# Mass/Light Relationship

*Most recent answer: 06/06/2008*

- Joshua Spudeno (age 27)

Shillington, Pa, USA

See

LeeH

*(published on 06/06/2008)*

## Follow-Up #1: solar sails

- Drew (age 23)

blacksburg va

*(published on 07/01/2008)*

## Follow-Up #2: Moving things with light pressure

- Ryan (age 13)

California

See:

LeeH

*(published on 03/19/2009)*

## Follow-Up #3: weighing light

- mohammad Imran (age 22)

NOIDA, U.P., India

The answer is yes, that when the light escapes from the box the weight of the box goes down a little.

I think, from a rough calculation, that about one part in 10

^{8}of the Sun's gravitational mass comes from the light in it. That calculation could easily be off a factor of ten either way, since I used very approximate numbers.

Q2. Also yes, if you heat something up, leaving everything else the same, it has more energy, i.e. more mass and more weight. At ordinary temperatures the effect is minuscule. In think the thermal contribution to the weight of ordinary matter at room temperature is less than one part in 10

^{13}or so.

Mike W,

*(published on 04/24/2009)*

## Follow-Up #4: Losing mass through light emission

- lovepreet (age 23)

bhagta ,punjab ,india

^{-19}ergs. That number divided by c

^{2}is 1.8 10

^{-36}kilograms. Even though there are lots and lots of photons in a laser beam it still adds up to an unmeasurable amount. Give up.

LeeH

Even if you radiate a kilowatt for a day, you lose about 10

^{8}Joules of energy. That's equivalent to 10

^{-9}kg of mass. Not a lot. Mike W.

*(published on 06/17/2009)*

## Follow-Up #5: absorbed light

- Nathan Garcia (age 17)

San Antonio, Texas

Yes, they'd just heat the box up.

2)"would that have any impact on the object at all?" Yes, it would heat up noticably. There would also be a very slight force pushing on it.

Mike W.

*(published on 06/18/2009)*

## Follow-Up #6: relativistic infinities?

- Matthew (age 37)

New York, NY

^{2}, then you can't have m-> infinity unless E does too. So, neither one does.

What people mean when they say 'm-> ∞' is that as v->c m keeps growing without any limit. So v can't reach c, because that would require an infinite amount of energy.

The specific form is that

E/c

^{2}=m=m

_{0}/sqrt(1-(v/c)

^{2}),

where m

_{0}is the mass as seen by someone moving along with the object, called the rest mass.

Now for your more interesting question. If light has E and hence m, how can it then travel at c? If light had m>0 when it was traveling at any v<c, we'd have a big problem. However, light can't travel at less than c. (But see comment below- here we're only talking about in a vacuum.). It only has E or m when traveling at c. For light, m

_{0}= 0.

A general form which covers the cases both of m

_{0}>0 and m

_{0}=0 is:

E

^{2}(1-(v/c)

^{2})=(m

_{0}c

^{2})

^{2}

When v=c, this requires m

_{0}=0.

^{ }Likewise when m

_{0}=0 it requires that E=0 or v=c. When m

_{0}>0, it gives the formula above.

^{}

Mike W.

^{}

^{ }

*(published on 06/25/2009)*

## Follow-Up #7: Velocity of light

- Joe

Edison, NJ, USA

LeeH

*(published on 08/24/2009)*

## Follow-Up #8: Light

- Luke (age 32)

Brisbane, Australia

You aren't accelerating anything when you turn on a light. The light is born traveling at c and stays that way.

There is no rule that "matter" is conserved because "matter" is not a defined quantity.

The pre-relativistic rules about conservation of mass and energy are replaced in Special Relativity by a unified conservation of energy. The energy that makes light comes from other sources, e.g. the electrical power supplied to your house.

When you are hit by light you do indeed pick up some momentum (p) as well as the obvious energy (which you can feel). The momentum is very small, however, since p=E/c for anything traveling at c. For example, 1 Watt of light energy hitting a surface exerts a force of 3.3 nano-Newtons on it. (6.6 nN if it's reflected rather than absorbed.) That can be measured with instruments, but not directly felt.

Mike W.

*(published on 09/01/2009)*

## Follow-Up #9: light in universe

- Wade Hampton (age 62)

Phoenix AZ USA

Mike W.

*(published on 09/15/2009)*

## Follow-Up #10: light and gravity

- Aryaki (age 17)

India

It's a little more complicated than just thinking of something following a projectile path, however, because it turns out that the curvature is twice as much as you would guess in that picture. Spacetime itself isn't flat when there's gravity, and the geometry of it is described by General Relativity.

Mike W.

*(published on 09/15/2009)*

## Follow-Up #11: Effect of light on universe

- Milo (age 32)

Seattle

Very localized light, for example from a supernova, can affect nearby regions but the overall effect is small. Consider the total effect of lightning bugs on a summer's eve; it's pretty but it doesn't give you enough light to read by.

LeeH

*(published on 09/16/2009)*

## Follow-Up #12: light bouncing off water

- Savannah (age 13)

Jacksonville, FL

Mike W.

*(published on 09/30/2009)*

## Follow-Up #13: Light speed, teleportation, and exact timing

- Danijel (age 27)

Houston, TX

Q2. Yes it's difficult to predict the exact time but it can be done. The problem is that general relativity screws things up when you want to have a precise time in the presence of gravitational field and relative velocities. In fact the famous Global Positioning System (GPS) has to use the theory of general relativity in order to make corrections for the earth's gravitational potential as well as relative velocities of the various satellite components. These involve microsecond time discrepancies, which imply 1,000 foot discrepancies in global positions.

See:

and then click on the Special and General Relativity topic.

LeeH

*(published on 10/06/2009)*

## Follow-Up #14: light, mass, matter

- Eli B (age 15)

CT USA

These days, we're partway in to the process of describing fields like electromagnetism in terms of some deeper more basic fields. However, these deeper ingredients will have no more resemblance to intuitive ideas of 'matter' than do our familiar electromagnetic fields. So far as we can tell, there are no little building blocks.

At some point the word 'matter' becomes essentially a meaningless label. There's some sort of underlying mathematical description (like the equations governing electromagnetism) and that's it.

Mike W.

*(published on 10/20/2009)*

## Follow-Up #15: Mass in modern physics.

- Brent (age 68)

Houston, tx USA

I think you might (understandably) be confused about a couple terms physicists like to use, most notably, "mass". I'd also like to point out that light is composed of photons, not electrons.

Ever since Einstein proposed special relativity, the word "mass" has come to mean very different things depending on the context. I personally think the misuse of the term "mass" is responsible for a lot of the confusion people have about modern physics.

First I'd like to distinguish mass and weight, we tend to naturally assume they are the same thing, but they are really not. Weight is essentially the gravitational force exerted by a body on an object. In our everyday life this is the force of gravity exerted by the earth on us and the objects around us. While it is true that something with more mass weighs more, they are not the same thing.

So what is mass? Before Einstein the word mass really only meant one thing: a measure of "inertia". What's inertia? It's a fancy term for "how hard something is to push". So a boulder is harder to push around than a pebble because it has more mass, which means more inertia.

Why did stuff get so confusing after Einstein? It has a lot to do with his most famous equation: E

_{o}=mc

^{2}. What many people don't know is that this equation isn't the full story. The more useful, but less ubiquitous equation is actually E=√[ (pc)

^{2}+(m

_{o}c

^{2})

^{2}] The simpler form comes out when p, which is momentum, is zero; when what we are describing isn't moving.

Why did I write the mass term as m

_{o}in the last equation? It's to clearly show that we mean it's the "rest mass" of the object we are describing.

^{}

You referred to rest mass in your question. This is generally what physicists talk about when they say "mass" in the context of modern physics. Rest mass is quite simply the mass something has in its own reference frame; its mass when it is not moving. Photons have zero rest mass. Anything with zero rest mass always moves at a speed c, which we call the speed of light.

Electrons, protons, neutrons, and pretty much everything else that we deal with in day to day life have rest mass. Anything with rest mass naturally gains more and more energy as we speed it up. This energy is equivalent to "inertial mass". Inertial mass is what you multiply the velocity by to get the momentum. One could think of this as the object gaining more "mass" as it speeds up, but physicists usually don't use the term that way.

The idea of "inertial mass" has an intuitive appeal in special relativity though: as you speed something up more and more (giving it more energy) you also increase its inertial mass. Earlier I said that inertia is "how hard something is to push". If the object is gaining inertia as it speeds up, then it would imply that it also gets harder to push. Well that is exactly what happens. When you take something and try to accelerate it to a significant fraction of the speed of light, it gets increasingly difficult to make it go any faster. This is why particle accelerators like the Large Hadron Collider are so complicated. They accelerate particles to 99.9999991% the speed of light, which requires monumental amounts of energy.

Another potentially appealing property of relativistic mass is that it is additive. This makes the quantities easy to deal with conceptually, since they add just like a classical mass would. The inertial mass also is the quantity that enters into gravity, so light does indeed have weight, but not much.

In conclusion, Einstein wasn't wrong, but the terminology needed to understand special relativity can get confusing and is often misinterpreted.

Matt J.

*(published on 02/28/2012)*