This post is intended for all firm believers of relativity:

John Doe is sitting in his rocketship on the surface of the Sun. John is getting hot, so he decides to head for Earth to get some cold lemonade. He turns his engines on and starts heading for Earth at a very high speed. Halfway to Earth he reaches the speed of .90c (relative to the Sun and the Earth).

At that moment, in his frame of reference, the Earth and the Sun are moving at very high speeds. According to relativity, the mass of the Earth and the Sun increase in John's frame of reference. Also, according to relativity, the distance between the Earth and the Sun decreases (length contraction) in his frame of reference as well.

The Earth's inertia (centrifugal force as it orbits the sun) increases and compensates for the increased mass of the Earth therebye preserving the Earth's orbit around the Sun. However, the increase in the mass of the Sun results in a larger gravitational pull on the Earth. If that's not bad enough, the contracted distance between Sun and the Earth results in an even larger gravitational pull.

According to relativity, the increased mass of the Sun, and the contracted distance between the Sun and the Earth, should result in a stronger gravitational field between the Earth and the Sun in John's frame of reference. This increased gravitational field should force the Earth's orbit around the Sun to degrade.

Question: Will John, in his frame of reference, eventually see the Earth fly into the sun, or is relative mass and contracted distance as real as magic fairies?? :)

Tom

Hi Tom,

Once again a misconception... Increase of relativistic mass is increase in kinetic energy. Energy is a relative quantity, not related to gravitational pull (at least not in the sense you use it). Increase of relativistic mass is not equal to an increase in restmass.

Bye!

Crisp

Crisp,

Even if you are right, and gravitational mass is not related to relative mass, you still didn't account for the contracted distance between the Earth and the Sun.

Tom

Tom,

You are incorrectly mixing Newtonian ideas of gravity with relativity. If you want to solve the problem correctly, you'll have to do the whole thing in the context of general relativity. You can't use length contraction in one sentence then use Newton's gravity law in the next sentence and hope to get to anything real.

Hi Tom,

"Even if you are right, and gravitational mass is not related to relative mass..."

They are related. You could say that (in special relativity) a particle's energy E is given by:

E = m₀c² + T

Where m₀ is the restmass (or classical Newtonian gravitational mass if you like) and T is the kinetic energy. You can associate a (relativistic) mass m to all this by putting

E = mc²

Substituting this into the first equation and dividing by ²:

m = m₀ + T / c²

Oh, I should stress that the kinetic energy T is not given by mv²/2 or something; this is a classical Newtonian definition which has a correction in the relativistic case.

"... you still didn't account for the contracted distance between the Earth and the Sun. "

Length contraction is only along the direction of motion, but since a rotating frame of reference (such as the earth's) is non-inertial, I wouldn't have a clue how to work this out in special relativity. I suggest using general relativity as James suggested.

Bye!

Crisp

We ascertained yesterday that relativistic energy increases in mass do not affect gravity.

Your assertation that the orbit is affected is also way off base. As Crisp and James points out you are mixing 3 distinctly different concepts badly.

From the frame of the center of mass of the Earth and Sun nothing changes. What John Doe sees is a <u>relative</u> affect.

Originally posted by Prosoothus

Halfway to Earth he reaches the speed of .90c (relative to the Sun and the Earth).

0.9c relative to the Sun and Earth? Isn't it simply 0.9c, regardless of Sun and Earth? I mean, if 0.9c is relative to anything, isn't it relative only to c in whatever medium is in question?

No, Adam. Anybody watching something travelling at c sees it travelling at c regardless of their own state of motion. That is not true at any other speed. All motion at other speeds must specify a particular frame of reference to make any sense.

That's what I mean. C is necessarily one set speed in any given medium. So anyone travelling at 0.9 C in whatever medium will go 0.9 of that speed regardless of whether there is a Sun and Earth or not. So why did he mention 0.9c "relative to the Sun and the Earth"?

<i>So anyone travelling at 0.9 C in whatever medium will go 0.9 of that speed regardless of whether there is a Sun and Earth or not.</i>

No. They will only go at 0.9 c relative to something else - in this case the sun and earth.

If you're also travelling at 0.9 c in the same direction relative to the sun and earth, you will observe that person going at zero speed relative to you. You must specify the reference frame.

Take another example, closer to home. You drive along the road at 100 km/hr. Somebody passes you doing 110 km/hr. Both speeds are given relative to the ground. But relative to you, the car passing you is going at 10 km/hr (actually a little less, due to relativistic effects).

James,

You are incorrectly mixing Newtonian ideas of gravity with relativity. If you want to solve the problem correctly, you'll have to do the whole thing in the context of general relativity. You can't use length contraction in one sentence then use Newton's gravity law in the next sentence and hope to get to anything real.

Are you saying that the classical formula for gravity doesn't apply at high speeds?? The only way to keep the Earth's orbit stable in John's frame of reference would be if gravity decreases with increased relative speed. I don't see how this would be possible.

Tom

Crisp and Thed,

There seems to be some confusion on whether an increase in relative mass results in an increase of gravitational mass. Thed is stating that it does not, while Crisp appears to be saying that it does.

What we can all agree on is that an increase in relative mass results in an increase of inertial mass (kinetic energy). However, if the inertial mass of an object moving at high relative speeds is not compensated by an equal gravitational mass, this can bring up many problems, especially when dealing with orbits of planets.

Wasn't it Einstein who suggested that inertial mass is always equal to gravitational mass?? Also, if an object's gravitational mass does not increase at high speeds, how can it be suggested that the object's mass increases? Wouldn't a "real" increase in mass result in both an increase in inertial and gravitational mass?? Since relative mass does not pass this test, should it be called "mass" at all?

Tom

Crisp,

Length contraction is only along the direction of motion, but since a rotating frame of reference (such as the earth's) is non-inertial, I wouldn't have a clue how to work this out in special relativity. I suggest using general relativity as James suggested.

For the sake of simplicity, just exclude the orbital (and rotational) motion of the Earth from the problem. The length contraction alone, which results in the decreased distance between the Sun and the Earth, should result in a stronger gravitational force. This stronger gravitational force will influence the Earths orbit regardless of the rotational or orbital motion of the Earth.

The only way this wouldn't happen is if the classical formula for gravity is no longer valid at high speeds, and that, according to general relativity, gravity decreases with increased speed.

Tom

Thed,

Your assertation that the orbit is affected is also way off base. As Crisp and James points out you are mixing 3 distinctly different concepts badly.

You stated that the gravitational mass of the Sun and the Earth has not increased in John's frame of reference. However, you can't ignore the fact that the inertial mass (kinetic energy) of the Sun and the Earth HAS increased in John's frame of reference. Since orbits are influenced by both inertial mass and gravitational mass, the change in one type of mass without an equal change in the other would affect the orbit.

Tom

Prosoothus

The length contraction alone, which results in the decreased distance between the Sun and the Earth, should result in a stronger gravitational force. This stronger gravitational force will influence the Earths orbit regardless of the rotational or orbital motion of the Earth.

This makes no sense at all. How would an observers contracted view of the distance between himself and an object have anything to do with the objects gravitational field ? You're getting way off base with this one.

according to general relativity, gravity decreases with increased speed.

Cite please.

Tom,

Newton's law F=Gmm/r² is non-relativistic. It is replaced in GR by Einstein's equation, which relates the spacetime curvature tensor to the stress-energy tensor. The stress-energy tensor depends on energy density and on momentum flows, so the tensor is velocity-dependent. That solves your problems with length contraction and so on.

Q,

This makes no sense at all. How would an observers contracted view of the distance between himself and an object have anything to do with the objects gravitational field ? You're getting way off base with this one.

I see that we returned back to the original problem: Is length contraction a reality or is it an illusion?

If length contraction is a reality then all physical phenomena will be influenced by it (for example gravity and electrostatic interactions). This would mean that contracted distance between two large masses would result in a stronger gravitational force in the moving observer's frame of reference. This stronger force would result in events in a moving frame of reference that never occur in a stationairy frame of reference.

If you see a mirage, you wouldn't know if it is real or an illusion by only looking at it. You would have to use your other senses to attempt to prove that it's real. But what if you didn't have any other senses??? You would then observe how the mirage influences it's surroundings. If it does somehow influence it's surroundings (other than by light) then you can induce that it is real.

The same applies for length contraction. If you can see the contracted space, but the contracted space has no effect on long distance forces (such as the gravitational or the electromagnetic) then it is not real. Length contraction is then only an illusion, and it must be accepted as one.

James stated that I should of used the formula for gravity in general relativity instead of the classical one. He implied that I would then get the correct answer. However, I can easily replace the large masses in my example with charged objects. As far as I know, there is no general relativity formula for electrostatic interactions. :)

Tom

James,

Newton's law F=Gmm/r2 is non-relativistic. It is replaced in GR by Einstein's equation, which relates the spacetime curvature tensor to the stress-energy tensor. The stress-energy tensor depends on energy density and on momentum flows, so the tensor is velocity-dependent. That solves your problems with length contraction and so on.

What about other long distance interactions such as the electrostatic interaction? Did Einsten compensate for the contracted distance between two charged bodies??

Tom

<i>As far as I know, there is no general relativity formula for electrostatic interactions.</i>

Yes, there is. There is a tensor for electromagnetic fields which is used in the context of general relativity.

James,

Yes, there is. There is a tensor for electromagnetic fields which is used in the context of general relativity.

Well, isn't that convenient. :mad:

:p

Tom

Originally posted by Prosoothus
As far as I know, there is no general relativity formula for electrostatic interactions. :)
Tom, if you completely understand a theory before attempting to undermine it, you stand the chance of being called a great scientist. If you do it the other way around, you will be labelled a crackpot.

Here are some good notes on GR: http://pancake.uchicago.edu/~carroll/notes/

The electromagnetic (0, 2) tensor F_{<font face="symbol">mn</font>} is introduced on page 16 of Chapter 1....

- Warren

<i>Well, isn't that convenient.</i>

Yup. :D

Hi Tom,

"Well, isn't that convenient."

Quite nice when it all pieces fit into the puzzle ;) ... Many people have thought on the problems you mentioned before, and they are all incorporated in a consistent way in SR/GR now...

Bye!

Crisp

Crisp,

Let me finish your sentence:

Many people have thought on the problems you mentioned before, and they are all incorporated in a consistent way in SR/GR, now whether those incorporations are valid, that's a whole another story. :)

Tom

Originally posted by Prosoothus
now whether those incorporations are valid, that's a whole another story.
Yes, Tom, you're more intelligent and more capable than all of the thousands of people before you who spent their entire lives mastering physics, and criticising its conclusions. You're smarter than all of the experimentalists who have verified all of the minutia of relativity to incredible precision. You, without so much as a textbook or an understanding of what a tensor is, are certainly able to set us all straight -- just because you're so damn smart.

Get a clue, dude.

- Warren

Will this be the last discussion on relativity on this board, thats the question :D

c'est moi,

Will this be the last discussion on relativity on this board, thats the question

Of course not. If it weren't for illogical theories like relativity, we would have nothing to discuss on sciforums. :)

Welcome back. Where were you hiding? Do you think that you're too good for us??? :)

Tom