# Mass, Gravity, Spacetime and everything

1. Sep 10, 2008

### Vrareti

After reading countless stuff on wikipedia I think that there's no definition for mass which I can understand (either that or there's no definition for it yet and we're waiting for LHC to come up with one). I came to the conclusion that we understand more stuff about gravity than mass and that's the reason these question came to my mind:

If gravity is a property of spacetime and assuming we understand gravity more than mass, why don't we try redefining mass using gravity? Shouldn't mass be a property of spacetime like an anomaly at a specific point acting as the "opposite" of gravity?

2. Sep 10, 2008

### atyy

3. Sep 10, 2008

### epkid08

What don't we know about mass?

4. Sep 10, 2008

### Vrareti

Although I can't understand most of it since I don't have a very strong physics background, I think that's exactly what I'm talking about!

Well as I said I can't understand any of the definitions of mass I could find. Can you tell me what mass is in simple words? (I'd really like a definition without words like 'material' and 'matter')

5. Sep 10, 2008

### epkid08

Try picturing mass as weight minus all gravitational forces, or potential weight.

6. Sep 10, 2008

### Primordial

Vrareti : you asked "Well as I said I can't understand any of the definitions of mass I could find. Can you tell me what mass is in simple words? (I'd really like a definition without words like 'material' and 'matter') "
To myself, it is potential energy in near perfect balance with space-time, such that it displays an inertial moment, via a gravitational effect on space-time.

7. Sep 10, 2008

### e2m2a

Some physicists who believe there is a link between inertia and the zero-point energy field of vacuum space would view mass as a coupling coefficient between force and acceleration as defined in Newton's second law.

8. Sep 11, 2008

### yuiop

The best discription for mass that I can think of is, that mass is a property that certain configurations of energy have.

First you have to clear what kind of mass you are thinking of. In modern times, when physicists refer to mass unqualified they mean "rest mass". Rest mass is the mass that a particle has when it is a rest with respect to the observer. By this definition light does not have rest mass becasue it can not be at rest with respect to the observer. When a particle has rest mass it can not move at the speed of light. If at has no rest mass then it has to move at the speed of light. That is one clear difference between having mass and not having mass. There are many other kinds of mass but physicists resist talking (or thinking) about other kinds of mass which is a pity because there is much to be learned. Rest mass is useful because because it is the same for a given particle, whatever the velocity of the particle relative to the observer.

Inertial mass is the property an object has of "resisting" acceleration. The greater the inertial mass of an object, the harder it is to acclerate (or slow down). In relativity, the inertial mass is sometime called the "relativistic mass" and this appears to increase when an object has motion relative to the observer. Inertial or relativistic mass is also assoiciated with the momentum of a particle. Inertial mass has two components. One is rest mass and the other component is the mass due its kinetic energy. While individual photons do not have rest mass they do have kinetic energy and by definition photons have inertial mass and momentum. Some physicists would like to have the concept of "relativistic mass" wiped from all textbooks and never mentioned again in polite society. One reason is that there are two kinds of relativistic mass. An object with motion parallel to the x axis resists being accelerated in the y or z directions diferently to how it resists being accelerated in the x direction so a concept of "parallel relativistic mass" and "transverse relativistic mass" is required and this is not very elegant. However, the concept of relativistic mass is right there in Einstein's original paper on relativity. Later on, Einstein declared something like it better not to think of mass for which no sensible definition can be given, but rather just think of the energy-momentum relationship. As you can see, even Einstein had difficulties defining mass.

Another reason physicists (and teachers) dislike the concept, is that when students learn about relativistic mass for the first timethey inevitably ask why a fast moving particle does not turn into a black hole. The answer is that gravitational mass and inertial mass are not the same thing, just as rest mass and inertial mass are not the same thing. However, the concept of inertial or relativistic mass has its uses, and the collision of a fast moving particle with a stationary particle of different mass can not be calculated by simply assuming momentum is proportional to mass times velocity.

An interesting example of relativistic mass is to consider the case of a flywheel enclosed in a box. If the flywheel is spinning inside the box, then the ox will be harder to accelerate than when the flywheel is not spinning. When the flywheel is spinning the box behaves as if it has more mass.

Another example is to consider a box lined with perfect mirrors. If the box is filled with photons that bounce around indefinately on the internal mirrors, the box will behave as if it had more mass, being harder to accelerate than when it dark inside the box. it will also act as a greater source of gravity and it will weigh more. So another way to think of mass is as "confined energy".

The next kind of mass is gravitational mass. Again, there two kinds of gravitational mass. One kind is "active" gravitational mass which is the property mass has that shapes the spacetime around it and tends to cause other objects to "gravitate" towards it. The other kind is "passive" gravitational mass which determines how an objects responds to the active gravitational mass of another object. In another thread we discussed how the passive gravitational mass is insignificant for a free falling object in general relativity and in fact a particle without any passive gravitational mass is still accelerated towards an object with active gravitational mass. Where passive gravitational mass is important is when an object is prevented from free falling. This mass is what is measured when we measure the weight of an object.

How gravitational mass relates to rest mass and relativistic mass is not entirely clear because the subject is generally avoided in the texts, but I suspect it is more closely aligned with rest mass than relativistic mass.

Another (possible) property of mass is that it can have charge. As far as I know, massles particles like photons do not have charge (but I am not certain about this statement).

Remember I said a box of photons has more gravitational and inertial mass than an empty box? How does that come about? Well, it can be shown mathematically, that two photons going in opposite directions can have rest mass when considered as a total system, while a single photon has no rest mass. If you really want to see the maths I will have to dig out an old post ;) So what is about two photons that can described as rest mass? Well it nothing physical. It is just the way the energy is configured.

To get an idea of why the way things are configured is important consider the case of the carbon atom. When a bunch of carbon atoms are configured one way, it transmits light very well, is a poor conductor of electricity, is very hard and is abrasiveis (i.e. it is what we call a diamond.) When configured another way, the same bunch of carbon atoms does not transmit light very well, is a good conductor of electricity (in one direction), is soft and is a lubricant (i.e. it is graphite).

See, never mentioned the words 'material' or 'matter' ;)

9. Sep 11, 2008

### yuiop

Forgot to mention somethng important about relativistic mass in my last post.

In the relativistic submarine paradox, the submarine appears length contracted according to an observer at rest with the water. According to that observer, the submarine displaces less water and so is less bouyant and should sink.

To an observer onboard the submarine, it is the water that is length contracted and so the submarine displaces more water and should be forced towards the surface.

Obviously both conclusions can not both be correct. Now introduce relativistic mass. To the observer at rest with the water, the submarine has more mass due to its relative motion and this reinforces his prediction that the submarine should sink.

To the observer onboard the submarine the water has more mass due to its relative motion and this reinforces his prediction that the submarine should rise.

The solution to the paradox is that the submarine sinks. (Google for "relativistic submarine paradox matsas") To resolve the paradox requires an understanding of how inertial mass varies with relative motion (relativistic mass) and how gravitational mass varies with relative motion. It can not be solved by adhering strictly to the mantra that there is only one notion of mass called rest mass.

If you are one of those people that thinks that length contraction is just a mathematical oddity that has no real significance and that mass does not vary with relative motion you will predict that the submarine niether sinks or rises and you would be wrong.

10. Sep 12, 2008

### Vrareti

Does an electron have mass?

I like this definition of "mass", although I don't kind understand the active and passive gravitational mass yet (but i'll try rereading that section many times). A question comes up from reading all of this: Has anyone tried to unify all these kinds of mass into one kind? Is it possible that what we perceive as rest mass is actually inertial mass generated by massless particles that move inside an invisible container-"box" like your example? And one more thing.. If the photons in that box were not to *touch* any wall or mirror but still keep moving all the time, would the inertial mass still appear bigger? In other words.. is the actual motion of the photon that causes this change in inertial mass or the "changing of it's direction". I don't know how to phrase that.. I mean can you really change the direction of a photon? Or do you just consume it and produce another one travelling in a different direction?

Last edited: Sep 12, 2008
11. Sep 12, 2008

### yuiop

The famous physicist Wheeler invented a concept called the Geon which is an elementary particle comprised of a self gravitating photon trapped in a loop. This is a nice idea because when a particle and its antiparticle anihilate the end result is two high energy photons going in opposite directions, indicating that the two particles with mass have components that can also can be photons. This is further reinforced by the fact that under certain ideal conditions it is known that two photons can combine to create a particle antiparticle pair. However, for some reason Wheeler's geon concept is not generally accepted. I think the general thought is that a trapped photon would in effect be a micro black hole and would be unstable. Wheeler tried to argue that physics at the elementary level is not not completely described by GR and that quantum effects might somehow stabilise a self gravitating photon. However, when Wheeler presented his idea to Einstein, it fell on deaf ears because Einstein basically did not like the new quantum ideas at that time. So at this time, it fair to say that it is not generally accepted that particles with mass are comprised of photons locked into micro orbits, but maybe that idea will come back round again with further developements in quantum theory. Personally I like the idea, but it can not be described as mainstream physics :(

..oh..and yes an electron does have mass .. about 9.10938 × 10^(-31) kilograms

and.... of course you can change the direction of photon (without a mirror or prism). Photons paths are known to bend in a gravational field and can be trapped in an orbit around a black hole called the photon sphere.

12. Sep 12, 2008

### Vrareti

This theory makes more sense to me than any other definition of mass out there. Where can I find more about it?

13. Sep 12, 2008

### yuiop

Yes, modern physics defines only one kind of mass and that is the rest mass. By that definition a photon is massless.

The other kinds of mass can generally be defined in terms of the rest mass although for the photon that causes difficulties because photons have momentum but no rest mass.

The equation for relativistic momentum is

$$p = \frac{m_o v}{\sqrt{1-v^2/c^2}}$$

Some people interpret that in terms of the Newtonian equation p = mv where m is the relativistic mass

$$m = \frac{m_o}{\sqrt{1-v^2/c^2}}$$

Nowadays that view is generally frowned upon and the equation

$$p = \frac{m_o v}{\sqrt{1-v^2/c^2}}$$

should be viewed as a non linear relationship between velocity and momentum that is not the same as the Newtonian momentum velocity relationship.

For a photon the momentum is 0/0*c using the above equation because the rest mass is zero and gamma term is zero so the momentum of a photon is undefined using that equation. The momentum is alternatively defined for a photon in terms of its frequency (f) as p = hf/c where h is the reduced Planck constant. The total energy of a photon is given by E = hf = pc. The total energy of a particle with mass is

$$E = m_o c^2/\sqrt{1-v^2/c^2}$$.

If we allow ourselves to think in terms of relativistic mass $$m_r$$ for the purposes of argument where

$$m_r = m_o/\sqrt{1-v^2/c^2}$$

then the total energy of a massive particle is $$E = m_r c^2$$

and it follows that $$m_r = E/c^2$$.

So now we can define the relativistic mass of a photon as

$$m_r = E/c^2 = hf/c^2 = p/c$$

So now it can be seen that the momentum of photon can be defined in terms of its relativistic mass

$$p = m_r*c$$

and since c is the velocity of the photon there is a clear analogy between the momentum of a photon and the momentum of a particle with rest mass where

$$p = m_r * v$$

For a photon it is clear that momentum is not a function of rest mass but a function of its relativistic (inertial) mass.

Last edited: Sep 12, 2008
14. Sep 12, 2008

### yuiop

Googling for "wheeler geon" would be a good place to start.

Maybe some members here can find a reference in a Wheeler text book for you. Unfortunately, the subject of geons can not be discussed in detail here because it is not part of the mainstream standard model and so it against the rules of this forum to even think about it, (even though Wheeler is a respected physicist that has written many widely used text books on General Relativity.)

15. Sep 12, 2008

### yuiop

This is a reply to a question by atyy in post #40 of another thread about photons https://www.physicsforums.com/showthread.php?t=251161&page=3 but I have put the reply here as I will not not be focusing just photons and do not want to be accused of hijacking that thread.

First, any statement like "the mass of a photon is zero" in any modern text where the type of mass is unspecified, then it should be assumed thay are talking about rest mass. So the statement could be stated as "the rest mass of a photon is zero". However, modern usage is that there is no other kind of mass, other than rest mass, so there is no need to use any term for mass other than simply mass.

Next I want to focus on the 3rd statement:

3) Inertial mass equals gravitational mass

Here is a simple thought experiment that demonstrates that statement is not true.

An observer is on an asteroid of mass (M) that has a tower and releases a test particle of mass (m) from the top of the tower and times how long it takes to fall a short distance (d). The distance d is sufficiently small relative to the combined height of the tower and radius of the asteriod (R) that the acceleration due to gravity can be considered to be constant over the distance d. The mass of the asteriod is also considered to be suffiently small that gravitational time dilation is insignificant relative to the kinetic time dilation of the extreme relativistic velocities that will be considered. Now say our observer on the asteroid measure a time interval of one second for the test object to fall 1 meter. The acceleration of the particle is calculated as

a = 2d/t^2 = 2 m/s/s

which also equates to

a = GM/R^2

That is a Newtonian equation but the velocity attained by a particle in falling one meter in the gravitational field of a small asteriod does not require a relativistic equation.

A second observer moving horizontally relative to the tower at 0.8c records the time for the particle to fall as

$$t' = \frac{t}{\sqrt{1-v^2/c^2}} = 1.666 seconds.$$

By his calculations the acceleration of the test particle due to gravity is

a' = 2d/t^2 = 2/(1.6666)^2 = 0.72 m/s/s

and so

a' = GM/R^2 * (1-v^2/c^2)

If we assume the gravitational constant G is constant and the R is taken to be (near enogh) constant since there is no transverse length contraction then the gravitational mass of the asteroid can be taken to be as M(1-v^2/c^2).

In other words the active gravitational mass of a moving object is less than when it is at rest by a factor of gamma squared.

The inertial (relativistic) mass of the asteroid is calculated as M/sqrt(1-v^2/c^2) so the gravitational mass is not the same as the inertial mass.

Since the rest mass of the asteroid is simply M then the gravitational mass is not the rest mass either.

So we have established that

3) Inertial mass equals gravitational mass

is not always true and

4) Rest mass equals gravitational mass

is not always true either.

Earlier, I suggested that the quantity M(1-v^2/c^2) that appears in the equation a' = GM/R^2 * (1-v^2/c^2) could be described as the active gravitational mass of the asteroid which I will denote as $M_g$ so the equation becomes:

$$a' = G \frac{M_g}{R^2}$$

Now iif we define the inertial mass of the test object as $m_i$ then the force of gravity acting on the stationary suspended test mass is:

$$F' = m'a' = m_i a' = G \frac{M_g m_i}{R^2} = G \frac{M m}{R^2} * \sqrt{1-v^2/c^2} = F * \sqrt{1-v^2/c^2}$$

which agrees with the already known result that transverse force in Special Relativity transforms as $$F' = F * \sqrt{1-v^2/c^2}$$

In summary, if you want to think in terms of different kinds of masses, then they could be defined as:

Inertial mass = $$\frac{ m_o}{\sqrt{1-v^2/c^2}}$$

and Active gravitational mass = $$M_o * (1-v^2/c^2)$$

From the above it should be apparent that the inertial mass is acting as the passive gravitational mass.

The equation for the active gravitational mass is specific to the thought experiment described here with all the necessary aproximations and does not claim to cover the general case. It is used here, just to illustrate that there is clear example that inertial mass and rest mass are not equal to active gravitational mass.

16. Sep 12, 2008

### Al68

LOL. The funny thing about the term "mainstream physics" is that it's used as if there were some big, objective, monolithic, authoritative source of physics knowledge with the title "Mainstream Physics", when reality is quite the opposite.

Al

17. Sep 12, 2008

### Vrareti

Another question.. If gravity is a property of spacetime, do you need mass to create gravity or do you need gravity to create mass? Which one of these two came first? In my mind gravity is the anomaly of spacetime in a specified position. Are we certain - is it proven - that mass creates this anomaly or can this anomaly just be there from the first place and when (and if) energy passes through it, it gets trapped and becomes what we conceive as mass (m = E/c^2)?

18. Sep 12, 2008

### yuiop

Well the mass of your own body creates its own gravity field around it. So the question can be answered by asking yourself if your gravity field is following you, or are you following the gravity field?

put another way. Can you be absolutely sure on a sunny day that your shadow is following you around or are following your shadow around?

19. Sep 12, 2008

### Vrareti

We know for sure that in a sunny day:
1) if my shadow exists i'm there right next to it
2) if i exist my shadow is right next to me

2 completely different facts and my question is like this:
1) if mass exists then gravity is right next to it <-- proven
2) if gravity exists then mass is right next to it <-- question!!

In other words.. If gravity came first (that space anomaly), is there a possibility that in such an anomaly in space, energy hasn't pass through yet so there's just gravity without mass next to it? Can dark matter be such a thing?

Last edited: Sep 12, 2008
20. Sep 12, 2008

### yuiop

I am not sure of the answer to your last question because as far as I know no one has observed such a thing, except in in the dark matter that has been displaced from colliding galaxies. Astronomers observe regions near those collisions where there is gravity causing gravitational lensing of more distant galaxies, but there is no visible matter where the "lens" is. This is thought to be dark matter that is found in most galazies that has been displaced during a collision. At this point of time, no one is certain what dark matter is ,but it thought to some sort of matter that is not visible and weakly interacts with other matter, so it does not slow down during the collision, unlike the hot gases from the colliding galaxies.