Take a look at this paper about General Relativity

[D H]

OK, make the ball a test particle. Measure the velocity using the method in your example. How can you tell how much time passes, when clocks all along the length of the rocket run at different rates due to gravitational time dilation? A clock at the tip of the rocket runs faster than a clock at the tail of the rocket.

 

Now you are grasping at straws. What gravitational time dilation are you talking about? You had better show this, mathemetically.

 

Even if you do that (which you cannot), I call BS. Only one clock is needed.

[Farsight]

Zanket: Sorry about the English thing. My mistake.

 

DH: Stop digging. If you travel very very fast you can traverse a great distance in what to you seems like a short time.

 

http://en.wikipedia.org/wiki/Time_dilation

 

Let's say you manage to accelerate to a huge velocity very close to c, such that you can travel a light year in what seems like 24 hours. You aren't actually exceeding c of course, but your time dilation is such that when you look at your shipboard clock, you passed Earth on Sunday, and Alpha Proxima on Thursday.

 

Whilst traversing this distance, your rocket hit a ball that was sitting motionless in space. This ball penetrated the rocket and traversed it from top to bottom. Now. As measured by your shipboard clock, what fraction of a second did it take the ball to traverse your rocket? Or let's look at it another way. How long did it take your rocket to traverse the ball? Oh, and let's say your rocket is 300,000 kilometres long.

 

http://en.wikipedia.org/wiki/Light-year

 

A light year is 9,460,730,472,580,800 metres. You traverse this in 24 hours according to your shipboard clock. Your rocket is 300,000,000 metres long. So it took you:

 

(300,000,000 / 9,460,730,472,580,800) * 24 hours

 

..to traverse the ball. There are 3600 seconds in an hour so that's:

 

(300,000,000 / 9,460,730,472,580,800) * 86,400 seconds

 

= 300,000,000 * 86,400 / 9,460,730,472,580,800 seconds

 

= 25,920,000,000,000 / 9,460,730,472,580,800 seconds

 

Chop both sides by a factor of a million:

 

25,920,000 / 9,460,730,472 seconds

 

And again:

 

25 / 9,460 seconds

 

Have I said enough yet?

[Zanket]

What gravitational time dilation are you talking about? You had better show this, mathemetically.

From The Relativistic Rocket:

... a clock attached to the rocket's ceiling (i.e. furthest from the motor) ages faster than a clock attached to its floor.

This is standard SR, so you can look up the math yourself.

 

Only one clock is needed.

As long as it runs at the same rate as all of the other clocks along the "known distance apart", which it will only when that distance is zero in the limit.

[D H]

DH: Stop digging. If you travel very very fast you can traverse a great distance in what to you seems like a short time.

 

No, you cannot. One can traverse what appears to be a great distance to some other observer. It does not look like a long distance to the traveler himself.

 

 

A light year is 9,460,730,472,580,800 metres. You traverse this in 24 hours according to your shipboard clock. Your rocket is 300,000,000 metres long. So it took you:

 

(300,000,000 / 9,460,730,472,580,800) * 24 hours

 

The frame mixing is highlighted. You are computing velocity as distance as measured in one frame divided by time measured in another.

 

 

From The Relativistic Rocket:

... a clock attached to the rocket's ceiling (i.e. furthest from the motor) ages faster than a clock attached to its floor.

This is standard SR, so you can look up the math yourself.

 

You left out a rather critical line:

For a standard-sized rocket with a survivable acceleration, this difference in how fast things age within its cabin is very small.

 

The effect is challenging to measure on a spaceship the size of the Earth: It is small. I asked you to show me the math. You did not. You showed a theoretical result, and no math. You did not quantify those effects nor did you show that the effects are uncompensatable.

 

Only one clock is needed.

As long as it runs at the same rate as all of the other clocks along the "known distance apart", which it will only when that distance is zero in the limit.

 

What other clocks? I said "I only need one clock."

[Zanket]

You left out a rather critical line:

For a standard-sized rocket with a survivable acceleration, this difference in how fast things age within its cabin is very small.

Here we’re talking about an arbitrarily short time elapsed in the crew’s frame, so we’re talking about an unsurvivable acceleration.

 

The effect is challenging to measure on a spaceship the size of the Earth: It is small.

The effect can be arbitrarily large on any spaceship undergoing extreme acceleration.

 

I asked you to show me the math. You did not. You showed a theoretical result, and no math.

It's not my job to tutor you on SR, a theory. You are arguing against the link I gave you from the Usenet Physics FAQ.

 

What other clocks? I said "I only need one clock."

When clocks along the length of the “known distance apart” run at various rates, what one clock will you use? You’d be mixing frames in that case.

[D H]

Here we’re talking about an arbitrarily short time elapsed in the crew’s frame ...

 

No we aren't. It takes a beam of light 0.3336 microseconds to traverse a spacecraft that is 100 meters long (your example). 0.3336 microseconds is quite measurable with modern instruments. I guarantee you that a ball (assuming it has some mass) takes longer than this to traverse the spacecraft in the frame of the crew.

 

Usenet Physics FAQ

 

Believe it or not, this is not the best source in the world. It is a Classics Illustrated version of physics. It is correct, but there is little explanatory background. It is mostly a compendium of equations that can be easily be applied incorrectly.

 

Take the equations of a relativistic rocket, for example. You misapplied the equations for a rocket undergoing constant acceleration here:

 

Section 1 shows that directly measured free-fall velocity asymptotes to c in a uniform gravitational field. The particle always falls through a uniform gravitational field (a succession of them, each applying only locally) since a nonuniform gravitational field is everywhere uniform locally.

 

Equations 12-21 in your paper only apply to a constant acceleration. They do not apply when jerk is present.

[Zanket]

No we aren't. It takes a beam of light 0.3336 microseconds to traverse a spacecraft that is 100 meters long (your example). 0.3336 microseconds is quite measurable with modern instruments. I guarantee you that a ball (assuming it has some mass) takes longer than this to traverse the spacecraft in the frame of the crew.

You’re using circular logic there. You’re basically saying “since I’m right that it takes time h/c for light to traverse, which is not an arbitrarily short time, then you’re wrong that the acceleration is unsurvivable”. But you’re wrong that it takes h/c. If you input an unsurvivable acceleration into eq. 19 then you would see that. Or you can input an acceleration as little as 1g into the equations for a super-long rocket; more on that below.

 

Believe it or not, this is not the best source in the world. It is a Classics Illustrated version of physics. It is correct, but there is little explanatory background.

All that matters here is that it is correct. My paper is not intended to be a tutorial on SR.

 

It is mostly a compendium of equations that can be easily be applied incorrectly.

The equations are simple, the descriptions of the variables are clear, and I walked you through how to use them. The site also uses them to report that my finding is correct, and you can double-check its results with the equations to verify that you are applying them correctly.

 

For example, the site reports that a crew can get from Earth to the Andromeda galaxy in 28 years on their clock. The proper distance between the Earth and Andromeda is 2 million light years. Let the ship have a proper length of 2 million light years. Let it be initially at rest with respect to Andromeda, with Andromeda near the tip of it. Then Andromeda can traverse the rocket in 28 years on the crew’s clock (upon which the tail of the ship reaches Andromeda), and in a shorter time if they accelerate at a higher rate. (This is not a “standard-sized rocket”, so you still have to measure velocity using a “known distance apart” that is zero in the limit.)

 

Equations 12-21 in your paper only apply to a constant acceleration. They do not apply when jerk is present.

There is no jerk present in a uniform gravitational field, by definition. An object falling in a uniform gravitational field accelerates at a constant rate. Hence the qualifier “uniform” = “constant”.

[D H]

You’re using circular logic there.

 

No. I am using well established theories backed up by observed facts. Objects cannot exceed the speed of light; none has been observed to do so. Your "theory" flies in the face of observations.

 

 

If you input an unsurvivable acceleration into eq. 19 then you would see that.

Your paper has one thing right: The velocity of an object relative to some other object asymptotes to c. You yourself disprove your own theory.

 

 

For example, the site reports that a crew can get from Earth to the Andromeda galaxy in 28 years on their clock. The proper distance between the Earth and Andromeda is 2 million light years. Let the ship have a proper length of 2 million light years. Let it be initially at rest with respect to Andromeda, with Andromeda near the tip of it. Then Andromeda can traverse the rocket in 28 years on the crew’s clock (upon which the tail of the ship reaches Andromeda), and in a shorter time if they accelerate at a higher rate. (This is not a “standard-sized rocket”, so you still have to measure velocity using a “known distance apart” that is zero in the limit.)

 

You are mixing frames again. The rocket can get to Andromeda in 28 years because, to the crew, the apparent distance to Andromeda has shrunk from 2 million light years to a bit less than 28 light years.

 

Andromeda can traverse the rocket in 28 years because, to an observer in Andromeda, the rocket has shrunk in length from 2 million light years to a bit less than 28 light years. Length contraction works both ways. There is no preferred frame of reference.

 

There is no jerk present in a uniform gravitational field, by definition. An object falling in a uniform gravitational field accelerates at a constant rate. Hence the qualifier “uniform” = “constant”.

 

Of course there isn't any jerk in a uniform field. The field generated by a massive body is not uniform. The acceleration in such a field is not uniform. Your treasured equations do not apply in such a field.

 

What value of a do you propose to use in these equations when the test particle changes its acceleration every step of the way on falling toward the star?

[Zanket]

No. I am using well established theories backed up by observed facts. Objects cannot exceed the speed of light; none has been observed to do so.

The equations always return v < c. I showed that your method of measuring velocity is invalid.

 

Your paper has one thing right: The velocity of an object relative to some other object asymptotes to c. You yourself disprove your own theory.

It disproves nothing in my paper. It’s a key point of it.

 

You are mixing frames again.

Nope. The Usenet Physics FAQ did not mix frames without anybody noticing for years.

 

The rocket can get to Andromeda in 28 years because, to the crew, the apparent distance to Andromeda has shrunk from 2 million light years to a bit less than 28 light years.

Irrelevant.

 

Andromeda can traverse the rocket in 28 years ...

You contradicted yourself yet again. Before you said it would take > h/c for an object to traverse the rocket in the crew's frame. Now you agree it can take < h/c, agreeing with me.

 

Of course there isn't any jerk in a uniform field. The field generated by a massive body is not uniform. The acceleration in such a field is not uniform. Your treasured equations do not apply in such a field.

Nor are they applied to such a field. You could not quote anything from my paper that does that.

 

What value of a do you propose to use in these equations when the test particle changes its acceleration every step of the way on falling toward the star?

Section 3 implicitly increases the value of a as the particle falls.

[D H]

I see that this "theory" has finally been moved to "Speculations". Arguing with you is pointless. Go to school, argue with your professors.

[Zanket]

Arguing with you is pointless because you disagree with SR, except when you contradict yourself.

[Cap'n Refsmmat]

Oh dear.

 

Let's stop that and start being sane please.

[Farsight]

Zanket:

 

I think you ought to change the introduction in your paper to talk about a meteorite falling past a 30m tree, and then about a stationary meteor puncturing a relativistic 30m rocket from top to bottom. The duration of the former is limited to c in the tree's frame, whilst the duration of the latter is not limited to c in the crew's frame. This is clearer than the receding star. Personally I'd also change the word "flaw" to something like "query".

 

Yes, there's something important here, but I'm not sure your conclusions are right. In fact I'm wondering whether you're going in the wrong direction. The black hole is the problem, because whilst you're falling from infinity to that event horizon I could be overtaking you in my powered spaceship: and as far as you're concerned, I'm travelling faster than c. I need to think some more about this. I'm pretty sure the answer will come in time.

[D H]

Oh dear.

 

Let's stop that and start being sane please.

 

Sorry for being rude, Zanket.

 

You will not find a flaw in the heart of relativity, special or general. The theories has been examined by some a vast number of people over the last one hundred years.

 

Instead of spending your energy trying to poke holes in some well-thought out theories, spend your energy pushing the boundaries of the theories. The theories do have problems at the centers of singularities, in that they lack a causal mechanism, and in that they don't mesh well with quantum mechanics.

[Farsight]

For the record, I don't think there's anything wrong with Special Relativity. But I don't think people properly understand what it really means. This makes me feel less confident about General Relativity, enough to listen to Zanket regardless of the longevity of the theory.

 

Please can we nail down this point:

 

a) The apparent velocity of a meteorite falling past a 30m tree is limited to c in the tree's frame.

 

b) The apparent velocity of a stationary meteor puncturing a relativistic 30m rocket from top to bottom is not limited to c in the crew's frame.

 

Everybody agrees with a, but can anybody give some cool calm maths to illustrate why b is right or wrong, with particular attention to the limit condition?

[Zanket]

I think you ought to change the introduction in your paper to talk about a meteorite falling past a 30m tree, and then about a stationary meteor puncturing a relativistic 30m rocket from top to bottom. The duration of the former is limited to c in the tree's frame, whilst the duration of the latter is not limited to c in the crew's frame.

Thanks for the suggestion. According to the equivalence principle, the duration of the traversal can be arbitrarily short in either frame. Otherwise an experiment could distinguish between the two situations in defiance of the equivalence principle. That’s the point that is used to show an inconsistency of GR.

 

Personally I'd also change the word "flaw" to something like "query".

As I recall you’ve brought this up before. I think that would be sugarcoating. It seems that many people take offense at “flaw”. But the word is properly used, and the paper proves its point, so I don’t care if the word offends. The paper is intended to be matter-of-fact and not diplomatic. I think those people will have a knee-jerk reaction no matter what words I use. These are people who want to suppress anything that disagrees with their cherished status quo, regardless of the evidence.

[Zanket]

Sorry for being rude, Zanket.

accepted, thanks

 

You will not find a flaw in the heart of relativity, special or general. The theories has been examined by some a vast number of people over the last one hundred years.

This is just an opinion. In science, facts determine whether there’s a flaw.

 

Instead of spending your energy trying to poke holes in some well-thought out theories, spend your energy pushing the boundaries of the theories. The theories do have problems at the centers of singularities, in that they lack a causal mechanism, and in that they don't mesh well with quantum mechanics.

In my paper, validly poking a hole in GR leads to a metric that is compatible with quantum mechanics and does not predict singularities, yet is still experimentally confirmed. Sometimes the status quo must be refuted in the process of deriving the successor. Newtonian mechanics was “well-thought out” for 200+ years. By your logic we should not have GR today.

 

For the record I will show mathematically that a ball can traverse a rocket in an arbitrarily short time in the frame of its crew, the point of my paper that you mainly disputed above. In the paper this point is leveraged to show a flaw of GR.

 

The relevant special relativistic equation is eq. 19 in my paper, which sources from the Usenet Physics FAQ here, and which is derived in section 6.2 of Gravitation by Misner, Thorne, and Wheeler:

 

T = acosh((a * d) + 1) / a

 

Definitions:

 

a = Positive acceleration felt by the crew, in geometric units

acosh = Inverse hyperbolic cosine function

d = Distance traversed by the rocket in the gantry’s frame

ly = light years

T = Time elapsed in the crew’s frame (i.e. how much the crew ages), in geometric units

y = years

 

Let the rocket have a proper length of one light year. Let the ball be at rest in the gantry’s frame, initially near the tip of the rocket. Then d = 1 ly and the equation measures the years elapsed in the crew’s frame for the tail of the rocket to reach the ball, i.e. for the ball to traverse the rocket. Here are some sample results:

 

d = 1 ly, a = 5 ly / y^2, T = 0.50 y

d = 1 ly, a = 10 ly / y^2, T = 0.31 y

d = 1 ly, a = 25 ly / y^2, T = 0.16 y

d = 1 ly, a = 50 ly / y^2, T = 0.09 y

 

The time T is inversely proportional to the acceleration. Then the time T can be arbitrarily short for any given d. The velocity v is always less than c, as reported by eq. 16.

[D H]

Please can we nail down this point:

 

a) The apparent velocity of a meteorite falling past a 30m tree is limited to c in the tree's frame.

 

b) The apparent velocity of a stationary meteor puncturing a relativistic 30m rocket from top to bottom is not limited to c in the crew's frame.

 

Everybody agrees with a, but can anybody give some cool calm maths to illustrate why b is right or wrong, with particular attention to the limit condition?

 

Using Zanket's logic, a is false as well. His star-rod-ball concept gives an arbitrarity high velocity even if the rocket is not accelerating. Try it. Give Zanket's 2 million light year long rocket an initial velocity that makes possible to travel 2 million light years (Andromeda observer) in 28 years (crew time).

 

This does not show either a or b are false. I showed that you are mixing frames.

 

That both are a and b are true is a direct consequence of the second hypothesis of special relativity. Note that this is an unproven hypothesis; it is axiomatic in relativity theory.

 

The kinds of mistakes both of you are making makes me think you have some concept of an absolute reference frame hidden in your logic somewhere.

[Zanket]

For the record, I don't think there's anything wrong with Special Relativity. But I don't think people properly understand what it really means.

Yes, that is evident in many of my discussions.

 

a) The apparent velocity of a meteorite falling past a 30m tree is limited to c in the tree's frame.

 

b) The apparent velocity of a stationary meteor puncturing a relativistic 30m rocket from top to bottom is not limited to c in the crew's frame.

My paper makes the following points: (b) is given by SR in section 8 of my paper. Then (a) is false according to the GR’s equivalence principle, which lets the tree and crew be analogous. But the paper shows that GR agrees with (a). Then GR is inconsistent; it contradicts itself.

[Farsight]

Aw, sugar that pill Zanket. I'll have to get back to you on that acceleration example.

 

That both are a and b are true is a direct consequence of the second hypothesis of special relativity...

 

Is that a typo DH? Aren't you saying b is false?

 

PS: I don't have a secret absolute reference frame. But I do have a touch of aether - not the old-style aether wind stuff, but a property of space that sets c and distinguishes it from nothing. This is space rather than spacetime, time is subjective to velocity, and while velocity is limited to c, speed is not. And my own typo is that I should have said The apparent speed rather than The apparent velocity.

[D H]

Is that a typo DH? Aren't you saying b is false?

 

No typo. Try it. Zanket's "logic" shows a to be false.

 

I don't buy any of Zanket's arguments. Both a and b are true.

 

I don't have a secret absolute reference frame. But I do have a touch of aether - not the old-style aether wind stuff, but a property of space that sets c and distinguishes it from nothing.

 

And the difference between this and an absolute reference frame are what?

[Farsight]

DH: the difference is that my spacetime is timeless. My c is fundamental, it's a velocity not a speed, and its true dimensions are not length and time because these depend on your velocity with respect to c. It means all reference frames are subjective, none are objective. That leaves me no room for an absolute reference frame. Semantics maybe to you, but it's important to me.

 

I guess I do refer to the Universe. If we sit motionless in space the stars are spherical, and a rod is 7m long. But if we zip around at .99c our time dilation is sevenfold, as is the length contraction. The stars are now like thickcrust pizzas all face-on, rotating in a very strange fashion. And the rod is maybe 7m long, or maybe 1m long depending on our direction of approach.

 

Sure, if the whole Universe was zipping along with us at .99c we wouldn't know the difference, the time dilation would be offset by the length contraction. The spinning stars would be spheres again. So I guess the Universe is my aether and my absolute reference frame, only I don't know and don't care if it's really absolute.

 

What's absolute enough is the spherical shape of Saturn with its circular rings, the shadow on its face that I can triangulate to work out a billion miles. If I blast off towards it at .99c I know it hasn't turned into a flat striped disc where Mars used to be.

[Ragib]

Can you prove with references that this is an issue? Let's be clear that you say this is an issue with any universe that always exists. I've read extensively on cosmology, and the only issue with entropy that I've seen is for a universe that always oscillates between a big bang and a big crunch. Is that the one you're talking about? Harrison says this issue is highly speculative.

 

Itll get you references later, I have my exams this week and its been about 4 years since i've read that information, cant remember where. But i believe entropy is also an issue for a universe that has existed for an infinite amount of time, surely. Even if not entropy, how about thermal eqilibrium? How does an eternal universe aviod that? Should the night sky be fully illuminated, seeing as the light from the most distant stars have reached us by now? And why favour an infinite amount of 1 diemension, time, and not space? they are the same. You are not claiming space is finite are you? Then how would it expand/contract as you say?

[Zanket]

That both are a and b are true is a direct consequence of the second hypothesis of special relativity.

You repeatedly said above that situation (b) is false; now you say it’s true. If both (a) and (b) are true then the equivalence principle is violated. The equivalence principle shows that, since (b) is true according to the relativistic rocket equations, (a) must be false.

[Zanket]

Is that a typo DH? Aren't you saying b is false?

He was arguing above that situation (b) is false. Now he’s saying that it’s true. I predict that next he’ll say it’s false again.