Ashish

Yes timo I agree with you that in 1D motion there is little bit information.

Ok then have a look once more, the parametric equation of circle ( x^x + y^y = r^r) is given by

x = r cos(t)

y = r sin(t)

where parameter comes to be as an angle drawn by x-axis to radius measured in counter-clockwise direction. So that makes a sense that the variable t or parameter is there.

but in case with helix, projectile motion, or any 3D motion there isn't any variable or parameter that can be observed.

My problem is that why cant be embed them in one. or its just to show how the value of one variable varies.

or in other words in my views time should not be taken as another dimension as its always there.

From the 2D and 3D plots, the motion can be understood rather well without a time coordinate. Try that with the 1D plot.

thanks for showing interest but be little more comprehensive

From past few days I've been studying Electromagnetic Field Theory by Sadiku. As electromagnetic field theory requires knowledge of vector calculus so while studying I came to struck up with a problem which is related to parametric equation, which is also related to motion in one dimension to two and three dimensions.

So let me explain my doubt

Take a look at figure: Below is the graph for position vs time

here in above graph what we really show is that how a position of an object or particle varies with respect to time. In other words position is a function of time. so if "x" is used for position and "t" for time then x(t) = f(t); some function

Now have a look at below figure its a projectile motion (motion in two dimensions)

and now for motion in three dimensions here are two figure shown below

In all graph of two and three dimension one thing to be noted is that the graph is plotted for the position of any particle or object, but there is no variable for time.

but wait they have been parametrized as

in 2D

x = f(t) and y = g(t); in a similar way

in 3D

x = f(t); y = g(t) and z = h(t)

but in case of one dimension motion why it is so we've plotted with respect to time.

And for the case in 2 and 3D we haven't . Well for 3D it seems to be difficult as there isn't any axis for taking "t" as variable but in 2D what the problem.

So my problem is why we use parametric equation for 2 and 3D.

I've saw in various documentaries and many books but I'm not remembering i.e. a black hole wraps the fabric of spacetime in such a way that all converges to a single point like structure as shown in above figure.

So I was wondering about the depth of curved to which it wraps the spacetime fabric.

thanks everybody but till now also I'm not satisfied. I think there is something more than what we've learn yet.

Well I used to think of functions and fields two be two different entity; for example:

Consider an area of circle, A(a) = pi*a² ----------------- (1)

magnitude of electric field of a charge q, E(a) = kq/a² ----------------- (2)

electric field of a charge q, E(a) = kq*a/a³----------- (3)

So equation (1) and (2) are simple scalar function and equation (3) is a vector function.

but do check the below image too which I've uploaded from the book

"Advanced Calculus, Robert C Wrede, Murray Spiegel, 2e" page no. 156

after this i thought that the entity (field) too which I used to think is different isn't but its too function that too vector function.

now the question comes in mind from direct intuition that the electric, magnetic and gravitational field we're learning is not the field but its only a function (vector function); but from this we didn't get the some real perspective of the physical field we've in our mind.

If I'm wrong then please do intimate me about this

How many atoms do you need to get temperature? two?

there are various property like temperature, pressure, liquid, gas, solid which have collective property i.e these property are useless until and unless there isn't any collection particles to which they're concerned.

but a question really comes in mind as quoted above like how much of collection of particle do we need to have to make it possible-for example consider single water molecule H2O, now can you tell me what is it a -

A) Solid

B) Liquid

C) Gas

hi michadelic

I too believe in you and in my view not only space-time, whole thing in this universe is discrete.

for example:

consider our UNIVERSE when viewed as a whole it may seems continuous but actually it isn't continuous at all, all of its constituents are discrete like planets, moons, stars etc.

and in microscopic view also atoms are not also continuous all its constituents are discrete like electrons, protons and neutrons.

There is always a minimum limit beyond which one cannot have discreteness.

But in my view i think field as an intrinsic property of charge, mass, magnet for electric, gravitational and magnetic interaction respectively.

Whenever there is a object having mass then there will be gravitational field of its own and similarly for charge and magnet.

and one more thing is that field has more something physical than only mathematical construct as swansont says; and we've not really understood it.

Merged post follows:

I agree with Ashish's interrogation.

IMHO it's all still unexplained stuff.

.

Well I dont know anything about IMHO but I really like your point......

A field is a section of a fibre bundle over a space-time manifold.

 

In plain language, a field is an assignment of a "value" at all points on space-time. You should note that the "value" need not be directly associated with an observable.

Well thanks for answering but What is it made up of

“Action at a distance” whenever this comes to play, in physics we tend to think of this in terms of fields whether it may be due to Electric, Magnetic and Gravitational (Well I know these only). Oh yes there’s one more and its Einstein’s Fields equation well I don’t know much about it.

So whats the real concepts behind field. Because from my intuition In order to make any change, movement or disturb something you need to touch it, for example if I want to move some object then I need to touch it and give it some force and that seems to be really in sense.

But on the other hand there are few physical phenomenon like Electric, Magnetic and Gravitational forces in which there in no need of actual physical contact as they have action at a distance.

In dictionary the formal meaning of “Field” is some sort of region. So in concerned with field in physics what really constitute field in each case as there is what that makes it possible to have such action at a distance.

that means there will not be any change in mass

I just want to know is mass dependent upon the temperature i.e. if there is an increase on a temperature of any body then does its mass change or it really effects the mass of that particular body

I can imagine many, many more than just 3 dimensions. You just have to know what you are looking for:

 

Let me give you an example:

 

Consider a single particle in space. It will use 3 dimensions just to describe its location, x, y, z. Now, consider further that that particle is moving. So it will will have velocities in the x,y,z directions as well, call them v_x, v_y, v_z. That velocity can really be considered a second set of dimensions.

 

A new dimension is needed when the current dimensions cannot adequately describe different states that can exist. In this case, using only position, one cannot adequately discriminate between a particle at rest at 0,0,0 or a particle zipping along at half the speed of light that just happens to be at 0,0,0 at a single instance in time. So, to adequately describe the differences in these two particles, you have to introduce the velocity dimensions as well.

 

This can be naturally extended again where the particle's accelerations could be another 3 dimensions. So, a single particle could need up to 9 dimensions to describe it. This is really only just about limited by your imagination. What if the size of the particle mattered? The particle volume could then be another dimension. What if it were made of different substances? A dimension capturing the concentration of the different materials in the particle could also be important.

 

Now, let's further expand this idea of the single particle to a multi-particle system where position and velocity are the properties of the particles we want to study. Say we were studying a system with N particles. To describe that system, we would actually need 6N dimensions to describe the state of that system. A system of 500 particle would need 3000 dimensions!

 

Let [math]P^{[N]}(\mathbf{x}_1,\mathbf{v}_1,\mathbf{x}_2,\mathbf{v}_2,...,\mathbf{x}_N,\mathbf{v}_N,t)[/math] denote the probability of finding the system in a state where particle 1 is within [math]d\mathbf{x}_1[/math] of position [math]\mathbf{x}_1[/math] with a velocity within [math]d\mathbf{v}_1[/math] of velocity [math]\mathbf{v}_1[/math], and so on for each of the N particles at time t.

 

The equation that describes the system is known as the Liouville Equation:

 

[math]\frac{\partial P}{\partial t} + \sum^{N}_{i=1}\mathbf{v}_i \cdot \frac{\partial P}{\partial \mathbf{x}_i} =0 [/math]

 

And, again, P is a function with 6N+1 (+1 for time) dimensions.

 

What "extra" dimensions come down to is the need to describe things that cannot be described by the "old" dimensions. They aren't necessarily some magical or unimaginable things. You just have to know what the math is saying they are, and know how to interpret them.

And that other set of dimension will also be in 3D how hard you try and if time then 4D. Because we cant imagine no..... we can imagine but we cant see.

And if you think so I'm wrong with my thinking can you show me any real world example of any object having dimensions more than 3. (ONLY IMAGE)

Merged post follows:

Watch this video http://www.youtube.com/watch?v=JkxieS-6WuA. It is obviously hard to explain how one can visualise beyond the third dimension, my visualisation kinda follows this video. It is a really good watch if your interested in string theory/ super-string theory/ m-theory/ f-theory.

I've seen it year before also and I'm able to comprehend upto 5D and after that it went off my mind.

But whatever its only explanation but hard to believe coz' human cannot visualize dimension more than 3D.

but could you make me to visualize it so as to make it comprehensive

First of all i dont have much knowledge of string theory.

String Theory talks about 11-Dimensions.

On the other hand all the things or object to which human can observe are 3D and for more details 1 for time, even this too make sense.

But according to string theory all the dimensions more than (3+1) are infinitesimal.

OK now consider a any mathematical function, f(x,y,z) which when plotted, you can see it in 3D and if you wanna see it more from that than you can zoom up to the limit of your computer performance, memory than also you'll not be available to see any further dimensions. This is not only the case with computer but in real paper and pencil also.

This is the beautiful pure world of theoretical mathematics where u can go upto any zoom or infinite.

But then also you cant see or imagine of any further dimensions.

Ok I can understand it

My aim was to calculate it and to see really that field are really moving.

It will be my pleasure if you can tell me that where I can get it over internet

well thanks for your reply

But I cant get it

Now please dont tell me to see some books because I dont have enough books on EM.

Can you derive it for me.

I've derived it but I'm not sure is it correct or not, please help me

Can you give me a clear derivation of electron electric field intensity which is placed in origin and oscillating in simple harmonic motion, at a distance "r" in the positive x direction.

can you tell me why?

I've read its electric field

In order to show unpolarized light we use the

can you tell me please about what this arrow on the unpolarized represent

whether it represent electric field or what?

Well while reading a chapter on EM waves I got confused about EM have momentum.

This really little bit confusing because momentum can only be of them who has a mass and in EM waves there nothing like mass or there isn't any thing that can have mass.

So can anybody clear out my problem either I may wrong.

ya its true that if I tell that there is nothing like a wave in this whole universe then there are certain phenonmena in QM which require wave i.e. matter wave.

So the question here is can a electron or let it be C60 structures as you've told (as its a particle, mean to say that it is composed of electon, proton, neutron and many other thing than how it can be a wave.

Please don't tell me here about according to DeBroglie wavelength.

Because I think there is someting a miss in this whole theory not only in QM or relativity but its from the core itself.

And the results like this have made me even more confident that there is nothing like a wave in this whole universe

Modern physics often describes the forces between particles in terms of the

actions of field particles or quanta. In the case of the familiar electromagnetic

interaction, the field particles are photons. In the language of modern physics, the

electromagnetic force is mediated (carried) by photons, which are the quanta of the

electromagnetic field. Likewise, the strong force is mediated by field particles

called gluons, the weak force is mediated by particles called the W and Z bosons,

and the gravitational force is thought to be mediated by quanta of the gravitational

field called gravitons. All of these field quanta have been detected except for

the graviton, which may never be found directly because of the weakness of the

gravitational field. From Servay college physics 7th ed.

Why to go toward maths i.e. first we must have a true underatanding of any phenomena by having some idea about it and certain imagination and after on do calculation over it through mathematics.

Its true that wave nature has explained various phenomena but then also we're missing something and resulting in entanglement.

But here I'm not talking any thing about QM and you've just told me about it.

I understood what you want to tell me, and if I'm saying that there is nothing like a wave then after all my studies over it I've come to the point it was just a mathematical tool and I've several reasons voilating all this.

In book "Motion Mountain-an adventure in physics"; I read about mass increase due to absorption of one green photon 3.7 * 10^(-31) kg.

means on absorption of green photon mass of the object or body increases.

Please tell me more about it.

Physical phenomena explained or proved on the basis of WAVE theory is the misconception at the core of physics which leads to entanglement in going ahead in physics. I mean to say that wave theory was just like a mathematical tool which was used in physics just to go ahead in physics but the real concept is only particle (Dont merge here the DeBroglie equation). And I really discard wave theory and any phenomena explained or proved on its base.Every thing is particle.

Wave, distribution of energy in space but the question here comes who is responsible for transferring energy from one place to another and its particle.

From past 5 year I'd a great study over wave and I've come to this point and I made so because of zeal for studying PHYSICS and also as since Quantum mechanics and relativity contradict each other thus creating entanglement for the unification of all four forces i.e in GUT.

I think one of the most mysterious tool (I call it) or theory used by physicist is wave and any phenomenon going to be proved on it will lead to entanglement. So theres a need to get the clear cut concept and not just by grasping over the ideas and theories studied or taught by.

What you all think am I right? and please tell me about how to publish a new theory with all its criteria.