# Do objects gain mass while approaching light speed?

• I
• LightningInAJar
In summary, relativistic mass is now a deprecated concept, as it is simply a confusing synonym for total energy. Matter, with no qualifier, means the invariant mass. Massive objects cannot reach the speed of light, as they always need to increase speed by 3×10^8 m/s to reach lightspeed. Higgs bosons don't work by accumulating on things anyway.

#### LightningInAJar

I watched a fermilab video claiming objects don't actually gain mass as they approach light speed. Is that true? What keeps things of mass from reaching the speed of light or beyond? I assume matter doesn't accumulate higgs-bosons while in motion?

Yes it is true. "Relativistic mass" is now a deprecated concept, as it is simply a confusing synonym for total energy. Mass, with no qualifier, means the invariant mass.

The reason massive objects cannot reach ##c## is that they are always free to regard themselves as "at rest", by the principle of relativity. Thus they always need to increase speed by ##3×10^8\mathrm{m/s}## to reach lightspeed.

Higgs bosons don't work by accumulating on things anyway.

IroAppe, topsquark and vanhees71

pinball1970, topsquark and vanhees71
LightningInAJar said:
I watched a fermilab video claiming objects don't actually gain mass as they approach light speed. Is that true?
They do not gain invariant mass, which is the thing that most physicists mean when they use the word mass.

LightningInAJar said:
What keeps things of mass from reaching the speed of light or beyond?
No finite amount of energy or momentum is sufficient to reach the speed of light.

topsquark, vanhees71, Ibix and 1 other person
LightningInAJar said:
What keeps things of mass from reaching the speed of light or beyond?
I'm going to expand a bit on my previous answer here. There are many ways to approach this.

I like my answer because it follows immediately from Einstein's postulates.

Dale's answer also works. Kinetic energy is ##E=(\gamma-1) mc^2## and momentum is ##p=\gamma mv## where ##\gamma=1/\sqrt{1-v^2/c^2}##, so no matter how much energy or momentum you supply you can only approach lightspeed because ##\gamma\rightarrow\infty## as ##v\rightarrow c##. (Incidentally, if you define relativistic mass ##m_r=\gamma m## then ##p=\gamma mv## becomes ##p=m_rv##, so the "relativistic mass goes to infinity" argument is just this one, but in obsolete terminology.)

Or you can observe that the mass is the modulus of the energy-momentum four vector, and things moving at light speed have a zero modulus. So "massless" and "can only travel at the speed of light" are synonyms in relativity, and "massive" and "cannot travel at the speed of light" are synonyms.

I'm sure there are other arguments. It depends what you like.

pinball1970, Klystron, topsquark and 2 others
Ibix said:
Or you can observe that the mass is the modulus of the energy-momentum four vector, and things moving at light speed have a zero modulus. So "massless" and "can only travel at the speed of light" are synonyms in relativity, and "massive" and "cannot travel at the speed of light" are synonyms.
This one is my actual preference, but usually it doesn't help beginners.

topsquark, vanhees71 and Ibix
I'd only be pedantic and not call it modulus. It's ##p_{\mu} p^{\mu}=m^2 c^2## with ##(p^{\mu})=(E/c,\vec{p})##. So ##m^2 c^2=(E/c)^2-\vec{p}^2##. The fundamental form of Minkowski space is not positive definite (and it's crucial to be so!) and thus it doesn't induce a norm on Minkowski space.

For particles and for reasons of causality you must have ##m^2 c^2=p_{\mu} p^{\mu} \geq 0## though, and that's why ##m^2 \geq 0##. One should also note that the case of massless "particles" is a special case, and one should not take the particle picture to seriously.

topsquark
vanhees71 said:
For particles and for reasons of causality you must have ##m^2 c^2=p_{\mu} p^{\mu} \geq 0## though, and that's why ##m^2 \geq 0##.
Someone should tell the tritium decay experiments …

topsquark, vanhees71 and malawi_glenn
vanhees71 said:
I'd only be pedantic and not call it modulus.
Is there a better name?

vanhees71
That's a good question! I'm not aware of a common name for a Minkowski product of a vector with itself.

Ibix
LightningInAJar said:
What keeps things of mass from reaching the speed of light or beyond?
The geometry of spacetime. Either there is an absolute fastest speed or there isn't. We know from doing experiments and designing equipment that there is.

nasu, Klystron, topsquark and 1 other person
If hypothetically we had a spaceship traveling faster and faster in space, but it's fuel tank isn't located on board and therefore not part of the ship's total mass could it then reach lightspeed? If say there were Dr. Strange portals transferring fuel from Earth to the moving ship over potentially unlimited distance. Could the ship be propelled much faster if the fuel mass becomes irrelevant?

Also did we learn anything new from the recent experiment that extracted matter from photons?

LightningInAJar said:
If hypothetically we had a spaceship traveling faster and faster in space, but it's fuel tank isn't located on board and therefore not part of the ship's total mass could it then reach lightspeed?
No. As already stated, nothing with non-zero mass can reach light speed. Full stop.
LightningInAJar said:
If say there were Dr. Strange portals transferring fuel from Earth to the moving ship over potentially unlimited distance.
If you are using magic you are only limited by what the scriptwriter wants. Magic does not work in the real world.
LightningInAJar said:
Also did we learn anything new from the recent experiment that extracted matter from photons?
Which experiment do you mean?

mattt, topsquark, malawi_glenn and 2 others
LightningInAJar said:
If hypothetically we had a spaceship traveling faster and faster in space, but it's fuel tank isn't located on board and therefore not part of the ship's total mass could it then reach lightspeed? If say there were Dr. Strange portals transferring fuel from Earth to the moving ship over potentially unlimited distance. Could the ship be propelled much faster if the fuel mass becomes irrelevant?
This is getting very, very close to the sort of unfounded speculation that is off limits here at PF.

The short answer to all of your questions is: no. What makes it no is the fact that the geometry of spacetime has a particular causal structure. (That is basically what @Mister T in post #11 was getting at.)

LightningInAJar said:
Also did we learn anything new from the recent experiment that extracted matter from photons?
No. The physics involved has been understood for decades; it just wasn't experimentally feasible to actually do it until now.

topsquark and vanhees71
My understanding is that relativistic mass is simply that mass quantity that is observed by some arbitrary observer, whereas proper mass is the mass that is observed by an observer that is at rest with respect to the mass. Thus, the term "relativistic mass" is a dependent on the motion state of the observer.

Motore and PeroK
swampwiz said:
My understanding is that relativistic mass is simply that mass quantity that is observed by some arbitrary observer, whereas proper mass is the mass that is observed by an observer that is at rest with respect to the mass.
No. "Relativistic mass" is the total energy divided by ##c^2##, which is the zeroth component of the four momentum. "Invariant mass" (aka "rest mass" or usually just "mass" these days) is the modulus of the four momentum. They are completely different things, and calling them both "mass" was confusing, not to mention that there are at least two different quantities called "relativistic mass". That's why "relativistic mass" is now a deprecated term.
swampwiz said:
Thus, the term "relativistic mass" is a dependent on the motion state of the observer.
Its value depends on the state of motion of the object in whatever frame you are working in, yes.

Last edited:
topsquark
Ibix said:
No. "Relativistic mass" is the total energy divided by ##c^2##, which is the zeroth component of the four momentum. "Invariant mass" (aka "rest mass" or usually just "mass" these days) is the modulus of the four momentum. They are completely different things, and calling them both "mass" was confusing, not to mention that there are at least two different quantities called "relativistic mass". That's why "relativistic mass" is now a deprecated term.

Its value depends on the state of motion of the object in whatever frame you are working in, yes.
But if an observer were to experimentally measure the mass of a moving body, wouldn't xe measure the relativistic mass?

PeroK
vanhees71 said:
That's a good question! I'm not aware of a common name for a Minkowski product of a vector with itself.
Well, as discussed in other threads, almost all textbooks on relativity call it norm or modulus, despite the imprecision that bothers you. Of course they know it is not a norm in the mathematical sense, but no other convenient name has caught on.

vanhees71
swampwiz said:
But if an observer were to experimentally measure the mass of a moving body, wouldn't xe measure the relativistic mass?
No. If an observer used some experiment and the number that resulted was the relativistic mass, then by definition that experiment would not be considered a measurement of mass.

vanhees71, PeroK and Ibix
swampwiz said:
But if an observer were to experimentally measure the mass of a moving body, wouldn't xe measure the relativistic mass?
There are experiments whose outcome depends on the relativistic mass. But they are not measures of mass, they are measures of relativistic mass.

swampwiz said:
But if an observer were to experimentally measure the mass of a moving body, wouldn't xe measure the relativistic mass?
Not if the experiment involved measuring gravitational attraction.

Also, relativistic mass is directional. If you apply a force to a mass, then its relativistic mass depends on which direction you apply the force. Which makes relativistic mass somewhat unphysical, IMO.

Why can't you accept that relativistic mass is an old idea that has been dropped from modern physics?

Forget about it and move on, or you'll never learn anything about relativity.

mattt, vanhees71, Vanadium 50 and 2 others
PeroK said:
Not if the experiment involved measuring gravitational attraction.
Depends a bit what you mean. You can argue by the equivalence principle that the weight of a horizontally moving object ought to depend on its transverse relativistic mass.

Consistent with your note that relativistic mass is directional, for an object sliding down a slope the weight depends on some mix of the transverse and longitudinal masses. So in relativity objects no longer have a single defined weight, and simply measuring its weight no longer gives you its mass (in any sense of the word) by any simple process.

swampwiz said:
But if an observer were to experimentally measure the mass of a moving body
How? In relativity, it's important to define the procedures for making measurements.

I don't understand the PF tendency to necropost a totally wrong answer.

"Relativistic mass" is a concept that existed in the professional literature for about two years, before it was realized that it was a lovely combination of "useless" and "wrong". Unfortunately, it persists in popularizations and Just Will Not Die. Equally unfortunately, people read these popularizations and think it makes them experts.

You can't mix relativistic mass and gravity, and you can't mix it with F=ma. Sometimes it gets the right answer. So does a stopped clock.

russ_watters, dextercioby, mattt and 6 others
This is a good place to tie off this thread.

vanhees71

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