# Is c=(E/m)^1/2 true? **URL:** \ **Category:** Factual Questions\ **Created:** [October 10, 2020, 7:01am UTC](https://boards.straightdope.com/t/is-c-e-m-1-2-true/922616 "2020-10-10T07:01:35Z")\ **Posts on this page:** 9\ **Page:** 2
**Author:** ![Asympotically\_fat](https://avatars.discourse-cdn.com/v4/letter/a/e47c2d/32.png) [@Asympotically\_fat](https://boards.straightdope.com/u/Asympotically_fat)\ **Post date:** [October 14, 2020, 12:30pm UTC](https://boards.straightdope.com/t/is-c-e-m-1-2-true/922616/21 "2020-10-14T12:30:52Z")
Yep, I think it is fair to say it is always meaningful to express mass in units of energy by using the conversion factor c^2. You can of course also always express energy using units of mass using the inverse conversion, but it is far less meanigful to talk of all energy being, or having, mass than all mass being energy. The mass of system is specifically the **rest** energy and the contirbution of its kinetic energy (i.e. its energy that is not its rest energy) to a system’s inertia is more complicated than the contribution of its mass. ---
**Author:** ![zimaane](https://avatars.discourse-cdn.com/v4/letter/z/a3d4f5/32.png) [@zimaane](https://boards.straightdope.com/u/zimaane)\ **Post date:** [October 14, 2020, 3:01pm UTC](https://boards.straightdope.com/t/is-c-e-m-1-2-true/922616/22 "2020-10-14T15:01:18Z")
In fact, Einstein and early interpreters of Einstein usually expressed the relationship in terms of the mass of the object, so M = E/c^2. The formulation E = Mc^2 only became common much later. ---
**Author:** ![Pasta](https://avatars.discourse-cdn.com/v4/letter/p/ecccb3/32.png) [@Pasta](https://boards.straightdope.com/u/Pasta)\ **Post date:** [October 14, 2020, 5:42pm UTC](https://boards.straightdope.com/t/is-c-e-m-1-2-true/922616/23 "2020-10-14T17:42:38Z")
> [@Asympotically\_fat](#): > > …but it is far less meanigful to talk of all energy being, or having, mass than all mass being energy. The mass of system is specifically the **rest** energy and the contirbution of its kinetic energy (i.e. its energy that is not its rest energy) to a system’s inertia is more complicated than the contribution of its mass. One just needs to use the full expression to make it meaningful. > [@zimaane](#): > > In fact, Einstein and early interpreters of Einstein usually expressed the relationship in terms of the mass of the object, so M = E/c^2. The formulation E = Mc^2 only became common much later. No, there isn’t some preferred arrangement like this from the past. At issue is that _E_=_mc_2 is not the full expression. It’s _E_2 = (_pc_)2 + (_mc_2)2, where _p_ is the momentum. When you consider an object at rest so that _p_=0, then you can arrange the leftovers however you want, but it’s a special case of the more general expression. And all those _c_’s are just to make historical momentum, mass, and energy units compatible. In more fundamental unit systems, it’s just _E_2 = _p_2 + _m_2. ---
**Author:** ![Asympotically\_fat](https://avatars.discourse-cdn.com/v4/letter/a/e47c2d/32.png) [@Asympotically\_fat](https://boards.straightdope.com/u/Asympotically_fat)\ **Post date:** [October 15, 2020, 12:55am UTC](https://boards.straightdope.com/t/is-c-e-m-1-2-true/922616/24 "2020-10-15T00:55:33Z")
Recognizing that (rest) mass is certain portion of the energy of a system, isn’t the same as recognising that energy in general has mass. You can define relativistic mass of course, though this comes from the definition of relativsitc momentum. Relativistic mass is just a synonym for a body’s/system’s energy and it is (mostly) thoguht of as being an unnecessary concept to introduce. The relativistic mass is a measure of a body’s inertia, but the complication is changing a body’s state of motion also changes the kinetic contribution. ---
**Author:** ![Folacin](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/folacin/32/3195_2.png) [@Folacin](https://boards.straightdope.com/u/Folacin)\ **Post date:** [October 29, 2020, 9:13pm UTC](https://boards.straightdope.com/t/is-c-e-m-1-2-true/922616/25 "2020-10-29T21:13:14Z")
I think this is a valid tangent, and hopefully my question will make sense: So, in my understanding, as you accelerate a mass, it gets heavier ( strictly more massive, I guess, but heavier works). The shorthand is it takes infinite energy to get the object moving at _c_. But velocity is a relative relationship between two objects. So, if I take three objects that are at rest relative to each other, and then apply constant acceleration to two of them in opposite directions, at some point won’t the two accelerating objects will be moving at .5_c_ relative to the ‘home’ object, and hence have a relative velocity of _c_ to each other? And then, won’t they be moving at \> _c_? I’m obviously missing some fundamental point here, but what is it? Please note that my formal physics education consists of “Physics for non-majors” about 40 years ago, although I’ve read several popular books discussing relativity. ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [October 29, 2020, 10:05pm UTC](https://boards.straightdope.com/t/is-c-e-m-1-2-true/922616/26 "2020-10-29T22:05:15Z")
Yes, if a spaceship constantly accelerates away from you then there can be a Rindler horizon where light you emit will never catch up with it, if that is what you mean. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [October 29, 2020, 10:26pm UTC](https://boards.straightdope.com/t/is-c-e-m-1-2-true/922616/27 "2020-10-29T22:26:49Z")
First of all, no, mass does not increase with velocity, unless you define “mass” in a really counterintuitive and nonstandard way. But the fact remains that you can’t accelerate anything to c, as it would take infinite energy. Second, it’s perfectly possible to have two objects, moving in opposite directions in some reference frame, each with a speed of 0.5 c or more relative to that reference frame. But they still won’t have a velocity of c with respect to each other. Velocities don’t add that way. ---
**Author:** ![Great\_Antibob](https://avatars.discourse-cdn.com/v4/letter/g/e47c2d/32.png) [@Great\_Antibob](https://boards.straightdope.com/u/Great_Antibob)\ **Post date:** [October 30, 2020, 12:12am UTC](https://boards.straightdope.com/t/is-c-e-m-1-2-true/922616/28 "2020-10-30T00:12:36Z")
> [@Folacin](#): > > So, in my understanding, as you accelerate a mass, it gets heavier ( strictly more massive, I guess, but heavier works). Not really. It’s more of a case that things “appear” weird when they go fast. It’s not entirely unrelated but think of the Doppler Effect. If you have a whistle on a train, it sounds higher pitched as it approaches you and lower pitched as it goes away. Standing on the train, the whistle sounds like it has a constant pitch. Likewise, the light from a star will appear “redder” or “bluer” (higher or lower frequency) if the star is moving generally towards us or away. But if you are in orbit of the star, the light doesn’t seem red- or blue-shifted. It’s not the great example, but it demonstrates that some measurable quantities are affected by our relative motion. In the case of mass, or more accurately momentum, something traveling at a high fraction of the speed of light will appear to us watching it to have a momentum that is greater than what you’d get by calculating the simple Newtonian momentum m\*v. One way that has been interpreted in the past (though disfavored now) is through the concept of relativistic mass, i.e. seems really massive, though the mass itself would not, within its own frame of reference, think it has gotten more massive. > [@Folacin](#): > > So, if I take three objects that are at rest relative to each other, and then apply constant acceleration to two of them in opposite directions, at some point won’t the two accelerating objects will be moving at .5_c_ relative to the ‘home’ object, and hence have a relative velocity of _c_ to each other? And then, won’t they be moving at \> _c_? No, as explained above. It’s one of the things about how the universe actually works. You can’t just add velocities and be truly accurate. When the velocities are very low (say highway speeds), it’s close enough to not matter - the difference is a tiny, tiny amount. For example, for 2 things moving away from each other at 100mph would actually measure the other at 200mph minus something like 0.00000001 mph. But when the velocities are close to the speed of light, things warp a lot more. Our intuition is pretty good at the low velocities we typically see, i.e. Newtonian mechanics is a very good approximation of truth for everyday human things. But our intuition is terrible at high velocities. ---
**Author:** ![Folacin](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/folacin/32/3195_2.png) [@Folacin](https://boards.straightdope.com/u/Folacin)\ **Post date:** [October 30, 2020, 12:26pm UTC](https://boards.straightdope.com/t/is-c-e-m-1-2-true/922616/29 "2020-10-30T12:26:29Z")
OK - so the main hole in my understanding is that velocities don’t actually add up, but, like many things when dealing with Newton vs. Einstein, it only matters when something is really big or going really fast. Thanks, all. [Previous page](https://boards.straightdope.com/t/is-c-e-m-1-2-true/922616.md?page=1)