Relativistic Mass and Energy


After watching the video on Einstein’s Theory of Relativity, many people have commented that the mass of an object does not actually increase as the object moves faster, and that the equation E=MC^2 is therefore not actually valid for objects in motion. The confusion surrounding this topic is due to what we mean by the word “mass”. It is true that the gravitational mass of an object does not change. That is, the gravitational attraction of an object does not increase due to the fact that the object is moving close to the speed of light. What does change is that the more an object’s speed approaches the speed of light, the greater the force necessary to increase the object’s speed even further. If a spaceship’s speed is equal to the speed of light, then an infinite force would be required to increase the spaceship’s speed any further. There are two ways to describe this phenomena. One way is to say that as an object approaches the speed of light, it changes the way in which it reacts to an applied force, but that its mass never changes. Another way to describe this phenomena is to introduce the concept of relativistic mass, and to say that the relativistic mass of the object increases. Both approaches give all the exact same predictions, so they are mathematically equivalent to each other. However, the relativistic mass can never be used to calculate the gravitational attraction of an object. The mass that an object has when it is at rest is what we call the object’s “rest mass”, and it is the rest mass that we use to determine gravity, even when the object is in motion. This is one of the reasons why many people feel that the concept of relativistic mass should never be used. Einstein initially used the concept of relativistic mass, but later regretted it, and insisted that only rest mass should be used. Advanced text books on Einstein’s Theory of relativity always only use rest mass. However, many introductory text books and videos still use the concept of relativistic mass. If it is the relativistic mass that is used in the equation E=MC^2 then this equation is still valid for objects with mass that are in motion. More information about Einstein’s Theory of Relativity is available in the other videos on this channel.

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96 thoughts on “Relativistic Mass and Energy”

  1. Physics Videos by Eugene Khutoryansky says:

    In case, you have not already seen them, I also uploaded several other videos recently.  As always, for each video that you like, you can help more people find it in their YouTube search engine by clicking the like button, and writing a comment.  Thanks.

  2. MrCristie1 says:

    So many great videos

  3. h0Nt667 says:

    I still don't get this concept of "relativistic mass". Why should not it behave like normal mass?

  4. Tiago Franca says:

    Great video as always!

  5. TheThePinkPrincess77 says:

    Thank you for making these videos!!!! How much work goes into each one? The animation is very detailed.

  6. cocoarecords says:

    Great job as always

  7. Alan Douglas says:

    Awesome stuff, keep up the great work.

  8. Yekta Coşkun says:

    How fast is gravitational interactions? Think it this way. When will earth go off from the orbit around sun when the sun disappeared in a moment. Would it be instantly or 8 mins later like light?

  9. Oleg says:

    Wery god video rly enjoy pls do more

  10. Daniel Lassander says:

    I love your videos, just wanted to let you know 🙂

  11. Jompster says:

    Awesome that you are updating this channel much more often now! 🙂

  12. Kent VanderVelden says:

    Fantastic video. You explain topics quite well.

  13. Seth Catalano says:

    So are gravitational mass and rest mass the same, at least in classical mechanics? And What about the Expanded form of the equation, E^2=(mc^2)^2+(pc)^2? Isn't this the equation for a moving object?

  14. blake301987 says:

    Awesome video, Thanks for making it!

  15. Andrew Karpinen says:

    E=MoC2 for an object at rest. The. Einstein Mass Energy Equivelence with MOMENTUM is E2=m2c4 + p2c2

  16. Umar says:

    As always, Awsome Video 🙂

  17. YellowKazooie says:

    "If a spaceship's speed is equal to the speed of light, then an infinite force would be required to increase the spaceship's speed even further"

    Not quite correct. You need an infinite amount of force just to get the spaceship to the speed of light to begin with.

  18. Morey Ellis says:

    If any size force is enough to cause even a really massive object to accelerate (granted only a tiny bit) why doesn't flicking something going 99.9999…% speed of light accelerate it to light speed?

  19. jdigi82 says:

    Another brilliant video! You are a genius. Thanks again!

  20. Mark G says:

    Then what changes as you go faster that prevents and object from going faster than light. Why do you need an infinite amount of energy at light speed but less than that at anything below it. If you are traveling at 99.999999999% light speed and you need a lot of energy to get you there (let's say a ridiculously large number) why does it then jump to infinity at the light speed barrier? No matter how big the amount of energy is infinity is infinitely bigger, which makes it tough for me to understand the answer.

  21. lar_kozz says:

    This phenomenon*

    Phenomena is plural

  22. Conceptual Engineering says:

    Hi eugene,plz make video about free fall acceleration why all objects regardless their mass fall freely with same acceleration, how spacetime or relativity theory explains this…plz it's request….thx

  23. Sirisha Nelanutula says:

    very interesting

  24. GaryKildall says:

    Increasing the mass of an electron is easy. But to keep energy trapped as mass that's difficult. Everyone having 2 mirrors is able to reflect photons in the visible spectrum from one mirror to the other mirror which gives the 'illusion' of a virtual space that exceeds the actual space. This is called recursion. A photon hits an electron in one mirror. Now an electron will orbit higher around its atom(s). However now very soon the electron will fall back to its original orbit. And hereby emitting a photon – although when the photon has enough energy the electron is too excited and leaves the atom. – (Photo Electric Effect) It is very important to know that the second photon emitted after the first photon excited the electron has a fraction less of energy. Therefore in this recursive virtual 'illusive' space photons will loose energy and there fore will shift in frequency. Which means that from the perspective of the photon the space between the 2 mirrors is actually folded. From our perspective we see this as infinity between the 2 mirrors, however try this experiment for yourself. Align the mirrors vertically. By theory described here for example a blue photon emitter like a blue laser will at end shift into infra red and finally out of visible spectrum. Now comes another important probability. Make sure the mirrors are as far away from each other as you can. In human practically setups it is not possible to observe this red shift frequency. (photon loosing energy while bouncing from one mirror to the other) because light speed is to high for this experiment to notice at small scale this assumed phenomenon. Now one can conclude perhaps a simple fact. From the photon's point of view it looks like space it travels is folded. And so we/I call this FOLDED SPACES by POINT OF VIEW. Compare this to a marble trapped between 2 walls. Put the marble in motion. The marble will hit a wall and will reflect to the other wall until all energy of motion (momentum) in the marble is lost (increasing inertia). This makes you asking yourself where did the energy of the trapped photons between the mirrors go? Yes the photons excited electrons. Yes energy was transferred into mass. Here we see a transformation of real energy into existing mass – THE EXCITED ELECTRON. However why is the electron not able to keep its increased mass? Because the electron orbits the atom/atoms it needs energy to sustain momentum. This is not possible for the electron and ATRACTIVE FORCE from the atom core – PROTONS – force the electron to release mass so mass is transferred back to energy – the emitted photon – again. But remember, the excited photon according theory has a very tiny fraction LESS of energy than photon which excited this electron. The most promosing fact is that with photons we are actually able to create mass, but at the cost of an incredible small amount of energy. However as said we are not yet able to sustain this energy to mass conversion in the excited electron. This is what we/I mean with zerofication of the universe. For a photon time does not exist. This is reason to assume described folded space theory. However it must not be forgotten that the original photon is lost and final photon is of a totally different magnitude.

  25. Caffeine111 says:

    You are much better than khan academy in explaining things. And the visuals are excellent.

  26. GaryKildall says:

    Anyone interested in over 10 thousand documents of Einstein? Then you have got something to read for the coming 10 years. I am not joking. Einstein worked until his death. The documents are very shocking.

  27. Marijke Vissers says:

    Even if i don't really understand this, and what it means in our live, it's beautifull anyway!

  28. Andrew Karpinen says:

    Eugene Khutoryansky, I'd like to ask you an unrelated question please. If you dont respond no biggie, I've always pondered a question I have and have never ran across the same idea. That is "We know that SPACE itself is expanding and not the Universe, however I question is there a possibility that all things in the Universe EXCEPT Space infinitely SHRINKING? I don't see where it would look any differently than what we observe now, and (loosely speaking) sounds just as Crazy as an Infinite Expansion. I'd like to disprove or rule this out so that I can free up some RAM on the Hard drive in my head. Thank you, I really like to know what you think.

  29. GaryKildall says:

    Imagine a rocket with endless fuel. This rocket has inertia. First fuel will be used to overwin inertia. Assume a stable amount of fuel to produce a stable propulsion force is available. Now relativity formulas say the faster the rocket goes the more energy it has. But this applies to the rocket fuel too. The faster the rocket goes the more energy per mass unit the fuel has. So actually you need less fuel per time to keep acceleration the faster the rocket goes. This relativistic energy changes the rockets inertia. But at a certain point relativistic energy suddenly rises exponentially causing exponential inertia for the rocket when approaching light speed. E=(mc^2)/(1-v^2/c^2)^0.5 and according to this formula both the energy potential of the rocket fuel and inertia of the rocket rise incredible so despite endless theoretical fuel lightspeed cannot be reached. But the good news is, the faster the rocket goes the more potent energy its fuel has as long as you keep below a certain treshold. Meaning to for example keep acceleration with 1g you need less and less fuel because of this relativistic phenomenon. But lightspeed can never been reached though. Regards, and thanks to the person telling me electron and positron create gamma rays when they meet each other. ( 511 kilo electron volt for each gamma photon. )

  30. Ørjan Solli says:

    M = E/C^2

  31. shaukeen yaar :D says:

    you must explain very deeply
    i had not understood many things:(

  32. Eduardo Policarpo says:

    you should do a video on non-euclidean geometry soon, 
    it would be great!

  33. Cat O' Schrodinger says:

    Love this topic. Love the music. Love Eugene!!

  34. Djalma Antonio says:


  35. Prom Etheus says:

    Much of this video is mainly correct, however it not true that the inertial mass explained in the video, is different in magnitude to gravitational mass, as this equivalence is actually the principle upon which Einstein's theory of General Relativity is founded. All objects have an agreed rest mass but their relativistic mass depends on the relative speed of the observer. The source in Einstein's field equation is (for stationary observers) the rest mass (and also energy and momentum/stress terms) but for observers approaching a large gravitational  mass at high speed, there are relativistic transformations in the distance, time and mass and this is all accommodated in the tensor formulation of his field equations. [For more details cf. General relativity: A concise guide for beginners" available from as an electronic download as is the precursor on special relativity.]

  36. C Martinez says:

    The moon circling the earth image looks like the moon could collide with the Earth at any second. Why doesn't that seem to be happening? In fact the moon is slowly getting further from the earth in reality.

  37. Gigio Bargigio says:

    how do you know your velocity in space? from your point of view your mass should be always the same because you are always still and the rest of the universe is moving!

  38. Bart Kwezelstaart says:

    So, if I understand correctly, f=m*a doesnt hold if we exclude the relativistic mass? Since accelarating an object at high speed requires more energy thus more force?

  39. Alexander Bray says:

    If I am moving close to the speed of light in a spaceship and I fire up the engine so that a constant force is provided, what would I experience in regards to my velocity?

  40. Derek Dilger says:

    Do you ever get tired of responding to compliment comments?

  41. Michael Bishop says:

    Is far as I know, the distinction is referred to in most texts as that between inertial mass and gravitational mass.
    Inertial mass increases with speed, while gravitational mass does not.

  42. Praveen Kumar says:

    what is meaning of "rest"? "rest" is relative to what?

  43. Mi 28 says:

    Pretty sure that all forms of energy constituting mass and therefore gravitational field is one of the cornerstones of general relativity.

  44. Anastasios Andronidis says:

    I'm confused… Here people clearly state that motion changes gravitation field. Thus a moving object is "heavier". What do I miss?

  45. Aleksandras Ignatavičius says:

    great videos

  46. Eduard says:

    After reading some discussions on the internet about this subject and thinking about it, I come to a slightly different conclusion:
    The gravitational field of objects moving within the same system relative to each other never changes, but this is different for objects which are not in the same system and are moving extremely fast relative to each other.
    For example, when the Earth and Moon would move at almost light speed relative to the rest of the solar system, Earth and Moon would indeed remain in the same relative orbit and would not fall to each other, but the gravity effect to the other, slow moving objects in the solar system would be much bigger. So gravity is relative, but it can change. It’s just like the relativity of time and length.
    Why? This is simply because of the relativity of kinetic energy.
    All energy contributes to inertia and to gravity, therefore increasing the “relativistic mass”, including kinetic energy.
    And when we do not work with the definition of “relativistic mass”, then we are using the definition of “relativistic momentum”, and then it is correct to say that momentum affects gravity, because momentum is kinetic energy.

  47. Lambertus says:

    But can rest mass be converted into other types of energy according to E = mc^2? And could the phenomenon you describe also be explained by time dilation, since F = m*a and acceleration as a concept requires time?

  48. ashish subedi says:

    what do u mean ha ?that mass does not increase with the increase of speed?then what einstein was wrong ?

  49. DK Kempion says:

    E=MC^2 is simply invalid for two very important reasons. First, C is max Acceleration and, therefore, no A exists beyond C. This means adding any value to C is invalid. Thus, multiplying C by M or squaring C is impossible – let alone doing both at the same time! Second, and the real reason this equation is invalid is because mass doesn't actually exist. M is only an apparent value; it's not real or true. This is a long-standing issue going back to Classical Greece. The fact is no one has ever challenged the concept of mass. I can elaborate but I don't think anyone is going to read my comment anyway.

    The mistake made in this video, as with many other claims out there, is in mixing Special Relativity (SR) with General Relativity (GR) by using both the above equation (mass-energy equivalence from SR) with relativistic mass (from GR). These theories are distinct and don't so easily overlap. Wanting to believe does not make true.

  50. alexgqh says:

    So relativistic mass is related to the energy required to speed up an object in motion and rest mass is the standard Density * Volume which is used to calculate gravitation pull, correct?

  51. samip science says:

    so less views.

  52. Bikash Thapa says:

    One way to describe this phenomena is "Higgs field" when the particle moving with speed of light it gets mass from Higgs field that's why they gets heavier actually mass from Higgs and that's the perfect description for relativistic mass

  53. Sylvo Totem says:

    +Physics Videos by Eugene Khutoryansky
    But if this effect of increased energy requirements to accelerate at higher speeds is called "relativistic mass", then does this mean, that DECREASING the speed of an object moving close to the speed of light costs the same amount of energy as to increase the speed?
    Because if it doesn't cost the same, then using the relativistic mass in equations doesn't give the same results as using rest mass, because you would need different amounts of mass depending on the direction of force

  54. Bryan Carter says:

    Owls always know what time it is.

  55. tString42 says:

    I didn't know that there was relativistic mass concept opposition. What would the other camp be called? Something related to forces?

  56. inertiaforce says:

    So time dilation as you approach the speed of light can be interpreted as an increase in inertia. You become harder to accelerate. And what is resistance to acceleration? Inertia. Your inertia is increasing as you go faster and faster. You become harder to accelerate. Most of the energy that is put into increasing your velocity goes into increasing your inertia. What do you think Eugene? Do you agree with this?

    I love your simulations. I bet Einstein would be pleased that you are able to communicate his ideas through simulation.

  57. Oscar Hernández Arzeta says:

    Awsome videos, great explanation and incredible choice of music, excellent work, keep them coming.

  58. Ed Friedman says:

    Virtually every physics book now avoids the use of the term 'rest mass'. There is only 'mass'. Those interested in a more detailed discussion about the history of teaching of this topic and the proper interpretation of 'mass' could refer to my lecture on the subject, found here.

  59. Mark Rowland says:

    An infinite amount of energy is required to accelerate any mass to the speed of light, not to exceed it. Am I wrong?

  60. Gautam Yajaman says:

    That lady is She-Hulk part 2

  61. Prom Etheus says:

    I think that aspects of this video are somewhat misleading. For example, as an object's kinetic energy increases, then due to E=mc^2  its inertial (relativistic mass) increases, and to re-express this as being an 'alternative way in which it will reacts to a force', is unnecessary. More importantly, the statement that the gravitational mass of an object does not increase with speed, even though its inertial (relativistic) mass does, flies in the face of  the main axiom of General Relativity viz. the equivalence of inertial and gravitational mass.[This is one of the reasons for the Gamma factor occurring in the stress tensor.]

  62. Mahian Ishraq says:

    Absolutely flawless.

  63. Anna Singley says:

    This is a great video. I am a pretty typical middle school student, and without this video I would be pretty lost. Thanks for the explanation of relativistic mass!

  64. 3effa says:

    Great video. I just wanted to know what the song in the background was.

  65. الكوابيس الثانيه says:

    السفر إلى خارج الكون​
    (( we need to Journey out of the universe ))

    We hope to bring an automated robot in order to send the robot beyond the limits of the universe. In order to discover multiple universes, we wish you to work by sending a robot in a spaceship beyond the limits of the universe. , Please work by sending a number of automated robots to beyond the limits of the universe. I want to know if there is time and place outside the universe? Want to know if there are multiple universes? , I want to know the secrets of the birth of multiple universes

    (( we need to Journey out of the universe ))

  66. Mister Right says:

    "Phenomena" is plural; "phenomenon" is singular.

  67. Abhinav Reigns says:

    if mass increases by 250% and velocity decreases by 20% calculate the % change in momentum and Kinetic energy?
    please answer sir

  68. Vaibhav Rajam says:

    Easiest mathematical explanation for E=mc2 :

  69. comic4relief says:

    'This' is singular, 'phenomena' plural.

  70. Dyslexic Artist Theory on the Physics of 'Time' says:

    Your videos are very good!!! To represent relativistic mass we can place the Lorentz contraction ˠ of space and time between the energy and mass of Einstein’s famous equation (E=ˠM˳C²)∞

  71. anuradha dhananjaya says:

    I love your videos

  72. anuradha dhananjaya says:

    Can you expain if a space ship fires a laser opposite direction where it moves.think there is a stationery observer watching it and at that movement he also fire a laser to the same direction parallel. At this event moving ship clock runs much fastet than us .am i correct?please expain it to me

  73. CHIN KEE HAW says:

    0:28 the correct equation is E^2=(mc^2)^2+(pc)^2

  74. Andrew Church says:

    It would take infinite energy for spaceship to REACH lightspeed. E=mc^2 is the total energy of an object in it’s own inertial frame. Two spaceships travelling away from me at 0.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 the speed of light, but both spaceships ARE STATIONARY compared to each other, and they can accelerate from each other just like rockets on earth do according to Newton, until they get super fast relative to each other.

    I, of course, would not be able to measure a change in their relative speeds but would measure a huge change in their momentums.

  75. valor36az says:

    I have watched your videos many times both the art and scientific value are exceptional, thank you for driving this content.

  76. Scott Paul says:

    Could the failure of relativistic mass to play a role in gravitational attraction be due to gravito-electromagnetic effects?

  77. Jitendra says:

    It's not the gravitational mass that increases, it's the inertial mass of an object. The gravitational mass is different than inertial mass irrespective of the state of motion. Moreover, these values are not equal. The Newtons law of Gravity uses gravitational mass whereas his second law of motion F=ma uses inertial mass.

  78. Navin Glettes says:


  79. the nature of reality says:

    Thanks so much , realyy that côused so many people

  80. Timothy Bedell says:

    I wish amazing things for you and your loved ones.

  81. Andi Tarigan says:

    It is weird. Imagine we have 2 clocks: 1 is dead, 1 is working. According to Einstein's relativity, the clock that is working will have its part moving, therefore it is heavier than the clock that is dead. But we know that the difference of mass between both clocks affects their weights due to earth's gravity. Thus, it means that relativistic mass must affect gravity.

  82. Harsh T says:

    Background music sounds so spooky😨😨

  83. Physics Videos by Eugene Khutoryansky says:

    You can help translate this video by adding subtitles in other languages. To add a translation, click on the following link:

    You will then be able to add translations for all the subtitles. You will also be able to provide a translation for the title of the video. Please remember to hit the submit button for both the title and for the subtitles, as they are submitted separately.

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  84. Amirhossein Moghtader says:

    What's the name of the Background music?

  85. Jon Bain says:

    If a photon departs my nose then relatively speaking my nose departs the photon at lightspeed. Thus my nose should have infinite mass relative to the photon. Which would make it a black hole at least. Then the photon could not depart my nose at all.

    But hey. Do'nt let me stop you worshipping idols.

  86. 99Gara99 says:

    Beautiful voice. Can't tell though whether this is computer generated or actual reading.

  87. md al amin says:

    how i calculate transformer. and thankyou for this video.

  88. S A Rahat says:

    According to your video, attraction of gravity is calculated by rest mass. But how does gravity attracts photon as its rest mass is zero?

  89. mrwan saprh says:

  90. mrwan saprh says:

    تم اكتشاف خطأ النسبية وبديلها

  91. Berg Mann says:


    Energy should not be calculated on the basis of the mass, because the mass is subject to the gravity of the existing place. This means that the mass energy on Jupiter is 14 times more than the same quantity on the Earth planet and this has nothing to do with the selected quantity
    The correct is to calculate the kinetic energy through the atomic weight of the tested material away from any external influences and this means a return to quantum mechanics and the amount of energy to the photon of Max Planck .

    The theory of relativity has forgotten that his energy law relates to the gravity of the earth and has not provided any free measure of mass outside gravity.
    The atomic weight of the mass is therefore the right measure for calculating the amount of energy independently.
    Unfortunately today we find the recognition of the validity of the thing or lack of validity subject to the power of the brand!
    Einstein has a big brand regardless of the validity of his sayings and theories .

  92. Kevin says:

    Your videos have inspired me to make my own videos on a brief introduction to radiochemistry. Thank you for your time and work!

  93. jkinkamo says:

    So does the slower time compensate increased inertia? How about an object on earth at 1 m height? If Earth travels at velocity near c then slower time would compensate the increased potential energy.

  94. Physics Videos by Eugene Khutoryansky says:

    To see subtitles in other languages: Click on the gear symbol under the video, then click on "subtitles." Then select the language (You may need to scroll up and down to see all the languages available).
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  95. Ĥina Ŝaeed says:

    Please explain me theoretically how mass increases when v=c

  96. Eric Su says:

    Relativistic mass is not real, of course. Conservation of momentum shows that mass is also conserved.

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