A Random Splattering....

[Slinkey]

.....of the ideas and thoughts in my head!

 

 

This is not a theory but merely me thinking out loud and seeing what thoughts it provokes in other people. The title may not turn out to be relevant but.... well, let's see.

 

The thread "Gravity is Time" got me to thinking about something else I once said to someone - acceleration = gravity. In this case I meant it in the way Einstein meant ie. if you were in a sealed windowless box (that had extraordinarily good vibration dampening) would you be able to tell if the box was simply sitting on the ground and you feel the 1g pull of the Earth or if you were in a rocket accelerating at 1g in a flat spacetime?

 

All things being equal would a clock inside this box clock tick at the same rate in both cases relative to an outside observer? I would assume it would, but it is just that, an assumption as I have not checked the literature.

 

I posed a question in the "Gravity is Time" thread about accelerating a 100kg 1m^3 box to such a speed that it becomes a black hole due to its increasing relativistic mass and decreasing relativistic volume and thus its increasing relativistic(?) gravitational field. Intuition tells me it should be equivalent to light speed and would be so for any object with any given mass. If we were to draw a graph of this what would it look like it we put the relativistic mass on one axis and relativistic gravitational field strength on the other axis?

 

A related question follows:

If we have a 1m^3 sphere with a mass of 100kg, how much mass would we have to pack inside this sphere (ignoring real world technical difficulties) in order to make a black hole? If we were to draw a graph showing the gravitational field strength on one axis and the mass on the other axis what would it look like?

 

Final question:

Would the two resultant graphs be identical?

 

My problem is that I am an ideas man. Years of reading popular science without doing much of the maths is a real downfall for me but I have a real good visio-spatial mind (I score in the 200 region on visio-spatial IQ tests) and thus get pictures in my mind that I cannot describe mathemtically.

 

What I am trying to ascertain is how close is the similarity between acceleration and gravity. The deeper question I am seeking to find an answer to is whether the time dilation we see when we accelerate particles in a supercollider can be explained by the increase in the particles relativistic mass?

 

Clearly, gravity and acceleration have some deep connection because wherever you find gravitational fields you find acceleration. Does this work the other way?

 

I have read recently about the Higgs field and how it assumed to be the reason things have mass in the universe (ref: The Fabric of the Cosmos by Brian Greene). According to Dr. Greene we are awash in a sea of higgs particles. Could higgs particles be the deeper connection I am looking for?

 

If higgs particles are the reason for mass then when we accelerate an object are we increasing its "higgs field" and where we find a massive object we also find a higgs field and the more massive the object the greater its higgs field?

 

Maybe I'm getting muddled here but it is better I express these ideas and thoughts than have them deluding me without correction.

 

Any ideas people? Am I just rambling:confused: or can you get a feel for what I am trying to decribe and point at:eyebrow:?

[ecoli]

The thread "Gravity is Time" got me to thinking about something else I once said to someone - acceleration = gravity.

 

not quite. F = mg for objects close to the surface of the earth. Force due to gravity is equal to mass time acceleration. The mass is all important.

[Slinkey]

not quite. F = mg for objects close to the surface of the earth. Force due to gravity is equal to mass time acceleration. The mass is all important.

 

I know. Clearly you didn't read what I wrote.

[Blue Fire]

Just a note about being able to tell the difference between gravity and acceleration:

assuming (from the OP)

if you were in a sealed windowless box (that had extraordinarily good vibration dampening) would you be able to tell if the box was simply sitting on the ground and you feel the 1g pull of the Earth or if you were in a rocket accelerating at 1g in a flat spacetime?

Yes! That is, if you had extremely sensitive/accurate measuring tools in the box with you. If you drop two balls, one from each of your outstretched arms, then you would find that each ball would drop toward the center of the Earth and thus trace out intersecting paths, if you were sitting on Earth. If you were simply undergoing acceleration (as in a rocket), the balls would drop exactly parallel to each other. Granted that, on Earth, the non-parallel drop of the balls would be very difficult to measure, but still detectable in theory.

[timo]

The thread "Gravity is Time" got me to thinking about something else I once said to someone - acceleration = gravity. In this case I meant it in the way Einstein meant ie. if you were in a sealed windowless box (that had extraordinarily good vibration dampening) would you be able to tell if the box was simply sitting on the ground and you feel the 1g pull of the Earth or if you were in a rocket accelerating at 1g in a flat spacetime?

Apart from nitpicker loopholes ("measure the inhomogenity"), I think the answer is no. Disclaimer: I did not read the post above prior to writing this, I just knew someone would come up with that.

 

All things being equal would a clock inside this box clock tick at the same rate in both cases relative to an outside observer? I would assume it would, but it is just that, an assumption as I have not checked the literature.

You'd have to define what "clocks ticking at the same rate" means. Due to different setups, you have kind-of different comparison scenarios for the canonic understanding of "clocks going slower". All halfways-sensible scenarios for checking whether the two clocks go at the same rate (via a 3rd observer) I can currently think of, I get to the answer: Most likely not.

 

I posed a question in the "Gravity is Time" thread about accelerating a 100kg 1m^3 box to such a speed that it becomes a black hole due to its increasing relativistic mass and decreasing relativistic volume and thus its increasing relativistic(?) gravitational field.

And no one told you that the conditions for a black hole are usually given in what comes closest to the frame of rest of the respective object? Suppose everyone was too busy with 61-dimensional quantum wormholes at the Planck scale (where space is quantized).

In other words: Contrary to its name and popular belief, Relativity primarily deals with things that are not relative to a frame of reference. Following that spirit, the statement of whether something is a black hole or not should also be independent of the frame, meaning an object that is no black hole at rest also is no black hole in any other frame. I'm not exactly a BH-expert, though.

 

Intuition tells me it should be equivalent to light speed and would be so for any object with any given mass. If we were to draw a graph of this what would it look like it we put the relativistic mass on one axis and relativistic gravitational field strength on the other axis?

I'm not sure what you'd plot. Even in the non-relativistic case, the acceleration due to gravity is

a) a vector, not a scalar.

b) dependent on the frame of reference.

 

A related question follows:

If we have a 1m^3 sphere with a mass of 100kg, how much mass would we have to pack inside this sphere (ignoring real world technical difficulties) in order to make a black hole?

Solve r=2Gm/c² with c being the speed of light, G being the gravitational constant and r being the radius of the sphere for the total mass (including the 100 initial kgs) m.

 

The deeper question I am seeking to find an answer to is whether the time dilation we see when we accelerate particles in a supercollider can be explained by the increase in the particles relativistic mass?

Express the speed of an object via its relativistic mass (which is just the laymen term for energy, btw), plug that into the relation for time dilatation and start explaining . It's not that we didn't have an explanation (in the sense of "we define spacetime as... and eigentime as... and therefore time dilatation), though. I'm quite happy with the standard explanation .

 

Clearly, gravity and acceleration have some deep connection because wherever you find gravitational fields you find acceleration.

The coffee on my table is probably in the gravitational field of earth. Luckily, it's acceleration is not observable. You somehow have to define what a gravitational field is, though. As I previously said, you'd ideally find a description of the gravitational field that is not relative to an observer. Since at least the understanding of acceleration that you most likely have in mind (the F=ma one) does not hold to that definition, you cannot equate that acceleration and the gravitational field.

 

I have read recently about the Higgs field and how it assumed to be the reason things have mass in the universe (ref: The Fabric of the Cosmos by Brian Greene). According to Dr. Greene we are awash in a sea of higgs particles. Could higgs particles be the deeper connection I am looking for?

Unlikely. Except for gauge theories with massive interaction fields, everything usually works fine by just assuming that a 1 kg rock has a mass of 1 kg. You are more likely looking for a good book on General Relativity and/or Differential Geometry.

 

If higgs particles are the reason for mass then when we accelerate an object are we increasing its "higgs field" and where we find a massive object we also find a higgs field and the more massive the object the greater its higgs field?

The dictionary particle physics <-> your notation is

mass <-> rest mass

energy <-> relativistic mass.

The Higgs Field is responsible for the rest mass of an elementary particle. Non-elementary particles can (and do) get their masses through other mechanisms.

 

Any ideas people? Am I just rambling:confused: or can you get a feel for what I am trying to decribe and point at:eyebrow:?

You get your points across quite well, I think.

[Slinkey]

...Granted that, on Earth, the non-parallel drop of the balls would be very difficult to measure, but still detectable in theory.

 

Indeed. I forgot about this too. Excellent point.