What are the dimensions of energy – quora ortega y gasset


Energy is defined as the ability to do work. Work is defined as a force acting through a distance so the basic dimensional units of energy are force x distance. Depending on which measurement system you favor, this could be foot-pounds, Newton-meters, or dyne-centimeters. Any combination of force and distance could be used to measure energy so you could have something like ounce-rods if you want to be different. Some of these units have defined names. A Newton-meter is defined as a Joule. (You frequently see Joules on surge suppressors.) A dyne-centimeter is defined as an erg. (There is an exercise machine named Ergometer.)

Energy comes in many forms so we have many special dimensional units for different forms on energy. On our electric bill, the amount of electric energy used is measured in kilowatt-hours (KH-h). Thermal (heat) energy is measured in calories or British Thermal units (BTUs). A calorie is the amount of energy necessary to raise the temperature of 1 gram of water by 1 degree Celsius. Similarly, a BTU is the amount of energy needed to raise the temperature of 1 pound of water by 1 degree Fahrenheit. There are also special units for magnetic energy, electric field energy, radiant energy, light energy, and sound energy. Since all of these special units of energy are still measuring energy, we can convert from one unit to another. 1 BTU is 1055.06 Joules. 1 KW-h is 3.6 million Joules. It is easy (today) to convert from one unit to another. You can type something like “36 ergs in foot pounds” in Google. It will tell you that 36 ergs equals 2.65522e-6 foot pounds. (That is 0.00000265522 foot-pounds. Ergs are small.)

One conversion worth mentioning is for nutritional energy. That chocolate chip cookie is listed as containing 200 “calories” but these are not the same calories that scientists and engineers use. Nutritional “calories” are really kilocalories (1000 calories). My diet analysis comes out to about 2000 “calories” per day, but it is really 2,000,000 calories.

It’s an interesting question, because it inherently contains an ambiguity which, if we research carefully, we may be able to solve in complementary fashion. Namely, there are “units” of energy, i.e. joules or kcal or foot-pounds or watt-hours or electron-volts or kilotons of TNT or solar-masses. But all of these are reducible to the SI units of kilograms x square meters / square seconds. Of course you can smaller and more convenient units according to your application, but they are all easily mathematically interchangeable by conversion factors, along with the corresponding units. This is the first meaning of “dimensions” in this context.

The second way in which energy involves dimensions involves how an energy packet manifests in space-time. Anything can have energy, in various ways or forms. For example, a photon of given frequency has a specific energy quantity; at the same time, the photon, when localized, is point-like, and has zero dimensions. But let’s take a tank of gasoline: it obviously has energy. Although the fuel takes up space, as a material substance, the energy itself here is a scalar quantity without any particular dimensions, beside those of energy as a quantitative amount of a certain unit, as explained above. Thirdly, energy can be attributed to mass in motion. But here, different from “momentum” which is mass x velocity, having the units mass x length / time, it is mv^2/2, thus it has the units mass x length squared / time squared. This expresses that the essence of energy is not merely the velocity, but the acceleration invested to attain that velocity. That’s where the energy becomes associated with a given material object.

"Dimension" is a word often misused. I think we all agree that a dimension is something that is measurable. Another definition of dimension is that it gives a ‘freedom of motion.’ But then we can’t really say that time is a dimension because we can’t really move in it, can we?

As said by someone else, Quantum theory talks about 11 dimensions and ‘branes’ that are ‘parallel universes.’ This is only one of many theories. It is not because it can be put down as an equation that it exists, even less that it can be understood. Let me give you a simple example: Relativity defines space and time as four dimensions. It means that wherever you are in the universe, you are at its center. Can you make a drawing of it? No, you can’t. But let me explain it this way: Imagine you live on earth witout continents; only sea. Then imagine you’re a fish in the middle of the sea … Hang on, did I write ‘middle?’ How can you be in the middle of the sea if it has no shores?

To figure out the universe, you can remove one spacial dimension and see it as a … sphere. But it is not a sphere. It is … the universe in space and time. And that’s why the Hubble red-shift shows all galaxies getting away from us, as if we were the center. And that’s why the Cosmic Microwave Background is coming from everywhere in the sky: because the Big Bang is not a point in space but a sphere around us!