Mass Gain

[Little Bang]

A proton accelerated up to a substantial portion of C gains mass (it is gaining mass as soon as it starts accelerating). Can someone elaborate. Does it have a larger diameter, gain more quarks or maybe pick up some dark matter. I know that it is relative to the observer so is it just the gain in energy required to achieve that velocity?

[CraigD]

A proton accelerated up to a substantial portion of C gains mass (it is gaining mass as soon as it starts accelerating). Can someone elaborate[?]

A proton, or any body with nonzero rest mass, increases in with any increase in speed, no matter how small. For example, a body moving at 1 m/s relative to an observer has about 1.000000000000000005 times the mass of one of identical rest mass at rest relative to the observer, as given by [math]M=\frac{M_0}{\sqrt{1-\left(\frac{v}{c}\right)^2}}[/math]

Does it have a larger diameter, …

Although the diameters of very small particles such as protons aren’t well-defined (they’re not truly little spheres), if one uses a body for which diameter is well-defined – for example, a pool ball – one would observe it to be slightly non-spherical, with a slightly decreased diameter measured parallel to its velocity, unchanged perpendicular to it.

… gain more quarks …

All baryons, including protons, always have exactly 3 quarks, though given the weird nature of phenomena at this scale, “have” doesn’t have its usual, macroscopic meaning. Counting the quarks in a hadron – anything made of quarks, both baryons and mesons – is complicated, the observation having as much to do with how its made as what’s “really there” (see, for example, “deep inelastic scattering”).

… or maybe pick up some dark matter.

There’s no such particle as “dark mater” in particle physics, and no clear consensus on what sort of particles constitute it, whether they are particles described by the standard model, extensions of it, or something completely different. All that one can really say about dark matter is that, by definition, we can’t currently detect it via photons absorbed or emitted by it, but can detect it by its gravitational effect on photons and ordinary fermionic matter.

I know that it is relative to the observer so is it just the gain in energy required to achieve that velocity?

Yes. The mass gained by an accelerated particle is exactly equivalent to the energy required to accelerate it, ignoring, of course, “inefficiency” energy lost due to interaction with other particles.

[arkain101]

A proton, or any body with nonzero rest mass, increases in with any increase in speed, no matter how small. For example, a body moving at 1 m/s relative to an observer has about 1.000000000000000005 times the mass of one of identical rest mass at rest relative to the observer,

 

I wonder, is such a result measurable? Possibly when considering a hyper velocity bullet? I guess what I am asking is, has any relativistic effect on a macroscopic object (and level) EVER been measured / observed? I've never heard of it as far as I remember.

[Little Bang]

We don't have any way to get an object larger than a proton to any significant portion of C. The mass gain of protons has been measured but you must understand that gain is relative to the observer. If the observer could somehow catch up to the proton he or she would see the proton as having it's normal mass. What I'm looking for is why we perceive this mass gain, what changes with the proton to make it have more mass in our observation.

[CraigD]

I wonder, is such a result measurable? Possibly when considering a hyper velocity bullet? I guess what I am asking is, has any relativistic effect on a macroscopic object (and level) EVER been measured / observed? I've never heard of it as far as I remember.

Relativistic effects in precise clock, such as those in GPS satellites, have been measured with good agreement with theory, but to the best of my knowledge, mass dilation of a macroscopic object, such as a bullet, has not.

 

Mass is in many ways one of the harder things to measure in fast-moving bodies. It’s impractical to use a scale, and practically impossible to detect by its gravitational force on test masses. The only experiment that come to my mind for detecting mass dilation would be to detect the slight difference between the classical and relativistic equations’ results for kinetic energy.

 

In principle, an expiriment something like this could be used:

• Shoot a 400 m/s bullet into a well-insulated container of water
  
• Measure the temperature increase of the water
  
• Shoot a 500 m/s bullet.
  
• Measure the temperature increase of the water

Classical mechanics predicts the second measurement will be [math]\left(\frac{500}{400}\right)^2 = 1.5625[/math] that of the first.

Relativity predicts the second measurement will be [math] \frac{\left(1- \left(\frac{500}{c}\right)^2\right)^{-\frac12} - \left(1- \left(\frac{400}{c}\right)^2\right)^{-\frac12} }{ \left(1- \left(\frac{400}{c}\right)^2\right)^{-\frac12} -1} \dot= 1.56250014[/math]

 

So if the first temperature increase was 50 C, you’d need a thermometer sensitive to about 0.000007 C to detect the predicted difference. The best thermometers are currently accurate to about 0.15 C, so this specific experiment seems beyond our current capabilities.

[CraigD]

We don't have any way to get an object larger than a proton to any significant portion of C.

This isn’t completely accurate.

 

The “LH” in accelerators like the new LHC stands for “large hadron”. In particular, the large hadron(s) that are accelerated by it are lead nuclei. Lead nuclei mass about 207 times as much as a proton. The LHC can accelerate them to over 99.99999 c.

 

It would be accurate to say we can’t accelerate object much larger than a proton, or anything larger than some atomic nucleus. The basic problem is that current accelerators accelerate charged particles only, so whatever body they accelerate must be strongly bound together, and have a large net charge. Macroscopic objects like pool balls are almost neutrally charged, and compared to atomic nuclei, are very loosely bound together.

What I'm looking for is why we perceive this mass gain, what changes with the proton to make it have more mass in our observation.

This is a difficult, somewhat philosophical bit of interpretation. Nothing about the proton changes relative to its own reference frame. It doesn’t suck up surrounding massive particles. The mass increase is entirely relative, having to do with the relative velocity of some observer.

 

I’d summarize it with no great satisfaction by saying that Relativity appears an innate feature of reality, not a phenomena due to some underlying mechanical goings-on. There aren’t, according to conventional theory, any interaction involving “mass dilate-ons” or any other particles, causing matter to follow the laws or relativity – though someone who really understands the Higgs field might correct me on this example. :Alien:

[Little Bang]

Tell me if I wrong. I think the relative mass gain of an object being accelerated up to a significant portion of C would look like a tangent curve. That would suggest it's momentum would also follow that curve. Doesn't this mean that the velocity to momentum ratio also follows this curve.

[CraigD]

I think the relative mass gain of an object being accelerated up to a significant portion of C would look like a tangent curve. That would suggest it's momentum would also follow that curve. Doesn't this mean that the velocity to momentum ratio also follows this curve.

I wouldn’t describe it as that.

 

Attached is a graph of relativistic momentum and kinetic energy and their ratios, created by the handy Graphing Calculator website.

 

The ratio of energy to momentum according to any recognizable physics is a velocity. I don’t think this ratio is of much significance.

[Little Bang]

Craig, how does QM explain why time is a variable?

[Erasmus00]

Craig, how does QM explain why time is a variable?

 

What do you mean by this? What else would time be?

[Little Bang]

We know why an animal eats, because it is hungry. So why does time slow down for anything that is accelerated?

[Erasmus00]

We know why an animal eats, because it is hungry. So why does time slow down for anything that is accelerated?

 

So you are asking why time varies with reference frame? This is different then being a variable (being something that doesn't take a fixed value in an equation).

 

I think the simplest thing I can suggest is this- if we have two observers and one measures a car's velocity to be 20 mph, and the other measures the exact same car to be moving at 30mph, what do we conclude? The two observers are using different coordinate systems. So why does velocity vary between two coordinate systems?

 

This question is rarely asked because we take this fact for granted and it seems obvious. Why is it obvious? Because for whatever reason it makes intuitive sense to us. However, the same "reason" velocity is different between frames is the same reason distance, time, and mass measurements can be different.

[CraigD]

Craig, how does QM explain why time is a variable?

I wouldn’t say that quantum mechanics makes any explanation why (if I understand your question correctly LB) time exists. It’s a theory of mechanics, and like classical mechanics, simply postulates the existence of three observable space-like dimensions, and one time-like one.

We know why an animal eats, because it is hungry. So why does time slow down for anything that is accelerated?

First, it’s important to understand that time dilation doesn’t require acceleration, only relative speed. If I observe some clock-like phenomena of a non-accelerating frame with a non-zero velocity relative to me, it will occur slower than the same phenomena observed of a frame with a lower or zero velocity. It isn’t necessary for the observed frame to have been accelerated.

 

It’s necessary that this occur, or one of the two postulates of Special Relativity – the principle of invariant light speed, that is, that one never observes light traveling faster than the speed of light in vacuum – can be violated.

 

A common illustration of this is the "light clock" thought experiment. Here’s a variation of it:

 

I’m traveling at 0.5 c relative to you. I have a clock that measures an interval of 1 nanosecond by measuring the passage of a very short duration burst of light traveling across a 0.299792458 m-wide gap of near perfect vacuum. You watch my clock from a comfortable distance, with my clock’s gap oriented perpendicular to your line of sight.

 

If you observe my clock measuring the same 1 ns duration as I do, you will observe the light pulse traveling not only across its measuring gap, but in the perpendicular direction of my velocity, a distance the Pythagorean theorem gives as [math]\sqrt{0.299792458^2 +(0.5 \cdot 0.299792458)^2} \dot= 0.335178158 \,\mbox{m}[/math], in 1 ns. You’ll observe the speed of light in vacuum for the particular photons used by my clock to be about 335178158 m/s, greater than its defined speed of 299792458 m/s.

 

This raises all sorts of problems, such as how did those photons “know” that and how we were observing them in order to travel faster than their usual speed. Special Relativity solves these problems by postulating that what I describe above never occurs, so these problems never arise.

 

A consequence of this is that you see my light clock running slower than I do, even though nothing has interfered with it (eg: rattled or accelerated it) to make it malfunction, and, in fact, I’ve observed it behaving as usual. As we like the convenience of clocks that keep the same time unless something explicable interferes with them, this is annoying, but it’s simply the way the universe appears to work. The explanation offered by Special Relativity - time dilation - is less troubling than ones in which light can travel any speed necessary to make time dilation not occur.

 

We might wish the universe worked differently – for example, that light behaved like tiny bullets, dependent on the velocity of their source, or like sound waves, dependent of the velocity and other characteristics of their medium – but all observations reveal that it works the way it does, not how we might wish it would.

[Little Bang]

You say time dilation doesn't require acceleration and you can prove this how? If what you say is true that would mean we could place a clock on the surface of the face of the moon towards earth and put an identical clock in space 10K meters from the moon and they would keep the same time?

[Little Bang]

You know what, I want to thank the members for an enjoyable learning experience but I don't see anything I can contribute or learn. Goodbye, good luck and may we all gain knowledge from that drop of water.