A mass dilation “paradox” though experiment

[Moontanman]

Moderation note: moved the first 11 post of this thread from “Can Neutron Star Become Black Hole”, because they apply to physics in general, not just to neutron stars and black holes

 

How about this thought experiment, if you had a neutron star that was within 1% of being massive enough to be a black home and you accelerated it to .9999% of the speed of light would it become a black hole? more importantly if it did become a black hole would it stop being a black hole if you decelerated it back to an apparent standstill?

[freeztar]

How about this thought experiment, if you had a neutron star that was within 1% of being massive enough to be a black home and you accelerated it to .9999% of the speed of light would it become a black hole?

 

I would say yes. The energy used to accelerate the star to that speed would add to its relativistic mass and push it over the threshold.

 

more importantly if it did become a black hole would it stop being a black hole if you decelerated it back to an apparent standstill?

 

That's a trickier question. ;)

I don't think it would immediately revert back to a neutron star, but that's a guess. :hihi:

[Moontanman]

Ive been giving this some thought, the old gears have been grinding away. If the mass of the object traveling close to the speed of light is real, then the mass of the universe from the point of view of the object must be real too, correct?

[freeztar]

Ive been giving this some thought, the old gears have been grinding away. If the mass of the object traveling close to the speed of light is real, then the mass of the universe from the point of view of the object must be real too, correct?

 

What do you mean by "real"?

[Moontanman]

What do you mean by "real"?

 

Real, if the mass of the accelerated neutron star is real then it becomes a black hole but if it's mass is real then the mass of the universe from the stand point of the Neutron star must be real too. I am saying that neither point of view is real so the neutron star would not collapse into a black hole any more than the rest of the universe is massive and compressed as seen from the stand point of the neutron star or any other accelerated object. Both points of view cannot be real so neither is.

[freeztar]

I'm still confused. Why would the mass not be real?

[Moontanman]

I'm still confused. Why would the mass not be real?

 

I say the mass is an illusion possibly produced possibly by time dilation or spatial compression..

 

#1. The reasoning is that if you accelerate an object to near light speed it becomes more massive, some say it's because more and more of the energy of acceleration goes to making the object more massive than it does to increasing the speed. But if you apply energy to decelerate the object the mass decreases. How does the object "know" to reject the energy of deceleration and accept the energy of acceleration.

 

#2. From the stand point of the object, lets say a human, it's the entire universe that has become more massive and compressed, not the object being accelerated, this has to be an illusion.

 

#3. If applying energy to an object to affect it's speed makes it more massive shouldn't it work both ways? Acceleration and deceleration? if not what happens to the energy you use to decelerate an object? Does it become negative mass to take away mass from the massive near c object?

 

Again I say these things are illusions produced by space/time compression at near light speed, not real mass increases.

[CraigD]

To increase the clarity of my explanations, I’ve rearranged the order of the several posts I respond to below.

If the mass of the object traveling close to the speed of light is real, then the mass of the universe from the point of view of the object must be real too, correct?

Yes. This is a clear requirement of the “no preferred frames” consequence of Relativity. It’s also true also of the other dilation effects, time and length.

… if you had a neutron star that was within 1% of being massive enough to be a black home and you accelerated it to .9999% of the speed of light would it become a black hole?

Short answer, no.

 

Like better-known “relativity paradoxes” such as the twins and the ladder, this one can be perplexing.

 

A couple of preliminaries:

• As noted above, since the laws of Relativity are relative, it’s not necessary to accelerate the neutron star for this thought experiment, but rather the observer. This gives is a bit more plausibility, I think, reducing the temptation to answer it with something like “there’s not enough resources around to possibly accelerate a neutron star that much”.
  
• The example can be rephrased to be more mundane than one involving neutron stars and black holes. This thought experiment isn’t about neutron stars or black holes, its about Relativity. So though I’ll keep my explanation in the original though experiment, keep in mind that it works as well using, say, the Earth, a spaceship, a bowling ball and a fragile table.
  

The core of the paradox is that different, irreversible events occur on a neutron star than within a black hole, so that even if a neutron star temporarily became a black hole, then returned to being a NS, things on it would be different than if it had been a neutron star the whole time. Both an observer nearly at rest relative to the NS (Alice) and one with a high speed relative to it (Bob) should, upon matching velocities and positions, must agree that they are seeing the same conditions on the NS.

 

Relativity demands that Bob really measured (say, via a gravimeter) a mass for the NS that, had Alice measured the same mass, would require that it collapse further into a black hole. Alice, however, measured its mass as requiring that it not collapse into a black hole.

 

The resolution is that, although Relativity requires that the laws of physics Bob observes of things near his velocity – his inertial frame – are the same regardless of his speed relative to Alice and the NS, they don’t require that they are the same for things with greatly different velocities than his, but rather precisely describe how they must differ. Time dilation, mass dilation, and length contraction are examples of these precise descriptions. A more complicated example is that, despite the mass of the NS being greater than possible for an NS that is at near rest relative to an observer, its mass is not greater than possible for an NS with the speed it has relative to Bob. In other words, because Bob can measure the speed of the NS relative to him, he can, via the same calculations that allow us to determine its real mass relative to Bob, calculate what its mass relative to itself must be, and, applying the laws governing neutron stars, determine that it does not collapse. In yet other words, because Bob’s mass isn’t significant to the NS, the correct frame to use in calculating what happens to the NS is its own. If Bob is to correctly use physics to predict what happens to the NS based on his velocity and mass measuring instrument’s data, he must use the Special Relativity part of physics.

 

Bob’s gravitometer really tells him the NS has a greater mass than Alice’s gravitometer tells her it has, and neither one of them see the NS collapse into a black hole.

I say the mass is an illusion possibly produced possibly by time dilation or spatial compression..

This conclusion is, I think due to a failure to truly grasp the very counterintuitive consequences and interpretations of Relativity.

#1. The reasoning is that if you accelerate an object to near light speed it becomes more massive, some say it's because more and more of the energy of acceleration goes to making the object more massive than it does to increasing the speed. But if you apply energy to decelerate the object the mass decreases. How does the object "know" to reject the energy of deceleration and accept the energy of acceleration.

Objects don’t “know” how much mass to gain or lose or how to exhibit any other relativistic effect, any more than a tree “knows” to show once side to one observer, and another to an observer in a different direction from it. Relativistic effects, like optical perspectives, are not “owned” by the object being observed, but by the position and velocity relationship between it and its observer.

 

Importantly, who or what is accelerated, or if anything is accelerated, isn’t important to SR. Only velocity is. Acceleration doesn’t cause SR effects. Only velocity does.

#2. From the stand point of the object, lets say a human, it's the entire universe that has become more massive and compressed, not the object being accelerated, this has to be an illusion.

As noted previously, yes, a mass/time/length dilated object observes the same mass/time/length dilation of the rest of the universe that the rest of the universe observes of it. Though counterintuitive, this is not an illusion.

#3. If applying energy to an object to affect it's speed makes it more massive shouldn't it work both ways? Acceleration and deceleration? if not what happens to the energy you use to decelerate an object? Does it become negative mass to take away mass from the massive near c object?

See the answer to #1.

Again I say these things are illusions produced by space/time compression at near light speed, not real mass increases.

Again, this conclusion is a misunderstanding of Special Relativity. Despite it’s conceptual and mathematical simplicity, SR can be very counterintuitive and difficult to understand.

[Moontanman]

Evidently I am just not flexible enough in my thinking to be able to see how both perspectives could be true at the same time.

[Moontanman]

In the "twins" experiment from the stand point of both twins times slows down for the other but the slow down is only real for the twin that left the earth. I just don't get it I'm afraid.

[CraigD]

Evidently I am just not flexible enough in my thinking to be able to see how both perspectives could be true at the same time.

It’s less a matter of flexible thinking than training intuition, I think. Seeing through apparent paradoxes of Relativity are critical to understanding the theory, so worth some effort.

 

In either Galilean or Einsteinian relativity, there are two significantly different perspectives only when the two observers have significantly different locations and/or velocities. When they’re not – including scenarios where observers that formerly had significantly different locations and velocities move and accelerate to match locations and velocities – they share a common perspective according to either relativity.

 

We’re all intuitively familiar with Galilean relativity from everyday phenomina such as the appearance when driving of objects moving outside our cars appearing to move while objects inside them appear stationary, while when on foot, the appearance that other cars and the objects inside them are moving. Galilean relativity, doesn’t postulate an invariant speed of light. Taken to its logical conclusion we would assume, as Newton appears to have, a corpuscular theory of light in which light emitted by a car moving toward us reaches us sooner than similar light emitted by a car moving away from us. Einsteinian relativity does, with direct logical consequences such as length contraction and time dilation, and slightly less direct ones such as mass dilation.

 

It’s encouraging, I think, to consider that the Galilean relativity with which most of us are so intuitively familiar was not intuitively familiar to most people in Galileo’s day. Our level of intuitive comfort with it is arguably due to our everyday environment’s smooth roads rails, cars and trains, and similar technology, vs. the rough roads seas, and conveyances of Galileo’s. Perhaps, if our future environment entails astronomical distances and spacecraft, we’ll be intuitively comfortable with Einsteinian relativity.

 

As we don’t currently, I can think of only two approaches to overcoming our intuitive resistance to Einsteinian relativity:

• Via immersive computer simulations or great scientific accuracy, we could effectively live in the above mentioned future environment.
  
• We can study physics, especially by working through apparent paradoxes like the ones discussed in these and other threads
  

Though developing realistic simulation software is IMHO a laudable pursuit, I uncertain that present computer-human interface technology is yet immersive enough to really effect our intuition. In any case, hypography is a text-based forum site, not a video game, so we’ll need to just keep working at physics the old-fashioned, text-based way.

[freeztar]

Relativity demands that Bob really measured (say, via a gravimeter) a mass for the NS that, had Alice measured the same mass, would require that it collapse further into a black hole. Alice, however, measured its mass as requiring that it not collapse into a black hole.

 

I must admit to being unfamiliar with this particular paradox, but it makes sense considering the others. Craig, are you aware of a good resource for further understanding the mass dilation paradox? Specifically, it would be nice to see the math behind it.

 

Some simple clarifications would help in my own understanding.

Why does the relativistic mass experienced by Alice not show her that the NS has breached the threshold? Is it somewhat analogous to Alice's measurements occurring in a series of rest frames (rest mass; like the Galilean car passengers)?