Wednesday, December 06, 2006

Time-Space Energy-Mass Equivalence

Nowadays, it is a generally known that mass is a form of energy. Einstein has pioneered this view with his time-space modeling. Within Einstein's view time and space are equivalent quantities, and time is only a fourth dimension where existence resides.

Following with that view came the inevitable conclusion: If time and space are equivalent then energy and mass are equivalent.** Below is the reasoning for that:

E = Energy equivalent to the mass (J)
m = mass (kg)
c = speed of light in vacuum (m/s)

E = m . c2
E / m = c2

If energy and mass are equivalent then the value of [ E / m ] is a unitless constant. This concludes that c2 is a unitless constant as well.

Now, say
K = positive unitless constant

Since energy and mass are equivalent, then a Joule equals a kilogram within a constant.

J = K.kg
N.m = K.kg
kg.m/s2.m = K.kg [divide both sides by kg]
=> m2/s2=K =>m2=K*s2 =>m=K.s


** A more descriptive claim would be: Time and space are equivalent if and only if energy and mass are equivalent

Fix: Removed references to unitless constants

PS: The scientific validity of claims is NOT asserted

13 comments:

The Observer said...

I dont want to sound like a fool, but I am trying to digest your assumption here, I dont think it is correct.

I dont think that assuming Mass to be another form of Energy means that Energy and Mass are equivilant.

In Einestain equation E = M.C^2

Energy resulted is equivilant to the transformation of a mass moving in speed's light.

Devil's Mind said...

As much as I know, what Einstein did was representing time geometrically. That is to say, he incorporated time as a geometric dimension. Everything followed from there.

So he practically made an equivalence between time and space. Equivalence between mass and energy followed that.

Now, there is something that a more knowledgeable person might help with. In nuclear reactions energy is released. The question is: Was mass converted to energy? OR Energy released has mass?

But even if we say that energy has mass, we still can claim a strong mathematical relationship between time-space equivalence and mass-energy equivalence.

Omar said...

as impressive as that is, something just doesn't click in what you have done.
E=mc^2 just says that energy and mass are exchangeable with a "constant" of proportionality of the speed of light squared. The word constant here does not mean "unit-less constant" as in the number 4, for instance. Rather constant here stands for the speed of light being constant, everywhere in the universe, in any physical circumstance.

c^2 has units of m^2/S^2, which when multiplied by mass, nicely works out to joules.

Omar said...

"In nuclear reactions energy is released. The question is: Was mass converted to energy? OR Energy released has mass?"

Nuetrons when weighed individually have actually a larger mass then when combined together in an atom, or when atoms are combined together. The loss of mass experienced by the neutron is what is converted to energy in a nuclear reaction.

Devil's Mind said...

We are here talking about a closed system. Does the system lose mass? I have long wanted to get a direct answer as to what is believed to happen.

What I found interesting was that in "particle physics" course we took in IGCSE, we used Joules as a unit of mass! (it was actually MeV - but it resolves to Joules since Energy = Charge * Voltage)

Tala said...

ok listen to this:

one of the fundamental laws of nature is the conservation of Energy principale, during an ineraction, energy change from one form to another, but the total amount of energy remains constant. energy cannot be created nor destroyed.
the first law of thermodynamics asserts that energy is a thermodynamic property. the second law of thermodynamics asserts that energy has quality as well as quantity. and actual processes occur in the direction of decreasing quality of energy. for example a hot cup of coffee cools to room temp. while a cup of cool coffee never gets hot by itself...

well i guess you can convert mass to energy, but what are the cases where you create mass from energy?

Book: fundamentals of fluid sciences
Author: Yunus Cengel

The Observer said...

"well i guess you can convert mass to energy, but what are the cases where you create mass from energy?"

I am not sure if they have done this on labs. I have read before about some experiment of speeding up atoms to reach speed light. I guess they have tested this up. At certain speed the physical aspects of the particles change.

Does anyone one has better info about this?

Devil's Mind said...

http://www2.slac.stanford.edu/vvc/theory/relativity.html - I have not read this text fully, once I do, I will post my understanding of it. Till then try to read it.

The Observer said...

Thanks for the link. It is a good read. I tried to understand. I guess that I have done fairly :). It reminded me of why I used to love physics at school.

Devil's Mind said...

I have to say, that no text I ever read was crystal clear about this very precise matter, and thus I am kind of confused.

consider this text: "Even in chemical processes there are tiny changes in mass which correspond to the energy released or absorbed in a process. When chemists talk about conservation of mass, they mean that the sum of the masses of the atoms involved does not change. However, the masses of molecules are slightly smaller than the sum of the masses of the atoms they contain (which is why molecules do not just fall apart into atoms). If we look at the actual molecular masses, we find tiny mass changes do occur in any chemical reaction." (source) - Here they contradict the law of conservation of mass.

In most texts I read, they say that mass is converted into energy in nuclear reactions. In many texts it is stated that the sum of mass and energy is constant, but not each independently. Thats to say, lost mass is gained as energy. (This view would mean mass is a form of energy)

After some readings (which forced me to remove all references to unitless constants), it is said that energy has mass, and that both mass and energy are conserved independently.

This requires more studying on my part as well as better explanations in texts, until then I think I have to retract my initial claims.

Thanks Omar, Tala, and The Observer for your constructive arguments.

Anyone with additional insight is welcome.

The Observer said...

You do your reading and keep us informed :)

Devil's Mind said...

Read this.

The proposition that time and space should have the same unit is not after all without supporters.

In the article I reference above, some scientists suggest that waves and particles should merge as one concept. Which means that energy is the same concept as mass. Hence time and space are the same concept! And thus, they are better represented with the same units.

So if the proposition to unify waves and particles as one concept is taken, this will indirectly mean that time and space are actually the same thing!

aaronoia said...

Yes, wave-particle duality is a discovery of quantum mechanics. Relativity shows that space and time are inseparable and thus should be considered as one. And string theory, which works to unify quantum mechanics and relativity, asserts that matter is nothing more than one-dimensional strands of energy vibrating in the space-time fabric; or matter is just organized energy being expressed in the third and fourth dimensions (time-space), kind of like a hologram.
The idea of there being only one form of existence, only energy, instead of two, energy and matter, is more parsimonious and makes sense when you think about it.
Why would there be two different types of existence that interact with each other instead of just one type of existence that interacts with itself by taking different forms? It's actually simpler that way.