# Mass at relativistic speeds

1. How do we know that objects mass increase as they approach the speed of light

2. How did whoever figured this out do so

1. How do we know that objects mass increase as they approach the speed of light

2. How did whoever figured this out do so

Mass doesn't "increase", total energy, $E=\frac{m_0c^2}{\sqrt{1-(v/c)^2}}$ is what increases.
Mass, $m_0$, is invariant.

Obsolete forms of relativity assume that "relativistic mass", $m=\frac{m_0}{\sqrt{1-(v/c)^2}}$, "increases". Modern interpretations have distanced themselves from the concept of "relativistic mass".

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phinds
Gold Member
1. How do we know that objects mass increase as they approach the speed of light

Keep in mind, all motion is relative and you, right now as you are reading this, are traveling at various speeds up to almost the speed of light, depending on what frame of reference is used for the measurement. Do you feel any more massive?

atyy
You will still find "relativistic mass" as a concept in modern materials like Feynman lectures http://www.feynmanlectures.caltech.edu/I_toc.html or these notes at the US particle accelerator school http://uspas.fnal.gov/materials/09VU/VU_Fund.shtml [Broken].

http://www.einstein-online.info/elementary/specialRT/emc is a quite readable presentation of experiments in which relativistic mass has to be taken into account.

An early paper on the increase of mass with energy is Einstein's https://www.fourmilab.ch/etexts/einstein/E_mc2/www/.

Because energy and relativistic mass are different names for the same quantity, "mass" in a relativistic context is nowadays most often taken to mean the rest mass or invariant mass.

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phinds
Gold Member
I hear from somewhere that the Universe is expanding at speeds greater than the speed of light. Does that count?
http://en.wikipedia.org/wiki/Faster-than-light#Universal_expansion

"Count" in what sense? Yes, objects in the universe are receding from each other at greater than c. For example, objects at the edge of our observable universe are receding from us at about 3c, but no speeding tickets are issued because recession velocity is not the same as two objects moving relative to each other within a single inertial frame of reference, which is limited to c.

Google "metric expansion" for more discussion.

You will still find "relativistic mass" as a concept in modern materials like Feynman lectures http://www.feynmanlectures.caltech.edu/I_toc.html

http://www.einstein-online.info/elementary/specialRT/emc is a quite readable presentation of experiments in which relativistic mass has to be taken into account.

Though I like Feynman Lectures on Physics, the above chapter on"Relativistic Mass" is downright awful. The page from the Max Plank institute is even worse. The above demonstrates that it can happen to the very best. :-)

Because energy and relativistic mass are different names for the same quantity, "mass" in a relativistic context is nowadays most often taken to mean the rest mass or invariant mass.

Yes, see post 2.

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jtbell
Mentor
You will still find "relativistic mass" as a concept in modern materials like Feynman lectures

The Feynman lectures are 50 years old. Most or all introductory textbooks of that era probably still used "relativistic mass." The textbook for my sophomore-level intro modern physics course in the early 1970s did. It also claimed that the solution to the twin paradox requires general relativity.

However, when I was a grad student in experimental particle physics beginning a few years later, none of the people I worked with used "relativistic mass." The only place I saw it was in an accelerator-physics textbook whose first edition was in the early 1950s.

Gold Member
"Count" in what sense?
haha. I guess I need more practise with English. Mass doesn't "increase", total energy, $E=\frac{m_0c^2}{\sqrt{1-(v/c)^2}}$ is what increases.
Mass, $m_0$, is invariant

How does the energy increase?

phinds
Gold Member
How does the energy increase?

You have to put energy into a system to make it move faster. That's where the energy comes from. No energy input, no increase in speed.

So basically the acceleration gives it the energy increase?

How does the energy increase?

$E=\frac{m_0c^2}{\sqrt{1-(v/c)^2}}$. Calculus shows that when v increases, E increases.

phinds
Gold Member
So basically the acceleration gives it the energy increase?

No, the ENERGY gives it the energy increase, which increases the speed. That is, the energy increase cause the speed to change, not the other way 'round. This is not exactly nitpicking; the way you've stated it, there would have to be a spontaneous increase in speed and that would CAUSE the energy increase, which is not how it works.

phinds
Gold Member
$E=\frac{m_0c^2}{\sqrt{1-(v/c)^2}}$. Calculus shows that when v increases, E increases.

Mathematically, that is the most convenient way of interpreting that equation but as I pointed out, that is not what happens physically. The energy has to increase for the speed to increase, otherwise you have cause and effect backwards.

Mathematically, that is the most convenient way of interpreting that equation but as I pointed out, that is not what happens physically. The energy has to increase for the speed to increase, otherwise you have cause and effect backwards.

The speed is increased via application of a force, a good example is the case of particle accelerators. Application of an (electrostatic) force onto the particle , accelerates it , such that its energy increases. See here, for a good explanation.

the way you've stated it, there would have to be a spontaneous increase in speed and that would CAUSE the energy increase, which is not how it works.

Energy increases according to $\dot E = \vec F \cdot \vec v$. Thus when starting from rest the energy can't increase if the speed doesn't increase first.

phinds
Gold Member
Energy increases according to $\dot E = \vec F \cdot \vec v$. Thus when starting from rest the energy can't increase if the speed doesn't increase first.

So you are saying that the speed increases magically, without the application of any force. I contend that that's backwards. How do you propose to increase the speed of anything without applying any force?

Nugatory
Mentor
Energy increases according to $\dot E = \vec F \cdot \vec v$. Thus when starting from rest the energy can't increase if the speed doesn't increase first.

There's no "first" here - they increase together smoothly from zero in the idealized case. Calculus was invented in large part because we needed a mathematical tool for dealing with these situations without falling into this "which came first" pitfall.

So you are saying that the speed increases magically, without the application of any force.

No, I'm saying energy isn't increasing without speed.

There's no "first" here - they increase together smoothly from zero in the idealized case.

For v=0 there is an increase of v bot not of E.

phinds
Gold Member
I give up.

Gold Member
No, I'm saying energy isn't increasing without speed.
Let's leave that equation and come to this ##E_k=\frac{1}{2}mv^2## (The kinetic energy equation)
Do you say that when you increase it's speed,it's kinetic energy increases or when it's kinetic energy increases,it's speed increases?

Consider an object 100m above Earth. When you leave it, it gains speed because it's potential energy is being transferred to kinetic energy.

ZapperZ
Staff Emeritus