4 ms·

Probably dumb question... and one I probably knew the answer to at some stage... why does the equation showing the conversion from mass to energy involve the co

Probably dumb question... and one I probably knew the answer to at some stage... why does the equation showing the conversion from mass to energy involve the constant of the speed of light?

maxxxxx 8y ago
E=mc2. The amount of energy in mass is determined by the speed of light. Not sure if I am phrasing this correctly...
- mikekchar 8y ago
  I wonder if it would be more understandable to say that m = E/c2. In other words what we think of as mass is really just a measure of energy bound up in particles. There is a relationship between mass and the speed of light that people may or may not know about. As you accelerate a particle towards the speed of light, the mass actually increases. Since the mass increases, it's harder to accelerate, which means that you need more energy to make it go faster. To get it to the speed of light you would need infinite energy and it would have infinite mass. We can also rewrite the equation as c = sqrt(E/m). In other words, the speed of light is determined from the ratio of energy to mass in the system. When looked at from this perspective, it's not really that surprising that the ratio of energy to mass is a constant. What's kind of surprising is that this constant is the speed of light. Even just trying to figure out how the units might work is a bit mind bending -- m/s = sqrt(g/J) I think this is where you start to understand that the concept of space, time, energy and mass are all intertwined. We kind of think of them as separate things because from our macro perspective, that's how they look. Under the hood, though, they are all intricately bound together. The consequences of special relativity (where this equation came from) is that space, time, and mass are functions of energy, which is both super cool and super confusing :-)
epicureanideal 8y ago
I don't think there's any "first principles" or philosophical/logical explanation for this... it's just an empirically determined fact, I think...
- deleted 8y ago
  [deleted]
i_am_proteus 8y ago
This is not a dumb question. The relationship was derived by some of physics' best minds in the early 20th century and requires an understanding of other physical principles and calculus to explain. I can't think of a concise/non-technical explanation. This Feynman lecture is about as close as you'll get: http://www.feynmanlectures.caltech.edu/I_15.html http://www.feynmanlectures.caltech.edu/I_15.html
dsr_ 8y ago
Mass is energy, energy is mass. What's the difference? They are at different points in a curve that relates space to time. If you trade away all the time, you get a maximum velocity: c. So the things moving at c don't experience time, and have momentum but not mass. http://www.math.ucr.edu/home/baez/physics/ParticleAndNuclear/photon_mass.html http://www.math.ucr.edu/home/baez/physics/ParticleAndNuclear... In the same direction, if you take a mass and accelerate it, it experiences less time. There you have relativistic time dilation, as beloved by science fiction stories. https://en.wikipedia.org/wiki/Time_dilation https://en.wikipedia.org/wiki/Time_dilation And you simultaneously get length contraction in the direction of each velocity: https://en.wikipedia.org/wiki/Length_contraction https://en.wikipedia.org/wiki/Length_contraction These are all aspects of the same thing. Really not a dumb question at all.
gpderetta 8y ago
IANAP, but I'll give a try: it is needed so that the units (mass, i.e. kg) in the equation balance out when expressed in the SI measurement system. For historical reasons we measure time and space using different units (seconds and meters in SI) but phisically space and time ought to be measured with the same unit. It is possible to construct such a measurement system, indeed many of them, known as natural units[1]. In natural units, c, i.e the ratio between the space and time unit, would be simply be set to dimensionless 1. In such a measurement system the E=mc^2 equation simply reduces to E=m i.e. each unit of max correspond to one unit of energy. [1] https://en.m.wikipedia.org/wiki/Natural_units https://en.m.wikipedia.org/wiki/Natural_units
jimmcslim 8y ago
Thank you all for your interesting and erudite answers!
infradig 8y ago
Lookup kinetic energy on Wikipedia. It will take you from KE = 1/2 Mv^2 to E = Mc^2 in a few small steps.
scentoni 8y ago
To comment on other answers about E=mc^2 and KE=1/2 mv^2, these are just different parts of the relativistic energy E=mc^2 cosh(eta) where eta is the velocity parameter. https://en.wikipedia.org/wiki/Proper_velocity https://en.wikipedia.org/wiki/Proper_velocity In terms of the coordinate velocity v, E=mc^2 cosh(atanh(v/c))=mc^2 / sqrt(1-(v/c)^2) = mc^2 (1 + 1/2 (v/c)^2 + 3/8 (v/c)^4 + ... So mc^2 is the irreducible energy due to mass and isn't relevant at low speeds because it doesn't change; the first-order approximation of kinetic energy is just 1/2 mv^2 and higher order terms aren't significant at low speeds. http://www.wolframalpha.com/input/?i=cosh(atanh(b) http://www.wolframalpha.com/input/?i=cosh(atanh(b))

Probably dumb question... and one I probably knew the answer to at some stage... why does the equation showing the conversion from mass to energy involve the constant of the speed of light?

maxxxxx 8y ago

E=mc2. The amount of energy in mass is determined by the speed of light. Not sure if I am phrasing this correctly...

mikekchar 8y ago
I wonder if it would be more understandable to say that m = E/c2. In other words what we think of as mass is really just a measure of energy bound up in particles. There is a relationship between mass and the speed of light that people may or may not know about. As you accelerate a particle towards the speed of light, the mass actually increases. Since the mass increases, it's harder to accelerate, which means that you need more energy to make it go faster. To get it to the speed of light you would need infinite energy and it would have infinite mass. We can also rewrite the equation as c = sqrt(E/m). In other words, the speed of light is determined from the ratio of energy to mass in the system. When looked at from this perspective, it's not really that surprising that the ratio of energy to mass is a constant. What's kind of surprising is that this constant is the speed of light. Even just trying to figure out how the units might work is a bit mind bending -- m/s = sqrt(g/J) I think this is where you start to understand that the concept of space, time, energy and mass are all intertwined. We kind of think of them as separate things because from our macro perspective, that's how they look. Under the hood, though, they are all intricately bound together. The consequences of special relativity (where this equation came from) is that space, time, and mass are functions of energy, which is both super cool and super confusing :-)

epicureanideal 8y ago

I don't think there's any "first principles" or philosophical/logical explanation for this... it's just an empirically determined fact, I think...

deleted 8y ago
[deleted]

i_am_proteus 8y ago

This is not a dumb question. The relationship was derived by some of physics' best minds in the early 20th century and requires an understanding of other physical principles and calculus to explain. I can't think of a concise/non-technical explanation. This Feynman lecture is about as close as you'll get: http://www.feynmanlectures.caltech.edu/I_15.html http://www.feynmanlectures.caltech.edu/I_15.html

dsr_ 8y ago

Mass is energy, energy is mass. What's the difference? They are at different points in a curve that relates space to time. If you trade away all the time, you get a maximum velocity: c. So the things moving at c don't experience time, and have momentum but not mass. http://www.math.ucr.edu/home/baez/physics/ParticleAndNuclear/photon_mass.html http://www.math.ucr.edu/home/baez/physics/ParticleAndNuclear... In the same direction, if you take a mass and accelerate it, it experiences less time. There you have relativistic time dilation, as beloved by science fiction stories. https://en.wikipedia.org/wiki/Time_dilation https://en.wikipedia.org/wiki/Time_dilation And you simultaneously get length contraction in the direction of each velocity: https://en.wikipedia.org/wiki/Length_contraction https://en.wikipedia.org/wiki/Length_contraction These are all aspects of the same thing. Really not a dumb question at all.

gpderetta 8y ago

IANAP, but I'll give a try: it is needed so that the units (mass, i.e. kg) in the equation balance out when expressed in the SI measurement system. For historical reasons we measure time and space using different units (seconds and meters in SI) but phisically space and time ought to be measured with the same unit. It is possible to construct such a measurement system, indeed many of them, known as natural units[1]. In natural units, c, i.e the ratio between the space and time unit, would be simply be set to dimensionless 1. In such a measurement system the E=mc^2 equation simply reduces to E=m i.e. each unit of max correspond to one unit of energy. [1] https://en.m.wikipedia.org/wiki/Natural_units https://en.m.wikipedia.org/wiki/Natural_units

jimmcslim 8y ago

Thank you all for your interesting and erudite answers!

infradig 8y ago

Lookup kinetic energy on Wikipedia. It will take you from KE = 1/2 Mv^2 to E = Mc^2 in a few small steps.

scentoni 8y ago

To comment on other answers about E=mc^2 and KE=1/2 mv^2, these are just different parts of the relativistic energy E=mc^2 cosh(eta) where eta is the velocity parameter. https://en.wikipedia.org/wiki/Proper_velocity https://en.wikipedia.org/wiki/Proper_velocity In terms of the coordinate velocity v, E=mc^2 cosh(atanh(v/c))=mc^2 / sqrt(1-(v/c)^2) = mc^2 (1 + 1/2 (v/c)^2 + 3/8 (v/c)^4 + ... So mc^2 is the irreducible energy due to mass and isn't relevant at low speeds because it doesn't change; the first-order approximation of kinetic energy is just 1/2 mv^2 and higher order terms aren't significant at low speeds. http://www.wolframalpha.com/input/?i=cosh(atanh(b) http://www.wolframalpha.com/input/?i=cosh(atanh(b))