Overlapping gradients?

[Paul Murphy]

I've enjoyed reading books by Stephen Hawking, Leonard Susskind, etc., but my lack of formal, methodical physics education has left me with a big gap in my understanding of relativity. I'd really appreciate it if you can educate me on the following...

 

Do the relativistic effects (time dilation, length compression, mass & gravity increases) that occur when an object approaches the speed of light affect just the quarks and electrons that the object is made of or is there a region of spacetime around the entire object that has a gradient of effects applied to it? If it's a region, which I suspect because of the mass increase and therefore a gravitational field, what happens when these regions overlap as objects pass near each other at high relative velocities? Which effects are shared, if any, by these objects?

Edited September 4, 2010 by Paul Murphy

[swansont]

It affects objects, not spacetime.

[Paul Murphy]

Thanks for the quick response. I just want to be clear on the answer, since this particular issue makes my understanding of the rest of relativity more difficult. If only the matter itself is affected, then is the addional mass gained by the object that is approaching the speed of light not normal mass which warps the surrounding space due to its gravitational field?

[Paul Murphy]

I think I've made progress and may have an answer:

 

The non-mathematical popular physics books I've been reading left me with the impression that time slows down, mass increases and length contracts in the direction of travel as an object approaches the speed of light without ever explaining that you can only say that these effects exist relative to another frame of reference. I now understand that there is no absolute motion and no absolute rest and every frame of reference is equally valid. My primary conceptual problem now lies with mass increasing with velocity. Since mass distorts spacetime via gravity and gravitational fields extend to the entire Universe, is there a separate topology of gravitational fields for each frame of reference independent of all differentially moving frames of reference? In essence, does each frame of reference have a separate topology of the Universe? Does every particle observed from a different frame of reference have a range of properties relative to every independent frame of reference?

 

I've been thinking about my question all morning and then I thought of the double-slit experiment where a single photon or particle appears to traverse every possible path and interfere with itself. I was also thinking about the sum over histories and the probabilistic nature of quantum mechanics. Is it possible that relativity's multiple independent frames of reference are the cause of the probability waves of quantum mechanics? If every particle has to have different properties when viewed from every relatively moving frame of reference, then maybe they do have all these different properties, each of which is described by a history in the sum over histories and the probability wave enumerates these properties in the other frames of reference and has the highest probability in the local frame of reference. I assume I'm completely wrong on this, but it made for an exciting few minutes while these ideas bloomed into my mind. I can't wait to hear from you and get a better understanding of what is going on.

Edited September 4, 2010 by Paul Murphy

[swansont]

First of all, mass does not increase. That's a pernicious theme which comes from misapplying mass-energy equivalence. The proper equation is [math]E^2 = p^2c^2 + m^2c^4[/math]

When you are moving, the momentum term increases, not the mass.

 

I don't think I've ever seen anyone try to explain sum over histories in this way. Photons are not even in an inertial frame — they travel at c, and objects with mass can't — so I don't know how you would do that.

[Paul Murphy]

First of all, mass does not increase. That's a pernicious theme which comes from misapplying mass-energy equivalence. The proper equation is [math]E^2 = p^2c^2 + m^2c^4[/math]

When you are moving, the momentum term increases, not the mass.

 

If it's momentum and not mass that increases, then a lot of the reading material from seemingly reliable sources is worded very badly, such as this University of Virginia article that states, among other things:

http://galileoandeinstein.physics.virginia.edu/lectures/mass_increase.html

 

 

Mass Really Does Increase with Speed

Deciding that masses of objects must depend on speed like this seems a heavy price to pay to rescue conservation of momentum! However, it is a prediction that is not difficult to check by experiment. The first confirmation came in 1908, measuring the mass of fast electrons in a vacuum tube. In fact, the electrons in an old style color TV tube are about half a percent heavier than electrons at rest, and this must be allowed for in calculating the magnetic fields used to guide them to the screen.

 

Much more dramatically, in modern particle accelerators very powerful electric fields are used to accelerate electrons, protons and other particles. It is found in practice that these particles become heavier and heavier as the speed of light is approached, and hence need greater and greater forces for further acceleration. Consequently, the speed of light is a natural absolute speed limit. Particles are accelerated to speeds where their mass is thousands of times greater than their mass measured at rest, usually called the “rest mass”.

If this is a scientifically incorrect, it is equally as bad for beginners like me as books that talk about relativistic effects, without thoroughly explaining that you can only say that these effects exist relative to another frame of reference. I think every Relativity book should start with the following statement to make everyone's life easier: There is no absolute motion, no absolute rest and every differentially moving frame of reference is equally valid.

 

I reformulated my original set of questions to be more general. I'm not trying to say any of this is true. I'm just trying to get to a point where I can understand why it is not true and get rid of at least one of my remaining misconceptions. Without a sufficienct math background, I have to try to take a plain English / logical approach to figuring this out.

 

Here is my latest iteration of assumptions and suggestions:

 

In Einstein’s Theory of Relativity, there is no absolute motion, no absolute rest and every differentially moving frame of reference is equally valid. Observers in differentially moving frames of reference will measure an object’s speed, radioactive decay rate (time) and mass to have different values. These measurements from differentially moving frames of reference are equally valid.

 

In the case of gravity, I suggest that an observer in one frame of reference will map the gravitational fields present in the Universe differently than an observer in a differentially moving frame of reference. In essence, each relatively moving frame of reference has a separate gravitational topology of the Universe. They would each create a different map of gravitational fields from their own equally valid perspectives.

 

I suggest that every particle that could potentially be observed has a range of properties that would be observed to have different values when measured from differentially moving frames of reference.

 

If particles could theoretically be measured to have different values for properties when viewed from relatively moving frames of reference, then maybe the values of these properties are described by a separate history in a way similar to Feynman’s Sum Over Histories and the probability wave for each property has the locally highest probability for the most likely value in each local frame of reference.

 

 

[swansont]

If it's momentum and not mass that increases, then a lot of the reading material from seemingly reliable sources is worded very badly

 

Yes, that's true. The use of relativistic mass is used to bridge understanding from the Newtonian/Galilean world into relativity, much like the wave-particle duality is used in quantum mechanics.

[Paul Murphy]

Yes, that's true. The use of relativistic mass is used to bridge understanding from the Newtonian/Galilean world into relativity, much like the wave-particle duality is used in quantum mechanics.

 

I'd imagine there many people like me on this forum who took something else in college and get interested in physics later in life. A lot of us probably don't have quite the math background neccessary to read college-level physics textbooks. Given the numerous sources of incomplete or downright incorrect information we newbies are likely to run across, I think it would be helpful to have a FMC (Frequently Misunderstood Concepts) sticky post. For Relativity, it might have items such as:

 

1. The difference between relativistic mass, rest mass and momentum

2. Those weird relativistic effects can only be said to exist relative to another frame of reference. Within every frame of reference, the laws of physics act normally and are the same for everyone.

3. Wild guesses, no matter how well intentioned, can be a slipery slope to quackdom.

 

I hope my guesses earlier haven't put me in category 3. I'm going to take a slower approach and try to learn the math. I'm keeping a notebook of specific questions that I come up with as I read and I'll iteratively try to answer them myself. If I'm really stuck, I'll post a specific question. Thanks.

[swansont]

The issue with relativistic mass, and why the notion persists, is that the concept doesn't cause any problems until you delve deeper into the physics.