# Does size increase or decrease as mass approaches c?

• Tokage
In summary, the energy transferred from the propellant to the rocket increases the mass of the rocket.
Tokage
I'm a bit confused. Relativity states that we should observe a shortening of say a spaceship when it moves close to (c) correct? But isn't one of the reasons we can't accelerate mass to (c) because rather than reaching any higher speeds when getting close to (c) it would just increase in mass?...I may have gotten completely wrong information, but if this is the case how can this shortening effect work with the idea that the mass would increase? Someone straighten me out please, thanks!

I think what you are confused is the relation between the mass and the size of an object. You should know that what an object gets closer and closer to speed of light, the mass of object tends to be infinite. On the other hand, because of the length contraction, the "ruler" or the unit length of the object will tends to be zero along traveling direction of the object. If we consider a spaceship, we will say that the mass of it is increasing and the size of it is decreasing (the spaceship becoming short).

What happens, then, is that we see the density of an accelerating object increasing rapidly.

Both length and mass are, of course, as measured by an outside observer, relative to whom the object is moving close to the speed of light. As measured by an observer moving with the object, nothing will have changed.

Didn't you just ask this question in reverse? As said in that thread, mass and size are not the same thing- as an object accelerates relative to an outside observer, the objects length, in the direction of motion, decreases- and so the volume decreases- while the mass increases. That means the observed density of the object increases rapidly.

Ahh, the two threads have been combined.

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You might want to refer to 'energy' instead. If we assume that 'energy' is a expression of interactions, as when you pull that throttle and expend your fuel then the energy reach infinity, more or less as you try to close to lights speed in a vacuum. I don't enjoy the idea of relative mass myself, if there was a invariant mass collected by acceleration it should express itself in the ships atoms as I see it, making them 'move'.

It's the same as the idea of 'potential energy' to me. A description only relevant to a relation, meaning that there will be no potential energy at all if I was to teleport your ship into a 'empty space' without 'matter'. The stress energy tensor sees it (the 'energy') as stored in space though, which is another way of describing it, more in vogue with my own notions about it. And yeah, totally my own interpretation.

Tokage said:
I'm a bit confused. Relativity states that we should observe a shortening of say a spaceship when it moves close to (c) correct? But isn't one of the reasons we can't accelerate mass to (c) because rather than reaching any higher speeds when getting close to (c) it would just increase in mass?...

The maximum accumulated speed difference you can obtain is simply the maximum speed of your thrusting medium, whether it is air, water, explosions, etc., relative to the center of momentum frame of the combined fuel, vehicle, and payload masses. In particle accelerators, your thrusting medium is the electromagnetic field of the accelerator, which propagates at the speed of light.

Tokage said:
I may have gotten completely wrong information, but if this is the case how can this shortening effect work with the idea that the mass would increase? Someone straighten me out please, thanks!

It depends on how you do the accounting.

Let's say I have propellant and a rocket.

The mass of the propellant is A, and the mass of the rocket is B. (To simplify matters, include payload mass as a part of B.)

Some of the energy of propellent A, which is all but a tiny fraction of its mass, is transferred to rocket B. Let's call that difference a "mass transferred", k. The detritus (A-k) is jettisoned out the rocket nozzle.

The mass transferred, k, times the speed of light squared, equals the kinetic energy of the rocket fuel going the other end, which has a much higher mass and much smaller velocity.

The combined energy of the propellent and rocket (A+B) has not changed here (i.e. (A+B)=(A-k)+(B+k)), however the mass of the rocket has gained some tiny amount of mass, while the propellant, which is the energy source, loses a tiny bit of it.

Now, if one were to accelerate the propellent and rocket (A+B) with a laser, then you would be increasing the mass of the propellent and rocket (A+B) at the expense of the energy source of the laser.

Eventually, the propellent and rocket (A+B) lose energy via heat. However, this is not in anyway direct evidence of acceleration, and nor it is required of acceleration. So any relationship between acceleration and mass loss is, to simply put, weak.

In the end, whether mass increases or decreases has little to do with acceleration. It has to do with what amount of energy is emitted or absorbed by an object. With the word "absorb" I don't mean to say that object itself gains energy, for after all, some objects, such as electrons, are identified as having an invariable mass. Rather, it is possible that energy fields, superimposing electrons and other particles, can themselves contribute to the mass at those electrons and other particles.

Nice description Kmarina :)

As for the size contracting, it does. It must if we want there to be a symmetry. And if there is one thing that SpaceTime takes seriously, then it has to be symmetries. Even Newtons concept of a 'action and reaction' talks about a symmetry. So the ship contracts from Earths point of view, whilst from the travelers view it will be the universe that does so. And both descriptions will be true. The contraction observed from Earth is a direct relation to the concept of a light-clock having a further distance to 'propagate' between the mirrors, if observed 'being in motion'. If you imagine it as two rods instead |_ placed like this with mirrors at their ends, you will find that the rod placed in the direction of the ships motion will be the one shrinking. The other rod, situated at a right angle to the first, will have no contraction at all (that's not perfectly true as it will become thinner, but its 'length' won't change) The one contracting has a direct relation to Earths observation of light bouncing between each rods end parts. If it didn't contract the light that to to the traveler must be the 'exact same' synchronized, to the Earth observer now would have different 'speeds', but as the rod shrinks the light speed will be the same, as measured from Earth. It is a tricky but beautiful idea placing most of what we think us know about matter, clocks and motion upside down, sort of :)

And the invariant mass of that ship will not change as far as I know. What will change depends on whom is observing, but as it takes a energy to produce a acceleration, and we can assume a symmetry relative that energy expended, then there must be a 'energy' stored in the 'systems relative motion'. Exactly how to see that I'm not sure though, but there is a equivalence. Stored in the frame you observe maybe, if you're 'Earth', which then would be the 'ship'. But if you're the traveler you might define it as stored in the contracted universe you observe instead, that as you won't measure any extra energy anywhere inside that ship, no matter the 'speed' measured relative your origin (Earth).

It's a weird subject, isn't it :)
==

This is assuming you stopping your engines coasting (uniform motion) when you measure. As long as you accelerate you will create a 'gravity' which, according to Einsteins principle of equivalence, in a constant (uniform) acceleration will be inseparable to a planets gravity.

And measuring in a acceleration will show you the same effects as you have on Earth (ignoring tidal forces) including blue and red shift and if using 'clocks' seemingly giving you different reading when comparing them. But that is the exact same as you will find with those clocks on Earth depending on their elevation from Earth's surface, as proven elegantly with atomic clocks.

And both descriptions builds on one single fact as I see it. Lights invariant speed in a vacuum 'c'. All of this is a direct effect from that constant. The light clocks that vary in a gravitational field when compared will 'locally', if measured by themselves, always give you one exact same invariant speed of light, namely 'c'.

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## 1. Does mass increase or decrease as it approaches the speed of light?

The mass of an object does not change as it approaches the speed of light. However, its inertia, or resistance to changes in motion, increases. This is known as relativistic mass and is a result of the object's energy increasing as it approaches the speed of light.

## 2. How does time dilation affect the size of an object as it approaches the speed of light?

As an object's speed approaches the speed of light, time dilation occurs, which means time slows down for the object. This can give the illusion that the object is smaller, but its size remains unchanged.

## 3. What is the relationship between mass and energy as an object approaches the speed of light?

As an object's speed approaches the speed of light, its energy increases. This is described by Einstein's famous equation, E=mc², which states that energy and mass are equivalent and can be converted into one another.

## 4. Can an object with mass ever reach the speed of light?

No, according to the theory of relativity, as an object's speed approaches the speed of light, its mass and energy also increase. At the speed of light, the object's mass would become infinite, making it impossible to accelerate any further.

## 5. How does the concept of relativity explain the relationship between size and mass approaching the speed of light?

The theory of relativity explains that an object's size and mass are relative to the observer's frame of reference. As an object approaches the speed of light, its size and mass may appear to change to an outside observer, but these changes are only apparent and do not affect the object's intrinsic characteristics.

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