# I Momentum of Light

#### bob012345

Gold Member
Summary
Momentum of Light is weird.
Light is a funny thing. If it could move slower it would have more momentum, not less! How weird is that? Or is that all wrong? I would appreciate comments on that.

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#### PeterDonis

Mentor
If it could move slower it would have more momentum, not less!
What are you basing this on?

#### bob012345

Gold Member
Momentum of light is Energy/c. If c were smaller, momentum is larger.

• Dale

#### Ibix

In sensible units, $c=1$ and the magnitude of light's momentum is equal to its energy. $c$ isn't best thought of as the speed of light. It's just the natural conversion factor between units of time and distance. It's a property of massless objects in spacetimes with a Lorentz signature that they travel at that speed.

That's a longwinded way of saying "you can't change $c$". Research reported as considering a changing $c$ is generally actually considering a changing fine structure constant.

#### Nugatory

Mentor
Momentum of light is Energy/c. If c were smaller, momentum is larger.
$c$ can’t be smaller because it’s a constant. What you’ve found is that if the energy is smaller then so is the momentum, and vice versa. That’s not such a strange result.

#### PeterDonis

Mentor
Research reported as considering a changing $c$ is generally actually considering a changing fine structure constant.
And, just to be clear, doing that would not change the relationship bewteen the momentum and energy of light. It would only change, for example, how much energy would be contained in light emitted from a particular physical process, such as a laser using a particular kind of atom.

• Ibix

#### bob012345

Gold Member
So, in a hypothetical universe where c has half it's value in our universe, assuming we could construct units of the same values when compared in both universes wouldn't light contain twice as much momentum per unit energy? And relativistic massive particles would also have more momentum per unit energy I think.

#### jbriggs444

Homework Helper
So, in a hypothetical universe where c has half it's value in our universe, assuming we could construct units of the same values when compared in both universes wouldn't light contain twice as much momentum per unit energy? And relativistic massive particles would also have more momentum per unit energy I think.
How do you plan to compare dimensionful values for sameness when they arise in different universes?

If you change the dimensionless fine structure constant while holding all other dimensionless constants unchanged then the question could be sensible (and the answer likely a tautology arising from the chosen system of natural units). As has been suggested already.

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#### pervect

Staff Emeritus
Summary: Momentum of Light is weird.

Light is a funny thing. If it could move slower it would have more momentum, not less! How weird is that? Or is that all wrong? I would appreciate comments on that.
In special relativity, the speed of light is assumed to be constant. In most cases (as in Einstein's formulation of the theory), this is by postulate, though occasionally different postulates are used and the result is derived rather than assumed.

If one assumes that the speed of light also can change while still assuming it remains constant, one can indeed get logical contradictions. The solution to this is fairly simple - don't assume that the speed of light is both constant, and also able to change, at the same time.

• nasu

#### PeterDonis

Mentor
in a hypothetical universe where c has half it's value in our universe
This universe could be our actual universe with standard meter sticks twice as long as the current ones. And in that case your claim would be false: light would have exactly the same momentum per unit of energy that it has now. The specific numbers associated with that momentum and energy would be different, but that wouldn't change any of the actual physics. You can't change physics by changing units.

• jbriggs444

#### PeterDonis

Mentor
You can't change physics by changing units.
And with that, which is basically the short answer to the OP's question, this thread is closed.

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