Why does c have to be the speed of light

• drinkey
In summary, the equation E=mc2 is determined by Einstein's theory of special relativity, where c represents the speed of light and c2 is a conversion factor between energy and speed. This means that for 1 kg of mass, the equivalent energy is 9 x 1016 Joules, and for 1 gram it is 9 x 1013 Joules. This is because the inertial mass of a moving object increases with speed, and the limit speed is c. Therefore, the energy formula constant must be c2.
drinkey
In e=Mc2 Does c have to be exactly the speed of light? Can it not be a slightly bigger or smaller number? Or does C squared simply represent an enormous number?

drinkey said:
In e=Mc2 Does c have to be exactly the speed of light? Can it not be a slightly bigger or smaller number? Or does C squared simply represent an enormous number?

Welcome to physicsforums!

Your question has been thoroughly discussed recently, here:

welcome to pf!

hi drinkey! welcome to pf!

(try using the X2 button just above the Reply box )
drinkey said:
In e=Mc2 Does c have to be exactly the speed of light?

yes

c2 is really only a conversion factor, between the units for energy and speed

if, instead of the metres and kilograms in the SI system, we used light-seconds and a similar light-based mass unit (such as is used in studying black holes), then the equation would just be e = m

Light moves at speed c because photons are massless.

Thanks for your answer TT. I read the thread suggested but now my brain hurts! I am a novice that did not do physics at school but am now fascinated by the subject. I saw this somewhere where a question was asked about the energy in a kg of matter (rest)

This is determined by Einstein's equation E = mc2, where c = velocity of light = 3 x 108 meters/sec. So c2 = 9 x 1016. For 1 kg of mass therefore the equivalent energy is 9 x 1016 Joules, for 1 gram it is 9 x 1013 Joules.

Note units, in the SI system energy is in Joules, mass in kg, distances in meters. If you keep to these units you will get consistent results.

So I get the conversion I still don't know why (above example) it has to be 1016 and not say 1015...

drinkey said:
[..] I read the thread suggested but now my brain hurts! I am a novice that did not do physics at school but am now fascinated by the subject. I saw this somewhere where a question was asked about the energy in a kg of matter (rest)

This is determined by Einstein's equation E = mc2, where c = velocity of light = 3 x 108 meters/sec. So c2 = 9 x 1016. For 1 kg of mass therefore the equivalent energy is 9 x 1016 Joules, for 1 gram it is 9 x 1013 Joules.

Note units, in the SI system energy is in Joules, mass in kg, distances in meters. If you keep to these units you will get consistent results.

So I get the conversion I still don't know why (above example) it has to be 1016 and not say 1015...
The best answer is, I think the one by DrStupid:

Now, this does require mathematical insight, together with know laws of physics. But then, your question was a mathematical question.

I'll try to clarify drStupid's summary:

E = m * constant, let's call that constant k. And you ask why should k be equal to c*c.

If E=m*k, then a change of energy dE = dm*k

A change of mass dm is given by Newton's force law (which is still valid):
Force is proportional to a change of momentum per time, and momentum is mass times speed. Maybe you did get that far with physics lessons.

In handy units that law is written as: F = d(m*v)/dt

After a little math drStupid got from these two equations that for a moving body, its inertial mass (resistance against acceleration) increases as follows:

m= m0 / √ (1- v2/k)

That can only be correct if the moving body can just not be accelerated to c, which is the limit speed. Then k=c2. (You can try what happens for other values of k!).

So, if the limit speed is c (and that is the case according to special relativity, because light has no rest mass), then the energy formula constant must be c2.

Last edited:

What is the significance of the speed of light in scientific research?

The speed of light, denoted by the symbol "c", is a fundamental constant in physics that plays a crucial role in a wide range of scientific research. It is the maximum speed at which all matter and information in the universe can travel, and its precise value has been determined through numerous experiments and observations over the years.

Why is the speed of light considered to be a universal constant?

The speed of light is considered to be a universal constant because it is the same for all observers, regardless of their relative motion or the motion of the source emitting the light. This is a key principle in Einstein's theory of relativity, which has been confirmed by countless experiments and is essential for our understanding of the laws of physics.

How was the speed of light first determined?

The first successful attempt to measure the speed of light was made by Danish astronomer Ole Rømer in the late 17th century. He observed the moons of Jupiter and noticed that their orbits were slightly longer when Earth was farther away from Jupiter, and slightly shorter when Earth was closer. From this, he was able to calculate the speed of light to be approximately 220,000 kilometers per second.

Can the speed of light be exceeded?

According to our current understanding of physics, nothing can travel faster than the speed of light. This is because as an object approaches the speed of light, its mass increases and it requires an infinite amount of energy to accelerate further. Therefore, it is considered to be a fundamental limit in the universe.

How does the speed of light impact everyday life?

The speed of light has a profound impact on our everyday life, even though we may not always realize it. It allows us to communicate quickly through modern technologies such as the internet and cell phones, and enables us to see the world around us through light and other electromagnetic waves. It also plays a crucial role in fields such as telecommunications, astronomy, and medical imaging.

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