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Questions on relativistic mass and directional relativity?

  1. Apr 11, 2015 #1
    Okay these are kind of layman questions but I appreciate the time and effort for answering.

    You've probably got the question like when a proton is in the LHC what do people mean by it gains mass as it reaches a faster speed

    I realize it gains acceleration mass in the way it's continually harder to accelerate and impossible to reach the speed of light, I've been browsing this question in the past and people could not seem to agree whether it gains weight assuming you could magically weigh it, that's the first question do protons very near the speed of light actually weigh more assuming you could magically weigh them? is the attraction to the earth greater ever so slightly?

    If they do weigh more, it must be relative weight in relation to the fact that the earth isn't moving as fast relatively

    so let's say i had two iron beams that were magically accelerated to very close the speed of light going opposite directions and passing near each other, since they would weigh more (assuming that is the case) would they have an appreciable attraction toward each other? what about if they passed near each other perpendicular?

    Also say we an electron and a proton accelerated near the speed of light in opposite directions going toward each other

    this question is assuming you'd agree that at a certain point, as a proton moves faster, its attraction to an electron weakens because of time dilation, i mean thinking about it, it must be a weaker attraction because there's less attraction compared to a proton moving much slower like one on earth, when something moves fast enough even chemical reactions would occur slower from time dilation

    but if the proton is moving opposite and not relative to the electron, would the proton have more attraction to that electron than it would to another electron it's moving relative to?

    thanks for answers, let me know if you want clarification before you answer, i'll explain what i mean pretty quick
    Last edited: Apr 11, 2015
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  3. Apr 11, 2015 #2


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    We have an FAQ on relativistic mass: https://www.physicsforums.com/threads/what-is-relativistic-mass-and-why-it-is-not-used-much.796527/ [Broken]

    You are right that we cannot weigh the fast-moving particle as it zooms by - you chose well when you applied the adverb "magically". Physics doesn't handle assumptions of magic very well because assuming magic is equivalent to assuming that the laws of physics don't apply - you can't expect to get sensible answers from the laws of physics under that assumption.

    What we can say is that if an object is zooming by, and you apply a force that is exactly perpendicular to its direction of motion (and note that anyone moving relative to you will not consider the force that you're applying to be perpendicular to the particle's motion), measure its lateral acceleration as a result of that force, and then try plugging that measured acceleration and the known force into Newton's ##F=ma## and solve for the mass, you will get a value greater than the mass you'd find if the object were at rest relative to you so that you could put it on a scale and weigh it.

    That leaves a lot of room for arguing about whether the object has "gained weight". As the FAQ suggests there are easier, more general, and more powerful ways of approaching relativistic motion. Thus, it not so much that people "cannot agree" about whether the object gains weight as that that's just not the best way of thinking about the whole problem.
    Last edited by a moderator: May 7, 2017
  4. Apr 11, 2015 #3
    ok ok but what about my other questions like the iron beam question? that would answer the weight question in a way that satisfies me
    Last edited by a moderator: May 7, 2017
  5. Apr 12, 2015 #4


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    Yes, two objects moving in opposite directions at relativistic speed will feel more gravitational pull toward each other.
  6. Apr 12, 2015 #5


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    Although (stevendaryl already knows this, I'm just mentioning it for others watching the thread who may not) you cannot just plug the relativistic mass into Newton's gravitational equation ##F=Gm_1m_2/r^2## and get the correct prediction for the increased gravitational pull.

    It's also important to remember that two objects moving in opposite directions is the exact same situation as either object at rest and the other one moving past - the only thing that matters is their relative speed.
  7. Apr 12, 2015 #6
    ok but why?

    ok, and i assume this has to do with time dilation in the fact that time is very slowed down and even more so because of the fact that they are traveling in opposite directions right? and in a sense, because there's more time there's more gravity? no that's probably the wrong answer right?

    see what i'm curious about is that I could logically say a proton's electromagnetic force to an electron weakens as they travel faster and faster in a hydrogen atom toward the speed of light, perhaps we see protons gain in mass as an increase in gravity in the LHC, but maybe it has less to do with that then we think? if the proton and electron lose electromagnetic force maybe that force isn't really lost, maybe if we move iron beams fast enough in opposite directions they will innately become a magnet, maybe it's magnetism, not gravity? i mean i don't think it's that way, i'm just ruling out options

    also there becomes something more then just relativity when looking at this, what i mean is we're measuring a protons increase "in mass" in relation to the earth in the LHC, because of time dilation the proton appears to move at very near the speed of light in comparison to the earth, but that's not the maximum difference a proton could have to the earth because the earth and the proton in the LHC are always moving in relative motion in regards to the fact that the earth is in orbit and moving with the galaxy etc

    let's say the earth is traveling 99.9% the speed of light and we do an LHC proton experiment and the proton is accelerated to 99.99999999999% of the speed of light, well the proton is still traveling with the earth with the original 99.9% the speed of light, so if there was a proton with the same energy of the LHC photon passing the earth in the opposite direction we should see it moving even faster than the proton in the LHC with time dilation etc, i mean it's simple logic things appear faster when they are passing you, like with cars on a highway, but my point is the to see a true increase in the "mass" gained in a proton, the LHC wouldn't work, because it's traveling with the earth galactically and in orbit, we don't know how fast the earth is really moving... How do we know the extent or potential of a proton's mass gain in the LHC when it is not truly traveling opposite the earth?

    maybe the iron beams will have a very substantial attraction with you add that to the equation? see i just don't get it, why would the gravity of an object increase as it travels faster opposite another object when they pass each other like cars in a highway? It would be more convenient for me to say this force didn't exist, but since i hear about it so much it confuses me
  8. Apr 12, 2015 #7


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    The earth IS travelling at 99.9% of the speed of light. Right now, even as I type this, the earth is moving at 99.9% of the speed of light relative to someone somewhere in the universe. If that person were to calculate the mass of the earth using the method that I described above (apply a known sideways force to the earth, see what the resulting acceleration is, use this to calculate the mass of the earth from ##F=ma##) that person would find that the earth's mass is greatly increased. Of course, as far as we're concerned, the earth is at rest with its mass unchanged and it's the other guy who is moving at 99.9% of lightspeed and has a greater mass. Meanwhile, a third observer moving relative to both the earth and the other guy would conclude that we are both moving and have gained mass as a result.

    This is why I said above that the only thing matters is the relative speed - if something is moving relative to you, your measurements of its mass will show an increase compared to what would be measured if it were at rest relative to you. Different observers moving at different speeds relative to the object will find different masses.

    There is no such thing as how fast anything is "really moving". All we have are relative speeds - the earth is at rest relative to the tree in my front yard, moving at 100 km/hr relative to the car I'm driving (more often we'd say that the earth is at rest and the car is moving at 100 km/hr, but it's the same thing either way) moving at several kilometers per second relative to the planet Mars (we say that it's Mars that is moving, but the average Martian won't see it that way; astronomers on both Mars and Earth will likely say that we're both wrong and choose the convention that it's the sun that is at rest with both Earth and Mars moving at different speeds relative to the sun).
  9. Apr 12, 2015 #8
    i get what you're saying and i agree but i still would like answers to some questions
  10. Apr 12, 2015 #9


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    An alternative approach is to start learning Special Relativity "properly". You may have reached the limit of what it is possible to understand and have explained without your getting a formal grasp of the basics. Imagine you'd never learned the rules of chess, say, but wanted to understand a game. Someone could say "white is attacking" or "black has made a mistake" and it makes sense, But, if you want to know "why did white move his Knight there?" Then, you've reached the point where you've got to learn the game!
  11. Apr 12, 2015 #10
    Nicely put!
  12. Apr 12, 2015 #11
    well my question is still valid and I don't really see how anything Nugatory has said has changed anything

    if no one wants to try and answer why two beams would have more attraction, i'm curious how much more attraction would they have compared with two beams on earth for instance

    this is basically how this stuff works, someone asks a question which has some merit but they use non-technical terms or it's impossible to correctly phrase the question, and then someone comes in and says "what do you mean by so and so?" and the question never really gets addressed or answered
  13. Apr 12, 2015 #12


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    You want a numerical answer? That requires a calculation, which is sort of complicated to do. However, let's change the problem slightly to make the calculation easier to do. Suppose you have many, many particles moving around inside a sphere of radius [itex]R[/itex]. The particles all have the same velocity [itex]v[/itex] and the same rest mass [itex]m[/itex]. The particles are approximately equally spread out within the sphere, and their velocities point in random directions (so that the total momentum adds up to zero).

    Then the total energy inside the sphere will be [itex]N \gamma m c^2[/itex], where [itex]m[/itex] is the mass of one particle, and [itex]N[/itex] is the number of particles, and [itex]\gamma = \dfrac{1}{\sqrt{1-\frac{v^2}{c^2}}}[/itex]. This system will have approximately the same gravitational effect as a sphere of radius [itex]R[/itex] and mass [itex]N \gamma m[/itex].

    For just two particles, or two beams, the calculation is more complicated. Do you really insist that somebody do that calculation for you?
  14. Apr 12, 2015 #13
    i guess more i'm curious as to a very general number, like two steel beams passing near each other like a foot away at opposite directions going 99.99999999999999999% speed of light

    if i took two steal beams on earth which were not moving relative to each other, i would visually detect no gravity between them, although a very small amount of gravity would be there, but in general how much greater would that attraction be with the beams moving near the speed of light? several times greater only? millions of times greater? i mean i'm talking about instantaneous measurement of gravity, while impossible, you should be able to stop the steel beams and see how close they went together for a measurement

    I just think it's an interesting effect, that gravity would increase, you'd think it would be taught more in schools etc

    and i just realized after looking at it i've been spelling steel wrong all this time
    Last edited: Apr 12, 2015
  15. Apr 12, 2015 #14


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    Gravity is so weak that a normal-sized object would have to be moving at a speed of 99.999999999999999999999999999999999999999999999999% of the speed of light (with some number of 9s, maybe 20 or so) to have a significant gravitational effect.
  16. Apr 12, 2015 #15
    well that pretty much answers my question, i don't see how suck a weak attraction could be attributed to anything else but gravity

    still i have 1 last thing, like a proton at 7 TeV in the LHC, we can't weigh it, but we can say it would have a gravitational increase of like how many factors? since what you said about the iron beams i can only assume the attraction would only be by a small factor maybe 2 to 20 times more?

    i've been working on a science theory for a while now, it's more abstract but i'm always confused by weird forces i can't understand

    also 1 more thing.... I'm happy with the answers so far so i won't mention it again, but the electron and the proton moving near the speed of light opposite directions, the electron would have a far greater attraction to the proton than would an electron and proton with the same distance between them moving the same direction at the same speed? they would basically have an increased attraction because they are not moving relative to each other at the same speed so they would not suffer time dilation as much right?
  17. Apr 12, 2015 #16
    I really think you should take a mathematical course on GR then, it'll definitely help.
  18. Apr 12, 2015 #17
    it only has some do to with GR, i could write a paper on it and not even mention it, but.... i pretty much know what answers i'm going to get from you guys, i'm more or less just feeling around, but i would like answers

    I don't think GR or SR are as complicated as you'd all have me believe, i've read about it, how it works, etc from various places many times over the years, knowing about how something works is far different than knowing why it works
    Last edited: Apr 12, 2015
  19. Apr 12, 2015 #18


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    Protons at rest have an energy of 940 MeV, at 7 TeV they have ~8000 times this energy. If you could put the whole LHC on a scale with infinite precision, you would notice that it got heavier by a few micrograms. Well, more than that as the energy stored in the magnets is much larger than the energy stored in the beams.

    A massive object, flying past earth (or anything else) very close to the speed of light, will get twice the deflection it would get with Newtonian gravity. That is the same factor light has.

    You would have to take into account the relativistic transformations of electromagnetic fields.

    Can you calculate the trajectory of an object in the Schwarzschild metric? What about the Kerr metric?
    Theories are not collections of words, they are formulas together with words describing how those equations are related to the universe - but the formulas are the main part.
  20. Apr 13, 2015 #19
    It might be worthwhile to ask yourself why you might more easily believe otherwise. What models or rules are you using to come to a different conclusion? Just coming to grips with that can put you a few steps toward understanding another model.
  21. Apr 13, 2015 #20
    this site lags my old video card for some reason, that and my head hurts, i guess i'll so just type on wordpad soo much easier

    ok i'm aware that the fields become stretched and there's more to account for, i'm basically only talking about the effects of time dilation
    i'll probably go to a particle physics subforum since the question could be phrased as a binding energy question
    such as the binding energy of a proton and electron at near light speeds, like i said before, the attraction of an electron and proton in a hydrogen atom should weaken as they approach light speed, but if an electron and proton were to pass each other going opposite directions, i think there might be an increase in attraction (not speaking gravitational), it's basically a binding energy question and if anyone has any links about opposing particles and their binding energies at near light speeds i would like to read them

    this might not do me any favors saying this but base particles have a lot to do with light speed, particles that are small enough cannot rotate enough internally so they must have a base speed in order to reach the speed of light (electrons quarks photons protons) but probably not neutrons, i believe all particles are composed of photons and i'm trying to figure out if the electron's attraction has more to do with internal rotating photon speed or external directional speed, it's harder than it looks to answer i guess but i've only been thinking about it for a weekish

    my head feels better now, btw thanks for the 2x deflection i remember reading that somewhere about how photons have twice the gravity or something, but it's interesting and i shouldn't have forgotten it

    i mean some of you are telling me i need to learn such and such, but literally you're wasting your time because i've been told that sooo many times over the years and i've also said exactly this response so many times over the years and this response talking about this response soo many times over the years, i go about this stuff my own way, i just can't learn in school settings etc
    Last edited: Apr 13, 2015
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