Relation between mass/energy and initial speed of particles

Light travels at the speed of light. Which is the fastest speed particles can go at.

When something with mass approaches the speed of light part of the energy of that acceleration is converted to mass, and more mass needs more energy to accelerate.

I think that I have understood this correctly.

Photons have no mass, hence goes initially the fastest speed possible, could it then be said that particles that does not go at the speed of light, does not go at the speed of light because they have mass?

Could it also be said that the more massive the particles, the slower they are initially?

Does all particles have an initial speed? Or is it only the photon?

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Yes.

What do you mean ``initially''?

 

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All that is more or less correct. Although the energy used to accelerate it isn't exactly converted into mass; the mass is relative, so if you were riding along next to the speeding object (i.e. its velocity was zero relative to you) then it would appear to just have its regular rest mass. It only gains mass according to the observer who thinks it is moving very fast.

This part is not so correct. There is no 'initial' speed that particles have, except that yes I guess you can say that massless particles have such an 'initial' speed and that it is c. It is always c though, you can never make it anything else (you can sort of cheat and make them slower in certain media but that is a bit different)

 

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Thank you, then I'm on the right track.

When created. Photons doesn't have to accelerate to the speed of light, but goes at the speed of light when created, I do realise that the creation of particles often involves speed (and thus the initial speed is obscured), but it should have a initial speed? Like light has a initial speed that it doesn't need accelerating to.

Also, because it has mass it goes slower than the speed of light, say, in a vacuum. So if it has greater mass does it move slower than if it has less mass?

 

Yes, but close to the speed of light these relations all become related to the speed of c right?

So that if you measure someone moving close to the speed of light it seems like they just don't move any faster than that (even if in the perspective of the "rocketeer" they think they are moving faster and faster and perhaps they even think that they are beyond the speed of light?)

So you say that particles that have mass doesn't have a initial speed, so that it only depends on the conditions that made them? (in a collision they would take on the speeds according to the energy of the collision?)

 

Hi Cyperium,
Maybe a specific situation will be useful:

Consider two high energy photons that interact and create a particle-antiparticle pair.
If the two photons had equal energies and collided head on, (ie we're considering the frame of reference where the total momentum is zero), then what will be the initial speeds of the created particle and antiparticle?

I can't answer this properly, and I'm hoping that someone who Knows What They're Talking About will answer it for me, but I'm going to have a stab for the sake of discussion

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From the conservation of momentum, we know that the created particles must have equal and opposite momentum.

From the conservation of energy, we know that their kinetic energy must be whatever is left from the photons after subtracting the particles' rest mass.

The larger the particle rest mass, the less is left over for kinetic energy, so in this particular case at least I think that yes, it could be said that the more massive the particles, the slower they are initially.

 

1. Yes
2. This is a bit confusing the way you have said it. No-one will ever observe something moving beyond the speed of light. Need to remember to consider the frame of reference.
3. Yes, though they may gain or lose a bit extra if the total masses of the initial and final particles are different. This is all thought of as conservation of energy however.

As for what Pete says, he is pretty much correct, except that two photons colliding head on won't annihilate

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. Well, actually I suppose they can but it's not very likely to happen. Positron-electron annihilation into two photons is a nicer standard example, or if you want something that creates massive particles then you can have positron + electron -> muon + antimuon (this is kind of a nice example because it won't happen unless you crash the positron and electron together with enough energy to make up the extra mass needed for the muons).

 

Ok, thank you for the replies.

Could it be since the mass to energy ratio is c^2 (a very high figure) the speed loss of the particles with mass is so great that it isn't noticed that it has any speed at all initially (excluding the speeds of eventual other particles involved)?

Also; doesn't pairs of particles have initial speed when they pop up from quantum vacuum (involving no collisions at all)?

I was thinking along the lines that the speed of light was converted partially to mass in those particles with mass, and that the rest of the energy made the particle go at the speed defined by its energy. In other words, photons go at the speed of light because that is what the particle is, speed (all its energy is kinetic and nothing is mass). If this was true, I could perhaps think of a valid scenario applying to gravity in a understandable and natural way.

 

Yes, but if they didn't know about special relativity and expected to be at the speed of light in a certain amount of time, they would see no appearent effeciency loss of the acceleration (since the increase of mass is oblivious to them) and no time-slowing or anything, to them it would seem like they are accelerating at normal speed beyond the speed of light. If only given the instruments on board.


As they wouldn't notice their mass increased there would be no way of knowing that they need much more energy in order to accelerate to the speed of light, right?

Actually the entire galaxy could be going near the speed of light without anyone knowing about it, as the mass increase aren't noticed and the speed of light is still a infinity of acceleration away, isn't that so?

Would they notice the fuel burning out faster? But since the mass of the fuel also increases that should also be taken into consideration? Or what kind of mass does the conversion produce? Perhaps the fuel efficiency is less because the greater amount of mass changes its properties?

 

This whole concept of initial speed doesn't really make sense. As soon as something is travelling at a speed less than c, you can view it from whatever reference frame you like such that it's speed is anything you like (so long as it is less than c) relative to you (you can even view it as going in whatever direction you like). If it is travelling at the speed of light however it does so in all reference frames, so your initial speed concept makes some kind of sense here. In this case the frequency of the photon is shifted in the different frames to satisfy momentum conservation and such.

They have different speeds in different reference frames. Although the vacuum is equivalent in all inertial reference frames so it doesn't actually look any different.

I think the thinking is not quite right here. For a photon, there is no frame of reference in which it has no momentum. For any massive particle, there is always some frame of reference in which it's momentum is zero (the so called 'rest frame'). Thus you can view your particle creation happening in some frame in which one of the products doesn't move, it just sits still, unless it is massless.

You are right, to them nothing much would change, they could just accelerate at a constant velocity and everything would stay the same. However, to any observer watching them, the acceleration would not be constant, it would in fact decrease and the vehicle would never reach the speed of light (measured relative to that observer). The guys inside the rocket would experience a constant force the whole time however, consistent with a constant acceleration.

You have to talk about velocities relative to something. The phrase "the galaxy is moving near the speed of light" doesn't mean anything on its own, you must say "the galaxy is moving near the speed of light relative to the other galaxies in our local group" or something (clearly this example is not the case)

In the rocket frame, all is as normal, they don't feel like their mass increases. It is only measured to increase by others in other reference frames.

 

I have a somewhat different question.

1: Time stops at c.
2: Time slows down gradually while approaching c.

Let's imagine that we are heading for another star 4 lightyears from us.

This isn't possible: (but enlightening)
Of course when we actually comes to c time stops and the universe shrinks to a dot so we would pass the entire universe in a 'blink' of time (yes, actually), actually arriving at the speed of light could then be seen as infinite speed, if only taken the time to arrive at a place at a certain point of time. (it would take 'no time' to get to 'everywhere in the universe' as space shrinks to a ?singularity? and time stops). So c is actually infinite speed because of the consequences it has on space and time.

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So it isn't possible to go at infinite speed (taken the considerations made above) as it would involve infinite energy.

But it is possible to go faster and faster to a point in which the speed of c is actually irrelevant, cause you would still seem to be arriving at the target at a speed higher than c, because time slows down, and because the distance shrinks.

You could then say that the limit of the speed of light is only the limit we observe objectivly. Subjective experience of speed would still be that there is no limit, cause you can't reach it, but you can still go as fast as you want since the subjective definition of speed is to take me a certain distance in a certain time (miles per hour sounds familiar), and distance shrinks and time shrinks the faster you go objectivly coming to a full stop (no distance, time stops) at c.

I guess you might find a hole in my idea, but if so then that would further my understanding.

 

Rapidity is the term used (since 1911) to refer to that particular speed-like parameter.

It is what you get if you measure speed using stationary rulers and moving clocks, or vice versa.

 

Ok, so it could be said that someone could reach a star 4 lightyears ahead in only 3 years of his own time, even if it would seem like much longer for a person observing?

 

Yep. They can reach it in an arbitrarily short amount of their own time so long as they travel close enough to c (though energy costs become huge). But to us watching from Earth they still take a little over 4 years.

 

That means that subjective reality is more consistant than objective reality if you ask me, though I know that objective reality is of course consistant in and out of itself, but subjective reality seems more natural, more to the point so to say

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Actually it almost seems like objective reality is making an effort to make it that way

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lol

 

Hmm, special relativity is pretty objective; if one knows special relativity one can predict what any other observer anywhere will see, and they will all agree. They directly observe different things but they all agree on the outcomes of experiments and whatnot. It is just that ones concept of space and time has to change. Although that is kind of what you said anyway I guess.
Now if you were talking about quantum mechanics then we get some true arguments about the subjective nature of reality.

 

Who's time?

 

Hello Cyperium

You could also say that the energy of acceleration is converted into a slower time rate and have the rest mass stay the same.

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How does energy convert into time?

 

Hello BenTheMan

That's a 64 billion dollar question. However, the conversion of energy into changing time rates does happen.

A star's loss of mass through nuclear fusion (creation of energy) will increase the time rate for that star. Anything experiencing centrifugal force will have a slower time rate than the axis of rotation. So any energy used to speed up or slow down the rotation is affecting time rates

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