E=mc^2

[Aki]

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?

[BlameTheEx]

Aki

 

Because it is simply the energy of motion. E=mv^2. That's the formula you would use for determining the energy of a thrown brick. The implication is that a motionless object is actually travelling at the speed of light.

 

There are 2 ways you can argue it:

 

1) Fundamental particles (of the type that sit around, not those like photons that only exist when travelling at C and have zero rest mass) may be standing waves. They are travelling at C, but just in circles, or perhaps in some more complicated mode.

 

2) An object at rest is travelling at the speed of C through the 4th dimension, Time.

 

Regardless, the formula is correct. It has been verified at Hiroshima.

[Tormod]

E=mc^2 describes the relation between energy and mass. The energy of a thrown brick is not calculated with this formula (Newton's laws are adequate), and the statement that "a motionless object is actually travelling at the speed of light" is one I have never heard of before.

 

The book E=mc2 - the biography of an equation explains why c (and c squared) are essential for the understanding of how matter and energy are related. He writes, "matter can be understood as energy in its most concentrated form".

 

He has a page on the web where he explains how to derive the formula yourself:

 

Relativity: Segourney derivative

http://davidbodanis.com/books/emc2/notes/relativity/sigdev/index.html

 

BTW, Aki, I highly recommend his book. It is a great read and it's where I read about Cecilia Payne which I mentioned to you in another thread!

 

I'm sure Bo has some insight into Einstein's theory of relaitivity, too.

[FrankM]

Since m and c are locally defined, would the energy be the same if I based the calculation

upon different numeric values for m or c?

 

Consider the hypothesis that an enterprising scientist on planet X identified the same formula. His planet

has a different rotation rate, and they use a different value for the time unit that defines the numeric value

for the speed of light. Let's make the issue simpler by assuming planet X just happens to use a unit of length

the same as the meter and a definition of mass that agrees with what we use.

 

Given the change in the one variable, is the result of the calculation the same on Planet X as it is here?

[Tormod]

I don't see how local variety would have any impact on the relativity theory. Since c is a universal constant it will be the same all over the universe, no matter what units it is defined as (as long as c is defined as the speed of light in vacuum).

 

Since c squared is such an incredibly large number, it hardly matters what m is. The same rules would apply for objects with any kind of mass, so no matter what planet you live on the theory would work since we are talking about relative sizes here. It would take the exact same amount of energy to accelerate an object weighing 1 earth kilo anywhere in the universe to relativistic speeds. Massless objects seem to trick the formula, however, but we recently discussed that in another thread (they have no rest mass because they are never at rest).

 

And I forgot to mention that the book I listed was written by David Bodanis, and the full title is E=mc2: A biography of the world's most famous equation.

[FrankM]

(as long as c is defined as the speed of light in vacuum)

 

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?

[Tormod]

Because the numbers will mean different things to different cultures. The relative values will be the same.

 

It doesn't matter if you pop binary or base ten units into the formula, nor if you use metric or imperial units. So it would not matter if you used earth units or Planet X units.

[Aki]

Originally posted by: BlameTheEx

 

 

2) An object at rest is travelling at the speed of C through the 4th dimension, Time.

 

 

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?

[Tormod]

Blame's statement requires proof. First of all, while time may be a dimension, it is not necessarily the "fourth" dimension. Secondly, since time is not a spatial dimension it is not possible to move through it. The speed of light is not a property of time. So I have no idea where Blame gets his idea that objects at rest travel trough time at the speed of light.

 

I'm afraid his statement is rather meaningless without some backup evidence.

 

First of all - what are the objects at rest moving in relation to?

[FrankM]

(Tormond) - Because the numbers will mean different things to different cultures. The relative values

will be the same.

 

It doesn't matter if you pop binary or base ten units into the formula, nor if you use metric or imperial

units. So it would not matter if you used earth units or Planet X units.

The numeric system used is not the issue, it is how a particular numeric value is defined, its unit value(s).

c is somewhat unique because it uses two "unit values" to define its numeric result, meters and

seconds.

 

Let me set the scenario a little different. The country of Exslavia, created by the breakup of a larger

country in Europe, has adopted a decimal system of time using 100,000 time segments per one earth

rotation. They still use the metric system for everything else as it fits into their decimal time system. Their

scientists calculate e=mc^2 exactly the same as the rest of the world except for one small change, they

use their unit of time, the decisec.

 

The decisec duration is 0.86400 of the second, which means their numeric value for the speed of light

would be 259020683.7 meters per decisec.

 

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.

 

The meter and the second are not true constants, thus the current numeric value for the speed of light is

a "defined" value.

[Moonchild]

Let's just put it in the simplest way we can:

 

The formula E=mc^2 is just a conversion between units of mass (kilogram) and units of energy (joules). Thus, if I had one kilogram of G.I. Joe doll, its equivalent in joules would be C^2. C^2 is just the conversion factor. Yes, it is intriguing that that's the actual conversion factor, but that's no reason to speculate there's something special or curious going on here.

[Aki]

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

[Tormod]

For simplicity just assume that light travels through standard space-time, ie 3 dimensions of space and one of time. That is the cosmological solution of the relativity formula.

[Tormod]

Originally posted by: FrankM

c is somewhat unique because it uses two "unit values" to define its numeric result, meters and

seconds.

 

No, we use two unit values to describe it. This argument is completely semantic. E=mc^2 will always give you the same results no matter what counting system you use.

 

Let me set the scenario a little different.

(snip)

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.

 

The meter and the second are not true constants, thus the current numeric value for the speed of light is

a "defined" value.

 

But you are going the wrong way. The speed of light is not invented by us. We use meters and seconds to define the observed value. The Exslavians would have to do the same. So the scientists of Exslavia would probably be intelligent enough not to put their own created values into a formula based on other numbers. If not, they would not be scientists but priests.

 

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.

[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.

 

If you were to take the speed though space in units of speed of light =1, and normal speed of time =1, then you find that for any travelling object:

 

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

 

You simply have a right angled triangle, with C, Velocity, and Velocity through time as the sides. It is as if the speed of an object is ALWAYS C and you can only change its direction within the 4 dimensions.

 

The formula is correct, but my interpretation is of course open to question.

[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) ?

[Moonchild]

Look fellas, there's nothing so "unique" about C^2. It's just a conversion factor...yes, a little curious that that's the value to convert between kg and joules, but other than that nothing serious to ponder. I hope that puts all your bad dreams to rest.