kjelleman

Gravitoelectromagnetism shows that you may formulate GR in the same form as Maxwell's equation within the same approximation scheme, i.e. low speed, weak field.

Why is this so?

The reason is that magnetism and induction are due to uniform and accelerated motion of charges and are actually motional consequences (same as relativistic effects). The corresponding effects therefore appear in GR which basically sums up the motional consequences starting from Newton's force law. The corresponding effects of magnetism and induction therefore also appear there.

For example, in the parallel motion of two massive objects the attraction is smaller than when being at rest. This is equivalent two the parallel motion of two charges where the reduction of the force is called magnetism.

This is an important aspect of GR since it provides a conceptual understanding of its basic mechanisms.

I guess we focus on physical time here, not aging or evolutionary.

In physics time is defined through Newton's force law. It is then easy to understand both space and time by utilizing relational mechanics which was first postulated by Leibniz. Here space is just distance between objects and time corresponds to the motion of the objects. Then it is clear that there is no absolute time nor absolute space, all must be related to something, a problem we encounter when trying to define meter and second.

Having this view of space and time, relativity e.g. becomes a piece of cake, both SR and GR.

What if a miniscule object was traveling at a relativistic speed (at least in excess of the speed of sound in the medium,anyway)?Would the resultant wave in the medium be constrained (immediately) to the normal speed of the wave in that medium?

 

So none of the speed of the miniscule object would be imparted to the speed of the wave which would be uniquely determined by the speed of a (sound) wave in that medium?

 

It is a separate point perhaps to the one explained by Swansont.

I think the really point here is that any wave traveling through a medium will have a velocity equal to the velocity of sound in that medium plus whatever velocity the medium itself has. For people traveling at different speeds relative to the medium, the speed of the sound wave will change relative to the observer.

 

The speed of light does not change in this manner with respect to the speed of the observer.

I assure you that he does not miss the point.

The point that is crucial is that the resultant velocity of 2 trains traveling each at 100km/h and passing each other is 200km/h. The resultant velocity of 2 trains travelling each at c and passing each other is...c.

I try to answer the question of this thread in a conceptual way as was asked for. To this end, I utilize the fact that the speed of light is independent of the velocity of its source. Do we agree on this?

 

Yes, they are unusual in this way. Waves requiring a medium don't do this. So no, it's not factually correct. A water wave moving forward on a train will move at some combined speed (v_wave + v_train, approximately, at low speeds) while a laser on a train moves forward at c, as seen by an external observer.

I think you miss the point here and it is crucial. Speed of sound, water pulse and light pulse, i.e. photon, are all independent of the speed of the source that emits them.

Let me reduce the rocket example to two interacting electrons, A and B, traveling one after another, B in front of A. And there is an observer measuring their equal velocity.

The interaction takes place by sending photons to each other which travel at the speed of light. The speed of the photon is independent of its source speed. Nothing strange with that, same thing with water and sound pulses.

When the pair of electrons move relative the observer, the photon from A to B will need to traverse a longer distance compared to when the electrons are at rest. When they move at the speed of light the photon from A will never reach B and therefore B cannot be accelerated further.

Concerning mass/momentum increase one needs to interpret the concept of mass. Mass is a description of how much a force affects an object. The weaker motional response to a force the higher mass. So in this case, at the speed of light and no motional change, we would experience this as infinite mass/momentum.

 

 

OK.

The problem that I see with that is, first of all, that according to SR the force that is experienced by the rocket in a co-moving reference system, is just the everyday reaction force; and the transformation factor of force in that direction is 1. In other words, according to SR, if we use the reference system in which the rocket is moving very fast, the force on the rocket is NOT reduced. Your assertion is therefore in disagreement with SR.

For reference you can look up §6 of https://www.fourmilab.ch/etexts/einstein/specrel/www/

Alternatively you can "google" the same in more modern texts, I found for example http://www.sciencebits.com/Transformation-Forces-Relativity (disclaimer: I did not check the derivation there).

 

Further, as far as I know our technology has not yet reached the point of verifying the theory for rockets; but it has been done for a somewhat similar case, that of electrons.

Probably you would apply the same reasoning as you did on accelerated electrons, and claim that these cannot reach the speed of light because the "push" of the electric field on the electron becomes infinitely small at speed c. (correct?).

That reasoning has effectively been disproved by the Bertozzi demonstration experiment, which verified the added kinetic energy at high speeds by measuring the energy that was released at impact. The electron is, as measured in the lab, truly a "high energy" or "heavy" particle in agreement with the amount of added kinetic energy according to SR.

Yes, you are right about force. It was my mistake to originally write force while I really meant acceleration which of course is the relevant quantity to consider in this context. Just replace force with acceleration and my argument should hold.

 

That sounds good, but I think that I can show that it is incorrect, as Janus remarked.

 

Let's try this: if your reasoning were to -the-point, then this means, if I correctly understand your "there won't be any repulsion", that at say 0.99999c the rocket's push will be very small according to you, and so the push will be ever smaller and smaller when going faster, and that is why the rocket cannot reach c?

 

If yes, then I will continue (or maybe someone else who knows what I'm getting at will do so, that's OK).

My answer is yes. (My last post today. Since I am new I have run out of post budget. See you tomorrow.)

This is incorrect. Even if we were to stipulate that you couldn't push something to greater than c speed relative to you for this reason, this would not explain why a rocket could not exceed light speed, as the velocity of a rocket is not limited to its exhaust velocity. (Modern chemical rockets can only generate exhaust velocities of ~4.5 km/sec, yet routinely attain velocities of better than 7 km/sec in order to achieve low Earth orbit.)

 

The c speed limit is "built in" to the very nature of space and time.

It is not a stipulation. Even your rocket need to obey the fact that every interaction basically is an interaction at a distance and this interaction is mediated at the speed of light. So if your rocket travel at speed of light and tries to accelerate through the repulsion effect there won't be any repulsion since the mediator of the force will not be received by the rocket/exhaust. (This mediator has the name photon)

The reason is that the force between objects is mediated at speed of light so if the object travels at the speed of light there won't be any active force on it and it can therefore not be accelerated further. So the basic question is: why is force mediated at speed of light?

To understand this phenomenon one cannot utilize concepts as mass and time since that results in circular reason. What we mean by mass and time is how much an object is influenced by a given force. A slower response to a force we conceive as larger mass and/or slower time. So what happens at speed of light? At this speed there is no interaction since the mediator of force is itself travelling at the speed of light. If the object move at speed of light the mediator cannot be received. This we experience as infinite mass/momentum and/or time standing still.

Please see chapter 9 of my text book for a more thorough discussion:

link deleted - rule 2.7

Hello Everybody. I am new to this forum. I work as professor in physics since 20 years and have taught in almost all different physics courses over the years.

I think the short question in this thread is interesting. I have myself struggled with the field concept and I have met many confused students in this respect and my teaching strategy concerning this concept is to declare that the field is a pure calculational aiding tool. It doesn't have any physical relevance. What happens ' between' two interacting objects, we have no access to, it is just speculations. Therefore physics need to be described field-free and the fields should be introduced afterwards as a model only. If you are interested in field-free physics I would like to recommend my text book:

https://link.springer.com/book/10.1007%2F978-3-319-13171-9

where part of it may be downloaded for free.

Best wishes,

Kjelleman