E=mc^2

[Aki]

Originally posted by: Tim_Lou

i think i got it.

imagine x-axis is time, y-axis is space.

there is a vector in the y-axis, a particle is travelling at a certain veloctiy in space.

there is also a vector in the x-axis, this particle is travelling at a certain... "velocity" in time.

 

and resultant of the 2 vectors is going side way... what does that mean?

if i change the "angle" to the x-axis a little bit, with the same total speed, the velocity in time-axis and space-axis would differ...maybe that could explain why when an object travel in a slower velocity, the velocity in time is larger.. if so... everything's speed is a constant! (the side way magnitude)

 

"(velocity through space) ^2 X (velocity through time) ^2 = 1."

hey, is it suppose to be

(velocity through space) ^2 + (velocity through time) ^2 = 1? (+ instead of X) ?

 

Blame and Tim Lou, it's starting to make some sense now.

 

Since light travels in a fast velocity, then does that mean that its time velocity is very small. Or is light an exceptional case?

[Tormod]

Originally posted by: BlameTheEx

Tormod/ Aki

 

Well, there IS some evidence of the idea of our travelling through time at the speed of light.

 

It may only be a way of looking at it, but the faster you travel through space, the slower you travel through time.

 

I don't get the reasoning behind this (and I still don't see any evidence).

 

Time dilution is not the same as travelling in time. If everything is moving at the speed of light, then

 

a) from what? towards what?

B) how do you know everything travels at the speed of light, and how is that speed measured?

c) why is there a limit in the direction you can travel in time but not in space?

[Freethinker]

Originally posted by: FrankM

If the Exslavians calculated e using their numeric value for c it is going to be smaller.

It is not the numeric system used, it's the definition of the units that controls the numeric value.

But "e" is measured in Joules which is measured by watts x seconds. Since the time element is common to both sides of the equation, the results would follow correctly in any various time based measurement variables.

[Freethinker]

Originally posted by: Tormod

I don't get the reasoning behind this (and I still don't see any evidence).

 

Time dilution is not the same as travelling in time.

Ah yes, this has been the stumbling point with almost all discussion with Blame on this. Claims of time dilation that are not supportable. And when we try to get proof, the request is ignored.

 

Relativity shows us that it would be impossible for matter to travel at the C as it would take an infinite amount of energy to accelerate matter to that speed. Minor complication to claiming that we ARE travelling at the speed of light.

[FrankM]

Tormond - 11/07/2004 10:57 AM - In Exslavia, E=mc^2 would probably look different because they

will have to rewrite all the formulas (because they have rewritten the units used to create the equation).

Nobody is claiming that E=mc^2 is a universal constant. However, what the formula describes is a

universal ratio, namely the relation between energy and mass.

The Exslavians have no need to change the formula, their selection of a different definition for their time

unit (digisec) is just as valid as the arbitrary selection (definition) of the meter and kilogram.

 

The formula does not describe a ratio, a ratio is a comparison between two values and gives a

quotient.

[Tormod]

Originally posted by: FrankM

The Exslavians have no need to change the formula, their selection of a different definition for their time

unit (digisec) is just as valid as the arbitrary selection (definition) of the meter and kilogram.

 

Sure. So if I build a clock that has 361 degrees I can then tell the whole world that their formulae for calculating, say, longitude or the position of stars in the sky are all wrong because my definition of degrees is better than theirs.

 

E=mc^2 is based on the assumption that c equals the speed of light in a vacuum. It does not matter how you express that value. If the speed of light happened to be 1,923,232,343 Exlavian minimalias per cubic litre it would not change the outcome one bit - as long as the end result of the equation is *also* noted in Exslavian notation.

 

However, when they redefine the second as in your example they undermine Einstein's formula because they will no longer get a correct value for c. Thus they will need an adjusted version of the formula.

 

Maybe this example is better:

In Exslavia, I am asked to measure the time it takes for an athlete to run the 100 meter dash. I measure it to be about 8.64 seconds. It is a world record! Wow!

 

But then I ask my (very intelligent) Norwegian colleague to measure it with his own watch. Hm...his clock shows an even 10 seconds.

 

What is wrong here?

[Tormod]

The formula does not describe a ratio, a ratio is a comparison between two values and gives a

quotient.

 

Yes. I meant to write "relationship". Sorry.

[Bo]

Aki wrote:

I've always wondered why you have to multiply the mass with the speed of light squared? Why not something like the Plank's energy or something else?

 

This arises if you calculate Kinetic energy's in (special) relativity. The point is that in relativity the notion of mass, is dependent on the relative speed of 2 observers; the faster the relative speed, the higfher the mass. This increase has a dependence on c. (well actually: v/c: the ratio (relative speed)/(speed of light). Lets call this 'increased mass' m and the 'rest mass' m0.

We then get: Kinetic Energy = mc^2-m0c^2. or: the kinetic energy is equal to the increase in mass, multiplied by c^2. Here the c^2 arises, because the change in mass is dependent on v/c.

Just to complete the story: we can rewrite the above equation as: Total energy == mc^2 = KE + m0 c^2

(i use == to say 'is defined by'), to get the standard equation in relativity.

 

 

Frank wrote:

The topic "Perfect Physical Constant" illustrates that how we define the speed of light is dependent upon

the units, and the meter and the second are man made. The speed of light is constant, but it can

have any numeric value we choose depending upon the assigned units. How can an energy formula be

valid if the numeric results can be varied by just changing the units?

 

The point is that the notion of mass (m) or energy (E) are also man-made. 1 Joule energy for example is defined as 1 (kg meter^2)/(second^2). So changing the units of meter, would also change the units of energy. The net difference would be that the formula would still be correct. This is a symmetry all physical formulas have; in other words there are no absolute units.

 

 

Aki wrote

This is kinda off topic, but does light travel at the same speed in other dimensions?

Well at least in the 3 spatial dimensions we see it moves at the same speed; i dont think we have any guarantee that the vacuum of other dimensions has exactly the same properties as the 3 we see, but i'm not really sure...

 

Blame wrote:

(velocity through space) ^2 X (velocity through time) ^2 = 1.

Well this is almost trivial... the best definition i can think of of 'velocity through time' is (time)/(distance). You take the squares to get rid of any vectorial dependence, and then you basicly have (time*distance)/(distance*time)=1. So i dont see anything new, i see the same thing as before, just redifined as v_new= 1/v_old

 

 

 

Bo

[BlameTheEx]

Tim_lou / All

 

Quote:

_________________________________

hey, is it suppose to be

(velocity through space) ^2 + (velocity through time) ^2 = 1? (+ instead of X) ?

____________________________________________________________

 

Boy is my face red! You are right of course. Sorry people.

 

Tormod.

 

a) From past to future.

 

B) I don't know, and could be wrong, but the maths makes it look that way. Time dilation can be measured in high velocity particles, by rate of decay. You just set (speed of decay)=1 for particles at rest. The experiment has been repeated many times. The faster they go, the slower they decay. This even though they are spinning round a cyclotron, and, as they are going round in circles, never get much nearer or further from an observer.

 

c) Because there is only one dimension for time, and 3 for space. I have argued before that the direction of time may be only a locally valid direction. The idea being that each point in space might have its own, and otherwise the 4 dimensions are equivalent, but that is a topic in another thread. The normal belief is that each observer has his own valid direction for time within the 4 dimensions.

 

Bo

 

You'r right, it IS almost trivial, but then I wasn't pretending otherwise (Er, at least it was once Tim corrected my error in the maths. Lol.), but it does show that the formula for time dilation is consistent with the idea of travelling through time at C. Of course I admit "consistent with" is not necessarily proof. Um, could you explain Vectorial dependance?

[Tormod]

Originally posted by: BlameTheEx

B) I don't know, and could be wrong, but the maths makes it look that way. Time dilation can be measured in high velocity particles, by rate of decay. You just set (speed of decay)=1 for particles at rest. The experiment has been repeated many times. The faster they go, the slower they decay. This even though they are spinning round a cyclotron, and, as they are going round in circles, never get much nearer or further from an observer.

 

Okay, I see the point you're making.

 

But there is a fallacy in this argument. Time dilation is relative. So from the particle's point of view the world around it will appear to slow down infinitely. The particle would experience it's own time as passing normally. This does not in any way require that it travels at the speed of light in the time dimension (I fail even to understand where the time dimension enters the equation here).

 

Sorry Blame, I don't mean to be obnoxious, but I really don't see how this mathematical trickery can be considered proof of any kind.

[BlameTheEx]

Tormod

 

Yep, Time dilation is relative, but this doesn't discount the argument.

 

The idea is that ANY object is travelling through time at the same speed in its own esteem. How fast its is travelling in time from another observes point of view depends on how much they share the same vector of time. The observer DEFINES the direction of time within what are otherwise 4 indistinguishable dimensions.

 

I am sorry that you consider the maths to be trickery. If it is there is not much I can do. The maths is an honest, simple, and well tested description of the truth. If we have been tricked complain to God.

 

Aki

 

Answering your earlier question

Quote:

_________________________________________________________________

that sounds interesting... I never realised that when we're sleeping, we're actually moving at the speed of light. So does this mean that we are an infinite amount of energy in the 4th dimension?

________________________________________________________________________

 

No.

 

The whole idea behind E=MC^2 is that like photons ALL particles travel at the speed of light. They are just not moving very far because they are standing waves. From this point of view, ALL particles have zero rest mass, hence they can travel at the speed of light with only finite energy. ALL the energy in matter is kinetic.

 

If you could bottle a photon (imagine a bottle made out of perfect mirrors) and weigh the bottle you would find that the bottle is heavier. E=MC^2 would defines the relationship between the weight of that photon and it's energy too. Indeed there is the opinion that an electron IS a photon somehow caught in a standing wave - a sort of a bottled photon.

[FrankM]

In Exslavia, I am asked to measure the time it takes for an athlete to run the 100 meter dash.

I measure it to be about 8.64 seconds. It is a world record! Wow!

I assume you were using an Exslavian stop watch to measure the 8.64 value, which would be in

digisecs rather than seconds.

 

I see no reason why we should be saddled with medieval units when we know that a decimal time

system would be easier to understand. I wouldn't define a circle of 361 degrees, I would be more logical.

My calculator already converts minutes and seconds of a degree into their decimal equivalents. A

1000 decideg circle would eliminate the cumbersome base 60 "degree" system currently in use.

 

Was the mass unit kilogram (kg) created to facilitate Einstein's formula?

[Bo]

hmm i'm affraid i just dont understand what you mean with velocity through time... especially if you travel through time with speed c. A main point here is i think c is given in meters/second. Travel through time would be given in seconds/seconds? or seconds/meter? (my initial guess, but (1/v)^2+v^2=1 only works for specific values of v)(whereas a * would work always of course)

 

As for the analogy given by tim: the 2 initial vectors on the time (t) and space(x) axis both mean that you travel a certain distance through time and space, to get to a certain point (x', t'). The vectors don't represent velocities. to get the velocity, you take the change in x-direction and devide that by the change in the t-direction. Or v=x'/t'. Or: "the amount of change in x, when you change 1 unit step in t".

of course you can do this definition the other way around: "the amount of change in t, when you change 1 unit step in x", and this would just be t'/x' or 1/v

 

 

Um, could you explain Vectorial dependance?

well, 1 is a scalar ('just a number'), but speed is a vector (it has direction). You can't write an equality between a scalar and a vector. (something with direction cant be equal to something without direction). The most obvious way to go from a vector to a scalar is by taking the length of the vector. this is done by taking the squareroot of the innerproduct of the vector. in my interpretation of the formula the square root wasn't necessary, because sqrt(1)=1.

so for example: a vector v=(x1, x2), then the length of v is: sqrt(v.v)=sqrt(x1^2+x2^2).

 

Bo

[Tormod]

Originally posted by: FrankM

In Exslavia, I am asked to measure the time it takes for an athlete to run the 100 meter dash.

I measure it to be about 8.64 seconds. It is a world record! Wow!

I assume you were using an Exslavian stop watch to measure the 8.64 value, which would be in

digisecs rather than seconds.

 

Of course. That was the point. That's why your Exslavian scientists appear to get different results when they apply their values to Einstein's formula. Yet their result is correct (in Exslavian notation, as I pointed out). Any scientist using metric values would of course know that to read the Exslavian result they would have to convert the value.

 

this is *exactly* how currency exchange calculators work (except the banks always have different figures when you buy than when you sell).

 

I see no reason why we should be saddled with medieval units when we know that a decimal time

system would be easier to understand. I wouldn't define a circle of 361 degrees, I would be more logical.

My calculator already converts minutes and seconds of a degree into their decimal equivalents. A

1000 decideg circle would eliminate the cumbersome base 60 "degree" system currently in use.

 

Neither would I defined a circle of 361 degrees. The point was that you can't just change the definition of a second and expect it to work with formulas that assume different values. So if the Exslavians have a different value for c then the value MUST instantly give 300,000 km/s when you press the "Old standard" button on their calculator.

 

Was the mass unit kilogram (kg) created to facilitate Einstein's formula?

 

FrankM, you keep turning the argument upside down. Einstein's formula does not require kilograms, nor seconds, to work. It only requires that the person trying to calculate E has a valid value for m and c.

[Freethinker]

Originally posted by: BlameTheEx

Yep, Time dilation is relative, but this doesn't discount the argument.

No, but not being able to ever validate it does.

[FrankM]

Einstein's formula does not require kilograms, nor seconds, to work. It only requires that the person

trying to calculate E has a valid value for m and c.

 

That was the whole point of the topic "Perfect physical constant". When you examine each of the SI

definitions of physical science units, how many of them can claim to have a valid relationship to

another? It was conceded that none of the physical science unit definitions are true constants

in themselves.

 

I do not contend that Einstein's energy to mass relationship formula is invalid on its face, it is not being

calculated using valid units. In practice, scientists have yet to achieve the actual calculated energy

yield from Einstein's formula using the given units. There are all kinds of explanations given for not

achieving the expected energy yield, mainly, we aren't doing if efficiently enough. Maybe they are using

the wrong "units".

[BlameTheEx]

Bo.

 

Velocity through time.

 

Hm. I could take the stand that if we travel through time from past to future, we must travel at a speed. However such an argument is just using words.

 

Ok. Time dilation occurs due to 3 known effects: Gravity, Velocity, and whatever causes the redshift of the hubble constant (Ok, Ok, Current wisdom is that redshift is due to velocity too, but it does no harm to keep an open mind). There is nothing wrong then in the idea that the "speed" of time can be a variable. But is it speed? Well, sort of. Time is the measure of things happening. ALL measures of time are measures of motion.

 

Take radioactive decay as a pertinent example. The components of an atom are in constant motion - spinning in orbits, of greater or lesser complexity. Due to the uncertainty principle there is a fixed chance of an interaction with every rotation. The slower the spin, the greater the time before an interaction occurs and the atom decays.

 

In the case of velocity caused time dilation that is what happens. The speed is reduced - only from our observers point of view of course.

 

Gravity caused time dilation is perhaps different. As best as I understand Einstein's theories the speed remains the same, but the distances increase. Space is stretched. I rather prefer the idea that speeds drop in this case also, rather than muck around with warped space, but that is a topic in another thread.

 

But what about my contention that everything travels at C? Well, that is the back to E=mc^2. The formula is dependent on that very idea. Consequentially, as C is a constant, the faster an object travels in space, the lower the component of velocity remaining for its internal motions.