- Causality 1 2 5 – Time Manipulating & Puzzle Game Show
- Causality 1 2 5 – Time Manipulating & Puzzle Game Board
2.1 Overview
In the lecture this week, we discuss the concept of causality and particularly focus on distinguishing between observational and experimental strategies for making causal claims from quantitative data. We will introduce the 'potential outcomes' framework for thinking about causal inference, and describe the 'fundamental problem of causal inference'. After describing why randomized experiments are considered the gold standard for estimating causal effects, we will outline different strategies for using observational data to answer causal questions. The example we will use throughout the lecture will be about the effects of health insurance on self-assessed measures of health.
The stickmen are at school now and your job is to inflict death upon them without being seen by the rest of the stickmen or else it's game over! Click items in the right order to cause a series of events that'll lead to their certain death! Do you think you can kill all sticks before the time ends? Play this funny challenging new free online flash point and click puzzle stick game here in. The controls in Causality are pretty straightforward and easy to understand. To make time move forward, just drag your finger down on the left hand side of the screen. To reverse time, drag upwards. This is a question that changes from philosophy to psychology to law to statistics. Here is the statistical definitions: 1. Temporal Precedence 3.
In seminar this week, we will cover the following topics:
- Folders and files
- Loading data using
read.csv()
- Missing data
We will also spend time thinking about the assumptions required to make causal claims from analyses of observational data.
Photoline 21 5000. Before coming to the seminar
- Please read chapter 2, 'Causality', in Quantitative Social Science: An Introduction
2.2 Seminar
Does a state's use of indiscriminate violence incite insurgent attacks? In today's seminar, we will analyse the relationship between indiscriminate violence and insurgent attacks using data about Russian artillery fire in Chechnya from 2000 to 2005. The data in this exercise is based on Lyall, J. 2009. 'Does Indiscriminate Violence Incite Insurgent Attacks?: Evidence from Chechnya.'. You can download the data by clicking on the link above.
2.2.1 Preliminaries
Files and folders
It is sensible when you start any data analysis project to make sure your computer is set up in an efficient way. Last week, you should have created a script with the name seminar1.R
. Hopefully, you will have saved this somewhere sensible! Our suggestion is that you create a folder on your computer with the name PUBL0055
which you can save all your scripts in throughout the course. If you didn't set up a folder like that on your computer, do so now.
Once you have a folder with the name PUBL0055
, make sure your seminar1.R
file is saved within it. Now create a new R script, and save that in your folder with the name seminar2.R
. Use this script to record all the code that you are working on this week. Each week you should start a new script and save it in this folder.
This week we will also be loading some data into R for analysis. Let's add a subfolder into your main PUBL0055
folder, and give it the name data
. The contents of your folder should now look something like this if you are working on a Mac:
And like this if you are working on a PC:
Working directories
If you open Rstudio, the first thing you should include at the beginning of your script is code to set the 'working directory'. This tells R where to look for scripts and data when you run your code. If you are working on a Mac and have saved your PUBL0055
folder on the desktop of your computer, for example, then you can tell R to work from that folder by running the following code:
If you were working on a Windows PC, you might use:
You can adjust the code above to direct R to look to wherever the relevant folder is stored on your computer. For instance, if your PUBL0055
folder is kept inside your UCL
folder, you could use setwd('~/Desktop/UCL/PUBL0055')
, and so on.
Loading data
Once you have downloaded the data, put the .csv
into the data
folder that you created earlier in the seminar, and then load the R script that you are using for this week. Now load the data using the read.csv()
function:
This function loads the data stored in 'chechen.csv'
into R, and then we are using the assignment operator - <-
- that we learned last week to create a new object. Once the data is loaded, you should see the chechen
object appear in the Environment
pane of Rstudio:
As you can see from the output above, this data has 318 rows (units), and 6 columns (variables). We will describe these below.
2.2.2 Indiscriminate Violence and Insurgency
A common view is that indiscriminate violence on behalf of the state can lead to increases in insurgent attacks by creating more cooperative relationships between citizens and insurgents. In particular, there is a large literature that relies on case-study evidence to suggests that when a state collectively targets a noncombatant population, this can provoke much greater levels of insurgent violence. An empirical difficulty in answering this question is that places that are subject to state-sponsored indiscriminate violence are likely to differ in many ways from places that are not subject to such violence.
In an attempt to overcome this problem (which is an example of the confounding bias that we discussed in the lecture), Lyall collected data on 159 events in which Russian artillery shelled a village. For each such event the data records the village where the shelling took place and whether it was in Groznyy (Chechnya's capital), how many people were killed, and the number of insurgent attacks 90 days before and 90 days after the date of the event. We then augment this data by observing the same information for a set of demographically and geographically similar villages that were not shelled during the same time periods. The main explanatory variable used in Lyall's analysis is therefore whether or not a village was struck by artillery fire by Russian forces – what Lyall interprets as an instance of indiscriminate violence.
The names and descriptions of variables in the data file chechen.csv
are
Name | Description |
---|---|
village | Name of village |
groznyy | Variable indicating whether a village is inGroznyy (1) or not (0) |
fire | Whether Russians struck a village with artillery fire(1) or not (0) |
deaths | Estimated number of individuals killed during Russian artillery fireor NA if not fired on |
preattack | The number of insurgent attacks in the 90 days before being fired on |
postattack | The number of insurgent attacks in the 90 days after being fired on |
Note that the same village may appear in the dataset several times as shelled and/or not shelled because Russian attacks occurred at different times and locations.
To get a sense of what this data.frame
contains, use the functions below:
head(chechen)
– shows the first six (by default) rows of the datastr(chechen)
– shows the 'structure' of the dataView(chechen)
– opens a spreadsheet-style viewer of the data
Question 1
For this question, we will learn to use the table()
function, which provides counts of the number of observations in our data that take distinct values for a given variable or pair of variables.
Causality 1 2 5 – Time Manipulating & Puzzle Game Show
The table function can be used to provide the number of respondents that fall into a given category for a single variable. To do this, simply provide the name of the variable of interest as the first argument to the table function:
Or it can be used to provide the number of respondents that fall into the combination of categories of two different variables. To do this, provide both variable names to the table function:
Look at the help file for this function for more information (?help
).
Use this function to answer the following questions:
- How many of villages were shelled by Russians? How many were not?
- How many villages were located in Groznyy? How many were not?
- Of the villages that were shelled by the Russians, how many were located in Groznyy?
- Of the villages that were not shelled by the Russians, how many were located in Groznyy?
1
Using the table function shows an equal number of shelled and not-shelled villages.
2
298 villages were located outside of Groznyy and 20 were located within Groznyy.
3 and 4
When applied to two variables, the counts for the first variable are indicated by the rows of the resulting matrix, and the counts for the second variable are indicated by the columns. So, in this case, of the 159 villages that were shelled by the Russians (second row), 152 were located outside of Groznyy and 7 were located in Groznyy. By contrast, 146 of the non-shelled villages were outside of Groznyy and 13 were located within Groznyy.
Question 2
In this question, we will investigate whether artillery attacks on villages in Groznyy were more lethal than attacks on villages outside of Groznyy. Note that for this question, you will have to use the mean function to calculate the mean of various subsets of the data. However, you will find that if you simply apply the mean function to the chechen$deaths
variable it does not produce the desired result:
R returns NA
because for some villages (those that were not subject to Russian attacks) we have no information on the number of deaths. In short, NA
is the R value for missing data. We can tell the mean()
function to estimate the mean only for those villages that we do have data for, and ignore the other villages by setting an additional argument for the mean function: mean(dataset_name$var_name, na.rm = TRUE).
Causality 1 2 5 – Time Manipulating & Puzzle Game Board
Conduct comparisons between Groznyy and non-Groznyy observations in terms of the mean level of deaths
. What do you find?
Artillery attacks killed on average 3.71 people in Groznyy but only 1.57 people from villages outside Grozny.
Question 3
Compare the average (mean) number of insurgent attacks for shelled villages and non-shelled villages using the postattack
variable. Would you conclude that indiscriminate violence reduces insurgent attacks? Why or why not?
The estimated difference in means reveals that while shelled villages see slightly fewer insurgent attacks than non-shelled villages, this difference is not large. The average number of insurgent attacks is 1.5 for observations of villages that were shelled vs 2.05 for the others. By itself, this comparison suggests that indiscriminate violence may slightly reduce insurgent attacks though the effect is not large.
Question 4
In the question above, we used the variable fire
to calculate the difference in means for the number of insurgent attacks in villages that were and were not attacked by the Russians. Is this difference in means likely to represent the causal effect of indiscriminate violence? Why or why not? Which assumptions are required to give this difference a causal interpretation? Give some thought to these questions, and write down your reasoning before reading the answer below.
Recall our discussion of confounding from the lecture. There we argued that making causal statements on the basis of evidence drawn from observational studies is difficult because confounding differences between treatment and control observations mean that the difference in means can result in a biased estimate of the average treatment effect. In essence, to make a causal statement on the basis of observational evidence of this type, one needs to assume that there are no confounding differences between treatment and control groups. That is, the only way in which these groups differ on average is with respect to whether or not they were subject to indiscriminate violence.
In this case, are there any plausible sources of confounding? Put another way, are the places that experienced Russian artillery fire likely to be similar on all characteristics other than their receipt of the 'treatment' of being shelled? At face value this seems unlikely, as there are many dimensions on which these groups of villages may differ. Unfortunately, it is not possible for us to assess the extent of these possible differences here, as we have not provided data on other characteristics of the villages. Although the set of non-shelled villages was selected by the researcher in a way to make them as demographically and geographically similar as possible to the set of shelled villages, we should remember that it is difficult to rule out the possibility of confounding bias in observational data of this sort.
Question 5
Considering only the pre-shelling periods, what is the difference between the average number of insurgent attacks for observations describing a shelled village and observations that do not? What does this suggest to you about the validity of comparison used for question 2?
Reveal answerDespite the fact that we cannot rule out the possibility of confounding, the evidence here is encouraging. In these periods, the average number of insurgency attacks was similar for villages that were later shelled and villages that were not shelled. If systematic differences between the two groups were confounding the treatment effects estimated in question 2, we would also expect there to be differences in the number of insurgency attacks in the period before the Russian shelling. As a consequence, although this is an observational study where artillery fire is not formally randomized, the similarity of these averages increases the credibility of the comparison of insurgency attacks between villages hit by Russian fire and those not.
Question 6
Create a new variable called diffattack
by calculating the difference in the number of insurgent attacks in the before and after periods using the following code:
Here we are using the assignment operator to create a new variable in our chechen
data. Positive values of this variable would indicate that the number of insurgent attacks increased after Russian shelling, and negative values indicate that the number of insurgent attacks decreased after shelling.
Using this variable, assess whether, for the villages that were shelled, the number of insurgent attacks increased after the villages were fired upon. What is the substantive interpretation of this result? Does this represent the causal effect of shelling on insurgent attacks? Why or why not?
Reveal answerIn villages that experienced shelling, the average number of insurgent attacks decreased by -0.62 from the period before to the period after the shelling. This is an example of a 'before and after' design which examines how the outcome variable changes from the pretreatment period to the posttreatment period for the same set of units. This estimate can only be considered a causal effect if we are willing to assume that – in the absence of the shelling – there would have been no change in the average number of insurgent attacks between these two time periods.
Question 7
Compute the mean difference in the diffattack
variable between shelled and non-shelled villages. Does this analysis support the claim that indiscriminate violence reduces insurgency attacks? Is the validity of this analysis improved over the analyses you conducted in the previous questions? Why or why not? Specifically, explain what additional factor this analysis addresses when compared to the analyses conducted in the previous questions.
In the villages that did not experience shelling, the average number of insurgent attacks decreased by -0.1 in the period after shelling. Compare this to the same before-and-after difference for shelled villages, where insurgent attacks decreased by -0.62. In other words, the decrease in insurgent attacks was larger in shelled villages than in non-shelled villages. The results support the conclusion that indiscriminate violence reduces insurgent attacks.
This analysis is an example of a 'difference in differences' design. What are the two differences we are comparing here? We have the difference in pre-and-post shelling insurgent attacks in shelled villages, and we are comparing that to the same difference in non-shelled villages. The key advantage of this analysis is that it takes into account any common time trend that exists for the two types of observations. If we assume that the trend in numbers of attacks pre- and post-shelling among villages that were not in fact shelled is what we would have observed in shelled villages had they not been shelled, then the difference in the differences between pre- and post-shelling attacks between the two village types can be attributed to the Russian artillery fire.
2.3 Homework
2.3.1 Demographic Change and Exclusionary Attitudes
This week's homework uses data based on: Enos, R. D. 2014. 'Causal Effect of Intergroup Contact on Exclusionary Attitudes.' Proceedings of the National Academy of Sciences 111(10): 3699–3704. You can download this data from the link at the top of the page. Once you have done so, store it in the data
subfolder you created earlier. Then start a new R script which you should save as homework2.R
.
Enos conducted a randomized field experiment assessing the extent to which individuals living in suburban communities around Boston, Massachusetts, were affected by exposure to demographic change.
Subjects in the experiment were individuals riding on the commuter train line and were overwhelmingly white. Every morning, multiple trains pass through various stations in suburban communities that were used for this study. For pairs of trains leaving the same station at roughly the same time, one was randomly assigned to receive the treatment and one was designated as a control. By doing so all the benefits of randomization apply for this dataset.
The treatment in this experiment was the presence of two native Spanish-speaking ‘confederates' (a term used in experiments to indicate that these individuals worked for the researcher, unbeknownst to the subjects) on the platform each morning prior to the train's arrival. The presence of these confederates, who would appear as Hispanic foreigners to the subjects, was intended to simulate the kind of demographic change anticipated for the United States in coming years. For those individuals in the control group, no such confederates were present on the platform. The treatment was administered for 10 days. Participants were asked questions related to immigration policy both before the experiment started and after the experiment had ended. The names and descriptions of variables in the data set boston.csv
are:
Name | Description |
---|---|
age | Age of individual at time of experiment |
male | Sex of individual, male (1) or female (0) |
income | Income group in dollars (not exact income) |
white | Indicator variable for whether individualidentifies as white (1) or not (0) |
college | Indicator variable for whether individualattended college (1) or not (0) |
usborn | Indicator variable for whether individual isborn in the US (1) or not (0) |
treatment | Indicator variable for whether an individualwas treated (1) or not (0) |
ideology | Self-placement on ideology spectrum from Very Liberal (1)through Moderate (3) to Very Conservative (5) |
numberim.pre | Policy opinion on question about increasing the numberimmigrants allowed in the country from Increased (1) to Decreased (5) |
numberim.post | Same question as above, asked later |
remain.pre | Policy opinion on question about allowing the children ofundocumented immigrants to remain in the country fromAllow (1) to Not Allow (5) |
remain.post | Same question as above, asked later |
english.pre | Policy opinion on question about passing a law establishingEnglish as the official language from Not Favor (1) to Favor (5) |
english.post | Same question as above, asked later |
Question 1
The benefit of randomly assigning individuals to the treatment or control groups is that the two groups should be similar, on average, in terms of their other characteristics, or 'covariates'. This is referred to as 'covariate balance.'
Use the mean function to determine whether the treatment and control groups are balanced with respect to the age (age
) and income (income
) variables. Also, compare the proportion of males (male
) in the treatment and control groups. Interpret these numbers.
(Hint: to calculate the proportion of observations with a given attribute on a binary variable, you can just use mean(data_frame_name$variable_name)
.)
Question 2
Individuals in the experiment were asked 'Do you think the number of immigrants from Mexico who are permitted to come to the United States to live should be increased, left the same, or decreased?' The response to this after the experiment is in the variable numberim.post
. The variable is coded on a 1 – 5 scale. Responses with values of 1 are inclusionary (‘pro-immigration') and responses with values of 5 are exclusionary (‘anti-immigration'). Calculate the mean value of this variable for the treatment and control groups. What is the difference in means? What does the result suggest about the effects of intergroup contact on exclusionary attitudes?
Question 3
Does having attended college influence the effect of being exposed to ‘outsiders' on exclusionary attitudes? Another way to ask the same question is this: is there evidence of a differential impact of treatment, conditional on attending college versus not attending college? Calculate the difference in means between treatment and control observations amongst those who attended college and those who did not. Interpret your results.
(Hint: You may want to subset the data using more than one logical condition here. For example, if I wanted to subset the data to include only the observations which were treated and went to college, I could use boston$numberim.post[boston$treatment 1 & boston$college 1]
.)
Question 4
Calculate the number of observations used to calculate each of the mean outcome values you used in the answer for question 3. What does this suggest about the reliability of the conclusions you drew from that analysis?
Causality is the relationship between causes and effects.[1][2] The notion of causality does not have an agreed upon definition in the sciences. Causality is also a topic studied from the perspectives of philosophy and statistics. From the perspective of physics, it is generally believed that causality cannot occur between an effect and an event that is not in the back (past) light cone of said effect. Similarly, a cause could not have an effect outside its front (future) light cone.
Subjects in the experiment were individuals riding on the commuter train line and were overwhelmingly white. Every morning, multiple trains pass through various stations in suburban communities that were used for this study. For pairs of trains leaving the same station at roughly the same time, one was randomly assigned to receive the treatment and one was designated as a control. By doing so all the benefits of randomization apply for this dataset.
The treatment in this experiment was the presence of two native Spanish-speaking ‘confederates' (a term used in experiments to indicate that these individuals worked for the researcher, unbeknownst to the subjects) on the platform each morning prior to the train's arrival. The presence of these confederates, who would appear as Hispanic foreigners to the subjects, was intended to simulate the kind of demographic change anticipated for the United States in coming years. For those individuals in the control group, no such confederates were present on the platform. The treatment was administered for 10 days. Participants were asked questions related to immigration policy both before the experiment started and after the experiment had ended. The names and descriptions of variables in the data set boston.csv
are:
Name | Description |
---|---|
age | Age of individual at time of experiment |
male | Sex of individual, male (1) or female (0) |
income | Income group in dollars (not exact income) |
white | Indicator variable for whether individualidentifies as white (1) or not (0) |
college | Indicator variable for whether individualattended college (1) or not (0) |
usborn | Indicator variable for whether individual isborn in the US (1) or not (0) |
treatment | Indicator variable for whether an individualwas treated (1) or not (0) |
ideology | Self-placement on ideology spectrum from Very Liberal (1)through Moderate (3) to Very Conservative (5) |
numberim.pre | Policy opinion on question about increasing the numberimmigrants allowed in the country from Increased (1) to Decreased (5) |
numberim.post | Same question as above, asked later |
remain.pre | Policy opinion on question about allowing the children ofundocumented immigrants to remain in the country fromAllow (1) to Not Allow (5) |
remain.post | Same question as above, asked later |
english.pre | Policy opinion on question about passing a law establishingEnglish as the official language from Not Favor (1) to Favor (5) |
english.post | Same question as above, asked later |
Question 1
The benefit of randomly assigning individuals to the treatment or control groups is that the two groups should be similar, on average, in terms of their other characteristics, or 'covariates'. This is referred to as 'covariate balance.'
Use the mean function to determine whether the treatment and control groups are balanced with respect to the age (age
) and income (income
) variables. Also, compare the proportion of males (male
) in the treatment and control groups. Interpret these numbers.
(Hint: to calculate the proportion of observations with a given attribute on a binary variable, you can just use mean(data_frame_name$variable_name)
.)
Question 2
Individuals in the experiment were asked 'Do you think the number of immigrants from Mexico who are permitted to come to the United States to live should be increased, left the same, or decreased?' The response to this after the experiment is in the variable numberim.post
. The variable is coded on a 1 – 5 scale. Responses with values of 1 are inclusionary (‘pro-immigration') and responses with values of 5 are exclusionary (‘anti-immigration'). Calculate the mean value of this variable for the treatment and control groups. What is the difference in means? What does the result suggest about the effects of intergroup contact on exclusionary attitudes?
Question 3
Does having attended college influence the effect of being exposed to ‘outsiders' on exclusionary attitudes? Another way to ask the same question is this: is there evidence of a differential impact of treatment, conditional on attending college versus not attending college? Calculate the difference in means between treatment and control observations amongst those who attended college and those who did not. Interpret your results.
(Hint: You may want to subset the data using more than one logical condition here. For example, if I wanted to subset the data to include only the observations which were treated and went to college, I could use boston$numberim.post[boston$treatment 1 & boston$college 1]
.)
Question 4
Calculate the number of observations used to calculate each of the mean outcome values you used in the answer for question 3. What does this suggest about the reliability of the conclusions you drew from that analysis?
Causality is the relationship between causes and effects.[1][2] The notion of causality does not have an agreed upon definition in the sciences. Causality is also a topic studied from the perspectives of philosophy and statistics. From the perspective of physics, it is generally believed that causality cannot occur between an effect and an event that is not in the back (past) light cone of said effect. Similarly, a cause could not have an effect outside its front (future) light cone.
Causality in physics[edit]
In classical physics, an effect cannot occur before its cause. In Einstein's theory of special relativity, causality means that an effect can not occur from a cause that is not in the back (past) light cone of that event. Similarly, a cause cannot have an effect outside its front (future) light cone. These restrictions are consistent with the grounded belief (or assumption) that causal influences cannot travel faster than the speed of light and/or backwards in time. In quantum field theory, observables of events with a spacelike relationship, 'elsewhere', have to commute, so the order of observations or measurements of such observables do not impact each other.
Causality in this context should not be confused with Newton's second law, which is related to the conservation of momentum, and is a consequence of the spatial homogeneity of physical laws. The word causality in this context means that all effects must have specific causes.[3] As discussed below, this is a principle that is violated in some theories of modern physics.
Records 1 5 8 – innovative personal database pdf. Another requirement, at least valid at the level of human experience, is that cause and effect be mediated across space and time (requirement of contiguity). This requirement has been very influential in the past, in the first place as a result of direct observation of causal processes (like pushing a cart), in the second place as a problematic aspect of Newton's theory of gravitation (attraction of the earth by the sun by means of action at a distance) replacing mechanistic proposals like Descartes' vortex theory; in the third place as an incentive to develop dynamic field theories (e.g., Maxwell's electrodynamics and Einstein's general theory of relativity) restoring contiguity in the transmission of influences in a more successful way than in Descartes' theory.
The empiricists' aversion to metaphysical explanations (like Descartes' vortex theory) lends heavy influence against the idea of the importance of causality. Causality has accordingly sometimes been downplayed (e.g., Newton's 'Hypotheses non fingo'). According to Ernst Mach[4] the notion of force in Newton's second law was pleonastic, tautological and superfluous. Indeed, it is possible to consider the Newtonian equations of motion of the gravitational interaction of two bodies,
- m1d2r1dt2=−m1m2G(r1−r2)|r1−r2|3;m2d2r2dt2=−m1m2G(r2−r1)|r2−r1|3,{displaystyle m_{1}{frac {d^{2}{mathbf {r} }_{1}}{dt^{2}}}=-{frac {m_{1}m_{2}G({mathbf {r} }_{1}-{mathbf {r} }_{2})}{|{mathbf {r} }_{1}-{mathbf {r} }_{2}|^{3}}};;m_{2}{frac {d^{2}{mathbf {r} }_{2}}{dt^{2}}}=-{frac {m_{1}m_{2}G({mathbf {r} }_{2}-{mathbf {r} }_{1})}{|{mathbf {r} }_{2}-{mathbf {r} }_{1}|^{3}}},}
as two coupled equations describing the positions r1(t){displaystyle scriptstyle {mathbf {r} }_{1}(t)} and r2(t){displaystyle scriptstyle {mathbf {r} }_{2}(t)} of the two bodies, without interpreting the right hand sides of these equations as forces; the equations just describe a process of interaction, without any necessity to interpret one body as the cause of the motion of the other, and allow one to predict the states of the system at later (as well as earlier) times.
The ordinary situations in which humans singled out some factors in a physical interaction as being prior and therefore supplying the 'because' of the interaction were often ones in which humans decided to bring about some state of affairs and directed their energies to producing that state of affairs—a process that took time to establish and left a new state of affairs that persisted beyond the time of activity of the actor. It would be difficult and pointless, however, to explain the motions of binary stars with respect to each other in that way.
The possibility of such a time-independent view is at the basis of the deductive-nomological (D-N) view of scientific explanation, considering an event to be explained if it can be subsumed under a scientific law. In the D-N view, a physical state is considered to be explained if, applying the (deterministic) law, it can be derived from given initial conditions. (Such initial conditions could include the momenta and distance from each other of binary stars at any given moment.) Such 'explanation by determinism' is sometimes referred to as causal determinism. A disadvantage of the D-N view is that causality and determinism are more or less identified. Thus, in classical physics, it was assumed that all events are caused by earlier ones according to the known laws of nature, culminating in Pierre-Simon Laplace's claim that if the current state of the world were known with precision, it could be computed for any time in the future or the past (see Laplace's demon). However, this is usually referred to as Laplace determinism (rather than `Laplace causality') because it hinges on determinism in mathematical models as dealt with in the mathematical Cauchy problem. Confusion of causality and determinism is particularly acute in quantum mechanics, this theory being acausal in the sense that it is unable in many cases to identify the causes of actually observed effects or to predict the effects of identical causes, but arguably deterministic in some interpretations (e.g. if the wave function is presumed not to actually collapse as in the many-worlds interpretation, or if its collapse is due to hidden variables, or simply redefining determinism as meaning that probabilities rather than specific effects are determined).
In modern physics, the notion of causality had to be clarified. The insights of the theory of special relativity confirmed the assumption of causality, but they made the meaning of the word 'simultaneous' observer-dependent.[5] Consequently, the relativistic principle of causality says that the cause must precede its effect according to all inertial observers. This is equivalent to the statement that the cause and its effect are separated by a timelike interval, and the effect belongs to the future of its cause. If a timelike interval separates the two events, this means that a signal could be sent between them at less than the speed of light. On the other hand, if signals could move faster than the speed of light, this would violate causality because it would allow a signal to be sent across spacelike intervals, which means that at least to some inertial observers the signal would travel backward in time. For this reason, special relativity does not allow communication faster than the speed of light.
In the theory of general relativity, the concept of causality is generalized in the most straightforward way: the effect must belong to the future light cone of its cause, even if the spacetime is curved. New subtleties must be taken into account when we investigate causality in quantum mechanics and relativistic quantum field theory in particular. In quantum field theory, causality is closely related to the principle of locality. However, the principle of locality is disputed: whether it strictly holds depends on the interpretation of quantum mechanics chosen, especially for experiments involving quantum entanglement that satisfy Bell's Theorem.
Despite these subtleties, causality remains an important and valid concept in physical theories. For example, the notion that events can be ordered into causes and effects is necessary to prevent (or at least outline) causality paradoxes such as the grandfather paradox, which asks what happens if a time-traveler kills his own grandfather before he ever meets the time-traveler's grandmother. See also Chronology protection conjecture.
Distributed causality[edit]
Theories in physics like the butterfly effect from chaos theory open up the possibility of a type of distributed parameter systems in causality.[citation needed] The butterfly effect theory proposes:
'Small variations of the initial condition of a nonlinear dynamical system may produce large variations in the long term behavior of the system.'
This opens up the opportunity to understand a distributed causality.
A related way to interpret the butterfly effect is to see it as highlighting the difference between the application of the notion of causality in physics and a more general use of causality as represented by Mackie's INUS conditions. In classical (Newtonian) physics, in general, only those conditions are (explicitly) taken into account, that are both necessary and sufficient. For instance, when a massive sphere is caused to roll down a slope starting from a point of unstable equilibrium, then its velocity is assumed to be caused by the force of gravity accelerating it; the small push that was needed to set it into motion is not explicitly dealt with as a cause. In order to be a physical cause there must be a certain proportionality with the ensuing effect. A distinction is drawn between triggering and causation of the ball's motion.[citation needed] By the same token the butterfly can be seen as triggering a tornado, its cause being assumed to be seated in the atmospherical energies already present beforehand, rather than in the movements of a butterfly.[citation needed]
Causal dynamical triangulation[edit]
Causal dynamical triangulation (abbreviated as 'CDT') invented by Renate Loll, Jan Ambjørn and Jerzy Jurkiewicz, and popularized by Fotini Markopoulou and Lee Smolin, is an approach to quantum gravity that like loop quantum gravity is background independent. This means that it does not assume any pre-existing arena (dimensional space), but rather attempts to show how the spacetime fabric itself evolves. The Loops '05 conference, hosted by many loop quantum gravity theorists, included several presentations which discussed CDT in great depth, and revealed it to be a pivotal insight for theorists. It has sparked considerable interest as it appears to have a good semi-classical description. At large scales, it re-creates the familiar 4-dimensional spacetime, but it shows spacetime to be 2-d near the Planck scale, and reveals a fractal structure on slices of constant time. Using a structure called a simplex, it divides spacetime into tiny triangular sections. A simplex is the generalized form of a triangle, in various dimensions. A 3-simplex is usually called a tetrahedron, and the 4-simplex, which is the basic building block in this theory, is also known as the pentatope, or pentachoron. Each simplex is geometrically flat, but simplices can be 'glued' together in a variety of ways to create curved spacetimes. Where previous attempts at triangulation of quantum spaces have produced jumbled universes with far too many dimensions, or minimal universes with too few, CDT avoids this problem by allowing only those configurations where cause precedes any effect. In other words, the timelines of all joined edges of simplices must agree.
Thus, maybe, causality lies in the foundation of the spacetime geometry.
Causal sets[edit]
In causal set theory, causality takes an even more prominent place. The basis for this approach to quantum gravity is in a theorem by David Malament. This theorem states that the causal structure of a spacetime suffices to reconstruct its conformal class. So knowing the conformal factor and the causal structure is enough to know the spacetime. Based on this, Rafael Sorkin proposed the idea of Causal Set Theory, which is a fundamentally discrete approach to quantum gravity. The causal structure of the spacetime is represented as a Poset, while the conformal factor can be reconstructed by identifying each poset element with a unit volume.
See also[edit]
- Causality – how one process influences another (general)
- Retrocausality – A thought experiment in philosophy of science based on elements of physics, addressing whether the future can affect the present and whether the present can affect the past
- Synchronicity – Concept, first introduced by analytical psychologist Carl Jung, which holds that events are 'meaningful coincidences'
- Wheeler–Feynman time-symmetric theory for electrodynamics – interpretation of electrodynamics
References[edit]
- ^Green, Celia (2003). The Lost Cause: Causation and the Mind–Body Problem. Oxford: Oxford Forum. ISBN0-9536772-1-4. Includes three chapters on causality at the microlevel in physics.
- ^Bunge, Mario (1959). Causality: the place of the causal principle in modern science. Cambridge: Harvard University Press.
- ^'Causality.' Cambridge English Dictionary. Accessed November 18, 2018. https://dictionary.cambridge.org/us/dictionary/english/causality
- ^Ernst Mach, Die Mechanik in ihrer Entwicklung, Historisch-kritisch dargestellt, Akademie-Verlag, Berlin, 1988, section 2.7.
- ^A. Einstein, 'Zur Elektrodynamik bewegter Koerper', Annalen der Physik17, 891–921 (1905).
Further reading[edit]
- Bohm, David. (2005). Causality and Chance in Modern Physics. London: Taylor and Francis.
- Miguel Espinoza, Théorie du déterminisme causal, L'Harmattan, Paris, 2006. ISBN2-296-01198-5.
External links[edit]
- Caltech Tutorial on Relativity — A nice discussion of how observers moving relatively to each other see different slices of time.
- Faster-than-c signals, special relativity, and causality. This article explains that faster than light signals do not necessarily lead to a violation of causality.
- by John G. Cramer:
- EPR Communication: Signals from the Future? 'In this column I want to tell you about this causality-violating communications scheme and its possible consequences.'
- The Transactional Interpretation of Quantum Mechanics '3.10 The Arrow of Time in the Transactional Interpretation – The formalism of quantum mechanics, at least in its relativistically invariant formulation, is completely even handed in dealing with the 'arrow' of time, the distinction between future and past time directions.'