How Does It Add Up

When people think about E = MC2, they tend to focus on the energy side of the equation, how much energy a tiny winy amount of mass would unleashed. But here we will try to look at it from the mass side of the equation.

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Let’s take a 20 year male, his height is 180 cm (5” 11’) and weight 98 kilograms (216 pounds). More than 20 years ago, this male didn’t exist.

In physics term, his weight of 98 kilograms, 21 years ago didn’t exist.

Now, we have a mass, that 21 years ago didn’t exist. The mass is not 98 kilograms, mind you, 98 kilograms is the weight of the man on Earth, which has a gravity constant of 9.8. To add to the caveat, the actual measurement of weight is actually Newton, not Kilogram.

The amount of this mass is 98 Newtons divided by 9.8 N/Kg, which is 10 Kilogram.

Since this male didn’t exist 21 years ago, his mass of 10 Kg also didn’t exist 21 years ago.

Think about it, 21 years ago, nothing; today, a 10 Kg of mass. 

In the span of 20 years, this mass of 10 Kg has been created. According to Einstein equation, for this male to exist, his mother and his body need to gather energy of 10 x 300,000,000 x 300,000,000 = 9 x 1017 Joules. That’s nine hundred thousand trillion Joules.

How much is 1 Joule?

Well, according to Wikipedia1 (OK, I’m not the most robust of scientific writer), one Joule is approximately:

  • the energy required to lift a small apple one metre straight up.
  • the energy released when that same apple falls one metre to the ground.
  • the energy released as heat by a person at rest, every hundredth of a second.

That doesn’t sound like much no?

How about 1 billion joule? That’s 1/6 of the chemical energy in one barrel of oil.

How about 1 trillion joule? That’s 1/60 of the energy released by the Hiroshima atom bomb

To put that to perspective, for this male to exist, his mother and him, need to gather energy equal to those released by 15,000 Hiroshima atom bombs.

And so far we only included his mass and have not included the energy he released at rest (100 Joules/ second) and at more vigorous activities (varies).

We won’t fuss about the energy he used because it would be relatively small to the energy needed to create his mass (20 years of rest would release heat equal to 63.1 billion joules, or 10 barrels of oil)

Now, is it conceivable that this man and his mother, in the span of 20 years, has consumed 15,000 thousand Hiroshima bomb? Or 150 million barrels of oil?

But something must have happen, because his mass didn’t exist 21 years ago and Einstein’s equation dictate that for his mass exist, energy in the amount of 9 x 1017 Joules need to be converted into mass.

Talking about consume, here might lies our solution. This male might not consume 150 million barrels of oil, but he consumes food.

Food has mass, so it’s very possible that his mass resulted from some sort of ‘mass transfer’ from the food he consumes to his body tissues. (On a side note, if this is the case, considering that the food is broken down and then reassembled, the ability of the human body to disassemble and assemble mass is remarkable)

How much food would he consume in 20 years of his life? Well, some references2 mentioned that the average person would consume 60-100 thousand pounds of food in their lifetime. Let’s take the average at 80 thousand pounds, assume that the lifespan for the average person is 60 years, and that one take less food in their first 20 years (the baby and children phase).

From that, let’s take a rough estimate that this 20 year old male would had consumed 22,000 pounds of food, or 10,000 Newton of food (weight of food), or 1020 kilogram of food (mass of food).

In order to gain his 10 Kilogram of mass, the person needs to consume 1,020 Kilogram of food.

As we can see, there’s a lot of inefficiency in the mass transfer process. And this inefficiency happens again and again in the food chain. That’s the whole point of why some say that eating soybeans and wheat is better to the environment than eating cow, since there’s a lot more energy and resources needed to make a cow.

Now, let’s take a much macro view. We’ve considered the mass of one male. And we considered it because in terms of physics, the existence of this male is really an amazing thing since he represents the creation of mass.

Let’s consider all humans that doesn’t exist 20 years ago. According to US Census Bureau3, there are now 2.415 billion people under 20 years old.

Let’s estimate the total mass of this 2.415 billion people with the following table

Age group Number of population Average Weight (N) Average Mass (Kg) Total Mass (Kg)
0-4 621,862,368 9.8 1     621,862,368.00
5-9 601,126,842 19.6 2  1,202,253,684.00
10-14 595,000,326 29.4 3  1,785,000,978.00
15-19 597,568,265 49 5  2,987,841,325.00
Grand Total of Mass (Kg)  6,596,958,355.00

We estimate their mass at 6.6 billion kilogram

 Reverting to our how much food they need to consume, well, in aggregate, they will consume 6.6 billion kilogram x (1 / 10 kilogram) x 1,020 kilogram food = 672 Billion Kilograms of food (mass)

All of this food would eventually derive their existence from the sun. No matter how you trace this mass back, almost all of this mass will have to come from the sun, since the sun is the ultimate source of energy for life on earth.

For this stage, we exclude things from both the supply and demand side of energy. On the supply side, we excluded geothermal energy, energy coming from inside the earth.

On the demand side, we excluded 4 things:

– Other animals or plants involved in the food chain leading to the human food

– The energy needed to create animals and plants that are in existence yet less than 20 years old (since the animals and plants involved in the food chain would by definition, perished)

– The energy to sustain the life people above 20 years old

– And the energy to sustain the life of all animals and plants in existence

Now, to create that 2.415 billion humans, 672 Billion Kilograms of food needed to be consumed, and thus created.  And since all of this food can be traced to the sun, it begs the question, how much energy does the earth receive? How much mass, in theory, the sun give to the earth? Is the mass of 2.415 billion of 20 year old human bigger or smaller than the mass sun give to the earth for 20 years?

According to NASA4, the earth receives 1.8 x 1017 Joules of energy from the Sun every second, assuming perfect energy to mass conversion, this will result to 2 Kilogram of mass per second.

So, in 20 years, the earth will receive 7,304 days/ 20 year x 86400 seconds/ day x 2 Kg / second = 1.26 billion Kilogram of mass from the sun.

Now, 672 Billion Kilogram of food is a far cry from 1.26 billion Kilogram of mass resulted from the Sun.

Come to think of it, there are 2.415 billion humans created in the last 20 years, yet the Earth only captures during 20 years, at perfect conversion, 1.26 billion Kilogram of mass.

This translates to 0,5 kilogram of Mass captured by the Earth to each person, or in weight, 5 Newton per person.

And if we remember the 4 demand exclusions we set above, the mass distribution would be much lower.

 How can it be that there are 2.415 billion of humans created in the last 20 years, yet in the same period of time, the earth only captures 1.26 billion Kilogram of mass from the sun?

 Several potential answers:

  1. My calculation is wrong. Feel free to check and give me feedback.
  2. The layers of assumptions used cause the mass number to be wrong. This could be true, but it doesn’t explain the existence of 2.415 billion humans yet only 1.26 billion Kilogram of mass receive from the sun
  3. The mass translation process is wrong; you don’t create 2.415 billion humans from the sun. Energy is not created or destroyed, if we exist, that means us, or what we eat, or what they eat, comes from energy. And right now, we’re looking at a whole bunch of mass, that previously doesn’t exist.
  4. Our population data is wrong. I quote US Census Bureau
  5. Our estimate on the number of energy and mass received from the sun is wrong. I quote NASA.
  6. Our mass, or our food chain’s mass, are derived from mass created in the past. And thus our mass creation are negative respective to the amount of energy derived from the sun. There are some questions on whether we are using more energy than the sun produce, but most of these questions focuses on the energy that we use, rather than the energy needed to make us, our mass, exist. 
  7. Something is wrong with the E = MC2 equation. But then, how do you explain the Kilotons or megatons written on Nuclear warheads? Well, if these numbers are derived from the E = MC2 calculation itself, then we have a circular formula. Unless we put a blast measurement tool next to an exploding TNT, record the entire blast force resulting from the explosion; put the same to an exploding Nuclear warhead, record the entire blast force resulting from that Nuclear force; then record the value of the two; then we only have a theoretical value of whether that nuclear blast is really x amount of TNT. The best thing we have to such a tool is seismic data, but I don’t know whether the explosion of a single TNT would give the same characteristics than with a Nuclear bomb, and thus whether the two would be really comparable.

 

Then, what is the exact reason for the mismatch? I don’t know, perhaps there are other reasons beyond what I outlined above, but I do know this, something doesn’t add up.

Reference:

  1. http://en.wikipedia.org/wiki/Joule
  2. http://www.thewolfeclinic.com/newsletter/newsletter0107.html; http://wiki.answers.com/Q/How_much_food_do_you_consume_in_a_lifetime
  3. http://www.census.gov/ipc/www/idb/worldpopinfo.php, http://www.census.gov/cgi-bin/broker
  4. http://helios.gsfc.nasa.gov/qa_sun.html#sunenergymass.

Quoted from the above site:

“At its distance of 1 Astronomical Unit (150 million km), the Earth is hit by the Sun’s energy flux F = 1400 Joules/s/m2. We call this quantity the “solar constant”, as this value averaged over each year is constant within better than 1% over time. With an Earth radius of approx 6400 km, the area, which is (pi * Earth’s radius)2, with which the Earth intercepts sunlight is (pi * Earth’s radius)2 = 1.3 x 1014 m2 making the amount of energy captured by the Earth each second:

F * (pi * Earth’s radius)2 = 1.8 x 1017 Joules/s

According to the same procedure as above this makes the mass to produce this amount of energy per second:

Mass captured as sunlight per second = 1.8 x 1017 / (3 x 108)2 kg/s = 2 kg/s”



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