Explain E = MC2

Originally posted by twhitehead
I think I am understanding better what you are saying, however, I am still certain that E=mc2 is a more general equation than E=m and it is wrong to simply call c or c2 a conversion factor just as it would be wrong to call 'a' a conversion factor in F=ma when we are talking about gravity at sea level. Just because we know a is constant (about 9.8m/s2 ) in ...[text shortened]... ng "in the special case of our universe where the speed of light is thought to be constant".

If space and time use the same units (call them N, for Natural units), then acceleration would have units of 1/N. One s in the denominator and the m in the numerator would cancel, leaving units of inverse time (or inverse natural units).

Velocity is different. There's only one s and one m. When they cancel there's nothing left.

Originally posted by zeeblebot
http://en.wikipedia.org/wiki/Speed_of_light#Fundamental_role_in_physics
...
Special relativity has many counter-intuitive implications, which have been verified in many experiments.[24] These include the equivalence of mass and energy (E = mc2), length contraction (moving objects shorten),[Note 4] and time dilation (moving clocks run slower). The factor ...[text shortened]... t mass.

Edit: replaced some characters (such as lowercase gamme with y) due to RHP mangling.

y = (1 - v**2/c**2)**(-1/2)

E = ymc**2

Originally posted by adam warlock
c is a universal, cosmological constant in modern day Physics while a (more normally g) is just an accidental value that we get near the surface of planet Earth

I am afraid I haven't got round to reading through the links you posted yet. They are rather long.
Can you at least explain to me whether you think it would be possible for a universe to have a different c, and if so whether it would affect what you are saying about the equation.
I was also not able to find any source that claimed that c is known to be a cosmological constant. Wikipedia implied it is as yet unknown whether that is the case.

Originally posted by twhitehead
Can you at least explain to me whether you think it would be possible for a universe to have a different c, and if so whether it would affect what you are saying about the equation.
I was also not able to find any source that claimed that c is known to be a cosmological constant. Wikipedia implied it is as yet unknown whether that is the case.

Can you at least explain to me whether you think it would be possible for a universe to have a different c, and if so whether it would affect what you are saying about the equation.

E=mc^2 follows from the following assumptions:
1- The speed of light in vacuum is independent from the movement of its source and from the movement of the observers.
2- The laws of Physics are the same for all inertial observers.

So if these two properties are respected in these other Universes E=mc^2 will follow.

I was also not able to find any source that claimed that c is known to be a cosmological constant. Wikipedia implied it is as yet unknown whether that is the case.

In the Physical Sciences what we know is very close to zero. And that's that. Never mind the fanfare, never mind the hype! If it's scientific that it isn't sure! So it's a good thing that you weren't able to find any source "that claimed that c is known to be a cosmological constant" c is assumed to be a cosmological constant. That's why I used the wording I used ("in modern day Physics"😉. So you start up with that assumption and some other too and derive a set of consequences that follow logically.

After this we set up experiments in the real world and see how good is the match up between our predictions and the results of controlled experiments. The match up is never 100% in any given case and no matter high the match up is the Scientific theory that is being tested is never right in any rational sense of the word right. What we conclude is that the theory is applicable on a given domain of validity.

This happens because in the physical sciences we don't get many results that are necessary and sufficient conditions. All testable testable theories are just implications and when get ourselves in a laboratory and test things out we are only testing the necessary condition. And from the validity of a necessary condition we can't conclude a dmaned thing about the validity of the sufficient condition.

Wikipedia implied it is as yet unknown whether that is the case

Can you please show me this.

Originally posted by adam warlock
E=mc^2 follows from the following assumptions:
1- The speed of light in vacuum is independent from the movement of its source and from the movement of the observers.
2- The laws of Physics are the same for all inertial observers.

So if these two properties are respected in these other Universes E=mc^2 will follow.

So clearly the speed of light is an integral part of the equation and not some apparently random (or universal) constant.
Unless I am mistaken from what little I read so far of the links you posted, c is the conversion factor between time and space dimensions. When you use 'natural units' you essentially treat time and space as equivalent dimensions, however, you can easily measure a metre in the three physical dimensions simply by rotating a ruler, not so easily for time, which is where c comes in. It tells us how to compare time to space.

Can you please show me this.
http://en.wikipedia.org/wiki/Physical_constant#How_constant_are_the_physical_constants.3F

Originally posted by twhitehead
So clearly the speed of light is an integral part of the equation and not some apparently random (or universal) constant.
Unless I am mistaken from what little I read so far of the links you posted, c is the conversion factor between time and space dimensions. When you use 'natural units' you essentially treat time and space as equivalent dimensions, how ...[text shortened]... /b]
http://en.wikipedia.org/wiki/Physical_constant#How_constant_are_the_physical_constants.3F

So clearly the speed of light is an integral part of the equation and not some apparently random (or universal) constant.

Why are you pointing this out?

Unless I am mistaken from what little I read so far of the links you posted, c is the conversion factor between time and space dimensions. When you use 'natural units' you essentially treat time and space as equivalent dimensions, however, you can easily measure a metre in the three physical dimensions simply by rotating a ruler, not so easily for time, which is where c comes in.

What does the bolded part means?

In natural units the units are redefined:

Distances are uniformly divided by the speed of light, changing units:

$ = d/c = m/v = m*s/m = s

Where $ is "relativity distance", not regular distance. Relativity distance is distance divided by the speed of light. This means units of relativity distance are meters divided by velocity, which is meters times seconds over meters, which is simply seconds.

So, "relativity distance" = regular distance divided by the speed of light. The speed of light is constant, so relativity distance is perfectly proportional to regular distance.

Seconds are perfectly proportional to meters times some constant just as centimeters are proportional to meters times some constant (in this case the constant is 1=0.1 cm/m, in the previous case the constant is c).

Therefore, just as centimeters can be used for distance instead of meters, seconds can be used instead of meters. The math is perfectly valid.

That's the mathematical reasoning for space-time equivalence.

you can easily measure a metre in the three physical dimensions simply by rotating a ruler, not so easily for time, which is where c comes in.

How many centimeters is a meter stick?

1 m*(100cm/m) = 100 cm

How many meters is a centimeter?

1 cm*(m/100cm) = 0.01 m

How many inches is the meter stick?

100 cm*(in/2.5cm) = 40 in.

How many seconds is the meter stick?

1 m*(s/3*10^8 m]) = 1/[3*10^8] s

1 m/c = 1/[3*10^8] s

How many meters is an hour?

1 hr*(60 min/hr)*(60 s/min)*(3*10^8 m/s) = 10800*10^8 m = 1.08*10^12 m

I bet you didn't know hours were so big!

Which is a greater distance; the distance from the Sun to the Earth (called an Astronomical Unit, AU), or an hour?

1 AU = 1.5*10^11 m*(1 hr/1.08*10^12 m) = (1.5/1.08)*10^(-1) hr

Wow, so the distance from the Earth to the Sun is a little less than 0.15 hr. How many minutes is that?

0.15 hr*(60 min/hr) ~ 9 min with a lot of rounding of numbers. Wow. One AU is about nine minutes plus or minus a little.

It takes a little over 8 minutes for sunlight to reach the Earth. Hmmm.

Maybe an AU is around nine minutes because it takes light about nine minutes to go one AU?

how did einstein happen to toss in c when he could have set it to 1 and left it out?

http://en.wikipedia.org/wiki/E_%3D_mc2#Meanings_of_the_strict_mass.E2.80.93energy_equivalence_formula.2C_E.C2.A0.3D.C2.A0mc.C2.B2

In a chemical or nuclear reaction, the mass of the atoms that come out is less than the mass of the atoms that go in, and the difference in mass shows up as heat and light which has the same relativistic mass as the difference (and also the same invariant mass in the center of mass frame of the system). In this case, the E in the formula is the energy released and removed, and the mass m is how much the mass decreases. In the same way, when any sort of energy is added to an isolated system, the increase in the mass is equal to the added energy divided by c². For example, when water is heated in a microwave oven, the oven adds about 1.11×10−17 kg of mass for every joule of heat added to the water.

Originally posted by zeeblebot
how did einstein happen to toss in c when he could have set it to 1 and left it out?

Usnig natural units depends upon Einstein's theories. So he couldn't use those units to derive them in the first place, could he?

I guess the simple way to look at it is - distances can be counted in hours if you're travelling at a steady speed.

Going to San Fransisco to Los Angeles takes roughly six hours at a steady speed on the freeway. So, when you want to tell someone how far you've gone, you can go "we've been driving for two hours".

Originally posted by AThousandYoung
I guess the simple way to look at it is - distances can be counted in hours if you're travelling at a steady speed.

Going to San Fransisco to Los Angeles takes roughly six hours at a steady speed on the freeway. So, when you want to tell someone how far you've gone, you can go "we've been driving for two hours".

Very nice! 😀

After some thought I think my issue is with natural units, not with the equation itself. I realize that the idea of natural units is to make time and distance essentially equivalent, but there is of course a conversion factor c. Although I realize that it is constant (or appears to be) for our universe, I am still uncomfortable with simply setting it to 1 and eliminating it.