# The Naked Scientists Forum

### Author Topic: Does Gravity Increase With Mass Dilation?  (Read 12206 times)

#### litespeed

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##### Does Gravity Increase With Mass Dilation?
« on: 15/11/2009 15:51:29 »
According to the ever faithfull E=mc2, a massive body increases mass when accelerated. I just wonder if it gravity increases as well?
« Last Edit: 25/11/2009 10:02:01 by chris »

#### Vern

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##### Re: Does Gravity Increase With Mass Dilation?
« Reply #1 on: 15/11/2009 17:25:52 »
I suspect it does but I haven't tried to work out the details.

#### LeeE

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##### Re: Does Gravity Increase With Mass Dilation?
« Reply #2 on: 16/11/2009 12:36:56 »
If you also factor in the apparent foreshortening, which reduces the effective volume and therefore increases its density, then it starts to look as though something that's accelerated to close to 'c' should seem, to a distant observer, to become a black hole.

#### litespeed

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##### Re: Does Gravity Increase With Mass Dilation?
« Reply #3 on: 16/11/2009 14:52:37 »
Lee,

Even if it doesn't look like black hole, the red shift would be so dramatic that it might become undetectible. The thing I find intriguing is the possibility of achieving relativistic velocities with normal propulsion methods [ionization etc]. The reason is that at 86 percent the speed of light, the apparent mass gain is either 50 percent or maybe one hundred percent.

So a 1G thruster will be reduced, at most, to .5G thruster. For science fiction purposes, that means future earthings COULD get out of town. Especially since their time clock will be slowed by half at 86 percent. I don't know how steep the mass increase curve is, but a 1G thruster might be able to cut that by another 50 percent in a reasonable period of acceleration time.

On a robotic scale, it seems to me we could send a probe out at relativistic speeds. And begin to get inter stellar reports back within a few years. Of course, as has been pointed out before, space is not empty, and at some speed or another a high speed vehicle could erode.

#### Mr. Scientist

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##### Re: Does Gravity Increase With Mass Dilation?
« Reply #4 on: 17/11/2009 19:55:37 »
It does. I also believe that charge increases as well, as it being the sole intrinsic mechanism of inertial energy, so charge generates mass - my theory anyhow.

#### Pmb

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##### Re: Does Gravity Increase With Mass Dilation?
« Reply #5 on: 18/11/2009 20:20:52 »
According to the ever faithfull E=mc2, a massive body increases mass when accelerated. I just wonder if it gravity increases as well?
Yes. It does. The abstract to the article Measuring the active gravitational mass of a moving object, D.W. Olson and R.C. Guarino, Am. J. Phys. 53(7), July 1985
Quote
If a heavy object with rest mass M moves past you with a velocity comparable to the speed of light, you will be attracted gravitationally towards its path as though it had an increased mass. If the relativistic in active gravitational mass is measured by the transverse (and longitudinal) velocities which such a moving mass induces in test particles initially at rest near its path, then we find, with this definition, that Mrel = g(1 + b)M. Therefore, in the ultrarelativistic limit, the active gravitational mass of a moving body, measured in this way, is not gM  but is 2gM .
where g = gamma, b = beta = v/c

Think of it like this - Since the inertial mass of a body increases with speed inertial mass is proportional to (active) gravitational mass, and the source of gravity is (active) gravitational mass then the strength of the gravitational field increaseses as well.

On a similar note - since light has inertial mass it too generates a gravitational field. E.g. the inertial mass, m, of a photon is defined by m = p/c where p = magnitude of momentum and c = speed of light. This comes from the defining relationship for inertial mass, i.e. p = mv. Therefore whatever has momentum has inertial mass.

Please note:  By "inertial mass" I am not referring to proper mass, aka rest mass. These are different quantities. Photons have zero proper mass and non-zero inertial mass. This is why a beam of light, where all the photons are moving in the same direction, generates a gravitational field.

It's bit more complicated that that of course. The mathematical object which completely defines mass is the stress-energy-momentum tensor, T. This is the source of gravity in the same way that the 4-current is the source of the electromagnetic field.

#### Pmb

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##### Re: Does Gravity Increase With Mass Dilation?
« Reply #6 on: 18/11/2009 20:23:32 »
I also believe that charge increases as well, as it being the sole intrinsic mechanism of inertial energy, so charge generates mass - my theory anyhow.
Charge is an scalar quantity (i.e. an invariant) and therefore does not depend on speed. If charge did increase with speed then a body's net charge would depend on temperaure. Since it doesn't then charge does not depend on speed.

#### Mr. Scientist

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##### Re: Does Gravity Increase With Mass Dilation?
« Reply #7 on: 19/11/2009 08:10:38 »
I also believe that charge increases as well, as it being the sole intrinsic mechanism of inertial energy, so charge generates mass - my theory anyhow.
Charge is an scalar quantity (i.e. an invariant) and therefore does not depend on speed. If charge did increase with speed then a body's net charge would depend on temperaure. Since it doesn't then charge does not depend on speed.

But then a paradox arises. It is true to say that charge does not depend on speed, but it'sm partially-true if you state that the presence of matter insists the presence of a charge. So really charge does depend the masses speed, since the larger the mass, the larger the gravitational charge, so there are certainly invariant relationships which i feel have not been investigated properly.

#### LeeE

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##### Re: Does Gravity Increase With Mass Dilation?
« Reply #8 on: 19/11/2009 14:58:12 »
Lee,

Even if it doesn't look like black hole, the red shift would be so dramatic that it might become undetectible. The thing I find intriguing is the possibility of achieving relativistic velocities with normal propulsion methods [ionization etc]. The reason is that at 86 percent the speed of light, the apparent mass gain is either 50 percent or maybe one hundred percent.

So a 1G thruster will be reduced, at most, to .5G thruster. For science fiction purposes, that means future earthings COULD get out of town. Especially since their time clock will be slowed by half at 86 percent. I don't know how steep the mass increase curve is, but a 1G thruster might be able to cut that by another 50 percent in a reasonable period of acceleration time.

On a robotic scale, it seems to me we could send a probe out at relativistic speeds. And begin to get inter stellar reports back within a few years. Of course, as has been pointed out before, space is not empty, and at some speed or another a high speed vehicle could erode.

Umm... redshift will only occur if it's traveling away from us; if it's heading towards us it'll be pretty bright (assuming that it's radiating)

The problem with reaction engines is the amount of fuel required, and which needs to be carried.  You can either burn the fuel quickly and get high thrust for a short period of time, or burn it slowly, at relatively high exhaust speeds, and get low thrust (much below even 0.5G) for a long period of time.  Even with ion-drive motors though, the thrust you get is way below 0.5G and they'll still run out of fuel before they approach relativistic speeds.

Light-sails don't really need any fuel, but they lose thrust with distance from their launching star, and possibly the only real solution is a Bussard Ramjet type engine, which scavenges its fuel from the interstellar medium using a very large diameter i.e. between kilometres and thousand-kilometer+ sized electro-magnetic scoops.  Incidentally, the scoops also help deal with the erosion issue.

#### litespeed

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##### Re: Does Gravity Increase With Mass Dilation?
« Reply #9 on: 19/11/2009 17:58:21 »
LeeE - You wrote: "The problem with reaction engines is the amount of fuel required, and which needs to be carried."

I just now remembered hearing that each individual cosmic ray carries the same energy as a tennis ball at one hundred miles per hour. Accordingly, the biggest variable for reaction fuel is not the amount of fuel itself, but the EXIT velocity of matter.

Assume a nuclear powered linear accelerator in your 'starship'.  All of a sudden you have reduced the issue to an ENGINEERING problem. Specifically, if you accelatate a particle to near the speed of light you actually create mass as you accelerate it out the back of your ship. A powerful enough linear accelerator will end up pushing a huge amount of mass [relative to what was injected into the accelorator] out the back.
« Last Edit: 19/11/2009 18:11:27 by litespeed »

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##### Re: Does Gravity Increase With Mass Dilation?
« Reply #10 on: 19/11/2009 19:43:59 »
Quote
A powerful enough linear accelerator will end up pushing a huge amount of mass [relative to what was injected into the accelorator] out the back.

You'd be creating mass by losing mass. The energy comes from the mass of the nuclear material.

#### litespeed

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##### Re: Does Gravity Increase With Mass Dilation?
« Reply #11 on: 19/11/2009 20:08:02 »
Madidus_Scientia - You wrote: "You'd be creating mass by losing mass. The energy comes from the mass of the nuclear material."

Very good, grasshopper! Energy can neither be created nor destroyed, it only changes form. Give me a good enough linear accelerator, a good enough nuclear reactor, and I convert mass in the reactor, to electromagnetic forces in the accelerator, to acceleration and increased mass out the back side of my 'starship'.

I doubt I will achieve the velocity/mass of a Cosmic Ray, and shoot it out my back side. But that IS the Gold Standard.

#### Mr. Scientist

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##### Re: Does Gravity Increase With Mass Dilation?
« Reply #12 on: 20/11/2009 02:03:37 »
Madidus_Scientia - You wrote: "You'd be creating mass by losing mass. The energy comes from the mass of the nuclear material."

Very good, grasshopper! Energy can neither be created nor destroyed, it only changes form. Give me a good enough linear accelerator, a good enough nuclear reactor, and I convert mass in the reactor, to electromagnetic forces in the accelerator, to acceleration and increased mass out the back side of my 'starship'.

I doubt I will achieve the velocity/mass of a Cosmic Ray, and shoot it out my back side. But that IS the Gold Standard.

No. You are both incorrect with that assumption. The first law of thermodynamics breaks down when quantum mechanics introduces the zero-point energy field.

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##### Re: Does Gravity Increase With Mass Dilation?
« Reply #13 on: 20/11/2009 14:15:33 »
How so?

#### Mr. Scientist

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##### Re: Does Gravity Increase With Mass Dilation?
« Reply #14 on: 20/11/2009 18:57:46 »
Because the ZPF allows for virtual particles to appear from the vacuum - this happens all the time, so it seems energy can be created.

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##### Re: Does Gravity Increase With Mass Dilation?
« Reply #15 on: 20/11/2009 20:06:37 »
And what does this have to do with nuclear powered particle accelerators?

Anyway, my understanding is that they appear in particle/anti-particle pairs, and the energy of the system remains constant, in line with the conservation of energy.

#### litespeed

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##### Re: Does Gravity Increase With Mass Dilation?
« Reply #16 on: 20/11/2009 20:22:00 »
Mr. S

I stand corrected; however, give me a good enough nuclear reactor, a good enough linear accelerator, and I will STILL spit relativistically dialated matter out my backside...and go FAST!

#### LeeE

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##### Re: Does Gravity Increase With Mass Dilation?
« Reply #17 on: 20/11/2009 22:37:02 »
Equivalent energy needs to be put into accelerating the relativistically enhanced mass as you get out from from using it: TANSTAAFL

#### Mr. Scientist

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##### Re: Does Gravity Increase With Mass Dilation?
« Reply #18 on: 21/11/2009 14:00:45 »
And what does this have to do with nuclear powered particle accelerators?

Anyway, my understanding is that they appear in particle/anti-particle pairs, and the energy of the system remains constant, in line with the conservation of energy.

Virtual particles do not always have the laws. The reason to that is very lengthly, but in a nutshell E=Mc^2 where The equation relating energy, mass and momentum in special relativity is:

E^2 = p^2c^2 + m^2c^4,

In the special case of a particle at rest (i.e. p = 0), the above equation reduces to E2 = m2c4. Because virtual particles do not posses a real matter then the mass and momentum relation fails, and is reduced specifically. In a deeper note, spontaneous symmetry breaking is also a form of violation where the solution E=\pm Mc^2 is not always true.

#### Mr. Scientist

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##### Re: Does Gravity Increase With Mass Dilation?
« Reply #19 on: 21/11/2009 14:03:22 »
And what does this have to do with nuclear powered particle accelerators?[€/b]

Anyway, my understanding is that they appear in particle/anti-particle pairs, and the energy of the system remains constant, in line with the conservation of energy.

Why not.. acceletators are designed to be exactly like the condition of a vaccuum. My statements so far have been very applicable, i believe anyway.

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##### Re: Does Gravity Increase With Mass Dilation?
« Reply #20 on: 21/11/2009 14:18:04 »
How does the energy in a vacuum have to do with the fact that as you produce energy from a nuclear reactor you lose mass? You told me I was incorrect

#### Mr. Scientist

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##### Re: Does Gravity Increase With Mass Dilation?
« Reply #21 on: 21/11/2009 14:30:44 »
you where. You stated with a related compliance with litespeed that:

''Madidus_Scientia - You wrote: "You'd be creating mass by losing mass. The energy comes from the mass of the nuclear material."

Very good, grasshopper! Energy can neither be created nor destroyed, it only changes form.''

You had obviously agreed on this no? Because if you are still doing to deny your mistake, i will cut myself from this conversation all-together.

#### litespeed

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##### Re: Does Gravity Increase With Mass Dilation?
« Reply #22 on: 22/11/2009 18:43:00 »
MS

I make no claim to understand the laws and exceptions to conservation of energy.  I simply point out I can create energy from mass in a reactor, consolidate some of that energy into electricity for my electro/magnetic linear accelerator.  The accelerator will then convert some of the electo/magnetic energy into 1) kinetic energy out the back of my starship as it expells protons; and 2) add some mass to the particles accelerated.

Even a small nuclear reactor could provide enough energy to propell my starship. The trick is to use as little mass as possible at the highest velocity possible out the back of the linear accelerator. We are talking very small amounts of accelerated mass needed for very long trips. As pointed out elsewhere, a single cosmic ray (mostly protons) traveling close to the speed of light arrive at earth with the same energy as a tennis ball at 100 mph.

IMH, a good enough reactor and a good enough accelerator could be operated for years by the number of protons in a single pack of cigarettes. Its not a matter of taking enough fuel with me; I have already chosen the size of my reactor. I just need to transfer the energy from the fuel in my reactor mass to kinetic energy out of my linear accelerator. The protons inserted into the accelerator are not fuel.

A simple analog: the protons work just like bullets fired from a gun. You get rercoil. A very small bullet can give one HELL of a recoil if it is pushed out the barrel fast enough.
« Last Edit: 22/11/2009 18:52:50 by litespeed »

#### hcm1955

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##### Does Gravity Increase With Mass Dilation?
« Reply #23 on: 06/05/2010 19:41:04 »
Maybe this question has already been answered but: Assuming two particles (X1 and X2) moving at relativistic velocities relative to each other.

X1 --->
|
d
|
<---X2

Is there some distance d and some velocity less than c where X1 and X2 will orbit each other?

The closer the bodies approach speed of light then the larger the force due to gravity (or the more space-time bends) hence the two bodies will move closer to each other.

Cheers,
Bert

#### Atomic-S

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##### Does Gravity Increase With Mass Dilation?
« Reply #24 on: 10/05/2010 05:43:09 »
That is a remarkable concept: that as the speed of 2 bodies that normally would be thrown apart increases, eventually a point is reached where the mass increases overcome the centrifugal tendency and the bodies start drawing together again. (Nasa had better watch out: launchng a spacecraft to fast might cause it to be attracted back to the Earth and crash). Well, this remarkable hypothesis might possibly be true under some extreme conditions, although I still have a bit of a problem believing that the rate of mass increase could ever overtake the tendency toward centrifugal separation. Maybe there is an expert opinion?

#### The Naked Scientists Forum

##### Does Gravity Increase With Mass Dilation?
« Reply #24 on: 10/05/2010 05:43:09 »