# Thread: Does light have a mass?

1. You can't directly measure the increased mass. To do that, you'd have to stop the particle, put it on a balance and measure its mass.
and

Where now m is called "the mass" but is not related to the mass you read when you put the object/particle on a balance.
If this means "getting things straight" then I am Santa Claus.

2. Can I have eighty billion AU dollars for christmas please?

3. How much?

Have you been nice? If so, the year is still long ...

4. Crisp,

In relativistic mechanics, the energy is defined through the restmass and the "kinetic" energy (which now has to be reinterpretted):

E2 = (m0c2)2 + p2c2

More momentum (roughly speaking: faster speed) = more energy. This relation can be rewritten to:

E = mc2
There is a BIG difference between the two formulas. The formulas only give the same result if the particle is at rest.

If you use the second formula, it gives the appearance that mass increases, but if you use the first formula(the correct one), you will find that mass DOES NOT increase with speed.

Tom

5. ## The formula's are the same...

Hi Tom,

I didn't expect you to agree on first sight of the formula's. Now I have to overcome my own lazyness and type in the whole derivation ... So here it goes:

First of all, let's write everything out explicitly. Bold letters refer to 3 dimensional vectors:

m = m<sub>0</sub> / sqrt(1 - v<sup>2</sup>/c<sup>2</sup>)

p = mv = m<sub>0</sub>v / sqrt(1 - v<sup>2</sup>/c<sup>2</sup>)

Now let's proceed to calculate E<sup>2</sup>/c<sup>2</sup> - p<sup>2</sup> using E = mc<sup>2</sup> and p = mv as defined above:

E<sup>2</sup>/c<sup>2</sup> - p<sup>2</sup>
= m<sup>2</sup>c<sup>2</sup> - p<sup>2</sup>
= m<sup>2</sup>c<sup>2</sup> - m<sup>2</sup>v<sup>2</sup>
= m<sup>2</sup>(c<sup>2</sup> - v<sup>2</sup>)
= m<sup>2</sup>c<sup>2</sup> (1 - v<sup>2</sup>/c<sup>2</sup> )

Now substitute the proper expression for m:

E<sup>2</sup>/c<sup>2</sup> - p<sup>2</sup>
= m<sup>2</sup>c<sup>2</sup> (1 - v<sup>2</sup>/c<sup>2</sup> )
= m<sub>0</sub><sup>2</sup>c<sup>2</sup> (1 - v<sup>2</sup>/c<sup>2</sup> ) / (1 - v<sup>2</sup>/c<sup>2</sup> )
= m<sub>0</sub><sup>2</sup>c<sup>2</sup>

Now that we have this, multiply both sides by c<sup>2</sup> and take the momentum term to the other side:

E<sup>2</sup> = m<sub>0</sub><sup>2</sup>c<sup>4</sup> + p<sup>2</sup>c<sup>2</sup>

Which is exactly the formula I listed above.

On all the mass confusion: I've posted on that quite some times already. If you want to find out more, do a search for "relativistic mass" (a term I prefer using when talking about relativity if confusion could possibly arise). It comes down to this: there is a difference between the concept of "mass" and "restmass". Restmass is what you would call "mass" in Newtonian mechanics. "Mass" in relativity is related to the energy (or in terms of the velocity as given by the formula above).

Hope this clarifies some things, even though I am afraid it raises more questions than it answers

Bye!

Crisp

6. ## Correction for a previous post

Hi all,

And I would also like to correct something I said a few posts earlier about kinetic energy (and how it reduces to the classical E<sub>k</sub> = m<sub>0</sub>v<sup>2</sup>/2). The proper deviation is as follows:

From all the formula's I mentioned in the post directly above, one can say that the energy consists of a contribution of the restmass m<sub>0</sub>c<sup>2</sup> and a kinetic energy contribution:

E = E<sub>k</sub> + m<sub>0</sub>c<sup>2</sup>

Using E = mc<sup>2</sup> (where m is now the "relativistic" mass as defined in the previous post) one finds:

E<sub>k</sub> = (m - m<sub>0</sub>)c<sup>2</sup>

Substituting the expression for m from the previous post yields:

E<sub>k</sub> = ((1 - v<sup>2</sup>/c<sup>2</sup>)<sup>-1/2</sup> - 1)m<sub>0</sub>c<sup>2</sup>

Creating a Taylor series expansion ( = an approximation for difficult to handle expressions) about (v/c) small gives:

E<sub>k</sub> = m<sub>0</sub>v<sup>2</sup>/2 + (3/8)m<sub>0</sub>v<sup>4</sup>/c<sup>2</sup> + ...

In the classical limit, which means looking at speeds very small compared to the speed of light, this reduces to: take the limit (v/c) -> 0:

E<sub>k</sub> = m<sub>0</sub>v<sup>2</sup>/2

Which is the classical Newtonian result. This is an example of how classical Newtonian results can be derived from the theory of Relativity by looking at small speeds.

Bye!

Crisp

7. Crisp,

If you pick up a rock, and throw it at a speed of 40km/h, the kinetic energy of the rock can be calculated using the formula E=(m*v^2)/2. However, if you throw the same rock at a speed of 80km/h the kinetic energy of the rock is quadrupled using the same formula. You will find that if you use the formula m = m0 / sqrt(1 - v2/c2) to calculate the mass of the rock under both cases, that the mass increase of the rock is negligable.

In other words, the energy of the rock quadrupled, even though there is no increase of mass of the rock.

But then you stated, using your formulas, that a particle's energy does not increase based on it's increasing kinetic energy, but that the increase is the result of increasing mass.

I guess the question would be: Can an objects kinetic energy increase significantly without increasing the objects mass???

Tom

8. Crisp,

I attempted to prove you wrong by determining the correlation between kinetic energy, and the increase in energy caused by increasing mass.

Unfortunately, the results showed that the increased kinetic energy(E=mv^2/2) is equal to the increased energy using the formulas E=mc^2 and m = m0 / sqrt(1 - v2/c2).

It appears that kinetic energy is the result of the increase in mass.

You won the first round, but it ain't over yet.

Tom

9. As I said previously:

How can one be sure that kinetic energy is increase of mass?

I think that's the point here: if KE = Mr then I have to agree with Crisp that the energy obtained is due to increas in mass.

if not, then it remains an open question (for me)
but I have still questions remaining on the interpretation of relativitic mass (and kinetic energy that is - I always had trouble to understand kinetic energy)

from where is the energy coming? in which form? who tells me that this really has something to do with increase in energy? Energy is defined as the possibility to do work but that's quite incomplete. It's like defining a shark by swimming. Actually, sharks sometimes rest in caves where they don't have to swim. As the speed increases the momentum increases (p=mv). Einstein changed this formula (I don't know anymore in what though ....) but because of that you get this new interpretation that as v approaches c, v stops increasing and it is mR who is supposed to increase. Is this acceptable? What about the catching-up model in this context? And yes there is more energy released when the particle is smashed --> couldn't this have anything to do with release of vacuum energy .... there's a lot of energy released (a small amount of mass releases a huge amount of energy) and that's [B]exactly[\B] what virtual particles need to maintain their presence (in form of mass)

10. You won the first round, but it ain't over yet.

Note: Crisp will most likely win them all.

11. From reading c'est moi's and Crisp's posts I've come to the conclusion that there are three different models that can explain the increasing energy of an accelerating object:

A) Kinetic energy does not exist. When a object accelerates, it absorbs energy and converts it to mass. When the object slows down or stops, the extra mass is converted back into energy. (This is Crisp's idea)

B) Kinetic energy does exist. As an object accelerates, it's mass remains constant but it's energy increases. As the object slows down or stops, this energy is transferred.

C) A combination of A and B. An object's mass increases as it accelerates, but it's energy also increases, independent of it's mass.

As c'est moi pointed out, it all comes down to a simple question: What is kinetic energy???

Which model do you think is correct: A, B, or C????

Tom

12. B) Kinetic energy does exist. As an object accelerates, it's mass remains constant but it's energy increases. As the object slows down or stops, this energy is transferred.
-> energy increases

A) Kinetic energy does not exist. When a object accelerates, it absorbs energy and converts it to mass.
-> energy absorbed

okay, from where is the energy coming? is this an enigma?

I'm interested to know what Crisp etc. think of my last idea, ie there is no increase in energy nor increase of mass during the motion of a body, there is only increasement of the momentum
it is *when* the IMPACT happens and a small (or a big) amount of mass is converted into energy that virtual particles have the possibility to remain (and are no longer virtual because of the energy that has been added) and that ONLY this accounts for the observed increase in energy which cannot be explained with the rest mass simply because nor the rest mass nor the inertial mass have anything to do with this
only the amount of energy (converted from mass) that was supplied to enable virtual particles to remain is important

13. c'est moi:

The increasing kinetic energy of an object as it speeds up must be provided by some source - basically whatever is causing the acceleration. There's no mystery there. Energy is simply converted from some other form into kinetic energy.

The bottom line with relativity is that it passes all experimental tests with flying colours. It may seem strange to you at first glance. Don't worry - it seems strange to <i>everyone</i> at first glance. But many things in physics defy common sense. The universe does not care about human notions of common sense. We have to match our ideas to what the universe does - not the other way around. Sometimes this leads to major reworking of our ways of thinking.

14. """The increasing kinetic energy of an object as it speeds up must be provided by some source - basically whatever is causing the acceleration. There's no mystery there. Energy is simply converted from some other form into kinetic energy.""""

converted from WHAT????
let's keep it simple, I throw my baseball in the air
from where is the kinetic energy coming? from the mechanical energy of my arm? How can mechanical energy suddenly become mass? which process allows this? etc. etc.

"""The bottom line with relativity is that it passes all experimental tests with flying colours.""""

I recall from the other thread that there is not a SINGLE experiment that has tested the very principle of relativity (ie, it is you or me who is moving, no preferred FOR). I still think it is not science and you still haven't answered my objection to this in the other thread. And again, countless experiments have been done where only ONE of the FOR has been tested (slowing down of clock, or muons entering atmosphere, etc...).

"""It may seem strange to you at first glance."""

I never found it strange. I always found it illogical. Maybe if Einstein was still be alive I could have a nice chat with him. He was quite a character .

"""Don't worry - it seems strange to everyone at first glance. But many things in physics defy common sense."""

again, it is not strange, and if something defies common sense then it is not correct
logic is the tool of the scientist
I do not believe a theory can counter common sense and be correct
the experiments need to be interpretted in a more logical way, i.e. clocks slow down because of quantum physical reasons, objects become larger/smaller because quantum physical reasons and not because some mathematical transformation, etc.
these more logical interpretations (which are in complete agreement with all experiments unlike you said one time) are prevented because of the relativity postulate from Einstein (btw, quantum physics does not counter my common sense though I believe it is certainly not the summum as many scientists believe - there is always better)

"""Sometimes this leads to major reworking of our ways of thinking."""

or sometimes this really leads to dogmatic attitudes
if tomorrow the graviton is discovered then general relativity is not correct even though it worked fine (note: or not -> see binary stars?)
Newtonian physics has been experimented upon endless times and is still in many cases absolutely correct, yet we know it's interpretations of the experiments are not even correct (see magnetic field etc.) You see, it is perfectly possible to have right predictions and wrong interpretations together.

15. Originally posted by c'est moi
[B"""Don't worry - it seems strange to everyone at first glance. But many things in physics defy common sense."""[/b]

again, it is not strange, and if something defies common sense then it is not correct
logic is the tool of the scientist
I do not believe a theory can counter common sense and be correct
C'est Moi, do you understand how semi-conductors work? I put it to you that the concept of 'holes' having positive charge and therfore capable of carrying current is about as nonsensical as it gets. Yet the transistor works. Luckily the Universe does not obey our preconceptions on what is right and wrong.

the experiments need to be interpretted in a more logical way, i.e. clocks slow down because of quantum physical reasons, objects become larger/smaller because quantum physical reasons and not because some mathematical transformation, etc.
No where in QM theory is this predicted. As I've said before, somewhere, the Relativistic result of E( &gamma; ) = M( &gamma; ) c &square; is part of the derivation of Schroedingers wave equations. QM uses this as a fact. If you say Special Relativity is wrong then so is QM. Hence you have to re-invent the whole of Physics since about 1900.

these more logical interpretations (which are in complete agreement with all experiments unlike you said one time)
In the usual fashion, where is the evidence for this statement.

are prevented because of the relativity postulate from Einstein (btw, quantum physics does not counter my common sense though I believe it is certainly not the summum as many scientists believe - there is always better)
I am curious. You think that Relativity (wherein energy is mass and vice versa) defies common sense yet you think the concept of a mass being a probability wave is logical, why?

"""Sometimes this leads to major reworking of our ways of thinking."""

or sometimes this really leads to dogmatic attitudes
Quite the opposite, the dogmatist would have thrown out Maxwell and Planck as that defied common sense and previous wisdom.

if tomorrow the graviton is discovered then general relativity is not correct even though it worked fine (note: or not -> see binary stars?)
Models are refined, what of it. The Graviton does not invalidate GR, it is just not predicted by it.

You keep quoting binary stars as a disproof of Relativity. Do you have a better explanation for the slow down in periods of binary pulsars?

Newtonian physics has been experimented upon endless times and is still in many cases absolutely correct, yet we know it's interpretations of the experiments are not even correct (see magnetic field etc.)
Newton's laws of motion say nothing of electric and magnetic fields.

But Maxwell's equation for Electromagnetism do not transform under the pre-Relativistic (Galilean) transforms yet it is correct.

To tie things togther, the Galilean transform conforms to your notions of common sense hence must be correct. If so, Maxwell must be wrong and the models of EM waves incorrect. Hence radio would not work.

How would you explain the precession of the perihelion of Mercury without Relativity?

You see, it is perfectly possible to have right predictions and wrong interpretations together.
The whole principle of science is that if the prediction, based on an interpretation, is found then the interpretation is assumed correct. If this where otherwise you would get no where. That would defy the logic you vaunt so much.

E.G. If QM's interpretation of particles as waves where wrong they would not diffract. As particles display a diffraction grating when passed through a grating, they are behaving as waves. when particles are accelerated by a force (any force) their kinetic enery and mass increase. Otherwise accelerators would not work.

16. I see nothing odd or strange about semiconductors and such. All electronics is about equilibrium. The charge is trying to find it, and the source is preventing it.

17. Thed,

From your example of positive semiconductor holes, you illustrated that an interpretation can be wrong, but the results of the interpretation can be correct, just like Relativity.

Tom

18. Thed, I'm getting déjà-vu's when I read your post which is the reason I don't feel like responding to it.
(I meant gravitational field, not magnetic field)

19. ## C'est Moi

So what if you meant gravitational field. All Newton had to say was that gravity exerted a force between two objects of masses M and m proportional to the product of the masses and the reciprocal of the square of distance.

This is not an interpretation. It is well tested and understood but in Newtonian physics it is quite static with no cause. It just is. How can the interpretations be wrong when there is nothing to interpret.

Again, how does Relativity defy common sense and Quantum Mechanics does not? Unless you are following a very different interpretation of QM than everyone else.

20. c'est moi:

"The increasing kinetic energy of an object as it speeds up must be provided by some source - basically whatever is causing the acceleration. There's no mystery there. Energy is simply converted from some other form into kinetic energy."

<i>converted from WHAT????
let's keep it simple, I throw my baseball in the air from where is the kinetic energy coming? from the mechanical energy of my arm? How can mechanical energy suddenly become mass? which process allows this? etc. etc.</i>

Yes, from the mechanical energy of your arm (provided by chemical reactions from the food you eat, which grows due to energy from the sun etc.) The energy doesn't become rest mass in this case - that would require a nuclear reaction. The energy becomes kinetic energy of the ball, which you can look at as relativistic mass if you want to.

<i>I recall from the other thread that there is not a SINGLE experiment that has tested the very principle of relativity (ie, it is you or me who is moving, no preferred FOR). I still think it is not science and you still haven't answered my objection to this in the other thread. And again, countless experiments have been done where only ONE of the FOR has been tested (slowing down of clock, or muons entering atmosphere, etc...). </i>

That's not true. Every experiment we do on Earth is in a reference frame in motion with respect to the sun. If we do the same experiment six months apart, the Earth is moving at a different speed in the opposite direction. We're testing multiple frames of reference all the time. The laws of physics are observed to work on Earth despite the fact that it orbits the sun and the sun orbits the galactic centre and the galaxy is moving with respect to other galaxies and so on.

<i>if something defies common sense then it is not correct</i>

Does the quantum mechanical 2-slit experiment make common sense to you? (i.e. that an electron, say, can go through both slits at the same time?) Does the fact that a pendulum's swing rate is the same regardless of the length of the pendulum make common sense to you? Does the fact that any two objects accelerate at the same rate due to gravity make common sense? Is it common sense that no force is needed to keep an object moving at constant speed?

Common sense is a very bad guide to what is true.

<i>the experiments need to be interpretted in a more logical way, i.e. clocks slow down because of quantum physical reasons, objects become larger/smaller because quantum physical reasons and not because some mathematical transformation, etc.</i>

So, you have an alternate theory which works, do you? That's fine, if you can show it matches observations. Which quantum physical reasons are you thinking of?

<i>if tomorrow the graviton is discovered then general relativity is not correct even though it worked fine</i>

Every scientist knows that GR is not the final theory. But whatever theory replaces it will have it as the "classical limit". It won't become wrong, but will become part of a larger theory.

<i>Newtonian physics has been experimented upon endless times and is still in many cases absolutely correct, yet we know it's interpretations of the experiments are not even correct (see magnetic field etc.)</i>

<i>You see, it is perfectly possible to have right predictions and wrong interpretations together.</i>

You'll have to show me some examples.

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