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I would just explain that a photon has zero mass, but nonzero energy and momentum and finite velocity. Intuitively (meaning: in a Newtonian universe), one woul

I would just explain that a photon has zero mass, but nonzero energy and momentum and finite velocity. Intuitively (meaning: in a Newtonian universe), one would think that a particle with zero mass would have to have infinite velocity to have nonzero energy and momentum, right? And yet, its velocity is finite. That demonstrates that the universe is not Newtonian. It also sets up an intuitive connection (which is what we're looking for here, right?) between the speed of light and one's intuitive sense of an infinite velocity. Again, of course, this brings us to the question of why the universe is this way: why it is Einsteinian rather than Newtonian. But that question really belongs to the realm of metaphysics, not that of physics.

ars 16y ago
Actually that question is easy to answer. The universe is Einsteinian because otherwise e could not equal mc2. And if that were the case then stars could not shine, and a TON of other things would not work. Atoms could not exist either. The reason is that as you go faster you have more energy (obviously) and since you have more energy your mass increases. Since your mass increases you need even more energy to increase your speed (since now you weigh more). Take that to the limit and you find that as you reach the speed of light your mass goes to infinity. So it's necessary that it's impossible to exceed the speed of light - for example if you had two objects each traveling at 51% of the speed of light (relative to third placed in between them). Then relative to each other they are going faster than light - which means they have more than infinite energy. Can't do that. So relativity is necessary if you want mass to be interchangeable with energy.
- diziet 16y ago
  You mean to say they will be approaching each other at 81%~ speed of light. http://en.wikipedia.org/wiki/Velocity-addition_formula http://en.wikipedia.org/wiki/Velocity-addition_formula Surely you must read up on modern physics a little bit, sir!
  - ars 16y ago
    That's the point - because relativity exists, the measured speed is not simply the addition of the two. I was explaining why that is necessary if you want e=mc2
    - diziet 16y ago
      The way you'd phrased it confused the matter further, though. I'd consider rewording some of it.
      - ars 16y ago
        So it's necessary that it's impossible to exceed the speed of light. For example if you had two objects each traveling at 51% of the speed of light (relative to third placed in between them). You only gave them a certain amount of energy, but if speeds were additive and you compared them then it would appear that their comparative speed was greater than the speed of light! And that would imply an infinite amount of energy, which would be a problem. Even if they were each traveling at 49% of the speed of light, so there are no issues of infinity, it takes a lot less energy to accelerate two object to 49% of the speed of light than it does to accelerate one to 98% of the speed of light (because it's a lot heavier when it's going that fast, so it contains far more energy), so you would have issues with conservation of energy. Because of all that, speeds are not additive, and they get adjusted in a way that keeps conservation of energy exactly correct. Therefor relativity is necessary if you want mass to be interchangeable with energy.
        diziet 16y ago
        I understand that you say that they're not additive, but I have a feeling you aren't really understanding what the actual math behind it is. Two objects traveling at 51% the speed of light relative to a third object placed between them (or anywhere else) would STILL travel at 81% the speed of light relative to each other. Please take a look at a very simple relativity homework solution to see if you misunderstand the math or the concepts of relativity (that happens to be the top result for "two spaceships approach each-other" on google)http://www.phy.duke.edu/courses/143/homework/hmwk3_solutions.pdf http://www.phy.duke.edu/courses/143/homework/hmwk3_solutions... [It's problem #2]
- adobriyan 16y ago
  Mass is scalar and therefore is invariant. "Increasing mass" inevitably leads to so-called "perpendicular mass" which must change and "proper" mass which must not change for equations of motion to stay correct. This "perpendicular" mass is unphysical. It's better to leave this concept.
  - ars 16y ago
    I've never heard of perpendicular mass, I tried googling for that and nothing came up. Rest mass is invariant, but the real mass, i.e. the one that makes it harder to accelerate, and that gives inertia, is not.

ars 16y ago

Actually that question is easy to answer. The universe is Einsteinian because otherwise e could not equal mc2. And if that were the case then stars could not shine, and a TON of other things would not work. Atoms could not exist either. The reason is that as you go faster you have more energy (obviously) and since you have more energy your mass increases. Since your mass increases you need even more energy to increase your speed (since now you weigh more). Take that to the limit and you find that as you reach the speed of light your mass goes to infinity. So it's necessary that it's impossible to exceed the speed of light - for example if you had two objects each traveling at 51% of the speed of light (relative to third placed in between them). Then relative to each other they are going faster than light - which means they have more than infinite energy. Can't do that. So relativity is necessary if you want mass to be interchangeable with energy.

diziet 16y ago
You mean to say they will be approaching each other at 81%~ speed of light. http://en.wikipedia.org/wiki/Velocity-addition_formula http://en.wikipedia.org/wiki/Velocity-addition_formula Surely you must read up on modern physics a little bit, sir!
- ars 16y ago
  That's the point - because relativity exists, the measured speed is not simply the addition of the two. I was explaining why that is necessary if you want e=mc2
  - diziet 16y ago
    The way you'd phrased it confused the matter further, though. I'd consider rewording some of it.
    - ars 16y ago
      So it's necessary that it's impossible to exceed the speed of light. For example if you had two objects each traveling at 51% of the speed of light (relative to third placed in between them). You only gave them a certain amount of energy, but if speeds were additive and you compared them then it would appear that their comparative speed was greater than the speed of light! And that would imply an infinite amount of energy, which would be a problem. Even if they were each traveling at 49% of the speed of light, so there are no issues of infinity, it takes a lot less energy to accelerate two object to 49% of the speed of light than it does to accelerate one to 98% of the speed of light (because it's a lot heavier when it's going that fast, so it contains far more energy), so you would have issues with conservation of energy. Because of all that, speeds are not additive, and they get adjusted in a way that keeps conservation of energy exactly correct. Therefor relativity is necessary if you want mass to be interchangeable with energy.
      - diziet 16y ago
        I understand that you say that they're not additive, but I have a feeling you aren't really understanding what the actual math behind it is. Two objects traveling at 51% the speed of light relative to a third object placed between them (or anywhere else) would STILL travel at 81% the speed of light relative to each other. Please take a look at a very simple relativity homework solution to see if you misunderstand the math or the concepts of relativity (that happens to be the top result for "two spaceships approach each-other" on google)http://www.phy.duke.edu/courses/143/homework/hmwk3_solutions.pdf http://www.phy.duke.edu/courses/143/homework/hmwk3_solutions... [It's problem #2]
adobriyan 16y ago
Mass is scalar and therefore is invariant. "Increasing mass" inevitably leads to so-called "perpendicular mass" which must change and "proper" mass which must not change for equations of motion to stay correct. This "perpendicular" mass is unphysical. It's better to leave this concept.
- ars 16y ago
  I've never heard of perpendicular mass, I tried googling for that and nothing came up. Rest mass is invariant, but the real mass, i.e. the one that makes it harder to accelerate, and that gives inertia, is not.