Twins paradox and other special relativity topic discussion

[HydrogenBond]

Moderation note: The first 17 posts of this thread were moved from the Alternative theories thread 16531, because they are a discussion of well-known theory, not the original threads alternative theory.

 

The twin paradox has to follow the laws of the conservation of energy. Only one twin was given energy relative to the other twin. Only one twin has the energy for real relativistic affects. Only the one with energy will show any real time dilation.

 

In other words relative velocity does not always express reality unless both references have the same energy. If we ignore the third equation of SR, which involved mass-energy, we can get results that can violate energy conservation to create special affects in math. The space-time affect in GR is also dependent on mass-energy, which is not reference dependent. The mass-energy is what creates the reference. The same is true of SR, with mass-energy or relativistic mass defining the real reference affects. I am not saying relative reference does not create the impression of this, but it may lack the energy to be real.

 

If we assume a relativity affect, that does not have the energy to back it up, we have created imaginary energy, which only exists conceptually. This gives us extra energy, conceptually, to create other imaginary things that will add up mathematically due to the original assumptions.

 

As an example, look at a train moving and a stationary observer. There are certain relative reference things that are useful. But if we do an energy balance based on reference, one reference sees the train moving and the other sees all the mountains in the background moving. If both are equal, I just created energy equal to the difference between mountains moving minus the train moving. Now I can use that energy to do other things. If I said, I only gave you enough energy to move the train, that tells us which reference is real and which is an illusion even if your eyes are being fooled. You can't trust your eyes and the assumption of relative reference. We have to assume we know the cut off between useful relative reference affects and that threshold where we begin to create extra energy. I am no expert but based on relative reference discussions it is not clear.

[Roadam]

My new twins' problem is completely symmetrical and there's no way to decide which would age less or more.

 

Each of them would see the other age more, but in fact they would arrive home being the same age. Special relativity is overly simplistic becouse it doesnt take accelerations into account.

[martillo]

Each of them would see the other age more, but in fact they would arrive home being the same age.

"In fact"?

How would you prove that?

If you were one of the twins you wouldn't say this.

 

You have three frames of observations, two in each twin and in this case you as if you were in the proposed spaceship.

 

Now, is not the matter to pick the observation you feel more comfortable with. The problem is just that there are three frames of observations with contradictory (incompatible) observations! This is the inconsistency.

 

As I say in Section 1.1 - A:

"

A right theory cannot be inconsistent; the same phenomenon must have consistent predictions in different referentials of observation."

[Qfwfq]

Well, if there are no waves and no particles what really exist?

Who says it must be an aut-aut?

 

What do you propose?

While physicists have learnt to perform calculations on the outcome of experiments, the exact reality of what these "little thingies" are is something our minds weren't designed to comprehend. Like other animals, we evolved to survive. Like other apes, we evolved a great ability to manipulate our environment, hand in hand with an ability and drive to understand it.

 

Unlike other apes, we evolved an exaggerated ability, going far beyond the necessity to procure food, drink and protection for the purpose of survival; we can afford to be a mob of lazy clods that avoid physical effort, keep ourselves overly fed and comfy, even at the cost of squandering resources and ruining the environment, and along with this we also developed the ability and habit of asking questions like "What is the world, what's it made of, how does it work and how did it come to exist?". These are unnecessary for our survival, the answers are such that our minds aren't designed for and we can only edge nearer to understanding them, but never completely will.

 

What are we doing here then?

We? We who? What's this, pluralis maestatis?

 

I talked about your approach to dicussion. Leaving isn't your only option, there's also that of polishing your conduct a bit. :shrug:

[jerrygg38]

It seems as if everyone is leaving out half the equation

 

F = d (MV) /d(t) = M d(v)/d(t) + V d(m)/d(t)

 

The force equals the mass time the deriviative of the velocity with respect to time plus the velocity times the deriviative of the mass with respect to time.

 

What the equation shows is that a force applied to a mass increases its velocity and at the same time increases its mass.

[Pyrotex]

It seems as if everyone is leaving out half the equation

 

F = d (MV) /d(t) = M d(v)/d(t) + V d(m)/d(t)

 

The force equals the mass time the deriviative of the velocity with respect to time plus the velocity times the deriviative of the mass with respect to time.

 

What the equation shows is that a force applied to a mass increases its velocity and at the same time increases its mass.

Actually, no. You're reading the second half of the equation backwards.

 

It says the Force is equal to the rate at which the momentum changes.

And momentum equals (velocity * mass).

 

The momentum will increase as velocity increases over time.

 

The momentum will decrease as the mass of the system decreases over time.

 

Given a rocket that generates a force by burning propellent, there are two factors changing the momentum of the rocket: the velocity is increasing; and the mass (of the rocket) is decreasing, because the propellent is being expelled from the rocket. In fact, THIS is what generates the Force--Newton's second law: for every reaction (force that accellerates the rocket) there is an equal and opposite reaction (counter-force that pushes the exhaust in the opposite direction).

 

The force does NOT cause the mass to change. The mass is changing due to the nature of the object (a rocket which burns propellent)--and this affects the calculation of the magnitude of the force being generated.

[jerrygg38]

Actually, no. You're reading the second half of the equation backwards.

 

 

 

The force does NOT cause the mass to change. The mass is changing due to the nature of the object (a rocket which burns propellent)--and this affects the calculation of the magnitude of the force being generated.

 

 

JG: You rocket analysis is adding a further complication. In that case the total mass of the fuel decreases due to the expelled fuel. Simultaneously the velocity of the rocket and remaining fuel increases and the mass of the rocket and the remaining fuel increases.

 

The more simple equation is when an external force is applied to the system. Let us take an object and connect a rocket to it for awhile. This applies a force to the object. However the object does not lose any material. Thus the velocity of the object increases and the increased velocity is accompanied by an increase of mass of the object.

[Roadam]

Mass is not increased when you are coming close to the speed of light, its just harder to accelerate, thus you can imagine having more mass.

[jerrygg38]

Mass is not increased when you are coming close to the speed of light, its just harder to accelerate, thus you can imagine having more mass.

 

 

JG: Yes a point is reached where the input energy equals the output radiated energy so you hit a limit. You end up with a constant velocity near light speed and a photon energy field which you can keep increasing with great effort and high radiation. Of course you also want to bring the temperature down to near absolute zero. What a mess!

 

It is better to look at the sub light speed mass/velocity changes.

[CraigD]

Mass is not increased when you are coming close to the speed of light, its just harder to accelerate, thus you can imagine having more mass.

JG: Yes a point is reached where the input energy equals the output radiated energy so you hit a limit. You end up with a constant velocity near light speed and a photon energy field which you can keep increasing with great effort and high radiation.

To the best of my knowledge, these claims aren’t a prediction of relativity, nor are theysupported by any experimental data. Roadam and jerrygg, do you have any evidence suggesting otherwise? :QuestionM

 

Roadam’s claim,

Mass is not increased when you are coming close to the speed of light, its just harder to accelerate, thus you can imagine having more mass.

is practically and philosophically interesting, because it implies that a body “being harder to accelerate” – what is usually termed in physics a body’s “inertia” – can in some cases be independent of a body’s mass. This contradicts mechanics in the classical limit, which defines the force [imath]F[/imath] required to produce a give acceleration [imath]A[/imath] – “how hard it is to accelerate” – as directly proportional to a body’s mass [imath]M[/imath], per the equation [imath]F = M \cdot A[/imath].

 

There are other definitions of mass. Two well know ones are the force of gravity [imath]F_G[/imath] stated in Newton's law of universal gravitation, given by [imath]F_G =\frac{G M_1 M_2}{r^2}[/imath], where [imath]G[/imath] is the gravitational constant, [imath]M_1[/imath] and [imath]M_2[/imath] are the mass of two bodies, and [imath]r[/imath] the distance between them, and mass–energy equivalence, given by [imath]E = M c^2[/imath], where [imath]E[/imath] is the energy resulting from the body’s annihilation, and [imath]c[/imath] the speed of light in vacuum.

 

There’s strong experimental support for the prediction that the mass of a body as defined by mass-energy equivalence increases relative to an observer as does it’s speed [imath]v[/imath], as give by special relativity’s [imath]M = \frac{M_0}{\sqrt{1 - \frac{v^2}{c^2}}}[/imath], where [imath]M_0[/imath] is the mass of the body as measured by an observer at rest relative to it. Such evidence comes from experiments in which charged particles – typically electrons – were accelerated to very high speeds (about .999996519 c) by devices such as the LEP in Geneva from 1989 to 2000, and collided with their antiparticle (positrons), and the total energy of their collision measured. Because the speed of the colliding particles and the total energy of their collision were precisely known, we can say with great confidence that special relativity’s prediction of their mass as defined by mass-energy equivalence is strongly confirmed.

 

That this also is true for a body’s mass as defined by universal gravitation (a question usually referred to as the equivalence of inertial and gravitational mass), while almost unanimously believe to be true by physicists, has to the best of my knowledge not be experimentally verified, or at least not to nearly the precision of special relativity vs. mass as defined by mass-energy equivalence and classical mechanics. Such a confirmation is technically difficult – which in modern experimental terms, equates to financially expensive – because the constant of gravitation is very small. In the case of the now-dismantled LEP, a detector of the difference in gravitational force due to the increase in mass of its accelerated leptons by a factor of about 379 would have to be extraordinarily sensitive. For example, a detector along the lines of the Cavendish experiment, using a 5 kg mass at a distance of 2 cm from the beam, would need a sensitivity of greater than [imath]10^{-29} \, \mbox{N}[/imath]. For comparison, the original Cavendish experiment, which has been improved upon only slightly in the past 2 centuries, had a sensitivity of about [imath]10^{-7} \, \mbox{N}[/imath].

 

It’s worth noting, however, that a deep understanding of what mass actually is, in terms of the interaction of fundamental particles, is at the cutting edge of modern physics. Although the prediction of 20th century theory continue to be well confirmed by increasingly good experiments, the philosophical why underlying these predictions remain very much open questions.

 

 

JG’s claim,

Yes a point is reached where the input energy equals the output radiated energy so you hit a limit. You end up with a constant velocity near light speed and a photon energy field which you can keep increasing with great effort and high radiation.

Appears to me strongly contradicted by accepted theory and all experimental evidence. Nonzero mass particles are routinely accelerated to very high speeds and measured with very sensitive detectors, as described above, yet not observed to radiate except when interacting with particles. If beams such as the electron beam in the LEP were radiating in the way JG describes, they would be very bright, but are not observed to emit photons at all.

[Roadam]

This is from Special relativity - Wikipedia, the free encyclopedia

 

[math]\mathbf{F} = \frac{m \gamma^3 v^{2}}{c^2} \, \mathbf{a}_{\parallel} + m \gamma \, (\mathbf{a}_{\parallel} + \mathbf{a}_{\perp}) \,[/math]

 

[math] = m \gamma^3 \left( \frac{v^{2}}{c^2} + 1 - \frac{v^{2}}{c^2} \right) \mathbf{a}_{\parallel} + m \gamma \, \mathbf{a}_{\perp} \,[/math]

[math] = m \gamma^3 \, \mathbf{a}_{\parallel} + m \gamma \, \mathbf{a}_{\perp} \,. [/math]

 

Sorry I didnt put a reference by my post. This is just relativistic mechanics. Thing is that I havent heard about this in my physics class in uni, according to wikipedia thats because relativistic mass is proportional to energy so the concept is not used anymore. And we really do everything with using transformations of energy.

 

//those equations were copied out of wikipedia and look bad, anyone know how to do those things? (moderation note: To render LaTeX math package such as the above, surround it with [math] ... LaTeX here ... [/math], as I have above)

[CraigD]

Mass is not increased when you are coming close to the speed of light, its just harder to accelerate, thus you can imagine having more mass.

To the best of my knowledge, these claims aren’t a prediction of relativity, nor are theysupported by any experimental data. Roadam and jerrygg, do you have any evidence suggesting otherwise? :QuestionM

This is from Special relativity - Wikipedia, the free encyclopedia

...

[math]F = m \gamma^3 \, \mathbf{a}_{\parallel} + m \gamma \, \mathbf{a}_{\perp} \,. [/math]

…

Sorry I didnt put a reference by my post. This is just relativistic mechanics.

I think I see the source of some confusion in the initial claim that “mass is not increasing”.

 

As the line just before it in the referenced wikipedia acticle notes, the [math]m[/math] in the above equation refers to the rest (also called invariant) mass, of the body. This is the mass of the body as measured by an observer with zero velocity relative to the body. I like to write this in some distinct way to avoid confusion, such as [imath]m_0[/imath]. By definition, [imath]m_0[/imath] doesn’t vary with the relative velocity of the body and its observer.

 

The statement “mass increases as a body approaches the speed of light” means that the body’s mass [imath]m_1[/imath], as measured by an observer with velocity relative to the body approaching the speed of light, increases. This is described by special relativity as

 

[math]m_1 = \gamma m_0[/math]

 

where the Lorentz factor [imath]\gamma[/imath] is

 

[math]\gamma = \frac1{\sqrt{1 - \left( \frac{v}{c}\right)^2}}[/math].

 

In short, special relativity states that the mass of a body as measured by an observer does increase as its speed relative to the observer increases.

[Pyrotex]

To add a point to Craig's excellent post, Special Relativity describes what a "stationary" observer OBSERVES. Since WE are assumed to be the non-moving observers, SR describes what WE would OBSERVE if we saw something "out there" moving near the speed of light. That's as far as SR goes.

 

If you set up a thought experiment and try to use SR to explain anything OTHER than what will be observed (basically by US, since we're the only observers around), then there is no way to experimentally test your experiment, and you're probably trying to interpret SR incorrectly.

[CraigD]

A good way, IMHO, to demystify the twins paradox is to describe it from the perspective of a “third person” distant observer at rest relative to the unaccelerating twin, assuming this third person can observe not only the two twins, but clocks worn by each twin, and light signals sent at regular intervals between the two twins.

 

By specifying a sufficiently distant observer, simultaneity differences for the third observer can be made so small they are insignificant.

 

Here’s an example where twin B, starting at the same position as twin A (with their two clocks synchronized), instantly accelerates to a velocity of 0.5 c directly away from A, then at a distance of 2.5 light seconds from A as measured by A, instantly reverse direction and returns:

  0.0000 A(0):0 B(0):0
 1.0000 A(1):0 A1:0 B(.866):.5
 1.1547 A(1.1547):0 A1:.1547 B(1):.5774 B1:.5774
 1.7321 B1:0 A(1.7321):0 A1:.7321 B(1.5):.866
 2.0000 A(2):0 A2:0 B(1.7321):1 A1:1
 2.3094 A(2.3094):0 A2:.3094 B(2):1.1547 B2:1.1547
 3.0000 A(3):0 A3:0 B2:.4641 A2:1 B(2.5981):1.5
 3.4641 A(3.4641):0 B2:0 A3:.4641 A2:1.4641 B(3):1.7321 B3:1.7321
 4.0000 A(4):0 A4:0 A3:1 B3:1.1962 B(3.4641):2 A2:2
 4.6188 A(4.6188):0 B3:.5774 A4:.6188 A3:1.6188 B(4):2.3094 B4:2.3094
 5.0000 A(5):0 A5:0 B3:.1962 A4:1 B4:1.9282 A3:2 B(4.3301):2.5
 5.1962 A(5.1962):0 B3:0 A5:.1962 A4:1.1962 B4:1.7321 A3:2.1962 B(4.5):2.4019
 5.3333 A(5.3333):0 A5:.3333 A4:1.3333 B4:1.5949 B(4.6188):2.3333 A3:2.3333
 5.7735 A(5.7735):0 A5:.7735 B4:1.1547 A4:1.7735 B(5):2.1132 B5:2.1132
 6.0000 A(6):0 A6:0 B4:.9282 A5:1 B5:1.8868 B(5.1962):2 A4:2
 6.6667 A(6.6667):0 B4:.2615 A6:.6667 B5:1.2201 B(5.7735):1.6667 A5:1.6667
 6.9282 A(6.9282):0 B4:0 A6:.9282 B5:.9585 B(6):1.5359 B6:1.5359
 7.0000 A(7):0 A7:0 B5:.8868 A6:1 B6:1.4641 B(6.0622):1.5
 7.3333 A(7.3333):0 A7:.3333 B5:.5534 B6:1.1308 B(6.3509):1.3333 A6:1.3333
 7.8868 A(7.8868):0 B5:0 B6:.5774 A7:.8868 B(6.8301):1.0566
 8.0000 A(8):0 A8:0 B6:.4641 B(6.9282):1 A7:1
 8.0829 A(8.0829):0 A8:.0829 B6:.3812 B(7):.9585 B7:.9585
 8.4641 A(8.4641):0 B6:0 A8:.4641 B7:.5774 B(7.3301):.7679
 8.6667 A(8.6667):0 B7:.3748 B(7.5056):.6667 A8:.6667
 9.0000 A(9):0 A9:0 B7:.0415 B(7.7942):.5
 9.0415 A(9.0415):0 B7:0 A9:.0415 B(7.8301):.4793
 9.2376 A(9.2376):0 A9:.2376 B(8):.3812 B8:.3812
 9.3333 A(9.3333):0 B8:.2855 A9:.3333 B(8.0829):.3333
 9.6188 B8:0 A(9.6188):0 B(8.3301):.1906
10.0000 A(10):0 B(8.6603):0

The leftmost number is the third person’s clock, the text and number to the right the positions of the twins. The numbers within ()s are the clock reading of each twin. Letter/number pairs (eg: A1) are light signals sent by each twin each second, as measured by their respective clocks. All of the data displayed is as observed by the third observer.

 

Note that for the first couple of seconds, each twin observes the other’s clock to be ticking slower than their own (A receives signal B1 at his clock reading 1.1547, B receives signal A1 at his clock reading 1.7321, A receives B2 at 3.4641, B receives A2 at 3.4641). For the last couple of seconds, each twin observes the other’s clock to be ticking faster than their own. B, however, observes A’s clock to begin ticking faster sooner than A observes B’s clock to begin ticking faster.

[Qfwfq]

It is perfectly correct to say that mass doesn't depend on velocity.

 

Lorentz covariant dynamics are the way to go and the clumsy, awkward and messy formulation that was initially used by Einstein is falling out of use, thank goodness, and along with it the notion of "relativistic mass" which is really just the sum (usually called total energy) of kinetic and rest energy.

 

One could go as far as doing away with the term mass altogether, but it's handy and the modern physicist uses it as a name for rest energy.

 

[math]f_i=m\frac{du_i}{d\tau}[/math]

[HydrogenBond]

The third equation of the SR provides a check and balance that allows up to define the hierarchy of relative reference, because it forces us to do an energy balance. For example, say we had a stationary reference and a rocket moving near C. The stationary reference sees SR affects coming from the rocket. The rocket see the SR affects occurring all around it, throughout the universe. This second affect take much more energy. This means stationary reference requires far less energy. Just based on what the two observers report, we know which is which using an energy balance.

 

Since we now know the rocket is at higher energy, we now know it is creating the SR affects that are being observed by both references. The mass equation tells us how much mass-energy is required, via velocity, to create all the observed SR affects. It also tells us, via the energy balance, which is which.

 

With GR the energy balance is done up front with GR directly related to mass-energy, which will then cause the space-time affects. The same is true of SR, with mass-energy required. If we get rid of the mass equation, we get rid of the source of the affect. This allows relative reference to create energy or perpetual motion affects.

 

Let us go back to the twins. What I would do is ask each to report what they see. The one on the ground only sees the rocket with SR. The twin on the rocket sees his brother, moon, earth and sun also showing SR. I know he is moving. He has the energy and he has the relativistic mass. Like GR, the rocket twin has the mass-energy so he also has the real space-time affect, where time can actually slow down. It is no surprise if you do an energy balance.

[modest]

A good way, IMHO, to demystify the twins paradox is to describe it from the perspective of a “third person” distant observer at rest relative to the unaccelerating twin, assuming this third person can observe not only the two twins, but clocks worn by each twin, and light signals sent at regular intervals between the two twins.

 

I've recently found Einstein's 1918 GR solution to the twin paradox that he outlined in Dialog about Objections against the Theory of Relativity very satisfying. I'm sure this is a perfectly normal solution to the twin scenario that many Hypographers are acquainted with, but I've just walked myself through the concept and math of it about a month ago and thought I'd share.

 

The link above is a translation from the original German and describes the GR solution very well. I won't butcher it with a summary.

 

~modest