Does a particle's weight increase with speed?

No, because gravity moves at the speed of light.

That's incorrect. Einstein proved this in 1905 although you may not recognize it as such. The derivation of the proof is on my website at:

http://www.newenglandphysics.org/physics_world/gr/weight_moving_body.htmAs far as redshift goes, I don't see how that has anything to do with this problem. I assume that what you really have in mind is gravitational time dilation. Gravitational redshift only appears if and when the light is moving through a gravitational field. In this experiment there's no light. I assume that you're referring to gravitational time dilation. However that's irrelevant. All that could effect is the amount that the weight will change. It has nothing to do with whether the weight is a function of speed. That's a fact that is observer independent since all observers can determine whether the spring balance will depend on speed or not.

There's one very important thing that you neglected to take into account and that's the equivalence principle of general relativity which states that a uniform gravitational field is equivalent to a uniformly accelerating frame of reference. This means that you can test this result by producing a uniform gravitational field by changing your frame of reference to a uniformly accelerating one. In that frame there are no time delays having to do with the finite speed of the propagation of changes in the gravitational field. Now read the article

**On the Electrodynamics of Moving Bodies** by Albert Einstein,

*Annalen der Physik*, 17lk, (1905). This paper is online on Fermi lab's website at:

https://www.fourmilab.ch/etexts/einstein/specrel/www/According to general relativity the weight of a body equals the transverse mass times the component of acceleration transverse to the bodies velocity. Transverse mass equals relativistic mass. This is the only mistake in Einstein's paper, i.e. he calculated the wrong value for the transverse mass (TR), m

_{t}. TR was defined and I believe measured before Einstein wrote this SR paper. Ohanian explains this in his book

**Einstein's Mistakes**. I placed that portion on my website for people to read.

It's at

http://www.newenglandphysics.org/other/Ohanians_Third_Mistake.pdfAs Ohanian explains, when Einstein calculated the transverse mass using the expression F = ma he used the force as measured in one frame but used the acceleration as measured in another frame. This is a very odd thing to do. When physicists measure quantities and then use the results of those measurements to calculate things like force and acceleration to get mass one must use the same frame of reference for all the measurements. That is to say, if you wish to predict what the particle will weigh when its moving on a spring balance then you must measure

*both* the acceleration and force in the same frame of reference. In this case TM was already defined. Why he chose to redefine it is confusing unless he was unaware of the results already obtained by others. In this case Max Abraham had already defined these terms three years earlier in 1902. See:

https://en.wikipedia.org/wiki/Mass_in_special_relativityThe author of that Wikipedia page refers to it as an

*unfortunate definition*.

The speed of gravity has nothing to do with this. The gravitational field is static and therefore the field isn't propagating. The

*only* time that you have to think about the speed of gravity is when the source of gravity, i.e.

**matter**, has a time dependence of the distribution.

There's a a bit of a story behind why I'm interested in this subject if you're interested. One of the reasons that I decided to study general relativity (GR) was to learn how to calculate the weight of an object moving at speeds close to the speed of light. I was trying to determine whether the concept of relativistic mass was equal to passive gravitational mass. I found out that it is by.

I have a friend at MIT who I was discussing this with him. The professor, Dr. Edmund Bertschinger, liked this problem so much that he's made it a homework problem and its been a homework problem every since I raised the subject over 16 years ago.

If you want to read it please see:

http://ocw.mit.edu/courses/physics/8-962-general-relativity-spring-2006/assignments/pset06.pdfAlthough he gets the same result that I do his solutions aren't available online. I can send it to you in a PM if you'd like to see how the professor solves the problem and gets the same result that I do. I also posted above a reference to an article in the American Journal of Physics which demonstrates that the moving body generates a larger gravitational field as it moves.

I think this is why it is important to keep the concept of proper mass alive.

I'm quite happy to see you use the term

**proper mass** rather than rest mass. I think that it'd be a serious mistake to think that by preferring relativistic mass over proper mass means abandoning the use of proper mass. That's be like abandoning proper time for coordinate time, which would also a be a serious mistake.