thorndike katzen experiment

Behavioral Inquiry

Where modern topics meet behavioral research, what cats taught thorndike about learning.

If you’ve heard the name Edward Thorndike, you are probably aware of the importance this psychologist had on early behavioral science. He was the one that coined the term law of effect, which is a theoretical precursor to the process of reinforcement. Thorndike was interested in psychology as an observable natural science, which at the time flew in the face of introspective methods. His work inspired many of the ideas and theories of B.F Skinner, and behaviorism as a whole, but what you might not know is that his big break came from what he learned from…cats.

People who are familiar with Thorndike’s law of effect are aware that his theory underwent several revisions, and his research came into criticism; but few would dispute that his dissertation on the associative processes of animals, and the puzzle box experiment raised the right questions that would lead to many of the processes within operant conditioning that we see used today. Thorndike owes much of that to the cats he worked with during the animal research. Thorndike was interested in animal learning. Could they learn? Were all their behaviors governed solely by reflex? If they could learn, what could they learn? Could they learn by observing others? To us modern readers, who are familiar generally with animal intelligence levels, this might seem like a no brainer, but in the late 19th century when Thorndike was doing his work a sizable amount of academics still held on to the old Cartesean view of animals as unconscious automatons. These cats, and Thorndike, would call that into question. They would demonstrate that they could not only learn, but overcome an obstacle that could not possibly be a part of their reflex system- a puzzle box. Cats solving puzzles?! Thorndike must be mad! (I’m not entirely sure his critics would have been that dramatic, but skepticism was definitely there.).

His experiment was simple. Place hungry cats within a box that required a simple action to open, in order to access food outside of the box. The puzzle box itself had a door which was shut by weighted string, and that string was attached to a lever or switch; by operating these, the door would open. There were other future experiments involving buttons which worked in a similar fashion, but the single response (which was not reflexive) was consistent. At first the cats wandered around the cage meowing, and circling, until they incidentally stepped or pushed on a lever, opened the door, and gained access to the food. This was not learning. This was incidentally triggering the device. BUT… when placed within the cage again, these cats were able to reduce their time wandering and meowing before they found the trigger and let themselves out. Thorndike tracked these times, noticing not only that these cats were able to find their way out faster each time, but also the rate at which this learning took place. Thorndike constructed a learning curve. The cats struggled at first, but got faster with each new trial until their rates of responding became efficient enough to level off. Thorndike believed that to even perform this type of learning required some intelligence intrinsic to the cats. Obviously some kind of intelligence that did not rely on language or introspection.

“From the lowest animals of which we can affirm intelligence up to man this type of intellect is found.”- Edward Thorndike “Meow.”- Edward Thorndike’s Cat

Thorndike’s initial hypotheses were not always correct or confirmed however. Learning through observation, for example, was something he could not capture with these puzzle box trials. During the initial trials, he was not able to observe a difference in the rates of cats’ responding learned through their own trial and error, and cats who observed others escaping by pressing the lever/switch. (Later studies with other animal subjects would, of course, demonstrate animal learning through observation could in fact occur with certain animals). He also believed there might be some level of insight from the cats which helped them learn these tasks, but that too was not confirmed by his initial experiment- cats seemed to be more gradual learners from experience. This type of learning, again, appeared not to rely on language or introspective thought. Thorndike noticed that when he first put cats inside the puzzle box, their behavior seemed “erratic” or “chaotic”, but after successive trials the became more focused on finding the trigger to opening the door and engaged in fewer responses which did not align with the task. The cats were no longer circling and meowing; they were approximating responses that were previously successful and allowed them access to food. Thorndike concluded from this that this was responding based on the law of effect; that it happened due to past consequences. This would later be called by behaviorists as reinforcement, and documentation of the three term contingency.

“There is no reasoning, no process of inference or comparison; there is no thinking about things, no putting two and two together; there are no ideas – the animal does not think of the box or of the food or of the act he is to perform.”- Edward Thorndike “…”- Edward Thorndike’s Cat operating a puzzle box trigger.

That’s not all. Thorndike also theorized that cats could engage in discrimination of human vocalizations, and behave differently in situations after being spoken to. Thorndike noticed that when he approached cats behind wired netting before feeding, they would leap up on to the netting and meow.

(this author’s cat demonstrating exactly that)

To test this, he tested a loud proclamation in each condition:

“I MUST FEED THOSE CATS! “ (emphasis not present in original text)

Preceding conditions where he fed the cats, and

“I will not feed them.” (lack of textual enthusiasm probably accurate)

preceding conditions where he did not feed the cats.

He tracked these presentations and trials using frequency data collection, and in the conditions where he spoke “I must feed those cats”, and fed the cats, he found that cats would leap up more readily in the future, over the phrase where he did not feed them. This concept would later be referred to as responding to a discriminative stimulus. The cats would leap up and approach Thorndike (up to 60 times in the original research!) in the first condition, but also reduced leaping up when he voiced that he would not feed them. Thorndike was well aware that these cats were not spontaneously learning the English language, but they were discriminating between two very similar vocalized stimuli, and responding based on their previous experience and reinforcement. These ideas were not commonplace, or as well established as they are today. In many ways, these advances brought up unheard of avenues for the theory of learning in both animals and humans.

The theoretical implications of these experiments would shape later behavioral research into principles of operant conditioning well into not only the 20th century boom of behavioral thoughts and ideas, but even our time now in the 21st century.

Pretty impressive for cats, isn’t it?

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Thorndike puzzle box

Learn about this topic in these articles:, use in conditioning experiments.

…placing a cat inside a “puzzle box,” an apparatus from which the animal could escape and obtain food only by pressing a panel, opening a catch, or pulling on a loop of string. Thorndike measured the speed with which the cat gained its release from the box on successive trials.…

Thorndike’s Law of Effect: Definition and Examples

Categories Behavior , Theories

The law of effect is an important psychological principle based on a pretty simple premise—behaviors that are followed by positive consequences are more likely to be repeated. At the same time, behaviors followed by negative consequences are less likely to be repeated. 

It was first proposed by psychologist Edward Thorndike and had a significant impact on the development of behavioral theories. 

Table of Contents

Origins of the Law of Effect

Edward Thorndike was an American psychologist who conducted a series of experiments known as the “puzzle box” experiments in the late 19th and early 20th centuries. These experiments were crucial in the development of Thorndike’s theory of learning and the formulation of the law of effect.

The puzzle box was a small, enclosed space with a door that could be opened by a specific response or action from the animal placed inside. In Thorndike’s experiments, this was typically a cat. Thorndike would place a hungry cat in the puzzle box and present it with a simple task to escape, such as pulling a lever or pressing a button. The cat would initially display random behaviors in attempting to escape.

Through repeated trials, Thorndike noticed that the cats eventually learned to associate certain behaviors with the opening of the door. When the cats were placed in the box again, they were much faster at displaying the required behavior. This demonstrates that the cats had learned the correct behaviors based on the outcomes of their previous experiences in the box.

How the Law of Effect Works

Learning starts when a person engages in some type of behavior, whether it’s a conscious action, a learned response, or an instinctive reaction.

Consequences

The behavior is followed by consequences, which can be either positive or negative. 

• Behaviors followed by positive outcomes or rewards are more likely to be reinforced. Positive reinforcement strengthens the connection between the behavior and its likelihood of repetition.
• Behaviors followed by negative outcomes or punishments are less likely to be repeated. Negative consequences weaken the association between the behavior and its recurrence.

Learning and Adaptation

After having a number of experiences that involve being exposed to a certain outcome or consequence, people eventually learn to associate specific behaviors with their outcomes.

That means that if a pleasant or desirable outcome happens, people will repeat the behavior. But if the behavior is followed by something aversive or unpleasant, they will likely avoid repeating those actions.

How the Law of Effect Influenced Psychology

The law of effect played an important role in the development of operant conditioning, a form of learning where behaviors are strengthened or weakened based on the consequences that follow them. B.F. Skinner expanded on Thorndike’s work, developing the theory further.

Operant conditioning involves reinforcement and punishment. Reinforcement increases the likelihood of a behavior occurring again, while punishment decreases that likelihood. 

Positive reinforcement involves adding a positive stimulus, while negative reinforcement involves removing an aversive stimulus. On the other hand, positive punishment adds an aversive stimulus, and negative punishment removes a positive stimulus.

Applications for the Law of Effect

The law of effect has practical applications in various fields, including education, parenting, and therapy. Understanding how consequences influence behavior allows educators and parents to shape and modify behaviors effectively. 

Positive reinforcement, for example, can be a powerful tool in encouraging desired behaviors in children and students.

In therapy, behavioral interventions often utilize the principles of the law of effect to help people change their behaviors. By identifying and altering the consequences associated with certain actions, therapists can assist clients in achieving behavioral change.

Businesses often apply the law of effect to influence employee motivation and productivity. Reward systems, recognition programs, and other positive reinforcements can motivate employees to enhance their performance.

Examples of the Law of Effect

To better understand how the law of effect may apply in different contexts, let’s explore a few examples.

Educators often use the law of effect in the classroom when they incorporate positive reinforcement and negative punishment to help manage classroom behavior. 

Consider a classroom scenario where a diligent student completes their homework on time. The teacher recognizes this effort by praising the student, creating a positive consequence. This positive reinforcement increases the likelihood that the student will promptly submit assignments.

On the other hand, if a student disrupts the class with unruly behavior, the teacher may impose negative punishment by temporarily revoking a privilege, such as recess. This consequence uses the law of effect to discourage disruptive actions.

Parents and caregivers can also apply the law of effect to help children’s behavior through consequences. For example, when a child cleans their room, a parent might employ positive reinforcement by offering extra playtime or a small reward.

This positive consequence strengthens the connection between cleaning up and positive outcomes, encouraging the child to repeat the behavior.

On the flip side, if a child engages in undesirable behavior, such as not following rules, a parent might implement negative punishment. Temporarily taking away a beloved toy serves as a consequence to deter the undesirable behavior. In both cases, the law of effect guides parents using consequences to mold their children’s actions.

In the workplace, the law of effect influences employee behavior through positive reinforcement and negative punishment strategies. 

Imagine an employee achieving a challenging sales target; the employer publicly recognizes this accomplishment, providing positive reinforcement. The acknowledgment serves to strengthen the link between outstanding sales performance and positive outcomes, motivating the employee to stay productive.

Therapists can also use the law of effect to help guide clients toward positive behavioral changes. For example, a therapist might offer praise and acknowledgment when a client sticks with their treatment plan by attending therapy sessions and taking their medication as directed. This positive consequence reinforces the commitment to personal growth, encouraging continued participation in therapy. 

Limitations of the Law of Effect

While influential, the law of effect is not without criticism. One potential weakness is that it tends to oversimplify complex human behavior. Instead of acknowledging the role of cognitive processes, individual differences, and emotions, it reduces behavior to a simple stimulus-response mechanism.

Despite its limitations, the law of effect remains a fundamental concept in psychology, providing valuable insights into how behaviors are acquired and maintained.

Key Points to Remember

• The law of effect, proposed by Edward Thorndike, states that behaviors followed by positive consequences are more likely to be repeated, while those followed by negative consequences are less likely to recur.
• Positive consequences, or reinforcement, strengthen the likelihood of a behavior reoccurring, while negative consequences, or punishment, weaken that likelihood.
• The concept is integral to operant conditioning, a form of learning that involves reinforcement and punishment to shape behavior.
• Practical applications include education, parenting, therapy, and organizational management, where understanding and manipulating consequences can effectively influence behavior.

Athalye, V. R., Santos, F. J., Carmena, J. M., & Costa, R. M. (2018). Evidence for a neural law of effect.  Science (New York, N.Y.) ,  359 (6379), 1024–1029. https://doi.org/10.1126/science.aao6058

Domjan, M. (2012). Law of Effect. In: Seel, N.M. (eds) Encyclopedia of the Sciences of Learning. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-1428-6_90

Kyonka, E.G.E. (2011). Law of Effect. In: Goldstein, S., Naglieri, J.A. (eds) Encyclopedia of Child Behavior and Development . Springer, Boston, MA. https://doi.org/10.1007/978-0-387-79061-9_1624

Nevin J. (1999). Analyzing Thorndike’s Law Of Effect: The Question Of Stimulus-response Bonds.  Journal of the Experimental Analysis of Behavior ,  72 (3), 447–450. https://doi.org/10.1901/jeab.1999.72-447

• DOI: 10.1901/JEAB.1999.72-433
• Corpus ID: 13873670

Thorndike's Puzzle Boxes And The Origins Of The Experimental Analysis Of Behavior.

• Published in Journal of The Experimental… 1 November 1999

Figures from this paper

60 Citations

Thorndike's legacy: learning, selection, and the law of effect., edward l. thorndike: the, edward l. thorndike: the selectionist connectionist., remarks on former and current behaviorism, l'éthologie, des anecdotes naturalistes à l'analyse quantitative et expérimentale du comportement, the core process in addictions and other impulses: hyperbolic discounting versus conditioning and cognitive framing, exploring innovation and behavioral flexibility in african lions (panthera leo) and snow leopards (panthera uncia), methods of cognitive psychology, basic properties of coherence: testing a core assumption of relational frame theory, 8 references, observational learning by cats., social learning and imitation, “animal intelligence”.

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Animal Intelligence

Animal behavior, the sane positivist: a biography of edward l. thorndike by geraldine joncich. middletown, conn.: wesleyan university press, 1968. 634 pp. $12.50., the sane positivist : a biography of edward l. thorndike, the nature of animal intelligence and the methods of investigating it., related papers.

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Thorndike's Experiment

At the very end of the 19th century Thorndike, one of most commonly mentioned connectionists and an important learning theorist, performed experiments first on chickens and later on cats and dogs to analyze how animals learn.

In one experiment, he placed a hungry cat inside a puzzle box , which had a mechanism that would open the doors of the box every time a string would be pulled or a button pushed. After each successful escape out of the box by opening its doors, the cat needed a bit less time to repeat the required process next time. The desired behavior slowly increased.

Based on this experiment Thorndike concluded that learning is incremental and not insightful , since the learning of the correct response occurred only through repetition trial and error forming of associations between situation and response. Established S-R connections are the key aspect of knowledge.

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Thorndike’s puzzle box and the learning curve in the cat experiment.

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Edward Thorndike: The Law of Effect

Saul McLeod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul McLeod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

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Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

On This Page:

• The law of effect states that connections leading to satisfying outcomes are strengthened while those leading to unsatisfying outcomes are weakened.
• Positive emotional responses, like rewards or praise, strengthen stimulus-response connections. Unpleasant responses weaken them.
• This establishes reinforcement as central to efficient and enduring learning. Reward is more impactful than punishment.
• Connections grow most robust when appropriate associations lead to fulfilling outcomes. The “effect” generated shapes future behavioral and cognitive patterns.

Thorndike Theory

The law of effect states that behaviors followed by pleasant or rewarding consequences are more likely to be repeated, while behaviors followed by unpleasant or punishing consequences are less likely to be repeated.

The principle was introduced in the early 20th century through experiments led by Edward Thorndike, who found that positive reinforcement strengthens associations and increases the frequency of specific behaviors.

The law of effect principle developed by Edward Thorndike suggested that:

“Responses that produce a satisfying effect in a particular situation become more likely to occur again in that situation, and responses that produce a discomforting effect become less likely to occur again in that situation (Gray, 2011, p. 108–109).”

Edward Thorndike (1898) is famous in psychology for his work on learning theory that leads to the development of operant conditioning within behaviorism .

Whereas classical conditioning depends on developing associations between events, operant conditioning involves learning from the consequences of our behavior.

Skinner wasn’t the first psychologist to study learning by consequences.  Indeed, Skinner’s theory of operant conditioning is built on the ideas of Edward Thorndike.

Experimental Evidence

Thorndike studied learning in animals (usually cats).  He devised a classic experiment using a puzzle box to empirically test the laws of learning.

• Thorndike put hungry cats in cages with automatic doors that could be opened by pressing a button inside the cage. Thorndike would time how long it took the cat to escape.
• At first, when placed in the cages, the cats displayed unsystematic trial-and-error behaviors, trying to escape. They scratched, bit, and wandered around the cages without identifiable patterns.
• Thorndike would then put food outside the cages to act as a stimulus and reward.  The cats experimented with different ways to escape the puzzle box and reach the fish.
• Eventually, they would stumble upon the lever which opened the cage.  When it had escaped, the cat was put in again, and once more, the time it took to escape was noted.  In successive trials, the cats would learn that pressing the lever would have favorable consequences , and they would adopt this behavior, becoming increasingly quick at pressing the lever.
• After many repetitions of being placed in the cages (around 10-12 times), the cats learned to press the button inside their cages, which opened the doors, allowing them to escape the cage and reach the food.

Edward Thorndike put forward a  Law of Effect, which stated that any behavior that is followed by pleasant consequences is likely to be repeated, and any behavior followed by unpleasant consequences is likely to be stopped.

Critical Evaluation

Thorndike (1905) introduced the concept of reinforcement and was the first to apply psychological principles to the area of learning.

His research led to many theories and laws of learning, such as operant conditioning. Skinner (1938), like Thorndike, put animals in boxes and observed them to see what they were able to learn.

Thorndike’s theory has implications for teaching such as preparing students mentally, using drills and repetition, providing feedback and rewards, and structuring material from simple to complex.

B.F. Skinner built upon Thorndike’s principles to develop his theory of operant conditioning. Skinner’s work involved the systematic study of how the consequences of a behavior influence its frequency in the future. He introduced the concepts of reinforcement (both positive and negative) and punishment to describe how consequences can modify behavior.

The learning theories of Thorndike and Pavlov were later synthesized by Hull (1935). Thorndike’s research drove comparative psychology for fifty years, and influenced countless psychologists over that period of time, and even still today.

Criticisms 

Critiques of the theory include that it views humans too mechanistically like animals, overlooks higher reasoning, focuses too narrowly on associations, and positions the learner too passively.

Here is a summary of some of the main critiques and limitations of Thorndike’s learning theory:

• Using animals like cats and dogs in experiments is controversial when making inferences about human learning, since animal and human cognition differ.
• The theory depicts humans as mechanistic, like animals, driven by automatic trial-and-error processes. However, human learning is more complex and not entirely explained through stimulus-response connections.
• By overemphasizing associations, the theory overlooks deeper reasoning, understanding, and meaning construction involved in learning.
• Definitions and conceptual knowledge are ignored in favor of strengthening mechanistic stimulus-response bonds.
• Learners are passive receptors rather than active or creative; educators provide rigid structured curricula rather than let learners construct knowledge.
• Learners require constant external motivation and reinforcement rather than having internal drivers.
• Failures are punished, and discipline is stressed more than conceptual grasp or successful processes.
• The focus is on isolated skills, facts, and hierarchical sequencing rather than integrated understanding.
• Evaluation only measures passive responses and test performance rather than deeper learning processes or contexts.

Application of Thorndike’s Learning Theory to Students’ Learning

Thorndike’s theory, when applied to student learning, emphasizes several key factors – the role of the environment, breaking tasks into detail parts, the importance of student responses, building stimulus-response connections, utilizing prior knowledge, repetition through drills and exercises, and giving rewards/praise.

Learning is results-focused, with the measurement of observable outcomes. Errors are immediately corrected. Repetition aims to ingrain behaviors until they become habit. Rewards strengthen desired behaviors, punishment weakens undesired behaviors.

Some pitfalls in the application include teachers becoming too authoritative, one-way communication, students remaining passive, and over-reliance on rote memorization. However, his theory effectively promotes preparation, readiness, practice, feedback, praise for progress, and sequential mastery from simple to complex.

Teachers arrange hierarchical lesson materials starting from simple concepts, break down learning into parts marked by specific skill mastery, provide examples, emphasize drill/repetition activities, offer regular assessments and corrections, deliver clear brief instructions, and utilize rewards to motivate. This style is most applicable for skill acquisition requiring significant practice.

For students, the theory instills habits of repetition, progress tracking, and associate positive outcomes to effort.

It can, however, be limited if students remain passive receivers of instruction rather than active or collaborative learners. Proper application encourages student discipline while avoiding strict, punishing environments.

Additional Laws of Learning In Thorndike’s Theory 

Thorndike’s theory explains that learning is the formation of connections between stimuli and responses. The laws of learning he proposed are the law of readiness, the law of exercise, and the law of effect.

Law of Readiness

• The law of readiness states that learners must be physically and mentally prepared for learning to occur.  This includes not being hungry, sick, or having other physical distractions or discomfort.
• Mentally, learners should be inclined and motivated to acquire the new knowledge or skill. If they are uninterested or opposed to learning it, the law states they will not learn effectively.
• Learners also require certain baseline knowledge and competencies before being ready to learn advanced concepts. If those prerequisites are lacking, acquisition of new info will be difficult.
• Overall, the law emphasizes learners’ reception and orientation as key prerequisites to successful learning. The right mindset and adequate foundation enables efficient uptake of new material.

Law of Exercise

• The law of exercise states that connections are strengthened through repetition and practice. 
• Frequent trials allow errors to be corrected and neural pathways related to the knowledge/skill to become more engrained.
• As associations are reinforced through drill and rehearsal, retrieval from long term memory also becomes more efficient.
• In sum, repeated exercise of learned material cements retention and fluency over time. Forgetting happens when such connections are not actively preserved through practice.

Gray, P. (2011). Psychology (6th ed.) New York: Worth Publishers.

Hull, C. L. (1935). The conflicting psychologies of learning—a way out . Psychological Review, 42(6) , 491.

Skinner, B. F. (1938). The behavior of organisms: An experimental analysis . New York: Appleton-Century.

Thorndike, E. L. (1898). Animal intelligence: An experimental study of the associative processes in animals. Psychological Monographs: General and Applied, 2(4), i-109.

Thorndike, E. L. (1905). The elements of psychology . New York: A. G. Seiler.

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Edward Thorndike Theory Explained

The Edward Thorndike theory is a learning theory that focuses on operant conditioning within behaviors. By studying animals, and usually just cats, he devised an experiment to determine how they learn new skills.

Thorndike created a puzzle box. He would then place a cat inside the box, but encourage it to escape by placing a treat outside of the box. Then he would measure the amount of time it took for the cat to escape. As he watched, the cats would experiment with different solutions to determine if or how they could escape so they could reach the treat.

Thorndike designed his puzzle box to have a lever inside of it. If the lever was pressed, then the cage would open. Eventually, the cat would stumble upon the lever as it looked for a way to escape, see the cage open, and then come out to take the treat. Once that happened, Thorndike would take the cat and place it back into the box. He would once again track the time it took the cat to escape.

What Thorndike found was that the cat would adopt the behavior of pressing the lever because the behavior produced a favorable result. They would complete the task faster and faster in subsequent attempts. This information would become the law of effect that he would propose in his theory.

How Does Operant Conditioning Change Behaviors?

Thorndike proposed that behaviors that are followed by a pleasant outcome create the conditions where a person wants to repeat the behavior. If behaviors are followed by an unpleasant outcome, then a person is likely to stop the behavior instead of repeating it.

The definition of “pleasantness” is defined by the individual. A person who sees a red burner on a stove top has a choice: to touch the burner or to not touch the burner. For most people, touching the hot burner resulted in pain, if not a burn, and that stops the behavior from being repeated.

For some, however, the pain or burn might be associated with a pleasant outcome. Maybe the person went to the doctor, was given several free treats, and then found a $100 bill on the ground. Although the pain was still a negative, the other events are seen as a positive, and that could encourage a repetition of the behavior.

The operant condition is therefore based on personal wants, needs, and expectations. A person who is hungry and hasn’t eaten in three days might choose any food, even if it doesn’t taste good, to relieve their hunger. A person who gets three meals per day might only choose specific foods to eat because the level of hunger being relieved isn’t as great.

This led Thorndike to create two additional laws that would become part of his theory.

Updating the Edward Thorndike Theory

One of the most important aspects of Thorndike’s theory is the law of readiness. This takes into account the motivational aspects a person has for a certain behavior. If a hungry wolf spots a prey animal, they’re likely to go hunting. If a hungry person spots a free granola bar, they’re likely to start eating.

Thorndike refers to this process as a “conduction unit.” It is an almost unconscious action and decision that is taken based on internal or external triggers that are being experienced.

There is also the law of exercise that Thorndike included with his theory. This law incorporates use and disuse. When the conduction units are experienced on a regular basis, the urge to complete the behavior grows stronger. It becomes almost impossible to resist the urges that occur once a trigger is encountered.

If the conduction units are not used regularly, then the urge to complete the process is not as great. Some people (and some animals) can resist the urge to complete the process.

Thorndike notes that these processes and laws are supplemented by 5 specific characteristics.

• Varied reactions and multiple responses.
• Individual attitudes.
• Partial activity familiarity.
• Element assimilation.
• Associative shifting.

Over time, Thorndike realized that simple exercise did not cause learning, but could influence the law of effect that he had proposed. He also began to question whether repetition was evidence of learning or evidence of unconscious habit development.

With the right rewards and punishments, the Edward Thorndike theory suggests that behaviors can be modified. Although there will always be some individuals who will choose negative outcomes repeatedly, the core of this theory shows how people and animals can learn on a basic level.

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How does the Kennedy-Thorndike experiment test for time-dilation?

From the Wikipedia page (as of 3/6/2023),

The Kennedy–Thorndike experiment, first conducted in 1932 by Roy J. Kennedy and Edward M. Thorndike, is a modified form of the Michelson–Morley experimental procedure, testing special relativity.[1] The modification is to make one arm of the classical Michelson–Morley (MM) apparatus shorter than the other one. While the Michelson–Morley experiment showed that the speed of light is independent of the orientation of the apparatus, the Kennedy–Thorndike experiment showed that it is also independent of the velocity of the apparatus in different inertial frames. It also served as a test to indirectly verify time dilation – while the negative result of the Michelson–Morley experiment can be explained by length contraction alone, the negative result of the Kennedy–Thorndike experiment requires time dilation in addition to length contraction to explain why no phase shifts will be detected while the Earth moves around the Sun.

The passage says that the original MM experiment had equal length arms (with respect to the rest frame) and the modification that comes with the KT experiment is that one of the arms is shortened. The passage claims that the KT experiment is able to test for time dilation as well as length contraction whereas the MM experiment only tests for length contraction. I understand how MM tests for length contraction (from the point of view of a relatively moving inertial observer), but how does KT test for time dilation? I would be interested in understanding this in more detail.

• special-relativity
• experimental-physics
• time-dilation

The way the KT experiment tests for time-dilation is similar to how the light-clock thought experiment can reveal time-dilation. They're not exactly the same, but I would argue the principles are very similar.

The reasoning here requires us to first accept Lorentz contraction. The MM experiment alone does not prove Lorentz contraction, because there are a number of possible theories that can account for the results of MM (dragged aether, ballistic/emission light theory), but a combination of late 19th century and early 20th century experiments do manage to narrow down on the fact that objects are Lorentz contracted when moving relative to some fixed inertial reference frame. With this in mind, let us take Lorentz contraction for granted.

To simplify things, I will also make the assumption that the lengths perpendicular to velocity are unaffected. This was apparently a hidden assumption of Kennedy and Thorndike when they claimed they could derive the full Lorentz transformation. See this passage in Wikipedia . (In fact, it is worth pointing out that Voigt transformations are an example that fits the MM and KT experiments but the time-dilation factor is different than the one we derive in this post.)

First, let us consider a simplified warm-up thought experiment. There will be issues concerning conventionality and relativity of simultaneity, so in order to avoid them and sweep them under the rug, I will fix a reference frame $F$ as the so-called stationary inertial reference frame, and I will analyze everything with respect to $F$ . Moreover, I will assume the speed of light is constant and isotropic in $F$ .

Let us consider a variant of the simplified MM/KT setup where we have an interferometer with two arms of lengths $L_{1}$ and $L_{2}$ that are $90^{\circ}$ apart, and the apparatus is moving in the direction of arm $\#1$ at speed $v$ according to $F$ . For simplicity, let us start by analyzing the pure kinematics of the situation. We can analyze this with light-rays or point-particles; we'll choose to consider light-rays.

Let $C_{I}$ (interferometer clock) be a clock placed right at the beam-splitter that moves with the interferometer, and let $C_{S}$ (stationary clock) be a clock that is stationary with respect to $F$ .

Suppose a light-ray is shot. When it meets the beams-splitter it splits into two rays going through the two arms. Assuming Lorentz contraction occurs with respect to $F$ , the arm lengths change: $L_{1}\rightarrow L_{1}/\gamma(v)$ and $L_{2}\rightarrow L_{2}$ . By doing some basic kinematics math, we find that the light-ray in arm $\#1$ takes $t_{1}(v) = 2L_{1}\gamma(v)/c$ time to go from the beam-splitter and back, and light-ray going in arm $\#2$ takes $t_{2}(v) = 2L_{2}\gamma(v)/c$ according to $C_{S}$ . Thus $C_{S}$ measures a time difference of $$ \Delta t_{S}(v) = t_{1}(v) - t_{2}(v) = \frac{2\gamma(v)}{c}(L_{1}-L_{2}). $$ Now what does clock $C_{I}$ measure? The results of the KT experiment indicate (this needs an explanation which is provided below) that the time difference measured by $C_{I}$ is \begin{align}\tag{$*$} \Delta t_{I}(v) = \frac{2}{c}(L_{1}-L_{2}). \end{align} If this is true, then it follows that from the point of view of frame $F$ clock $C_{I}$ runs slower, and $$ \Delta t_{S}(v) = \gamma(v)\Delta t_{I}(v). $$ This is precisely the statement of time-dilation.

Ok, but Kennedy and Thorndike didn't have access to atomic clocks in 1932, so how could you do this without atomic clocks? They may not have had access to atomic clocks, but just like Michelson and Morelay, they could take advantage of light interference to tease out timing differences.

We will relate light interference and clock timings to each other in the following way. Let $C_{I}$ be a clock placed right at the beam-splitter that moves with the interferometer, let $C_{I}'$ be a clock placed right at the light source that moves with the interferometer, and let $C_{S}$ be a clock that is stationary with respect to $F$ . Suppose the setup is moving at speed $v$ in direction of arm $\#1$ wrt $F$ .

Let $C_{I}'$ measure the time period $\Delta T_{I}(v)$ of each wave-cycle of the light leaving the light source. Let $C_{I}$ measure the difference $\Delta t_{I}(v)$ between the two times it takes for light to make a round-trip in each of the arms. We also let $\Delta T_{S}(v)$ and $\Delta t_{S}(v)$ be the respective times as measured by clock $C_{S}$ .

We make the assumption that clock $C_{I}'$ and the light source, if they are slowed or sped up at all wrt $F$ , are slowed or sped up by the same factor wrt $F$ . Thus, \begin{align}\tag{1} \Delta T_{I}(v) = \Delta T_{I}(0) \end{align} for all $v$ . Further, we make the assumption that clocks $C_{I}$ and $C_{I}'$ are slowed or sped up by the same factor wrt $F$ , which implies that both are slower or faster than $C_{S}$ by the same factor. Consequently, we have \begin{align}\tag{2} \frac{\Delta T_{I}(v)}{\Delta T_{S}(v)} = \frac{\Delta t_{I}(v)}{\Delta t_{S}(v)} \end{align} for all $v$ . Also, we point out that at $v=0$ , clocks $C_{I}$ , $C_{I}'$ , and $C_{S}$ all tick at the same rate, so \begin{align}\tag{3} \Delta T_{S}(0) = \Delta T_{I}(0). \end{align} By the same reasoning as in Part 1, $$ \Delta t_{S}(v) = \frac{2\gamma(v)}{c}(L_{1}-L_{2}) $$ for all $v$ . In particular, \begin{align}\tag{4} \Delta t_{S}(v) = \gamma(v)\Delta t_{S}(0) \end{align} for all $v$ .

As the light splits at the beam-splitter, makes its round-trips, and returns to the beam-splitter, the resulting phase difference is $$ \Delta\phi(v) = \frac{\Delta t_{S}(v)}{T_{S}(v)}. $$ The result of the KT experiment is that $\Delta\phi(v)$ does not depend on $v$ . In particular, we have $\Delta\phi(v) = \Delta\phi(0)$ , so then \begin{align}\tag{5} \frac{\Delta t_{S}(v)}{\Delta T_{S}(v)} = \frac{\Delta t_{S}(0)}{\Delta T_{S}(0)} \end{align}

Now we will put all the equations $(1)$ - $(5)$ together. By $(5)$ and $(4)$ , $$ \gamma(v) = \frac{\Delta T_{S}(v)}{\Delta T_{S}(0)}. $$ By $(3)$ , this is $$ \gamma(v) = \frac{\Delta T_{S}(v)}{\Delta T_{I}(0)}. $$ By $(2)$ , this is $$ \gamma(v) = \frac{\Delta T_{I}(v)\cdot \Delta t_{S}(v)/\Delta t_{I}(v)}{\Delta T_{I}(0)} = \frac{\Delta T_{I}(v)}{\Delta T_{I}(0)}\cdot\frac{\Delta t_{S}(v)}{\Delta t_{I}(v)}. $$ By $(1)$ , this is $$ \gamma(v) = \frac{\Delta t_{S}(v)}{\Delta t_{I}(v)}, $$ and we arrive at the equation $$ \Delta t_{S}(v) = \gamma(v)\Delta t_{I}(v), $$ which is the statement of time-dilation.

Some other notes:

• The result of Part 2 can be used to deduce equation $(*)$ in Part 1. This is the way the KT experiment implies $(*)$ .
• The real experiment took place not only at different speeds, but also at different orientations.
• As I said in my post, the real experiments didn't involve precision timing with atomic clocks. So then what exactly was time-dilated? The answer is the light source. If you trace the logic carefully, you will find that the time-dilation only pertains to the light source. I invoked clocks explicitly only for the sake of exposition, but they are of course not needed here.

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