change in mass near light speed

B

bogz

Temporal Navigator
I sent RMT a PM about this but I'm kind of impatient and wanted to see if anyone else could help.

When you approach the speed of light and that "mass increase" happens, does your mass increase from your own point of view? Or does it only appear to increase to an observer? In other words, is mass relative similar to how time is relative?
 
I'll let Darby handle that one. But it will involve the distinction of rest (invariant) mass vs. relativistic mass. In fact, that Wiki may answer your question, and this equation may show you the difference.

And this may be the summary description you are looking for:
<font color="red"> "In general, for closed systems and single observers, relativistic mass is conserved (each observer sees it constant over time), but is not invariant (that is, different observers see different values). Invariant mass, however, is both conserved and invariant (all single observers see the same value, which does not change over time)." [/COLOR]

But let Darby do the finessing here. :D
RMT
 
so the local object moving does not feel a local increase in mass, it's just observers who would see that object has being heavier than if they were observing from inside the moving object... so mass is relative just like time?? for some reason that's even more counter-intuitive to me...
 
bogz,

The change in mass is relative. You could have six different observers moving at six different high velocities with respect to each other and each would determine a different mass for each of the other five. But each of the six would observe no change in their own mass.

If you plug in general relativity and place them in situations where their velocities closely approach c they would observe some bizzare changes to spacetime. Spacetime itself would tend to collapse and fold up in front of them. At the speed of light it would become a point of zero dimension which is another way of stating that a photon is spread out over all of spacetime or that time comes to a stop at the speed of light. It comes to a stop in the sense that you could reach any place in the universe in zero time because the entire universe occupies zero space (its a point of zero dimension).

I agree that all of this is counter intuitive. But special relativity is one of the physical theories that has been tested over and over tens of thousands of times and has never failed. It does correctly express reality. It's our intuition that is "wrong" because we don't personally experience either high relativistic velocities or strong field general relativistic gravitation. On the other hand Newtonian physics still works out quite nicely for we mortals in our every day lives and it is well matched to our intuitions about every day reality.
 
Thx guys. I hear lots about how time is relative, and there are all kinds of thought experiments to explain how it works. And there are experiments I've heard about that prove time is relative.

Mass being relative is new to me. I've never heard one example or thought experiment about it. Time gets all the attention.

You could have six different observers moving at six different high velocities with respect to each other and each would determine a different mass for each of the other five. But each of the six would observe no change in their own mass.
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What about gravity? As relativistic mass increases, does it's gravity increase also? If so, does this increased gravity appear to affect nearby objects for an observer while having no effect on these same nearby objects for the local observer?

That's the part that I don't understand, and can't picture in my head... Your physical position in space isn't relative also is it?
 
bogz,

Welcome.

Mass being relative is new to me. I've never heard one example or thought experiment about it. Time gets all the attention.
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This one has been verified by physical experiment thousands of times going back to the 1950's. We've had the ability to boost electron velocities to 99.9997% c in particle accelerators since the 1950's. The physicists would apply the Lorentz formula and calculate that the momentum of the electron should exceed the Newtonian expected value by a factor of ~410 and when they would actually measure the momentum of the particles the value was well within the limits of their predictions. Today we can boost the momentum to over 7000X - and experiment continues to verify the theory. Electrons are boosted to about 1 part in a billion less than the speed of light.
 
Your physical position in space isn't relative also is it?
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Yes. You have to fix your position by three spatial coordinates and one time coordinate - you're at 5th and Main, on the fourth floor at noon (having lunch).

But the positions are not just relative, they are arbitrary. They work just fine on the local scale but they do nothing at all to tell you where you are in "the universe" because there is no center of the universe. There is no fixed point that says "begin here to measure all other positions". Because time itself is relative between astronomically distant observers the fourth coordinate (time) is also relative.

But there's another sense in which position is relative. Right now you are in motion relative to most everything else in hte universe travelling at a very low velocity as compared to the speed of light. The relative velocities aren't going to introduce any significant Special Relativistic effects. You can look out, see the stars and fix your position relative to them. But if you accelerate yourself to very near the speed of light, as I described in my first post, your position in spacetime becomes very vague from your perspective. Spacetime around you gets very warped and begins to fold up into a singularity. But an observer in a rest frame who can see you would not have any problem (at least in theory) fixing your location relative to the stars around you. Spacetime for that observer will appear to be quite normal.
 
the positions are not just relative, they are arbitrary.
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Does relativistic mass cause an increase in gravity though? If it does, I can't wrap my head around where tiny objects affected by this gravity really are. The local observer would not see anything abnormal as it was moving. Tiny objects around it would be affected as expected. For the distant observer they would see this very massive object tossing around these tiny objects due to the increased gravity. So where the heck are these tiny objects? Are they physically in two places at the same time. Or is it just an 'optical illusion' so to speak, because we rely on photons traveling vast distances to make said observations?

The arbitrary part I've heard you explain before. I guess what I don't understand about that is what benefit would having a fixed origin give us? Would it make any equations easier to understand, or would it make certain types of physical theories possible which are ruled out today without this "point of origin". The arbitrary part doesn't bug me as much as the relative mass/gravity issue.
 
Bogz,

It's been a while since we visited this thread so I'll return to it.

We say that both velocity and time in special relativity are not absolute but are relative based on the conditions of the situation that different observers of an event find themvelves in. But all is not relative in special relativity. There is a velocity that is absolute that all observers will agree on for every object in the universe, not just photons.

That velocity for all objects traveling through spacetime, not just space or time, is precisely the speed of light. You, me, Ray - everything, has a spacetime velocity of the speed of light. I'll give you a couple of days to ponder why this is implied by special relativity.
 
Are you saying:

dx² + dy² + dz² + dt² = c²

Oops that doesn't work....

(dx² + dy² + dz² + dt²)/dt² = c²
(dx/dt)² + (dy/dt)² + (dz/dt)² + 1 = c²

?
 
TimeLord,

Very good. Make the entire thing a 4-vector and not divide the components by dt.

dx^2 + dy^2 + dz^2 + dt^2 = 1 = c (the A-roofs are there
).

Or make it really simple and state:

A-roof^2 = 1 where c=1 and we understand that the A-roof is the 4-vector for spacetime translation. As your circumflex indicates, its a unit vector.

The full special relativity math is somewhat more complex but the implication of special relativity is that no matter what the spatial component is for your translation the sum of the spatial and temporal components is always 1, the speed of light. You speed up, the clock slows down. You slow down, the clock speeds up. But the slowing down and speeding up always changes the two components precisely by the amount that conserves the unit vector.

Rates of movement in time or space alone is relative. But the net rate of motion in spacetime is absolute for all observers. If you travel at the speed of light your clock stops. If you are at rest you stop and your clock ticks away at its fastest rate possible, c.
 
lol I don't know where those A things came from. I guess the forum didn't like the squared signs. /ttiforum/images/graemlins/yum.gif

Is there a way to make dx, dy, &amp; dz., imaginary? Then you could have:

dx^2 + dy^2 + dz^2 + dt^2 = 1
dt^2 = 1 - dx^2 - dy^2 - dz^2
dx^2 = (i DX)^2 = -DX^2
dy^2 = (i DY)^2 = -DY^2
dz^2 = (i DZ)^2 = -DZ^2
dx^2 = 1 + DX^2 + DY^2 + DZ^2
dt^2 &gt; 1

Hmmm I don't know. What about dt^2 having 2 solutions? dt can be positive or negative.
 
I don't know where those A things came from.
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The A-roof (hat, circumflex) is just indicating that each component (x,y,z,t) is an element of the unit vector.

And you're correct about two solutions. Negative velocities are just a switch of signs - movement in the opposite direction. Negative time would indicate running the event backwards. But because it's squared quantities, the solutions would be (+/-1^2 ) = 1.
 
TimeLord,

I was reading Demitri's thread and saw all those A-roofs popping up in his posts. Then it occured to me what you meant by wondering where those A-roofs came from - it was a glitch. So, you didn't put the A-roofs in the equations, but they appeared as glitches - and they just happen to be appropriate because the equation actually does describe a unit vector.

Weird coincidence.
 
lol I didn't even think about them representing a unit vector. You're right! Maybe we discovered a hidden 'feature' of the forum. (self-modifying math posts) :D
 
It's been a while since we visited this thread so I'll return to it.
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Sorry Darby, I'm still stuck on relative mass (and gravity).

Let's say an observer is very far away watching a ship moving very fast travel through an asteroid field.

The ship is flying through the asteroid field and can see from looking out the window that the asteroids are hardly affected by it's local gravity.

The far away observer will see the ship as being very massive because it's moving very fast. And it has a lot of gravity because it's so massive. And the asteroids are going to appear to be sucked into the gravitational "wake" left by the speeding ship.

After the ship leaves the asteroid field matches the relative velocity of the observer and watches the asteroid field for a few hours.

As time goes on, the asteroid field will look very different for both parties would it not? The distant observer would be watching the aftermath of a massive object passing through a bunch of asteroids, and the local space ship would see a quiet bunch of rocks that are moving pretty much the same as when the ship entered. That is the part I can't understand. What am I missing?
 
bogz,

Great questions! I read your post a few nights ago but didn't have time to either digest or make answer. I re-read the post tonight and have to admit that I have to ponder the questions for a while before attempting an answer. I'm fairly comfortable conversing about Special Relativity but the questions involve General Relativity. The scenario involves not only velocities but great distances and gravitation all of which have to be considered. I will attempt to answer them as time goes forward but I have to say that the answer will probably be wrong. GR is a very difficult science. The scenario on its face appears to me to be far beyond my competence. But as I said, very good (and intuitive) questions.
 
As time goes on, the asteroid field will look very different for both parties would it not?
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Sure. They would trivially see a difference based solely on the difference in their positions and velocities WRT the asteroid field. If I have your thoughts correct this isn't the situation that you're asking about. I think that the question is whether or not the increase in mass is real and therefore is the increased gravitation of the fast moving ship real. The answer in GR is yes: E = mc^2.

You've increased the velocity of the fast ship which increases its kinetic energy. Increase the energy and you increase the mass. Gravitation is a function of mass. Increased mass increases the gravitation of the ship.

The observer in the fast ship won't see it quite that way. What he'll see is an increase in the velocity of the asteroids. He will see their relativistic mass increase. But that's under SR, not GR. And that's where it gets tricky. Special Relativity ignores gravitation by design. If you lived in 1910 and only knew about special relativity you would use the Lorentz transformations and plug and chug your numbers into Newtonian gravity equations which assume a force at a distance as contrasted with GR which describes it as a spacetime curvature. You might well assume that the asteroids' mass and gravity increased for all observers independent on their frames of reference. That's not correct. In GR the ship alone would experience the "real" increase in mass and it alone would experience an increased local warping of spacetime, not the asteroids. You couldn't sit on an asteroid, watch the fast ship whiz bye and notice that you'd somehow gained weight because the asteroid was suddenly more massive.

One thing won't happen to the fast ship, no matter how fast it travels: the increase in mass will not cause it to collapse into a black hole. If it is not hidden behind an event horizon when it is at rest WRT the far away observer it will never fall behind an event horizon based solely on increased relative velocity (given the upper bound speed limit as being less than the speed of light for all massive bodies).

It's just these complex issues that caused Einstein to have to ponder how to describe gravity in GR for 10 years after publishing special relativity. Special relativity is described using ordinary differential and partial differential calculus and in effect involves nothing more than a "small" adjustment to Newton's equations (even though the change in assumptions about how the world actually works were huge). He had to go back to school and study differential and analytic geometry in order to correctly formulate GR because ODE and PDE calculus are insufficient to describe curved spacetime geometry.
 
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