In regard to relativity, is length contraction only a illusion, that appears when one tries to measure length from one reference frame. In other words, no contraction actually happens, its all an illution of the measurement.

Time dilation appeares real, however, clocks actually move slower, and this has been experimentally verified in experiments such as Hafele and Keating Experiment (http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html)

In other words is time dilation more real than length contraction?

Probability,

Welcome to sciforums.

Time dilation appeares real, however, clocks actually move slower, and this has been experimentally verified in experiments such as Hafele and Keating Experiment

If time dilation was real then clocks wouldn't run any slower since clocks measure the speed of reactions and not time itself. If you don't understand what I mean, check out this thread:

http://www.sciforums.com/showthread.php?s=&threadid=17610

Note: My opinions are NOT the opinions of the general scientific community. Take everything I say with a grain of salt.

Tom

Originally posted by Probability
In regard to relativity, is length contraction only a illusion, that appears when one tries to measure length from one reference frame. In other words, no contraction actually happens, its all an illution of the measurement.

Time dilation appeares real, however, clocks actually move slower, and this has been experimentally verified in experiments such as Hafele and Keating Experiment (http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html)

In other words is time dilation more real than length contraction?

Length (the interval between two points in space) contracts when one object is moving relative to another - when the two objects return to the same locality, travelling at the same velocity, the original length is recovered.

The change in the rate at which time passes (the interval between two instants in time) also appears when one object is moving relative to another and disappears when they get back together.

The clock dial records a summation of time intervals but it's the rate of ticking that's important in your question.

Cheers,

Ron.

Probablility,

FYI: As Prosoothus above indicates, I too am dislike by certain members of this board because I do not hold Relativity in the highest regard.

Having said that let me suggest that you should keep an open mind and decide for yourself and not because a believer says it is so.

With respect to time dilation, I am inclined to believe that it is either an illusion and not reality or that it is not properly described by Relativity.

Length contraction I agree with Relativity.

If you have any interest in alternative views please go to my home page by clicking on my name.


Thanks.

I agree that contraction and time dilation are illusions. The reason it has been measureable is that particles that are speeding take longer to decay. However, these particles' decay is measured while still in motion, so the illusion is carried on into the measurement. If, however, the particles were slowed down, they would gain a REAL time dilation due to the (negative) acceleration as described in GENERAL relativity (the second relativity put out by Einstein in 1915). It says that gravity = acceleration and that both dilate time for real. High speed only slows clocks apparently... since uniform motion is relative, both the "speeding" individual and the "stationary" individual will measure the other's clocks as being slow! See a post near the end of "the twin paradox" for more...

I thought we were all in agreement that a question was to be answered with conventional science unless it was specifically accepted by the poster to entertain crackpot science. It disgusts me when someone has a valid question, and the first responses are from our resident poorly-educated anti-relativity zealots.

- Warren

Probability,

Notwithstanding to the views on invalidity of Length Contraction or Time Dilation or both, if u realize time dilation is more real then a proven fact of velocity of light remaining constatnt in all frames of reference tells that length contraction too need to be more real. Please search for "Kinematic relativistic Blue Shift" in any authenticated site. Which will tell u how TD & LC are real and dependent on each other. All the best..

Originally posted by chroot
I thought we were all in agreement that a question was to be answered with conventional science unless it was specifically accepted by the poster to entertain crackpot science. It disgusts me when someone has a valid question, and the first responses are from our resident poorly-educated anti-relativity zealots.

- Warren

yeah, prosoothus, i thought we cleared this up.

we have to assume that people coming to this board to ask questions are asking questions about orthodox science, not prosoothus-science.

thats not cool

Chroot,
Regarding your comments about poorly educated whatever...
Suggest you review Special Relativity. The equations are symmetrical. It wouldn't be relativity if it didn't consider motion, even at relativistic speeds, to be relative. Only acceleration is absolute. Try applying relativistic equations to see what a "moving" person would see when viewing a "stationary" clock. Take 2 aspirin and call me when you get back from alpha centauri...

I am only interested in conventional science (20th century relativity), please.

Imagine one wants to simulate relativity in a computer. Now we all know how to simulate Newtonian physics in a computer, that is not too difficult. However with relativity things are not as straigtforward.

The idea is that all possible reference frames in this universe must correlate, if one wants to model a simulated universe that all reference frames build upon. The idea is to have one master reference frame, for example the center of gravity of the simulated universe. That master reference frame one can call the "actual" universe, from wich all other reference frames are calculated.

The problem with this simulation arrives if length contraction is "actual", then each possible reference frame must have a separate universe being modeled, each with its own lengths of objects. Hence my original question, is time dilation more real than length contraction.

Or is is possible to only have one actual representation of the universe from wich all possible reference frames are derived? Like in Newtonian simulations, one can have one absolute simulated universe, from wich all other relative speeds can be calcualted.

Time dilation, however can be modeled, I suppose, with an time that varies in "clock tick" length for different objects, depending on relative speed. I suppose there exist an "absolute" time for each moving object that correlate with all other objects. I am not saying that this absolute time is the same for all objects - after all time dilation exists - however what I am assuming is that all reference frames must be able to agree on a master reference frame's time for each moving object. How else can one calculate time dilation?

I find this a difficult subject, sorry if I am a bit unclear.

That's okay, the universe can be a complicated place.
The way I see it, if you want to designate one spot as the "absolute" frame of reference there will be no problem. From that position, objects will have a certain length and rate of time and these will be contracted and dilated if that object is speeding by at relativistic velocity. From a speeding rocket, however, the clock in that position will also be seen to be dilated, and an object there will be seen by the rocket to be contracted. It's all according to who is measuring. Time will slow by black holes and accelerating rockets, but every point of reference will agree on that. Ask anybody but chroot about this stuff. Lethe seems to have the best grasp, though I understand there are a few others who also have demonstrated a thorough understanding of the concepts. I tell you what, find a book that explains it and then come back and quote it to chroot, it might settle alot of dissention! (I doubt he'd listen, though);)

Originally posted by synergy
Ask anybody but chroot about this stuff. Lethe seems to have the best grasp, though I understand there are a few others who also have demonstrated a thorough understanding of the concepts. I tell you what, find a book that explains it and then come back and quote it to chroot, it might settle alot of dissention! (I doubt he'd listen, though);)
Lethe is definitely further along in his education.

What makes you think you're going to find a textbook that disagrees with me? What statement have I made that is not supported?

- Warren

chroot and lethe,

I thought we were all in agreement that a question was to be answered with conventional science unless it was specifically accepted by the poster to entertain crackpot science.

yeah, prosoothus, i thought we cleared this up.

we have to assume that people coming to this board to ask questions are asking questions about orthodox science, not prosoothus-science.

thats not cool

Are the two of you idiots??? Can't you read??? Let me show you in a larger font if you missed it in my post:

Note: My opinions are NOT the opinions of the general scientific community. Take everything I say with a grain of salt.

Tom

Originally posted by Prosoothus
Note: My opinions are NOT the opinions of the general scientific community. Take everything I say with a grain of salt.
Tom


i don t really think that s good enough. unorthodox ideas should get one thread each, and they should stay in there threads.

they should not, under any circumstances, be used to answer newbies questions. we all agreed on the crackpot thread on top that that is very repugnant.

ok?

also, please don t call me an idiot. i m not going to get into name-calling with you.

lethe,

i don t really think that s good enough. unorthodox ideas should get one thread each, and they should stay in there threads.

That's your opinion.

also, please don t call me an idiot.

Then stop acting like one. Anyone who read my first post can clearly see that I wasn't trying to deceive Probability. It's not my fault that you can't stand unconventional models. This is a forum; a place for introducing new ideas and debating them. If this bothers you, then you can go to a library and read a textbook about physics. You won't have to worry about running into any "unconventional ideas" in a textbook.

Tom

Originally posted by Prosoothus
lethe,



That's your opinion.



Then stop acting like one. Anyone who read my first post can clearly see that I wasn't trying to deceive Probability. It's not my fault that you can't stand unconventional models. This is a forum; a place for introducing new ideas and debating them. If this bothers you, then you can go to a library and read a textbook about physics. You won't have to worry about running into any "unconventional ideas" in a textbook.

Tom

you know, that s just fucked up. it s not just my opinion. we discussed this on another thread, and it is the opinion of the majority of the people on this board. go back and read how strongly some people feel about it.

i often find your callous disregard for the logic of conventional science personally insulting, but i don t degenerate into name calling. i was going to draft a nice mathematical reply to your twin paradox thread. now i think i m going to put you on my ignore list instead. fuck you.

Originally posted by Prosoothus
Then stop acting like one.
grrrrrrr

Anyone who read my first post can clearly see that I wasn't trying to deceive Probability. It's not my fault that you can't stand unconventional models.
The problem is he would probably take it as an alternate but correct theory. Being the only person who believes your theory you should not try and spread it until you can get physicsist to back you up.

This is a forum; a place for introducing new ideas and debating them. If this bothers you, then you can go to a library and read a textbook about physics. You won't have to worry about running into any "unconventional ideas" in a textbook.
Wow... you got something right! This is a forum!

However people who are ignorant and refuse to examine the existing theories should be tarred and feathered.

lethe,

i was going to draft a nice mathematical reply to your twin paradox thread.

Yeah, sure you were. You were probably waiting for the thread to reach page ten, right???

now i think i m going to put you on my ignore list instead. fuck you.

Good. Both you and chroot can put me on your ignore lists. That would really make my day.

I thought the whole point of the two threads at the top of the P+M forum was to increase the signal-to-noise ratio around here to facilitate learning.

Anyway...

Originally posted by Probability:
In regard to relativity, is length contraction only a illusion, that appears when one tries to measure length from one reference frame. In other words, no contraction actually happens, its all an illution of the measurement.


According to relativity, length contraction is real. Consider a thought experiment in which a meter stick moves past a wall. Let the meter stick have a flare at each end. A stationary observer (with respect to the wall) measures the length of the meter stick by igniting the flares simultaneously (in his frame) and noting the distance between marks on the wall. According to relativity, he will find that that distance is actually less than 1m.

Now, a macroscopic experiment such as that is not yet possible to execute, but we can do relativistic experiments in particle accelerators.


Time dilation appeares real, however, clocks actually move slower, and this has been experimentally verified in experiments such as Hafele and Keating Experiment


Yes, that is correct.


In other words is time dilation more real than length contraction?


No, if you look at the Lorentz transformation, you will see that both effects are measurable in principle.

Tom

Prosoothus
Prosoothus is offline New Post 03-03-03 05:05 PM This person is on your Ignore List.

Probability – Another example about the reality of length contraction involves the muon (http://theory.uwinnipeg.ca/mod_tech/node135.html). Search the page for “muon”, and continue reading on the next page about it. (Lots more on Google of course.) The only way the muons can reach the ground in the numbers observed is if they physically experience the atmosphere of the Earth as contracted.

zanket,

The only way the muons can reach the ground in the numbers observed is if they physically experience the atmosphere of the Earth as contracted.

No, that's not true. If time was dilated for the muons it would result in the same effect.

Tom

Originally posted by Tom2

According to relativity, length contraction is real. Consider a thought experiment in which a meter stick moves past a wall. Let the meter stick have a flare at each end. A stationary observer (with respect to the wall) measures the length of the meter stick by igniting the flares simultaneously (in his frame) and noting the distance between marks on the wall. According to relativity, he will find that that distance is actually less than 1m.


The thing that I find difficult is if you have multiple observers, each in a different reference frame with a different velocity, observing the same object. If length contraction is real, the same observed object will have different lengths! The same meter stick will physically be at different lengths! Multiple universes, one for each reference frame to resolve this?

I acutally realized something now. To the above problem I guess the solution lies in each reference frame has a different meter stick to which the measures other objects, and that meter stick differs and balances out exactly. For example if someone measures an object to be 2m, and another measures the same object to be 1.8m and a third person measures the same object to be 1.6m, then all are right, since there meter stick which each use to measure, also shrinks the same in each reference frame, ie their respective meter sticks are 1m, 0.9m and 0.8m respectively.

Originally posted by Prosoothus
No, that's not true. If time was dilated for the muons it would result in the same effect.
Time dilation and length contraction are essentially two sides of the same coin. You can't have one without the other. They are two manifestations of the same basic "effect."

- Warren

Originally posted by chroot
Time dilation and length contraction are essentially two sides of the same coin. You can't have one without the other. They are two manifestations of the same basic "effect."

True. And time isn’t dilated for the muons; your own clock always runs at 100% from your perspective.

chroot,

Time dilation and length contraction are essentially two sides of the same coin. You can't have one without the other. They are two manifestations of the same basic "effect."

You're right. The irony is that length contraction might not exist at all in relativity. Einstein could have just as easily assumed that there are two time dilations instead of one time dilation and one length contraction. However, it also turns out that the results of the Michelson-Morley experiment can be explained with only one time dilation and no length contractions. But in that case you must assume that the principle of invariance of light is incorrect.

Tom

Originally posted by Prosoothus
Einstein could have just as easily assumed that there are two time dilations instead of one time dilation and one length contraction.
Uhh... lol... no.

- Warren

chroot,

Uhh... lol... no.

I see you don't understand. As you know, the beam of light that is parallel with the axis of travel in the Michelson-Morley would take longer to reach the target than the beam of light that is perpendicular to the axis of travel of the Michelson-Morley inferometer through the aether.

Einstein assumed, from the results of the M-M experiment, that in the axis that is parallel with the motion of the apparatus both time dilation and length contraction are keeping the speed of the light constant, while on the axis that is perpendicular to the motion of the apparatus, only time dilation is required to keep the speed of the light constant. Instead of assuming that length contraction exists, Einstein could have claimed that there is a greater time dilation in the axis that is parallel to the axis of travel of the M-M inferometer, than there is in the axis that is perpendicular to the axis of travel of the M-M inferometer.

Let me show you the math:

Instead of assuming that

t=t0/(gamma)

and

l=l0*gamma

You could assume that:

t1=t0/gamma

t2=t0/gamma^2

Where t1 is the time dilation in the axis that is perpendicular to the axis of travel of the M-M inferometer, and t2 is the time dilation that is in the axis that is parallel to the axis of travel of the M-M inferometer.

As you can see, no length contraction is required.

Length contraction and time dilation are derived hand-in-hand from the assertion that the speed of light is always c. That's it. There's no more black magic.

- Warren

chroot, lethe, JR, I'm sorry - but I'm outa here. I spend my time trying to educate (and learn) but I've had it with sciforums. Try to keep up the good work - I'm too tired to do it - even as a simple engineer.

Regards,

Ron.

Originally posted by Probability
The thing that I find difficult is if you have multiple observers, each in a different reference frame with a different velocity, observing the same object. If length contraction is real, the same observed object will have different lengths! The same meter stick will physically be at different lengths!


That's right.


Multiple universes, one for each reference frame to resolve this?

Resolve 'what', exactly?

Length is not absolute. It appears that length is absolute in everyday life because the effect of length contraction is so minute at everyday speeds. There is no need for multiple universes or anything so fanciful.

Tom

Originally posted by Prosoothus
Einstein could have just as easily assumed that there are two time dilations instead of one time dilation and one length contraction.


What makes you think that Einstein 'assumed' length contraction and time dilation?

Tom

I acutally realized something now. To the above problem I guess the solution lies in each reference frame has a different meter stick to which the measures other objects, and that meter stick differs and balances out exactly.

Probability,
You're right about this, all measurements of length are comparisons of something with our yardstick. But how does the length actually change? (And it really does!) I say this, too, is a matter of timing. Consider this:
You have one yardstick that you want to measure when its moving. Its identicle to your other yardstick when at rest. Now start the one stick moving long-ways (one end first, the other end last). This fast moving yardstick will pass close to your rest stick and when it does it will be momentarily aligned with it end to end. You must have two cameras, each one snapping a shot of either end of your yarstick as the moving one passes. The trick is to time both cameras to fire simultaneously . That is, what is simultaneous to you. But simultaniety is relative- it's different for different observers. An observer traveling with the moving yardstick, for example, will see that the photos of the two yardsticks show their ends positioned "wrong" because your cameras didn't fire simultaneously. Hope I said all this right. ;)

Tom2,

What makes you think that Einstein 'assumed' length contraction and time dilation?

Because in the Michelson-Morley experiment, the two beams of light hit the target at the same time. Based on the results of the experiment, there are five models that can explain it:

A) The two beams of light reach the target at the same time, but their speed is not equal to c. Therefore:

1) Length is contracted in the axis that is parallel with the velocity vector of the M-M inferometer through the aether.

2) Time is dilated in the axis that is parallel with the velocity vector of the M-M inferometer through the aether.

B) The two beams of light reach the target at the same time AND their speed is equal to c. Therefore:

3) There are two length contractions. The length contraction in the axis that is parallel with the velocity vector is greater than the length contraction in the axis that is perpendicular to the velocity vector of the M-M inferometer through the aether.

4) There is one length contraction and one time dilation. The time dilates equally in all axes, but the length contracts only in the axis that is parallel with the velocity vector of the M-M inferometer through the aether.

5) There are two time dilations. The time dilation in the axis that is parallel with the velocity vector is greater than the time dilation in the axis that is perpendicular to the velocity vector of the M-M inferometer through the aether.

Why did Einstein choose number 4 out of these 5 options?? I don't even know why he chose option B. Maybe that's why everyone says that relativity is based on an assumption.

Tom

Oh my lord. Tom, quit your blue-sky speculation. Go look up Einstein's papers, and read them.

- Warren

Originally posted by Tom2
Resolve 'what', exactly?



Well, what I was thinking about was having superimposed matter of different lengths. However, when I wrote it I thought that one would have multiple absolute lengths of the same stick. Now I realize that the yardstick which one uses to define a unit of length also differs between different reference frames, so that the same piece of matter can have different lengths.

BTW, if there exists no absolute lengths, then how does "Le Grand Ordinateur" implement this world? In other words, how would one simulate relativity in a computer?

So basically, the meter stick doesn't contract, it only appears to because of simultanaety being disturbed. Or it contracts but simultanaety is preserved. Or a little of both. But since time measures distance and vice-versa, doesn't the point become a little moot? I'm still not convinced two objects can't be going faster than light relative to each other if we just state that we can never observe that phenomenon from the outside - our measurements are warped. If you think about time dilation and two high speed rockets, you'll realize that what may seem to us a light-year might seem to a slower-aging astronaut to only take 6 months to travel. Two rockets a light year apart would then seem to them to only take 3 months to reach each other, by their own clocks. This of course assuming constant, relativistic acceleration to skew the clocks. Who's to say that our measurements are correct, THEY say they came together faster than light speed could account for.

Originally posted by Probability
BTW, if there exists no absolute lengths, then how does "Le Grand Ordinateur" implement this world? In other words, how would one simulate relativity in a computer? Kinda off topic, but maybe they'd just simulate everything from the obeserver's perspective. No need to simulate if it's not being seen.

Prosoothus,

Forget the Michelson Morley experiment for a minute. That is not how Einstein developed SR at all. I know that I have linked you to On the Electrodynamics of Moving Bodies at least a dozen times in the past, and you seemed to be allergic to reading it.

Here it is again:
http://www.fourmilab.ch/etexts/einstein/specrel/www

The development of SR has nothing to do with the M-M experiment. It has to do with Maxwell's Conundrum, namely:

If you were traveling at the speed of light, could you see your own reflection?

Furthermore, the Galilean transformation, which leaves the laws of mechanics invariant, does not leave the laws of electrodynamics invariant. This led physicists to ponder one of three options:

1. The laws of electrodynamics are incorrect.
2. There are two coordinate transformations intrinsic to nature, one for mechanics and one for EM.
3. The Galilean transformation is incorrect.

The first two options are positively repugnant. #1 because of the close agreement of EM with experiment, and #2 because it would imply that the universe could somehow "know" whether you are doing an experiment in mechanics or EM.

That leaves only option 3, and that is what Einstein chose. In doing so, he assumed two things:

1. The laws of physics (not just mechanics) are the same in every reference frame.
2. The speed of light is independent of the speed of the source.

From that, he derived (not assumed) length contraction and time dilation.

Tom

Tom2,

Forget the Michelson Morley experiment for a minute. That is not how Einstein developed SR at all. I know that I have linked you to On the Electrodynamics of Moving Bodies at least a dozen times in the past, and you seemed to be allergic to reading it.

This is the first time you posted it here on sciforums, that I can recall. I just downloaded it, and I'll take a look at it later.

1. The laws of physics (not just mechanics) are the same in every reference frame.
2. The speed of light is independent of the speed of the source.

From that, he derived (not assumed) length contraction and time dilation.

I'm saying that instead of deriving length contraction and time dilation from his assumptions, he could have derived two length contractions with no time dilation, or two time dilations with no length contraction. All three of these models can equally explain the principle of invariance of light.

Originally posted by Prosoothus
I'm saying that instead of deriving length contraction and time dilation from his assumptions, he could have derived two length contractions with no time dilation, or two time dilations with no length contraction. All three of these models can equally explain the principle of invariance of light.

Nope.

There are two options from which to choose:

1. There is not an ultimate speed in the universe.
2. There is an ultimate speed in the universe.

Developing physics from option 1 will lead you uniquely to the Galilean transformation. Developing physics from option 2 will lead you uniquely to the Lorentz transformation.

Any third (or fourth or fifth...) transformation is the result of a mathematical error.

Tom

Tom,

Developing physics from option 2 will lead you uniquely to the Lorentz transformation.

But the Lorentz transformations don't have to represent time dilation AND length contraction, they can represent two time dilations, or two length contractions. Let me show you:

In relativity:

t=t0/gamma
L=L0*gamma

c=v1 * 1/gamma(t)
c=v2 * 1/gamma(t) * gamma(L)

In the two time dilation model:

t1=t0/gamma
t2=t0/gamma

c=v1 * 1/gamma(t1)
c=v2 * 1/gamma(t1) * 1/gamma(t2)

In the two length contraction model:

L1=L0*gamma
L2=L0*gamma

c=v1 * gamma(L1)
c=v2 * gamma(L2)

__________________________________________________

To see what v1 and v2 represent, see attachment.

gamma=sqrt(1-v^2/c^2)

__________________________________________________

As you can see, all three models give the same results(c), and they can all equally explain the principle of invariance of light.

I hope that you understand what I'm saying so that I won't have to show you step by step how I obtained these results (it's a pain in the ass to post formulas on sciforums).

Originally posted by Prosoothus
But the Lorentz transformations don't have to represent time dilation AND length contraction,


Yes they do.


In relativity:

t=t0/gamma
L=L0*gamma


That is not the Lorentz transformation.

The LT, which is (in 1D):

x'=(gamma)(x-vt)
t'=(gamma)(t-vx/c^2)

is necessarily implied by the postulates of relativity. Furthermore, length contraction and time dilation are necessarily implied by the LT. It really doesn't matter how you obtained those results, because I know without seeing the derivation that the starting relations will not leave Maxwell's equations unchanged under a coordinate transformation.

Tom

Tom2,

That is not the Lorentz transformation.

The formulas I provided are the Lorentz transformations for the roundtrip speed of light. The formulas you provided are the Lorentz boost transformations for the one-way speed of light.

You can replace the length contraction in the Lorentz transformations with another time dilation, and get the same results.

Originally posted by Prosoothus
The formulas I provided are the Lorentz transformations for the roundtrip speed of light. The formulas you provided are the Lorentz boost transformations for the one-way speed of light.


No, what I posted is the Lorentz transformation, and what you posted is a special case of the Lorentz transformation.


You can replace the length contraction in the Lorentz transformations with another time dilation, and get the same results.

No, you will not get the same results. If you have a transformation that leaves only spatial intervals (or only time intervals) unchanged, you will not have a coordinate transformation that leaves Maxwell's equations invariant.

Tom

Tom2,

No, you will not get the same results. If you have a transformation that leaves only spatial intervals (or only time intervals) unchanged, you will not have a coordinate transformation that leaves Maxwell's equations invariant.

I'm not suggesting having only one time dilation, or one length contraction, I'm suggesting replacing the time dilation with another length contraction or replacing the length contraction with another time dilation.

I'll have to look into the Maxwell's equations invariant that you are referring to. My assumptions are only derived from my knowledge of the Michelson-Morley experiment.

Originally posted by Prosoothus
I'm not suggesting having only one time dilation, or one length contraction, I'm suggesting replacing the time dilation with another length contraction or replacing the length contraction with another time dilation.


OK, but my objection still stands.


I'll have to look into the Maxwell's equations invariant that you are referring to. My assumptions are only derived from my knowledge of the Michelson-Morley experiment.

Yes, please do look into it. The coupling of spatial and temporal intervals is necessarily implied by the postulates of relativity, and it is developed from scratch in Einstein's paper. If you try to devise a coordinate transformation without both of them, it will not leave the equations of physics unchanged from one frame to the next.

Tom