Equivalence Principle

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Re: Equivalence Principle
« Reply #90 on: January 17, 2020, 05:18:25 PM »
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It depends on 2 things:
The velocity of the elevator relative to the observer at rest and
The angle that the observer at rest shines the light.

And that is a key part, picking a different velocity for the elevator just means the light is starting at a different angle.

OK till here. Ignore till to the below "same result" or quote as you already know what I'm saying.

Make it simpler;

Each case has its own elevator. Outside observer who doesn't change its position, shines a horizontal beam of light in each case at two different times t1 and t2. Let

The elevator of case #1 passes upward in front of outside observer who is at rest and shines a beam of light at time t1.

The elevator of case #2 passes upward in front of outside observer who is at rest and shines a beam of light at time t2.

The bending of light in each case would be different due to the difference in magnitude of constant velocity (10 m/s and 200 m/s)

We can use one elevator but it has to pass upward two times (one for each case) in front of the outside observer who is at rest (doesn't change his position)  and shines a horizontal beam of light in each case at two different times t1 and t2.

same result.
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It is also clear that by adjusting the angle as necessary, theta 2 for this case 2 can be the same as theta 2 for your case 2, and that theta 1 will be the same.

This means there is no need for it to be the velocity that causes it and instead it can be caused by a different initial angle of light.

These can also be compared to the case where the velocity of the elevator is 0 relative to the outside observer.

So instead of focusing on the velocity, which makes no sense at all without some outside observer to use as a reference, we should instead focus on the initial angle of the light.
I'll be back once I get it.

But the question is the person who stands alone on the floor of elevator accelerating upward constantly canít differentiate if he in elevator or on earth when shines a beam of light towards the vertical wall of elevator whether moving at lower or higher velocities.
« Last Edit: January 17, 2020, 09:08:48 PM by E E K »

Re: Equivalence Principle
« Reply #91 on: January 18, 2020, 02:19:50 AM »
But the question is the person who stands alone on the floor of elevator accelerating upward constantly canít differentiate if he in elevator or on earth when shines a beam of light towards the vertical wall of elevator whether moving at lower or higher velocities.
Lower or higher velocity relative to what?
Your outside observer at rest?

On Earth you cannot use that as a comparison as it isn't there.
All you have to use is the light.
That means you need to use the initial angle of the light, i.e. the light as if the elevator was at a constant velocity when the light entered.

Again, that means instead of focusing on the speed of the elevator as it passes your "observer at rest" you need to focus on the initial angle of the light.

Re: Equivalence Principle
« Reply #92 on: January 18, 2020, 04:15:56 AM »
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Lower or higher velocity relative to what?
Your outside observer at rest?
I meant the onboard observer couldn't feel the velocities either high or low. I just mentioned it for the bending of light reasons. No need of outside observer in this case.
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On Earth you cannot use that as a comparison as it isn't there.
Yes

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All you have to use is the light.
hat means you need to use the initial angle of the light, i.e. the light as if the elevator was at a constant velocity when the light entered.
So the problem seems here. Why would the onboard observer who just feels himself on the ground, flashes a beam light towards the verticals of the wall of the elevator, needs an external light that entered the elevator for the use of initial angle? We don't need outside observer either at rest or moving along the elevator in this case in order to use the initial angle. Doesn't the onboard observer just feel his standing normal like on the ground? if yes then he is just fine w/o the outside observer. So he can flash a beam of light towards the vertical wall anytime if he wants. 

Is there any reference about the use of initial angle?
« Last Edit: January 18, 2020, 04:17:46 AM by E E K »

Re: Equivalence Principle
« Reply #93 on: January 18, 2020, 05:08:09 AM »
So the problem seems here. Why would the onboard observer who just feels himself on the ground, flashes a beam light towards the verticals of the wall of the elevator, needs an external light that entered the elevator for the use of initial angle? We don't need outside observer either at rest or moving along the elevator in this case in order to use the initial angle. Doesn't the onboard observer just feel his standing normal like on the ground? if yes then he is just fine w/o the outside observer. So he can flash a beam of light towards the vertical wall anytime if he wants. 

Is there any reference about the use of initial angle?
They don't need an external light, they just need to use whatever the initial angle of the light is.
If they are shining it horizontally, then that initial angle would be 0, which in your cases corresponds to a velocity of 0.
In order to get a different curve they will need to angle the light in a different direction.
For example, to match your 10 m/s case, they need to angle the light downwards. To match the 200 m/s case they need to angle it down even further.

There aren't any references I know of which focus on the initial angle specifically. Instead the ones I know start with a reference frame where the elevator is at rest initially and go from there.

But instead of that you want to try to bring up different velocities relative to an outside observer, yet you then act like the light starts off at the same angle.

Re: Equivalence Principle
« Reply #94 on: January 18, 2020, 01:54:07 PM »
Earth is to elevator Ė Elevator is to earth.  Both derive Equivalence Principle which states gravity bends light but the problem is, how would one measure the initial angle when a beam of light itself is not even horizontal across the elevator resting on the ground when it has zero motion. Non-equivalency starts from here. Anyway, I believe no has tried yet to measure its value.

I donít think a person needs a speedometer for the adjustment of initial angle (as you said) when he feels a similar uniform gravitational field of the earth if he stands alone on the floor of the elevator accelerating constantly upward. Gain in the bending of the light beam shows an accretion in the gravitational field. So if we ignore the adjustment of an initial angle then does this mean that the said person on the floor of the elevator feels more gravity when he sees an increase in the bending of a light beam?

Re: Equivalence Principle
« Reply #95 on: January 18, 2020, 03:47:34 PM »
Earth is to elevator Ė Elevator is to earth.  Both derive Equivalence Principle which states gravity bends light but the problem is, how would one measure the initial angle when a beam of light itself is not even horizontal across the elevator resting on the ground when it has zero motion. Non-equivalency starts from here. Anyway, I believe no has tried yet to measure its value.
No, that would still be equivalency.
That is because when it is on the ground with zero motion it is exposed to gravity which causes the bending of light, just like if it was accelerating upwards.

You would measure the initial angle just like you would measure any angle for light. But the simplest way would be to control the initial angle either by having a unidirectional light source which has all bar one path obstructed, and thus the initial angle is based upon that direction, or you have a laser which is pointed in a particular direction.

No one has measured it for Earth as it is tiny.
As an approximation, for light travelling horizontally at c across a distance of w, in a gravitational field of g (or equivalently in an elevator accelerating at a=-g):
Light will take t=w/c to traverse the distance.
In this distance it will have accelerated downwards and have dropped a total of 0.5*g*t^2=0.5*g*w^2/c^2.
Ignoring the relativistic corrections, the vertical component of its velocity will be g*w/c. This means it will be travelling at an angle of atan((g*w/c)/c)=atan(g*w/c^2).

To put in some actual numbers.
Lets assume you have a horizontal light path 100 km long.
For simplicity, we will ignore the curvature of Earth.
Then due to Earth's gravity, light will have bent such that it leaves ~546 nm below where it entered and instead of travelling perfectly horizontally, it will be travelling with an angle of depression of roughly 6*10^-10 degrees or roughly 2 microarcseconds.

These are far too small to be measurable.

However gravitational lensing (i.e. gravity bending light) has been observed for other, more massive objects, like the sun.

Gain in the bending of the light beam shows an accretion in the gravitational field. So if we ignore the adjustment of an initial angle then does this mean that the said person on the floor of the elevator feels more gravity when he sees an increase in the bending of a light beam?
That depends upon what you mean by an increase in the bending. If you are ignoring the initial angle then that increase in "bending" could just be due to the change in initial angle.

However, if the initial angle is the same, then an increase in the amount of bending would require more acceleration for the elevator in deep space, or an increase in gravity for the observer on Earth.

An increase in bending (i.e. how much the slope changes) means g and a are higher.
An increase in the magnitude of the slope could be due to that, or a steeper angle.

Re: Equivalence Principle
« Reply #96 on: January 21, 2020, 03:26:28 AM »
Initial Angle:

Non-equivalency starts if a beam of light shines towards the elevator of the subject other than horizontal.  The simple example is the vertical clock as shown in the original question. Let d is the distance in between the upper and lower mirror. At rest, a pulse takes t = d/c.  When the elevator accelerating upward @ 9.8 m/s/s then,

A pulse if fired from the upper mirror takes t1 = d/c to reach lower mirror
A pulse if fired from the lower mirror takes t2 = d/c to reach upper mirror

This means t1<t<t2. Both t1 and t2 are not equal to ĒtĒ therefore what would you do with time t1 or t2 even if you adjust the initial angle. Similarly,

A beam of light if shines at an initial angle (downward) inside an accelerating elevator bends. Just conduct the experiment in reverse direction - A beam of light if shines at an initial angle (upward) inside an accelerating elevator bends. Here it takes more time as compared to beam of light if shines downward  -  Right

Solar Eclipse: The light from star to the observer on earth follows a straight line in the absence of sun. Light bends if it enters the gravitational field of the sun Ė(#1)

But the speed of light reduces when it leaves the gravitational field sun -(#2). as explained above or

This can be explained by the elevator used in equivalence principle if we shine a beam of light (not horizontal but upward at an initial angle) towards the elevator accelerating upward @ rate of 9.8 m/s/s. The speed of light reduces when it leaves the gravitational field.

So if you agree with #1 then you should also agree with #2.

Moreover, acceleration (gravity) bends light but an apple follows straight line if released. 
« Last Edit: January 21, 2020, 12:36:21 PM by E E K »

Re: Equivalence Principle
« Reply #97 on: January 21, 2020, 12:53:44 PM »
The simple example is the vertical clock as shown in the original question. Let d is the distance in between the upper and lower mirror. At rest, a pulse takes t = d/c.  When the elevator accelerating upward @ 9.8 m/s/s then,

A pulse if fired from the upper mirror takes t1 = d/c to reach lower mirror
A pulse if fired from the lower mirror takes t2 = d/c to reach upper mirror

This means t1<t<t2. Both t1 and t2 are not equal to ĒtĒ therefore what would you do with time t1 or t2 even if you adjust the initial angle.
This applies both, to the case with gravity and the case with an accelerating elevator.
So there is still equivalency.

Remember, the equivalency principle doesn't demand that light going up and down are equivalent. It focuses on gravity and accelerating frames.
So having a difference between light going up and down isn't a problem.

But the speed of light reduces when it leaves the gravitational field sun -(#2). as explained above or
This is actually a lot more complex than that.
Lets assume it follows a path straight through the sun (without interacting with it).
Then it starts out outside a gravitational field travelling at c.
As it enters the gravitational field it speeds up.
This continues until it reaches its peak as it passes through the sun.
Then as it starts coming out the other side, it is going slower.
Then as it gets higher, the gravitational field gets weaker and it speeds up.

But again, this has nothing to do with non-equivalency.
The same would happen with the elevator if you change a to match.

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sokarul

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Re: Equivalence Principle
« Reply #98 on: January 21, 2020, 12:57:25 PM »
The speed of light doesnít change due to gravity. The wavelength changes.
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Re: Equivalence Principle
« Reply #99 on: January 21, 2020, 01:25:35 PM »
The speed of light doesnít change due to gravity. The wavelength changes.
I was under the impression that it would based upon general relativity, where it becomes anisotropic; which also explains why light doesn't escape a black hole.

If it was just modifying the wavelength, then light should still escape a black hole, just being red-shifted.

Re: Equivalence Principle
« Reply #100 on: January 21, 2020, 04:34:05 PM »
So the denser medium around the sun didn't have any role it was just its gravity which bent the light oncoming from star to the observer on earth

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rabinoz

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Re: Equivalence Principle
« Reply #101 on: January 21, 2020, 07:21:50 PM »
So the denser medium around the sun didn't have any role it was just its gravity which bent the light oncoming from star to the observer on earth
What denser medium around the Sun?
Quote from: COSMOS
The SAO Encyclopedia of Astronomy: Corona, The outermost layer
The outermost layer of the Sun is known as the corona. Due to its low density of particles (roughly 10-13 kg/m3) we can see right through it, and the underlying chromosphere, down to the photosphere Ė the visible surface of the Sun.
And further away from the Sun the density of the Solar wind has a density of about 1.46 x 10-20 kg/m3.

To put that into perspective, the density of air at sea-level is about 1.225 kg/m3.

So, I doubt that the denser medium around the Sun had anything to do with it.

Re: Equivalence Principle
« Reply #102 on: January 22, 2020, 03:13:20 AM »
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What denser medium around the Sun?
Actually I meant a hotter medium, which shifts the position of the object so indirectly the light coming from it- Refraction. Last summer, I noticed a wire of fence shifted its original position upward when I looked closely at through radiations emitting from the surface of my car on a hot afternoon Ė it seems I deleted video mistakenly.

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rabinoz

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Re: Equivalence Principle
« Reply #103 on: January 22, 2020, 03:23:43 AM »
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What denser medium around the Sun?
Actually I meant a hotter medium, which shifts the position of the object so indirectly the light coming from it- Refraction. Last summer, I noticed a wire of fence shifted its original position upward when I looked closely at through radiations emitting from the surface of my car on a hot afternoon Ė it seems I deleted video mistakenly.
That is due to the refractive index of hotter air being slightly less than the refractive index of cooler air.
But the space near the Sun is almost a vacuum.
Why would a "hotter vacuum" refract light any differently front a "cooler vacuum"?

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sokarul

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Re: Equivalence Principle
« Reply #104 on: January 22, 2020, 06:53:35 AM »
The speed of light doesnít change due to gravity. The wavelength changes.
I was under the impression that it would based upon general relativity, where it becomes anisotropic; which also explains why light doesn't escape a black hole.

If it was just modifying the wavelength, then light should still escape a black hole, just being red-shifted.
Iím trying to reminder without looking it up. The speed of light should be constant in all reference frames. Iím not sure if it applies to the event horizon. Gravitational redshift is apart of the equivalence principle.
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Re: Equivalence Principle
« Reply #105 on: January 22, 2020, 11:45:53 AM »
Iím trying to reminder without looking it up. The speed of light should be constant in all reference frames. Iím not sure if it applies to the event horizon. Gravitational redshift is apart of the equivalence principle.
I'm fairly sure that is meant to be all inertial reference frames.
Non-inertial frames can then have the speed of light change.
A classic example of that is the Sagnac effect for a rotating reference frame.
In a rotating reference frame light will take a different amount of time to go clockwise vs counterclockwise around a loop, yet the distance around the loop is the same (as it is the same loop).

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sokarul

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Re: Equivalence Principle
« Reply #106 on: January 22, 2020, 06:21:04 PM »
Iím trying to reminder without looking it up. The speed of light should be constant in all reference frames. Iím not sure if it applies to the event horizon. Gravitational redshift is apart of the equivalence principle.
I'm fairly sure that is meant to be all inertial reference frames.
That is true.
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Non-inertial frames can then have the speed of light change.
A classic example of that is the Sagnac effect for a rotating reference frame.
In a rotating reference frame light will take a different amount of time to go clockwise vs counterclockwise around a loop, yet the distance around the loop is the same (as it is the same loop).
I have seen all those threads. You do have to watch out for the phase shift, which isn't a change in the speed of light. Many of the formulas posted have c and wavelength.
The delta t=4Aomega/c2 is another example.

This is a good source.
https://physics.stackexchange.com/questions/262925/speed-of-light-when-accelerating

It does explain the Rindler coordinates where like can be faster but then adds if you check the speed of light it's not.
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Re: Equivalence Principle
« Reply #107 on: January 23, 2020, 12:14:23 AM »
This is a good source.
https://physics.stackexchange.com/questions/262925/speed-of-light-when-accelerating
It does explain the Rindler coordinates where like can be faster but then adds if you check the speed of light it's not.
But only for the position exactly at where (and when) the observer is.
At positions away from that, the speed of light is different in the accelerating frame.

This then makes sense with the Sagnac effect, where as the light travels the loop, it is away from your position and thus travels at a different speed in your rotating frame.

It also adds in time dilation, which I had been ignoring to keep it simple.

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sokarul

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Re: Equivalence Principle
« Reply #108 on: January 23, 2020, 06:53:13 PM »
This is a good source.
https://physics.stackexchange.com/questions/262925/speed-of-light-when-accelerating
It does explain the Rindler coordinates where like can be faster but then adds if you check the speed of light it's not.
But only for the position exactly at where (and when) the observer is.
At positions away from that, the speed of light is different in the accelerating frame.

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This then makes sense with the Sagnac effect, where as the light travels the loop, it is away from your position and thus travels at a different speed in your rotating frame.
Could be. But distance plays a part to make the interference pattern.

https://en.m.wikipedia.org/wiki/Sagnac_effect

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It also adds in time dilation, which I had been ignoring to keep it simple.

We would have to add length contraction then as well.
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Re: Equivalence Principle
« Reply #109 on: January 26, 2020, 11:49:41 PM »
Although an onboard observer feels like ground condition in the elevator of the subject, in reality, he/she isnít at rest, therefore, the changes in the wavelength of the light for the onboard observer would be different than on earth where an observer is at rest. An onboard person has a very close observation of a pulse of light when the elevator changes its velocities close to the speed to the light if a beam of light shins in reverse direction (upward at an angle) as explained earlier.

Re: Equivalence Principle
« Reply #110 on: January 27, 2020, 12:40:18 AM »
Although an onboard observer feels like ground condition in the elevator of the subject, in reality, he/she isnít at rest, therefore, the changes in the wavelength of the light for the onboard observer would be different than on earth where an observer is at rest.
Why?
The entire point of the equivalence principle is that they are the same, that gravity will produce the same changes as acceleration.

An onboard person has a very close observation of a pulse of light when the elevator changes its velocities close to the speed to the light
The speed of light relative to what?
Again, just like before, this isn't going to have anything to do with the velocity of the elevator.
It will be based upon some arbitrary reference which produces vastly different conditions.

Re: Equivalence Principle
« Reply #111 on: January 27, 2020, 06:53:05 PM »
one word - FRAME / Non-inertial frame

Re: Equivalence Principle
« Reply #112 on: January 28, 2020, 12:01:02 AM »
one word - FRAME / Non-inertial frame
And the whole point of the equivalence principle is that standing on the surface of a planet with a gravitational field is not an inertial frame. Instead it is an inertial frame, where a simple demonstration of that is to throw 2 objects upwards, and note that they don't just continue moving upwards and instead they stop and fall back down.

Re: Equivalence Principle
« Reply #113 on: January 28, 2020, 02:58:28 AM »
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The speed of light relative to what?

On earth: relative to the stationary observer
In elevator: relative to the onboard observer either moving upward @ the rate of 9.8 m/s/s - or at rest.

Re: Equivalence Principle
« Reply #114 on: January 28, 2020, 03:20:32 AM »
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The speed of light relative to what?

On earth: relative to the stationary observer
In elevator: relative to the onboard observer either moving upward @ the rate of 9.8 m/s/s - or at rest.
That literally makes no sense at all.
You were appealing to the velocity of the elevator.
For the person on Earth that would be the velocity of Earth relative to Earth. It makes no sense at all.
Likewise you are now having it be the velocity of the elevator relative to the elevator. It makes no sense at all.

Re: Equivalence Principle
« Reply #115 on: January 30, 2020, 10:02:58 AM »
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You were appealing to the velocity of the elevator.
Didn't we deduct acceleration of released object from the said velocity

Re: Equivalence Principle
« Reply #116 on: January 30, 2020, 12:37:43 PM »
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You were appealing to the velocity of the elevator.
Didn't we deduct acceleration of released object from the said velocity
No, for the released object, we focused on its velocity relative to the elevator.
But you are trying to break equivalence by appealing to the velocity of the elevator.

Re: Equivalence Principle
« Reply #117 on: February 01, 2020, 09:01:26 PM »
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No, for the released object, we focused on its velocity relative to the elevator.
But you are trying to break equivalence by appealing to the velocity of the elevator.
Thatís why the onboard observer feels falling of the released object equivalent to on earth. The same observer sees the aforementioned pulse or beam of light.

Similarly, both the apple and the earth fall towards each other but in the elevator of equivalency, only one object falls toward the other. striking timing are not equivalent again. - Please ignore if I mentioned it earlier.

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rabinoz

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Re: Equivalence Principle
« Reply #118 on: February 01, 2020, 09:31:43 PM »
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No, for the released object, we focused on its velocity relative to the elevator.
But you are trying to break equivalence by appealing to the velocity of the elevator.
Thatís why the onboard observer feels falling of the released object equivalent to on earth. The same observer sees the aforementioned pulse or beam of light.

Similarly, both the apple and the earth fall towards each other but in the elevator of equivalency, only one object falls toward the other. striking timing are not equivalent again. - Please ignore if I mentioned it earlier.
It's been brought up numerous times and it's totally irrelevant because:
You are observing from within the elevator sitting on the Earth. Any slight acceleration of the Earth would be completely undetectable.

To get an idea of just how undetectable just realise that the mass of the Earth is 5.972 x 1024 kg and the mass of an apple about 0.15 kg (yes, I weighed some).

So please forget about the Earth's acceleration towards the apple. Even a 3,000,000 kg rocket is quite insignificant.

But remember it's only a thought experiment to illustrate a principle. I honestly don't know what you hope to prove with all of this.

Re: Equivalence Principle
« Reply #119 on: February 02, 2020, 02:44:31 AM »
Similarly, both the apple and the earth fall towards each other but in the elevator of equivalency, only one object falls toward the other. striking timing are not equivalent again. - Please ignore if I mentioned it earlier.
You did mention it, and I had already addressed it.
This depends on the mass of Earth and how the elevator is being accelerated/its mass.
With any normal method of propulsion, the elevator will accelerate at an increased rate while the object is falling.
But this change should be insignificant.