even though its center of mass is stationary relative to the ground) that it will feel no gravitational force and hover.

The final concluding sentence of http://arxiv.org/PS_cache/gr-qc/pdf/9909/9909014v1.pdf" says: "We can thus tell our students with confidence that kinetic energy has weight, not just as a theoretical expectation, but as an experimental fact." I interpret Carlip's statement to mean that a horizontally moving particle has greater kinetic energy than a non horizontally moving particle and therefore a weighs more and requires a greater compensating force to maintian a constant altitude, which is the answer to the question posed in the OP.

@cos. I will look at your analogy when I have more time although it seems to be a big diversion from your original question in the OP and perhaps deserves its own thread. Briefly:

Your 'point with infinite density at the centre of the region' is presumably what is also known as a singularity - a totally hypothetical concept that has never been located. I cannot accept that it has 'infinite density' i.e. that it has a density equivalent to that of the entire universe.

The average density of the universe is probably quite low (something like one atom per cubic meter on average). I assume you really meant a density equivalent to the entire universe sqeezed into a single point with zero volume?

For what it worth, I think your original question about mass dilation and the force of gravity is a very good question, that has exposed some fundamental differences of opinions here and it might be better to focus on that and clear that issue up.

 

[starthaus]

You seem to be saying that particles in the LHC are effectively orbiting the Earth. You also made it clear earlier that you do not think relativistic mass (or a term that looks like it) plays no part in calculating the gravitational force acting on a particle.

I do not "think", I have proven it by showing the exact equations (see Rindler).
Moreover, I have also pointed out that the curving of the trajectories, be it at LHC or in our CRTs is not a function of "relativistic mass" (see the OP title) but a result of the magnetic field of the Earth via the Lorentz force (see the reference to de-gaussing).

There appears to be a fundamental difference in opinion between the memebers of this forum

Physics is not decided by voting. Besides, the only members of this forum that are still going against the cold facts of Rindler's math (which can also be found in MTW, BTW) is you and cos.

which can be encapsulted in the answer to this this simple question. "Does a spinning brick weigh more than a non spinning brick?" I think most people here would say yes and you seem to be saying that no,

No, we all agree that "energy gravitates". That is not the point.

 

[starthaus]

I interpret Carlip's statement to mean that a horizontally moving particle has greater kinetic energy than a non horizontally moving particle and therefore a weighs more and requires a greater compensating force to maintian a constant altitude, which is the answer to the question posed in the OP.

That is not a bad interpretation . Unfortunately it is not supported by the equations of motion I posted some time ago. One simple reason is that , simplistically speaking, a body moving at a higher tangential speed is subjected to a higher centrifugal force. The Euler-Lagrange formalism I presented takes this into consideration, yours doesn't.

 

[George Jones]

I interpret Carlip's statement to mean that a horizontally moving particle has greater kinetic energy than a non horizontally moving particle and therefore a weighs more and requires a greater compensating force to maintian a constant altitude, which is the answer to the question posed in the OP.

I've done a down-and-dirty back-of-the-envelope calculation that *seems* to indicate that this is true.

That is not a bad interpretation . Unfortunately it is not supported by the equations of motion I posted some time ago.

Actually, I think that the equation that you posted might support this view. I want to do a more detailed calculation for a massive particle moving at a substantial fraction of the speed of light in the weak gravitational field of the Earth. With certainty, I won't have time to work on this calculation tonight. I'm not sure, but I might give it a go tomorrow.

 

[starthaus]

Actually, I think that the equation that you posted might support this view. I want to do a more detailed calculation for a massive particle moving at a substantial fraction of the speed of light in the weak gravitational field of the Earth. With certainty, I won't have time to work on this calculation tonight. I'm not sure, but I might give it a go tomorrow.

I sincerely doubt it but I would be interested in seeing your calculations, the mass of the moving object does not affect its equation of motion.

 

[Frame Dragger]

I sincerely doubt it but I would be interested in seeing your calculations, the mass of the moving object does not affect its equation of motion.

Whoa, starthaus, that's just rude as hell! If you "know what you know" and don't care to discuss matters or even see the work of someone who may be as or more qualified than you... why come here at all?

 

[starthaus]

Whoa, starthaus, that's just rude as hell! If you "know what you know" and don't care to discuss matters or even see the work of someone who may be as or more qualified than you... why come here at all?

What are you talking about? I posted the equations and their derivation long ago (post 20).

 

[George Jones]

I sincerely doubt it but I would be interested in seeing your calculations, the mass of the moving object does not affect its equation of motion.

But speed does.

 

[starthaus]

But speed does.

We have had this discussion in the other thread, so why don't we wait for your derivation.

 

[cos]

Firstly your comment -

You don't have to worry about "terminating the discussion"; you fired it up after a 4+ day break...

It was unintentional; my son-in-law suffered a fatal accident and I tended to his affairs.

Secondly -

I'm not twisting anything, anymore than I am secretly editing your posts...

I made no suggestion that you are "secretly" editing my posts but challenged that you are deliberately editing same as indicated by your refusal to appropriately respond to my analogy of a distant source emitting beams in both directions.

Let me pose this to you: Take your light beams and have them at orbital distance from the BH/BS, but now make it the original star. Do you still believe that the velocity of light is determined by its distance from the star?

From the point of view of a far distant observer - yes! Viz -

Were you able to understand my depiction of your looking at a distant source that emits beams of light to your right hand side and your left hand side then the source accelerates? Are you of the opinion that the beam that is moving in the same direction as the source will not be moving away from the source at a slower rate than the other beam or are you of the opinion that the principle of equivalence does not apply to this concept?

I think you need to explain how it applies, and how that squares with GR.

I have already explained how it applies! I do not need to show how it squares with GR; it squares with the principle of equivalence!

In accordance with the principle of equivalence - the accelerating source is analogous to a source that is at a fixed distance from a massive gravitational source e.g a black star.

Do you agree with my suggestion regarding the compression and expansion of the light beams with respect to the accelerating source and that in accordance with the principle of equivalence the accelerating source is analogous to the situation of a source that is at a fixed distance from a black star?

The black star will, for a brief period of time, obviously have a similar mass-gravitational field strength as the star before it collapsed so if the source is at a fixed distance from that object the beam that is traveling toward same will have a greater velocity away from the source than the beam that is headed in the opposite direction from your far distant perspective!

Nigel Calder expressed this more succinctly in his book 'Einstein's Universe' wherein he wrote (62, BBC, 1979) -

"Light travels more readily and faster [my italics] towards the center of gravity than away from it." (N.B. from the point of view of a distant observer).

The rest of your post is irrelevant to the above material a response to which may clarify the situation but if you have decided on "Me gone.." at least I've responded to your applicable comments.

 

[yuiop]

It was unintentional; my son-in-law suffered a fatal accident and I tended to his affairs.

Hi Cos, I am very sorry to hear this. My deepest sympathy to you and your family.

Let me pose this to you: Take your light beams and have them at orbital distance from the BH/BS, but now make it the original star. Do you still believe that the velocity of light is determined by its distance from the star?

From the point of view of a far distant observer - yes!

I believe you and FD are cross purposes here again. FD is talking about distance from the center of the BH compared to distance from the surface of a star and the two quantities are obviously different and will yield different results. You are talking about distance from the center of the BH and from the center of a star and this is the more normal way of doing things and yields identical answers. Just to make it clear. If the Sun was to collapse to a black hole with a singularity, the time dilation effects at a given radius (from the center of the gravitational mass) outside the event horizon would remain unchanged.

To local observers the speed of light is only determined to appear to be constant due to the fact that their measuring rods and clocks are distorted by that gravitational field.

It might surprise you that I tend to agree with you here, but this is a philosophical point of view. In relativity, what is measured is considered real and different observers will have a different reality. What you or I consider to be "really happening" behind the scenes is philosphical and generally discouraged in this sub forum.

It is noted that neither of you responded to my analogy so I will repeat it in the hope that you will answer.

You are looking at a light source that is some distance from you and contained within your reference frame - it is stationary. External to and concentric with the light source is a semi-transparent sphere.

The source simultaneously projects beams of light to your right hand side (A) and to your left (B). Those beams will, according to light speed constancy, reach the sphere at the same instant from your point of view (assuming no influence by any gravitational field) as well as from the point of view of an observer standing alongside the source.

The source starts accelerating to your right but the sphere remains stationary. Beam B will reach the sphere before A ergo beam B is traveling away from its sourcefaster than A.

I think you have this the wrong way around. If the source accelerates away from the center in A direction, then the A beams arrives at the sphere before the B beams (according to an observer at rest with the sphere). In a crude Galilean sense, the A beam is traveling slower relative to the source than the B beam, but the universe is not Galilean. In relativity (the correct theory) you need to use relativistic velocity addition and the speed of the light beams relative to the source is always c according to any observer in flat space, which is what you are talking about in this instance.

Now imagine that a source and its associated semi-transparent sphere are (hypothetically) located at a fixed distance from a black star . According to the principle of equivalence this is analogous to the source accelerating in the above depiction.

This is a very poor interpretation/ application of the equivalence principle. In your analogy, an observer at point A on the stationary sphere sees the light from the source blue shifted. In a gravitational field a stationary observer high up sees light from a source lower down as red shifted. (The opposite). The observer at A sees the Doppler shift of the light source continuously changing over time while a stationary observer in a real gravitational field sees the Doppler shift as constant. The source eventually crashes into A, while to a stationary observer in a gravitational field the gravitational source remians at a constant distance from the stationary observer (by definition). In other words your analogy might be closer to the point of view of an observer falling towards the gravitational source, but I have not looked at that closely.

If you really want to examine the issue of the applicability of the equivalence principle, then I really believe that it deserves its own thread. Something to consider is that the equivalence principle is only usually valid locally. Over large distances, tidal effects have a significant effect and the EP does not hold.

 

[cos]

It was unintentional; my son-in-law suffered a fatal accident and I tended to his affairs.

Hi Cos, I am very sorry to hear this. My deepest sympathy to you and your family.

Thanks kev.

Let me pose this to you: Take your light beams and have them at orbital distance from the BH/BS, but now make it the original star. Do you still believe that the velocity of light is determined by its distance from the star?

From the point of view of a far distant observer - yes!

I believe you and FD are at cross purposes here again. FD is talking about distance from the center of the BH compared to distance from the surface of a star and the two quantities are obviously different and will yield different results.

Whilst the two quantities are obviously different and will yield different results this makes no difference to the fact that the beams moving toward the BH will travel faster away from the source than those moving in the opposite direction.

To local observers the speed of light is only determined to appear to be constant due to the fact that their measuring rods and clocks are distorted by that gravitational field.

It might surprise you that I tend to agree with you here, but this is a philosophical point of view. In relativity, what is measured is considered real and different observers will have a different reality. What you or I consider to be "really happening" behind the scenes is philosphical and generally discouraged in this sub forum.

There's nothing philosophical about it. If I am at a great distance from the event and determine that the beam traveling 'inward' is accelerating then move to the location of the source where I determine constancy for both beams I am fully entitled to insist that I only determine constancy due to the fact that, as experimentally determined, my measuring devices are distorted, changed, due to their, now, location in an extremely intense gravitational field.

If I am located on top of a mountain and compare my clock with one at that location I should (ideally) find that they are ticking over at the same rate as each other. If I then move to sea-level I would also find that a clock at that location is ticking over at the same rate as my clock.

If I look back at the mountain-top clock I could either be of the opinion that it is physically ticking over at a faster rate than it was when I was at that location (which, in my opinion, is a philosophical solipsist attitude) or (as determined by the Wallops Island experiment) that my clock, now located in a stronger gravitational tidal area, is ticking over at a slower rate than it was when I was atop the mountain in accordance with general theory.

I would be extremely disappointed to find that this sub forum only encourages/accepts discussions relating to a non-reality theory that refers to experiments being carried out in an otherwise empty universe that contains nothing more than essential equipment and associated observers i.e. no extant gravitational fields rather than one to which Einstein, in his introduction to general theory, applied the reality of extant gravitational fields stating that the SR law of the constancy of the speed of light required modification.

The source starts accelerating to your right but the sphere remains stationary. Beam B will reach the sphere before A ergo beam B is traveling away from its source faster than A.

I think you have this the wrong way around. If the source accelerates away from the center in A direction, then the A beams arrives at the sphere before the B beams (according to an observer at rest with the sphere).

The A beam would arrive at the sphere before the B beam only if the source is moving with constant velocity!

The source is accelerating! It is 'catching up' with the front edge of the A beam. Other than in section 4, SR's light speed constancy specifically applies to inertial reference frames not frames that are accelerating and whilst it is pointed out that acceleration can be 'written into' SR we end up with GR hence there seems to be little point in such an exercise.

Now imagine that a source and its associated semi-transparent sphere are (hypothetically) located at a fixed distance from a black star . According to the principle of equivalence this is analogous to the source accelerating in the above depiction.

This is a very poor interpretation/ application of the equivalence principle.

Would you please explain why there is any difference with respect to the EP between an object that is at a fixed distance from a gravitational source and one that is on the surface of, for example, a collapsed star - or a ship that is at a fixed distance from the Earth and one that has landed on the planet?

In your analogy, an observer at point A on the stationary sphere sees the light from the source blue shifted.

In my analogy there is no observer at point A on the stationary sphere to see the light from the source blue shifted!

My analogy specifically and only applies to a far distant observer who sees no doppler shift (other than an extremely minimal amount as a result of aberration).

In a gravitational field a stationary observer high up sees light from a source lower down as red shifted. (The opposite).

It would be appreciated if we could discuss my analogy in accordance with the conditions of same. The far distant observer is looking at beams of light that are moving away from their source at right angles to him ergo neither directly toward, nor directly away, from him.

My observer does not see light from a source that is 'lower down' than he is and is moving toward him. He 'sees' light from a source that is at a fixed distance from a center of gravity.

It is not the frequency of the beams that has any application to my depiction but the distance from the tips of the beams to their source.

 

[collinsmark]

Hello all,

Going back to the original subject regarding the possible increase in gravitational force of particles in an accelerator (such as the LHC)...

Can't this question be answered simply in terms of energy?

Maybe it would be simpler to just use the previous analogy of a hoop/disk spinning on a platform, compared to one that is not spinning (of just use the LHC example if you'd rather).

Suppose the hoop's rest mass is m. Suppose you supply enough external energy to the spinning the hoop that the hoop's kinetic energy becomes KE = (\gamma-1) mc^2, making the total energy of the hoop E = \gamma mc^2, then wouldn't the gravitational force increase by \gamma compared to the non-spinning hoop?

I don't have Rindler's book, but it almost seems like somebody is saying that Rindler's book indicates that energy has no contribution to gravity (although I can't verify it directly without the book, I assume Rindler is not saying that).

Perhaps I'm really missing something, but if the total energy of the system is increased to \gamma mc^2 (compared to the rest energy mc^2) then the force required to maintain altitude would increase by a factor of \gamma, even if \gamma is 4 or 400 000.

It's been my understanding that gravity works basically the same way on all forms of energy, and [rest] mass is just one type of energy. Soo...(unless I'm really missing something) the answer seems kinda obvious.