Deepak Kapur

 

Take a large handful of cubes - place two to make a line, four to make a square and eight to make a cube. If it was additive it would be 4 to make a square and six to make a cube - BUT IT ISNT. To make it doubly clear place three to make a line, then nine to make a square and 27 to make a cube - no addition here whatsoever.

 

You need one coordinate to describe a straight line, two to describe a rectangle and three to describe the box - the units follow; metres, metres^2 and metres^3.

 

Neat ideas are just hot air if they don't comply with nature

Thanks for your answer. I also knew it to be the same, the way you described it...

But...

Somehow, I cannot wrap my head (may be an empty one) around the concepts of 'addition' and 'multiplication'.

1. When two balls collide, we multiply their masses.

2. When two forces act , we add forces.

My question is that when two balls collide, they are actually exerting force only.... so why to multiply?????

Let me try to explain what I am saying...........

Suppose there is a big ball. Two small balls collide with it from different sides.

a) We usually form an equation in which all the 3 masses are multiplied.

b) Why can't we take the collision by two small balls as forces acting on the big ball and in fact add the two small masses in our equation.

 

It would not be a constant of proportionality otherwise. maths is axiomatic - you need to work within the rules of the axiomatic system you have chosen. And you need to stick to the definitions and nomenclature which that system uses.

 

Once you start re-inventing terms or affirming that a definition has a deeper non-arbitrary meaning then you are getting into very muddy waters. y= kx goes through the origin and has a slope of k; y = j+x only goes though origin if j = 0 and has a slope of 1. These are not the same lines unless k=1 and j=0 - in other cases they are easily shown to be different. Claiming that one is as good a fit to the definition of the other is meaningless.

I am not affirming anything, I just want to satisfy my curiosity.

Another example...

A cube has length 2m. Its volume is 8m3.

Why are the units multiplied (I.e. meter cube).

Shouldn't they be added?

I push a ball hard. It starts to move.

1. Does it accelerate only for the time 'from my hand touching it' to 'my hand leaving it'?

2. After my hand leaves the ball, it attains uniform motion ( assuming no kind of friction). What sustains this uniform motion?

3. Why does the ball ever move? Why doesn't the energy that I supply to it just gets distributed as its internal energy?

As ajb said, locally is a small enough region of space-time. This is a region which is so small that the effects of gravity are negligible. So you can use special relativity here.

 

Local space-time: Put simply, imagine you are inside a small enough elevator which is in free-fall above the Earth. You feel weightless. Any objects in the elevator fall at the same rate of acceleration as you do (ignoring air effects). So these object appear to be floating alongside you. It feels the same as if the elevator is in outer space with no gravity. This is a local region of space-time.

 

Global space-time: Now imagine a second elevator at the same height above Earth but far away. The two elevators fall towards the center of the Earth. Thus they get closer together as they fall. Here the effects of gravity are observable. If you look from your elevator to the other, you see it getting closer to you over time. So you can tell that you are in a gravitational field and not floating in space. This is a global region of space-time. Over this region, general relativity is required.

 

As I say in Einstein Relatively Simple, "gravity does not show its effects locally -- over a small enough space and time. The effects of gravity are only seen on a global scale."

Isn't local speed of light affected by the spontaneous creation of particles in empty space?

 

Of course if you know that k is a constant then you can just change variables to get Y=x' and now we do have Y/x' =1 = constant.

I was just wondering......

Wherever any constant of proportionality (or even any co-efficient ) is used it is always multiplied and never added.

Is it because of our preference or is this the way nature works?

 

we will not see prior to the dark ages due to the mean free of photons, our best hope of gathering direct observational information prior to the dark ages lies in the neutrino background. However out ability to detect neutrinos is limited. As such much of the physics prior to inflation is conjectural, we also cannot simulate the temperatures involved in the lab. Though we are making progress with the LHC research.

 

for more information

 

http://arxiv.org/pdf/hep-th/0503203.pdf "Particle Physics and Inflationary Cosmology" by Andrei Linde

http://www.wiese.itp.unibe.ch/lectures/universe.pdf:" Particle Physics of the Early universe" by Uwe-Jens Wiese Thermodynamics, Big bang Nucleosynthesis

Do you mean information/detection/measurement=Creation

In mathematics, two variables are proportional if a change in one is always accompanied by a change in the other, and if the changes are always related by use of a constant.

i.e. y=kx

Doesn’t the above definition apply to

Y=k+x

Was there light at the very instant of Big Bang?

1. Some people say that an eternal God/mind is the creator of this universe, i.e the universe is contingent.

 

2. Some others say that some fundamental particle (s) has have always existed and it's their interplay, we call universe.

 

3. Still, some others say that our universe arose spontaneously from nothing.

 

 

In my view, each of the above scenario needs explanation.

 

Be it Eternal God, eternal matter or spontaneous creation, one can always ask,

 

What is the mechanism that led to eternal God, eternal matter or spontaneous creation?

 

If we get hold of some mechanism to explain the above points, again the question arises as to what is the mechanism of the mechanism that we have found out to explain the above three positions.

 

In the light of what is mentioned above, can we say that,

 

'Knowledge is infinite as there can be no end to our questions'

 

 

 

 

 

 

 

Actually, I wanted to say that the so called 'big questions'-which are considered to the source of all that there is- are also infinite.

So, in principle, one can keep on asking logical questions about the origin of the universe ad infinitum, whatever may be our answer regarding its origin.

If say after say n questions, we start getting the same answer again and again, our next question can be,

Why is it that we are getting the same answer again and again? What is the mechanism behind this sameness of answers?

It's not about the finiteness of human life, its about the logical endlessness of the valid questions that can be asked.

I find myself continually agreeing with Swansont. The argument against the reality of time can only come to life when we start exploring the consequences. To simply state that time is unreal makes our position clear, but it is uninteresting unless we can show that we can incorporate this hypothesis into a sensible metaphysical (therefore general) theory.

 

As it happens we can, but the point remains true even if we cannot. If someone says time is unreal we can always say - so what?

From what you have said, it follows,

If someone says atom/electron/matter/sun/moon/reality is unreal we can always say - so what?

IMHO this is not the kind of attitude that science strives for.

1. Some people say that an eternal God/mind is the creator of this universe, i.e the universe is contingent.

2. Some others say that some fundamental particle (s) has have always existed and it's their interplay, we call universe.

3. Still, some others say that our universe arose spontaneously from nothing.

In my view, each of the above scenario needs explanation.

Be it Eternal God, eternal matter or spontaneous creation, one can always ask,

What is the mechanism that led to eternal God, eternal matter or spontaneous creation?

If we get hold of some mechanism to explain the above points, again the question arises as to what is the mechanism of the mechanism that we have found out to explain the above three positions.

In the light of what is mentioned above, can we say that,

'Knowledge is infinite as there can be no end to our questions'

It is said that,

Speed of light is c, locally.

What does locally mean here?

Exactly right Swansont, it seems to me. Either we take time for granted or we venture into metaphysics.

 

This is precisely the point Weyl makes in regard to the continuum. Time as a series of locations is a perfectly adequate idea for physics and the only idea that would work. If it does not work in metaphysics then this need be of no interest in physics. I'm surprised it is not of more interest to physicists on their days off, but the definition of these things puts time beyond the reach of physics as a discipline. For a fundamental theory of time or anything else we would have to return to first principles. We would have to return all the way to the arguments of Parmenides and Zeno.

I think, motion is the natural state of all entities in this universe.

Rest is just a special case when two objects have the same velocity.

So, motion is inextricably linked to our physics. Change in motion is interpreted as 'time'.

In a universe, where everything is static ( even electrons and nucleons), we wouldn't even conceptualize/think of time. In fact, it's doubtful whether a universe without motion can even exist.

That all depends on context. Unless you are talking relativity, kicking a ball harder, doesn't give it more mass, it gives it more acceleration. It's (your green bit) more the reverse, the greater the mass, the greater the force needed (to give the same acceleration). You're confusing yourself by picking a parameter to change, without thinking about what that change really means.

 

 

Only if the units make sense. Force has certain units, mass has certain units and acceleration has certain units. It doesn't matter which set of units you are using (e.g. slugs or kilograms) as long as they are all consistent. It's bad to use metric for one thing and imperial for another; it's even worse to measure Force in tulips and mass in whales per second. The units have to make sense for the formula to make sense.

 

 

Well, in a way it's true. If the acceleration stays the same, a greater force will kick a ball of greater mass.

 

That doesn't mean the force is creating or changing the mass.

 

If you kick a ball with some force, you will accelerate it by some amount. If you kick the ball with more force, you won't change it's mass - you'll give it more acceleration.

 

In your example you arbitrarily chose to triple the acceleration. For F=ma to still balance, that would mean kicking a less-mass ball with the same force, or a same-mass ball with more force.

 

Edit: and it's not "... the numerical value of force that is proportional to numerical value of mass", it is "... the numerical value of force that is proportional to numerical value of acceleration x mass". You can't just ignore one parameter. If you choose to keep acceleration fixed, a greater force will accelerate a greater mass. Like kicking a heavier ball, harder, to get the same acceleration. The harder kick is not creating more mass - kick a ball of the same mass, with greater force won't give the same acceleration. You can't have your cake and eat it too.

 

 

 

No. The example was pay per day, and that's proportional to hourly rate and hours worked per day.

 

It's a direct comparison.

Thanks for elaborate reply.

I don't want to argue, I just want to clarify things

1. Suppose I apply such a huge force to a ball that its speed approaches the speed of light. In this case It would mean 'more the force, more the mass'.

I know you would tell me that I am confusing things and a separate equation is needed for such a scenario.

My 2nd point is as follows.......

2. If we need a second equation this time, does it mean that,

'an equation does not only describe nature but it describes our view point (thoughts, mind) as well?'

Thanks.

BTW, I have been banned by 'Physics Forums' over and over again . I tried different 'avatars' but they found it every time and closed my account.

So, don't ban me. It's they who directed me here.

If you kick a ball, you apply a force to it. That accelerates it, and it ends up moving at some speed. The formula F=ma shows the relationship between the force and the acceleration - and the mass of that ball.

 

If you kick the ball with 3 times the original force, it'll get 3 times the original acceleration. Makes sense doesn't it? Kick the ball harder, it'll go faster (and further).

 

If you kick another ball that has 3 times the mass of the first ball, you'll have to kick it with 3 times the original force, to accelerate it as much as the first ball with the first kick. Makes sense doesn't it? Kick a heavier ball, and it'll need a harder kick to accelerate as much as a lighter ball.

 

If you want to kick a ball with 3 times the mass of the first ball, and you want to give it 3 times the acceleration that you gave that first ball with that first kick, you'll need to kick it 9 times as hard as the first kick. (That's the a x m coming into it).

 

 

Maybe to give you a totally different (or not?) example:

 

Say you work at a shop where you get paid $5.00 an hour and you work 8 hours a day. What do you earn in a day?

 

Days pay = Hourly rate x Hours worked per day

 

Days pay = $5.00 x 8 = $40.00

 

Now, that's not saying that the concept "day" equals the concept of "dollar". The hourly rate of 5 isn't making the hours you work in a day 40 ... it's still 8. The formula is just relating the values.

 

Someone earning $10 dollars an hour, would only have to work 4 hours to earn as much. Someone earning $2.50 an hour would have to work 16 hours, to earn as much.

 

The unit analysis works out, too.

Days pay unit is dollars per day; Hour rate unit is dollars per hour; Hours worked per day = hours per day; so ...

 

dollars per day = dollars per hour x hours per day

dollars per day = (dollars x hours) per (hour x day)

dollars per day = (dollars x hours) per (hour x day)

dollars per day = dollars per day

 

... the units always need to balance; try that with F=ma.

I know what I am saying is annoying because I also know what the 'correct' interpretation is.

I just want to say that do we have to cherry pick our conclusions from any equation, when it offers other possibility/possibilities?

F=ma very well conveys the idea that Force is proportional to mass,as pointed out by Delta 1212. Doesn't it mean, greater the force, greater the mass? Why?

I don't get the idea behind 'units' because they can be set in different ways and in every system of unit, the idea that 'force is proportional to mass' will be there.

If you say its the numerical value of force that is proportional to numerical value of mass, again it means greater the force greater the mass.

Plz take pains to see the equation from my point of view ( even if it is wrong).

In the example of wages, it is the 'pay' that is proportional to the 'no. of hours worked'. This is different from F=ma situation.

F=ma means "The amount of force is directly proportional to the amount of mass times the amount of acceleration."

 

In your scenario, the equal sign means "the amount of force is directly proportional to the amount of mass" not "force and mass are the same thing."

I think here 'equal' means really 'equal' and not just 'proportional'

In this and similar examples, you have to take care with the units. You have set a = 1 m/s/s or what ever units you are using.

I take a similar example.

F=ma

Put a=3

F=3m

or

F=m+m+m

(i.e the force acting on a body = adding mass of a body to itself 3 times)

In other words, when this Force acts on a body, does the body's mass really become triple its previous mass?

Actually both wood and iron are made of protons, neutrons and electrons. Simply their configurations are different.

 

There is no two pieces of irons with equal structure (due to f.e. contamination).

and there is no two pieces of woods with equal structure.

They are just more or less similar, but never equal. Like finger prints.

 

 

First of all, you should start from analysis of what acceleration and velocity is.

 

Velocity is change of position of measured object over time.

 

f.e. we measure object to be at locations:

at t=0 x=0

at t=1 x=10

at t=2 x=20

at t=3 x=30

 

We can subtract locations of object at different times

x(t1)-x(t0)

to receive distance object traveled (in meters).

If we will then divide it by t1-t0 (in seconds),

we will receive velocity (in meters per seconds).

 

v=(x(t1)-x(t0))/(t1-t0)

 

so position of object at time t is x(t)=x(0)+v*t = x(t0) + (x(t1)-x(t0))/(t1-t0) * t

 

Velocity is constant in this example. Thus acceleration is 0, and force is 0.

 

 

Acceleration can be calculated by taking two velocities at two different times:

Imagine measured data:

t=0 v=0

t=1 v=1

t=2 v=2

t=3 v=3

 

Velocity is increasing over time.

 

Acceleration is

a=(v(t1)-v(t0))/(t1-t0)

 

Velocities in meters/seconds divided by seconds, gives acceleration in meters/seconds^2.

 

If v(t1) is equal to v(t0), velocity is constant, and we have no acceleration.

 

Force in Newtons is mass in kilograms multiplied by acceleration in meters per seconds^2.

 

Momentum is p=m*v [kg*m/s]

 

So force will be also F=(p(t1)-p(t0))/(t1-t0)

Change of momentum over time.

Thanks for the clarification.

Do you mean that in this example 'mass' and 'acceleration' interact with each other?

I think, 'mass' and 'acceleration' are properties/quantities of the same object/body.

Objects can interact, how can the quantities interact?

Hi all,

F=ma

If a=1, F=m

How can force and mass be equated and become equal. They are different entities.

It' s same like saying wood=iron

According to uncertainty principle, it's not possible to measure the position and momentum of an atomic particle ( say electron) simultaneously.

Now, suppose a scientist grows so small in size that an electron is the size of a big ball (or planet) for him.

Is uncertainity principle applicable for the scientist also.

Does it mean that it's only the size difference that we construe as quantum phenomenon.

Just being curious!

How much spacetime is there inside the event horizon of a non-spinning uncharged black hole of mass M? I know that a black hole has a Schwarzschild radius of [math]r = \frac{2GM}{c^2}[/math] and a sphere a volume of [math]V = \frac{4}{3} \pi r^3[/math], for a black hole volume of [math]\frac{32}{4} \frac{\pi G^3 M^3}{c^6}[/math].

 

However, I think the above volume would be in our metric rather than accounting for the distortions of spacetime. If you account for spacetime distortion when measuring the volume, what would you get?

I think these equations are derived assuming that normal physical laws operate inside a black hole. At such a high density, I doubt the concept of space is valid. Moreover new theories like the 'String Theory' may altogether dispense with the concept of space-time. It's only a matter of time. I pray to God to give mankind at least 'a single law' that is proof against new theories and inquiries.