Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: EvaH on 30/07/2020 12:34:10
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Rupert asks:
I don't understand why the speed of light is such a hard barrier. I understand that the equations show that the mass of an object tends to infinity as the speed of light is reached - but why? Why does the speed of an object change its mass?
Can you help?
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Perhaps, thinking in terms of inertia would help.
This problem was well known to the people involved in the transport of goods by horse drawn canal barges. A lot of energy was needed to overcome the inertia of a stationary, loaded barge, but once an optimum speed had been reached much less energy was required to maintain that motion. However, should the person in charge of the barge decide to try to increase the speed, he found that a very significant amount of energy was needed to achieve only a small amount of acceleration. Most of the additional energy seemed to go into producing a larger bow wave. In other words, the faster the horse tried to pull the barge, the more weight the unfortunate animal had to pull along. Or, expressed in different terms, the more inertia it had to overcome.
Much the same thing happens when we try to accelerate an object close to the speed of light. In this case, though, the weight does not come from picking up pre-existing mass, such as the water in the canal, it comes, or so books of popular science generally tell us, directly from the conversion of energy to matter, according to E=mc².
I suspect this is just the tip of the iceberg. The next question must be; in whose RF which effect occurs.
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Relativistic mass is a slippery concept. Physicists tend to speak of rest mass, aka invariant mass, which is the mass an object has in the reference frame in which it is motionless. They usually do not speak of relativistic mass but of energy. However, you want to know about mass so here we go.
Imagine a space ship traveling at 0.99 lightspeed. Now the pilot turns on the engine to the power level expected to produce an acceleration of 1 g. He feels an acceleration of 1 g and anything he drops to the floor falls at the expected rate.
But to an outside observer, the space ship is not accelerating at 1 g but at about 1/7 g. Because of Special Relativity, time on the space ship has been dilated (stretched out) so that 1 second on the space ship clock lasts 7 seconds on the observer’s clock. Because the acceleration is only 1/7 what the outside observer expects, the mass of the space ship must be 7 times as much as expected, i.e., 7 times the rest mass.
If the space ship were to hit something (1) the amount of energy expended would be accordance with the mass being 7 times the rest mass. Relativistic mass is real. But as I said, physicists prefer to talk about energy when speaking of relativistic speeds.
(1) The pilot’s last words at 1/7 normal speed S-S-S-S-H-H-H-H-I-I-I-I-I-I-I-[CRASH!!!]
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Relativistic mass is a slippery concept. Physicists tend to speak of rest mass, aka invariant mass, which is the mass an object has in the reference frame in which it is motionless. They usually do not speak of relativistic mass but of energy. However, you want to know about mass so here we go.
Imagine a space ship traveling at 0.99 lightspeed. Now the pilot turns on the engine to the power level expected to produce an acceleration of 1 g. He feels an acceleration of 1 g and anything he drops to the floor falls at the expected rate.
But to an outside observer, the space ship is not accelerating at 1 g but at about 1/7 g. Because of Special Relativity, time on the space ship has been dilated (stretched out) so that 1 second on the space ship clock lasts 7 seconds on the observer’s clock. Because the acceleration is only 1/7 what the outside observer expects, the mass of the space ship must be 7 times as much as expected, i.e., 7 times the rest mass.
The Outside observer would measure a much smaller acceleration than 1/7 g. Assume the rocket accelerates by its own measure for 1 sec, thus changing its velocity by 9.8 m/sec( again by its own measure). Due to the way velocities add in Relativity, the outside observer only measures an increase of velocity of much less than 9.8 m/sec, and that this increase occurs over 7 sec rather than 1 sec.
If the space ship were to hit something (1) the amount of energy expended would be accordance with the mass being 7 times the rest mass. Relativistic mass is real. But as I said, physicists prefer to talk about energy when speaking of relativistic speeds.
You would only say that the energy increases as if the mass increased if you try to use the Newtonian expression for kinetic energy: KE = mv^2/2
However, in Relativity, the KE increases by a different expression.
KE = (1/sqrt(1-v^2/c^2 )-1) mc^2
This does not involve any mass increase, just that the relationship between velocity and KE behaves differently than predicted by Newton.
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Relativistic mass is a slippery concept. Physicists tend to speak of rest mass, aka invariant mass, which is the mass an object has in the reference frame in which it is motionless. They usually do not speak of relativistic mass but of energy. However, you want to know about mass so here we go.
Imagine a space ship traveling at 0.99 lightspeed. Now the pilot turns on the engine to the power level expected to produce an acceleration of 1 g. He feels an acceleration of 1 g and anything he drops to the floor falls at the expected rate.
But to an outside observer, the space ship is not accelerating at 1 g but at about 1/7 g. Because of Special Relativity, time on the space ship has been dilated (stretched out) so that 1 second on the space ship clock lasts 7 seconds on the observer’s clock. Because the acceleration is only 1/7 what the outside observer expects, the mass of the space ship must be 7 times as much as expected, i.e., 7 times the rest mass.
The Outside observer would measure a much smaller acceleration than 1/7 g. Assume the rocket accelerates by its own measure for 1 sec, thus changing its velocity by 9.8 m/sec( again by its own measure). Due to the way velocities add in Relativity, the outside observer only measures an increase of velocity of much less than 9.8 m/sec, and that this increase occurs over 7 sec rather than 1 sec.
If the space ship were to hit something (1) the amount of energy expended would be accordance with the mass being 7 times the rest mass. Relativistic mass is real. But as I said, physicists prefer to talk about energy when speaking of relativistic speeds.
You would only say that the energy increases as if the mass increased if you try to use the Newtonian expression for kinetic energy: KE = mv^2/2
However, in Relativity, the KE increases by a different expression.
KE = (1/sqrt(1-v^2/c^2 )-1) mc^2
This does not involve any mass increase, just that the relationship between velocity and KE behaves differently than predicted by Newton.
This is why physicists do not like to talk about relativistic mass, but about energy. It gets unnecessarily complicated when energy is much more useful.
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Think of two cars colliding, does their mass energy change with the speed they have?
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the weirdest thing about it is not that a relative speed add to the energy. It's that there is a 'stop' called 'c'. 'c' Is infinite, there is no value above it.
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There is one more weird thing to it. You need two objects to define this mass energy. Which means that in a universe consisting of only one object there should be no mass energy definable, except its mass, as defined locally.
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aka gravity and 'spin'
But 'spin' in this circumstance should be very hard to prove. Assuming it to be a constant uniform 'speed'.
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If you assume that a clock and 'c' has a equivalence it means that your clock stops at 'c', relative any definition of a 'outside', as some inertial 'origin' (earth) that you then define yourself moving from. It does not mean that your clock stops locally defined though. Neither does it mean that you can't measure light to still 'propagate' at 'c', relative yourself.
In your universe you become the 'inertial observer' relative that light propagating.
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The alternative might be to assume that a absolute (universally agreed on) frame exist, and that 'c' is the 'speed limit'. That would give each object inside a universe a defined absolute 'speed', not a relative. But that frame of reference is so far unknown, and all experiments we have done so far states it doesn't exist.
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what you find instead are equivalences. It's a logic of sorts.
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'c' Is infinite
I disagree. c = 299,792,458 metres per second (exactly).
This is definitely considerably less than infinity.
I think what you are saying is:
- According to relativity, the mass of a moving object (v<c) increases as the mass of an object increases as SQRT(1-v2/c2)
- This says that the mass of an object approaching c is approaches infinity
- which could be loosely translated as "the mass or energy of an object traveling at v=c is infinite".
The main problem with this loose translation is that it gets tripped up with massless objects like photons.
- Photons cannot approach c, they always move at c.
- When photons move at c, they don't have infinite energy, but a very finite energy, as defined by their frequency & Plank's constant.
'c' Is infinite, there is no value above it.
It's true that we know of nothing traveling faster than c, but there are things that look like they are traveling faster than c (from our angle).
- Some of these are due to jets from black holes emitting particles traveling at almost the speed of light.
- Others are more mundane, with the flash of a supernova lighting up a spherical shell of gas and dust previously puffed off the dying star. The flash illuminates the entire shell of gas simultaneously. But from our point of view, the light reflected from the dust reaches us at different times- and the expanding circle of light appears to expand faster than the speed of light.
See: https://en.wikipedia.org/wiki/Superluminal_motion
There is an oddity in the equations of relativity: for speed v>c, SQRT(1-v2/c2) is not infinite.
- It becomes what mathematicians describe as "imaginary", which is different from "does not exist"
- But it is sometimes challenging to apply a real interpretation to "imaginary" numbers
- In this case, the mass is imaginary, but the energy would be real
- Some scientists have tried to search for such "tachyons", without success
See: https://en.wikipedia.org/wiki/Tachyon
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It is infinite practically. you can't pass it, it's a value you won't exceed. Unless you know something I don't?
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It's about borders, the way I think Evan.
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And yes, photons are said to propagate at 'c'. But if it is a 'field ' of / with emanations then I think of them not as much as 'propagating', as instead coming in and out of existence, depending on how you want to define it. And thinking this way we still find 'c' as a limiter of our measurements. So to me 'c' is more than just a number.
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(1) The pilot’s last words at 1/7 normal speed S-S-S-S-H-H-H-H-I-I-I-I-I-I-I-[CRASH!!!]
I once worked with a forensic phonetician. One of his interests was assessing stress levels from cockpit voice recorders. His most significant finding was that, regardless of the pilots' native language, the last word before impact was always "sh1t". Yes, folks, from Day One they teach you "in an emergency, speak English", and it sticks. The odd thing is that the magic word isn't in the ICAO Standard Vocabulary.
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Quote from: yor_on
'c' Is infinite
I disagree. c = 299,792,458 metres per second (exactly).
This is definitely considerably less than infinity.
Give the man some credit - not his native language. Try "asymptote".
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Nah, it's simple. to us it is infinite. If we by a infinity define it as something we never will reach.
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and you made me laugh Alan. Reminded me of the time I got thrown of my bike :)
the only thing I remember saying was 'What !!'