Why nothing can go faster than speed of light.

[kjelleman]

 

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.)

[Tim88]

 

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.)

 

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.

Edited April 19, 2017 by Tim88

[kjelleman]

 

 

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.

[Tim88]

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.

 

A limit speed implies that the acceleration goes to zero; that's just saying the same thing with other words.

[kjelleman]

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.

[swansont]

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.

 

 

In the electrons' frame they are at rest, and there is no problem. And you can analyze the problem in whatever inertial frame you wish.

[geordief]

The speed of the photon is independent of its source speed. Nothing strange with that, same thing with water and sound pulses.

 

 

ls this factually correct? The speed and direction of any wave (eg a sound wave ) is also independent of the state of motion of the emitting body ?

 

Light waves are not unusual in this behaviour?

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.

I am struggling a bit with this.Does that imply that a rocket with a very low exhaust velocity can in theory approach (not reach) the speed c given enough time?

 

Is the final speed just determined by the amount of onboard fuel compared to the initial mass of the rocket?

[swansont]

 

ls this factually correct? The speed and direction of any wave (eg a sound wave ) is also independent of the state of motion of the emitting body ?

 

Light waves are not unusual in this behaviour?

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.

[kjelleman]

 

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.

[swansont]

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.

 

 

The salient point here, as this is related to relativity, is measurement in other frames. The speed of light is invariant. The speed of sound is not.

[koti]

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.

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.

[geordief]

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.

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.

Edited April 20, 2017 by geordief

[Delta1212]

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.

[koti]

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.

 

With a minor adjustment that the velocity of sound is different in different mediums. In solids it's the highest from what I recall.

[Janus]

 

I am struggling a bit with this.Does that imply that a rocket with a very low exhaust velocity can in theory approach (not reach) the speed c given enough time?

 

Is the final speed just determined by the amount of onboard fuel compared to the initial mass of the rocket?

Yes, under Newtonian physics this is shown by the rocket equation:

[math] \Delta v = v_e \ln \left( \frac{M_i}{M_f} \right )[/math]

 

where v_e is the exhaust velocity.

M_i is the initial rocket mass (rocket+fuel)

M_f is the final rocket mass (rocket+ remaining fuel(if any))

 

Under Relativity, this becomes:

 

[math]\Delta v = c \tanh \left ( \frac{v_e}{c} \ln \left ( \frac{M_i}{M_f} \right ) \right )[/math]

 

While any exhaust velocity will theoretically get you up to near c, the lower it is, the larger M_i has to be relative to Mf.

 

For example, at typical chemical rocket exhaust velocities, to reach even 0.1% of c would require something in the order of 40 times the mass of Jupiter of fuel for every kg of payload. (For this final velocity it doesn't really matter which of the two equations above you use)

 

If you were able to increase your exhaust velocity by a factor of 100, this will drop to just under 2 kg of fuel per kg of payload.

 

So while exhaust velocity doesn't put a theoretical limit to final velocity (other than the relativistic one), it does determine the efficiency of the rocket and thus can determine a practical limit.

[kjelleman]

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?

[geordief]

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.

Right ,but for an observer traveling at the same speed as the medium the wave will travel at the exact same speed regardless of whatever object (moving at whatever velocity) caused** the wave?

 

 

** "caused" ="emitted" ?

 

With a minor adjustment that the velocity of sound is different in different mediums. In solids it's the highest from what I recall.

I was told that the maximum speed of sound was c.

 

I think it might be so in a black hole.

 

 

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?

 

I won't answer (as I am not qualified) but I guess that is widely accepted.

Yes, under Newtonian physics this is shown by the rocket equation:

[math] \Delta v = v_e \ln \left( \frac{M_i}{M_f} \right )[/math]

 

where v_e is the exhaust velocity.

M_i is the initial rocket mass (rocket+fuel)

M_f is the final rocket mass (rocket+ remaining fuel(if any))

 

Under Relativity, this becomes:

 

[math]\Delta v = c \tanh \left ( \frac{v_e}{c} \ln \left ( \frac{M_i}{M_f} \right ) \right )[/math]

 

While any exhaust velocity will theoretically get you up to near c, the lower it is, the larger M_i has to be relative to Mf.

 

For example, at typical chemical rocket exhaust velocities, to reach even 0.1% of c would require something in the order of 40 times the mass of Jupiter of fuel for every kg of payload. (For this final velocity it doesn't really matter which of the two equations above you use)

 

If you were able to increase your exhaust velocity by a factor of 100, this will drop to just under 2 kg of fuel per kg of payload.

 

So while exhaust velocity doesn't put a theoretical limit to final velocity (other than the relativistic one), it does determine the efficiency of the rocket and thus can determine a practical limit.

thanks for clearing that up. Those are amazing figures by the way (the one related to Jupiter).

Edited April 20, 2017 by geordief

[koti]

+1 Janus.

I know its off topic but could you give your quick opinion on the NASA ion engine who everybody went crazy on some time ago?

[studiot]

Here is some maths to help the discussion along.

 

It is impossible, in Special Relativity, to compose two velocities to make a velocity greater then c in the same frame.

 

Suppose A, B and C are three uniformly moving observers.

 

B measures the velocity of A relative to himself as v and the velocity of C relative to himself as w.

 

What does he make the velocity of A relative to C as both these approach c?

 

Einstein's formula for composing velocities is (derived by a double application of the Lorenz transformation)

 

[math]\frac{{v + w}}{{1 + \frac{{vw}}{{{c^2}}}}}[/math]

where v and w are measured along the same line.

So as the velocity of both A and C approaches light speed we have

[math]\mathop {\lim }\limits_{v,w \to c} V = \frac{{v + w}}{{1 + \frac{{vw}}{{{c^2}}}}} = \frac{{c + c}}{{1 + \frac{{{c^2}}}{{{c^2}}}}} = c[/math]

Edited April 20, 2017 by studiot

[Janus]

+1 Janus.

I know its off topic but could you give your quick opinion on the NASA ion engine who everybody went crazy on some time ago?

Plus: High exhaust velocity (~10 times that for a chemical rocket) allows for better payload to fuel ratios.

Minus: Low thrust means low acceleration rate, and thus it takes a longer time to reach maximum velocity.

 

For an example, the Dawn probe spent 270 days under thrust, using under 72 kg of Xenon propellant (dry mass of probe is 747.1 kg), while achieving a delta v of 1.6 km/sec( Put another way, at full thrust it would take 4 days for Dawn to accelerate up to 60 mph.)

 

Great for moving around the Solar system efficiently, not so great if you want to do it fast.

[koti]

Plus: High exhaust velocity (~10 times that for a chemical rocket) allows for better payload to fuel ratios.

Minus: Low thrust means low acceleration rate, and thus it takes a longer time to reach maximum velocity.

 

For an example, the Dawn probe spent 270 days under thrust, using under 72 kg of Xenon propellant (dry mass of probe is 747.1 kg), while achieving a delta v of 1.6 km/sec( Put another way, at full thrust it would take 4 days for Dawn to accelerate up to 60 mph.)

 

Great for moving around the Solar system efficiently, not so great if you want to do it fast.

 

Janus, I apologize, I was writing while frying and flipping pancakes. I meant to ask about the NASA "impossible" EM drive engine.

[Janus]

 

Here is some maths to help the discussion along.

 

It is impossible, in Special Relativity, to compose two velocities to make a velocity greater then c in the same frame.

 

Suppose A, B and C are three uniformly moving observers.

 

B measures the velocity of A relative to himself as v and the velocity of C relative to himself as w.

 

What does he make the velocity of A relative to C as both these approach c?

 

Einstein's formula for composing velocities is (derived by a double application of the Lorenz transformation)

 

[math]\frac{{v + w}}{{1 + \frac{{vw}}{{{c^2}}}}}[/math]

where v and w are measured along the same line.

So as the velocity of both A and C approaches light speed we have

[math]\mathop {\lim }\limits_{v,w \to c} V = \frac{{v + w}}{{1 + \frac{{vw}}{{{c^2}}}}} = \frac{{c + c}}{{1 + \frac{{{c^2}}}{{{c^2}}}}} = c[/math]

 

As to how this would apply to an accelerating rocket:

Assume as your rocket accelerates it drops off beacons(which maintain the velocity of the rocket upon release.

 

After reaching a speed of v relative to the Earth the rocket drops a beacon, and then continues to accelerate to v relative to the beacon. At which point, the beacon is moving at v relative to the Earth and the rocket is moving at v relative to the beacon. According to the Earth or the rocket, the relative velocity between them will be

[math] \frac{2v}{1+\frac{v^2}{c^2}}[/math]

Which will be less than 2v.

The ship now drops another beacon and accelerates to v relative to it.

It is now moving at

[math] \frac{2v}{1+\frac{v^2}{c^2}}[/math]

relative to the first beacon.

If we label this V₂

Then his velocity with respect to the Earth will be

[math] \frac{V_2+v}{1+\frac{vV_2}{c^2}}[/math]

which is less than V₂ + v.

 

He can keep doing this forever, dropping beacons and accelerating to v relative to the last beacon dropped, and still will never reach c relative to the Earth.

[Pugdaddy]

 

Why nothing can go faster than speed of light.

If someone fired a killing light beam at some one else, and you went faster than the speed of light, you would see the person die before the light beam hit them. So isn't that reason enough?

[geordief]

If someone fired a killing light beam at some one else, and you went faster than the speed of light, you would see the person die before the light beam hit them. So isn't that reason enough?

Why wouldn't you just arrive before he was killed?

You could move him out of the way and save his life

[imatfaal]

Let's get off the topic of moving faster than the speed of light - even (especially) as a thought experiment. It is not possible and contrary to known physics - any conclusions will be a bit pointless.