Stuff that can't be right in relativity

[Demonslayer]

Hi, new guy here.

 

There are a couple of things I have issues with concerning the relativity theory.

 

The first is the matter of accelerating a mass up to the speed of light.

It is said that doing this would require infinite energy and that this is supported by particle accelerator experiments.

When you are accelerating a particle with energy supplied from a system at rest, it is true that you would require infinite energy. It's all relative right?

If the energy for acceleration was supplied from an on-board energy source on a spaceship, the mass of the energy source (and it's energy) would increase at the same rate as the mass of the spaceship.

I can't see how the argument that accelerating something to light speed requires infinite energy, can be true.

It should be easier to accelerate a spaceship than a subatomic particle to such speeds.

 

 

The second thing is time dilation.

Gravity causes time dilation, right?

Time goes slower on Earth than on Mars, right?

Velocity difference between two objects causes time dilation, right?

Gravity is equivalent to acceleration, right?

Time dilation doesn't have two causes does it?

The true cause of time dilation must be acceleration.

 

If the universe came from a single point then every velocity difference must have developed due to things accelerating in different directions and rates relative to each other. Every velocity difference must have been caused by an acceleration.

So my conclusion is that every twin-paradox thought experiment that does not take acceleration into account will be wrong. If I accelerate to the speed of light by 1G and afterwards decelerate at the same rate, time dilation will not happen relative to time on earth (supposing we lived that long).

Is there anything wrong with my reasoning here?

 

I'm not saying that the relativity theory is wrong, just the interpretations of its implications.

Edited June 20, 2008 by Demonslayer
Grammer

[swansont]

Hi, new guy here.

 

There are a couple of things I have issues with concerning the relativity theory.

 

The first is the matter of accelerating a mass up to the speed of light.

It is said that doing this would require infinite energy and that this is supported by particle accelerator experiments.

When you are accelerating a particle with energy supplied from a system at rest, it is true that you would require infinite energy. It's all relative right?

If the energy for acceleration was supplied from an on-board energy source on a spaceship, the mass of the energy source (and it's energy) would increase at the same rate as the mass of the spaceship.

I can't see how the argument that accelerating something to light speed requires infinite energy, can be true.

It should be easier to accelerate a spaceship than a subatomic particle to such speeds.

 

The rest mass doesn't increase. (and relativistic mass doesn't increase in your own frame)

 

 

The second thing is time dilation.

Gravity causes time dilation, right?

Time goes slower on Earth than on Mars, right?

Velocity difference between two objects causes time dilation, right?

Gravity is equivalent to acceleration, right?

Time dilation doesn't have two causes does it?

The true cause of time dilation must be acceleration.

 

 

Yes, dilation has more than one cause.

[Demonslayer]

The rest mass doesn't increase. (and relativistic mass doesn't increase in your own frame)

 

 

 

 

Yes, dilation has more than one cause.

The relativistic mass of the fuel increases at the same rate as the relativistic mass of the ship. So, no problem with energy supply.

Relative to your own frame you have just as much energy available as if you stood still.

 

If two things originated from the same thing/place (Big bang), and they are now traveling at different velocities relative to each other, then one or both must have accelerated relative to the other or relative to the origin. Thus, any relative movement in the universe is a result of acceleration.

Thus, time dilation is caused by acceleration/gravity, not velocity differences.

This implies that the total time dilation is not dependent on its final velocity difference, but on the amount of acceleration/deceleration/gravity it has experienced since the first measurement.

[swansont]

The relativistic mass of the fuel increases at the same rate as the relativistic mass of the ship. So, no problem with energy supply.

Relative to your own frame you have just as much energy available as if you stood still.

 

Your mass in your own frame is unchanged. And the way you are trying to use relativistic mass violates conservation of energy — you're basically "double booking" the kinetic energy.

 

If two things originated from the same thing/place (Big bang), and they are now traveling at different velocities relative to each other, then one or both must have accelerated relative to the other or relative to the origin. Thus, any relative movement in the universe is a result of acceleration.

Thus, time dilation is caused by acceleration/gravity, not velocity differences.

This implies that the total time dilation is not dependent on its final velocity difference, but on the amount of acceleration/deceleration/gravity it has experienced since the first measurement.

 

It is trivial to show that e.g. the twin "paradox" is unaffected by the value of the acceleration at the turnaround. Time dilation is a combination of the two effects; this is easily seen in effects from satellites traveling at different orbital speeds and at different potentials.

[Demonslayer]

Your mass in your own frame is unchanged. And the way you are trying to use relativistic mass violates conservation of energy — you're basically "double booking" the kinetic energy.

So you're saying that the mass of my fuel does not change along with the mass of my spaceship? Does my fuel contain less energy if I'm traveling faster?

When you're accelerating a particle in an accelerator you are using energy supplied from a different frame.

 

 

It is trivial to show that e.g. the twin "paradox" is unaffected by the value of the acceleration at the turnaround. Time dilation is a combination of the two effects; this is easily seen in effects from satellites traveling at different orbital speeds and at different potentials.

Trivial? Has it been observed?

It seems very counter-intuitive that time dilation has two causes.

[ydoaPs]

Mass is invariant.

[Demonslayer]

Mass is invariant.

This I know, but observed mass (or effects of it) depends on your frame and the frame the the observed object.

Mass is cited as the reason why we can't accelerate a particle to light speed.

[ydoaPs]

Where?

[iNow]

YD... where, what?

 

Any object with mass cannot be accelerated to the speed of light. (Or, were you perhaps asking where it's stated that mass depends on frame?)

 

 

 

Also, Demonslayer, mass is an inherent property. Here is a straight forward set of questions and answers:

 

http://helios.gsfc.nasa.gov/qa_gp_sl.html

[Phi for All]

Where?

Brevity is the soul of wit, not the soul of communication.

[swansont]

So you're saying that the mass of my fuel does not change along with the mass of my spaceship? Does my fuel contain less energy if I'm traveling faster?

When you're accelerating a particle in an accelerator you are using energy supplied from a different frame.

 

The fuel contains the same amount of energy in all frames; you use the invariant mass. The so-called relativistic mass is the sum of the rest mass and the mass equivalent of your kinetic energy. You can't use your kinetic energy to increase your kinetic energy.

 

 

Trivial? Has it been observed?

It seems very counter-intuitive that time dilation has two causes.

 

Trivial in the sense that the kinematic time dilation does not have an acceleration term in it, and correctly predicts time dilation that is observed.

 

"Counter-intuitive" is not a valid objection, though. We see things that look Galilean, and that nature actually behaves with a Lorentz transform instead is not obvious.

 

The time dilation seen on GPS satellites is found by adding the gravitational and kinematic values. Same for satellites in other orbits.

[Janus]

Thus, time dilation is caused by acceleration/gravity, not velocity differences.

Example 1.

Two spacecraft. Both accelerate at the same rate for the same period of time. They coast. One ship then decelerates, stops and accelerates back to the starting point, when it arrives its stops. The second ship continues to coast, and then after some time, returns to the the starting point, using the exact same accelerations as the first ship. Upon its return, it will have acged less than the ship that returned earlier, even though both ships experienced the exact same acceleration history.

 

Example 2. Place two radioactive samples in centrifuges. The radii of the centrifuges are such that both samples travel at the same speed while spinning, but each experience a different g-Force while doing so. Spin the samples up for a equal amount of time. At the end they will aged the same while have experienced different acceleration forces.

 

Now take the same samples but rig the centrifuges to exert the same g-force on each sample while they travel at different speeds. At the end of the experiment, the sample that traveled at the greater speed will have aged less.

 

A version of this experiment has actually been performed and verified.

 

 

 

This implies that the total time dilation is not dependent on its final velocity difference, but on the amount of acceleration/deceleration/gravity it has experienced since the first measurement.

 

You also seem to be suffering from a common misconception about time dilation due to gravity; that is it due to the gravitational force experienced by the object. This is not true. It is due to a difference in gravitational potential.

 

For example, you gave the situation of a clock running faster on Mars than on Earth, which is fine, as long as you don't think it is just due to the weaker surface gravity. For instance, a clock will run slower on the surface of Uranus than on Earth, but the surface gravity on Uranus is slightly less than on Earth.

[iNow]

So, what is causing the difference with the example of Uranus, then? I presume it is moving at a faster velocity around the sun relative to Earth. Is that an accurate perspective?

[Janus]

So, what is causing the difference with the example of Uranus, then? I presume it is moving at a faster velocity around the sun relative to Earth. Is that an accurate perspective?

 

The clock is at a lower gravitational potential.

 

Gravitational potential is found by:

 

[math]G_{p}= -\frac{GMm}{d}[/math]

 

Gravitational force is found by:

 

[math]G_f= \frac{GMm}{d^2}[/math]

 

For Earth, The acceleration for a 1 kg object would be:

 

[math]G_f= \frac{G 5.97 x10^24} {(6.378x10^6)^2} = 9.793 m/sec[/math]

 

for Uranus:

 

[math]G_f= \frac{G 8.68 x10^25} {(2.556x10^7)^2} = 8.87 m/sec[/math]

 

Now compare gravitational potential for the same mass:

 

Earth:

 

[math]G_{p}= -\frac{G 5.97x10^24}{6.378x10^6} = -6.245e7[/math]

 

Uranus:

 

[math]G_{p}= -\frac{G 8.68x10^25}{2.556x10^7} = -2.266e8[/math]

 

(A larger negative potential is a lower potential, for example, the potential on the Moon's surface would be -2.822e6)

[iNow]

Thanks, Janus. As per usual, your response was very helpful.

[Mr Skeptic]

I'm one of those people who thought that the time dilation was due to gravitational force. Thanks Janos.

[Demonslayer]

The fuel contains the same amount of energy in all frames; you use the invariant mass. The so-called relativistic mass is the sum of the rest mass and the mass equivalent of your kinetic energy. You can't use your kinetic energy to increase your kinetic energy.

It seems that the difference between gravitational force and gravitational potential was not explained very clearly when we were taught relativity theory.

Still, every velocity difference in the universe must be caused by an acceleration, making acceleration the ultimate cause of any time-dilation. A velocity difference can never be created without accelerating one or both of the frames involved. So I still can't see how time-dilation can have two causes.

 

But no one has really given me a satisfactory explanation about why they say mass is a hinder to achieving light speed when mass does not change within the frame of my own spaceship. I can not have kinetic energy relative to myself, so I am not using my kinetic energy to increase my kinetic energy.

My fuel contains as much energy at rest as it does at 0.99 c since the energy is proportional to the mass of the fuel.

 

Example 1.

Two spacecraft. Both accelerate at the same rate for the same period of time. They coast. One ship then decelerates, stops and accelerates back to the starting point, when it arrives its stops. The second ship continues to coast, and then after some time, returns to the the starting point, using the exact same accelerations as the first ship. Upon its return, it will have acged less than the ship that returned earlier, even though both ships experienced the exact same acceleration history.

 

Example 2. Place two radioactive samples in centrifuges. The radii of the centrifuges are such that both samples travel at the same speed while spinning, but each experience a different g-Force while doing so. Spin the samples up for a equal amount of time. At the end they will aged the same while have experienced different acceleration forces.

 

Now take the same samples but rig the centrifuges to exert the same g-force on each sample while they travel at different speeds. At the end of the experiment, the sample that traveled at the greater speed will have aged less.

 

A version of this experiment has actually been performed and verified.

Example 1. Has not been experimentally verified and does therefore not constitute evidence.

Example 2. Each sample must be accelerated up to its rotational speed, this offsets the differences i G-forces.

Do you have a link or something that describes this experiment?

Edited June 24, 2008 by Demonslayer
multiple post merged

[swansont]

It seems that the difference between gravitational force and gravitational potential was not explained very clearly when we were taught relativity theory.

Still, every velocity difference in the universe must be caused by an acceleration, making acceleration the ultimate cause of any time-dilation. A velocity difference can never be created without accelerating one or both of the frames involved. So I still can't see how time-dilation can have two causes.

 

Yes, as you point out, speed and acceleration are related, you could solve for the dilation in terms of a, if there was acceleration during the whole time. But that may not be the case. What if the acceleration ceases? What if you synchronize the cocks after the acceleration? They still will not run at the same rate.

 

The dilation between two frames is dependent on their relative speeds. That's what you need to know to determine it. You appear to be looking for the metaphysical "cause," which is a separate question.

 

 

But no one has really given me a satisfactory explanation about why they say mass is a hinder to achieving light speed when mass does not change within the frame of my own spaceship. I can not have kinetic energy relative to myself, so I am not using my kinetic energy to increase my kinetic energy.

My fuel contains as much energy at rest as it does at 0.99 c since the energy is proportional to the mass of the fuel.

 

Energy as a function of speed diverges at v=c; that's the asymptote.

 

At low speeds we know that adding the same amount of energy has diminishing returns. If you want to double your speed, you need four times the energy. At higher speeds this ends up diverging faster.

 

Example 1. Has not been experimentally verified and does therefore not constitute evidence.

Example 2. Each sample must be accelerated up to its rotational speed, this offsets the differences i G-forces.

Do you have a link or something that describes this experiment?

#1 hasn't been done in that form, but the equivalent has been done in other forms, such as the Hafele-Keating experiment. Clocks in planes traveling at different speeds relative to an inertial frame ran at different rates, in agreement with the theory.

[Demonslayer]

Ok, thanks. I'll do a little more research and see if I understand the argument.

You appear to be looking for the metaphysical "cause," which is a separate question.

I don't see anything metaphysical about it. If a particle's velocity today relative to "us" is directly correlated to "its" and "our" acceleration since the beginning of the universe (or since we last measured it), then acceleration must be the true "cause" of time dilation.

 

Clocks in planes traveling at different speeds relative to an inertial frame ran at different rates, in agreement with the theory.

Planes at different speeds have had different accelerations to reach that speed.

I see how it is easier to use speed rather than acceleration to calculate time dilation, but it really boils down to the same thing.

[D H]

Planes at different speeds have had different accelerations to reach that speed. I see how it is easier to use speed rather than acceleration to calculate time dilation, but it really boils down to the same thing.

The clock hypothesis states that relativistic effects result from relative instantanous velocity and do not depend on any higher derivatives of velocity (acceleration, jerk, ...). See the Physics FAQ, " Does a clock's acceleration affect its timing rate?". While this is a hypothesis (i.e., an assumption) of relativity, the hypothesis has been experimentally verified for accelerations up to 10¹⁸g.

[swansont]

I don't see anything metaphysical about it. If a particle's velocity today relative to "us" is directly correlated to "its" and "our" acceleration since the beginning of the universe (or since we last measured it), then acceleration must be the true "cause" of time dilation.

 

As I pointed out, knowing the acceleration doesn't tell you the dilation. That's not the proximate cause of it. It's like asking someone how they broke their leg and having the answer be, "I was born." It's a prerequisite, but not the actual cause.

 

 

Planes at different speeds have had different accelerations to reach that speed.

I see how it is easier to use speed rather than acceleration to calculate time dilation, but it really boils down to the same thing.

 

They all started from rest on the earth and underwent similar accelerations to have similar speeds with respect to the earth.

[ydoaPs]

I don't know much about relativity, but I thought the time dilation and length contraction were due to energy differences between frames caused by the relative nature of motion.

[swansont]

I don't know much about relativity, but I thought the time dilation and length contraction were due to energy differences between frames caused by the relative nature of motion.

 

Differences in potential, which is energy per unit mass.

[Pete]

The first is the matter of accelerating a mass up to the speed of light.

It is said that doing this would require infinite energy and that this is supported by particle accelerator experiments.

That is correct.

When you are accelerating a particle with energy supplied from a system at rest, it is true that you would require infinite energy.

That is true.

It's all relative right?

A vague question but I'll say no.

If the energy for acceleration was supplied from an on-board energy source on a spaceship, the mass of the energy source (and it's energy) would increase at the same rate as the mass of the spaceship.

The energy of a spaceship cannot come from itself. If it did then the energy of the spaceship would remain constant and its speed would never change. The way a spaceship accelerates is by ejecting matter. The momentum given to the ejected matter is balanced by the increased momentum of the ship.

I can't see how the argument that accelerating something to light speed requires infinite energy, can be true.

Hopefully the above explanation will help. What exactly is the source of your objection?

The second thing is time dilation.

Gravity causes time dilation, right?

Time dilation is the phenomena in which two clocks of identical construction tick at different rates. In order for there to be gravitational time dilation there must be two different clocks being compared. When the two clocks are at two different gravitational potentials then the clocks will run at different rates.

Time goes slower on Earth than on Mars, right?

Remember that we have to refer to two clocks to speak about time dilation. If we are speaking about a distant clock which is outside a gravitational potential Call this clock S) then a clock on the Earth's surface will run slower than a clock on the surface of Mars as compared to the clock S.

Velocity difference between two objects causes time dilation, right?

Yes.

Gravity is equivalent to acceleration, right?

To be precise - A uniform gravitational field is equivalent to a uniformly accelerating frame of reference. Or, similarly, the gravitational force is an inertial force.

Time dilation doesn't have two causes does it?

Yes, in the sense described above.

The true cause of time dilation must be acceleration.

No.

So my conclusion is that every twin-paradox thought experiment that does not take acceleration into account will be wrong.

No. In fact the twin paradox doesn't even need acceleration for it to occur. All that is required is non-symmetry of worldlines. If we concern ourselves only with the time readings on clocks then we can observe the readings on two clocks that are synchronized as they pass each other. E.g. let a clock be whizzing by the Earth in the direction of the destination and let the clock be set to zero when the clock passes Earth. When it passes by the destination let there be a second clock passing by the destination in the direction of Earth and let the clocks be synchronized as they pass. When the second clock passes by the Earth it will have a smaller reading on it than the clock on the Earth.

Mass is invariant.

Proper mass is invariant and relativistic mass is not. What "mass" means when unqualified can always be determined by the context in which it is used.

But no one has really given me a satisfactory explanation about why they say mass is a hinder to achieving light speed when mass does not change within the frame of my own spaceship.

The mass of a body is a function of its speed. The larger its value the greater the momentum of the body, i.e. mass defines momentum. When the momentum is larger then it takes a larger force to change it by the same amount that the same force changes it when the speed is less. The value of the mass is a function of velocity and becomes infinite as v -> c. Explained in another way - mass is a body's measure of its resistance to changes in speed. The greater the speed the greater the mass and thus the harder it is to accelerate. As the speed approaches the speed of light the energy required getting it to that speed approaches infinity.

I don't know much about relativity, but I thought the time dilation and length contraction were due to energy differences between frames caused by the relative nature of motion.

Time dilation and length contraction are geometric concepts and not dynamic ones and as such there is no relationship between them and energy. Only when one starts to bring energy into it can relationships between them be discussed.

 

Pete

[alwynj48]

Hi, new guy here.

 

snip

If the energy for acceleration was supplied from an on-board energy source on a spaceship, the mass of the energy source (and it's energy) would increase at the same rate as the mass of the spaceship.

I can't see how the argument that accelerating something to light speed requires infinite energy, can be true.snip.

 

It’s interesting to consider how much energy is required in the moving frame.

This is given by 1/2mv^2 where m is the mass being accelerated and v is the velocity attained

If the velocity required is c then the energy required is 1/2mc^2. The amount of mass that must be converted to generate that energy is given by E=mc^2. Ie the energy required is equivalent to half the rest mass of the object that’s accelerated. Note I may have missed out a factor due to the units but I think its ok if consistent units are used.

Ok so far we have managed to accelerate to the velocity of light and only used a finite amount of fuel equal to half the mass of the object we are accelerating. Admittedly where using a 100% efficient mass to energy converter but this is a thought experiment so that’s ok. However the mass must be carried on board and accelerated which will require additional energy (mass) to accelerate it. I have not done the maths but I suspect it would show for a finite amount of fuel you can get arbitrarily close to c but never c unless you start with an infinite amount of fuel..

 

Note We don’t have any 100% mass to energy converters and the usual method of propulsion, by ejecting the products of an energetic chemical reaction out of a nozzle probably have efficiencies in nano percents.

 

As a side note I am new here so hi all you science freaks.