(ELI5) why can’t massless particles travel infinitely fast?

• B
• balls
Beyond this speed, the laws of physics break down and we can't say what happens to the particle. Massless particles simply don't work the same as massive particles. They are fundamentally different kinds of entities and you can't apply the same intuitions to them.

balls

TL;DR Summary
why can’t you push something that’s massless with a finite amount of energy to make it travel infinitely fast.
I feel like if something is massless it should be able to travel infinitely fast with any amount of energy. When you have something with mass, you would need an infinite amount of energy to push it infinitely fast, but if the thing you’re pushing is massless, you should be able to push it with a finite amount of energy to make it travel infinitely fast, but you can only push it to about 300,000 km/s, why?

What have you done on your own to answer this? This comes across as "I just don't believe in Relativity", which is kind of hard to counter.

vanhees71
balls said:
I feel like
The short, blunt answer to this is, Nature doesn't care about your feelings. We know from an enormous amount of experimental data that massless particles travel at the speed of light.

balls said:
if the thing you’re pushing is massless, you
...cannot "push" it at all. It always travels at the same speed.

balls said:
you can only push it to about 300,000 km/s, why?
No, you don't "push" a massless particle to the speed of light. It always travels at the speed of light.

In other words, massless particles simply don't work the same as massive particles. They are fundamentally different kinds of entities and you can't apply the same intuitions to them.

russ_watters, DennisN, robphy and 2 others
C is also the speed of causality. If it were infinite, causality would not exist. An effect cannot occur from a cause that is not in the back (past) light cone of that event.

LOL, Today I Learned that ELI5 = "Explain it Like I'm 5"

SammyS, russ_watters, anorlunda and 1 other person
berkeman said:
LOL, Today I Learned that ELI5 = "Explain it Like I'm 5"
LOL. I was wondering what that meant!

PeterDonis said:
To be fair, Nature doesn't care about anybody's feelings. No privileged observers.

DaveC426913, vanhees71, strangerep and 1 other person
balls said:
Summary: why can’t you push something that’s massless with a finite amount of energy to make it travel infinitely fast.

you should be able to push it with a finite amount of energy to make it travel infinitely fast, but you can only push it to about 300,000 km/s, why?
The relationship between mass, energy, and momentum is: ##m^2 c^2=E^2/c^2-p^2## then for a massless object ##m=0## so this simplifies to $$E=pc$$
The relationship between velocity, energy, and momentum is $$v=pc^2/E$$
Combining these we get that for a massless object $$v=pc^2/E=pc^2/pc=c$$

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john.phillip, Grinkle and vanhees71
There is a deeper question here that has been stumbled upon by the OP, perhaps unwittingly. It boils down to the different meaning of ”mass” in relativity and classical mechanics. In classical mechanics, mass is inertia, a resistance to acceleration typically found in Newton’s second law. In relativity, mass is rest energy and is not directly related to inertia by definition. In fact, in relativity inertia is direction dependent for moving objects. One of the big insights of relativity is the fact that at low speeds the inertia is equal to the rest energy - hence the use of the same nomenclature and ##E = mc^2##.

If you just consider Newton’s second law and think ##F=ma## for something ”massless” it does seem to make sense that acceleration would become infinite. But Newton’s second law in the form presented is only strictly valid in an object’s rest frame and a massless particle has no rest frame.

Mister T, vanhees71 and robphy
CoolMint said:
C is also the speed of causality. If it were infinite, causality would not exist. An effect cannot occur from a cause that is not in the back (past) light cone of that event.
Galilean / Newtonian physics has an infinite maximum signal speed.
But it also has a causal structure.
(Technical point: the Galilean causal order is not a total order
when the relation is irreflexive: that is, it is a strict partial-order.
Physically speaking,
pairs of events can be ordered as long as they are not "simultaneous"
(i.e., if they are "spacelike-related in the Galilean spacetime").
https://en.wikipedia.org/wiki/Partially_ordered_set#Non-strict_partial_order )

Massless particles have "4-momentum" along the future-pointing cone (dashed cyan ray) in an energy-momentum diagram.

Although not shown for the ##m=0##-case,
increasing ##E## would require that ##p## increase such that
the new 4-momentum is still along the same dashed-cyan ray, but further up.
This is what special-relativity tells us.
And this agrees well with the experimental evidence.

Dale
robphy said:
increasing ##E## would require that ##p## increase such that
the new 4-momentum is still along the same dashed-cyan ray, but further up.
This is what special-relativity tells us.
And this agrees well with the experimental evidence.
To put this another way, adding energy to a massless particle doesn't increase its speed, it increases its frequency.

robphy
balls said:
(ELI5) why can’t massless particles travel infinitely fast?
Because according to the laws of physics, there exists a general speed limit.

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The constant speed, c, of light forces us to model a geometry where there is a trade-off between speed and time. An object traveling faster appears to a stationary observer to have its time go slower. In that geometry, there is no speed greater than c.

Orodruin said:
There is a deeper question here that has been stumbled upon by the OP, perhaps unwittingly. It boils down to the different meaning of ”mass” in relativity and classical mechanics. In classical mechanics, mass is inertia, a resistance to acceleration typically found in Newton’s second law. In relativity, mass is rest energy and is not directly related to inertia by definition. In fact, in relativity inertia is direction dependent for moving objects. One of the big insights of relativity is the fact that at low speeds the inertia is equal to the rest energy - hence the use of the same nomenclature and ##E = mc^2##.

If you just consider Newton’s second law and think ##F=ma## for something ”massless” it does seem to make sense that acceleration would become infinite. But Newton’s second law in the form presented is only strictly valid in an object’s rest frame and a massless particle has no rest frame.
In addition massless particles do not make sense in Newtonian physics, particularly not in quantum mechanics.

bhobba and malawi_glenn
robphy said:
Maarten Havinga said:
From the reference frame of the massless particle,

...snip...

(Correct me if I'm wrong)
There is no such reference frame of a massless particle.

Here is an old post on why I say this:

punchline:
A set of reasonable properties of a "reference frame"
as applied to particles with nonzero mass
has problems
when applying them to particles with zero invariant-mass.

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Ibix, bhobba and Doc Al
balls said:
I feel like if something is massless it should be able to travel infinitely fast (...) but you can only push it to about 300,000 km/s, why?

I like Dale's answer and there's a video that touches the core of the issue (with a hat trick) and hopefully does not deviate too much from the ELI5 requirement:

Dale
balls said:
Summary: why can’t you push something that’s massless with a finite amount of energy to make it travel infinitely fast.
Because there's no such thing as infinitely fast. The fastest speed possible is ##c##.