Johnny5

Hello' date='

 

What do you think about this theory?

 

www.webcom.com/musics/mass.pdf

 

From the definitions of Planck units of length and time is deduced a correspondence between mass and time equal to [tex]m=@'t[/tex], where @' is a constant that has dimension of force. The similarity of this equation with the equation [tex]l=ct[/tex], could allows us to extrapolate a possible physical meaning for this correspondence

 

I can't understand it, it's in spanish. Do you speak spanish? If not why in the world would you read that?

As for the other things you are trying to say, inertial mass isn't supposed to be a function of time.

Do you know the differential calculus? If so, I can show you in what sense mass isn't a function of time.

Gents' date=' what do you think of this in relation to the main topic?

 

http://www.generativeart.com/2000/MCGUIRE.HTM[/quote']

 

I think its quite good. I don't know much about fractal geometry, although I do know that there's a link between it and chaos theory, and the concept of random.

 

It all goes to the meaning of the term 'deterministic.'

 

In my estimation, scientists do not yet have the concept of 'random' down.

If Newton's laws or special relativity are seen to hold, you are not in an accelerating frame. Specific applications to do this for rotations include the Foucalt pendulum and the Sagnac interferometer.

SR totally aside, because I don't want to get into that with you here, do you regard an 'accelerating frame' as 100% equivalent to one in which inertial forces are being felt?

Forgive that, if it's not totally clear.

As for the Foucalt pendulum, I have yet to understand the experiment.

I need to understand gyroscopic motion, i know that much.

I read that Foucalt is actually the one who first developed a gyroscope, and was using it, in conjunction with his giant pendulum, to draw inferences about the earth's rotation.

Let me see if i can find the pictures I was looking at, of some very old gyroscopes:

Here are a few pictures of some old gyroscopes, and a brief article on Foucault: Gyroscopes

c is the same in any inertial frame.

 

What is the contradiction?

What do you consider to be an inertial frame?

I'm afraid i am not seeing something help would be apreciated.

 

you toss a stone upwards off a 63m cliff at 8 meters per second

how long til it hits the ground?

Unfortunately' date=' latex isn't working.

Let's see...

The simplest way to do this, is to treat the event set theoretically.

i will have to explain, because I am one of few who do this.

Here is your given information:

Cliff height above ground=63 meters

Initial speed= 8 meters per second.

Initial direction of projectile motion=straight up

Start the clock at the moment you release the projectile.

There is a moment in time at which the object comes to rest in the frame.

That is one subevent, and lasts for time T1.

There is a second subevent, which begins when the first subevent ends, and ends when the object strikes the ground.

Denote the amount of time of the second subevent by T2.

The whole is the union of the parts. So the time of the whole event is T1+T2.

First compute T1, then compute T2, then add them to obtain the answer.

Here is the kinematical formula for constant acceleration:

D= v[sub']0[/sub]t + 1/2 a t²

The acceleration due to gravity has magnitude 9.8 meters per second squared, and its direction is opposite to the direction of motion.

So for subevent one we have:

D= 8t - (9.8/2) t²

Now, as you can see this is one equation in one unknown.

The height that the object rises wasn't given, nor was the time of flight t.

So we need a second equation in the same two unknowns, and then we can solve for T1, which is the amount of time between when the stone is released, to the moment in time at which it comes to rest in the frame.

Here is a link to the kinematical equations for constant acceleration:

Look and you will see this one;

D = (v_i+v_f)t/2

We know the initial speed is 8 m/s

And we know the final speed is 0 m/s

Keep in mind that speed is a strictly non-negative quantity (distance traveled divided by time of travel).

Ok so...

Using the formula above we have:

D = 8t/2=4t

And we also have:

D= 8t - (9.8/2) t²

So we have two equations in two unknowns, so we can now solve for both unknowns. It is the time of the first subevent that we are concerned with, so we need to eliminate D.

By direct substitution we have:

4t= 8t - (9.8/2) t²

9.8/2 = 4.9 therefore

4t= 8t - 4.9t²

Hence:

4.9t²+ 4t-8t=0

Hence:

4.9t²+ -4t=0

Factor out a t to obtain:

t(4.9t -4) =0

One root is zero, which cannot be an amount of time, because an amount of time is a strictly positive quantity, hence we want the other root, namely the one for which:

4.9t -4 =0

So:

4.9t = 4

So:

t = 4/4.9 = .81 seconds

So the amount of time of the first subevent is .81 seconds.

T1=.81 seconds

Now, we have to compute the amount of time for the second subevent.

During this part of the whole event, the object falls to the earth from higher than 63 meters.

Let D be the height the object rose above the cliff during the first subevent.

Then the distance which the object falls during the second part, is 63+D.

We need to know that in order to compute the time of the second subevent T2.

We already know this:

D =4t

So T1=.81 hence

D = 4(.81) = 3.26 meters

H = 63 + 3.26 = 66.26

The amount of time of the second subevent satisfies the following equation:

H = v₀t + (9.8/2) t²

Now during this part of the whole event, the initial speed is zero. The magnitude of the acceleration hasn't changed, but the direction of motion has. So during the first subevent, the center of mass of the object was decelerating in the frame, during the second subevent, the center of mass is accelerating in the frame.

So the initial speed is zero, hence:

H = (9.8/2) t²

Hence:

66.26 = (9.8/2) t²

Hence:

66.26 = 4.9 t²

Hence:

13.52 = t²

Hence:

3.67 = t

So the time of the second subevent is 3.67 seconds:

T2 = 3.67 seconds

And

T1 = .81 seconds

So

T=T1+T2 = 3.67+.81 = 4.48 seconds

Unless I made an error. You can compare with other peoples calculations.

Regards

PS: The thing about breaking the whole event into mutually exclusive and collectively exhaustive parts, is because:

1. It leads to the right answer.

2. It will help you analyze problems in special relativity theory.

Guys' date=' serious question for you.

 

do you realise what question you are asking?

 

do you see that you are asking if human reality is able to be represented by numbers?

 

will you confirm that for me so I know you know.[/quote']

 

I don't think that anyone is claiming that reality is able to be represented by numbers. I'm not sure what that means.

 

This thread is about determinism, and quantum mechanics, and it has veered slightly to the issue of Godel's incompleteness theorem, and a possible connection to universal turing machines and determinism. Numbers are used to quantify things in the sciences. If you want to question whether or not that is valid in any particular scenario, then go right ahead. It is not pointless to wonder whether or not the distance between two points in space is accurately representence by the real number system.

 

You will find many physicists leaning nowadays to the natural number system, and quantization of variables... in quantum mechanics energy is quantized.

 

In fact, Ernst mach wrote something about this, let me see if i can find his quote, because it seems appropriate:

 

Ernst Mach wrote (p. 596 in ref. 1), "The view that makes mechanics the basis of the remaining branches of physics, and explains all physical phenomena by mechanical ideas, is in our judgment a prejudice. ... The mechanical theory of nature, is, undoubtedly, in a historical view, both intelligible and pardonable; and it may also, for a time, have been of much value. But, upon the whole, it is an artificial conception."

 

Classical mechanics is indeed inappropriate as a starting point for physics because it is not fundamental; rather, it is the limit of an incoherent aggregation of an enormous number of quantum elements. To make contact with the fundamental nature of matter, we must work in a coherent context where the quantum reality is preserved. source

 

As you can see, Mach had a leaning to the natural number system {1,2,3,4,...}.

 

Whether or not a given quantity of physics can be represented by natural numbers is a good question.

 

The concept of pi seconds does seem meaningless.

 

But then again, the concept of a quantum unit of time has difficulties which have yet to be overcome.

 

But scientists have to explain reality using numbers. They also use their natural language. But numbers are the basis of the "hard sciences."

 

Without numbers, scientists would never have been able to develop computers.

 

So even if you cannot model reality using numbers... you sure as hell can change it by using numbers.

 

Merely look at the existence of a computer, and you will see that's true.

 

Regards

If you are going to ask about time dilation and accelerating frames see:

http://www.scienceforums.net/forums/showthread.php?t=11321

Post #37 & #38

I wasn't planning to complexify things by disscussing how SR holds up to acceleration. Right now I just wanted to see whether or not Dr Swanson claimed that V is the relative speed between two frames. He did.

t is the time measured by the observer in his own frame

t' is the time that passes in the other frame' date=' as measured by the observer

v is the speed of the other frame with respect to the observer

c is the speed of light in vacuum

 

 

D probably means "delta" so the time variables represent intervals between two events[/quote']

 

Well then we are assigning all the symbols the same meaning, so why do we not agree that there is a contradiction?

 

Actually maybe not. You have c = "speed of light in vacuum"

 

What frame is c in precisely?

Well this is certainly news to me. What exactly was Godel's error?

And I do hope you realize that set theory itself is incomplete? It wouldn't help your cause at all to use a "set theoretic analysis" to then refute Godel.

It is best to show what I mean symbolically, rather than debate set theory.

I only ran through his argument once, for a week or so, found a weak point, and haven't looked at it again.

I could just show you what I mean, and then you could critique it.

Let me make sure I copied everything down correctly, here is your exact question again:

Originally Posted by J.C.MacSwell

Picture yourself in space at the center of a system that includes you, a solar mass 200 million miles away to your right and a 2 solar mass 100 million miles away to your left. You are at the center of mass.

 

Which way would you be pulled by gravity?

I will use a diagram this time, to represent the given information:

M..........X....................m

X represents my position, M_x will represent my mass.

The distance from me to m is twice the distance from me to M.

M=2m

F_L = (2m)(M_x)/R²

F_R =(m)(M_x)/(2R)²

F_L = 4(2m)(M_x)/4R²

F_L = 4(2m)(M_x)/(2R)²

F_L = 8(m)(M_x)/(2R)²

F_L = 8F_R

The answer is above is correct.

The gravitational force to the left is 8 times greater than the gravitational force to the right.

I see your point. Center of mass is linear, and gravitation is inverse r^2.

I could just have known that from the formulas for both.

Let me comare things.

Here is the formula for the center of mass of an N body system.

MR = S m_ir_i

The indice ranges from i=1 to i=N, in the summation. M is the total system mass, and mi is the mass of the ith body. R is the position vector of the center of mass in some arbitrary reference frame, and ri is the position vector of the ith body.

So:

M = S m_i

Let us choose our frame to be the CM frame, then in particular, R=0... the zero vector.

So, in the center of mass frame, the following statement is true:

M0 = S m_ir_i

Hence:

0 = S m_ir_i

Now, the system is a closed three body system hence the following statement is true in the CM frame:

0 = m₁r₁+m₂r₂+m₃r₃

Using the original symbols for the three masses we have:

0 = Mr₁+M_xr₂+mr₃

Now, my position happens to be at the center of mass of the system, that is, r2=0, but this should be inferrable.

Let me not a-priori assume that my position is the center of mass of the system, but let me formulate true statements from a frame in which the center of mass of Mx is the origin. Therefore, for sure r2=0, and it should be inferrable that this frame happens to be the CM frame of the system.

Since r2=0 it follows that:

0 = Mr₁+mr₃

0 = 2mr₁+mr₃

0 = 2r₁+r₃

-2r₁=r₃

The previous statement was stipulated to be true, hence the center of mass of Mx is the CM of the frame.

I didn't know that the concept of hypersphere is used to explain redshift. I certaintly don't believe that is necessary.

At this point, i would focus upon the definition of 'hypersphere' most importantly, does the idea have direction of motion constant, yet you return to where you were.

This came up in post 12 of this thread, and rather than having the topic there branch, I thought i just might move my question to another post. Here is what arose in the other thread:

Originally Posted by LKL

How do you know if that something is spinning or not? What

If Newton's laws or special relativity are seen to hold, you are not in an accelerating frame. Specific applications to do this for rotations include the Foucalt pendulum and the Sagnac interferometer.

Here is what i would ask you about.

You say that if special relativity holds then you are not in an accelerating frame.

Here is my question.

Could you run through an explanation of the time dilation formula of SR for me. Specifically, I want to see how you explain each of the letters in the formula, be they constants, or variables. I suppose I am most focused on v.

Dt` = Dt (1-v^2/c^2)^(-1/2)

Yes! I have been saying this for years. Godel's proof works within the realm of math which in turn is constructed upon a set of underlying axioms. Thus Godel's incompleteness theorem only holds true for systems of mathematics which obey that underlying set of postulates.

 

Godel himself wrote extensively on the subject and his main argument seemed to be the insistance that because his proof holds true for our set of axioms then it still disproves it for whatever higher level system our mathematics is a subset of. He had a great deal of reasoning behind that assertion' date=' but personally I think it's all bullshit.[/quote']

 

A set theoretic analysis of his work will reveal his error. He had several incompleteness theorems. Do you know of a way to isolate an error in either of them?

Check again.

 

Center of mass is linear and gravitation is inverse squared

I didnt do any calculation i just sort of blurted out the answer.

Let me see...

You say i have a mass of 2M on my left and a mass of M on my right.

but the mass of 2M is twice as far away from me as the M mass.

Let me use the mathematics, its the only way for me to be certain of the answer.

denote my mass by m

The gravitational force on me to the left is given by:

F = (2M)(m)/R^2

and the gravitational force on me to the right is given by:

F = (M)(m)/r^2

and the distance from me to the mass on my right is 200 million miles

and the distance from me to the mass on my left is 100 million miles.

therefore

R=2r

Picture yourself in space at the center of a system that includes you' date=' a solar mass 200 million miles away to your right and a 2 solar mass 100 million miles away to your left. You are at the center of mass.

 

Which way would you be pulled by gravity?[/quote']

 

Both directions, yet equally and so i would remain at rest in the CM frame.

It depends on your reference frame. If you set it at the center of the earth, then it will be zero, since potential gravitational energy is m*g*h. Now, if the reference frame was placed on the surface of the earth, then it would be different.

mgh is not an exact formula.

This is why i want to use gravitational field theory for everything.

Regarding experimental analysis of precession' date=' how about a forced-precession device? Something that spins a flywheel while at the same time rotating its axis. Might be fun![/quote']

 

Like a flywheel in an engine?

 

A heavy disc of metal attached to the rear of the crankshaft. It smoothes the firing impulses of the engine and keeps the crankshaft turning during periods when no firing takes place. The starter also engages the flywheel to start the engine. Figure 16 The flywheel is mounted to the rear of the crankshaft source

 

Flywheel

If you had a closed system, and chose an inertial frame based on the center of mass being at rest, then the center of mass would stay at rest. The gravitational net force at this point would not necessarily be zero, nor would it necessarily stay zero if it was.

Can we discuss this further?

Introduce the mathematical tools necessary to discuss it.

Hi' date=' All!....my first posting here.

 

I Find the Pythagorean Triples mentioned in one of the threads and curious to know what they are....if you will, please.[/quote']

 

Definition: Any natural numbers A,B,C such that A^2+B^2=C^2 represent a Pythagorean triple of numbers.

 

Examples given:

 

3^2+4^2=5^2

 

6^2 + 8^2=10^2

 

So 3,4,5 is a Pythagorean triple, and 6,8,10 is a Pythagorean triple.

Why don't you look it up yourself? It's not that hard to find. Is your objective here to learn something or is it to test everyone's patience?

 

What you are being asked to do is to learn the statement of the theorem so that you stop with these ridiculous strawman arguments (and if what you're doing isn't childish' date=' then I don't know what is).

 

The theorem does not say that every nth degree polynomial will have n points of intersection with the x-axis. That is the result of you forcing the word "distinct" in between "n" and "roots" in the following statement:

 

[i']Every polynomial equation of degree n with complex coefficients has n roots in the complex numbers.[/i]

 

Simply put: You are arguing against a statement that is not equivalent to the statement of the Fundamental Theorem of Algebra. Since the thing you are arguing against is a non-theorem, it's no surprise that you are able to topple it so easily. No one is impressed.

Ok let me think about what you are saying. By the way you should know me by now, I don't play games.

I just don't like contradictions. So let me slowly sift through what you have said up there.

Ok, firstly you say look up the theorem. Well i have done that. I will do it again, then quote it below.

Fundamental theorem of algebra

Every polynomial equation of degree n with complex coefficients has n roots in the complex numbers.

Gauss' proof of the FTA

Here is another link:

Fundamental theorem of algebra

Here is how that site explains it:

The fundamental theorem of algebra (now considered something of a Quick Facts about: misnomer

An incorrect or unsuitable namemisnomer by many mathematicians) states that every complex Quick Facts about: polynomial

A mathematical expression that is the sum of a number of termspolynomial of degree n has exactly n zeroes, counted with multiplicity. More formally, if

(where the coefficients a0, ..., an−1 can be Quick Facts about: real

An old small silver Spanish coinreal or Quick Facts about: complex

(psychoanalysis) a combination of emotions and impulses that have been rejected from awareness but still influence a person's behaviorcomplex numbers),

then there exist (not necessarily distinct) complex numbers z1, ..., zn such that

 

This shows

that the Quick Facts about: field

A piece of land cleared of trees and usually enclosedfield of Quick Facts about: complex numbers

A number of the form a+bi where a and b are real numbers and i is the square root of -1complex numbers, unlike the field of Quick Facts about: real numbers

Any rational or irrational numberreal numbers, is Quick Facts about: algebraically closed

Quick Summary not found for this subjectalgebraically closed. An easy consequence is that the product of all the roots equals (−1)n a0 and the sum of all the roots equals -an−1.

Notice how the above site says, "NOT NECESSARILY DISTINCT'

Ahem...

The fundamental theorem of algebra:

Every polynomial p(x) with complex coefficients of degree >= 1 has a complex root.

 

The statement that a complex polynomial with degree n >= 1 has n roots is in fact a statement where multiplicity is encounted. The "real" theorem is the one stated above (if you allow multiple roots' date=' then the second statement can easily be shown by induction).

 

Other formulations of the theorem is:

- Every complex polynomial have a factorization where no polynomial factor is of degree greater than 1.

- C splits over C.

- The field C of complex numbers is algebraically closed.

I suggest you should allow yourself to look into some books introducing you to the field of abstract algebra. Then you hopefully would understand the concept of [i']i[/i]; it is more to it than lower calculus is telling you.

Thank you, now we are getting to the bottom of things.

Rate was fine' date=' it just isn't usually called G. You can think of that as the speed at which the clock runs (which is the rate at which the time is changing), and make some analogies to kinematics, since the same math will apply. The clock can also accelerate, i.e. the rate can change, which is called drift.

[/quote']

 

Here is something on GPS and clock drift. I presume this is what you meant by clock drift:

 

Satellite clock error data

 

So a changing clock rate is called drift.

 

It would be nice if there was some universal clock which had no drift.

Regarding experimental analysis of precession' date=' how about a forced-precession device? Something that spins a flywheel while at the same time rotating its axis. Might be fun![/quote']

 

What exactly is a flywheel? I know your other post talks about it, and I wanted to run through the math, generate the equations.

 

I don't know much about non-Euclidean geometry, pretty much all of my knowledge stems from the book "Readable Relativity", so I'll just quote some of the main points concerning rotation. Suppose there's a rotating disc, an observer some distance from it(on the same plane) who regards the disk as rotating about its center axis and an observer on the disc. They both consider the other observer rotating about the center axis and so on. It gets interesting when the guy on the disc draws a circle using the center of the disc as its center and goes on to measure its diameter and circumference. When he's measuring its diameter, the outside observer doesn't find his rule contracting. When he's measuring the circumference, however, the outside observer will see the rule contracting. So, they can't agree even on the value of pi.

 

This is what I want to think about. Agreement on the value of pi for example.

 

I want to have access to a thorough knowledge of rotation.

This is very funny. Why don't you prove the theorem Matt?

You are the professional mathematician, not I.

Oh, for pity's sake Johnny, learn about repeated roots, or roots "with multiplicity" and stop with these childish postings. By your own reasoning it has two linear factors.

But you say 'roots' in the plural Matthew.

yet there can be only one.

x^2-4x+4=0

I don't think it's childish by the way. I am serious, there is only one root.

Draw an X axis, and a Y axis, plot the graph of

x^2-4x+4

ok let that have been done.

So here is the function which you have plotted on Maple, or Mathematica, or what have you:

y(x) = x^2-4x+4

Now, look at the plot and tell me how many times the curve intersects the x axis?

One or two?