# Physics questions on relativity **URL:** \ **Category:** Factual Questions\ **Created:** [October 23, 2005, 4:36pm UTC](https://boards.straightdope.com/t/physics-questions-on-relativity/327537 "2005-10-23T16:36:17Z")\ **Posts on this page:** 18\ **Page:** 1
**Author:** ![Wesley\_Clark](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/wesley_clark/32/20581_2.png) [@Wesley\_Clark](https://boards.straightdope.com/u/Wesley_Clark)\ **Post date:** [October 23, 2005, 4:36pm UTC](https://boards.straightdope.com/t/physics-questions-on-relativity/327537/1 "2005-10-23T16:36:17Z")
1. Why is the formula E=MC^2? Why isn’t it E=(1/2)MC^2 since the formula for kinetic energy is one half mass \* velocity squared? Is it a totally different equation. 2. Are the laws of newtonian physics untrue? Newtonian physics is based on things like time, mass and velocity. But according to relativity as velocity increases time decreases and mass increases. So just by moving aren’t time and mass changing, making newtonian mechanics untrue? I assume the changes are so minor that they won’t even matter for purposes here on earth. ---
**Author:** ![Shagnasty](https://avatars.discourse-cdn.com/v4/letter/s/9dc877/32.png) [@Shagnasty](https://boards.straightdope.com/u/Shagnasty)\ **Post date:** [October 23, 2005, 4:51pm UTC](https://boards.straightdope.com/t/physics-questions-on-relativity/327537/2 "2005-10-23T16:51:09Z")
> [@Wesley Clark](#): > > 1. Are the laws of newtonian physics untrue? Newtonian physics is based on things like time, mass and velocity. But according to relativity as velocity increases time decreases and mass increases. So just by moving aren’t time and mass changing, making newtonian mechanics untrue? I assume the changes are so minor that they won’t even matter for purposes here on earth. I believe you have it right for #2. Newtonian physics is untrue in the overall sense but the calculations are perfectly good for most things that we want to calculate. They are also much easier to understand and teach so we stick with them for day to day stuff. Areas that we have to resort to the theory of relativity are calculating space flights and in the calculations for Global Positioning Systems. ---
**Author:** ![Quartz](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/quartz/32/267_2.png) [@Quartz](https://boards.straightdope.com/u/Quartz)\ **Post date:** [October 23, 2005, 5:54pm UTC](https://boards.straightdope.com/t/physics-questions-on-relativity/327537/3 "2005-10-23T17:54:43Z")
> [@Wesley Clark](#): > > 1. Are the laws of newtonian physics untrue? Newtonian physics is based on things like time, mass and velocity. But according to relativity as velocity increases time decreases and mass increases. True, but the Newtonian system is _good enough_ for everyday use. It’s like you saying that something will cost ‘a tenner’ when the cost is actually £9.99. Or rounding to two decimal places instead of five e.g. using 3.14 for Pi instead of 3.14159. Some day, we’ll discover laws which give us an even better model. ---
**Author:** ![Waterman](https://avatars.discourse-cdn.com/v4/letter/w/b2d939/32.png) [@Waterman](https://boards.straightdope.com/u/Waterman)\ **Post date:** [October 23, 2005, 6:12pm UTC](https://boards.straightdope.com/t/physics-questions-on-relativity/327537/4 "2005-10-23T18:12:58Z")
It was my understanding that Newtonian Physics and Relativity part ways only as the speed of an object approaches the speed of light. Since most of us are left to deal with a world where airplane travel at subsonic speed is the highest speed we experience, then I don’t believe, as **Quartz** has said, we have anything to worry about. ---
**Author:** ![Waterman](https://avatars.discourse-cdn.com/v4/letter/w/b2d939/32.png) [@Waterman](https://boards.straightdope.com/u/Waterman)\ **Post date:** [October 23, 2005, 7:35pm UTC](https://boards.straightdope.com/t/physics-questions-on-relativity/327537/5 "2005-10-23T19:35:13Z")
> [@Wesley Clark](#): > > 1. Why is the formula E=MC^2? Why isn’t it E=(1/2)MC^2 since the formula for kinetic energy is one half mass \* velocity squared? Is it a totally different equation… The relationship E=mc^2 is the equation for the **rest energy** of a particle having a resting mass equal to m. The kinetic energy (1/2mv^2) is the difference between a particles total energy and its rest energy. In summary, the two equations are for different concepts. ---
**Author:** ![tim314](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tim314/32/3468_2.png) [@tim314](https://boards.straightdope.com/u/tim314)\ **Post date:** [October 23, 2005, 10:23pm UTC](https://boards.straightdope.com/t/physics-questions-on-relativity/327537/6 "2005-10-23T22:23:47Z")
As has been said, E = mc[sup]2[/sup] gives the energy stored in the particle when it’s at rest, whereas 1/2 mv[sup]2[/sup] is the kinetic energy of the particle – i.e., the additional energy it has if it’s moving at speed v. However, the two are related. The way Einstein derived E = mc[sup]2[/sup] is by showing that if a particle moving with speed v were to emit light with total energy E (emitting equal amounts in both directions so as not to change the speed of the particle), then its kinetic energy must change by 1/2 (E/c[sup]2[/sup])v[sup]2[/sup] (to lowest order, anyway). Since kinetic energy is 1/2 mv[sup]2[/sup], this says the mass of the particle changes by E/c[sup]2[/sup]. If we take E to be the total energy stored in the particle (excluding kinetic energy), then when the particle radiates energy E its mass should drop from m to zero, a change of m. Thus, m = E/c[sup]2[/sup], or in other words, E = mc[sup]2[/sup] ---
**Author:** ![Pleonast](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pleonast/32/1183_2.png) [@Pleonast](https://boards.straightdope.com/u/Pleonast)\ **Post date:** [October 23, 2005, 10:54pm UTC](https://boards.straightdope.com/t/physics-questions-on-relativity/327537/7 "2005-10-23T22:54:30Z")
The Newtonian equation for kinetic energy _K_ = [sup]1[/sup]/[sub]2[/sub] _m v_[sup]2[/sup] is the low-velocity limit of the relativistic kinetic energy, _K_ = _E_ - _E_[sub]0[/sub]. The rest energy is _E_[sub]0[/sub] = _m c_[sup]2[/sup], and total energy is _E_ = _g m c_[sup]2[/sup], where the factor gamma _g_ = (1 - (_v_/_c_)[sup]2[/sup])[sup]-1/2[/sup]. The gamma factor increases without bound as the object’s speed approaches the speed of light. But in the low velocity limit, we have (using a binomial expansion) _g_ = 1 + [sup]1[/sup]/[sub]2[/sub] (_v_/_c_)[sup]2[/sup] + higher order terms we ignore because they are small. And so starting from _K_ = (_g_ - 1) _m c_[sup]2[/sup] which is approximately _K_ = (1 + [sup]1[/sup]/[sub]2[/sub] (_v_/_c_)[sup]2[/sup] - 1) _m c_[sup]2[/sup], and thus _K_ = [sup]1[/sup]/[sub]2[/sub] _m v_[sup]2[/sup]. The fractional error of the approximation is about -[sup]3[/sup]/[sub]8[/sub] (_v_/_c_)[sup]4[/sup]. For example, a jetliner going 300 m/s will have about 1 part in about 10[sup]24[/sup] more kinetic energy than suggested by Newton. ---
**Author:** ![TJdude825](https://avatars.discourse-cdn.com/v4/letter/t/dec6dc/32.png) [@TJdude825](https://boards.straightdope.com/u/TJdude825)\ **Post date:** [October 24, 2005, 2:43am UTC](https://boards.straightdope.com/t/physics-questions-on-relativity/327537/8 "2005-10-24T02:43:37Z")
> [@Wesley Clark](#): > > 1. Are the laws of newtonian physics untrue? Newtonian physics is based on things like time, mass and velocity. But according to relativity as velocity increases time decreases and mass increases. So just by moving aren’t time and mass changing, making newtonian mechanics untrue? I assume the changes are so minor that they won’t even matter for purposes here on earth. Saying that Newtonian physics is inaccurate for everyday speeds (speeds nowhere near the speed of light) is like saying that the probability of a die landing on a given number isn’t EXACTLY 1/6, because it’s probably not manufactured perfectly, and therefore one number has slightly higher probability than another. You’re right, but there are MUCH bigger factors to take into account. ---
**Author:** ![Ring](https://avatars.discourse-cdn.com/v4/letter/r/6a8cbe/32.png) [@Ring](https://boards.straightdope.com/u/Ring)\ **Post date:** [October 24, 2005, 3:35am UTC](https://boards.straightdope.com/t/physics-questions-on-relativity/327537/9 "2005-10-24T03:35:37Z")
The complete equation for relativistic energy is: E[sup]2[/sup] = m[sup]2[/sup]c[sup]4[/sup] + p[sup]2[/sup]c[sup]2[/sup] When the particle is at rest its momentum § equals zero, so E[sup]2[/sup] = m[sup]2[/sup]c[sup]4[/sup] + 0 E = mc[sup]2[/sup] ---
**Author:** ![commasense](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/commasense/32/3017_2.png) [@commasense](https://boards.straightdope.com/u/commasense)\ **Post date:** [October 24, 2005, 3:53am UTC](https://boards.straightdope.com/t/physics-questions-on-relativity/327537/10 "2005-10-24T03:53:24Z")
> [@Shagnasty](#): > > IAreas that we have to resort to the theory of relativity are calculating space flights… No cite, but I’ve heard or read that the trajectories of all spacecraft are calculated using only Newtonian mechanics. Putting the Cassini-Huygens mission on target to within ten miles after a trip of over a billion miles to Saturn didn’t require any reference to relativity. ---
**Author:** ![Ring](https://avatars.discourse-cdn.com/v4/letter/r/6a8cbe/32.png) [@Ring](https://boards.straightdope.com/u/Ring)\ **Post date:** [October 24, 2005, 4:16am UTC](https://boards.straightdope.com/t/physics-questions-on-relativity/327537/11 "2005-10-24T04:16:00Z")
> [@Ring](#): > > The complete equation for relativistic energy is: > > E[sup]2[/sup] = m[sup]2[/sup]c[sup]4[/sup] + p[sup]2[/sup]c[sup]2[/sup] > > When the particle is at rest its momentum (p) equals zero, so > > E[sup]2[/sup] = m[sup]2[/sup]c[sup]4[/sup] + 0 > > E = mc[sup]2[/sup] That should read, “The complete relativistic equation for energy is.” Energy is energy for God’s sake. One of the things that I think is most interesting about this equation is that it clearly shows that a system of photons with a zero momentum frame has mass. Something I don’t think a lot of people are aware of. ---
**Author:** ![Pleonast](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pleonast/32/1183_2.png) [@Pleonast](https://boards.straightdope.com/u/Pleonast)\ **Post date:** [October 24, 2005, 3:16pm UTC](https://boards.straightdope.com/t/physics-questions-on-relativity/327537/12 "2005-10-24T15:16:57Z")
> [@](#): > > Originally posted by **Pleonast** in error > _The fractional error of the approximation is about -[sup]3[/sup]/[sub]8[/sub] (v/c)[sup]4[/sup]. For example, a jetliner going 300 m/s will have about 1 part in about 10[sup]24[/sup] more kinetic energy than suggested by Newton._ Sorry, it should -[sup]3[/sup]/[sub]4[/sub] (_v/c_)[sup]2[/sup], and about 1 part in 10[sup]12[/sup]. ---
**Author:** ![Omphaloskeptic](https://avatars.discourse-cdn.com/v4/letter/o/bcef8e/32.png) [@Omphaloskeptic](https://boards.straightdope.com/u/Omphaloskeptic)\ **Post date:** [October 24, 2005, 5:28pm UTC](https://boards.straightdope.com/t/physics-questions-on-relativity/327537/13 "2005-10-24T17:28:52Z")
> [@commasense](#): > > No cite, but I’ve heard or read that the trajectories of all spacecraft are calculated using only Newtonian mechanics. Putting the Cassini-Huygens mission on target to within ten miles after a trip of over a billion miles to Saturn didn’t require any reference to relativity. This is not really a statement about the accuracy of Newtonian mechanics; it’s a statement about the **inaccuracy** of our rockets. No, really. By far the largest source of endpoint error in the launch of Cassini (or any space probe) is in the initial pointing error of the spacecraft right after launch: it’s not going at exactly the velocity planned for it because of imperfections in the thrusters and attitude sensors. These errors so far overwhelm any relativistic corrections that there’s no point in doing the relativistic calculations. The only reason Cassini made it to Saturn is **feedback** , in the form of midcourse corrections. [This article](http://www.britastro.org/journal/archive/cassini.htm) describes a “picture-perfect” launch, with a pointing error of “only” 0.005°; at Saturn’s distance that “insignificant” error would translate into an error of about 100000km, without the corrections done along the way. Note, however, that relativistic corrections (Doppler shifts and time-dilation) are necessary for maintaining phase lock in spacecraft communications. ([This](http://arxiv.org/abs/gr-qc/0104064) is an interesting article discussing some of these corrections for the Pioneer probes.) ---
**Author:** ![Omphaloskeptic](https://avatars.discourse-cdn.com/v4/letter/o/bcef8e/32.png) [@Omphaloskeptic](https://boards.straightdope.com/u/Omphaloskeptic)\ **Post date:** [October 24, 2005, 5:49pm UTC](https://boards.straightdope.com/t/physics-questions-on-relativity/327537/14 "2005-10-24T17:49:17Z")
> [@Omphaloskeptic](#): > > [This article](http://www.britastro.org/journal/archive/cassini.htm) describes a “picture-perfect” launch, with a pointing error of “only” **0.005°** ; at Saturn’s distance that “insignificant” error would translate into an error of about 100000km, without the corrections done along the way. … Typo, should be 0.004°. ---
**Author:** ![commasense](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/commasense/32/3017_2.png) [@commasense](https://boards.straightdope.com/u/commasense)\ **Post date:** [October 24, 2005, 5:53pm UTC](https://boards.straightdope.com/t/physics-questions-on-relativity/327537/15 "2005-10-24T17:53:28Z")
My point was not how perfect we are at aiming spacecraft, but that our fastest and most far-ranging vehicles are so far from traveling at the speed of light that even on a trip of a billion miles we don’t have to account for relativistic effects, except in communicating with them by radio. ---
**Author:** ![D\_B\_Cooper](https://avatars.discourse-cdn.com/v4/letter/d/bcef8e/32.png) [@D\_B\_Cooper](https://boards.straightdope.com/u/D_B_Cooper)\ **Post date:** [October 24, 2005, 7:04pm UTC](https://boards.straightdope.com/t/physics-questions-on-relativity/327537/16 "2005-10-24T19:04:51Z")
KE=1/2mv^2 is used for kinetic energy calculation, when one needs to find the either the mass, velocity or total kinetic energy for a moving object. E=mc^2 is used to find the energy stored in an obect if it was to be broken apart in energy, where all of the matter is converted into energy. KE=1/2mv^2 and PE=mgh show the conservation of energy in terms of motion. E=mc^2 shows that matter can be made into energy, and vice-a-versa. The effect of space-time dialation and such are so very minimal that it is seen as trivial by many scientists. I recall a relitivity lesson in which an identical twin became like 453 mircoseconds younger than his brother due to his time in space. I can’t remember the exact length of his stay, but it around a year total. ---
**Author:** ![Omphaloskeptic](https://avatars.discourse-cdn.com/v4/letter/o/bcef8e/32.png) [@Omphaloskeptic](https://boards.straightdope.com/u/Omphaloskeptic)\ **Post date:** [October 24, 2005, 7:06pm UTC](https://boards.straightdope.com/t/physics-questions-on-relativity/327537/17 "2005-10-24T19:06:26Z")
> [@commasense](#): > > My point was not how perfect we are at aiming spacecraft, but that our fastest and most far-ranging vehicles are so far from traveling at the speed of light that even on a trip of a billion miles we don’t have to account for relativistic effects, except in communicating with them by radio. Sure. But my point was that the tiny error you quoted – 10 km error over 10AU – doesn’t really say anything about the accuracy of the Newtonian approximation. Even if there were pretty substantial unaccounted-for relativistic effects, the midcourse corrections would handle them. (Of course, if the relativistic effects were huge, you might run out of thruster fuel first.) ---
**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 24, 2005, 7:29pm UTC](https://boards.straightdope.com/t/physics-questions-on-relativity/327537/18 "2005-10-24T19:29:32Z")
> [@](#): > > My point was not how perfect we are at aiming spacecraft, but that our fastest and most far-ranging vehicles are so far from traveling at the speed of light that even on a trip of a billion miles we don’t have to account for relativistic effects, except in communicating with them by radio. On the other hand: Electrons in a wire in a simple DC circuit typically have an average speed of a fraction of a centimeter per second. But we _can’t_ ignore the relativistic effects from the motion of those electrons. Even though the effects are so small on each individual electron, there are so many electrons that it can add up to produce an easily-measured magnetic field. Newtonian mechanics is _always_ only an approximation. Sometimes it’s a good enough approximation, and sometimes it’s not.