Exploring Mass Dilation: The Effects of Acceleration on Relativistic Mass

[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.